Finite Group Databasebeta

← #35570358

Subgroups — #35570358

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#24910606C211yesmaximal, characteristic, complemented
5#24910583C211yesmaximal, characteristic, complemented
6#24910583C211yesmaximal, characteristic, complemented
7#24910528C211yesmaximal, characteristic, complemented
8#24910511C211yesmaximal, characteristic, complemented
9#24910511C211yesmaximal, characteristic, complemented
10#24910504C211yesmaximal, characteristic, complemented
11#24910498C211yesmaximal, characteristic, complemented
12#24910461C211yesmaximal, characteristic, complemented
13#24910449C211yesmaximal, characteristic, complemented
14#24910446C211yesmaximal, characteristic, complemented
15#24910443C211yesmaximal, characteristic, complemented
16#24910440C211yesmaximal, characteristic, complemented
17#24910254C211yesmaximal, characteristic, complemented
18#24910250C211yesmaximal, characteristic, complemented
19#24910234C211yesmaximal, characteristic, complemented
20#24910234C211yesmaximal, characteristic, complemented
21#24910164C211yesmaximal, characteristic, complemented
22#24910161C211yesmaximal, characteristic, complemented
23#24910153C211yesmaximal, characteristic, complemented
24#24910153C211yesmaximal, characteristic, complemented
25#24910126C211yesmaximal, characteristic, complemented
26#24910122C211yesmaximal, characteristic, complemented
27#24910119C211yesmaximal, characteristic, complemented
28#24909988C211yesmaximal, characteristic, complemented
29#24909973C211yesmaximal, characteristic, complemented
30C4×#14581764C211yesmaximal, characteristic, complemented
31C83×#2328C211yesmaximal, 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
49C2×D4×Dic83C2211yescharacteristic, complemented
50C2×D4×Dic83C2211yescharacteristic, complemented
51C2×C4×C22⋊D83C2211yescharacteristic
52C2×C4×C22⋊D83C2211yescharacteristic
53C2×C4×C22⋊D83C2211yescharacteristic
54C2×C4×C22⋊D83C2211yescharacteristic
55C2×(C22⋊D83)⋊C4C2211yescharacteristic
56C2×(C22⋊D83)⋊C4C2211yescharacteristic
57C2×#14581748C2211yescharacteristic, complemented
58C2×#14581748C2211yescharacteristic, complemented
59C22×(C2×D83)⋊C4C2211yescharacteristic
60C2×C22⋊C4×D83C2211yescharacteristic
61C2×C22⋊C4×D83C2211yescharacteristic
62C22×C4×Dic83C2211yescharacteristic, complemented
63#19127604C2211yescharacteristic
64#19127604C2211yescharacteristic
65#19127604C2211yescharacteristic, complemented
66#19127604C2211yescharacteristic, complemented
67#19127601C2211yescharacteristic
68#19127601C2211yescharacteristic
69#19127601C2211yescharacteristic
70#19127601C2211yescharacteristic
71#19127601C2211yescharacteristic
72#19127601C2211yescharacteristic
73#19127598C2211yescharacteristic, complemented
74#19127598C2211yescharacteristic, complemented
75#19127598C2211yescharacteristic, complemented
76#19127598C2211yescharacteristic, complemented
77#19127596C2211yescharacteristic, complemented
78#19127596C2211yescharacteristic, complemented
79#19127595C2211yescharacteristic
80#19127595C2211yescharacteristic
81#19127595C2211yescharacteristic
82#19127595C2211yescharacteristic
83#19127595C2211yescharacteristic, complemented
84#19127595C2211yescharacteristic, complemented
85#19127593C2211yescharacteristic
86#19127593C2211yescharacteristic
87#19127593C2211yescharacteristic
88#19127593C2211yescharacteristic
89#19127592C2211yescharacteristic
90#19127592C2211yescharacteristic
91#19127591C2211yescharacteristic
92#19127591C2211yescharacteristic
93#19127590C2211yescharacteristic
94#19127590C2211yescharacteristic
95#19127590C2211yescharacteristic
96#19127590C2211yescharacteristic
97#19127589C2211yescharacteristic
98#19127589C2211yescharacteristic
99#19127589C2211yescharacteristic, complemented
100#19127589C2211yescharacteristic, complemented
101#19127589C2211yescharacteristic, complemented
102#19127589C2211yescharacteristic, complemented
103#19127588C2211yescharacteristic, complemented
104#19127588C2211yescharacteristic, complemented
105#19127588C2211yescharacteristic, complemented
106#19127588C2211yescharacteristic, complemented
107#19127585C2211yescharacteristic, complemented
108#19127585C2211yescharacteristic, complemented
109#19127583C2211yescharacteristic, complemented
110#19127583C2211yescharacteristic, complemented
111#19127583C2211yescharacteristic, complemented
112#19127583C2211yescharacteristic, complemented
113#19127582C2211yescharacteristic, complemented
114#19127582C2211yescharacteristic, complemented
115#19127581C2211yescharacteristic
116#19127581C2211yescharacteristic
117#19127581C2211yescharacteristic, complemented
118#19127581C2211yescharacteristic, complemented
119#19127580C2211yescharacteristic
120#19127580C2211yescharacteristic
121#19127578C2211yescharacteristic
122#19127578C2211yescharacteristic
123#19127578C2211yescharacteristic
124#19127578C2211yescharacteristic
125#19127577C2211yescharacteristic
126#19127577C2211yescharacteristic
127#19127577C2211yescharacteristic
128#19127577C2211yescharacteristic
129#19127577C2211yescharacteristic
130#19127577C2211yescharacteristic
131#19127575C2211yescharacteristic
132#19127575C2211yescharacteristic
133#19127575C2211yescharacteristic
134#19127575C2211yescharacteristic
135#19127574C2211yescharacteristic
136#19127574C2211yescharacteristic
137#19127574C2211yescharacteristic, complemented
138#19127574C2211yescharacteristic, complemented
139#19127573C2211yescharacteristic
140#19127573C2211yescharacteristic, complemented
141#19127572C2211yescharacteristic
142#19127572C2211yescharacteristic
143#19127562C2211yescharacteristic, complemented
144#19127559C2211yescharacteristic, complemented
145#19127559C2211yescharacteristic, complemented
146#19127559C2211yescharacteristic, complemented
147#19127559C2211yescharacteristic, complemented
148#19127556C2211yescharacteristic
149C4×Dic83⋊C4C2211yescharacteristic, complemented
150C4×Dic83⋊C4C2211yescharacteristic, complemented
151C4×C4⋊Dic83C2211yescharacteristic, complemented
152C4×C4⋊Dic83C2211yescharacteristic, complemented
153#19127552C2211yescharacteristic, complemented
154#19127552C2211yescharacteristic, complemented
155#19127552C2211yescharacteristic, complemented
156#19127552C2211yescharacteristic, complemented
157C22⋊C4×Dic83C2211yescharacteristic
158C22⋊C4×Dic83C2211yescharacteristic
159C22⋊C4×Dic83C2211yescharacteristic, complemented
160C22⋊C4×Dic83C2211yescharacteristic, complemented
161C22⋊C4×Dic83C2211yescharacteristic, complemented
162C22⋊C4×Dic83C2211yescharacteristic, complemented
163C4×(C2×D83)⋊C4C2211yescharacteristic
164C4×(C2×D83)⋊C4C2211yescharacteristic
165C4×C22⋊Dic83C2211yescharacteristic
166C4×C22⋊Dic83C2211yescharacteristic, complemented
167#19127548C2211yescharacteristic
168#19127548C2211yescharacteristic
169#19127548C2211yescharacteristic
170#19127548C2211yescharacteristic
171C2×C83⋊#95C2211yescharacteristic, complemented
172C2×C83⋊#95C2211yescharacteristic, complemented
173C2×#127×C83C2211yescharacteristic
174C2×C4×D4×C83C2211yescharacteristic
175C2×C4×D4×C83C2211yescharacteristic, complemented
176#390×C83C2211yescharacteristic
177#390×C83C2211yescharacteristic, complemented
178#386×C83C2211yescharacteristic
179#386×C83C2211yescharacteristic
180#386×C83C2211yescharacteristic
181#386×C83C2211yescharacteristic
182#386×C83C2211yescharacteristic, complemented
183#386×C83C2211yescharacteristic, complemented
184#386×C83C2211yescharacteristic, complemented
185#386×C83C2211yescharacteristic, complemented
186#382×C83C2211yescharacteristic, complemented
187#376×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—
222D4×Dic83—42no—
223D4×Dic83—42no—
224C4×C22⋊D83—42no—
225C4×C22⋊D83—42no—
226C4×C22⋊D83—42no—
227C4×C22⋊D83—42no—
228(C22⋊D83)⋊C4—42no—
229(C22⋊D83)⋊C4—42no—
230#14581748—42no—
231#14581748—42no—
232C2×C4⋊Dic83C2311yescharacteristic
233C2×C4⋊Dic83C2311yescharacteristic
234C2×C4⋊Dic83C2311yescharacteristic
235C2×C4⋊Dic83C2311yescharacteristic
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×Dic83⋊C4C2311yescharacteristic
251C2×Dic83⋊C4C2311yescharacteristic
252C2×Dic83⋊C4C2311yescharacteristic
253C2×Dic83⋊C4C2311yescharacteristic
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×C22⋊Dic83C2311yescharacteristic
269C2×C22⋊Dic83C2311yescharacteristic
270C2×C22⋊Dic83C2311yescharacteristic
271C2×C22⋊Dic83C2311yescharacteristic
272C2×(C2×D83)⋊C4—42no—
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
287C2×(C2×D83)⋊C4C2311yescharacteristic
288C2×(C2×D83)⋊C4C2311yescharacteristic
289C2×(C2×D83)⋊C4C2311yescharacteristic
290C2×(C2×D83)⋊C4C2311yescharacteristic
291C22⋊C4×D83—42no—
292C22⋊C4×D83—42no—
293C2×C4×Dic83—42no—
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
304C2×C4×Dic83C2311yescharacteristic
305C2×C4×Dic83C2311yescharacteristic
306C2×C4×Dic83C2311yescharacteristic
307C2×C4×Dic83C2311yescharacteristic
308C2×C4×Dic83C2311yescharacteristic
309C2×C4×Dic83C2311yescharacteristic
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
336C83⋊#95C2311yescharacteristic
337C83⋊#95C2311yescharacteristic
338C22×D4×C83C2311yescharacteristic
339C22×D4×C83C2311yescharacteristic
340C22×D4×C83C2311yescharacteristic
341C22×D4×C83C2311yescharacteristic
342C22×D4×C83C2311yescharacteristic
343C22×D4×C83C2311yescharacteristic
344C23×C4×C83C2311yescharacteristic
345C23×C4×C83C2311yescharacteristic
346C23×C4×C83C2311yescharacteristic
347C23×C4×C83C2311yescharacteristic
348#127×C83C2×C418yescomplemented
349C4×D4×C83—42no—
350C4×D4×C83—42no—
351C2×C4⋊C4×C83C2311yescharacteristic
352C2×C4⋊C4×C83C2311yescharacteristic
353C2×C22⋊C4×C83C2311yescharacteristic
354C2×C22⋊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×C42×C83C2311yescharacteristic
366C2×C42×C83C2311yescharacteristic
367C2×C42×C83C2311yescharacteristic
368#95×C83C2311yescharacteristic
369#95×C83C2311yescharacteristic
370#95×C83C2311yescharacteristic
371#95×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—22no—
406C22×Dic83—22no—
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—22no—
451C4⋊Dic83—22no—
452C4⋊Dic83—41no—
453C4⋊Dic83—41no—
454Dic83⋊C4—22no—
455Dic83⋊C4—22no—
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⋊C4—41no—
465Dic83⋊C4—41no—
466Dic83⋊C4C22×C414yes—
467Dic83⋊C4C22×C414yes—
468Dic83⋊C4C22×C414yes—
469Dic83⋊C4C22×C414yes—
470Dic83⋊C4C22×C414yes—
471Dic83⋊C4C22×C414yes—
472C22⋊Dic83—22no—
473C22⋊Dic83—22no—
474C22⋊Dic83—22no—
475C22⋊Dic83—22no—
476C22⋊Dic83—41no—
477C22⋊Dic83—41no—
478C22⋊Dic83—41no—
479C22⋊Dic83—41no—
480C22⋊Dic83—41no—
481C22⋊Dic83—41no—
482C22⋊Dic83—41no—
483C22⋊Dic83—41no—
484C22⋊Dic83C22×C414yes—
485C22⋊Dic83C22×C414yes—
486C22⋊Dic83C22×C414yes—
487C22⋊Dic83C22×C414yes—
488C22⋊Dic83C22×C414yes—
489C22⋊Dic83C22×C414yes—
490(C2×D83)⋊C4—22no—
491(C2×D83)⋊C4—22no—
492(C2×D83)⋊C4—22no—
493(C2×D83)⋊C4—22no—
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)⋊C4—41no—
501(C2×D83)⋊C4—41no—
502(C2×D83)⋊C4C22×C414yes—
503(C2×D83)⋊C4C22×C414yes—
504(C2×D83)⋊C4C22×C414yes—
505(C2×D83)⋊C4C22×C414yes—
506(C2×D83)⋊C4C22×C414yes—
507(C2×D83)⋊C4C22×C414yes—
508C4×Dic83—22no—
509C4×Dic83—22no—
510C4×Dic83—22no—
511C4×Dic83—22no—
512C4×Dic83—41no—
513C4×Dic83—41no—
514C4×Dic83—41no—
515C4×Dic83—41no—
516C4×Dic83—41no—
517C4×Dic83—41no—
518C4×Dic83—41no—
519C4×Dic83—41no—
520C4×Dic83—41no—
521C4×Dic83—41no—
522C4×Dic83—41no—
523C4×Dic83—41no—
524C24×C83C2411yescharacteristic
525C24×C83C2411yescharacteristic
526C24×C83C2411yescharacteristic
527C24×C83C2411yescharacteristic
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×C83—41no—
537C2×D4×C83—41no—
538C2×D4×C83—41no—
539C2×D4×C83—41no—
540C2×D4×C83C22×C414yes—
541C2×D4×C83C22×C414yes—
542C2×D4×C83C22×C414yes—
543C2×D4×C83C22×C414yes—
544C2×D4×C83C22×C414yes—
545C2×D4×C83C22×C414yes—
546C22×C4×C83—22no—
547C22×C4×C83—22no—
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×C83—41no—
555C22×C4×C83—41no—
556C22×C4×C83—41no—
557C22×C4×C83—41no—
558C22×C4×C83C2411yescharacteristic
559C22×C4×C83C2411yescharacteristic
560C22×C4×C83C2411yescharacteristic
561C22×C4×C83C2411yescharacteristic
562C22×C4×C83C2411yescharacteristic
563C22×C4×C83C2411yescharacteristic
564C22×C4×C83C2411yescharacteristic
565C22×C4×C83C2411yescharacteristic
566C22×C4×C83C2411yescharacteristic
567C22×C4×C83C2411yescharacteristic
568C22×C4×C83C2411yescharacteristic
569C4⋊C4×C83—41no—
570C4⋊C4×C83—41no—
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—
581C22⋊C4×C83—41no—
582C22⋊C4×C83—41no—
583C42×C83—22no—
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—21no—
671C2×C4×C83—44no—
672C2×C4×C83—82no—
673C2×C4×C83—82no—
674C2×C4×C83—82no—
675C2×C4×C83C23×C412yes—
676C2×C4×C83C23×C412yes—
677C2×C4×C83C23×C412yes—
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—44no—
720C2×Dic83—44no—
721C2×Dic83—44no—
722C2×Dic83—44no—
723C2×Dic83—82no—
724C2×Dic83—82no—
725C2×Dic83—82no—
726C2×Dic83C23×C412yes—
727C2×Dic83C23×C412yes—
728C2×Dic83C23×C412yes—
729C2×Dic83C23×C412yes—
730C2×Dic83C23×C412yes—
731C2×Dic83C23×C412yes—
732C2×Dic83H(5,𝔽2)12yes—
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—41no—
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—22no—
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#2366—831no—
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#2328D8311yescharacteristic, complemented
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×D4—831no—
884C2×C4×D4—831no—
885C2×C4×D4C2×D8311yescharacteristic
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#390—831no—
902#390—831no—
903#390C2×D8311yescharacteristic
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#386C2×D8311yescharacteristic
964#386C2×D8311yescharacteristic
965#386C2×D8311yescharacteristic
966#386C2×D8311yescharacteristic
967#386C2×D8311yescharacteristic, complemented
968#386C2×D8311yescharacteristic, complemented
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#382C2×D8311yescharacteristic, complemented
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⋊C4—831no—
997C4×C4⋊C4—831no—
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#376C2×D8311yescharacteristic, complemented
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—3322no—
1061C4×D4—3322no—
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⋊C4—831no—
1093C2×C4⋊C4—831no—
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×C42—831no—
1163C2×C42—831no—
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#95C22×D8311yescharacteristic
1196#95C22×D8311yescharacteristic
1197#95C22×D8311yescharacteristic
1198#95C22×D8311yescharacteristic
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—41no—
1255C22×C4—41no—
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—834no—
1289C22×C4—834no—
1290C22×C4—834no—
1291C22×C4—831no—
1292C22×C4—831no—
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—1662no—
1306C22×C4—1662no—
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—41no—
1323C4⋊C4—41no—
1324C4⋊C4—3321no—
1325C4⋊C4—3321no—
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—834no—
1337C4⋊C4—834no—
1338C4⋊C4—834no—
1339C4⋊C4—834no—
1340C4⋊C4—834no—
1341C4⋊C4—834no—
1342C4⋊C4—1662no—
1343C4⋊C4—1662no—
1344C4⋊C4—1662no—
1345C4⋊C4—1662no—
1346C22⋊C4—22no—
1347C22⋊C4—22no—
1348C22⋊C4—41no—
1349C22⋊C4—41no—
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—834no—
1375C22⋊C4—834no—
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—1662no—
1387C22⋊C4—1662no—
1388C22⋊C4—1662no—
1389C22⋊C4—1662no—
1390C22⋊C4—1662no—
1391C22⋊C4—1662no—
1392C22⋊C4—1662no—
1393C22⋊C4—1662no—
1394C42—22no—
1395C42—41no—
1396C42—3321no—
1397C42—3321no—
1398C42—3321no—
1399C42—3321no—
1400C42—3321no—
1401C42—3321no—
1402C42—3321no—
1403C42—3321no—
1404C42—3321no—
1405C42—3321no—
1406C42—3321no—
1407C42—3321no—
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—21no—
1504C2×C4—44no—
1505C2×C4—82no—
1506C2×C4—82no—
1507C2×C4—82no—
1508C2×C4—3324no—
1509C2×C4—3324no—
1510C2×C4—3324no—
1511C2×C4—3324no—
1512C2×C4—832no—
1513C2×C4—832no—
1514C2×C4—832no—
1515C2×C4—832no—
1516C2×C4—832no—
1517C2×C4—832no—
1518C2×C4—832no—
1519C2×C4—832no—
1520C2×C4—6642no—
1521C2×C4—6642no—
1522C2×C4—6642no—
1523C2×C4—6642no—
1524C2×C4—6642no—
1525C2×C4—6642no—
1526C2×C4—6642no—
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×C4—1661no—
1561C2×C4C22×C4×D8312yes—
1562C2×C4C22×C4×D8312yes—
1563C2×C4C22×C4×D8312yes—
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
1610C22H(5,𝔽2)×D8311yescharacteristic
1611C22C2×#1458183711yescharacteristic
1612C22#1912853611yescharacteristic
1613C22#1912853611yescharacteristic
1614C22#1912853711yescharacteristic
1615C4—22no—
1616C4—22no—
1617C4—22no—
1618C4—22no—
1619C4—41no—
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—1662no—
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
1647C2#2492066711yescharacteristic
1648C2C4×#1458183711yescharacteristic
1649C2#2492164611yescharacteristic
1650C2#2492176611yescharacteristic
1651C2#2492183311yescharacteristic
1652C2#2492213511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2328C2
socle, cosocleC23×C83C25
prime radicalC2×#19128438C2
hypercenter#2328D83
hypocenterC83#34517
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2328

Complements

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

NH ≅ G/Ntype
2. #24910621C2semidirect
3. #24910614C2semidirect
4. #24910606C2semidirect
5. #24910583C2semidirect
6. #24910583C2semidirect
7. #24910528C2semidirect
8. #24910511C2semidirect
9. #24910511C2semidirect
10. #24910504C2semidirect
11. #24910498C2semidirect
12. #24910461C2semidirect
13. #24910449C2semidirect
14. #24910446C2semidirect
15. #24910443C2semidirect
16. #24910440C2semidirect
17. #24910254C2semidirect
18. #24910250C2semidirect
19. #24910234C2semidirect
20. #24910234C2semidirect
21. #24910164C2semidirect
22. #24910161C2semidirect
23. #24910153C2semidirect
24. #24910153C2semidirect
25. #24910126C2semidirect
26. #24910122C2semidirect
27. #24910119C2semidirect
28. #24909988C2semidirect
29. #24909973C2semidirect
30. C4×#14581764C2semidirect
31. C83×#2328C2semidirect
32. #19128438C4semidirect
49. C2×D4×Dic83C22semidirect
50. C2×D4×Dic83C22semidirect
57. C2×#14581748C22semidirect
58. C2×#14581748C22semidirect
62. C22×C4×Dic83C22semidirect
65. #19127604C22semidirect
66. #19127604C22semidirect
73. #19127598C22semidirect
74. #19127598C22semidirect
75. #19127598C22semidirect
76. #19127598C22semidirect
77. #19127596C22semidirect
78. #19127596C22semidirect
83. #19127595C22semidirect
84. #19127595C22semidirect
99. #19127589C22semidirect
100. #19127589C22semidirect
101. #19127589C22semidirect
102. #19127589C22semidirect
103. #19127588C22semidirect
104. #19127588C22semidirect
105. #19127588C22semidirect
106. #19127588C22semidirect
107. #19127585C22semidirect
108. #19127585C22semidirect
109. #19127583C22semidirect
110. #19127583C22semidirect
111. #19127583C22semidirect
112. #19127583C22semidirect
113. #19127582C22semidirect
114. #19127582C22semidirect
117. #19127581C22semidirect
118. #19127581C22semidirect
137. #19127574C22semidirect
138. #19127574C22semidirect
140. #19127573C22semidirect
143. #19127562C22semidirect
144. #19127559C22semidirect
145. #19127559C22semidirect
146. #19127559C22semidirect
147. #19127559C22semidirect
149. C4×Dic83⋊C4C22semidirect
150. C4×Dic83⋊C4C22semidirect
151. C4×C4⋊Dic83C22semidirect
152. C4×C4⋊Dic83C22semidirect
153. #19127552C22semidirect
154. #19127552C22semidirect
155. #19127552C22semidirect
156. #19127552C22semidirect
159. C22⋊C4×Dic83C22semidirect
160. C22⋊C4×Dic83C22semidirect
161. C22⋊C4×Dic83C22semidirect
162. C22⋊C4×Dic83C22semidirect
166. C4×C22⋊Dic83C22semidirect
171. C2×C83⋊#95C22semidirect
172. C2×C83⋊#95C22semidirect
175. C2×C4×D4×C83C22semidirect
177. #390×C83C22semidirect
182. #386×C83C22semidirect
183. #386×C83C22semidirect
184. #386×C83C22semidirect
185. #386×C83C22semidirect
186. #382×C83C22semidirect
187. #376×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
348. #127×C83C2×C4semidirect
847. #2328D83semidirect
858. C83#34517semidirect
886. C2×C4×D4C2×D83semidirect
904. #390C2×D83semidirect
967. #386C2×D83semidirect
968. #386C2×D83semidirect
969. #386C2×D83semidirect
970. #386C2×D83semidirect
983. #382C2×D83semidirect
1012. #376C2×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
#249106062
#249105832
#249105282
#249105112
#249105042
#249104982
#249104612
#249104492
#249104462
#249104432
#249104402
#249102542
#249102502
#249102342
#249101642
#249101612
#249101532
#249101262
#249101222
#249101192
#249099882
#249099732
C4×#145817642
C83×#23282
#3451783