Finite Group Databasebeta

← #35566879

Subgroups — #35566879

Order 21248.

2436 conjugacy classes of subgroups.

The subgroup lattice has 1540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128435C211yesmaximal, characteristic
2#24910537C211yesmaximal, characteristic, complemented
3#24910535C211yesmaximal, characteristic, complemented
4#24910535C211yesmaximal, characteristic, complemented
5#24910531C211yesmaximal, characteristic, complemented
6#24910526C211yesmaximal, characteristic
7#24910462C211yesmaximal, characteristic, complemented
8#24910460C211yesmaximal, characteristic, complemented
9#24910449C211yesmaximal, characteristic, complemented
10#24910417C211yesmaximal, characteristic, complemented
11#24910413C211yesmaximal, characteristic, complemented
12#24910409C211yesmaximal, characteristic, complemented
13#24910377C211yesmaximal, characteristic, complemented
14#24910370C211yesmaximal, characteristic, complemented
15#24910369C211yesmaximal, characteristic, complemented
16#24910259C211yesmaximal, characteristic, complemented
17#24910257C211yesmaximal, characteristic, complemented
18#24910256C211yesmaximal, characteristic, complemented
19#24910254C211yesmaximal, characteristic, complemented
20#24910169C211yesmaximal, characteristic, complemented
21#24910169C211yesmaximal, characteristic, complemented
22C4×#14581788C211yesmaximal, characteristic
23#24910004C211yesmaximal, characteristic, complemented
24C4×#14581778C211yesmaximal, characteristic, complemented
25#24909936C211yesmaximal, characteristic, complemented
26#24909923C211yesmaximal, characteristic, complemented
27#24909922C211yesmaximal, characteristic, complemented
28#24909822C211yesmaximal, characteristic, complemented
29#24909821C211yesmaximal, characteristic, complemented
30C4×#14581757C211yesmaximal, characteristic, complemented
31C83×#2359C211yesmaximal, characteristic, complemented
32#19128435C4116yescomplemented
33C2×#14581788C2211yescharacteristic
34C2×#14581778C2211yescharacteristic
35C2×#14581778C2211yescharacteristic
36C2×#14581778C2211yescharacteristic
37C2×#14581778C2211yescharacteristic
38C2×#14581777C2211yescharacteristic
39C2×#14581777C2211yescharacteristic
40C2×#14581773C2211yescharacteristic
41C2×C4×Dic166C2211yescharacteristic
42C2×C4×Dic166C2211yescharacteristic
43C2×#14581757C2211yescharacteristic
44C2×#14581757C2211yescharacteristic
45C2×#14581757C2211yescharacteristic
46C2×#14581757C2211yescharacteristic
47C2×C4×D332C2211yescharacteristic
48C2×C4×C22⋊D83C2211yescharacteristic
49C2×C4×C22⋊D83C2211yescharacteristic
50C2×C4×C22⋊D83C2211yescharacteristic
51C2×C4×C22⋊D83C2211yescharacteristic
52C2×C4×C22⋊D83C2211yescharacteristic
53C2×C4×C22⋊D83C2211yescharacteristic
54C2×C4×C22⋊D83C2211yescharacteristic
55C2×C4×C22⋊D83C2211yescharacteristic
56C2×(C22⋊D83)⋊C4C2211yescharacteristic
57C2×(C22⋊D83)⋊C4C2211yescharacteristic
58C2×(C22⋊D83)⋊C4C2211yescharacteristic
59C2×(C22⋊D83)⋊C4C2211yescharacteristic
60C2×#14581750C2211yescharacteristic
61C2×#14581749C2211yescharacteristic
62C2×#14581748C2211yescharacteristic
63#19127605C2211yescharacteristic
64#19127605C2211yescharacteristic
65#19127605C2211yescharacteristic
66#19127605C2211yescharacteristic
67#19127604C2211yescharacteristic
68#19127602C2211yescharacteristic
69#19127601C2211yescharacteristic
70#19127601C2211yescharacteristic
71#19127601C2211yescharacteristic
72#19127601C2211yescharacteristic
73#19127601C2211yescharacteristic
74#19127601C2211yescharacteristic
75#19127601C2211yescharacteristic
76#19127601C2211yescharacteristic
77#19127600C2211yescharacteristic
78#19127598C2211yescharacteristic
79#19127598C2211yescharacteristic
80#19127598C2211yescharacteristic
81#19127596C2211yescharacteristic
82#19127596C2211yescharacteristic
83#19127596C2211yescharacteristic
84#19127595C2211yescharacteristic
85#19127595C2211yescharacteristic
86#19127595C2211yescharacteristic
87#19127595C2211yescharacteristic
88#19127594C2211yescharacteristic
89#19127594C2211yescharacteristic
90#19127594C2211yescharacteristic
91#19127594C2211yescharacteristic
92#19127593C2211yescharacteristic
93#19127593C2211yescharacteristic
94#19127592C2211yescharacteristic
95#19127592C2211yescharacteristic
96#19127592C2211yescharacteristic
97#19127592C2211yescharacteristic
98#19127591C2211yescharacteristic
99#19127591C2211yescharacteristic
100#19127591C2211yescharacteristic
101#19127591C2211yescharacteristic
102#19127590C2211yescharacteristic
103#19127590C2211yescharacteristic
104#19127589C2211yescharacteristic
105#19127589C2211yescharacteristic
106#19127588C2211yescharacteristic
107#19127587C2211yescharacteristic
108#19127587C2211yescharacteristic
109#19127585C2211yescharacteristic
110#19127583C2211yescharacteristic
111#19127582C2211yescharacteristic
112#19127581C2211yescharacteristic
113#19127579C2211yescharacteristic
114#19127579C2211yescharacteristic
115#19127576C2211yescharacteristic
116#19127575C2211yescharacteristic
117#19127575C2211yescharacteristic
118#19127575C2211yescharacteristic
119#19127575C2211yescharacteristic
120#19127574C2211yescharacteristic
121#19127574C2211yescharacteristic
122#19127574C2211yescharacteristic
123#19127572C2211yescharacteristic
124#19127572C2211yescharacteristic
125#19127570C2211yescharacteristic
126#19127570C2211yescharacteristic
127#19127570C2211yescharacteristic
128#19127565C2211yescharacteristic
129#19127565C2211yescharacteristic
130#19127561C2211yescharacteristic
131#19127560C2211yescharacteristic
132#19127559C2211yescharacteristic
133#19127558C2211yescharacteristic
134C4⋊C4×Dic83C2211yescharacteristic
135C4⋊C4×Dic83C2211yescharacteristic
136C4⋊C4×Dic83C2211yescharacteristic
137C4×Dic83⋊C4C2211yescharacteristic
138C4×Dic83⋊C4C2211yescharacteristic
139C4×Dic83⋊C4C2211yescharacteristic
140C4×Dic83⋊C4C2211yescharacteristic
141C4×Dic83⋊C4C2211yescharacteristic
142#19127552C2211yescharacteristic
143#19127552C2211yescharacteristic
144#19127552C2211yescharacteristic
145#19127552C2211yescharacteristic
146#19127552C2211yescharacteristic
147#19127552C2211yescharacteristic
148#19127552C2211yescharacteristic
149#19127552C2211yescharacteristic
150#19127552C2211yescharacteristic
151C22⋊C4×Dic83C2211yescharacteristic
152C22⋊C4×Dic83C2211yescharacteristic
153C22⋊C4×Dic83C2211yescharacteristic
154C4×(C2×D83)⋊C4C2211yescharacteristic
155C4×(C2×D83)⋊C4C2211yescharacteristic
156C4×(C2×D83)⋊C4C2211yescharacteristic
157C4×C22⋊Dic83C2211yescharacteristic
158C4×C22⋊Dic83C2211yescharacteristic
159C4×C22⋊Dic83C2211yescharacteristic
160#19127548C2211yescharacteristic
161#19127548C2211yescharacteristic
162#19127548C2211yescharacteristic
163#19127548C2211yescharacteristic
164#19127548C2211yescharacteristic
165#19127546C2211yescharacteristic
166#19127546C2211yescharacteristic
167C2×C83⋊#95C2211yescharacteristic
168#95×D83C2211yescharacteristic
169#95×D83C2211yescharacteristic
170C42×Dic83C2211yescharacteristic
171C42×Dic83C2211yescharacteristic
172C42×Dic83C2211yescharacteristic
173C2×#123×C83C2211yescharacteristic
174C2×C4×D4×C83C2211yescharacteristic
175C2×#117×C83C2211yescharacteristic
176#389×C83C2211yescharacteristic
177#388×C83C2211yescharacteristic
178#388×C83C2211yescharacteristic
179#387×C83C2211yescharacteristic
180#387×C83C2211yescharacteristic
181#386×C83C2211yescharacteristic
182#385×C83C2211yescharacteristic
183#385×C83C2211yescharacteristic
184C4×C4⋊C4×C83C2211yescharacteristic
185C4×C22⋊C4×C83C2211yescharacteristic
186C4×C22⋊C4×C83C2211yescharacteristic
187C2×#95×C83C2211yescharacteristic
188C22×Dic166C2311yescharacteristic
189C22×Dic166C2311yescharacteristic
190C22×D332C2311yescharacteristic
191C22×C22⋊D83C2311yescharacteristic
192C22×C22⋊D83C2311yescharacteristic
193C22×C22⋊D83C2311yescharacteristic
194C22×C22⋊D83C2311yescharacteristic
195C23×Dic83C2311yescharacteristic
196C23×Dic83C2311yescharacteristic
197C22×C4×D83C2311yescharacteristic
198C22×C4×D83C2311yescharacteristic
199C22×C4×D83C2311yescharacteristic
200C22×C4×D83C2311yescharacteristic
201C22×C4×D83C2311yescharacteristic
202C22×C4×D83C2311yescharacteristic
203#14581788C2×C418yes—
204#14581778C2×C418yescomplemented
205#14581778C2×C418yescomplemented
206#14581778C2×C418yescomplemented
207#14581778C2×C418yescomplemented
208#14581777C2×C418yescomplemented
209#14581777C2×C418yescomplemented
210#14581773C2×C418yescomplemented
211C4×Dic166—24no—
212C4×Dic166—42no—
213#14581757—24no—
214#14581757—42no—
215#14581757C2×C418yescomplemented
216#14581757C2×C418yescomplemented
217C4×D332—42no—
218C4×C22⋊D83—24no—
219C4×C22⋊D83—24no—
220C4×C22⋊D83—24no—
221C4×C22⋊D83—42no—
222C4×C22⋊D83—42no—
223C4×C22⋊D83—42no—
224C4×C22⋊D83C2×C418yescomplemented
225C4×C22⋊D83C2×C418yescomplemented
226(C22⋊D83)⋊C4—24no—
227(C22⋊D83)⋊C4—42no—
228(C22⋊D83)⋊C4C2×C418yescomplemented
229(C22⋊D83)⋊C4C2×C418yescomplemented
230#14581750—42no—
231#14581749—42no—
232#14581748—42no—
233C2×C4⋊Dic83C2311yescharacteristic
234C2×C4⋊Dic83C2311yescharacteristic
235C2×C4⋊Dic83C2311yescharacteristic
236C2×C4⋊Dic83C2311yescharacteristic
237C2×C4⋊Dic83C2311yescharacteristic
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×Dic83⋊C4C2311yescharacteristic
255C2×Dic83⋊C4C2311yescharacteristic
256C2×Dic83⋊C4C2311yescharacteristic
257C2×Dic83⋊C4C2311yescharacteristic
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)⋊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
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×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
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
310C2×C4×Dic83C2311yescharacteristic
311C2×C4×Dic83C2311yescharacteristic
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
339C23×C4×C83C2311yescharacteristic
340C23×C4×C83C2311yescharacteristic
341C23×C4×C83C2311yescharacteristic
342C23×C4×C83C2311yescharacteristic
343#123×C83C2×C418yescomplemented
344C4×D4×C83—42no—
345#117×C83—42no—
346C2×C4⋊C4×C83C2311yescharacteristic
347C2×C4⋊C4×C83C2311yescharacteristic
348C2×C4⋊C4×C83C2311yescharacteristic
349C2×C4⋊C4×C83C2311yescharacteristic
350C2×C4⋊C4×C83C2311yescharacteristic
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×C42×C83C2311yescharacteristic
362C2×C42×C83C2311yescharacteristic
363C2×C42×C83C2311yescharacteristic
364C2×C42×C83C2311yescharacteristic
365C2×C42×C83C2311yescharacteristic
366#95×C83C2311yescharacteristic
367#95×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×D83C2411yescharacteristic
377C23×D83C2411yescharacteristic
378C2×Dic166—22no—
379C2×Dic166—22no—
380C2×Dic166—22no—
381C2×Dic166—22no—
382C2×Dic166C22×C414yes—
383C2×Dic166C22×C414yes—
384C2×D332—41no—
385C2×D332—41no—
386C2×D332C22×C414yes—
387C2×C22⋊D83—22no—
388C2×C22⋊D83—22no—
389C2×C22⋊D83—22no—
390C2×C22⋊D83—22no—
391C2×C22⋊D83—22no—
392C2×C22⋊D83—22no—
393C2×C22⋊D83—22no—
394C2×C22⋊D83—22no—
395C2×C22⋊D83C22×C414yes—
396C2×C22⋊D83C22×C414yes—
397C2×C22⋊D83C22×C414yes—
398C2×C22⋊D83C22×C414yes—
399C22×Dic83—22no—
400C22×Dic83—41no—
401C22×Dic83—41no—
402C22×Dic83—41no—
403C22×Dic83—41no—
404C22×Dic83C22×C414yes—
405C22×Dic83C2411yescharacteristic
406C22×Dic83C2411yescharacteristic
407C22×Dic83C2411yescharacteristic
408C22×Dic83C2411yescharacteristic
409C22×Dic83C2411yescharacteristic
410C22×Dic83C2411yescharacteristic
411C22×Dic83C2411yescharacteristic
412C22×Dic83C2411yescharacteristic
413C22×Dic83C2411yescharacteristic
414C22×Dic83C2411yescharacteristic
415C22×Dic83C2411yescharacteristic
416C22×Dic83C2411yescharacteristic
417C22×Dic83C2411yescharacteristic
418C22×Dic83C2411yescharacteristic
419C2×C4×D83—22no—
420C2×C4×D83—22no—
421C2×C4×D83—22no—
422C2×C4×D83—22no—
423C2×C4×D83—41no—
424C2×C4×D83—41no—
425C2×C4×D83—41no—
426C2×C4×D83—41no—
427C2×C4×D83—41no—
428C2×C4×D83—41no—
429C2×C4×D83—41no—
430C2×C4×D83—41no—
431C2×C4×D83—41no—
432C2×C4×D83—41no—
433C2×C4×D83—41no—
434C2×C4×D83—41no—
435C2×C4×D83C22×C414yes—
436C2×C4×D83C22×C414yes—
437C4⋊Dic83—22no—
438C4⋊Dic83—41no—
439C4⋊Dic83—41no—
440C4⋊Dic83—41no—
441C4⋊Dic83—41no—
442Dic83⋊C4—22no—
443Dic83⋊C4—22no—
444Dic83⋊C4—22no—
445Dic83⋊C4—22no—
446Dic83⋊C4—22no—
447Dic83⋊C4—22no—
448Dic83⋊C4—22no—
449Dic83⋊C4—22no—
450Dic83⋊C4—22no—
451Dic83⋊C4—22no—
452Dic83⋊C4—41no—
453Dic83⋊C4—41no—
454Dic83⋊C4—41no—
455Dic83⋊C4—41no—
456Dic83⋊C4—41no—
457Dic83⋊C4C22×C414yes—
458Dic83⋊C4C22×C414yes—
459Dic83⋊C4C22×C414yes—
460Dic83⋊C4C22×C414yes—
461Dic83⋊C4#4114yes—
462C22⋊Dic83—22no—
463C22⋊Dic83—22no—
464C22⋊Dic83—22no—
465C22⋊Dic83—41no—
466C22⋊Dic83—41no—
467C22⋊Dic83—41no—
468C22⋊Dic83—41no—
469C22⋊Dic83C22×C414yes—
470C22⋊Dic83C22×C414yes—
471C22⋊Dic83C22×C414yes—
472(C2×D83)⋊C4—22no—
473(C2×D83)⋊C4—22no—
474(C2×D83)⋊C4—22no—
475(C2×D83)⋊C4—22no—
476(C2×D83)⋊C4—22no—
477(C2×D83)⋊C4—22no—
478(C2×D83)⋊C4—41no—
479(C2×D83)⋊C4—41no—
480(C2×D83)⋊C4—41no—
481(C2×D83)⋊C4—41no—
482(C2×D83)⋊C4—41no—
483(C2×D83)⋊C4—41no—
484(C2×D83)⋊C4C22×C414yes—
485(C2×D83)⋊C4C22×C414yes—
486(C2×D83)⋊C4C22×C414yes—
487(C2×D83)⋊C4C22×C414yes—
488(C2×D83)⋊C4C22×C414yes—
489(C2×D83)⋊C4C22×C414yes—
490C4×Dic83—22no—
491C4×Dic83—22no—
492C4×Dic83—22no—
493C4×Dic83—22no—
494C4×Dic83—22no—
495C4×Dic83—22no—
496C4×Dic83—22no—
497C4×Dic83—22no—
498C4×Dic83—22no—
499C4×Dic83—22no—
500C4×Dic83—22no—
501C4×Dic83—41no—
502C4×Dic83—41no—
503C4×Dic83—41no—
504C4×Dic83—41no—
505C4×Dic83—41no—
506C4×Dic83—41no—
507C4×Dic83—41no—
508C4×Dic83—41no—
509C4×Dic83—41no—
510C4×Dic83C22×C414yes—
511C4×Dic83C22×C414yes—
512C4×Dic83C22×C414yes—
513C4×Dic83C22×C414yes—
514C4×Dic83C22×C414yes—
515C4×Dic83#4114yes—
516C24×C83C2411yescharacteristic
517C24×C83C2411yescharacteristic
518C2×D4×C83—41no—
519C2×D4×C83—41no—
520C2×D4×C83C22×C414yes—
521C22×C4×C83—22no—
522C22×C4×C83—22no—
523C22×C4×C83—22no—
524C22×C4×C83—41no—
525C22×C4×C83—41no—
526C22×C4×C83—41no—
527C22×C4×C83—41no—
528C22×C4×C83—41no—
529C22×C4×C83—41no—
530C22×C4×C83—41no—
531C22×C4×C83—41no—
532C22×C4×C83C22×C414yes—
533C22×C4×C83C2411yescharacteristic
534C22×C4×C83C2411yescharacteristic
535C22×C4×C83C2411yescharacteristic
536C22×C4×C83C2411yescharacteristic
537C22×C4×C83C2411yescharacteristic
538C22×C4×C83C2411yescharacteristic
539C22×C4×C83C2411yescharacteristic
540C22×C4×C83C2411yescharacteristic
541C22×C4×C83C2411yescharacteristic
542C22×C4×C83C2411yescharacteristic
543C22×C4×C83C2411yescharacteristic
544C22×C4×C83C2411yescharacteristic
545C22×C4×C83C2411yescharacteristic
546C4⋊C4×C83—22no—
547C4⋊C4×C83—22no—
548C4⋊C4×C83—41no—
549C4⋊C4×C83—41no—
550C4⋊C4×C83—41no—
551C4⋊C4×C83C22×C414yes—
552C4⋊C4×C83C22×C414yes—
553C22⋊C4×C83—22no—
554C22⋊C4×C83—22no—
555C22⋊C4×C83—22no—
556C22⋊C4×C83—41no—
557C22⋊C4×C83—41no—
558C22⋊C4×C83C22×C414yes—
559C22⋊C4×C83C22×C414yes—
560C22⋊C4×C83C22×C414yes—
561C42×C83—22no—
562C42×C83—22no—
563C42×C83—22no—
564C42×C83—41no—
565C42×C83—41no—
566C23×C83—21no—
567C23×C83—21no—
568C23×C83—21no—
569C23×C83—21no—
570C23×C83—21no—
571C23×C83—21no—
572C23×C83—21no—
573C23×C83—21no—
574C23×C83—21no—
575C23×C83—21no—
576C23×C83—21no—
577C23×C83—21no—
578C23×C83C23×C412yes—
579C23×C83C23×C412yes—
580C23×C83C2511yescharacteristic
581C22×D83—21no—
582C22×D83—21no—
583C22×D83—21no—
584C22×D83—21no—
585C22×D83—21no—
586C22×D83—21no—
587C22×D83—21no—
588C22×D83—21no—
589C22×D83—21no—
590C22×D83—21no—
591C22×D83—21no—
592C22×D83—21no—
593C22×D83C23×C412yes—
594C22×D83C23×C412yes—
595D4×C83—44no—
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—21no—
624C2×C4×C83—21no—
625C2×C4×C83—21no—
626C2×C4×C83—21no—
627C2×C4×C83—44no—
628C2×C4×C83—82no—
629C2×C4×C83—82no—
630C2×C4×C83—82no—
631C2×C4×C83C23×C412yes—
632C2×C4×C83C23×C412yes—
633C2×C4×C83C23×C412yes—
634C2×C4×C83C23×C412yes—
635C2×C4×C83C23×C412yes—
636C2×C4×C83C2×#4112yes—
637C2×C4×C83C2×#4112yes—
638C2×C4×C83H(5,𝔽2)12yes—
639C22⋊D83—28no—
640C22⋊D83—28no—
641C22⋊D83—28no—
642C22⋊D83—28no—
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—21no—
670C2×Dic83—21no—
671C2×Dic83—21no—
672C2×Dic83—21no—
673C2×Dic83—44no—
674C2×Dic83—82no—
675C2×Dic83C23×C412yes—
676C2×Dic83C23×C412yes—
677C2×Dic83C23×C412yes—
678C2×Dic83C23×C412yes—
679C2×Dic83C23×C412yes—
680C2×Dic83C23×C412yes—
681C2×Dic83C2×#4112yes—
682C2×Dic83C2×#4112yes—
683C2×Dic83C2×#4112yes—
684C2×Dic83C2×#4112yes—
685C2×Dic83H(5,𝔽2)12yes—
686C2×Dic832−1+412yes—
687D332—44no—
688C4×D83—44no—
689C4×D83—44no—
690C4×D83—82no—
691C4×D83—82no—
692C4×D83—82no—
693C4×D83—82no—
694Dic166—28no—
695Dic166—28no—
696C22×C83—22no—
697C22×C83—22no—
698C22×C83—22no—
699C22×C83—22no—
700C22×C83—22no—
701C22×C83—22no—
702C22×C83—41no—
703C22×C83—41no—
704C22×C83—41no—
705C22×C83—41no—
706C22×C83—41no—
707C22×C83—41no—
708C22×C83—41no—
709C22×C83—41no—
710C22×C83C24×C411yescharacteristic
711C22×C83C22×#4111yescharacteristic
712C22×C83C22×#4111yescharacteristic
713C22×C83C2×H(5,𝔽2)11yescharacteristic
714C22×C83C2×H(5,𝔽2)11yescharacteristic
715C22×C83C2×2−1+411yescharacteristic
716C22×C83#58511yescharacteristic
717C2×D83—22no—
718C2×D83—22no—
719C2×D83—22no—
720C2×D83—22no—
721C2×D83—22no—
722C2×D83—22no—
723C2×D83—41no—
724C2×D83—41no—
725C2×D83—41no—
726C2×D83—41no—
727C2×D83—41no—
728C2×D83—41no—
729C2×D83—41no—
730C2×D83—41no—
731C4×C83—22no—
732C4×C83—22no—
733C4×C83—22no—
734C4×C83—22no—
735C4×C83—22no—
736C4×C83—22no—
737C4×C83—22no—
738C4×C83—22no—
739C4×C83—41no—
740C4×C83—41no—
741C4×C83—41no—
742C4×C83—41no—
743C4×C83—41no—
744Dic83—22no—
745Dic83—22no—
746Dic83—22no—
747Dic83—22no—
748Dic83—22no—
749Dic83—22no—
750Dic83—41no—
751Dic83—41no—
752Dic83—41no—
753Dic83—41no—
754Dic83—41no—
755Dic83—41no—
756Dic83C4×#4114yes—
757Dic83#52014yes—
758#34331—831nomaximal, Sylow
759C2×C83—42no—
760C2×C83—42no—
761C2×C83C2×C4×#4111yescharacteristic
762C2×C83C2×#52011yescharacteristic
763C2×C83C4×H(5,𝔽2)11yescharacteristic
764C2×C83#350711yescharacteristic
765C2×C83#350811yescharacteristic
766C2×C83#351411yescharacteristic
767C2×C83#352211yescharacteristic
768D83—42no—
769D83—42no—
770C2×#559—831no—
771#2367—831no—
772#2367—831no—
773#2367—831no—
774#2367—831no—
775#2366—831no—
776#2359—831no—
777#2359—831no—
778#2359—831no—
779#2359D8311yescharacteristic, complemented
780#2355—831no—
781#2354—831no—
782#2354—831no—
783Q8×C4⋊C4—831no—
784#2349—831no—
785#2349—831no—
786#2335—831no—
787#2335—831no—
788#2335—831no—
789#2335—831no—
790#2326—831no—
791#2326—831no—
792C4×#127—831no—
793C4×#124—831no—
794C4×#124—831no—
795#2295—831no—
796#2293—831no—
797#2293—831no—
798#2275—831no—
799#2275—831no—
800C42×Q8—831no—
801C83#3433111yescharacteristic, complemented, Sylow
802#559—8316no—
803C2×#127—831no—
804C2×#124—831no—
805C2×#124—831no—
806C2×#124—831no—
807C2×#124—831no—
808C2×#123—831no—
809C2×#123—831no—
810C2×#123—831no—
811C2×#123C2×D8311yescharacteristic
812C2×C4×Q8—831no—
813C2×C4×Q8—831no—
814C2×C4×Q8—831no—
815C2×C4×Q8—831no—
816C2×C4×Q8—831no—
817C2×C4×Q8—831no—
818C2×C4×D4—831no—
819C2×C4×D4—831no—
820C2×C4×D4—831no—
821C2×C4×D4—831no—
822C2×C4×D4—831no—
823C2×C4×D4—831no—
824C2×C4×D4—831no—
825C2×C4×D4—831no—
826C2×C4×D4—831no—
827C2×C4×D4—831no—
828C2×C4×D4—831no—
829C2×C4×D4—831no—
830C2×C4×D4—831no—
831C2×C4×D4C2×D8311yescharacteristic
832C2×#117—831no—
833C2×#117—831no—
834C2×#117—831no—
835C2×#117C2×D8311yescharacteristic
836#391—831no—
837#391—831no—
838#391—831no—
839#391—831no—
840#390—831no—
841#390—831no—
842#390—831no—
843#390—831no—
844#390—831no—
845#390—831no—
846#390—831no—
847#390—831no—
848#390—831no—
849#390—831no—
850#389—831no—
851#389—831no—
852#389—831no—
853#389—831no—
854#389—831no—
855#389—831no—
856#389—831no—
857#389C2×D8311yescharacteristic
858#388—831no—
859#388—831no—
860#388—831no—
861#388—831no—
862#388—831no—
863#388—831no—
864#388—831no—
865#388—831no—
866#388—831no—
867#388—831no—
868#388—831no—
869#388—831no—
870#388—831no—
871#388—831no—
872#388—831no—
873#388—831no—
874#388—831no—
875#388—831no—
876#388—831no—
877#388—831no—
878#388—831no—
879#388—831no—
880#388C2×D8311yescharacteristic
881#388C2×D8311yescharacteristic
882#387—831no—
883#387—831no—
884#387—831no—
885#387—831no—
886#387—831no—
887#387—831no—
888#387C2×D8311yescharacteristic
889#387C2×D8311yescharacteristic
890#386—831no—
891#386—831no—
892#386—831no—
893#386C2×D8311yescharacteristic
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#385C2×D8311yescharacteristic
905#385C2×D8311yescharacteristic
906#384—831no—
907#384—831no—
908#384—831no—
909#382—831no—
910#382—831no—
911#380—831no—
912#380—831no—
913#380—831no—
914#380—831no—
915C4×C4⋊C4—831no—
916C4×C4⋊C4—831no—
917C4×C4⋊C4—831no—
918C4×C4⋊C4—831no—
919C4×C4⋊C4—831no—
920C4×C4⋊C4—831no—
921C4×C4⋊C4—831no—
922C4×C4⋊C4—831no—
923C4×C4⋊C4—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
933C4×C22⋊C4—831no—
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⋊C4—831no—
945C4×C22⋊C4—831no—
946C4×C22⋊C4—831no—
947C4×C22⋊C4C2×D8311yescharacteristic
948C4×C22⋊C4C2×D8311yescharacteristic
949#376—831no—
950#376—831no—
951C2×#95—831no—
952C2×#95—831no—
953C2×#95—831no—
954C2×#95C2×D8311yescharacteristic
955C43—831no—
956C43—831no—
957C43—831no—
958C22×Q8—831no—
959C22×Q8—831no—
960C22×D4—831no—
961C22×D4—831no—
962C22×D4—831no—
963C22×D4—831no—
964C22×D4—831no—
965C22×D4C22×D8311yescharacteristic
966C23×C4—831no—
967C23×C4—831no—
968C23×C4—831no—
969C23×C4—831no—
970C23×C4—831no—
971C23×C4—831no—
972C23×C4—831no—
973C23×C4—831no—
974C23×C4C22×D8311yescharacteristic
975C23×C4C22×D8311yescharacteristic
976C23×C4C22×D8311yescharacteristic
977C23×C4C22×D8311yescharacteristic
978#127—838no—
979#124—838no—
980#124—838no—
981#124—838no—
982#124—838no—
983#123—838no—
984#123—838no—
985#123—838no—
986#123C4×D8318yescomplemented
987C4×Q8—3322no—
988C4×Q8—3322no—
989C4×Q8—838no—
990C4×Q8—838no—
991C4×Q8—1664no—
992C4×Q8—1664no—
993C4×D4—42no—
994C4×D4—3322no—
995C4×D4—3322no—
996C4×D4—3322no—
997C4×D4—3322no—
998C4×D4—3322no—
999C4×D4—838no—
1000C4×D4—838no—
1001C4×D4—838no—
1002C4×D4—838no—
1003C4×D4—1664no—
1004C4×D4—1664no—
1005C4×D4—1664no—
1006C4×D4—1664no—
1007#117—42no—
1008#117—3322no—
1009#117—3322no—
1010#117—3322no—
1011C2×C4⋊C4—831no—
1012C2×C4⋊C4—831no—
1013C2×C4⋊C4—831no—
1014C2×C4⋊C4—831no—
1015C2×C4⋊C4—831no—
1016C2×C4⋊C4—831no—
1017C2×C4⋊C4—831no—
1018C2×C4⋊C4—831no—
1019C2×C4⋊C4—831no—
1020C2×C4⋊C4—831no—
1021C2×C4⋊C4—831no—
1022C2×C4⋊C4—831no—
1023C2×C4⋊C4—831no—
1024C2×C4⋊C4—831no—
1025C2×C4⋊C4—831no—
1026C2×C4⋊C4—831no—
1027C2×C4⋊C4—831no—
1028C2×C4⋊C4—831no—
1029C2×C4⋊C4—831no—
1030C2×C4⋊C4—831no—
1031C2×C4⋊C4—831no—
1032C2×C4⋊C4—831no—
1033C2×C4⋊C4—831no—
1034C2×C4⋊C4—831no—
1035C2×C4⋊C4—831no—
1036C2×C4⋊C4C22×D8311yescharacteristic
1037C2×C4⋊C4C22×D8311yescharacteristic
1038C2×C4⋊C4C22×D8311yescharacteristic
1039C2×C4⋊C4C22×D8311yescharacteristic
1040C2×C4⋊C4C22×D8311yescharacteristic
1041C2×C4⋊C4C22×D8311yescharacteristic
1042C2×C4⋊C4C22×D8311yescharacteristic
1043C2×C22⋊C4—831no—
1044C2×C22⋊C4—831no—
1045C2×C22⋊C4—831no—
1046C2×C22⋊C4—831no—
1047C2×C22⋊C4—831no—
1048C2×C22⋊C4—831no—
1049C2×C22⋊C4—831no—
1050C2×C22⋊C4—831no—
1051C2×C22⋊C4—831no—
1052C2×C22⋊C4—831no—
1053C2×C22⋊C4—831no—
1054C2×C22⋊C4—831no—
1055C2×C22⋊C4—831no—
1056C2×C22⋊C4—831no—
1057C2×C22⋊C4—831no—
1058C2×C22⋊C4—831no—
1059C2×C22⋊C4—831no—
1060C2×C22⋊C4—831no—
1061C2×C22⋊C4—831no—
1062C2×C22⋊C4—831no—
1063C2×C22⋊C4—831no—
1064C2×C22⋊C4—831no—
1065C2×C22⋊C4—831no—
1066C2×C22⋊C4—831no—
1067C2×C22⋊C4—831no—
1068C2×C22⋊C4—831no—
1069C2×C22⋊C4—831no—
1070C2×C22⋊C4—831no—
1071C2×C22⋊C4C22×D8311yescharacteristic
1072C2×C22⋊C4C22×D8311yescharacteristic
1073C2×C22⋊C4C22×D8311yescharacteristic
1074C2×C22⋊C4C22×D8311yescharacteristic
1075C2×C22⋊C4C22×D8311yescharacteristic
1076C2×C22⋊C4C22×D8311yescharacteristic
1077C2×C22⋊C4C22×D8311yescharacteristic
1078C2×C22⋊C4C22×D8311yescharacteristic
1079C2×C42—831no—
1080C2×C42—831no—
1081C2×C42—831no—
1082C2×C42—831no—
1083C2×C42—831no—
1084C2×C42—831no—
1085C2×C42—831no—
1086C2×C42—831no—
1087C2×C42—831no—
1088C2×C42—831no—
1089C2×C42—831no—
1090C2×C42—831no—
1091C2×C42—831no—
1092C2×C42—831no—
1093C2×C42—831no—
1094C2×C42—831no—
1095C2×C42—831no—
1096C2×C42—831no—
1097C2×C42—831no—
1098C2×C42—831no—
1099C2×C42—831no—
1100C2×C42—831no—
1101C2×C42—831no—
1102C2×C42—831no—
1103C2×C42—831no—
1104C2×C42—831no—
1105C2×C42C22×D8311yescharacteristic
1106C2×C42C22×D8311yescharacteristic
1107C2×C42C22×D8311yescharacteristic
1108C2×C42C22×D8311yescharacteristic
1109C2×C42C22×D8311yescharacteristic
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#95—831no—
1124#95—831no—
1125#95—831no—
1126#95—831no—
1127#95—831no—
1128#95—831no—
1129#95—831no—
1130#95—831no—
1131#95—831no—
1132#95—831no—
1133#95—831no—
1134#95—831no—
1135#95—831no—
1136#95C22×D8311yescharacteristic
1137#95C22×D8311yescharacteristic
1138#95C22×D8311yescharacteristic
1139#95C22×D8311yescharacteristic
1140#95C22×D8311yescharacteristic
1141#95C22×D8311yescharacteristic
1142#95C22×D8311yescharacteristic
1143#95C22×D8311yescharacteristic
1144#95C22×D8311yescharacteristic
1145#95C22×D8311yescharacteristic
1146C24—831no—
1147C24—831no—
1148C24C23×D8311yescharacteristic
1149C24C23×D8311yescharacteristic
1150C2×Q8—834no—
1151C2×Q8—834no—
1152C2×Q8—1662no—
1153C2×Q8—1662no—
1154C2×Q8—1662no—
1155C2×Q8—1662no—
1156C2×D4—41no—
1157C2×D4—41no—
1158C2×D4—3321no—
1159C2×D4—3321no—
1160C2×D4—834no—
1161C2×D4—834no—
1162C2×D4—834no—
1163C2×D4—834no—
1164C2×D4—834no—
1165C2×D4—1662no—
1166C2×D4—1662no—
1167C2×D4—1662no—
1168C2×D4—1662no—
1169C2×D4—1662no—
1170C2×D4—1662no—
1171C2×D4—1662no—
1172C2×D4—1662no—
1173C2×D4C2×C4×D8314yes—
1174C22×C4—22no—
1175C22×C4—22no—
1176C22×C4—22no—
1177C22×C4—41no—
1178C22×C4—41no—
1179C22×C4—41no—
1180C22×C4—41no—
1181C22×C4—41no—
1182C22×C4—41no—
1183C22×C4—41no—
1184C22×C4—41no—
1185C22×C4—3321no—
1186C22×C4—3321no—
1187C22×C4—3321no—
1188C22×C4—3321no—
1189C22×C4—3321no—
1190C22×C4—3321no—
1191C22×C4—3321no—
1192C22×C4—3321no—
1193C22×C4—3321no—
1194C22×C4—3321no—
1195C22×C4—3321no—
1196C22×C4—3321no—
1197C22×C4—3321no—
1198C22×C4—3321no—
1199C22×C4—3321no—
1200C22×C4—3321no—
1201C22×C4—834no—
1202C22×C4—834no—
1203C22×C4—834no—
1204C22×C4—831no—
1205C22×C4—831no—
1206C22×C4—831no—
1207C22×C4—831no—
1208C22×C4—831no—
1209C22×C4—831no—
1210C22×C4—831no—
1211C22×C4—831no—
1212C22×C4—831no—
1213C22×C4—831no—
1214C22×C4—831no—
1215C22×C4—831no—
1216C22×C4—831no—
1217C22×C4—831no—
1218C22×C4—1662no—
1219C22×C4—1662no—
1220C22×C4—1662no—
1221C22×C4—1662no—
1222C22×C4—1662no—
1223C22×C4C2×C4×D8314yes—
1224C22×C4C23×D8311yescharacteristic
1225C22×C4C23×D8311yescharacteristic
1226C22×C4C23×D8311yescharacteristic
1227C22×C4C23×D8311yescharacteristic
1228C22×C4C23×D8311yescharacteristic
1229C22×C4C23×D8311yescharacteristic
1230C22×C4C23×D8311yescharacteristic
1231C22×C4C23×D8311yescharacteristic
1232C22×C4C23×D8311yescharacteristic
1233C22×C4C23×D8311yescharacteristic
1234C22×C4C23×D8311yescharacteristic
1235C22×C4C23×D8311yescharacteristic
1236C22×C4C23×D8311yescharacteristic
1237C4⋊C4—22no—
1238C4⋊C4—22no—
1239C4⋊C4—41no—
1240C4⋊C4—41no—
1241C4⋊C4—41no—
1242C4⋊C4—3321no—
1243C4⋊C4—3321no—
1244C4⋊C4—3321no—
1245C4⋊C4—3321no—
1246C4⋊C4—3321no—
1247C4⋊C4—3321no—
1248C4⋊C4—3321no—
1249C4⋊C4—3321no—
1250C4⋊C4—3321no—
1251C4⋊C4—834no—
1252C4⋊C4—834no—
1253C4⋊C4—834no—
1254C4⋊C4—834no—
1255C4⋊C4—834no—
1256C4⋊C4—1662no—
1257C4⋊C4—1662no—
1258C4⋊C4—1662no—
1259C4⋊C4—1662no—
1260C4⋊C4—1662no—
1261C4⋊C4—1662no—
1262C4⋊C4—1662no—
1263C4⋊C4—1662no—
1264C4⋊C4—1662no—
1265C4⋊C4—1662no—
1266C4⋊C4—1662no—
1267C4⋊C4C2×C4×D8314yes—
1268C4⋊C4C2×C4×D8314yes—
1269C22⋊C4—22no—
1270C22⋊C4—22no—
1271C22⋊C4—22no—
1272C22⋊C4—41no—
1273C22⋊C4—41no—
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—834no—
1285C22⋊C4—834no—
1286C22⋊C4—834no—
1287C22⋊C4—834no—
1288C22⋊C4—834no—
1289C22⋊C4—834no—
1290C22⋊C4—834no—
1291C22⋊C4—834no—
1292C22⋊C4—834no—
1293C22⋊C4—1662no—
1294C22⋊C4—1662no—
1295C22⋊C4—1662no—
1296C22⋊C4—1662no—
1297C22⋊C4—1662no—
1298C22⋊C4—1662no—
1299C22⋊C4—1662no—
1300C22⋊C4—1662no—
1301C22⋊C4—1662no—
1302C22⋊C4C2×C4×D8314yes—
1303C22⋊C4C2×C4×D8314yes—
1304C22⋊C4C2×C4×D8314yes—
1305C42—22no—
1306C42—22no—
1307C42—22no—
1308C42—41no—
1309C42—41no—
1310C42—3321no—
1311C42—3321no—
1312C42—3321no—
1313C42—3321no—
1314C42—3321no—
1315C42—3321no—
1316C42—3321no—
1317C42—3321no—
1318C42—3321no—
1319C42—834no—
1320C42—834no—
1321C42—834no—
1322C42—834no—
1323C42—834no—
1324C42—834no—
1325C42—1662no—
1326C42—1662no—
1327C42—1662no—
1328C42—1662no—
1329C42—1662no—
1330C42—1662no—
1331C42—1662no—
1332C42—1662no—
1333C42—1662no—
1334C42—1662no—
1335C42—1662no—
1336C23—21no—
1337C23—21no—
1338C23—21no—
1339C23—21no—
1340C23—21no—
1341C23—21no—
1342C23—21no—
1343C23—21no—
1344C23—21no—
1345C23—21no—
1346C23—21no—
1347C23—21no—
1348C23—832no—
1349C23—832no—
1350C23—1661no—
1351C23—1661no—
1352C23—1661no—
1353C23—1661no—
1354C23—1661no—
1355C23—1661no—
1356C23—1661no—
1357C23—1661no—
1358C23—1661no—
1359C23—1661no—
1360C23—1661no—
1361C23—1661no—
1362C23C22×C4×D8312yes—
1363C23C22×C4×D8312yes—
1364C23C24×D8311yescharacteristic
1365Q8—1668no—
1366Q8—1668no—
1367D4—44no—
1368D4—3324no—
1369D4—1668no—
1370D4—1668no—
1371D4—1668no—
1372D4—1668no—
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—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—44no—
1405C2×C4—82no—
1406C2×C4—82no—
1407C2×C4—82no—
1408C2×C4—3324no—
1409C2×C4—3324no—
1410C2×C4—3324no—
1411C2×C4—832no—
1412C2×C4—832no—
1413C2×C4—832no—
1414C2×C4—832no—
1415C2×C4—832no—
1416C2×C4—832no—
1417C2×C4—832no—
1418C2×C4—832no—
1419C2×C4—832no—
1420C2×C4—832no—
1421C2×C4—832no—
1422C2×C4—832no—
1423C2×C4—6642no—
1424C2×C4—6642no—
1425C2×C4—6642no—
1426C2×C4—6642no—
1427C2×C4—6642no—
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×C4—1661no—
1442C2×C4—1661no—
1443C2×C4—1661no—
1444C2×C4—1661no—
1445C2×C4—1661no—
1446C2×C4—1661no—
1447C2×C4—1661no—
1448C2×C4—1661no—
1449C2×C4—1661no—
1450C2×C4—1661no—
1451C2×C4—1661no—
1452C2×C4—1661no—
1453C2×C4—1661no—
1454C2×C4—1661no—
1455C2×C4—1661no—
1456C2×C4—1661no—
1457C2×C4—1661no—
1458C2×C4C22×C4×D8312yes—
1459C2×C4C22×C4×D8312yes—
1460C2×C4C22×C4×D8312yes—
1461C2×C4C22×C4×D8312yes—
1462C2×C4C22×C4×D8312yes—
1463C2×C4#41×D8312yes—
1464C2×C4#41×D8312yes—
1465C2×C4#1458183712yes—
1466C22—22no—
1467C22—22no—
1468C22—22no—
1469C22—22no—
1470C22—22no—
1471C22—22no—
1472C22—41no—
1473C22—41no—
1474C22—41no—
1475C22—41no—
1476C22—41no—
1477C22—41no—
1478C22—41no—
1479C22—41no—
1480C22—3321no—
1481C22—3321no—
1482C22—3321no—
1483C22—3321no—
1484C22—3321no—
1485C22—3321no—
1486C22—3321no—
1487C22—3321no—
1488C22—1662no—
1489C22—1662no—
1490C22—1662no—
1491C22—1662no—
1492C22—1662no—
1493C22—1662no—
1494C22C23×C4×D8311yescharacteristic
1495C22C2×#41×D8311yescharacteristic
1496C22C2×#41×D8311yescharacteristic
1497C22H(5,𝔽2)×D8311yescharacteristic
1498C22C2×#1458183711yescharacteristic
1499C222−1+4×D8311yescharacteristic
1500C22#1912853711yescharacteristic
1501C4—22no—
1502C4—22no—
1503C4—22no—
1504C4—22no—
1505C4—22no—
1506C4—22no—
1507C4—22no—
1508C4—22no—
1509C4—41no—
1510C4—41no—
1511C4—41no—
1512C4—41no—
1513C4—41no—
1514C4—3321no—
1515C4—3321no—
1516C4—3321no—
1517C4—3321no—
1518C4—3321no—
1519C4—3321no—
1520C4—834no—
1521C4—834no—
1522C4—1662no—
1523C4—1662no—
1524C4—1662no—
1525C4—1662no—
1526C4—1662no—
1527C4—1662no—
1528C2—42no—
1529C2—42no—
1530C2—3322no—
1531C2—3322no—
1532C2C4×#41×D8311yescharacteristic
1533C2#520×D8311yescharacteristic
1534C2C4×#1458183711yescharacteristic
1535C2#2492132211yescharacteristic
1536C2#2492133111yescharacteristic
1537C2#2492141311yescharacteristic
1538C2#2492154111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2359C2
socle, cosocleC23×C83C25
prime radicalC2×#14581788C22
hypercenter#2359D83
hypocenterC83#34331
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2359

Complements

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

NH ≅ G/Ntype
2. #24910537C2semidirect
3. #24910535C2semidirect
4. #24910535C2semidirect
5. #24910531C2semidirect
7. #24910462C2semidirect
8. #24910460C2semidirect
9. #24910449C2semidirect
10. #24910417C2semidirect
11. #24910413C2semidirect
12. #24910409C2semidirect
13. #24910377C2semidirect
14. #24910370C2semidirect
15. #24910369C2semidirect
16. #24910259C2semidirect
17. #24910257C2semidirect
18. #24910256C2semidirect
19. #24910254C2semidirect
20. #24910169C2semidirect
21. #24910169C2semidirect
23. #24910004C2semidirect
24. C4×#14581778C2semidirect
25. #24909936C2semidirect
26. #24909923C2semidirect
27. #24909922C2semidirect
28. #24909822C2semidirect
29. #24909821C2semidirect
30. C4×#14581757C2semidirect
31. C83×#2359C2semidirect
32. #19128435C4semidirect
204. #14581778C2×C4semidirect
205. #14581778C2×C4semidirect
206. #14581778C2×C4semidirect
207. #14581778C2×C4semidirect
208. #14581777C2×C4semidirect
209. #14581777C2×C4semidirect
210. #14581773C2×C4semidirect
215. #14581757C2×C4semidirect
216. #14581757C2×C4semidirect
224. C4×C22⋊D83C2×C4semidirect
225. C4×C22⋊D83C2×C4semidirect
228. (C22⋊D83)⋊C4C2×C4semidirect
229. (C22⋊D83)⋊C4C2×C4semidirect
343. #123×C83C2×C4semidirect
779. #2359D83semidirect
801. C83#34331semidirect
986. #123C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191284352
#249105372
#249105352
#249105312
#249105262
#249104622
#249104602
#249104492
#249104172
#249104132
#249104092
#249103772
#249103702
#249103692
#249102592
#249102572
#249102562
#249102542
#249101692
C4×#145817882
#249100042
C4×#145817782
#249099362
#249099232
#249099222
#249098222
#249098212
C4×#145817572
C83×#23592
#3433183