Finite Group Databasebeta

← #36312956

Subgroups — #36312956

Order 21248.

6930 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921283C218yesmaximal, complemented
2#24921277C214yesmaximal, complemented
3#24921274C214yesmaximal, complemented
4#24921271C212yesmaximal, complemented
5#24921268C212yesmaximal, complemented
6#24921266C211yesmaximal, characteristic, complemented
7#24921263C214yesmaximal, complemented
8#24921261C212yesmaximal, complemented
9#24921259C214yesmaximal, complemented
10#24921042C214yesmaximal, complemented
11#24921042C218yesmaximal, complemented
12Q8×#13050589C214yesmaximal, complemented
13#24920867C212yesmaximal, complemented
14#24920865C214yesmaximal, complemented
15C2×#19128253C214yesmaximal, complemented
16#533×D83C212yesmaximal, complemented
17#24920661C212yesmaximal
18C2×C4×#13050589C211yesmaximal, characteristic
19C83×#3501C211yesmaximal, characteristic, complemented
20C22×#13050589C2211yescharacteristic
21Q8×Dic166C2214yescomplemented
22#19128431C2214yescomplemented
23#19128431C2218yescomplemented
24#19128429C2214yescomplemented
25#19128429C2218yescomplemented
26#19128428C2218yescomplemented
27#19128428C2218yescomplemented
28#19128428C2218yescomplemented
29#19128426C2214yescomplemented
30#19128426C2218yescomplemented
31#19128410C2218yescomplemented
32#19128410C2218yescomplemented
33#19128410C2218yescomplemented
34#19128409C2218yescomplemented
35#19128409C22116yescomplemented
36#19128408C2218yescomplemented
37#19128408C2214yescomplemented
38#19128406C2218yescomplemented
39#19128406C22116yescomplemented
40#19128405C22116yescomplemented
41#19128405C22116yescomplemented
42#19128405C22116yescomplemented
43D4×Dic166C2218yescomplemented
44D4×Dic166C2214yescomplemented
45Q8×C22⋊D83C2218yescomplemented
46#19128364C2218yescomplemented
47#19128364C22116yescomplemented
48#19128332C2212yes—
49#19128331C2218yescomplemented
50#19128330C2218yes—
51#19128330C2218yes—
52#19128330C22116yescomplemented
53#19128330C22116yescomplemented
54#19128329C2214yes—
55#19128328C2218yescomplemented
56#19128327C2218yes—
57#19128327C2214yes—
58#19128326C2218yes—
59#19128258C2212yes—
60#19128257C2218yescomplemented
61#19128257C2214yescomplemented
62#19128256C2218yescomplemented
63#19128256C2212yescomplemented
64#19128256C2212yescomplemented
65#19128255C2214yescomplemented
66#19128255C2214yescomplemented
67#19128254C2214yes—
68#19128253C2214yes—
69#19128253C2218yes—
70#19128253C2218yes—
71#19128253C2214yes—
72#19128253C2218yes—
73#19128253C22116yescomplemented
74#19128253C22116yescomplemented
75#19128253C2218yescomplemented
76#19128253C2218yescomplemented
77#19128253C2218yescomplemented
78#19128253C2218yescomplemented
79C2×#14581791C2214yescomplemented
80C2×#14581790C2214yescomplemented
81C4⋊Q8×D83C2212yescomplemented
82C4⋊Q8×D83C2212yescomplemented
83C2×#14581782C2218yescomplemented
84#125×D83C2214yescomplemented
85C2×#14581771C2214yes—
86C2×#14581769C2218yes—
87C22⋊Q8×D83C2214yes—
88C22⋊Q8×D83C2214yes—
89#19128180C2218yes—
90#19128180C2218yes—
91#19128178C2214yes—
92#19128176C2212yes—
93#19128174C2218yes—
94C4×#13050589C2214yes—
95C4×#13050589C2214yes—
96C4×#13050589C2214yes—
97C4×#13050589C2214yes—
98C4×#13050589C2218yes—
99C4×#13050589C2218yes—
100C2×Q8×Dic83C2214yescomplemented
101C2×C4×Dic166C2211yescharacteristic
102C2×#14581757C2211yescharacteristic
103C2×#14581757C2218yescomplemented
104C2×#14581757C2214yescomplemented
105C4×Q8×D83C2214yescomplemented
106C4×Q8×D83C2214yescomplemented
107C2×D4×Dic83C2211yescharacteristic
108C2×C4×C22⋊D83C2212yes—
109C2×(C22⋊D83)⋊C4C2212yes—
110C2×#14581750C2211yescharacteristic
111C2×#14581748C2212yes—
112C2×#14581748C2218yes—
113#117×D83C2214yes—
114C22×C4×Dic83C2212yes—
115C2×C42×D83C2211yescharacteristic
116#554×C83C2214yescomplemented
117#554×C83C2218yescomplemented
118D4×Q8×C83C2214yescomplemented
119#544×C83C2212yes—
120#543×C83C2214yes—
121#533×C83C2212yes—
122C2×C22⋊Q8×C83C2214yes—
123#518×C83C2212yes—
124C2×C4×D4×C83C2211yescharacteristic
125C2×#13050589Q8116yescomplemented
126C2×#13050589C2314yes—
127C2×#13050589C2314yes—
128C22×Dic166C2318yes—
129C22×Dic166C2314yes—
130C22×Dic166C2311yescharacteristic
131C2×Q8×D83C2314yes—
132C2×Q8×D83C2314yes—
133C22×C22⋊D83C2312yes—
134C23×Dic83C2312yes—
135C23×Dic83C2312yes—
136C22×C4×D83C2311yescharacteristic
137C22×C4×D83C2311yescharacteristic
138C22×C4×D83C2311yescharacteristic
139#14581792C2318yes—
140#14581792C2312yes—
141#14581792C2312yes—
142#14581791C2318yes—
143#14581791C2318yes—
144#14581791C23116yes—
145#14581791C23116yes—
146#14581791C2314yes—
147#14581791C2318yes—
148#14581791C2318yes—
149#14581791C2314yes—
150#14581791C2318yes—
151#14581791C2314yes—
152#14581791C2314yes—
153#14581790C2318yes—
154#14581790C23116yes—
155#14581790C23116yes—
156#14581790C2314yes—
157#14581790C2318yes—
158#14581790C2318yes—
159#14581790C2314yes—
160#14581784C2318yes—
161#14581784C2314yes—
162#14581783C2318yes—
163#14581783C2318yes—
164#14581783C2314yes—
165#14581783C2314yes—
166#14581782C23116yes—
167#14581782C23116yes—
168#14581782C23116yes—
169#14581782C23116yes—
170#14581782C23116yes—
171#14581782C2318yes—
172#14581782C23116yes—
173#14581782C23116yes—
174#14581782C2318yes—
175#14581772C23116yes—
176#14581772C2314yes—
177#14581772C2314yes—
178#14581771C2318yes—
179#14581771C2314yes—
180#14581771C23116yes—
181#14581771C23116yes—
182#14581771C2318yes—
183#14581771C2318yes—
184#14581771C2314yes—
185#14581770C23116yes—
186#14581770C23116yes—
187#14581770C2318yes—
188#14581770C2318yes—
189#14581769C23116yes—
190#14581769C2318yes—
191#14581769C23116yes—
192#14581769C23116yes—
193#14581769C23116yes—
194#14581769C23116yes—
195#14581769C23116yes—
196#14581769C23116yes—
197#14581769C2318yes—
198#14581768C23116yes—
199#14581768C2314yes—
200#14581768C2314yes—
201Q8×Dic83C2318yes—
202Q8×Dic83C2318yes—
203Q8×Dic83C2314yes—
204Q8×Dic83C2314yes—
205Q8×Dic83C2318yes—
206C4×Dic166C2314yes—
207C4×Dic166C2318yes—
208C4×Dic166C2318yes—
209C4×Dic166C2314yes—
210C4×Dic166C2314yes—
211C4×Dic166C2314yes—
212C4×Dic166C2318yes—
213C4×Dic166C2318yes—
214#14581757C23116yes—
215#14581757C2318yes—
216#14581757C2318yes—
217#14581757C23116yes—
218#14581757C2314yes—
219#14581757C2318yes—
220#14581757C2314yes—
221#14581757C2318yes—
222#14581757C2314yes—
223#14581757C2314yes—
224#14581757C23116yes—
225#14581757C2318yes—
226#14581757C2318yes—
227#14581757C2318yes—
228D4×Dic83C2314yes—
229D4×Dic83C2318yes—
230D4×Dic83C2318yes—
231D4×Dic83C2314yes—
232C4×C22⋊D83C2318yes—
233C4×C22⋊D83C23116yes—
234C4×C22⋊D83C23116yes—
235C4×C22⋊D83C2318yes—
236(C22⋊D83)⋊C4C2318yes—
237(C22⋊D83)⋊C4C23116yes—
238(C22⋊D83)⋊C4C23116yes—
239(C22⋊D83)⋊C4C2318yes—
240#14581751C2314yes—
241#14581750C2314yes—
242#14581750C2314yes—
243#14581750C2314yes—
244#14581750C2314yes—
245#14581749C2318yes—
246#14581748C23116yes—
247#14581748C2318yes—
248#14581748C23116yes—
249#14581748C2318yes—
250#14581748C2318yes—
251#14581748C23116yes—
252C2×C4⋊Dic83C2311yescharacteristic
253C2×C4⋊Dic83C2318yes—
254C2×C4⋊Dic83C2314yes—
255C2×Dic83⋊C4C2312yes—
256C2×Dic83⋊C4C2312yes—
257C2×Dic83⋊C4C2318yes—
258C2×Dic83⋊C4C2318yes—
259C2×Dic83⋊C4C2318yes—
260C2×Dic83⋊C4C2318yes—
261C2×Dic83⋊C4C2318yes—
262C4⋊C4×D83C2314yes—
263C4⋊C4×D83C2314yes—
264C4⋊C4×D83C2314yes—
265C4⋊C4×D83C2318yes—
266C4⋊C4×D83C2318yes—
267C4⋊C4×D83C2314yes—
268C2×C22⋊Dic83C2312yes—
269C2×C22⋊Dic83C2318yes—
270C2×(C2×D83)⋊C4C2312yes—
271C22⋊C4×D83C2318yes—
272C2×C4×Dic83C2311yescharacteristic
273C2×C4×Dic83C2311yescharacteristic
274C2×C4×Dic83C2311yescharacteristic
275C2×C4×Dic83C2312yes—
276C2×C4×Dic83C2312yes—
277C2×C4×Dic83C2312yes—
278C2×C4×Dic83C2314yes—
279C2×C4×Dic83C2314yes—
280C2×C4×Dic83C2314yes—
281C2×C4×Dic83C2314yes—
282C2×C4×Dic83C2318yes—
283C2×C4×Dic83C2318yes—
284C42×D83C2312yes—
285C42×D83C2312yes—
286C42×D83C2312yes—
287C42×D83C2312yes—
288C42×D83C2318yes—
289C22×Q8×C83C2314yes—
290C22×D4×C83C2311yescharacteristic
291C23×C4×C83C2312yes—
292C4⋊Q8×C83C2318yes—
293C4⋊Q8×C83C2312yes—
294C4⋊Q8×C83C2312yes—
295#125×C83C2318yes—
296#125×C83C2314yes—
297C22⋊Q8×C83C2318yes—
298C22⋊Q8×C83C2314yes—
299C22⋊Q8×C83C23116yes—
300C22⋊Q8×C83C23116yes—
301C22⋊Q8×C83C2318yes—
302C22⋊Q8×C83C2314yes—
303C22⋊Q8×C83C2318yes—
304C4×Q8×C83C2314yes—
305C4×Q8×C83C2314yes—
306C4×D4×C83C2314yes—
307C4×D4×C83C2318yes—
308C4×D4×C83C2314yes—
309C4×D4×C83C2318yes—
310#117×C83C2314yes—
311C2×C4⋊C4×C83C2311yescharacteristic
312C2×C4⋊C4×C83C2318yes—
313C2×C4⋊C4×C83C2314yes—
314C2×C22⋊C4×C83C2312yes—
315C2×C22⋊C4×C83C2318yes—
316C2×C42×C83C2311yescharacteristic
317C23×D83C2411yescharacteristic
318#13050589C2×Q8132yescomplemented
319#13050589C2×Q8132yescomplemented
320C2×Dic166—416no—
321C2×Dic166—48no—
322C2×Dic166C2×Q818yescomplemented
323C2×Dic166C2418yes—
324C2×Dic166C2414yes—
325C2×Dic166C2414yes—
326C2×Dic166C2418yes—
327C2×Dic166C24116yes—
328C2×Dic166C2418yes—
329C2×Dic166C2414yes—
330Q8×D83—48no—
331Q8×D83—48no—
332C2×C22⋊D83C2×Q8116yescomplemented
333C2×C22⋊D83C2418yes—
334C22×Dic83—44no—
335C22×Dic83C2×Q8116yescomplemented
336C22×Dic83C2411yescharacteristic
337C22×Dic83C2414yes—
338C22×Dic83C2411yescharacteristic
339C22×Dic83C2412yes—
340C22×Dic83C2414yes—
341C22×Dic83C2418yes—
342C22×Dic83C2418yes—
343C22×Dic83C2411yescharacteristic
344C22×Dic83C2412yes—
345C22×Dic83C2414yes—
346C22×Dic83C2414yes—
347C2×C4×D83—42no—
348C2×C4×D83—42no—
349C2×C4×D83C2×Q818yescomplemented
350C2×C4×D83C2412yes—
351C2×C4×D83C2412yes—
352C2×C4×D83C2418yes—
353C2×C4×D83C2412yes—
354C2×C4×D83C2412yes—
355C2×C4×D83C2418yes—
356C2×C4×D83C2412yes—
357C2×C4×D83C2412yes—
358C4⋊Dic83C2414yes—
359C4⋊Dic83C24116yes—
360C4⋊Dic83C2414yes—
361C4⋊Dic83C2418yes—
362C4⋊Dic83C2418yes—
363C4⋊Dic83C2418yes—
364C4⋊Dic83C2414yes—
365C4⋊Dic83C2414yes—
366C4⋊Dic83C2414yes—
367Dic83⋊C4C24116yes—
368Dic83⋊C4C2418yes—
369Dic83⋊C4C2418yes—
370Dic83⋊C4C24116yes—
371Dic83⋊C4C2418yes—
372Dic83⋊C4C24116yes—
373Dic83⋊C4C2418yes—
374Dic83⋊C4C2418yes—
375Dic83⋊C4C2418yes—
376Dic83⋊C4C2418yes—
377Dic83⋊C4C24116yes—
378Dic83⋊C4C2418yes—
379Dic83⋊C4C2418yes—
380Dic83⋊C4C2418yes—
381Dic83⋊C4C24116yes—
382C22⋊Dic83C2418yes—
383C22⋊Dic83C2418yes—
384C22⋊Dic83C24116yes—
385(C2×D83)⋊C4C2418yes—
386(C2×D83)⋊C4C2418yes—
387(C2×D83)⋊C4C2418yes—
388C4×Dic83C2411yescharacteristic
389C4×Dic83C2412yes—
390C4×Dic83C2414yes—
391C4×Dic83C2414yes—
392C4×Dic83C2414yes—
393C4×Dic83C24116yes—
394C4×Dic83C24116yes—
395C4×Dic83C2412yes—
396C4×Dic83C2418yes—
397C4×Dic83C2411yescharacteristic
398C4×Dic83C2414yes—
399C4×Dic83C2414yes—
400C4×Dic83C2412yes—
401C4×Dic83C2411yescharacteristic
402C4×Dic83C2411yescharacteristic
403C4×Dic83C2412yes—
404C4×Dic83C2418yes—
405C4×Dic83C2418yes—
406C4×Dic83C2414yes—
407C24×C83C2412yes—
408C2×Q8×C83—48no—
409C2×Q8×C83C2414yes—
410C2×Q8×C83C2418yes—
411C2×Q8×C83C2414yes—
412C2×D4×C83C2×Q818yescomplemented
413C2×D4×C83C2414yes—
414C22×C4×C83—44no—
415C22×C4×C83C2411yescharacteristic
416C22×C4×C83C2414yes—
417C22×C4×C83C2411yescharacteristic
418C22×C4×C83C2412yes—
419C22×C4×C83C2418yes—
420C22×C4×C83C2418yes—
421C22×C4×C83C2414yes—
422C22×C4×C83C2411yescharacteristic
423C4⋊C4×C83C2418yes—
424C4⋊C4×C83C24116yes—
425C4⋊C4×C83C2418yes—
426C4⋊C4×C83C2418yes—
427C4⋊C4×C83C2414yes—
428C4⋊C4×C83C2414yes—
429C4⋊C4×C83C2414yes—
430C4⋊C4×C83C2414yes—
431C4⋊C4×C83C2414yes—
432C22⋊C4×C83C2418yes—
433C22⋊C4×C83C2418yes—
434C22⋊C4×C83C24116yes—
435C42×C83C2412yes—
436C42×C83C2418yes—
437C42×C83C2412yes—
438C23×C83—42no—
439C23×C83—42no—
440C23×C83C22×Q818yes—
441C23×C83C2511yescharacteristic
442C23×C83C2514yes—
443C22×D83—41no—
444C22×D83—41no—
445C22×D83C22×Q814yes—
446C22×D83C2512yes—
447Q8×C83—28no—
448Q8×C83—48no—
449Q8×C83—44no—
450D4×C83C22×Q8116yes—
451C2×C4×C83—22no—
452C2×C4×C83—28no—
453C2×C4×C83—42no—
454C2×C4×C83—44no—
455C2×C4×C83—48no—
456C2×C4×C83—41no—
457C2×C4×C83—48no—
458C2×C4×C83C22×Q814yes—
459C2×C4×C83C2512yes—
460C2×C4×C83C2511yescharacteristic
461C2×C4×C83C2518yes—
462C2×C4×C83C2518yes—
463C2×C4×C83C2514yes—
464C2×C4×C83C2512yes—
465C2×C4×C83C2511yescharacteristic
466C22⋊D83C22×Q8132yes—
467C2×Dic83—22no—
468C2×Dic83—28no—
469C2×Dic83—41no—
470C2×Dic83—42no—
471C2×Dic83—44no—
472C2×Dic83—48no—
473C2×Dic83—48no—
474C2×Dic83C22×Q814yes—
475C2×Dic83C22×Q818yes—
476C2×Dic83C22×Q8116yes—
477C2×Dic83C22×Q8116yes—
478C2×Dic83C2511yescharacteristic
479C2×Dic83C2514yes—
480C2×Dic83C2518yes—
481C2×Dic83C2518yes—
482C2×Dic83C2512yes—
483C2×Dic83C2511yescharacteristic
484C2×Dic83C2514yes—
485C2×Dic83C2511yescharacteristic
486C2×Dic83C2511yescharacteristic
487C4×D83—24no—
488C4×D83—24no—
489C4×D83—42no—
490C4×D83—42no—
491C4×D83—48no—
492C4×D83—48no—
493C4×D83C22×Q818yes—
494C4×D83C22×Q818yes—
495Dic166—28no—
496Dic166—216no—
497Dic166—44no—
498Dic166—48no—
499Dic166—48no—
500Dic166—416no—
501Dic166C22×Q8116yes—
502C22×C83—24no—
503C22×C83—21no—
504C22×C83—24no—
505C22×C83—21no—
506C22×C83—48no—
507C22×C83C23×Q812yes—
508C22×C83C23×Q818yes—
509C22×C83C2611yescharacteristic
510C2×D83—22no—
511C2×D83—22no—
512C2×D83—44no—
513C2×D83C23×Q814yes—
514C4×C83—28no—
515C4×C83—22no—
516C4×C83—24no—
517C4×C83—28no—
518C4×C83—21no—
519C4×C83C23×Q814yes—
520C4×C83#58512yes—
521Dic83—28no—
522Dic83—28no—
523Dic83—22no—
524Dic83—24no—
525Dic83—21no—
526Dic83C23×Q818yes—
527Dic83C23×Q812yes—
528Dic83C23×Q812yes—
529Dic83#58512yes—
530#62813—831nomaximal, Sylow
531C2×C83—22no—
532C2×C83—28no—
533C2×C83C24×Q811yescharacteristic
534C2×C83C2×#58511yescharacteristic
535C2×C83C2×#58511yescharacteristic
536D83—24no—
537#3504—838no—
538#3503—834no—
539#3503—834no—
540#3502—832no—
541#3502—832no—
542#3501—834no—
543#3501—834no—
544#3501—832no—
545#3501—831no—
546#3501D8311yescharacteristic, complemented
547Q8×#41—834no—
548Q8×#41—838no—
549Q8×#41—834no—
550#3458—832no—
551#3458—834no—
552C2×#533—832no—
553C2×#533—834no—
554#3428—832no—
555C2×C4×#41—831no—
556C83#6281311yescharacteristic, complemented, Sylow
557C22×#41—831no—
558Q82—838no—
559Q82—834no—
560Q82—834no—
561#557—834no—
562#557—838no—
563#557—838no—
564#557—838no—
565#557—838no—
566#557—834no—
567#557—838no—
568#554—8316no—
569#554—8316no—
570#554—8316no—
571#554—838no—
572#554—8316no—
573#554—834no—
574#554—838no—
575#554—838no—
576#554—838no—
577#554—838no—
578#554—838no—
579#554—8316no—
580#554C2×D8314yescomplemented
581#554C2×D8318yescomplemented
582D4×Q8—838no—
583D4×Q8—838no—
584D4×Q8—8316no—
585D4×Q8—838no—
586D4×Q8—834no—
587D4×Q8C2×D8314yescomplemented
588#544—838no—
589#544—838no—
590#544—838no—
591#544—838no—
592#544—8316no—
593#544—8316no—
594#544—834no—
595#544—832no—
596#544C2×D8312yes—
597#543—838no—
598#543—838no—
599#543—834no—
600#543C2×D8314yes—
601#533—832no—
602#533—832no—
603#533—838no—
604#533—834no—
605#533—838no—
606#533—834no—
607#533—834no—
608#533—838no—
609#533—838no—
610#533—838no—
611#533—838no—
612#533—838no—
613#533—838no—
614#533—838no—
615#533—8316no—
616#533—8316no—
617#533—834no—
618#533—834no—
619#533—834no—
620#533—832no—
621#533C2×D8312yes—
622C2×C4⋊Q8—834no—
623C2×C4⋊Q8—832no—
624C2×C4⋊Q8—832no—
625C2×C4⋊Q8—834no—
626C2×#125—834no—
627C2×#125—838no—
628C2×C22⋊Q8—834no—
629C2×C22⋊Q8—834no—
630C2×C22⋊Q8—834no—
631C2×C22⋊Q8—838no—
632C2×C22⋊Q8C2×D8314yes—
633#520—838no—
634#520—838no—
635#519—834no—
636#518—832no—
637#518—838no—
638#518C2×D8312yes—
639C4×#41—834no—
640C4×#41—834no—
641C4×#41—834no—
642C4×#41—834no—
643C4×#41—838no—
644C4×#41—838no—
645C2×C4×Q8—834no—
646C2×C4×Q8—834no—
647C2×C4×Q8—834no—
648C2×C4×Q8—831no—
649C2×C4×Q8—834no—
650C2×C4×Q8—838no—
651C2×C4×Q8—831no—
652C2×C4×D4—831no—
653C2×C4×D4—832no—
654C2×C4×D4—832no—
655C2×C4×D4C2×D8311yescharacteristic
656C2×#117—834no—
657C2×#117—831no—
658C2×#117—832no—
659C2×#117—838no—
660C22×C42—832no—
661C22×C42—831no—
662C2×#41—8316no—
663C2×#41—834no—
664C2×#41—834no—
665C22×Q8—834no—
666C22×Q8—834no—
667C22×Q8—834no—
668C22×Q8—838no—
669C22×Q8—831no—
670C22×Q8C22×D8314yes—
671C22×D4—832no—
672C22×D4C22×D8311yescharacteristic
673C23×C4—832no—
674C23×C4—831no—
675C23×C4—831no—
676C23×C4—832no—
677C23×C4—831no—
678C23×C4C22×D8312yes—
679C4⋊Q8—834no—
680C4⋊Q8—838no—
681C4⋊Q8—834no—
682C4⋊Q8—838no—
683C4⋊Q8—838no—
684C4⋊Q8—8316no—
685C4⋊Q8—8316no—
686C4⋊Q8—834no—
687C4⋊Q8—834no—
688C4⋊Q8—838no—
689C4⋊Q8—838no—
690C4⋊Q8—834no—
691C4⋊Q8—834no—
692C4⋊Q8—838no—
693C4⋊Q8—8316no—
694C4⋊Q8—8316no—
695C4⋊Q8—838no—
696C4⋊Q8—838no—
697C4⋊Q8—832no—
698C4⋊Q8—832no—
699C4⋊Q8—838no—
700C4⋊Q8C22×D8312yes—
701C4⋊Q8C22×D8312yes—
702C4⋊Q8C22×D8318yes—
703#125—838no—
704#125—838no—
705#125—8316no—
706#125—8316no—
707#125—8316no—
708#125—834no—
709#125—834no—
710#125—8316no—
711#125—8316no—
712#125—8316no—
713#125—8316no—
714#125—838no—
715#125—838no—
716#125—834no—
717#125—838no—
718#125C22×D8314yes—
719#125C22×D8318yes—
720C22⋊Q8—834no—
721C22⋊Q8—834no—
722C22⋊Q8—8316no—
723C22⋊Q8—834no—
724C22⋊Q8—838no—
725C22⋊Q8—834no—
726C22⋊Q8—838no—
727C22⋊Q8—838no—
728C22⋊Q8—8316no—
729C22⋊Q8—8316no—
730C22⋊Q8—838no—
731C22⋊Q8—838no—
732C22⋊Q8—8316no—
733C22⋊Q8—8316no—
734C22⋊Q8—834no—
735C22⋊Q8—834no—
736C22⋊Q8—8316no—
737C22⋊Q8—838no—
738C22⋊Q8—8316no—
739C22⋊Q8—838no—
740C22⋊Q8—8316no—
741C22⋊Q8—8316no—
742C22⋊Q8—8316no—
743C22⋊Q8—8316no—
744C22⋊Q8—8316no—
745C22⋊Q8—8316no—
746C22⋊Q8C22×D8314yes—
747C22⋊Q8C22×D8314yes—
748C22⋊Q8C22×D8318yes—
749C22⋊Q8C22×D8318yes—
750C22⋊Q8C22×D8318yes—
751C22⋊Q8C22×D83116yes—
752C22⋊Q8C22×D83116yes—
753C4×Q8—834no—
754C4×Q8—838no—
755C4×Q8—834no—
756C4×Q8—838no—
757C4×Q8—838no—
758C4×Q8—834no—
759C4×Q8—838no—
760C4×Q8—834no—
761C4×Q8—834no—
762C4×Q8—834no—
763C4×Q8—838no—
764C4×Q8—8316no—
765C4×Q8—838no—
766C4×Q8—8316no—
767C4×Q8—838no—
768C4×Q8—838no—
769C4×Q8—8316no—
770C4×Q8—838no—
771C4×Q8—838no—
772C4×Q8—834no—
773C4×Q8—834no—
774C4×Q8—838no—
775C4×Q8—834no—
776C4×Q8—838no—
777C4×Q8—834no—
778C4×Q8—838no—
779C4×Q8—838no—
780C4×Q8C22×D8314yes—
781C4×Q8C22×D8314yes—
782C4×D4—834no—
783C4×D4—834no—
784C4×D4—838no—
785C4×D4—838no—
786C4×D4—838no—
787C4×D4—838no—
788C4×D4—8316no—
789C4×D4—8316no—
790C4×D4—838no—
791C4×D4—838no—
792C4×D4—8316no—
793C4×D4—8316no—
794C4×D4C22×D8314yes—
795C4×D4C22×D8314yes—
796C4×D4C22×D8318yes—
797C4×D4C22×D8318yes—
798#117—834no—
799#117—834no—
800#117—834no—
801#117—834no—
802#117—834no—
803#117—838no—
804#117—838no—
805#117—8316no—
806#117—838no—
807#117—8316no—
808#117—8316no—
809#117—838no—
810#117C22×D8314yes—
811C2×C4⋊C4—832no—
812C2×C4⋊C4—832no—
813C2×C4⋊C4—831no—
814C2×C4⋊C4—838no—
815C2×C4⋊C4—838no—
816C2×C4⋊C4—838no—
817C2×C4⋊C4—838no—
818C2×C4⋊C4—838no—
819C2×C4⋊C4—838no—
820C2×C4⋊C4—834no—
821C2×C4⋊C4—834no—
822C2×C4⋊C4—834no—
823C2×C4⋊C4—838no—
824C2×C4⋊C4—838no—
825C2×C4⋊C4—834no—
826C2×C4⋊C4—834no—
827C2×C4⋊C4C22×D8311yescharacteristic
828C2×C4⋊C4C22×D8318yes—
829C2×C4⋊C4C22×D8314yes—
830C2×C22⋊C4—832no—
831C2×C22⋊C4—838no—
832C2×C22⋊C4—832no—
833C2×C22⋊C4—838no—
834C2×C22⋊C4C22×D8312yes—
835C2×C22⋊C4C22×D8318yes—
836C2×C42—832no—
837C2×C42—831no—
838C2×C42—838no—
839C2×C42—838no—
840C2×C42—832no—
841C2×C42—831no—
842C2×C42—832no—
843C2×C42—834no—
844C2×C42—834no—
845C2×C42—834no—
846C2×C42—834no—
847C2×C42—831no—
848C2×C42—838no—
849C2×C42—832no—
850C2×C42—832no—
851C2×C42—832no—
852C2×C42—832no—
853C2×C42C22×D8311yescharacteristic
854C24—831no—
855C24C23×D8312yes—
856#41—8332no—
857#41—8332no—
858C2×Q8—48no—
859C2×Q8—3328no—
860C2×Q8—33216no—
861C2×Q8—3328no—
862C2×Q8—3328no—
863C2×Q8—838no—
864C2×Q8—838no—
865C2×Q8—838no—
866C2×Q8—8316no—
867C2×Q8—834no—
868C2×Q8—834no—
869C2×Q8—838no—
870C2×Q8—834no—
871C2×Q8C23×D8314yes—
872C2×Q8C23×D8318yes—
873C2×Q8C23×D8314yes—
874C2×D4—8316no—
875C2×D4—838no—
876C2×D4Q8×D8318yescomplemented
877C2×D4C23×D8314yes—
878C22×C4—44no—
879C22×C4—3322no—
880C22×C4—3322no—
881C22×C4—3324no—
882C22×C4—831no—
883C22×C4—832no—
884C22×C4—834no—
885C22×C4—838no—
886C22×C4—838no—
887C22×C4—832no—
888C22×C4—832no—
889C22×C4—838no—
890C22×C4—838no—
891C22×C4—8316no—
892C22×C4—834no—
893C22×C4—831no—
894C22×C4—834no—
895C22×C4—832no—
896C22×C4—838no—
897C22×C4—832no—
898C22×C4—832no—
899C22×C4—831no—
900C22×C4—834no—
901C22×C4—832no—
902C22×C4—832no—
903C22×C4C23×D8311yescharacteristic
904C22×C4C23×D8314yes—
905C22×C4C23×D8312yes—
906C22×C4C23×D8314yes—
907C22×C4C23×D8311yescharacteristic
908C22×C4C23×D8318yes—
909C22×C4C23×D8318yes—
910C22×C4C23×D8311yescharacteristic
911C4⋊C4—838no—
912C4⋊C4—838no—
913C4⋊C4—838no—
914C4⋊C4—838no—
915C4⋊C4—838no—
916C4⋊C4—838no—
917C4⋊C4—834no—
918C4⋊C4—838no—
919C4⋊C4—8316no—
920C4⋊C4—8316no—
921C4⋊C4—838no—
922C4⋊C4—834no—
923C4⋊C4—834no—
924C4⋊C4—834no—
925C4⋊C4—8316no—
926C4⋊C4—8316no—
927C4⋊C4—838no—
928C4⋊C4—8316no—
929C4⋊C4—838no—
930C4⋊C4—838no—
931C4⋊C4—838no—
932C4⋊C4—8316no—
933C4⋊C4—838no—
934C4⋊C4—834no—
935C4⋊C4C23×D8318yes—
936C4⋊C4C23×D8314yes—
937C4⋊C4C23×D8314yes—
938C4⋊C4C23×D8314yes—
939C4⋊C4C23×D8314yes—
940C4⋊C4C23×D8318yes—
941C4⋊C4C23×D8314yes—
942C4⋊C4C23×D83116yes—
943C4⋊C4C23×D8318yes—
944C22⋊C4—838no—
945C22⋊C4—838no—
946C22⋊C4—8316no—
947C22⋊C4—838no—
948C22⋊C4—838no—
949C22⋊C4—838no—
950C22⋊C4C23×D8318yes—
951C22⋊C4C23×D8318yes—
952C22⋊C4C23×D83116yes—
953C42—831no—
954C42—831no—
955C42—831no—
956C42—831no—
957C42—834no—
958C42—838no—
959C42—838no—
960C42—832no—
961C42—834no—
962C42—832no—
963C42—834no—
964C42—834no—
965C42—832no—
966C42—834no—
967C42—834no—
968C42—832no—
969C42—8316no—
970C42—8316no—
971C42—838no—
972C42C23×D8312yes—
973C42C23×D8312yes—
974C42C23×D8318yes—
975C23—42no—
976C23—42no—
977C23—3321no—
978C23—3321no—
979C23—834no—
980C23—832no—
981C23C2×Q8×D8318yes—
982C23C24×D8311yescharacteristic
983C23C24×D8314yes—
984Q8—28no—
985Q8—48no—
986Q8—44no—
987Q8—33216no—
988Q8—3324no—
989Q8—3328no—
990Q8—3328no—
991Q8—8316no—
992Q8—16616no—
993Q8—1668no—
994D4—8332no—
995D4C2×Q8×D83116yes—
996C2×C4—22no—
997C2×C4—28no—
998C2×C4—44no—
999C2×C4—42no—
1000C2×C4—41no—
1001C2×C4—48no—
1002C2×C4—48no—
1003C2×C4—3322no—
1004C2×C4—3322no—
1005C2×C4—3328no—
1006C2×C4—3328no—
1007C2×C4—3324no—
1008C2×C4—3322no—
1009C2×C4—3321no—
1010C2×C4—3328no—
1011C2×C4—3328no—
1012C2×C4—834no—
1013C2×C4—838no—
1014C2×C4—8316no—
1015C2×C4—8316no—
1016C2×C4—831no—
1017C2×C4—834no—
1018C2×C4—831no—
1019C2×C4—831no—
1020C2×C4—838no—
1021C2×C4—838no—
1022C2×C4—831no—
1023C2×C4—838no—
1024C2×C4—834no—
1025C2×C4—838no—
1026C2×C4—832no—
1027C2×C4—1664no—
1028C2×C4—1662no—
1029C2×C4—1668no—
1030C2×C4—1664no—
1031C2×C4C2×Q8×D8314yes—
1032C2×C4C24×D8311yescharacteristic
1033C2×C4C24×D8314yes—
1034C2×C4C24×D8318yes—
1035C2×C4C24×D8318yes—
1036C2×C4C24×D8312yes—
1037C2×C4C24×D8312yes—
1038C2×C4C24×D8311yescharacteristic
1039C22—24no—
1040C22—21no—
1041C22—24no—
1042C22—21no—
1043C22—48no—
1044C22—3324no—
1045C22—834no—
1046C22—1662no—
1047C22—1662no—
1048C22C22×Q8×D8312yes—
1049C22C22×Q8×D8318yes—
1050C22C25×D8311yescharacteristic
1051C4—28no—
1052C4—22no—
1053C4—21no—
1054C4—24no—
1055C4—28no—
1056C4—832no—
1057C4—832no—
1058C4—838no—
1059C4—832no—
1060C4—1661no—
1061C4—1668no—
1062C4—1664no—
1063C4—1668no—
1064C4—1662no—
1065C4C22×Q8×D8314yes—
1066C4#1912853612yes—
1067C2—22no—
1068C2—28no—
1069C2—1664no—
1070C2C23×Q8×D8311yescharacteristic
1071C2#585×D8311yescharacteristic
1072C2C2×#1912853611yescharacteristic
subgroupG/H
center, FrattiniC22C25×D83
commutator, socle, cosocleC22×C83C26
FittingC83×#3501C2
prime radicalC22×#13050589C22
hypercenter#3501D83
hypocenterC83#62813
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #24921283C2semidirect
2. #24921277C2semidirect
3. #24921274C2semidirect
4. #24921271C2semidirect
5. #24921268C2semidirect
6. #24921266C2semidirect
7. #24921263C2semidirect
8. #24921261C2semidirect
9. #24921259C2semidirect
10. #24921042C2semidirect
11. #24921042C2semidirect
12. Q8×#13050589C2semidirect
13. #24920867C2semidirect
14. #24920865C2semidirect
15. C2×#19128253C2semidirect
16. #533×D83C2semidirect
19. C83×#3501C2semidirect
21. Q8×Dic166C22semidirect
22. #19128431C22semidirect
23. #19128431C22semidirect
24. #19128429C22semidirect
25. #19128429C22semidirect
26. #19128428C22semidirect
27. #19128428C22semidirect
28. #19128428C22semidirect
29. #19128426C22semidirect
30. #19128426C22semidirect
31. #19128410C22semidirect
32. #19128410C22semidirect
33. #19128410C22semidirect
34. #19128409C22semidirect
35. #19128409C22semidirect
36. #19128408C22semidirect
37. #19128408C22semidirect
38. #19128406C22semidirect
39. #19128406C22semidirect
40. #19128405C22semidirect
41. #19128405C22semidirect
42. #19128405C22semidirect
43. D4×Dic166C22semidirect
44. D4×Dic166C22semidirect
45. Q8×C22⋊D83C22semidirect
46. #19128364C22semidirect
47. #19128364C22semidirect
49. #19128331C22semidirect
52. #19128330C22semidirect
53. #19128330C22semidirect
55. #19128328C22semidirect
60. #19128257C22semidirect
61. #19128257C22semidirect
62. #19128256C22semidirect
63. #19128256C22semidirect
64. #19128256C22semidirect
65. #19128255C22semidirect
66. #19128255C22semidirect
73. #19128253C22semidirect
74. #19128253C22semidirect
75. #19128253C22semidirect
76. #19128253C22semidirect
77. #19128253C22semidirect
78. #19128253C22semidirect
79. C2×#14581791C22semidirect
80. C2×#14581790C22semidirect
81. C4⋊Q8×D83C22semidirect
82. C4⋊Q8×D83C22semidirect
83. C2×#14581782C22semidirect
84. #125×D83C22semidirect
100. C2×Q8×Dic83C22semidirect
103. C2×#14581757C22semidirect
104. C2×#14581757C22semidirect
105. C4×Q8×D83C22semidirect
106. C4×Q8×D83C22semidirect
116. #554×C83C22semidirect
117. #554×C83C22semidirect
118. D4×Q8×C83C22semidirect
125. C2×#13050589Q8semidirect
318. #13050589C2×Q8semidirect
319. #13050589C2×Q8semidirect
322. C2×Dic166C2×Q8semidirect
332. C2×C22⋊D83C2×Q8semidirect
335. C22×Dic83C2×Q8semidirect
349. C2×C4×D83C2×Q8semidirect
412. C2×D4×C83C2×Q8semidirect
546. #3501D83semidirect
556. C83#62813semidirect
580. #554C2×D83semidirect
581. #554C2×D83semidirect
587. D4×Q8C2×D83semidirect
876. C2×D4Q8×D83semidirect

Maximal subgroups

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

subgroupindex
#249212832
#249212772
#249212742
#249212712
#249212682
#249212662
#249212632
#249212612
#249212592
#249210422
Q8×#130505892
#249208672
#249208652
C2×#191282532
#533×D832
#249206612
C2×C4×#130505892
C83×#35012
#6281383