Finite Group Databasebeta

← #35570345

Subgroups — #35570345

Order 21248.

2464 conjugacy classes of subgroups.

The subgroup lattice has 1654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128438C211yesmaximal, characteristic
2#24910621C211yesmaximal, characteristic, complemented
3#24910614C211yesmaximal, characteristic, complemented
4#24910613C211yesmaximal, characteristic, complemented
5#24910579C211yesmaximal, characteristic, complemented
6#24910579C211yesmaximal, characteristic, complemented
7#24910508C211yesmaximal, characteristic, complemented
8#24910508C211yesmaximal, characteristic, complemented
9#24910504C211yesmaximal, characteristic, complemented
10#24910498C211yesmaximal, characteristic, complemented
11#24910461C211yesmaximal, characteristic, complemented
12#24910449C211yesmaximal, characteristic, complemented
13#24910444C211yesmaximal, characteristic, complemented
14#24910443C211yesmaximal, characteristic, complemented
15#24910440C211yesmaximal, characteristic, complemented
16#24910254C211yesmaximal, characteristic, complemented
17#24910250C211yesmaximal, characteristic, complemented
18#24910238C211yesmaximal, characteristic, complemented
19#24910238C211yesmaximal, characteristic, complemented
20#24910189C211yesmaximal, characteristic, complemented
21#24910164C211yesmaximal, characteristic, complemented
22#24910161C211yesmaximal, characteristic, complemented
23#24910149C211yesmaximal, characteristic, complemented
24#24910149C211yesmaximal, characteristic, complemented
25#24910122C211yesmaximal, characteristic, complemented
26#24910119C211yesmaximal, characteristic, complemented
27#24910117C211yesmaximal, characteristic, complemented
28C4×#14581773C211yesmaximal, characteristic, complemented
29#24909973C211yesmaximal, characteristic, complemented
30C4×#14581764C211yesmaximal, characteristic, complemented
31C83×#2366C211yesmaximal, characteristic, complemented
32#19128438C4116yescomplemented
33C2×#14581786C2211yescharacteristic
34C2×#14581786C2211yescharacteristic
35C2×#14581773C2211yescharacteristic
36C2×#14581773C2211yescharacteristic
37C2×#14581773C2211yescharacteristic
38C2×#14581764C2211yescharacteristic
39C2×#14581764C2211yescharacteristic
40C2×#14581764C2211yescharacteristic
41C2×#14581764C2211yescharacteristic
42C2×#14581764C2211yescharacteristic
43C2×#14581764C2211yescharacteristic
44C2×#14581760C2211yescharacteristic
45C2×#14581760C2211yescharacteristic
46C2×#14581760C2211yescharacteristic
47C2×D4×Dic83C2211yescharacteristic
48C2×D4×Dic83C2211yescharacteristic, complemented
49C2×C4×C22⋊D83C2211yescharacteristic
50C2×C4×C22⋊D83C2211yescharacteristic
51C2×(C22⋊D83)⋊C4C2211yescharacteristic
52C2×(C22⋊D83)⋊C4C2211yescharacteristic
53C2×(C22⋊D83)⋊C4C2211yescharacteristic
54C2×(C22⋊D83)⋊C4C2211yescharacteristic
55C2×#14581748C2211yescharacteristic, complemented
56C2×#14581748C2211yescharacteristic, complemented
57C22×(C2×D83)⋊C4C2211yescharacteristic
58C2×C22⋊C4×D83C2211yescharacteristic
59C2×C22⋊C4×D83C2211yescharacteristic
60C22×C4×Dic83C2211yescharacteristic, complemented
61#19127604C2211yescharacteristic
62#19127604C2211yescharacteristic, complemented
63#19127601C2211yescharacteristic
64#19127601C2211yescharacteristic
65#19127601C2211yescharacteristic
66#19127601C2211yescharacteristic
67#19127601C2211yescharacteristic
68#19127601C2211yescharacteristic
69#19127598C2211yescharacteristic, complemented
70#19127598C2211yescharacteristic, complemented
71#19127596C2211yescharacteristic, complemented
72#19127596C2211yescharacteristic, complemented
73#19127596C2211yescharacteristic, complemented
74#19127596C2211yescharacteristic, complemented
75#19127595C2211yescharacteristic
76#19127595C2211yescharacteristic
77#19127595C2211yescharacteristic, complemented
78#19127595C2211yescharacteristic, complemented
79#19127595C2211yescharacteristic, complemented
80#19127595C2211yescharacteristic, complemented
81#19127593C2211yescharacteristic
82#19127593C2211yescharacteristic
83#19127592C2211yescharacteristic
84#19127592C2211yescharacteristic
85#19127592C2211yescharacteristic
86#19127592C2211yescharacteristic
87#19127591C2211yescharacteristic
88#19127591C2211yescharacteristic
89#19127591C2211yescharacteristic
90#19127591C2211yescharacteristic
91#19127590C2211yescharacteristic
92#19127590C2211yescharacteristic
93#19127589C2211yescharacteristic
94#19127589C2211yescharacteristic
95#19127589C2211yescharacteristic
96#19127589C2211yescharacteristic
97#19127589C2211yescharacteristic, complemented
98#19127589C2211yescharacteristic, complemented
99#19127588C2211yescharacteristic, complemented
100#19127588C2211yescharacteristic, complemented
101#19127585C2211yescharacteristic, complemented
102#19127585C2211yescharacteristic, complemented
103#19127585C2211yescharacteristic, complemented
104#19127585C2211yescharacteristic, complemented
105#19127583C2211yescharacteristic, complemented
106#19127583C2211yescharacteristic, complemented
107#19127582C2211yescharacteristic, complemented
108#19127582C2211yescharacteristic, complemented
109#19127582C2211yescharacteristic, complemented
110#19127582C2211yescharacteristic, complemented
111#19127581C2211yescharacteristic
112#19127581C2211yescharacteristic
113#19127581C2211yescharacteristic
114#19127581C2211yescharacteristic
115#19127581C2211yescharacteristic, complemented
116#19127581C2211yescharacteristic, complemented
117#19127581C2211yescharacteristic, complemented
118#19127581C2211yescharacteristic, complemented
119#19127580C2211yescharacteristic
120#19127580C2211yescharacteristic
121#19127580C2211yescharacteristic
122#19127580C2211yescharacteristic
123#19127578C2211yescharacteristic
124#19127578C2211yescharacteristic
125#19127577C2211yescharacteristic
126#19127577C2211yescharacteristic
127#19127577C2211yescharacteristic
128#19127577C2211yescharacteristic
129#19127577C2211yescharacteristic
130#19127577C2211yescharacteristic
131#19127575C2211yescharacteristic
132#19127575C2211yescharacteristic
133#19127574C2211yescharacteristic
134#19127574C2211yescharacteristic, complemented
135#19127573C2211yescharacteristic
136#19127573C2211yescharacteristic
137#19127573C2211yescharacteristic, complemented
138#19127573C2211yescharacteristic, complemented
139#19127572C2211yescharacteristic
140#19127572C2211yescharacteristic
141#19127572C2211yescharacteristic
142#19127572C2211yescharacteristic
143#19127567C2211yescharacteristic, complemented
144#19127562C2211yescharacteristic, complemented
145#19127559C2211yescharacteristic, complemented
146#19127559C2211yescharacteristic, complemented
147#19127559C2211yescharacteristic, complemented
148#19127559C2211yescharacteristic, complemented
149#19127556C2211yescharacteristic
150C4×Dic83⋊C4C2211yescharacteristic, complemented
151C4×Dic83⋊C4C2211yescharacteristic, complemented
152C4×Dic83⋊C4C2211yescharacteristic, complemented
153C4×Dic83⋊C4C2211yescharacteristic, complemented
154#19127552C2211yescharacteristic, complemented
155#19127552C2211yescharacteristic, complemented
156C22⋊C4×Dic83C2211yescharacteristic
157C22⋊C4×Dic83C2211yescharacteristic, complemented
158C22⋊C4×Dic83C2211yescharacteristic, complemented
159C22⋊C4×Dic83C2211yescharacteristic, complemented
160C4×(C2×D83)⋊C4C2211yescharacteristic
161C4×(C2×D83)⋊C4C2211yescharacteristic
162C4×(C2×D83)⋊C4C2211yescharacteristic
163C4×(C2×D83)⋊C4C2211yescharacteristic
164C4×C22⋊Dic83C2211yescharacteristic
165C4×C22⋊Dic83C2211yescharacteristic
166C4×C22⋊Dic83C2211yescharacteristic, complemented
167C4×C22⋊Dic83C2211yescharacteristic, complemented
168#19127548C2211yescharacteristic
169#19127548C2211yescharacteristic
170#19127547C2211yescharacteristic, complemented
171C2×C83⋊#95C2211yescharacteristic, complemented
172C2×C83⋊#95C2211yescharacteristic, complemented
173C2×#127×C83C2211yescharacteristic
174C2×C4×D4×C83C2211yescharacteristic
175C2×C4×D4×C83C2211yescharacteristic
176C2×C4×D4×C83C2211yescharacteristic, complemented
177C2×C4×D4×C83C2211yescharacteristic, complemented
178#390×C83C2211yescharacteristic
179#390×C83C2211yescharacteristic
180#390×C83C2211yescharacteristic, complemented
181#390×C83C2211yescharacteristic, complemented
182#386×C83C2211yescharacteristic
183#386×C83C2211yescharacteristic
184#386×C83C2211yescharacteristic, complemented
185#386×C83C2211yescharacteristic, complemented
186C4×C4⋊C4×C83C2211yescharacteristic, complemented
187C4×C4⋊C4×C83C2211yescharacteristic, complemented
188C24×D83C2311yescharacteristic
189C22×C22⋊D83C2311yescharacteristic
190C22×C22⋊D83C2311yescharacteristic
191C22×C22⋊D83C2311yescharacteristic
192C22×C22⋊D83C2311yescharacteristic
193C22×C22⋊D83C2311yescharacteristic
194C22×C22⋊D83C2311yescharacteristic
195C23×Dic83C2311yescharacteristic
196C23×Dic83C2311yescharacteristic
197C23×Dic83C2311yescharacteristic
198C23×Dic83C2311yescharacteristic
199C23×Dic83C2311yescharacteristic
200C23×Dic83C2311yescharacteristic
201C23×Dic83C2311yescharacteristic
202C22×C4×D83C2311yescharacteristic
203C22×C4×D83C2311yescharacteristic
204C22×C4×D83C2311yescharacteristic
205C22×C4×D83C2311yescharacteristic
206#14581786C2×C418yescomplemented
207#14581786C2×C418yescomplemented
208#14581773C2×C418yescomplemented
209#14581773C2×C418yescomplemented
210#14581773C2×C418yescomplemented
211#14581764C2×C418yescomplemented
212#14581764C2×C418yescomplemented
213#14581764C2×C418yescomplemented
214#14581764C2×C418yescomplemented
215#14581764C2×C418yescomplemented
216#14581764C2×C418yescomplemented
217#14581760C2×C418yescomplemented
218#14581760C2×C418yescomplemented
219#14581760C2×C418yescomplemented
220D4×Dic83—42no—
221D4×Dic83—42no—
222C4×C22⋊D83—42no—
223C4×C22⋊D83—42no—
224(C22⋊D83)⋊C4—42no—
225(C22⋊D83)⋊C4—42no—
226(C22⋊D83)⋊C4—42no—
227(C22⋊D83)⋊C4—42no—
228#14581748—42no—
229#14581748—42no—
230C2×C4⋊Dic83C2311yescharacteristic
231C2×C4⋊Dic83C2311yescharacteristic
232C2×Dic83⋊C4C2311yescharacteristic
233C2×Dic83⋊C4C2311yescharacteristic
234C2×Dic83⋊C4C2311yescharacteristic
235C2×Dic83⋊C4C2311yescharacteristic
236C2×Dic83⋊C4C2311yescharacteristic
237C2×Dic83⋊C4C2311yescharacteristic
238C2×Dic83⋊C4C2311yescharacteristic
239C2×Dic83⋊C4C2311yescharacteristic
240C2×Dic83⋊C4C2311yescharacteristic
241C2×Dic83⋊C4C2311yescharacteristic
242C2×Dic83⋊C4C2311yescharacteristic
243C2×Dic83⋊C4C2311yescharacteristic
244C2×Dic83⋊C4C2311yescharacteristic
245C2×Dic83⋊C4C2311yescharacteristic
246C2×Dic83⋊C4C2311yescharacteristic
247C2×Dic83⋊C4C2311yescharacteristic
248C2×Dic83⋊C4C2311yescharacteristic
249C2×Dic83⋊C4C2311yescharacteristic
250C2×C22⋊Dic83C2311yescharacteristic
251C2×C22⋊Dic83C2311yescharacteristic
252C2×C22⋊Dic83C2311yescharacteristic
253C2×C22⋊Dic83C2311yescharacteristic
254C2×C22⋊Dic83C2311yescharacteristic
255C2×C22⋊Dic83C2311yescharacteristic
256C2×C22⋊Dic83C2311yescharacteristic
257C2×C22⋊Dic83C2311yescharacteristic
258C2×C22⋊Dic83C2311yescharacteristic
259C2×C22⋊Dic83C2311yescharacteristic
260C2×C22⋊Dic83C2311yescharacteristic
261C2×C22⋊Dic83C2311yescharacteristic
262C2×C22⋊Dic83C2311yescharacteristic
263C2×C22⋊Dic83C2311yescharacteristic
264C2×C22⋊Dic83C2311yescharacteristic
265C2×C22⋊Dic83C2311yescharacteristic
266C2×C22⋊Dic83C2311yescharacteristic
267C2×C22⋊Dic83C2311yescharacteristic
268C2×(C2×D83)⋊C4—42no—
269C2×(C2×D83)⋊C4C2311yescharacteristic
270C2×(C2×D83)⋊C4C2311yescharacteristic
271C2×(C2×D83)⋊C4C2311yescharacteristic
272C2×(C2×D83)⋊C4C2311yescharacteristic
273C2×(C2×D83)⋊C4C2311yescharacteristic
274C2×(C2×D83)⋊C4C2311yescharacteristic
275C2×(C2×D83)⋊C4C2311yescharacteristic
276C2×(C2×D83)⋊C4C2311yescharacteristic
277C2×(C2×D83)⋊C4C2311yescharacteristic
278C2×(C2×D83)⋊C4C2311yescharacteristic
279C2×(C2×D83)⋊C4C2311yescharacteristic
280C2×(C2×D83)⋊C4C2311yescharacteristic
281C2×(C2×D83)⋊C4C2311yescharacteristic
282C2×(C2×D83)⋊C4C2311yescharacteristic
283C2×(C2×D83)⋊C4C2311yescharacteristic
284C2×(C2×D83)⋊C4C2311yescharacteristic
285C2×(C2×D83)⋊C4C2311yescharacteristic
286C2×(C2×D83)⋊C4C2311yescharacteristic
287C22⋊C4×D83—42no—
288C22⋊C4×D83—42no—
289C2×C4×Dic83—42no—
290C2×C4×Dic83C2311yescharacteristic
291C2×C4×Dic83C2311yescharacteristic
292C2×C4×Dic83C2311yescharacteristic
293C2×C4×Dic83C2311yescharacteristic
294C2×C4×Dic83C2311yescharacteristic
295C2×C4×Dic83C2311yescharacteristic
296C2×C4×Dic83C2311yescharacteristic
297C2×C4×Dic83C2311yescharacteristic
298C2×C4×Dic83C2311yescharacteristic
299C2×C4×Dic83C2311yescharacteristic
300C2×C4×Dic83C2311yescharacteristic
301C2×C4×Dic83C2311yescharacteristic
302C2×C4×Dic83C2311yescharacteristic
303C2×C4×Dic83C2311yescharacteristic
304C83⋊#95C2311yescharacteristic
305C83⋊#95C2311yescharacteristic
306C83⋊#95C2311yescharacteristic
307C83⋊#95C2311yescharacteristic
308C83⋊#95C2311yescharacteristic
309C83⋊#95C2311yescharacteristic
310C83⋊#95C2311yescharacteristic
311C83⋊#95C2311yescharacteristic
312C83⋊#95C2311yescharacteristic
313C83⋊#95C2311yescharacteristic
314C83⋊#95C2311yescharacteristic
315C83⋊#95C2311yescharacteristic
316C83⋊#95C2311yescharacteristic
317C83⋊#95C2311yescharacteristic
318C83⋊#95C2311yescharacteristic
319C83⋊#95C2311yescharacteristic
320C83⋊#95C2311yescharacteristic
321C83⋊#95C2311yescharacteristic
322C83⋊#95C2311yescharacteristic
323C83⋊#95C2311yescharacteristic
324C83⋊#95C2311yescharacteristic
325C83⋊#95C2311yescharacteristic
326C83⋊#95C2311yescharacteristic
327C83⋊#95C2311yescharacteristic
328C83⋊#95C2311yescharacteristic
329C83⋊#95C2311yescharacteristic
330C83⋊#95C2311yescharacteristic
331C83⋊#95C2311yescharacteristic
332C83⋊#95C2311yescharacteristic
333C83⋊#95C2311yescharacteristic
334C83⋊#95C2311yescharacteristic
335C83⋊#95C2311yescharacteristic
336C22×D4×C83C2311yescharacteristic
337C22×D4×C83C2311yescharacteristic
338C22×D4×C83C2311yescharacteristic
339C22×D4×C83C2311yescharacteristic
340C22×D4×C83C2311yescharacteristic
341C22×D4×C83C2311yescharacteristic
342C23×C4×C83C2311yescharacteristic
343C23×C4×C83C2311yescharacteristic
344C23×C4×C83C2311yescharacteristic
345C23×C4×C83C2311yescharacteristic
346#127×C83C2×C418yescomplemented
347C4×D4×C83—42no—
348C4×D4×C83—42no—
349C4×D4×C83—42no—
350C4×D4×C83—42no—
351C2×C4⋊C4×C83C2311yescharacteristic
352C2×C4⋊C4×C83C2311yescharacteristic
353C2×C4⋊C4×C83C2311yescharacteristic
354C2×C4⋊C4×C83C2311yescharacteristic
355C2×C22⋊C4×C83C2311yescharacteristic
356C2×C22⋊C4×C83C2311yescharacteristic
357C2×C22⋊C4×C83C2311yescharacteristic
358C2×C22⋊C4×C83C2311yescharacteristic
359C2×C22⋊C4×C83C2311yescharacteristic
360C2×C22⋊C4×C83C2311yescharacteristic
361C2×C22⋊C4×C83C2311yescharacteristic
362C2×C22⋊C4×C83C2311yescharacteristic
363C2×C22⋊C4×C83C2311yescharacteristic
364C2×C22⋊C4×C83C2311yescharacteristic
365C2×C22⋊C4×C83C2311yescharacteristic
366C2×C22⋊C4×C83C2311yescharacteristic
367C2×C42×C83C2311yescharacteristic
368C2×C42×C83C2311yescharacteristic
369C2×C42×C83C2311yescharacteristic
370C2×C42×C83C2311yescharacteristic
371C2×C42×C83C2311yescharacteristic
372#95×C83C2311yescharacteristic
373#95×C83C2311yescharacteristic
374#95×C83C2311yescharacteristic
375#95×C83C2311yescharacteristic
376C23×D83—41no—
377C23×D83—41no—
378C23×D83—41no—
379C23×D83—41no—
380C23×D83—41no—
381C23×D83—41no—
382C23×D83C22×C414yes—
383C23×D83C2411yescharacteristic
384C23×D83C2411yescharacteristic
385C2×C22⋊D83—41no—
386C2×C22⋊D83—41no—
387C2×C22⋊D83—41no—
388C2×C22⋊D83—41no—
389C2×C22⋊D83—41no—
390C2×C22⋊D83—41no—
391C2×C22⋊D83—41no—
392C2×C22⋊D83—41no—
393C2×C22⋊D83—41no—
394C2×C22⋊D83—41no—
395C2×C22⋊D83—41no—
396C2×C22⋊D83—41no—
397C2×C22⋊D83C22×C414yes—
398C2×C22⋊D83C22×C414yes—
399C2×C22⋊D83C22×C414yes—
400C2×C22⋊D83C22×C414yes—
401C2×C22⋊D83C22×C414yes—
402C2×C22⋊D83C22×C414yes—
403C22×Dic83—22no—
404C22×Dic83—22no—
405C22×Dic83—41no—
406C22×Dic83—41no—
407C22×Dic83—41no—
408C22×Dic83—41no—
409C22×Dic83—41no—
410C22×Dic83—41no—
411C22×Dic83—41no—
412C22×Dic83—41no—
413C22×Dic83—41no—
414C22×Dic83—41no—
415C22×Dic83—41no—
416C22×Dic83—41no—
417C22×Dic83—41no—
418C22×Dic83—41no—
419C22×Dic83—41no—
420C22×Dic83—41no—
421C22×Dic83C22×C414yes—
422C22×Dic83C22×C414yes—
423C22×Dic83C22×C414yes—
424C22×Dic83C2411yescharacteristic
425C22×Dic83C2411yescharacteristic
426C22×Dic83C2411yescharacteristic
427C22×Dic83C2411yescharacteristic
428C22×Dic83C2411yescharacteristic
429C22×Dic83C2411yescharacteristic
430C22×Dic83C2411yescharacteristic
431C22×Dic83C2411yescharacteristic
432C22×Dic83C2411yescharacteristic
433C22×Dic83C2411yescharacteristic
434C22×Dic83C2411yescharacteristic
435C22×Dic83C2411yescharacteristic
436C22×Dic83C2411yescharacteristic
437C22×Dic83C2411yescharacteristic
438C2×C4×D83—22no—
439C2×C4×D83—22no—
440C2×C4×D83—41no—
441C2×C4×D83—41no—
442C2×C4×D83—41no—
443C2×C4×D83—41no—
444C2×C4×D83—41no—
445C2×C4×D83—41no—
446C2×C4×D83—41no—
447C2×C4×D83—41no—
448C2×C4×D83—41no—
449C2×C4×D83—41no—
450C4⋊Dic83—41no—
451C4⋊Dic83—41no—
452Dic83⋊C4—22no—
453Dic83⋊C4—22no—
454Dic83⋊C4—41no—
455Dic83⋊C4—41no—
456Dic83⋊C4—41no—
457Dic83⋊C4—41no—
458Dic83⋊C4—41no—
459Dic83⋊C4—41no—
460Dic83⋊C4—41no—
461Dic83⋊C4—41no—
462Dic83⋊C4—41no—
463Dic83⋊C4—41no—
464Dic83⋊C4C22×C414yes—
465Dic83⋊C4C22×C414yes—
466Dic83⋊C4C22×C414yes—
467Dic83⋊C4C22×C414yes—
468Dic83⋊C4C22×C414yes—
469Dic83⋊C4C22×C414yes—
470C22⋊Dic83—22no—
471C22⋊Dic83—22no—
472C22⋊Dic83—41no—
473C22⋊Dic83—41no—
474C22⋊Dic83—41no—
475C22⋊Dic83—41no—
476C22⋊Dic83—41no—
477C22⋊Dic83—41no—
478C22⋊Dic83—41no—
479C22⋊Dic83—41no—
480C22⋊Dic83—41no—
481C22⋊Dic83—41no—
482C22⋊Dic83C22×C414yes—
483C22⋊Dic83C22×C414yes—
484C22⋊Dic83C22×C414yes—
485C22⋊Dic83C22×C414yes—
486C22⋊Dic83C22×C414yes—
487C22⋊Dic83C22×C414yes—
488(C2×D83)⋊C4—22no—
489(C2×D83)⋊C4—22no—
490(C2×D83)⋊C4—22no—
491(C2×D83)⋊C4—22no—
492(C2×D83)⋊C4—41no—
493(C2×D83)⋊C4—41no—
494(C2×D83)⋊C4—41no—
495(C2×D83)⋊C4—41no—
496(C2×D83)⋊C4—41no—
497(C2×D83)⋊C4—41no—
498(C2×D83)⋊C4—41no—
499(C2×D83)⋊C4—41no—
500(C2×D83)⋊C4C22×C414yes—
501(C2×D83)⋊C4C22×C414yes—
502(C2×D83)⋊C4C22×C414yes—
503(C2×D83)⋊C4C22×C414yes—
504(C2×D83)⋊C4C22×C414yes—
505(C2×D83)⋊C4C22×C414yes—
506C4×Dic83—22no—
507C4×Dic83—22no—
508C4×Dic83—22no—
509C4×Dic83—22no—
510C4×Dic83—22no—
511C4×Dic83—41no—
512C4×Dic83—41no—
513C4×Dic83—41no—
514C4×Dic83—41no—
515C4×Dic83—41no—
516C4×Dic83—41no—
517C4×Dic83—41no—
518C4×Dic83—41no—
519C4×Dic83—41no—
520C24×C83C2411yescharacteristic
521C24×C83C2411yescharacteristic
522C24×C83C2411yescharacteristic
523C24×C83C2411yescharacteristic
524C2×D4×C83—41no—
525C2×D4×C83—41no—
526C2×D4×C83—41no—
527C2×D4×C83—41no—
528C2×D4×C83—41no—
529C2×D4×C83—41no—
530C2×D4×C83—41no—
531C2×D4×C83—41no—
532C2×D4×C83—41no—
533C2×D4×C83—41no—
534C2×D4×C83—41no—
535C2×D4×C83—41no—
536C2×D4×C83C22×C414yes—
537C2×D4×C83C22×C414yes—
538C2×D4×C83C22×C414yes—
539C2×D4×C83C22×C414yes—
540C2×D4×C83C22×C414yes—
541C2×D4×C83C22×C414yes—
542C22×C4×C83—22no—
543C22×C4×C83—22no—
544C22×C4×C83—22no—
545C22×C4×C83—22no—
546C22×C4×C83—41no—
547C22×C4×C83—41no—
548C22×C4×C83—41no—
549C22×C4×C83—41no—
550C22×C4×C83—41no—
551C22×C4×C83—41no—
552C22×C4×C83—41no—
553C22×C4×C83—41no—
554C22×C4×C83C2411yescharacteristic
555C22×C4×C83C2411yescharacteristic
556C22×C4×C83C2411yescharacteristic
557C22×C4×C83C2411yescharacteristic
558C22×C4×C83C2411yescharacteristic
559C22×C4×C83C2411yescharacteristic
560C22×C4×C83C2411yescharacteristic
561C22×C4×C83C2411yescharacteristic
562C22×C4×C83C2411yescharacteristic
563C22×C4×C83C2411yescharacteristic
564C22×C4×C83C2411yescharacteristic
565C4⋊C4×C83—22no—
566C4⋊C4×C83—22no—
567C4⋊C4×C83—41no—
568C4⋊C4×C83—41no—
569C22⋊C4×C83—22no—
570C22⋊C4×C83—22no—
571C22⋊C4×C83—22no—
572C22⋊C4×C83—22no—
573C22⋊C4×C83—41no—
574C22⋊C4×C83—41no—
575C22⋊C4×C83—41no—
576C22⋊C4×C83—41no—
577C22⋊C4×C83—41no—
578C22⋊C4×C83—41no—
579C22⋊C4×C83—41no—
580C22⋊C4×C83—41no—
581C42×C83—41no—
582C42×C83—41no—
583C42×C83—41no—
584C42×C83—41no—
585C42×C83C22×C414yes—
586C23×C83—21no—
587C23×C83—21no—
588C23×C83—21no—
589C23×C83—21no—
590C23×C83—21no—
591C23×C83—21no—
592C23×C83—21no—
593C23×C83—21no—
594C23×C83—21no—
595C23×C83—21no—
596C23×C83—21no—
597C23×C83—21no—
598C23×C83—21no—
599C23×C83—21no—
600C23×C83—21no—
601C23×C83—21no—
602C23×C83—21no—
603C23×C83—21no—
604C23×C83—21no—
605C23×C83—21no—
606C23×C83—21no—
607C23×C83—21no—
608C23×C83—21no—
609C23×C83—21no—
610C23×C83C23×C412yes—
611C23×C83C23×C412yes—
612C23×C83C23×C412yes—
613C23×C83C23×C412yes—
614C23×C83C2511yescharacteristic
615C22×D83—21no—
616C22×D83—21no—
617C22×D83—21no—
618C22×D83—21no—
619C22×D83—21no—
620C22×D83—21no—
621C22×D83—21no—
622C22×D83—21no—
623C22×D83—21no—
624C22×D83—21no—
625C22×D83—21no—
626C22×D83—21no—
627C22×D83—44no—
628C22×D83—44no—
629C22×D83—44no—
630C22×D83—82no—
631C22×D83—82no—
632C22×D83—82no—
633C22×D83—82no—
634C22×D83C23×C412yes—
635C22×D83C23×C412yes—
636D4×C83—44no—
637D4×C83—44no—
638D4×C83—44no—
639D4×C83—44no—
640D4×C83—44no—
641D4×C83—44no—
642C2×C4×C83—21no—
643C2×C4×C83—21no—
644C2×C4×C83—21no—
645C2×C4×C83—21no—
646C2×C4×C83—21no—
647C2×C4×C83—21no—
648C2×C4×C83—21no—
649C2×C4×C83—21no—
650C2×C4×C83—21no—
651C2×C4×C83—21no—
652C2×C4×C83—21no—
653C2×C4×C83—21no—
654C2×C4×C83—21no—
655C2×C4×C83—21no—
656C2×C4×C83—21no—
657C2×C4×C83—21no—
658C2×C4×C83—21no—
659C2×C4×C83—21no—
660C2×C4×C83—21no—
661C2×C4×C83—21no—
662C2×C4×C83—21no—
663C2×C4×C83—21no—
664C2×C4×C83—21no—
665C2×C4×C83—21no—
666C2×C4×C83—21no—
667C2×C4×C83—21no—
668C2×C4×C83—21no—
669C2×C4×C83—21no—
670C2×C4×C83—44no—
671C2×C4×C83—82no—
672C2×C4×C83—82no—
673C2×C4×C83—82no—
674C2×C4×C83C23×C412yes—
675C2×C4×C83C23×C412yes—
676C2×C4×C83C23×C412yes—
677C2×C4×C83H(5,𝔽2)12yes—
678C2×C4×C83H(5,𝔽2)12yes—
679C22⋊D83—44no—
680C22⋊D83—44no—
681C22⋊D83—44no—
682C22⋊D83—44no—
683C22⋊D83—44no—
684C22⋊D83—44no—
685C2×Dic83—21no—
686C2×Dic83—21no—
687C2×Dic83—21no—
688C2×Dic83—21no—
689C2×Dic83—21no—
690C2×Dic83—21no—
691C2×Dic83—21no—
692C2×Dic83—21no—
693C2×Dic83—21no—
694C2×Dic83—21no—
695C2×Dic83—21no—
696C2×Dic83—21no—
697C2×Dic83—21no—
698C2×Dic83—21no—
699C2×Dic83—21no—
700C2×Dic83—21no—
701C2×Dic83—21no—
702C2×Dic83—21no—
703C2×Dic83—21no—
704C2×Dic83—21no—
705C2×Dic83—21no—
706C2×Dic83—21no—
707C2×Dic83—21no—
708C2×Dic83—21no—
709C2×Dic83—21no—
710C2×Dic83—21no—
711C2×Dic83—21no—
712C2×Dic83—21no—
713C2×Dic83—21no—
714C2×Dic83—21no—
715C2×Dic83—21no—
716C2×Dic83—21no—
717C2×Dic83—21no—
718C2×Dic83—21no—
719C2×Dic83—21no—
720C2×Dic83—44no—
721C2×Dic83—44no—
722C2×Dic83—44no—
723C2×Dic83—44no—
724C2×Dic83—82no—
725C2×Dic83—82no—
726C2×Dic83—82no—
727C2×Dic83C23×C412yes—
728C2×Dic83C23×C412yes—
729C2×Dic83C23×C412yes—
730C2×Dic83C23×C412yes—
731C2×Dic83C23×C412yes—
732C2×Dic83C23×C412yes—
733C2×Dic83H(5,𝔽2)12yes—
734C4×D83—82no—
735C4×D83—82no—
736C4×D83—82no—
737C4×D83—82no—
738C22×C83—22no—
739C22×C83—22no—
740C22×C83—22no—
741C22×C83—22no—
742C22×C83—22no—
743C22×C83—22no—
744C22×C83—22no—
745C22×C83—22no—
746C22×C83—22no—
747C22×C83—22no—
748C22×C83—22no—
749C22×C83—22no—
750C22×C83—41no—
751C22×C83—41no—
752C22×C83—41no—
753C22×C83—41no—
754C22×C83—41no—
755C22×C83—41no—
756C22×C83—41no—
757C22×C83—41no—
758C22×C83—41no—
759C22×C83—41no—
760C22×C83—41no—
761C22×C83—41no—
762C22×C83—41no—
763C22×C83—41no—
764C22×C83—41no—
765C22×C83—41no—
766C22×C83C24×C411yescharacteristic
767C22×C83C2×H(5,𝔽2)11yescharacteristic
768C22×C83C2×H(5,𝔽2)11yescharacteristic
769C22×C83C2×H(5,𝔽2)11yescharacteristic
770C22×C83#58511yescharacteristic
771C22×C83#58511yescharacteristic
772C22×C83#58511yescharacteristic
773C2×D83—22no—
774C2×D83—22no—
775C2×D83—22no—
776C2×D83—22no—
777C2×D83—22no—
778C2×D83—22no—
779C2×D83—41no—
780C2×D83—41no—
781C2×D83—41no—
782C2×D83—41no—
783C2×D83—41no—
784C2×D83—41no—
785C2×D83—41no—
786C2×D83—41no—
787C2×D83—88no—
788C4×C83—22no—
789C4×C83—22no—
790C4×C83—22no—
791C4×C83—22no—
792C4×C83—22no—
793C4×C83—41no—
794C4×C83—41no—
795C4×C83—41no—
796C4×C83—41no—
797C4×C83—41no—
798C4×C83—41no—
799Dic83—22no—
800Dic83—22no—
801Dic83—22no—
802Dic83—22no—
803Dic83—22no—
804Dic83—22no—
805Dic83—22no—
806Dic83—41no—
807Dic83—41no—
808Dic83—41no—
809Dic83—41no—
810Dic83—41no—
811Dic83—41no—
812Dic83—41no—
813#34517—831nomaximal, Sylow
814C2×C83—42no—
815C2×C83—42no—
816C2×C83—42no—
817C2×C83—42no—
818C2×C83C4×H(5,𝔽2)11yescharacteristic
819C2×C83C4×H(5,𝔽2)11yescharacteristic
820C2×C83C4×H(5,𝔽2)11yescharacteristic
821C2×C83#353411yescharacteristic
822C2×C83#354211yescharacteristic
823C2×C83#354611yescharacteristic
824C2×C83#356611yescharacteristic
825D83—42no—
826D83—42no—
827C2×#560—831no—
828#2377—831no—
829#2377—831no—
830#2376—831no—
831#2373—831no—
832#2373—831no—
833#2366D8311yescharacteristic, complemented
834#2364—831no—
835#2364—831no—
836#2363—831no—
837#2363—831no—
838#2359—831no—
839#2359—831no—
840#2358—831no—
841#2358—831no—
842#2358—831no—
843#2335—831no—
844#2335—831no—
845#2334—831no—
846#2334—831no—
847#2328—831no—
848#2325—831no—
849#2325—831no—
850#2324—831no—
851#2324—831no—
852#2321—831no—
853#2321—831no—
854#2321—831no—
855C4×#123—831no—
856C4×#121—831no—
857C4×#121—831no—
858C83#3451711yescharacteristic, complemented, Sylow
859#560—8316no—
860C2×#127C2×D8311yescharacteristic
861C2×#126—831no—
862C2×#126—831no—
863C2×#123—831no—
864C2×#123—831no—
865C2×#123—831no—
866C2×#121—831no—
867C2×#121—831no—
868C2×#121—831no—
869C2×#121—831no—
870C2×#121—831no—
871C2×#121—831no—
872C2×#120—831no—
873C2×#120—831no—
874C2×#120—831no—
875C2×C4×D4—831no—
876C2×C4×D4—831no—
877C2×C4×D4—831no—
878C2×C4×D4—831no—
879C2×C4×D4—831no—
880C2×C4×D4—831no—
881C2×C4×D4—831no—
882C2×C4×D4—831no—
883C2×C4×D4C2×D8311yescharacteristic
884C2×C4×D4C2×D8311yescharacteristic
885C2×C4×D4C2×D8311yescharacteristic, complemented
886C2×C4×D4C2×D8311yescharacteristic, complemented
887C2×#117—831no—
888C2×#117—831no—
889C22×C22⋊C4—831no—
890C22×C22⋊C4—831no—
891C22×C22⋊C4—831no—
892C22×C42—831no—
893#390—831no—
894#390—831no—
895#390—831no—
896#390—831no—
897#390—831no—
898#390—831no—
899#390—831no—
900#390—831no—
901#390C2×D8311yescharacteristic
902#390C2×D8311yescharacteristic
903#390C2×D8311yescharacteristic, complemented
904#390C2×D8311yescharacteristic, complemented
905#389—831no—
906#389—831no—
907#389—831no—
908#389—831no—
909#389—831no—
910#389—831no—
911#388—831no—
912#388—831no—
913#388—831no—
914#388—831no—
915#388—831no—
916#388—831no—
917#388—831no—
918#388—831no—
919#388—831no—
920#388—831no—
921#388—831no—
922#388—831no—
923#388—831no—
924#388—831no—
925#388—831no—
926#388—831no—
927#388—831no—
928#388—831no—
929#388—831no—
930#388—831no—
931#388—831no—
932#388—831no—
933#388—831no—
934#388—831no—
935#387—831no—
936#387—831no—
937#387—831no—
938#387—831no—
939#387—831no—
940#387—831no—
941#387—831no—
942#387—831no—
943#387—831no—
944#387—831no—
945#387—831no—
946#387—831no—
947#386—831no—
948#386—831no—
949#386—831no—
950#386—831no—
951#386—831no—
952#386—831no—
953#386—831no—
954#386—831no—
955#386—831no—
956#386—831no—
957#386—831no—
958#386—831no—
959#386—831no—
960#386—831no—
961#386—831no—
962#386—831no—
963#386—831no—
964#386—831no—
965#386—831no—
966#386—831no—
967#386C2×D8311yescharacteristic
968#386C2×D8311yescharacteristic
969#386C2×D8311yescharacteristic, complemented
970#386C2×D8311yescharacteristic, complemented
971#385—831no—
972#385—831no—
973#385—831no—
974#385—831no—
975#385—831no—
976#385—831no—
977#385—831no—
978#385—831no—
979#385—831no—
980#385—831no—
981#385—831no—
982#385—831no—
983#382—831no—
984#381—831no—
985#380—831no—
986#380—831no—
987#380—831no—
988#380—831no—
989#379—831no—
990C4×C4⋊C4—831no—
991C4×C4⋊C4—831no—
992C4×C4⋊C4—831no—
993C4×C4⋊C4—831no—
994C4×C4⋊C4—831no—
995C4×C4⋊C4—831no—
996C4×C4⋊C4C2×D8311yescharacteristic, complemented
997C4×C4⋊C4C2×D8311yescharacteristic, complemented
998C4×C22⋊C4—831no—
999C4×C22⋊C4—831no—
1000C4×C22⋊C4—831no—
1001C4×C22⋊C4—831no—
1002C4×C22⋊C4—831no—
1003C4×C22⋊C4—831no—
1004C4×C22⋊C4—831no—
1005C4×C22⋊C4—831no—
1006C4×C22⋊C4—831no—
1007C4×C22⋊C4—831no—
1008C4×C22⋊C4—831no—
1009C4×C22⋊C4—831no—
1010C4×C22⋊C4—831no—
1011C4×C22⋊C4—831no—
1012#376—831no—
1013C2×#95—831no—
1014C2×#95—831no—
1015C25—831no—
1016C22×D4—831no—
1017C22×D4—831no—
1018C22×D4—831no—
1019C22×D4—831no—
1020C22×D4—831no—
1021C22×D4—831no—
1022C22×D4C22×D8311yescharacteristic
1023C22×D4C22×D8311yescharacteristic
1024C22×D4C22×D8311yescharacteristic
1025C22×D4C22×D8311yescharacteristic
1026C22×D4C22×D8311yescharacteristic
1027C22×D4C22×D8311yescharacteristic
1028C23×C4—831no—
1029C23×C4—831no—
1030C23×C4—831no—
1031C23×C4—831no—
1032C23×C4—831no—
1033C23×C4—831no—
1034C23×C4—831no—
1035C23×C4—831no—
1036C23×C4—831no—
1037C23×C4—831no—
1038C23×C4—831no—
1039C23×C4C22×D8311yescharacteristic
1040C23×C4C22×D8311yescharacteristic
1041C23×C4C22×D8311yescharacteristic
1042C23×C4C22×D8311yescharacteristic
1043#127C4×D8318yescomplemented
1044#126—838no—
1045#126—838no—
1046#123—838no—
1047#123—838no—
1048#123—838no—
1049#121—838no—
1050#121—838no—
1051#121—838no—
1052#121—838no—
1053#121—838no—
1054#121—838no—
1055#120—838no—
1056#120—838no—
1057#120—838no—
1058C4×D4—42no—
1059C4×D4—42no—
1060C4×D4—42no—
1061C4×D4—42no—
1062C4×D4—3322no—
1063C4×D4—3322no—
1064C4×D4—3322no—
1065C4×D4—3322no—
1066C4×D4—3322no—
1067C4×D4—3322no—
1068C4×D4—3322no—
1069C4×D4—3322no—
1070#117—3322no—
1071#117—3322no—
1072C2×C4⋊C4—831no—
1073C2×C4⋊C4—831no—
1074C2×C4⋊C4—831no—
1075C2×C4⋊C4—831no—
1076C2×C4⋊C4—831no—
1077C2×C4⋊C4—831no—
1078C2×C4⋊C4—831no—
1079C2×C4⋊C4—831no—
1080C2×C4⋊C4—831no—
1081C2×C4⋊C4—831no—
1082C2×C4⋊C4—831no—
1083C2×C4⋊C4—831no—
1084C2×C4⋊C4—831no—
1085C2×C4⋊C4—831no—
1086C2×C4⋊C4—831no—
1087C2×C4⋊C4—831no—
1088C2×C4⋊C4—831no—
1089C2×C4⋊C4—831no—
1090C2×C4⋊C4—831no—
1091C2×C4⋊C4—831no—
1092C2×C4⋊C4C22×D8311yescharacteristic
1093C2×C4⋊C4C22×D8311yescharacteristic
1094C2×C4⋊C4C22×D8311yescharacteristic
1095C2×C4⋊C4C22×D8311yescharacteristic
1096C2×C22⋊C4—3322no—
1097C2×C22⋊C4—3322no—
1098C2×C22⋊C4—3322no—
1099C2×C22⋊C4—831no—
1100C2×C22⋊C4—831no—
1101C2×C22⋊C4—831no—
1102C2×C22⋊C4—831no—
1103C2×C22⋊C4—831no—
1104C2×C22⋊C4—831no—
1105C2×C22⋊C4—831no—
1106C2×C22⋊C4—831no—
1107C2×C22⋊C4—831no—
1108C2×C22⋊C4—831no—
1109C2×C22⋊C4—831no—
1110C2×C22⋊C4—831no—
1111C2×C22⋊C4—831no—
1112C2×C22⋊C4—831no—
1113C2×C22⋊C4—831no—
1114C2×C22⋊C4—831no—
1115C2×C22⋊C4—831no—
1116C2×C22⋊C4—831no—
1117C2×C22⋊C4—831no—
1118C2×C22⋊C4—831no—
1119C2×C22⋊C4—831no—
1120C2×C22⋊C4—831no—
1121C2×C22⋊C4—831no—
1122C2×C22⋊C4—831no—
1123C2×C22⋊C4—831no—
1124C2×C22⋊C4—831no—
1125C2×C22⋊C4—831no—
1126C2×C22⋊C4—831no—
1127C2×C22⋊C4—831no—
1128C2×C22⋊C4—831no—
1129C2×C22⋊C4—831no—
1130C2×C22⋊C4—831no—
1131C2×C22⋊C4—831no—
1132C2×C22⋊C4—831no—
1133C2×C22⋊C4—831no—
1134C2×C22⋊C4—831no—
1135C2×C22⋊C4C22×D8311yescharacteristic
1136C2×C22⋊C4C22×D8311yescharacteristic
1137C2×C22⋊C4C22×D8311yescharacteristic
1138C2×C22⋊C4C22×D8311yescharacteristic
1139C2×C22⋊C4C22×D8311yescharacteristic
1140C2×C22⋊C4C22×D8311yescharacteristic
1141C2×C22⋊C4C22×D8311yescharacteristic
1142C2×C22⋊C4C22×D8311yescharacteristic
1143C2×C22⋊C4C22×D8311yescharacteristic
1144C2×C22⋊C4C22×D8311yescharacteristic
1145C2×C22⋊C4C22×D8311yescharacteristic
1146C2×C22⋊C4C22×D8311yescharacteristic
1147C2×C42—3322no—
1148C2×C42—831no—
1149C2×C42—831no—
1150C2×C42—831no—
1151C2×C42—831no—
1152C2×C42—831no—
1153C2×C42—831no—
1154C2×C42—831no—
1155C2×C42—831no—
1156C2×C42—831no—
1157C2×C42—831no—
1158C2×C42—831no—
1159C2×C42—831no—
1160C2×C42—831no—
1161C2×C42—831no—
1162C2×C42C22×D8311yescharacteristic
1163C2×C42C22×D8311yescharacteristic
1164C2×C42C22×D8311yescharacteristic
1165C2×C42C22×D8311yescharacteristic
1166C2×C42C22×D8311yescharacteristic
1167#95—831no—
1168#95—831no—
1169#95—831no—
1170#95—831no—
1171#95—831no—
1172#95—831no—
1173#95—831no—
1174#95—831no—
1175#95—831no—
1176#95—831no—
1177#95—831no—
1178#95—831no—
1179#95—831no—
1180#95—831no—
1181#95—831no—
1182#95—831no—
1183#95—831no—
1184#95—831no—
1185#95—831no—
1186#95—831no—
1187#95—831no—
1188#95—831no—
1189#95—831no—
1190#95—831no—
1191#95—831no—
1192#95—831no—
1193#95—831no—
1194#95—831no—
1195#95—831no—
1196#95—831no—
1197#95—831no—
1198#95—831no—
1199#95C22×D8311yescharacteristic
1200#95C22×D8311yescharacteristic
1201#95C22×D8311yescharacteristic
1202#95C22×D8311yescharacteristic
1203C24—3321no—
1204C24—3321no—
1205C24—3321no—
1206C24—3321no—
1207C24—3321no—
1208C24—3321no—
1209C24—834no—
1210C24—831no—
1211C24—831no—
1212C24C23×D8311yescharacteristic
1213C24C23×D8311yescharacteristic
1214C24C23×D8311yescharacteristic
1215C24C23×D8311yescharacteristic
1216C2×D4—41no—
1217C2×D4—41no—
1218C2×D4—41no—
1219C2×D4—41no—
1220C2×D4—41no—
1221C2×D4—41no—
1222C2×D4—41no—
1223C2×D4—41no—
1224C2×D4—41no—
1225C2×D4—41no—
1226C2×D4—41no—
1227C2×D4—41no—
1228C2×D4—3321no—
1229C2×D4—3321no—
1230C2×D4—3321no—
1231C2×D4—3321no—
1232C2×D4—3321no—
1233C2×D4—3321no—
1234C2×D4—3321no—
1235C2×D4—3321no—
1236C2×D4—3321no—
1237C2×D4—3321no—
1238C2×D4—3321no—
1239C2×D4—3321no—
1240C2×D4—834no—
1241C2×D4—834no—
1242C2×D4—834no—
1243C2×D4—834no—
1244C2×D4—834no—
1245C2×D4—834no—
1246C2×D4C2×C4×D8314yes—
1247C2×D4C2×C4×D8314yes—
1248C2×D4C2×C4×D8314yes—
1249C2×D4C2×C4×D8314yes—
1250C2×D4C2×C4×D8314yes—
1251C2×D4C2×C4×D8314yes—
1252C22×C4—22no—
1253C22×C4—22no—
1254C22×C4—22no—
1255C22×C4—22no—
1256C22×C4—41no—
1257C22×C4—41no—
1258C22×C4—41no—
1259C22×C4—41no—
1260C22×C4—41no—
1261C22×C4—41no—
1262C22×C4—41no—
1263C22×C4—41no—
1264C22×C4—3321no—
1265C22×C4—3321no—
1266C22×C4—3321no—
1267C22×C4—3321no—
1268C22×C4—3321no—
1269C22×C4—3321no—
1270C22×C4—3321no—
1271C22×C4—3321no—
1272C22×C4—3321no—
1273C22×C4—3321no—
1274C22×C4—3321no—
1275C22×C4—3321no—
1276C22×C4—3321no—
1277C22×C4—3321no—
1278C22×C4—3321no—
1279C22×C4—3321no—
1280C22×C4—3321no—
1281C22×C4—3321no—
1282C22×C4—3321no—
1283C22×C4—3321no—
1284C22×C4—3321no—
1285C22×C4—3321no—
1286C22×C4—3321no—
1287C22×C4—3321no—
1288C22×C4—3321no—
1289C22×C4—3321no—
1290C22×C4—834no—
1291C22×C4—834no—
1292C22×C4—834no—
1293C22×C4—831no—
1294C22×C4—831no—
1295C22×C4—831no—
1296C22×C4—831no—
1297C22×C4—831no—
1298C22×C4—831no—
1299C22×C4—831no—
1300C22×C4—831no—
1301C22×C4—831no—
1302C22×C4—831no—
1303C22×C4—831no—
1304C22×C4—831no—
1305C22×C4—831no—
1306C22×C4—831no—
1307C22×C4—1662no—
1308C22×C4—1662no—
1309C22×C4—1662no—
1310C22×C4—1662no—
1311C22×C4C23×D8311yescharacteristic
1312C22×C4C23×D8311yescharacteristic
1313C22×C4C23×D8311yescharacteristic
1314C22×C4C23×D8311yescharacteristic
1315C22×C4C23×D8311yescharacteristic
1316C22×C4C23×D8311yescharacteristic
1317C22×C4C23×D8311yescharacteristic
1318C22×C4C23×D8311yescharacteristic
1319C22×C4C23×D8311yescharacteristic
1320C22×C4C23×D8311yescharacteristic
1321C22×C4C23×D8311yescharacteristic
1322C4⋊C4—22no—
1323C4⋊C4—22no—
1324C4⋊C4—41no—
1325C4⋊C4—41no—
1326C4⋊C4—3321no—
1327C4⋊C4—3321no—
1328C4⋊C4—3321no—
1329C4⋊C4—3321no—
1330C4⋊C4—3321no—
1331C4⋊C4—3321no—
1332C4⋊C4—3321no—
1333C4⋊C4—3321no—
1334C4⋊C4—3321no—
1335C4⋊C4—3321no—
1336C4⋊C4—3321no—
1337C4⋊C4—3321no—
1338C4⋊C4—834no—
1339C4⋊C4—834no—
1340C4⋊C4—834no—
1341C4⋊C4—834no—
1342C4⋊C4—834no—
1343C4⋊C4—834no—
1344C4⋊C4—1662no—
1345C4⋊C4—1662no—
1346C22⋊C4—22no—
1347C22⋊C4—22no—
1348C22⋊C4—22no—
1349C22⋊C4—22no—
1350C22⋊C4—41no—
1351C22⋊C4—41no—
1352C22⋊C4—41no—
1353C22⋊C4—41no—
1354C22⋊C4—41no—
1355C22⋊C4—41no—
1356C22⋊C4—41no—
1357C22⋊C4—41no—
1358C22⋊C4—3321no—
1359C22⋊C4—3321no—
1360C22⋊C4—3321no—
1361C22⋊C4—3321no—
1362C22⋊C4—3321no—
1363C22⋊C4—3321no—
1364C22⋊C4—3321no—
1365C22⋊C4—3321no—
1366C22⋊C4—3321no—
1367C22⋊C4—3321no—
1368C22⋊C4—3321no—
1369C22⋊C4—3321no—
1370C22⋊C4—3321no—
1371C22⋊C4—3321no—
1372C22⋊C4—3321no—
1373C22⋊C4—3321no—
1374C22⋊C4—3321no—
1375C22⋊C4—3321no—
1376C22⋊C4—834no—
1377C22⋊C4—834no—
1378C22⋊C4—834no—
1379C22⋊C4—834no—
1380C22⋊C4—834no—
1381C22⋊C4—834no—
1382C22⋊C4—834no—
1383C22⋊C4—834no—
1384C22⋊C4—834no—
1385C22⋊C4—834no—
1386C22⋊C4—834no—
1387C22⋊C4—834no—
1388C22⋊C4—1662no—
1389C22⋊C4—1662no—
1390C22⋊C4—1662no—
1391C22⋊C4—1662no—
1392C22⋊C4—1662no—
1393C22⋊C4—1662no—
1394C42—41no—
1395C42—41no—
1396C42—41no—
1397C42—41no—
1398C42—3321no—
1399C42—3321no—
1400C42—3321no—
1401C42—3321no—
1402C42—3321no—
1403C42—3321no—
1404C42—3321no—
1405C42—3321no—
1406C42—3321no—
1407C42—1662no—
1408C42—1662no—
1409C42—1662no—
1410C42—1662no—
1411C42—1662no—
1412C42C2×C4×D8314yes—
1413C23—21no—
1414C23—21no—
1415C23—21no—
1416C23—21no—
1417C23—21no—
1418C23—21no—
1419C23—21no—
1420C23—21no—
1421C23—21no—
1422C23—21no—
1423C23—21no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—21no—
1428C23—21no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—21no—
1434C23—21no—
1435C23—21no—
1436C23—21no—
1437C23—3324no—
1438C23—3324no—
1439C23—3324no—
1440C23—832no—
1441C23—832no—
1442C23—6642no—
1443C23—6642no—
1444C23—6642no—
1445C23—6642no—
1446C23—1661no—
1447C23—1661no—
1448C23—1661no—
1449C23—1661no—
1450C23—1661no—
1451C23—1661no—
1452C23—1661no—
1453C23—1661no—
1454C23—1661no—
1455C23—1661no—
1456C23—1661no—
1457C23—1661no—
1458C23C22×C4×D8312yes—
1459C23C22×C4×D8312yes—
1460C23C22×C4×D8312yes—
1461C23C22×C4×D8312yes—
1462C23C24×D8311yescharacteristic
1463D4—44no—
1464D4—44no—
1465D4—44no—
1466D4—44no—
1467D4—44no—
1468D4—44no—
1469D4—3324no—
1470D4—3324no—
1471D4—3324no—
1472D4—3324no—
1473D4—3324no—
1474D4—3324no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—44no—
1504C2×C4—82no—
1505C2×C4—82no—
1506C2×C4—82no—
1507C2×C4—3324no—
1508C2×C4—3324no—
1509C2×C4—3324no—
1510C2×C4—3324no—
1511C2×C4—832no—
1512C2×C4—832no—
1513C2×C4—832no—
1514C2×C4—832no—
1515C2×C4—832no—
1516C2×C4—832no—
1517C2×C4—832no—
1518C2×C4—6642no—
1519C2×C4—6642no—
1520C2×C4—6642no—
1521C2×C4—6642no—
1522C2×C4—6642no—
1523C2×C4—6642no—
1524C2×C4—6642no—
1525C2×C4—1661no—
1526C2×C4—1661no—
1527C2×C4—1661no—
1528C2×C4—1661no—
1529C2×C4—1661no—
1530C2×C4—1661no—
1531C2×C4—1661no—
1532C2×C4—1661no—
1533C2×C4—1661no—
1534C2×C4—1661no—
1535C2×C4—1661no—
1536C2×C4—1661no—
1537C2×C4—1661no—
1538C2×C4—1661no—
1539C2×C4—1661no—
1540C2×C4—1661no—
1541C2×C4—1661no—
1542C2×C4—1661no—
1543C2×C4—1661no—
1544C2×C4—1661no—
1545C2×C4—1661no—
1546C2×C4—1661no—
1547C2×C4—1661no—
1548C2×C4—1661no—
1549C2×C4—1661no—
1550C2×C4—1661no—
1551C2×C4—1661no—
1552C2×C4—1661no—
1553C2×C4—1661no—
1554C2×C4—1661no—
1555C2×C4—1661no—
1556C2×C4—1661no—
1557C2×C4—1661no—
1558C2×C4—1661no—
1559C2×C4—1661no—
1560C2×C4C22×C4×D8312yes—
1561C2×C4C22×C4×D8312yes—
1562C2×C4C22×C4×D8312yes—
1563C2×C4#1458183712yes—
1564C2×C4#1458183712yes—
1565C22—22no—
1566C22—22no—
1567C22—22no—
1568C22—22no—
1569C22—22no—
1570C22—22no—
1571C22—22no—
1572C22—22no—
1573C22—22no—
1574C22—22no—
1575C22—22no—
1576C22—22no—
1577C22—41no—
1578C22—41no—
1579C22—41no—
1580C22—41no—
1581C22—41no—
1582C22—41no—
1583C22—41no—
1584C22—41no—
1585C22—41no—
1586C22—41no—
1587C22—41no—
1588C22—41no—
1589C22—41no—
1590C22—41no—
1591C22—41no—
1592C22—41no—
1593C22—3321no—
1594C22—3321no—
1595C22—3321no—
1596C22—3321no—
1597C22—3321no—
1598C22—3321no—
1599C22—3321no—
1600C22—3321no—
1601C22—6648no—
1602C22—1662no—
1603C22—1662no—
1604C22—1662no—
1605C22—1662no—
1606C22—1662no—
1607C22—1662no—
1608C22C23×C4×D8311yescharacteristic
1609C22H(5,𝔽2)×D8311yescharacteristic
1610C22C2×#1458183711yescharacteristic
1611C22C2×#1458183711yescharacteristic
1612C22#1912853611yescharacteristic
1613C22#1912853711yescharacteristic
1614C22#1912853711yescharacteristic
1615C4—22no—
1616C4—22no—
1617C4—22no—
1618C4—22no—
1619C4—22no—
1620C4—41no—
1621C4—41no—
1622C4—41no—
1623C4—41no—
1624C4—41no—
1625C4—41no—
1626C4—3321no—
1627C4—3321no—
1628C4—3321no—
1629C4—3321no—
1630C4—3321no—
1631C4—3321no—
1632C4—3321no—
1633C4—1662no—
1634C4—1662no—
1635C4—1662no—
1636C4—1662no—
1637C4—1662no—
1638C4—1662no—
1639C4—1662no—
1640C2—42no—
1641C2—42no—
1642C2—42no—
1643C2—42no—
1644C2—3322no—
1645C2—3322no—
1646C2#2492066711yescharacteristic
1647C2C4×#1458183711yescharacteristic
1648C2C4×#1458183711yescharacteristic
1649C2#2492164111yescharacteristic
1650C2#2492176911yescharacteristic
1651C2#2492182211yescharacteristic
1652C2#2492213211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2366C2
socle, cosocleC23×C83C25
prime radicalC2×#19128438C2
hypercenter#2366D83
hypocenterC83#34517
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2366

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #24910621C2semidirect
3. #24910614C2semidirect
4. #24910613C2semidirect
5. #24910579C2semidirect
6. #24910579C2semidirect
7. #24910508C2semidirect
8. #24910508C2semidirect
9. #24910504C2semidirect
10. #24910498C2semidirect
11. #24910461C2semidirect
12. #24910449C2semidirect
13. #24910444C2semidirect
14. #24910443C2semidirect
15. #24910440C2semidirect
16. #24910254C2semidirect
17. #24910250C2semidirect
18. #24910238C2semidirect
19. #24910238C2semidirect
20. #24910189C2semidirect
21. #24910164C2semidirect
22. #24910161C2semidirect
23. #24910149C2semidirect
24. #24910149C2semidirect
25. #24910122C2semidirect
26. #24910119C2semidirect
27. #24910117C2semidirect
28. C4×#14581773C2semidirect
29. #24909973C2semidirect
30. C4×#14581764C2semidirect
31. C83×#2366C2semidirect
32. #19128438C4semidirect
48. C2×D4×Dic83C22semidirect
55. C2×#14581748C22semidirect
56. C2×#14581748C22semidirect
60. C22×C4×Dic83C22semidirect
62. #19127604C22semidirect
69. #19127598C22semidirect
70. #19127598C22semidirect
71. #19127596C22semidirect
72. #19127596C22semidirect
73. #19127596C22semidirect
74. #19127596C22semidirect
77. #19127595C22semidirect
78. #19127595C22semidirect
79. #19127595C22semidirect
80. #19127595C22semidirect
97. #19127589C22semidirect
98. #19127589C22semidirect
99. #19127588C22semidirect
100. #19127588C22semidirect
101. #19127585C22semidirect
102. #19127585C22semidirect
103. #19127585C22semidirect
104. #19127585C22semidirect
105. #19127583C22semidirect
106. #19127583C22semidirect
107. #19127582C22semidirect
108. #19127582C22semidirect
109. #19127582C22semidirect
110. #19127582C22semidirect
115. #19127581C22semidirect
116. #19127581C22semidirect
117. #19127581C22semidirect
118. #19127581C22semidirect
134. #19127574C22semidirect
137. #19127573C22semidirect
138. #19127573C22semidirect
143. #19127567C22semidirect
144. #19127562C22semidirect
145. #19127559C22semidirect
146. #19127559C22semidirect
147. #19127559C22semidirect
148. #19127559C22semidirect
150. C4×Dic83⋊C4C22semidirect
151. C4×Dic83⋊C4C22semidirect
152. C4×Dic83⋊C4C22semidirect
153. C4×Dic83⋊C4C22semidirect
154. #19127552C22semidirect
155. #19127552C22semidirect
157. C22⋊C4×Dic83C22semidirect
158. C22⋊C4×Dic83C22semidirect
159. C22⋊C4×Dic83C22semidirect
166. C4×C22⋊Dic83C22semidirect
167. C4×C22⋊Dic83C22semidirect
170. #19127547C22semidirect
171. C2×C83⋊#95C22semidirect
172. C2×C83⋊#95C22semidirect
176. C2×C4×D4×C83C22semidirect
177. C2×C4×D4×C83C22semidirect
180. #390×C83C22semidirect
181. #390×C83C22semidirect
184. #386×C83C22semidirect
185. #386×C83C22semidirect
186. C4×C4⋊C4×C83C22semidirect
187. C4×C4⋊C4×C83C22semidirect
206. #14581786C2×C4semidirect
207. #14581786C2×C4semidirect
208. #14581773C2×C4semidirect
209. #14581773C2×C4semidirect
210. #14581773C2×C4semidirect
211. #14581764C2×C4semidirect
212. #14581764C2×C4semidirect
213. #14581764C2×C4semidirect
214. #14581764C2×C4semidirect
215. #14581764C2×C4semidirect
216. #14581764C2×C4semidirect
217. #14581760C2×C4semidirect
218. #14581760C2×C4semidirect
219. #14581760C2×C4semidirect
346. #127×C83C2×C4semidirect
833. #2366D83semidirect
858. C83#34517semidirect
885. C2×C4×D4C2×D83semidirect
886. C2×C4×D4C2×D83semidirect
903. #390C2×D83semidirect
904. #390C2×D83semidirect
969. #386C2×D83semidirect
970. #386C2×D83semidirect
996. C4×C4⋊C4C2×D83semidirect
997. C4×C4⋊C4C2×D83semidirect
1043. #127C4×D83semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#191284382
#249106212
#249106142
#249106132
#249105792
#249105082
#249105042
#249104982
#249104612
#249104492
#249104442
#249104432
#249104402
#249102542
#249102502
#249102382
#249101892
#249101642
#249101612
#249101492
#249101222
#249101192
#249101172
C4×#145817732
#249099732
C4×#145817642
C83×#23662
#3451783