Finite Group Databasebeta

← #35568997

Subgroups — #35568997

Order 21248.

2292 conjugacy classes of subgroups.

The subgroup lattice has 1522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128381C211yesmaximal, characteristic
2#24910651C211yesmaximal, characteristic, complemented
3#24910624C211yesmaximal, characteristic, complemented
4#24910613C211yesmaximal, characteristic, complemented
5#24910605C211yesmaximal, characteristic, complemented
6#24910581C211yesmaximal, characteristic, complemented
7#24910464C211yesmaximal, characteristic, complemented
8#24910452C211yesmaximal, characteristic, complemented
9#24910440C211yesmaximal, characteristic
10#24910386C211yesmaximal, characteristic, complemented
11#24910361C211yesmaximal, characteristic, complemented
12#24910357C211yesmaximal, characteristic, complemented
13#24910326C211yesmaximal, characteristic, complemented
14#24910307C211yesmaximal, characteristic, complemented
15#24910306C211yesmaximal, characteristic, complemented
16#24910278C211yesmaximal, characteristic, complemented
17#24910248C211yesmaximal, characteristic, complemented
18#24910245C211yesmaximal, characteristic, complemented
19#24910240C211yesmaximal, characteristic, complemented
20#24910195C211yesmaximal, characteristic, complemented
21#24910139C211yesmaximal, characteristic, complemented
22#24910128C211yesmaximal, characteristic, complemented
23#24910122C211yesmaximal, characteristic
24#24910104C211yesmaximal, characteristic, complemented
25#24910093C211yesmaximal, characteristic, complemented
26#24910074C211yesmaximal, characteristic, complemented
27#24910068C211yesmaximal, characteristic, complemented
28C4×#14581774C211yesmaximal, characteristic, complemented
29#24909943C211yesmaximal, characteristic, complemented
30#388×D83C211yesmaximal, characteristic, complemented
31C83×#2367C211yesmaximal, characteristic, complemented
32#19128381C4116yescomplemented
33C2×#14581785C2211yescharacteristic
34C2×#14581785C2211yescharacteristic
35C2×#14581774C2211yescharacteristic
36C2×#14581774C2211yescharacteristic
37C2×#14581773C2211yescharacteristic
38C2×#14581768C2211yescharacteristic
39C2×#14581768C2211yescharacteristic
40C2×#14581760C2211yescharacteristic
41C2×C4×C22⋊D83C2211yescharacteristic
42C2×(C22⋊D83)⋊C4C2211yescharacteristic
43C2×(C22⋊D83)⋊C4C2211yescharacteristic
44C2×(C22⋊D83)⋊C4C2211yescharacteristic
45C2×#14581749C2211yescharacteristic
46C2×#14581749C2211yescharacteristic
47C2×#14581749C2211yescharacteristic
48C2×#14581749C2211yescharacteristic
49C22×Dic83⋊C4C2211yescharacteristic, complemented
50C2×C4⋊C4×D83C2211yescharacteristic
51C22×(C2×D83)⋊C4C2211yescharacteristic
52C2×C22⋊C4×D83C2211yescharacteristic
53C2×C22⋊C4×D83C2211yescharacteristic
54C2×C22⋊C4×D83C2211yescharacteristic
55C2×C22⋊C4×D83C2211yescharacteristic
56C2×C42×D83C2211yescharacteristic
57#19127608C2211yescharacteristic, complemented
58#19127608C2211yescharacteristic, complemented
59#19127601C2211yescharacteristic
60#19127601C2211yescharacteristic
61#19127599C2211yescharacteristic, complemented
62#19127598C2211yescharacteristic, complemented
63#19127598C2211yescharacteristic, complemented
64#19127598C2211yescharacteristic, complemented
65#19127598C2211yescharacteristic, complemented
66#19127597C2211yescharacteristic, complemented
67#19127596C2211yescharacteristic, complemented
68#19127596C2211yescharacteristic, complemented
69#19127596C2211yescharacteristic, complemented
70#19127596C2211yescharacteristic, complemented
71#19127596C2211yescharacteristic, complemented
72#19127596C2211yescharacteristic, complemented
73#19127595C2211yescharacteristic
74#19127595C2211yescharacteristic
75#19127595C2211yescharacteristic
76#19127595C2211yescharacteristic
77#19127595C2211yescharacteristic, complemented
78#19127595C2211yescharacteristic, complemented
79#19127594C2211yescharacteristic
80#19127594C2211yescharacteristic
81#19127594C2211yescharacteristic, complemented
82#19127594C2211yescharacteristic, complemented
83#19127593C2211yescharacteristic
84#19127592C2211yescharacteristic
85#19127592C2211yescharacteristic
86#19127592C2211yescharacteristic
87#19127592C2211yescharacteristic
88#19127592C2211yescharacteristic
89#19127591C2211yescharacteristic
90#19127591C2211yescharacteristic
91#19127591C2211yescharacteristic
92#19127590C2211yescharacteristic
93#19127590C2211yescharacteristic
94#19127590C2211yescharacteristic
95#19127589C2211yescharacteristic
96#19127589C2211yescharacteristic
97#19127586C2211yescharacteristic, complemented
98#19127586C2211yescharacteristic, complemented
99#19127585C2211yescharacteristic, complemented
100#19127585C2211yescharacteristic, complemented
101#19127585C2211yescharacteristic, complemented
102#19127585C2211yescharacteristic, complemented
103#19127585C2211yescharacteristic, complemented
104#19127585C2211yescharacteristic, complemented
105#19127584C2211yescharacteristic, complemented
106#19127584C2211yescharacteristic, complemented
107#19127583C2211yescharacteristic, complemented
108#19127583C2211yescharacteristic, complemented
109#19127583C2211yescharacteristic, complemented
110#19127583C2211yescharacteristic, complemented
111#19127582C2211yescharacteristic, complemented
112#19127582C2211yescharacteristic, complemented
113#19127581C2211yescharacteristic
114#19127581C2211yescharacteristic
115#19127580C2211yescharacteristic
116#19127578C2211yescharacteristic
117#19127577C2211yescharacteristic
118#19127577C2211yescharacteristic
119#19127576C2211yescharacteristic
120#19127576C2211yescharacteristic, complemented
121#19127575C2211yescharacteristic
122#19127575C2211yescharacteristic
123#19127575C2211yescharacteristic
124#19127574C2211yescharacteristic
125#19127574C2211yescharacteristic
126#19127574C2211yescharacteristic
127#19127573C2211yescharacteristic
128#19127573C2211yescharacteristic
129#19127573C2211yescharacteristic, complemented
130#19127572C2211yescharacteristic
131#19127572C2211yescharacteristic
132#19127572C2211yescharacteristic
133#19127572C2211yescharacteristic
134#19127572C2211yescharacteristic
135#19127570C2211yescharacteristic, complemented
136#19127569C2211yescharacteristic, complemented
137#19127568C2211yescharacteristic, complemented
138#19127566C2211yescharacteristic, complemented
139#19127565C2211yescharacteristic, complemented
140#19127563C2211yescharacteristic
141#19127563C2211yescharacteristic
142#19127562C2211yescharacteristic, complemented
143#19127560C2211yescharacteristic
144#19127560C2211yescharacteristic
145#19127560C2211yescharacteristic
146#19127559C2211yescharacteristic, complemented
147#19127559C2211yescharacteristic, complemented
148#19127558C2211yescharacteristic
149#19127558C2211yescharacteristic
150#19127558C2211yescharacteristic
151#19127556C2211yescharacteristic
152C4⋊C4×Dic83C2211yescharacteristic, complemented
153C4×Dic83⋊C4C2211yescharacteristic, complemented
154C4×Dic83⋊C4C2211yescharacteristic, complemented
155C4×Dic83⋊C4C2211yescharacteristic, complemented
156C4×Dic83⋊C4C2211yescharacteristic, complemented
157C4×C4⋊Dic83C2211yescharacteristic, complemented
158C4×C4⋊Dic83C2211yescharacteristic, complemented
159#19127552C2211yescharacteristic, complemented
160C22⋊C4×Dic83C2211yescharacteristic
161C22⋊C4×Dic83C2211yescharacteristic
162C22⋊C4×Dic83C2211yescharacteristic, complemented
163C4×(C2×D83)⋊C4C2211yescharacteristic
164C4×(C2×D83)⋊C4C2211yescharacteristic
165C4×(C2×D83)⋊C4C2211yescharacteristic
166C4×(C2×D83)⋊C4C2211yescharacteristic
167C4×C22⋊Dic83C2211yescharacteristic, complemented
168#19127548C2211yescharacteristic
169#19127548C2211yescharacteristic
170#19127546C2211yescharacteristic, complemented
171#95×D83C2211yescharacteristic
172#95×D83C2211yescharacteristic
173C2×#124×C83C2211yescharacteristic
174C2×C4×Q8×C83C2211yescharacteristic, complemented
175C2×C4×D4×C83C2211yescharacteristic
176#391×C83C2211yescharacteristic, complemented
177#390×C83C2211yescharacteristic
178#388×C83C2211yescharacteristic
179#388×C83C2211yescharacteristic
180#388×C83C2211yescharacteristic, complemented
181#388×C83C2211yescharacteristic, complemented
182#385×C83C2211yescharacteristic
183#385×C83C2211yescharacteristic, complemented
184C4×C4⋊C4×C83C2211yescharacteristic, complemented
185C4×C4⋊C4×C83C2211yescharacteristic, complemented
186C4×C22⋊C4×C83C2211yescharacteristic
187C4×C22⋊C4×C83C2211yescharacteristic, complemented
188C24×D83C2311yescharacteristic
189C22×C22⋊D83C2311yescharacteristic
190C22×C22⋊D83C2311yescharacteristic
191C23×Dic83C2311yescharacteristic
192C23×Dic83C2311yescharacteristic
193C23×Dic83C2311yescharacteristic
194C22×C4×D83C2311yescharacteristic
195C22×C4×D83C2311yescharacteristic
196C22×C4×D83C2311yescharacteristic
197C22×C4×D83C2311yescharacteristic
198C22×C4×D83C2311yescharacteristic
199C22×C4×D83C2311yescharacteristic
200C22×C4×D83C2311yescharacteristic
201C22×C4×D83C2311yescharacteristic
202#14581785C2×C418yescomplemented
203#14581785C2×C418yescomplemented
204#14581774C2×C418yescomplemented
205#14581774C2×C418yescomplemented
206#14581773C2×C418yescomplemented
207#14581768C2×C418yescomplemented
208#14581768C2×C418yescomplemented
209#14581760C2×C418yes—
210C4×C22⋊D83—42no—
211(C22⋊D83)⋊C4—42no—
212(C22⋊D83)⋊C4C2×C418yescomplemented
213(C22⋊D83)⋊C4C2×C418yescomplemented
214#14581749—42no—
215#14581749—42no—
216#14581749C2×C418yescomplemented
217#14581749C2×C418yescomplemented
218C2×C4⋊Dic83C2311yescharacteristic
219C2×C4⋊Dic83C2311yescharacteristic
220C2×C4⋊Dic83C2311yescharacteristic
221C2×C4⋊Dic83C2311yescharacteristic
222C2×C4⋊Dic83C2311yescharacteristic
223C2×C4⋊Dic83C2311yescharacteristic
224C2×Dic83⋊C4—42no—
225C2×Dic83⋊C4C2311yescharacteristic
226C2×Dic83⋊C4C2311yescharacteristic
227C2×Dic83⋊C4C2311yescharacteristic
228C2×Dic83⋊C4C2311yescharacteristic
229C2×Dic83⋊C4C2311yescharacteristic
230C2×Dic83⋊C4C2311yescharacteristic
231C2×Dic83⋊C4C2311yescharacteristic
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
247C4⋊C4×D83—42no—
248C2×C22⋊Dic83C2311yescharacteristic
249C2×C22⋊Dic83C2311yescharacteristic
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×(C2×D83)⋊C4—42no—
259C2×(C2×D83)⋊C4C2311yescharacteristic
260C2×(C2×D83)⋊C4C2311yescharacteristic
261C2×(C2×D83)⋊C4C2311yescharacteristic
262C2×(C2×D83)⋊C4C2311yescharacteristic
263C2×(C2×D83)⋊C4C2311yescharacteristic
264C2×(C2×D83)⋊C4C2311yescharacteristic
265C2×(C2×D83)⋊C4C2311yescharacteristic
266C2×(C2×D83)⋊C4C2311yescharacteristic
267C2×(C2×D83)⋊C4C2311yescharacteristic
268C2×(C2×D83)⋊C4C2311yescharacteristic
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
277C22⋊C4×D83—42no—
278C22⋊C4×D83—42no—
279C22⋊C4×D83C2×C418yescomplemented
280C22⋊C4×D83C2×C418yescomplemented
281C2×C4×Dic83C2311yescharacteristic
282C2×C4×Dic83C2311yescharacteristic
283C2×C4×Dic83C2311yescharacteristic
284C2×C4×Dic83C2311yescharacteristic
285C2×C4×Dic83C2311yescharacteristic
286C2×C4×Dic83C2311yescharacteristic
287C2×C4×Dic83C2311yescharacteristic
288C2×C4×Dic83C2311yescharacteristic
289C2×C4×Dic83C2311yescharacteristic
290C2×C4×Dic83C2311yescharacteristic
291C2×C4×Dic83C2311yescharacteristic
292C2×C4×Dic83C2311yescharacteristic
293C2×C4×Dic83C2311yescharacteristic
294C2×C4×Dic83C2311yescharacteristic
295C42×D83—42no—
296C83⋊#95C2311yescharacteristic
297C83⋊#95C2311yescharacteristic
298C83⋊#95C2311yescharacteristic
299C83⋊#95C2311yescharacteristic
300C83⋊#95C2311yescharacteristic
301C83⋊#95C2311yescharacteristic
302C83⋊#95C2311yescharacteristic
303C83⋊#95C2311yescharacteristic
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
332C22×Q8×C83C2311yescharacteristic
333C22×D4×C83C2311yescharacteristic
334C23×C4×C83C2311yescharacteristic
335C23×C4×C83C2311yescharacteristic
336#124×C83C2×C418yescomplemented
337C4×Q8×C83—42no—
338C4×D4×C83—42no—
339C2×C4⋊C4×C83C2311yescharacteristic
340C2×C4⋊C4×C83C2311yescharacteristic
341C2×C4⋊C4×C83C2311yescharacteristic
342C2×C4⋊C4×C83C2311yescharacteristic
343C2×C4⋊C4×C83C2311yescharacteristic
344C2×C4⋊C4×C83C2311yescharacteristic
345C2×C22⋊C4×C83C2311yescharacteristic
346C2×C22⋊C4×C83C2311yescharacteristic
347C2×C22⋊C4×C83C2311yescharacteristic
348C2×C22⋊C4×C83C2311yescharacteristic
349C2×C22⋊C4×C83C2311yescharacteristic
350C2×C22⋊C4×C83C2311yescharacteristic
351C2×C22⋊C4×C83C2311yescharacteristic
352C2×C22⋊C4×C83C2311yescharacteristic
353C2×C22⋊C4×C83C2311yescharacteristic
354C2×C22⋊C4×C83C2311yescharacteristic
355C2×C42×C83C2311yescharacteristic
356C2×C42×C83C2311yescharacteristic
357C2×C42×C83C2311yescharacteristic
358C2×C42×C83C2311yescharacteristic
359C2×C42×C83C2311yescharacteristic
360C2×C42×C83C2311yescharacteristic
361C2×C42×C83C2311yescharacteristic
362#95×C83C2311yescharacteristic
363#95×C83C2311yescharacteristic
364#95×C83C2311yescharacteristic
365#95×C83C2311yescharacteristic
366#95×C83C2311yescharacteristic
367#95×C83C2311yescharacteristic
368#95×C83C2311yescharacteristic
369#95×C83C2311yescharacteristic
370C23×D83—22no—
371C23×D83—22no—
372C23×D83—41no—
373C23×D83—41no—
374C23×D83—41no—
375C23×D83—41no—
376C23×D83C22×C414yes—
377C23×D83C2411yescharacteristic
378C23×D83C2411yescharacteristic
379C2×C22⋊D83—22no—
380C2×C22⋊D83—22no—
381C2×C22⋊D83—41no—
382C2×C22⋊D83—41no—
383C2×C22⋊D83C22×C414yes—
384C2×C22⋊D83C22×C414yes—
385C22×Dic83—41no—
386C22×Dic83—41no—
387C22×Dic83—41no—
388C22×Dic83—41no—
389C22×Dic83—41no—
390C22×Dic83—41no—
391C22×Dic83—41no—
392C22×Dic83—41no—
393C22×Dic83C22×C414yes—
394C22×Dic83C2411yescharacteristic
395C22×Dic83C2411yescharacteristic
396C22×Dic83C2411yescharacteristic
397C22×Dic83C2411yescharacteristic
398C22×Dic83C2411yescharacteristic
399C22×Dic83C2411yescharacteristic
400C22×Dic83C2411yescharacteristic
401C22×Dic83C2411yescharacteristic
402C22×Dic83C2411yescharacteristic
403C22×Dic83C2411yescharacteristic
404C22×Dic83C2411yescharacteristic
405C22×Dic83C2411yescharacteristic
406C22×Dic83C2411yescharacteristic
407C22×Dic83C2411yescharacteristic
408C2×C4×D83—22no—
409C2×C4×D83—22no—
410C2×C4×D83—22no—
411C2×C4×D83—22no—
412C2×C4×D83—22no—
413C2×C4×D83—22no—
414C2×C4×D83—22no—
415C2×C4×D83—41no—
416C2×C4×D83—41no—
417C2×C4×D83—41no—
418C2×C4×D83—41no—
419C2×C4×D83—41no—
420C2×C4×D83—41no—
421C2×C4×D83—41no—
422C2×C4×D83—41no—
423C2×C4×D83—41no—
424C2×C4×D83—41no—
425C2×C4×D83—41no—
426C2×C4×D83—41no—
427C2×C4×D83—41no—
428C2×C4×D83C22×C414yes—
429C2×C4×D83C22×C414yes—
430C2×C4×D83C22×C414yes—
431C2×C4×D83C22×C414yes—
432C4⋊Dic83—41no—
433C4⋊Dic83—41no—
434C4⋊Dic83—41no—
435C4⋊Dic83—41no—
436C4⋊Dic83C22×C414yes—
437C4⋊Dic83C22×C414yes—
438Dic83⋊C4—22no—
439Dic83⋊C4—22no—
440Dic83⋊C4—41no—
441Dic83⋊C4—41no—
442Dic83⋊C4—41no—
443Dic83⋊C4—41no—
444Dic83⋊C4—41no—
445Dic83⋊C4—41no—
446Dic83⋊C4—41no—
447Dic83⋊C4—41no—
448Dic83⋊C4—41no—
449Dic83⋊C4—41no—
450Dic83⋊C4—41no—
451Dic83⋊C4—41no—
452Dic83⋊C4—41no—
453Dic83⋊C4—41no—
454Dic83⋊C4C22×C414yes—
455Dic83⋊C4C22×C414yes—
456Dic83⋊C4C22×C414yes—
457Dic83⋊C4C22×C414yes—
458Dic83⋊C4C22×C414yes—
459Dic83⋊C4C22×C414yes—
460C22⋊Dic83—41no—
461C22⋊Dic83—41no—
462C22⋊Dic83—41no—
463C22⋊Dic83—41no—
464C22⋊Dic83—41no—
465C22⋊Dic83—41no—
466C22⋊Dic83C22×C414yes—
467C22⋊Dic83C22×C414yes—
468C22⋊Dic83C22×C414yes—
469C22⋊Dic83C22×C414yes—
470(C2×D83)⋊C4—22no—
471(C2×D83)⋊C4—22no—
472(C2×D83)⋊C4—22no—
473(C2×D83)⋊C4—22no—
474(C2×D83)⋊C4—22no—
475(C2×D83)⋊C4—41no—
476(C2×D83)⋊C4—41no—
477(C2×D83)⋊C4—41no—
478(C2×D83)⋊C4—41no—
479(C2×D83)⋊C4—41no—
480(C2×D83)⋊C4—41no—
481(C2×D83)⋊C4—41no—
482(C2×D83)⋊C4C22×C414yes—
483(C2×D83)⋊C4C22×C414yes—
484(C2×D83)⋊C4C22×C414yes—
485(C2×D83)⋊C4C22×C414yes—
486(C2×D83)⋊C4C22×C414yes—
487(C2×D83)⋊C4C22×C414yes—
488C4×Dic83—41no—
489C4×Dic83—41no—
490C4×Dic83—41no—
491C4×Dic83—41no—
492C4×Dic83—41no—
493C4×Dic83—41no—
494C4×Dic83—41no—
495C4×Dic83—41no—
496C4×Dic83—41no—
497C4×Dic83—41no—
498C4×Dic83—41no—
499C4×Dic83—41no—
500C4×Dic83C22×C414yes—
501C4×Dic83C22×C414yes—
502C24×C83C2411yescharacteristic
503C24×C83C2411yescharacteristic
504C2×Q8×C83—41no—
505C2×Q8×C83—41no—
506C2×Q8×C83C22×C414yes—
507C2×D4×C83—41no—
508C2×D4×C83—41no—
509C2×D4×C83C22×C414yes—
510C22×C4×C83—22no—
511C22×C4×C83—41no—
512C22×C4×C83—41no—
513C22×C4×C83—41no—
514C22×C4×C83—41no—
515C22×C4×C83—41no—
516C22×C4×C83C2411yescharacteristic
517C22×C4×C83C2411yescharacteristic
518C22×C4×C83C2411yescharacteristic
519C22×C4×C83C2411yescharacteristic
520C22×C4×C83C2411yescharacteristic
521C22×C4×C83C2411yescharacteristic
522C22×C4×C83C2411yescharacteristic
523C22×C4×C83C2411yescharacteristic
524C22×C4×C83C2411yescharacteristic
525C22×C4×C83C2411yescharacteristic
526C22×C4×C83C2411yescharacteristic
527C22×C4×C83C2411yescharacteristic
528C22×C4×C83C2411yescharacteristic
529C4⋊C4×C83—22no—
530C4⋊C4×C83—22no—
531C4⋊C4×C83—41no—
532C4⋊C4×C83—41no—
533C4⋊C4×C83—41no—
534C4⋊C4×C83—41no—
535C22⋊C4×C83—22no—
536C22⋊C4×C83—41no—
537C22⋊C4×C83—41no—
538C22⋊C4×C83—41no—
539C22⋊C4×C83—41no—
540C22⋊C4×C83—41no—
541C22⋊C4×C83C22×C414yes—
542C22⋊C4×C83C22×C414yes—
543C22⋊C4×C83C22×C414yes—
544C22⋊C4×C83C22×C414yes—
545C42×C83—22no—
546C42×C83—41no—
547C42×C83—41no—
548C42×C83—41no—
549C42×C83—41no—
550C42×C83—41no—
551C42×C83C22×C414yes—
552C23×C83—21no—
553C23×C83—21no—
554C23×C83—21no—
555C23×C83—21no—
556C23×C83—21no—
557C23×C83—21no—
558C23×C83—21no—
559C23×C83—21no—
560C23×C83—21no—
561C23×C83—21no—
562C23×C83—21no—
563C23×C83—21no—
564C23×C83C23×C412yes—
565C23×C83C23×C412yes—
566C23×C83C2511yescharacteristic
567C22×D83—21no—
568C22×D83—21no—
569C22×D83—21no—
570C22×D83—21no—
571C22×D83—21no—
572C22×D83—21no—
573C22×D83—21no—
574C22×D83—21no—
575C22×D83—21no—
576C22×D83—21no—
577C22×D83—28no—
578C22×D83—44no—
579C22×D83—44no—
580C22×D83—82no—
581C22×D83—82no—
582C22×D83—82no—
583C22×D83—82no—
584C22×D83C23×C412yes—
585C22×D83C23×C412yes—
586C22×D83H(5,𝔽2)12yes—
587C22×D832−1+412yes—
588Q8×C83—44no—
589D4×C83—44no—
590C2×C4×C83—21no—
591C2×C4×C83—21no—
592C2×C4×C83—21no—
593C2×C4×C83—21no—
594C2×C4×C83—21no—
595C2×C4×C83—21no—
596C2×C4×C83—21no—
597C2×C4×C83—21no—
598C2×C4×C83—21no—
599C2×C4×C83—21no—
600C2×C4×C83—21no—
601C2×C4×C83—21no—
602C2×C4×C83—21no—
603C2×C4×C83—21no—
604C2×C4×C83—21no—
605C2×C4×C83—21no—
606C2×C4×C83—21no—
607C2×C4×C83—21no—
608C2×C4×C83—21no—
609C2×C4×C83—21no—
610C2×C4×C83—21no—
611C2×C4×C83—21no—
612C2×C4×C83—21no—
613C2×C4×C83—21no—
614C2×C4×C83—21no—
615C2×C4×C83—21no—
616C2×C4×C83—21no—
617C2×C4×C83—21no—
618C2×C4×C83—21no—
619C2×C4×C83—21no—
620C2×C4×C83—21no—
621C2×C4×C83—21no—
622C2×C4×C83—21no—
623C2×C4×C83—82no—
624C2×C4×C83—82no—
625C2×C4×C83C23×C412yes—
626C2×C4×C83C23×C412yes—
627C2×C4×C83C23×C412yes—
628C2×C4×C83C23×C412yes—
629C2×C4×C83C23×C412yes—
630C2×C4×C83H(5,𝔽2)12yes—
631C22⋊D83—28no—
632C22⋊D83—44no—
633C2×Dic83—21no—
634C2×Dic83—21no—
635C2×Dic83—21no—
636C2×Dic83—21no—
637C2×Dic83—21no—
638C2×Dic83—21no—
639C2×Dic83—21no—
640C2×Dic83—21no—
641C2×Dic83—21no—
642C2×Dic83—21no—
643C2×Dic83—21no—
644C2×Dic83—21no—
645C2×Dic83—21no—
646C2×Dic83—21no—
647C2×Dic83—21no—
648C2×Dic83—21no—
649C2×Dic83—21no—
650C2×Dic83—21no—
651C2×Dic83—21no—
652C2×Dic83—21no—
653C2×Dic83—21no—
654C2×Dic83—21no—
655C2×Dic83—21no—
656C2×Dic83—21no—
657C2×Dic83—21no—
658C2×Dic83—21no—
659C2×Dic83—21no—
660C2×Dic83—21no—
661C2×Dic83—21no—
662C2×Dic83—21no—
663C2×Dic83—21no—
664C2×Dic83—21no—
665C2×Dic83—21no—
666C2×Dic83—21no—
667C2×Dic83—21no—
668C2×Dic83—21no—
669C2×Dic83—44no—
670C2×Dic83—82no—
671C2×Dic83—82no—
672C2×Dic83C23×C412yes—
673C2×Dic83C23×C412yes—
674C2×Dic83C23×C412yes—
675C2×Dic83C23×C412yes—
676C2×Dic83C23×C412yes—
677C2×Dic83C23×C412yes—
678C4×D83—28no—
679C4×D83—44no—
680C4×D83—44no—
681C4×D83—44no—
682C4×D83—44no—
683C4×D83—44no—
684C4×D83—82no—
685C4×D83—82no—
686C22×C83—22no—
687C22×C83—22no—
688C22×C83—22no—
689C22×C83—22no—
690C22×C83—22no—
691C22×C83—22no—
692C22×C83—41no—
693C22×C83—41no—
694C22×C83—41no—
695C22×C83—41no—
696C22×C83—41no—
697C22×C83—41no—
698C22×C83—41no—
699C22×C83—41no—
700C22×C83C24×C411yescharacteristic
701C22×C83C2×H(5,𝔽2)11yescharacteristic
702C22×C83C2×H(5,𝔽2)11yescharacteristic
703C22×C83C2×2−1+411yescharacteristic
704C22×C83#58511yescharacteristic
705C22×C83#58511yescharacteristic
706C22×C83#58511yescharacteristic
707C2×D83—22no—
708C2×D83—22no—
709C2×D83—22no—
710C2×D83—22no—
711C2×D83—22no—
712C2×D83—22no—
713C2×D83—22no—
714C2×D83—22no—
715C2×D83—22no—
716C2×D83—41no—
717C2×D83—41no—
718C2×D83—41no—
719C2×D83—41no—
720C2×D83—88no—
721C2×D83#52014yes—
722C4×C83—22no—
723C4×C83—22no—
724C4×C83—22no—
725C4×C83—22no—
726C4×C83—22no—
727C4×C83—22no—
728C4×C83—41no—
729C4×C83—41no—
730C4×C83—41no—
731C4×C83—41no—
732C4×C83—41no—
733C4×C83—41no—
734C4×C83—41no—
735Dic83—22no—
736Dic83—22no—
737Dic83—22no—
738Dic83—22no—
739Dic83—22no—
740Dic83—22no—
741Dic83—41no—
742Dic83—41no—
743Dic83—41no—
744Dic83—41no—
745Dic83—41no—
746Dic83—41no—
747Dic83—41no—
748Dic83—41no—
749#34458—831nomaximal, Sylow
750C2×C83—42no—
751C2×C83—42no—
752C2×C83C2×#52011yescharacteristic
753C2×C83#342811yescharacteristic
754C2×C83C4×H(5,𝔽2)11yescharacteristic
755C2×C83#353311yescharacteristic
756C2×C83#353411yescharacteristic
757C2×C83#356111yescharacteristic
758C2×C83#356411yescharacteristic
759D83—24no—
760D83—42no—
761C2×#551—831no—
762#2383—831no—
763#2378—831no—
764#2376—831no—
765#2376—831no—
766#2373—831no—
767#2367D8311yescharacteristic, complemented
768#2360—831no—
769#2359—831no—
770#2358—831no—
771#2352—831no—
772D4×C4⋊C4—831no—
773#2347—831no—
774#2343—831no—
775#2342—831no—
776#2342—831no—
777#2337—831no—
778#2335—831no—
779#2334—831no—
780#2334—831no—
781#2329—831no—
782#2323—831no—
783#2322—831no—
784#2321—831no—
785#2319—831no—
786#2318—831no—
787#2315—831no—
788#2314—831no—
789C4×#123—831no—
790#2296—831no—
791C2×#388—831no—
792C83#3445811yescharacteristic, complemented, Sylow
793#551—8316no—
794C2×#126—831no—
795C2×#126—831no—
796C2×#124C2×D8311yescharacteristic
797C2×#123—831no—
798C2×#123—831no—
799C2×#123—831no—
800C2×C22⋊Q8—831no—
801C2×C22⋊Q8—831no—
802C2×#120—831no—
803C2×C4×Q8C2×D8311yescharacteristic, complemented
804C2×C4×D4—831no—
805C2×C4×D4—831no—
806C2×C4×D4—831no—
807C2×C4×D4—831no—
808C2×C4×D4C2×D8311yescharacteristic
809C2×#117—831no—
810C2×#117—831no—
811C2×#117—831no—
812C2×#117—831no—
813C22×C4⋊C4—831no—
814C22×C4⋊C4—831no—
815C22×C22⋊C4—831no—
816C22×C22⋊C4—831no—
817C22×C22⋊C4—831no—
818C22×C22⋊C4—831no—
819C22×C22⋊C4—831no—
820C22×C42—831no—
821#391—831no—
822#391—831no—
823#391C2×D8311yescharacteristic, complemented
824#390—831no—
825#390—831no—
826#390C2×D8311yescharacteristic
827#389—831no—
828#389—831no—
829#389—831no—
830#389—831no—
831#389—831no—
832#389—831no—
833#389—831no—
834#389—831no—
835#389—831no—
836#389—831no—
837#389—831no—
838#389—831no—
839#388—831no—
840#388—831no—
841#388—831no—
842#388—831no—
843#388—831no—
844#388—831no—
845#388—831no—
846#388—831no—
847#388—831no—
848#388—831no—
849#388—831no—
850#388—831no—
851#388—831no—
852#388—831no—
853#388—831no—
854#388—831no—
855#388—831no—
856#388—831no—
857#388—831no—
858#388—831no—
859#388—831no—
860#388—831no—
861#388—831no—
862#388—831no—
863#388C2×D8311yescharacteristic
864#388C2×D8311yescharacteristic
865#388C2×D8311yescharacteristic, complemented
866#388C2×D8311yescharacteristic, complemented
867#387—831no—
868#387—831no—
869#387—831no—
870#387—831no—
871#387—831no—
872#387—831no—
873#387—831no—
874#387—831no—
875#387—831no—
876#387—831no—
877#387—831no—
878#387—831no—
879#387—831no—
880#387—831no—
881#387—831no—
882#387—831no—
883#386—831no—
884#386—831no—
885#386—831no—
886#386—831no—
887#386—831no—
888#386—831no—
889#385—831no—
890#385—831no—
891#385—831no—
892#385—831no—
893#385—831no—
894#385—831no—
895#385—831no—
896#385—831no—
897#385—831no—
898#385—831no—
899#385—831no—
900#385—831no—
901#385—831no—
902#385—831no—
903#385—831no—
904#385—831no—
905#385C2×D8311yescharacteristic
906#385C2×D8311yescharacteristic, complemented
907#384—831no—
908#383—831no—
909#383—831no—
910#382—831no—
911#382—831no—
912#381—831no—
913#381—831no—
914#381—831no—
915#380—831no—
916#380—831no—
917#380—831no—
918#380—831no—
919#380—831no—
920#380—831no—
921#380—831no—
922#380—831no—
923#379—831no—
924C4×C4⋊C4—831no—
925C4×C4⋊C4—831no—
926C4×C4⋊C4—831no—
927C4×C4⋊C4—831no—
928C4×C4⋊C4—831no—
929C4×C4⋊C4—831no—
930C4×C4⋊C4—831no—
931C4×C4⋊C4—831no—
932C4×C4⋊C4C2×D8311yescharacteristic, complemented
933C4×C4⋊C4C2×D8311yescharacteristic, complemented
934C4×C22⋊C4—831no—
935C4×C22⋊C4—831no—
936C4×C22⋊C4—831no—
937C4×C22⋊C4—831no—
938C4×C22⋊C4—831no—
939C4×C22⋊C4—831no—
940C4×C22⋊C4—831no—
941C4×C22⋊C4—831no—
942C4×C22⋊C4—831no—
943C4×C22⋊C4—831no—
944C4×C22⋊C4C2×D8311yescharacteristic
945C4×C22⋊C4C2×D8311yescharacteristic, complemented
946#376—831no—
947C2×#95—831no—
948C2×#95—831no—
949C25—831no—
950C22×Q8C22×D8311yescharacteristic
951C22×D4—831no—
952C22×D4—831no—
953C22×D4C22×D8311yescharacteristic
954C23×C4—831no—
955C23×C4—831no—
956C23×C4—831no—
957C23×C4—831no—
958C23×C4—831no—
959C23×C4—831no—
960C23×C4—831no—
961C23×C4—831no—
962C23×C4—831no—
963C23×C4—831no—
964C23×C4—831no—
965C23×C4C22×D8311yescharacteristic
966C23×C4C22×D8311yescharacteristic
967#126—838no—
968#126—838no—
969#124C4×D8318yescomplemented
970#123—838no—
971#123—838no—
972#123—838no—
973C22⋊Q8—838no—
974C22⋊Q8—838no—
975#120—838no—
976C4×Q8—42no—
977C4×D4—42no—
978C4×D4—3322no—
979C4×D4—3322no—
980C4×D4—838no—
981C4×D4—838no—
982#117—3322no—
983#117—3322no—
984#117—838no—
985#117—838no—
986C2×C4⋊C4—3322no—
987C2×C4⋊C4—3322no—
988C2×C4⋊C4—831no—
989C2×C4⋊C4—831no—
990C2×C4⋊C4—831no—
991C2×C4⋊C4—831no—
992C2×C4⋊C4—831no—
993C2×C4⋊C4—831no—
994C2×C4⋊C4—831no—
995C2×C4⋊C4—831no—
996C2×C4⋊C4—831no—
997C2×C4⋊C4—831no—
998C2×C4⋊C4—831no—
999C2×C4⋊C4—831no—
1000C2×C4⋊C4—831no—
1001C2×C4⋊C4—831no—
1002C2×C4⋊C4—831no—
1003C2×C4⋊C4—831no—
1004C2×C4⋊C4—831no—
1005C2×C4⋊C4—831no—
1006C2×C4⋊C4—831no—
1007C2×C4⋊C4—831no—
1008C2×C4⋊C4—831no—
1009C2×C4⋊C4—831no—
1010C2×C4⋊C4—831no—
1011C2×C4⋊C4—831no—
1012C2×C4⋊C4—831no—
1013C2×C4⋊C4—831no—
1014C2×C4⋊C4—831no—
1015C2×C4⋊C4—831no—
1016C2×C4⋊C4C22×D8311yescharacteristic
1017C2×C4⋊C4C22×D8311yescharacteristic
1018C2×C4⋊C4C22×D8311yescharacteristic
1019C2×C4⋊C4C22×D8311yescharacteristic
1020C2×C4⋊C4C22×D8311yescharacteristic
1021C2×C4⋊C4C22×D8311yescharacteristic
1022C2×C22⋊C4—3322no—
1023C2×C22⋊C4—3322no—
1024C2×C22⋊C4—3322no—
1025C2×C22⋊C4—831no—
1026C2×C22⋊C4—831no—
1027C2×C22⋊C4—831no—
1028C2×C22⋊C4—831no—
1029C2×C22⋊C4—831no—
1030C2×C22⋊C4—831no—
1031C2×C22⋊C4—831no—
1032C2×C22⋊C4—831no—
1033C2×C22⋊C4—831no—
1034C2×C22⋊C4—831no—
1035C2×C22⋊C4—831no—
1036C2×C22⋊C4—831no—
1037C2×C22⋊C4—831no—
1038C2×C22⋊C4—831no—
1039C2×C22⋊C4—831no—
1040C2×C22⋊C4—831no—
1041C2×C22⋊C4—831no—
1042C2×C22⋊C4—831no—
1043C2×C22⋊C4—831no—
1044C2×C22⋊C4—831no—
1045C2×C22⋊C4—831no—
1046C2×C22⋊C4—831no—
1047C2×C22⋊C4—831no—
1048C2×C22⋊C4—838no—
1049C2×C22⋊C4—838no—
1050C2×C22⋊C4—831no—
1051C2×C22⋊C4—831no—
1052C2×C22⋊C4—831no—
1053C2×C22⋊C4—831no—
1054C2×C22⋊C4—831no—
1055C2×C22⋊C4C22×D8311yescharacteristic
1056C2×C22⋊C4C22×D8311yescharacteristic
1057C2×C22⋊C4C22×D8311yescharacteristic
1058C2×C22⋊C4C22×D8311yescharacteristic
1059C2×C22⋊C4C22×D8311yescharacteristic
1060C2×C22⋊C4C22×D8311yescharacteristic
1061C2×C22⋊C4C22×D8311yescharacteristic
1062C2×C22⋊C4C22×D8311yescharacteristic
1063C2×C22⋊C4C22×D8311yescharacteristic
1064C2×C22⋊C4C22×D8311yescharacteristic
1065C2×C42—3322no—
1066C2×C42—831no—
1067C2×C42—831no—
1068C2×C42—831no—
1069C2×C42—831no—
1070C2×C42—831no—
1071C2×C42—831no—
1072C2×C42—831no—
1073C2×C42—831no—
1074C2×C42—831no—
1075C2×C42—831no—
1076C2×C42—831no—
1077C2×C42—831no—
1078C2×C42—831no—
1079C2×C42—831no—
1080C2×C42C22×D8311yescharacteristic
1081C2×C42C22×D8311yescharacteristic
1082C2×C42C22×D8311yescharacteristic
1083C2×C42C22×D8311yescharacteristic
1084C2×C42C22×D8311yescharacteristic
1085C2×C42C22×D8311yescharacteristic
1086C2×C42C22×D8311yescharacteristic
1087#95—831no—
1088#95—831no—
1089#95—831no—
1090#95—831no—
1091#95—831no—
1092#95—831no—
1093#95—831no—
1094#95—831no—
1095#95—831no—
1096#95—831no—
1097#95—831no—
1098#95—831no—
1099#95—831no—
1100#95—831no—
1101#95—831no—
1102#95—831no—
1103#95—831no—
1104#95—831no—
1105#95—831no—
1106#95—831no—
1107#95—831no—
1108#95—831no—
1109#95—831no—
1110#95—831no—
1111#95—831no—
1112#95—831no—
1113#95—831no—
1114#95—831no—
1115#95—831no—
1116#95—831no—
1117#95—831no—
1118#95—831no—
1119#95—831no—
1120#95—831no—
1121#95—831no—
1122#95—831no—
1123#95C22×D8311yescharacteristic
1124#95C22×D8311yescharacteristic
1125#95C22×D8311yescharacteristic
1126#95C22×D8311yescharacteristic
1127#95C22×D8311yescharacteristic
1128#95C22×D8311yescharacteristic
1129#95C22×D8311yescharacteristic
1130#95C22×D8311yescharacteristic
1131C24—3321no—
1132C24—3321no—
1133C24—3321no—
1134C24—3321no—
1135C24—834no—
1136C24—831no—
1137C24—831no—
1138C24—1662no—
1139C24—1662no—
1140C24C23×D8311yescharacteristic
1141C24C23×D8311yescharacteristic
1142C2×Q8—41no—
1143C2×Q8—41no—
1144C2×Q8C2×C4×D8314yes—
1145C2×D4—41no—
1146C2×D4—41no—
1147C2×D4—3321no—
1148C2×D4—3321no—
1149C2×D4—834no—
1150C2×D4—834no—
1151C2×D4—1662no—
1152C2×D4—1662no—
1153C2×D4C2×C4×D8314yes—
1154C22×C4—22no—
1155C22×C4—41no—
1156C22×C4—41no—
1157C22×C4—41no—
1158C22×C4—41no—
1159C22×C4—41no—
1160C22×C4—3321no—
1161C22×C4—3321no—
1162C22×C4—3321no—
1163C22×C4—3321no—
1164C22×C4—3321no—
1165C22×C4—3321no—
1166C22×C4—3321no—
1167C22×C4—3321no—
1168C22×C4—3321no—
1169C22×C4—3321no—
1170C22×C4—3321no—
1171C22×C4—3321no—
1172C22×C4—3321no—
1173C22×C4—3321no—
1174C22×C4—3321no—
1175C22×C4—3321no—
1176C22×C4—3321no—
1177C22×C4—3321no—
1178C22×C4—3321no—
1179C22×C4—3321no—
1180C22×C4—3321no—
1181C22×C4—834no—
1182C22×C4—834no—
1183C22×C4—834no—
1184C22×C4—834no—
1185C22×C4—831no—
1186C22×C4—831no—
1187C22×C4—831no—
1188C22×C4—831no—
1189C22×C4—831no—
1190C22×C4—831no—
1191C22×C4—834no—
1192C22×C4—831no—
1193C22×C4—831no—
1194C22×C4—831no—
1195C22×C4—831no—
1196C22×C4—831no—
1197C22×C4—831no—
1198C22×C4—831no—
1199C22×C4—831no—
1200C22×C4—1662no—
1201C22×C4—1662no—
1202C22×C4—1662no—
1203C22×C4—1662no—
1204C22×C4—1662no—
1205C22×C4—1662no—
1206C22×C4—1662no—
1207C22×C4C23×D8311yescharacteristic
1208C22×C4C23×D8311yescharacteristic
1209C22×C4C23×D8311yescharacteristic
1210C22×C4C23×D8311yescharacteristic
1211C22×C4C23×D8311yescharacteristic
1212C22×C4C23×D8311yescharacteristic
1213C22×C4C23×D8311yescharacteristic
1214C22×C4C23×D8311yescharacteristic
1215C22×C4C23×D8311yescharacteristic
1216C22×C4C23×D8311yescharacteristic
1217C22×C4C23×D8311yescharacteristic
1218C22×C4C23×D8311yescharacteristic
1219C22×C4C23×D8311yescharacteristic
1220C4⋊C4—22no—
1221C4⋊C4—22no—
1222C4⋊C4—41no—
1223C4⋊C4—41no—
1224C4⋊C4—41no—
1225C4⋊C4—41no—
1226C4⋊C4—3321no—
1227C4⋊C4—3321no—
1228C4⋊C4—3321no—
1229C4⋊C4—3321no—
1230C4⋊C4—3321no—
1231C4⋊C4—3321no—
1232C4⋊C4—3321no—
1233C4⋊C4—3321no—
1234C4⋊C4—3321no—
1235C4⋊C4—3321no—
1236C4⋊C4—3321no—
1237C4⋊C4—3321no—
1238C4⋊C4—3321no—
1239C4⋊C4—3321no—
1240C4⋊C4—3321no—
1241C4⋊C4—3321no—
1242C4⋊C4—3321no—
1243C4⋊C4—3321no—
1244C4⋊C4—834no—
1245C4⋊C4—834no—
1246C4⋊C4—834no—
1247C4⋊C4—834no—
1248C4⋊C4—834no—
1249C4⋊C4—834no—
1250C4⋊C4—834no—
1251C4⋊C4—834no—
1252C4⋊C4—1662no—
1253C4⋊C4—1662no—
1254C22⋊C4—22no—
1255C22⋊C4—41no—
1256C22⋊C4—41no—
1257C22⋊C4—41no—
1258C22⋊C4—41no—
1259C22⋊C4—41no—
1260C22⋊C4—3321no—
1261C22⋊C4—3321no—
1262C22⋊C4—3321no—
1263C22⋊C4—3321no—
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—834no—
1274C22⋊C4—834no—
1275C22⋊C4—834no—
1276C22⋊C4—834no—
1277C22⋊C4—834no—
1278C22⋊C4—834no—
1279C22⋊C4—834no—
1280C22⋊C4—834no—
1281C22⋊C4—834no—
1282C22⋊C4—834no—
1283C22⋊C4—1662no—
1284C22⋊C4—1662no—
1285C22⋊C4—1662no—
1286C22⋊C4—1662no—
1287C22⋊C4—1662no—
1288C22⋊C4C2×C4×D8314yes—
1289C22⋊C4C2×C4×D8314yes—
1290C22⋊C4C2×C4×D8314yes—
1291C22⋊C4C2×C4×D8314yes—
1292C42—22no—
1293C42—41no—
1294C42—41no—
1295C42—41no—
1296C42—41no—
1297C42—41no—
1298C42—3321no—
1299C42—3321no—
1300C42—3321no—
1301C42—3321no—
1302C42—3321no—
1303C42—3321no—
1304C42—3321no—
1305C42—3321no—
1306C42—3321no—
1307C42—3321no—
1308C42—3321no—
1309C42—3321no—
1310C42—834no—
1311C42—834no—
1312C42C2×C4×D8314yes—
1313C23—21no—
1314C23—21no—
1315C23—21no—
1316C23—21no—
1317C23—21no—
1318C23—21no—
1319C23—21no—
1320C23—21no—
1321C23—21no—
1322C23—21no—
1323C23—21no—
1324C23—21no—
1325C23—3324no—
1326C23—3324no—
1327C23—832no—
1328C23—832no—
1329C23—832no—
1330C23—832no—
1331C23—6642no—
1332C23—6642no—
1333C23—6642no—
1334C23—6642no—
1335C23—1668no—
1336C23—1661no—
1337C23—1661no—
1338C23—1661no—
1339C23—1661no—
1340C23—1661no—
1341C23—1661no—
1342C23—1661no—
1343C23—1661no—
1344C23—1661no—
1345C23—1661no—
1346C23C22×C4×D8312yes—
1347C23C22×C4×D8312yes—
1348C23C24×D8311yescharacteristic
1349Q8—44no—
1350D4—44no—
1351D4—3324no—
1352D4—1668no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—82no—
1387C2×C4—82no—
1388C2×C4—3324no—
1389C2×C4—3324no—
1390C2×C4—3324no—
1391C2×C4—3324no—
1392C2×C4—3324no—
1393C2×C4—3324no—
1394C2×C4—832no—
1395C2×C4—832no—
1396C2×C4—832no—
1397C2×C4—832no—
1398C2×C4—832no—
1399C2×C4—832no—
1400C2×C4—6642no—
1401C2×C4—6642no—
1402C2×C4—6642no—
1403C2×C4—6642no—
1404C2×C4—1668no—
1405C2×C4—1661no—
1406C2×C4—1661no—
1407C2×C4—1661no—
1408C2×C4—1661no—
1409C2×C4—1661no—
1410C2×C4—1661no—
1411C2×C4—1661no—
1412C2×C4—1661no—
1413C2×C4—1661no—
1414C2×C4—1661no—
1415C2×C4—1661no—
1416C2×C4—1661no—
1417C2×C4—1661no—
1418C2×C4—1661no—
1419C2×C4—1661no—
1420C2×C4—1661no—
1421C2×C4—1661no—
1422C2×C4—1661no—
1423C2×C4—1661no—
1424C2×C4—1661no—
1425C2×C4—1661no—
1426C2×C4—1661no—
1427C2×C4—1661no—
1428C2×C4—1661no—
1429C2×C4—1661no—
1430C2×C4—1661no—
1431C2×C4—1661no—
1432C2×C4—1661no—
1433C2×C4—1661no—
1434C2×C4—1661no—
1435C2×C4—1661no—
1436C2×C4—1661no—
1437C2×C4—1661no—
1438C2×C4—1661no—
1439C2×C4—1661no—
1440C2×C4—1661no—
1441C2×C4C22×C4×D8312yes—
1442C2×C4C22×C4×D8312yes—
1443C2×C4C22×C4×D8312yes—
1444C2×C4C22×C4×D8312yes—
1445C2×C4C22×C4×D8312yes—
1446C2×C4#1458183712yes—
1447C22—22no—
1448C22—22no—
1449C22—22no—
1450C22—22no—
1451C22—22no—
1452C22—22no—
1453C22—41no—
1454C22—41no—
1455C22—41no—
1456C22—41no—
1457C22—41no—
1458C22—41no—
1459C22—41no—
1460C22—41no—
1461C22—3321no—
1462C22—3321no—
1463C22—3321no—
1464C22—3321no—
1465C22—834no—
1466C22—6648no—
1467C22—1662no—
1468C22—1662no—
1469C22—1662no—
1470C22—1662no—
1471C22—1662no—
1472C22—1662no—
1473C22—1662no—
1474C22—1662no—
1475C22—1662no—
1476C22C23×C4×D8311yescharacteristic
1477C22H(5,𝔽2)×D8311yescharacteristic
1478C22C2×#1458183711yescharacteristic
1479C222−1+4×D8311yescharacteristic
1480C22#1912853711yescharacteristic
1481C22#1912853711yescharacteristic
1482C22#1912853711yescharacteristic
1483C4—22no—
1484C4—22no—
1485C4—22no—
1486C4—22no—
1487C4—22no—
1488C4—22no—
1489C4—41no—
1490C4—41no—
1491C4—41no—
1492C4—41no—
1493C4—41no—
1494C4—41no—
1495C4—41no—
1496C4—3321no—
1497C4—3321no—
1498C4—3321no—
1499C4—3321no—
1500C4—3321no—
1501C4—3321no—
1502C4—3321no—
1503C4—3321no—
1504C4—1662no—
1505C4—1662no—
1506C4—1662no—
1507C4—1662no—
1508C4—1662no—
1509C4—1662no—
1510C2—42no—
1511C2—42no—
1512C2—3322no—
1513C2—1664no—
1514C2#520×D8311yescharacteristic
1515C2#2492066211yescharacteristic
1516C2C4×#1458183711yescharacteristic
1517C2#2492163711yescharacteristic
1518C2#2492164811yescharacteristic
1519C2#2492202611yescharacteristic
1520C2#2492208211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2367C2
socle, cosocleC23×C83C25
prime radicalC2×#14581760C22
hypercenter#2367D83
hypocenterC83#34458
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2367

Complements

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

NH ≅ G/Ntype
2. #24910651C2semidirect
3. #24910624C2semidirect
4. #24910613C2semidirect
5. #24910605C2semidirect
6. #24910581C2semidirect
7. #24910464C2semidirect
8. #24910452C2semidirect
10. #24910386C2semidirect
11. #24910361C2semidirect
12. #24910357C2semidirect
13. #24910326C2semidirect
14. #24910307C2semidirect
15. #24910306C2semidirect
16. #24910278C2semidirect
17. #24910248C2semidirect
18. #24910245C2semidirect
19. #24910240C2semidirect
20. #24910195C2semidirect
21. #24910139C2semidirect
22. #24910128C2semidirect
24. #24910104C2semidirect
25. #24910093C2semidirect
26. #24910074C2semidirect
27. #24910068C2semidirect
28. C4×#14581774C2semidirect
29. #24909943C2semidirect
30. #388×D83C2semidirect
31. C83×#2367C2semidirect
32. #19128381C4semidirect
49. C22×Dic83⋊C4C22semidirect
57. #19127608C22semidirect
58. #19127608C22semidirect
61. #19127599C22semidirect
62. #19127598C22semidirect
63. #19127598C22semidirect
64. #19127598C22semidirect
65. #19127598C22semidirect
66. #19127597C22semidirect
67. #19127596C22semidirect
68. #19127596C22semidirect
69. #19127596C22semidirect
70. #19127596C22semidirect
71. #19127596C22semidirect
72. #19127596C22semidirect
77. #19127595C22semidirect
78. #19127595C22semidirect
81. #19127594C22semidirect
82. #19127594C22semidirect
97. #19127586C22semidirect
98. #19127586C22semidirect
99. #19127585C22semidirect
100. #19127585C22semidirect
101. #19127585C22semidirect
102. #19127585C22semidirect
103. #19127585C22semidirect
104. #19127585C22semidirect
105. #19127584C22semidirect
106. #19127584C22semidirect
107. #19127583C22semidirect
108. #19127583C22semidirect
109. #19127583C22semidirect
110. #19127583C22semidirect
111. #19127582C22semidirect
112. #19127582C22semidirect
120. #19127576C22semidirect
129. #19127573C22semidirect
135. #19127570C22semidirect
136. #19127569C22semidirect
137. #19127568C22semidirect
138. #19127566C22semidirect
139. #19127565C22semidirect
142. #19127562C22semidirect
146. #19127559C22semidirect
147. #19127559C22semidirect
152. C4⋊C4×Dic83C22semidirect
153. C4×Dic83⋊C4C22semidirect
154. C4×Dic83⋊C4C22semidirect
155. C4×Dic83⋊C4C22semidirect
156. C4×Dic83⋊C4C22semidirect
157. C4×C4⋊Dic83C22semidirect
158. C4×C4⋊Dic83C22semidirect
159. #19127552C22semidirect
162. C22⋊C4×Dic83C22semidirect
167. C4×C22⋊Dic83C22semidirect
170. #19127546C22semidirect
174. C2×C4×Q8×C83C22semidirect
176. #391×C83C22semidirect
180. #388×C83C22semidirect
181. #388×C83C22semidirect
183. #385×C83C22semidirect
184. C4×C4⋊C4×C83C22semidirect
185. C4×C4⋊C4×C83C22semidirect
187. C4×C22⋊C4×C83C22semidirect
202. #14581785C2×C4semidirect
203. #14581785C2×C4semidirect
204. #14581774C2×C4semidirect
205. #14581774C2×C4semidirect
206. #14581773C2×C4semidirect
207. #14581768C2×C4semidirect
208. #14581768C2×C4semidirect
212. (C22⋊D83)⋊C4C2×C4semidirect
213. (C22⋊D83)⋊C4C2×C4semidirect
216. #14581749C2×C4semidirect
217. #14581749C2×C4semidirect
279. C22⋊C4×D83C2×C4semidirect
280. C22⋊C4×D83C2×C4semidirect
336. #124×C83C2×C4semidirect
767. #2367D83semidirect
792. C83#34458semidirect
803. C2×C4×Q8C2×D83semidirect
823. #391C2×D83semidirect
865. #388C2×D83semidirect
866. #388C2×D83semidirect
906. #385C2×D83semidirect
932. C4×C4⋊C4C2×D83semidirect
933. C4×C4⋊C4C2×D83semidirect
945. C4×C22⋊C4C2×D83semidirect
969. #124C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191283812
#249106512
#249106242
#249106132
#249106052
#249105812
#249104642
#249104522
#249104402
#249103862
#249103612
#249103572
#249103262
#249103072
#249103062
#249102782
#249102482
#249102452
#249102402
#249101952
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#249101222
#249101042
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C4×#145817742
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C83×#23672
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