Finite Group Databasebeta

← #32905682

Subgroups — #32905682

Order 18176.

7094 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602433C213yesmaximal, complemented
2#22602431C211yesmaximal, characteristic, complemented
3#22602426C211yesmaximal, characteristic, complemented
4#22602424C213yesmaximal, complemented
5#22602334C212yesmaximal, complemented
6#22602330C216yesmaximal, complemented
7#22602206C213yesmaximal, complemented
8#22602203C213yesmaximal, complemented
9#22602149C211yesmaximal, characteristic, complemented
10#22602110C211yesmaximal, characteristic, complemented
11#22602048C216yesmaximal, complemented
12#22601990C212yesmaximal, complemented
13#22601958C216yesmaximal, complemented
14#22601957C212yesmaximal, complemented
15#22601935C211yesmaximal, characteristic, complemented
16#22601933C213yesmaximal, complemented
17#22601918C213yesmaximal, complemented
18#22601771C216yesmaximal, complemented
19#22601637C213yesmaximal, complemented
20#22601633C213yesmaximal, complemented
21C4×#14556176C212yesmaximal, complemented
22C2×C4×Q8×D71C211yesmaximal, characteristic, complemented
23Q8×#41×C71C211yesmaximal, characteristic, complemented
24C2×#14556176C2212yes—
25C22×Q8×D71C2211yescharacteristic
26#17986734C2213yescomplemented
27#17986734C2213yescomplemented
28#17986732C2216yescomplemented
29#17986729C2213yescomplemented
30#17986728C2211yescharacteristic, complemented
31#17986727C2213yescomplemented
32#17986726C2216yescomplemented
33#17986725C2212yescomplemented
34#17986724C2216yescomplemented
35#17986724C2213yescomplemented
36#17986723C2216yescomplemented
37#17986722C2213yescomplemented
38#17986721C2216yescomplemented
39#17986721C2216yescomplemented
40#17986720C22112yescomplemented
41#17986719C2213yescomplemented
42#17986710C2213yescomplemented
43#17986707C2216yes—
44#17986705C2216yescomplemented
45#17986703C22112yes—
46#17986698C22112yes—
47#17986697C2216yes—
48#17986695C2216yes—
49#17986690C2216yes—
50#17986684C2216yescomplemented
51#17986683C2216yes—
52#17986683C2216yescomplemented
53#17986681C22112yes—
54#17986681C22112yescomplemented
55#17986671C2211yescharacteristic, complemented
56#17986670C2213yescomplemented
57#17986664C2216yes—
58#17986664C2213yescomplemented
59Q8×C22⋊D71C2212yes—
60#17986662C2216yes—
61#17986661C2212yes—
62#17986660C2212yes—
63#17986660C2212yescomplemented
64#17986659C2216yes—
65#17986659C2216yescomplemented
66#17986658C2216yes—
67#17986652C2216yes—
68#17986651C22112yes—
69#17986650C2216yes—
70#17986626C2216yes—
71#17986623C2216yescomplemented
72#17986622C2216yescomplemented
73#17986619C22112yescomplemented
74#17986610C2216yescomplemented
75#17986609C2216yescomplemented
76#17986608C22112yescomplemented
77#17986597C22112yes—
78#17986595C22112yes—
79#17986579C2216yes—
80#17986574C2216yes—
81#17986572C2216yes—
82#17986554C2213yes—
83#17986554C2213yes—
84#17986553C2213yes—
85#17986553C2213yes—
86#17986553C2216yescomplemented
87#17986553C22112yescomplemented
88#17986552C2213yes—
89#17986550C2213yes—
90#17986550C2213yes—
91#17986549C2213yes—
92#17986546C2213yes—
93#17986546C2213yes—
94#17986545C2213yes—
95#17986536C2216yes—
96#17986536C2213yes—
97#17986536C2213yes—
98#17986536C2216yes—
99#17986536C2216yescomplemented
100#17986535C2216yes—
101#17986535C2216yes—
102#17986534C2216yes—
103#17986534C2216yes—
104#17986533C2216yescomplemented
105#17986531C2213yes—
106#17986531C2213yes—
107#17986529C2216yes—
108#17986529C2216yes—
109#17986527C2216yes—
110#17986527C2216yes—
111#17986527C22112yescomplemented
112#17986512C2216yes—
113#17986512C2216yes—
114#17986511C2213yes—
115#17986508C2216yes—
116#17986508C2216yes—
117#17986506C2211yescharacteristic
118#17986481C2216yes—
119#17986481C2212yescomplemented
120#17986480C2216yes—
121#17986480C2216yescomplemented
122#17986477C2212yescomplemented
123#17986475C2212yes—
124#17986475C2216yescomplemented
125C4×#11765866C2216yes—
126C4×#11765866C2216yes—
127C4×#11765866C2212yescomplemented
128C4×#11765865C2216yes—
129C4×#11765865C2213yes—
130C4×#11765865C2216yes—
131C4×#11765865C2216yescomplemented
132#17986467C2216yes—
133C2×Q8×Dic71C2211yescharacteristic
134C2×C4×Dic142C2213yes—
135C2×#14556093C2213yes—
136C4×Q8×D71C2213yes—
137C4×Q8×D71C2211yescharacteristic
138C4×Q8×D71C2211yescharacteristic
139C4×Q8×D71C2213yes—
140C4×Q8×D71C2211yescharacteristic
141C4×Q8×D71C2213yes—
142C4×Q8×D71C2211yescharacteristic
143C4×Q8×D71C2213yes—
144C4×Q8×D71C2216yescomplemented
145C2×C4⋊C4×D71C2213yes—
146C2×C42×D71C2213yes—
147Q82×C71C2211yescharacteristic, complemented
148#557×C71C2213yescomplemented
149#554×C71C2216yes—
150#554×C71C2213yescomplemented
151D4×Q8×C71C2212yes—
152D4×Q8×C71C2211yescharacteristic, complemented
153#533×C71C2213yes—
154#533×C71C2216yescomplemented
155C4×#41×C71C2213yes—
156C2×C4×Q8×C71C2211yescharacteristic
157C2×C4×Q8×C71C2212yescomplemented
158#14556176—216no—
159C2×#11765866C2316yes—
160C2×#11765866C2312yes—
161C2×#11765866C2316yes—
162C2×#11765865C2316yes—
163C2×#11765865C2316yes—
164C2×#11765865C2313yes—
165C2×#11765865C2316yes—
166C22×Dic142C2313yes—
167C2×Q8×D71—28no—
168C2×Q8×D71C2313yes—
169C2×Q8×D71C2313yes—
170C2×Q8×D71C2311yescharacteristic
171C2×Q8×D71C2316yes—
172C2×Q8×D71C2311yescharacteristic
173C22×C4×D71C2313yes—
174C22×C4×D71C2311yescharacteristic
175C22×C4×D71C2313yes—
176#14556128C2313yes—
177#14556127C23112yes—
178#14556127C2316yes—
179#14556127C2313yes—
180#14556127C2313yes—
181#14556126C2316yes—
182#14556126C23112yes—
183#14556126C2313yes—
184#14556125C2313yes—
185#14556124C2313yes—
186#14556123C23112yes—
187#14556123C23112yes—
188#14556123C2316yes—
189#14556123C23112yes—
190#14556123C2316yes—
191#14556123C23112yes—
192#14556122C23112yes—
193#14556121C23112yes—
194#14556121C2316yes—
195#14556121C2316yes—
196#14556120C2316yes—
197#14556119C2316yes—
198#14556119C2316yes—
199#14556119C2316yes—
200#14556119C2313yes—
201#14556119C2313yes—
202#14556118C23112yes—
203#14556118C23112yes—
204#14556118C23112yes—
205#14556118C2316yes—
206#14556118C23112yes—
207#14556118C2316yes—
208#14556117C2316yes—
209#14556117C2316yes—
210#14556117C2316yes—
211#14556117C2313yes—
212#14556116C2316yes—
213#14556116C2316yes—
214#14556115C2313yes—
215#14556114C23112yes—
216#14556114C2316yes—
217#14556114C2316yes—
218#14556113C23112yes—
219#14556113C2316yes—
220#14556113C23112yes—
221#14556113C23112yes—
222#14556113C23112yes—
223#14556113C2316yes—
224#14556112C2316yes—
225#14556111C23112yes—
226#14556110C2316yes—
227#14556110C23112yes—
228#14556110C2316yes—
229#14556109C2312yes—
230#14556108C2316yes—
231#14556108C23112yes—
232#14556108C2313yes—
233#14556108C2313yes—
234#14556107C2316yes—
235#14556106C23112yes—
236#14556106C23112yes—
237#14556106C23112yes—
238#14556106C2316yes—
239#14556106C23112yes—
240#14556106C2316yes—
241#14556105C2316yes—
242#14556105C2316yes—
243#14556104C2316yes—
244#14556104C2316yes—
245#14556104C2316yes—
246#14556104C23112yes—
247#14556104C2316yes—
248#14556104C2311yescharacteristic
249#14556104C2311yescharacteristic
250#14556103C2316yes—
251#14556103C2316yes—
252#14556103C2316yes—
253#14556103C2313yes—
254#14556103C2313yes—
255#14556102C2316yes—
256#14556102C2316yes—
257#14556102C2316yes—
258#14556101C2316yes—
259#14556101C23112yes—
260#14556101C2316yes—
261#14556100C2316yes—
262#14556100C2316yes—
263#14556099C2311yescharacteristic
264#14556099C2311yescharacteristic
265#14556098C2316yes—
266#14556096C2312yes—
267Q8×Dic71C2316yes—
268Q8×Dic71C2313yes—
269Q8×Dic71C2312yes—
270Q8×Dic71C2311yescharacteristic
271Q8×Dic71C2316yes—
272Q8×Dic71C2313yes—
273Q8×Dic71C2311yescharacteristic
274Q8×Dic71C2316yes—
275C4×Dic142C2316yes—
276C4×Dic142C2316yes—
277C4×Dic142C2313yes—
278C4×Dic142C2316yes—
279C4×Dic142C2313yes—
280C4×Dic142C2313yes—
281C4×Dic142C2316yes—
282C4×Dic142C2313yes—
283C4×Dic142C2316yes—
284C4×Dic142C2316yes—
285C4×Dic142C2313yes—
286C4×Dic142C2313yes—
287C4×Dic142C2316yes—
288#14556093C2316yes—
289#14556093C2313yes—
290#14556093C2316yes—
291#14556093C2313yes—
292#14556093C23112yes—
293#14556093C2316yes—
294#14556093C2313yes—
295#14556093C2313yes—
296#14556093C2316yes—
297#14556093C2316yes—
298C4×D284C2316yes—
299C4×D284C2316yes—
300C4×D284C2316yes—
301C4×D284C2313yes—
302C4×D284C2313yes—
303C4×D284C2316yes—
304C4×D284C2316yes—
305C4×D284C2316yes—
306C4×D284C2316yes—
307#14556090C23112yes—
308#14556090C2316yes—
309#14556090C2316yes—
310#14556090C23112yes—
311#14556090C2316yes—
312#14556090C2316yes—
313#14556090C2316yes—
314C4×C22⋊D71C2316yes—
315C4×C22⋊D71C2316yes—
316C4×C22⋊D71C2316yes—
317C4×C22⋊D71C23112yes—
318C4×C22⋊D71C2316yes—
319C4×C22⋊D71C2316yes—
320C4×C22⋊D71C2316yes—
321C4×C22⋊D71C2312yes—
322C4×C22⋊D71C2312yes—
323C4×C22⋊D71C2316yes—
324C4×C22⋊D71C2316yes—
325(C22⋊D71)⋊C4C23112yes—
326(C22⋊D71)⋊C4C23112yes—
327#14556087C2316yes—
328#14556087C2316yes—
329#14556087C2316yes—
330#14556087C2311yescharacteristic
331#14556086C2316yes—
332#14556086C23112yes—
333#14556086C2316yes—
334#14556086C23112yes—
335#14556086C2316yes—
336#14556085C2316yes—
337#14556085C2316yes—
338#14556085C2316yes—
339#14556085C23112yes—
340#14556085C2316yes—
341#14556085C23112yes—
342#14556085C2316yes—
343C2×C4⋊Dic71C2313yes—
344C2×Dic71⋊C4C2316yes—
345C4⋊C4×D71C2313yes—
346C4⋊C4×D71C2316yes—
347C4⋊C4×D71C2313yes—
348C4⋊C4×D71C2316yes—
349C4⋊C4×D71C23112yes—
350C4⋊C4×D71C2313yes—
351C4⋊C4×D71C2316yes—
352C4⋊C4×D71C2313yes—
353C2×C4×Dic71C2313yes—
354C2×C4×Dic71C2313yes—
355C2×C4×Dic71C2313yes—
356C42×D71C2313yes—
357C42×D71C2313yes—
358C42×D71C2313yes—
359C42×D71C2313yes—
360C42×D71C2313yes—
361C42×D71C2313yes—
362C42×D71C2313yes—
363C42×D71C2313yes—
364C42×D71C23112yes—
365C42×D71C2316yes—
366C2×#41×C71C2311yescharacteristic
367C22×Q8×C71C2311yescharacteristic
368C22×Q8×C71C2312yes—
369C4⋊Q8×C71C2316yes—
370C4⋊Q8×C71C2316yes—
371C4⋊Q8×C71C2313yes—
372C4⋊Q8×C71C2313yes—
373#125×C71C23112yes—
374#125×C71C2316yes—
375C22⋊Q8×C71C2316yes—
376C22⋊Q8×C71C2316yes—
377C22⋊Q8×C71C23112yes—
378C22⋊Q8×C71C2316yes—
379C22⋊Q8×C71C2316yes—
380C4×Q8×C71C2312yes—
381C4×Q8×C71C2311yescharacteristic
382C4×Q8×C71C2311yescharacteristic
383C4×Q8×C71C2313yes—
384C4×Q8×C71C2313yes—
385C4×Q8×C71C2316yes—
386C4×Q8×C71C2316yes—
387C4×Q8×C71C2313yes—
388C4×Q8×C71C2313yes—
389C4×Q8×C71C2316yes—
390C4×D4×C71C2316yes—
391C4×D4×C71C2313yes—
392C4×D4×C71C2316yes—
393C4×D4×C71C2313yes—
394#117×C71C2313yes—
395#117×C71C2316yes—
396C2×C4⋊C4×C71C2316yes—
397C2×C4⋊C4×C71C2313yes—
398C2×C42×C71C2313yes—
399C2×C42×C71C2316yes—
400C23×D71C2411yescharacteristic
401#11765866—28no—
402#11765866—224no—
403#11765866—412no—
404#11765865—212no—
405#11765865—224no—
406#11765865—224no—
407#11765865—412no—
408C2×Dic142—212no—
409C2×Dic142C2416yes—
410C2×Dic142C2413yes—
411C2×Dic142C2416yes—
412C2×Dic142C2413yes—
413C2×Dic142C2416yes—
414C2×Dic142C2413yes—
415Q8×D71—24no—
416Q8×D71—212no—
417Q8×D71—212no—
418Q8×D71—224no—
419Q8×D71#4118yescomplemented
420C2×D284C2416yes—
421C2×D284C2416yes—
422C2×D284C2416yes—
423C2×D284C2413yes—
424C2×D284C2416yes—
425C2×C22⋊D71C2412yes—
426C2×C22⋊D71C2412yes—
427C2×C22⋊D71C2416yes—
428C2×C22⋊D71C2416yes—
429C2×C22⋊D71C2416yes—
430C22×Dic71C2413yes—
431C22×Dic71C2411yescharacteristic
432C22×Dic71C2413yes—
433C2×C4×D71—24no—
434C2×C4×D71—212no—
435C2×C4×D71—46no—
436C2×C4×D71C2413yes—
437C2×C4×D71C2413yes—
438C2×C4×D71C2413yes—
439C2×C4×D71C2413yes—
440C2×C4×D71C2413yes—
441C2×C4×D71C2411yescharacteristic
442C2×C4×D71C2411yescharacteristic
443C2×C4×D71C2411yescharacteristic
444C2×C4×D71C2411yescharacteristic
445C2×C4×D71C24112yes—
446C2×C4×D71C2416yes—
447C2×C4×D71C2416yes—
448C2×C4×D71C2413yes—
449C2×C4×D71C2413yes—
450C2×C4×D71C2416yes—
451C2×C4×D71C24112yes—
452C2×C4×D71C2413yes—
453C4⋊Dic71C2413yes—
454C4⋊Dic71C2413yes—
455C4⋊Dic71C2416yes—
456C4⋊Dic71C2416yes—
457C4⋊Dic71C2416yes—
458C4⋊Dic71C2416yes—
459C4⋊Dic71C2416yes—
460C4⋊Dic71C2416yes—
461C4⋊Dic71C2411yescharacteristic
462C4⋊Dic71C2411yescharacteristic
463C4⋊Dic71C2416yes—
464Dic71⋊C4C2416yes—
465Dic71⋊C4C2416yes—
466Dic71⋊C4C2416yes—
467Dic71⋊C4C2416yes—
468Dic71⋊C4C2416yes—
469Dic71⋊C4C2416yes—
470Dic71⋊C4C2416yes—
471Dic71⋊C4C2412yes—
472Dic71⋊C4C2412yes—
473Dic71⋊C4C24112yes—
474Dic71⋊C4C24112yes—
475Dic71⋊C4C2416yes—
476Dic71⋊C4C2416yes—
477Dic71⋊C4C2416yes—
478Dic71⋊C4C2416yes—
479Dic71⋊C4C2416yes—
480C22⋊Dic71C2412yes—
481C22⋊Dic71C2412yes—
482C22⋊Dic71C2416yes—
483C22⋊Dic71C2412yes—
484C22⋊Dic71C2416yes—
485(C2×D71)⋊C4C2412yes—
486(C2×D71)⋊C4C2412yes—
487(C2×D71)⋊C4C2416yes—
488(C2×D71)⋊C4C2416yes—
489(C2×D71)⋊C4C2416yes—
490(C2×D71)⋊C4C24112yes—
491(C2×D71)⋊C4C2416yes—
492(C2×D71)⋊C4C2416yes—
493(C2×D71)⋊C4C24112yes—
494(C2×D71)⋊C4C24112yes—
495(C2×D71)⋊C4C2416yes—
496(C2×D71)⋊C4C2416yes—
497(C2×D71)⋊C4C2416yes—
498(C2×D71)⋊C4C24112yes—
499C4×Dic71C2413yes—
500C4×Dic71C2412yes—
501C4×Dic71C2413yes—
502C4×Dic71C2413yes—
503C4×Dic71C2413yes—
504C4×Dic71C2413yes—
505C4×Dic71C2413yes—
506C4×Dic71C2413yes—
507C4×Dic71C2413yes—
508C4×Dic71C2413yes—
509C4×Dic71C2413yes—
510C4×Dic71C2413yes—
511C4×Dic71C2413yes—
512C4×Dic71C24112yes—
513C4×Dic71C2416yes—
514C4×Dic71C2416yes—
515C4×Dic71C24112yes—
516#41×C71—24no—
517C2×Q8×C71—24no—
518C2×Q8×C71—28no—
519C2×Q8×C71C2413yes—
520C2×Q8×C71C2416yes—
521C2×Q8×C71C2411yescharacteristic
522C2×Q8×C71C2416yes—
523C2×Q8×C71C2411yescharacteristic
524C2×D4×C71C2412yes—
525C2×D4×C71C2411yescharacteristic
526C22×C4×C71C2413yes—
527C22×C4×C71C2416yes—
528C22×C4×C71C2412yes—
529C22×C4×C71C2413yes—
530C22×C4×C71C2416yes—
531C22×C4×C71C2411yescharacteristic
532C4⋊C4×C71C2413yes—
533C4⋊C4×C71C2416yes—
534C4⋊C4×C71C24112yes—
535C4⋊C4×C71C2413yes—
536C4⋊C4×C71C2416yes—
537C4⋊C4×C71C2413yes—
538C4⋊C4×C71C2413yes—
539C4⋊C4×C71C2416yes—
540C4⋊C4×C71C2416yes—
541C4⋊C4×C71C2416yes—
542C4⋊C4×C71C24112yes—
543C22⋊C4×C71C2416yes—
544C22⋊C4×C71C2416yes—
545C22⋊C4×C71C2416yes—
546C42×C71C2413yes—
547C42×C71C2413yes—
548C42×C71C2416yes—
549C42×C71C2413yes—
550C42×C71C2416yes—
551C42×C71C2413yes—
552C42×C71C2416yes—
553C23×C71C2512yes—
554C23×C71C2511yescharacteristic
555C22×D71—22no—
556C22×D71—22no—
557C22×D71—22no—
558C22×D71C2516yes—
559C22×D71C2511yescharacteristic
560C22×D71C2511yescharacteristic
561Q8×C71—26no—
562Q8×C71—212no—
563Q8×C71—22no—
564Q8×C71—46no—
565Q8×C71C2×#4114yes—
566D4×C71—24no—
567D4×C71—22no—
568C2×C4×C71—26no—
569C2×C4×C71—212no—
570C2×C4×C71—24no—
571C2×C4×C71—43no—
572C2×C4×C71—46no—
573C2×C4×C712−1+414yescomplemented
574C2×C4×C71C2512yes—
575C2×C4×C71C2513yes—
576C2×C4×C71C2513yes—
577C2×C4×C71C2516yes—
578C2×C4×C71C2516yes—
579C2×C4×C71C2513yes—
580C2×C4×C71C2513yes—
581C2×C4×C71C2511yescharacteristic
582C2×C4×C71C2511yescharacteristic
583C22⋊D71—212no—
584C22⋊D71—24no—
585C22⋊D71—24no—
586C22⋊D71—212no—
587C22⋊D71—46no—
588C2×Dic71—22no—
589C2×Dic71—26no—
590C2×Dic71—43no—
591C2×Dic71C2511yescharacteristic
592C2×Dic71C2511yescharacteristic
593C2×Dic71C2513yes—
594C2×Dic71C2516yes—
595C2×Dic71C2513yes—
596C2×Dic71C2512yes—
597C2×Dic71C2512yes—
598C2×Dic71C2513yes—
599C2×Dic71C2513yes—
600D284—212no—
601D284—212no—
602D284—212no—
603D284—26no—
604D284—46no—
605C4×D71—26no—
606C4×D71—26no—
607C4×D71—26no—
608C4×D71—26no—
609C4×D71—212no—
610C4×D71—22no—
611C4×D71—22no—
612C4×D71—22no—
613C4×D71—22no—
614C4×D71—212no—
615C4×D71—26no—
616C4×D71—224no—
617C4×D71—43no—
618C4×D71—43no—
619C4×D71—46no—
620C4×D71—412no—
621C4×D71C2×#41112yes—
622Dic142—26no—
623Dic142—26no—
624Dic142—212no—
625Dic142—212no—
626Dic142—46no—
627Dic142C2×#41112yes—
628C22×C71—21no—
629C22×C71—21no—
630C22×C71—22no—
631C22×C71—22no—
632C22×C71—22no—
633C22×C71C2×2−1+412yes—
634C22×C71C2611yescharacteristic
635C2×D71—28no—
636C2×D71—21no—
637C2×D71—21no—
638C2×D71—21no—
639C2×D71—21no—
640C2×D71—26no—
641C2×D71—26no—
642C2×D71—26no—
643C2×D71C22×#4112yes—
644C2×D71#58512yes—
645C4×C71—23no—
646C4×C71—26no—
647C4×C71—22no—
648C4×C71—26no—
649C4×C71—23no—
650C4×C71—23no—
651C4×C71C22×#4116yes—
652C4×C71C2×2−1+412yes—
653C4×C71C2×2−1+412yes—
654Dic71—23no—
655Dic71—22no—
656Dic71—26no—
657Dic71—21no—
658Dic71—21no—
659Dic71—22no—
660Dic71—23no—
661Dic71—23no—
662Dic71C22×#4116yes—
663#62788—711nomaximal, Sylow
664C2×C71—22no—
665C2×C71—42no—
666C2×C71C23×#4111yescharacteristic
667C2×C71C22×2−1+411yescharacteristic
668C2×C71C2×#58511yescharacteristic
669D71—22no—
670D71—22no—
671D71—46no—
672#3523—713no—
673#3523—711no—
674#3522—711no—
675#3522—713no—
676#3516—716no—
677#3516—712no—
678#3507—713no—
679#3507—713no—
680#3502—711no—
681#3497—711no—
682#3492—716no—
683#3486—712no—
684#3482—716no—
685#3482—712no—
686#3480—713no—
687#3480—711no—
688Q8×#41—713no—
689Q8×#41D7111yescharacteristic, complemented
690#3461—716no—
691#3444—713no—
692#3444—713no—
693C4×2−1+4—712no—
694C22×C4×Q8—711no—
695C71#6278811yescharacteristic, complemented, Sylow
696C2×2−1+4—712no—
697C23×Q8—711no—
698#559—713no—
699#559—713no—
700#559—716no—
701Q82—713no—
702Q82C2×D7111yescharacteristic, complemented
703#557—713no—
704#557—716no—
705#557—716no—
706#557—713no—
707#557—711no—
708#557—712no—
709#557C2×D7113yescomplemented
710#556—716no—
711#556—7112no—
712#556—716no—
713#556—713no—
714#556—716no—
715#556—713no—
716#554—713no—
717#554—716no—
718#554—7112no—
719#554—716no—
720#554C2×D7116yes—
721#554C2×D7113yescomplemented
722#553—716no—
723#553—7112no—
724#553—716no—
725#552—7112no—
726#552—7112no—
727#552—716no—
728#552—716no—
729#552—716no—
730#552—716no—
731#550—711no—
732#550—713no—
733D4×Q8—712no—
734D4×Q8—716no—
735D4×Q8—713no—
736D4×Q8—716no—
737D4×Q8C2×D7112yes—
738D4×Q8C2×D7111yescharacteristic, complemented
739#548—712no—
740#548—712no—
741#548—716no—
742#548—716no—
743#548—712no—
744#548—716no—
745#547—716no—
746#547—7112no—
747#547—716no—
748#544—716no—
749#542—716no—
750#542—7112no—
751#542—716no—
752#541—716no—
753#541—7112no—
754#541—716no—
755#539—7112no—
756#539—7112no—
757#537—716no—
758#536—716no—
759#536—716no—
760#533—713no—
761#533—713no—
762#533—713no—
763#533—713no—
764#533—7112no—
765#533—716no—
766#533—713no—
767#533C2×D7113yes—
768#533C2×D7116yescomplemented
769#532—713no—
770#532—713no—
771#532—713no—
772#532—713no—
773#532—713no—
774#532—713no—
775#529—716no—
776#529—716no—
777#529—716no—
778#529—716no—
779#529—716no—
780#529—716no—
781#529—713no—
782#529—713no—
783#529—716no—
784#529—713no—
785#529—716no—
786#529—716no—
787#529—713no—
788#529—716no—
789#529—716no—
790#529—7112no—
791#529—716no—
792#525—711no—
793#525—716no—
794#525—716no—
795#525—716no—
796#525—716no—
797#525—713no—
798#520—716no—
799#520—712no—
800#520—716no—
801#520—716no—
802#519—712no—
803#519—712no—
804#519—716no—
805C4×#41—716no—
806C4×#41—712no—
807C4×#41—716no—
808C4×#41—716no—
809C4×#41—716no—
810C4×#41—716no—
811C4×#41—713no—
812C4×#41—716no—
813C4×#41C2×D7113yes—
814C2×C4×Q8—711no—
815C2×C4×Q8—711no—
816C2×C4×Q8—713no—
817C2×C4×Q8—711no—
818C2×C4×Q8—713no—
819C2×C4×Q8—711no—
820C2×C4×Q8—713no—
821C2×C4×Q8—711no—
822C2×C4×Q8—713no—
823C2×C4×Q8—716no—
824C2×C4×Q8—713no—
825C2×C4×Q8—713no—
826C2×C4×Q8C2×D7111yescharacteristic
827C2×C4×Q8C2×D7112yescomplemented
828C22×C4⋊C4—713no—
829C22×C42—713no—
8302−1+4—14216no—
831C2×#41—716no—
832C2×#41—716no—
833C2×#41—712no—
834C2×#41—716no—
835C2×#41—713no—
836C2×#41—716no—
837C2×#41—716no—
838C2×#41C22×D7111yescharacteristic
839C22×Q8—711no—
840C22×Q8—713no—
841C22×Q8—713no—
842C22×Q8—711no—
843C22×Q8—716no—
844C22×Q8—713no—
845C22×Q8—1428no—
846C22×Q8C22×D7111yescharacteristic
847C22×Q8C22×D7112yes—
848C23×C4—713no—
849C23×C4—713no—
850C23×C4—711no—
851C4⋊Q8—713no—
852C4⋊Q8—716no—
853C4⋊Q8—7112no—
854C4⋊Q8—713no—
855C4⋊Q8—713no—
856C4⋊Q8—7112no—
857C4⋊Q8—716no—
858C4⋊Q8—713no—
859C4⋊Q8C22×D7113yes—
860C4⋊Q8C22×D7113yes—
861C4⋊Q8C22×D7116yes—
862C4⋊Q8C22×D7116yes—
863#127—713no—
864#127—713no—
865#126—716no—
866#126—7112no—
867#126—716no—
868#126—7112no—
869#126—7112no—
870#126—7112no—
871#126—716no—
872#126—716no—
873#126—7112no—
874#126—7112no—
875#125—716no—
876#125—716no—
877#125—716no—
878#125—716no—
879#125—713no—
880#125—713no—
881#125—7112no—
882#125—716no—
883#125—7112no—
884#125—7112no—
885#125—7112no—
886#125—716no—
887#125C22×D7116yes—
888#125C22×D71112yes—
889#124—716no—
890#124—716no—
891#124—713no—
892#124—716no—
893#124—713no—
894#124—716no—
895#124—716no—
896#124—7112no—
897#124—716no—
898#124—716no—
899#123—712no—
900#123—7112no—
901#123—716no—
902#123—7112no—
903#123—716no—
904#123—7112no—
905#123—7112no—
906#123—7112no—
907#123—716no—
908#123—716no—
909#123—716no—
910#123—7112no—
911C22⋊Q8—711no—
912C22⋊Q8—711no—
913C22⋊Q8—716no—
914C22⋊Q8—716no—
915C22⋊Q8—716no—
916C22⋊Q8—716no—
917C22⋊Q8—7112no—
918C22⋊Q8—716no—
919C22⋊Q8—713no—
920C22⋊Q8—713no—
921C22⋊Q8—716no—
922C22⋊Q8—716no—
923C22⋊Q8—7112no—
924C22⋊Q8—7112no—
925C22⋊Q8—716no—
926C22⋊Q8—7112no—
927C22⋊Q8—7112no—
928C22⋊Q8—7112no—
929C22⋊Q8—716no—
930C22⋊Q8—716no—
931C22⋊Q8C22×D7116yes—
932C22⋊Q8C22×D7116yes—
933C22⋊Q8C22×D7116yes—
934C22⋊Q8C22×D7116yes—
935C22⋊Q8C22×D71112yes—
936#121—711no—
937#121—711no—
938#121—716no—
939#121—716no—
940#121—716no—
941#121—716no—
942#121—716no—
943#121—713no—
944#121—713no—
945#121—716no—
946#121—716no—
947#121—716no—
948#121—716no—
949#121—716no—
950#121—7112no—
951#120—712no—
952#120—716no—
953C4×Q8—711no—
954C4×Q8—713no—
955C4×Q8—711no—
956C4×Q8—713no—
957C4×Q8—716no—
958C4×Q8—716no—
959C4×Q8—712no—
960C4×Q8—716no—
961C4×Q8—713no—
962C4×Q8—716no—
963C4×Q8—713no—
964C4×Q8—713no—
965C4×Q8—716no—
966C4×Q8—713no—
967C4×Q8—716no—
968C4×Q8—7112no—
969C4×Q8—716no—
970C4×Q8—716no—
971C4×Q8—713no—
972C4×Q8—716no—
973C4×Q8—713no—
974C4×Q8—713no—
975C4×Q8—713no—
976C4×Q8—716no—
977C4×Q8—716no—
978C4×Q8—716no—
979C4×Q8—716no—
980C4×Q8—716no—
981C4×Q8—716no—
982C4×Q8—713no—
983C4×Q8—713no—
984C4×Q8C22×D7111yescharacteristic
985C4×Q8C22×D7113yes—
986C4×Q8C22×D7111yescharacteristic
987C4×Q8C22×D7113yes—
988C4×Q8C22×D7116yes—
989C4×Q8C22×D7112yes—
990C4×Q8C22×D7116yes—
991C4×Q8C22×D7116yes—
992C4×Q8C22×D7113yes—
993C4×Q8C22×D7113yes—
994C4×D4—712no—
995C4×D4—712no—
996C4×D4—716no—
997C4×D4—716no—
998C4×D4—716no—
999C4×D4—7112no—
1000C4×D4—716no—
1001C4×D4—716no—
1002C4×D4—716no—
1003C4×D4—716no—
1004C4×D4—716no—
1005C4×D4—7112no—
1006C4×D4—716no—
1007C4×D4—716no—
1008C4×D4—7112no—
1009C4×D4—716no—
1010C4×D4—716no—
1011C4×D4—716no—
1012C4×D4—7112no—
1013C4×D4—7112no—
1014C4×D4—716no—
1015C4×D4—716no—
1016C4×D4—716no—
1017C4×D4—716no—
1018C4×D4—716no—
1019C4×D4—716no—
1020C4×D4—716no—
1021C4×D4—713no—
1022C4×D4—713no—
1023C4×D4C22×D7116yes—
1024C4×D4C22×D7116yes—
1025C4×D4C22×D7113yes—
1026C4×D4C22×D7113yes—
1027#117—711no—
1028#117—716no—
1029#117—716no—
1030#117—716no—
1031#117—716no—
1032#117—7112no—
1033#117—716no—
1034#117—716no—
1035#117—7112no—
1036#117—716no—
1037#117—716no—
1038#117—7112no—
1039#117—716no—
1040#117—7112no—
1041#117—716no—
1042#117—716no—
1043#117C22×D7113yes—
1044#117C22×D7116yes—
1045C2×C4⋊C4—716no—
1046C2×C4⋊C4—713no—
1047C2×C4⋊C4—713no—
1048C2×C4⋊C4—713no—
1049C2×C4⋊C4—716no—
1050C2×C4⋊C4—716no—
1051C2×C4⋊C4—713no—
1052C2×C4⋊C4—713no—
1053C2×C4⋊C4—7112no—
1054C2×C4⋊C4—716no—
1055C2×C4⋊C4C22×D7113yes—
1056C2×C4⋊C4C22×D7116yes—
1057C2×C42—713no—
1058C2×C42—713no—
1059C2×C42—713no—
1060C2×C42—713no—
1061C2×C42—713no—
1062C2×C42—713no—
1063C2×C42—713no—
1064C2×C42—713no—
1065C2×C42—713no—
1066C2×C42—713no—
1067C2×C42—713no—
1068C2×C42—7112no—
1069C2×C42—716no—
1070C2×C42C22×D7113yes—
1071C2×C42C22×D7116yes—
1072C24—711no—
1073#41—24no—
1074#41—28412no—
1075#41—28412no—
1076#41—14224no—
1077#41—14224no—
1078#41—14224no—
1079#41—1428no—
1080#41—14212no—
1081C2×Q8—24no—
1082C2×Q8—28no—
1083C2×Q8—718no—
1084C2×Q8—716no—
1085C2×Q8—713no—
1086C2×Q8—713no—
1087C2×Q8—716no—
1088C2×Q8—713no—
1089C2×Q8—716no—
1090C2×Q8—14212no—
1091C2×Q8—14212no—
1092C2×Q8—14212no—
1093C2×Q8—14224no—
1094C2×Q8—1424no—
1095C2×Q8C23×D7113yes—
1096C2×Q8C23×D7116yes—
1097C2×Q8C23×D7111yescharacteristic
1098C2×Q8C23×D7116yes—
1099C2×Q8C23×D7111yescharacteristic
1100C2×D4—716no—
1101C2×D4—716no—
1102C2×D4—712no—
1103C2×D4—712no—
1104C2×D4—716no—
1105C2×D4—716no—
1106C2×D4—713no—
1107C2×D4—716no—
1108C2×D4—716no—
1109C2×D4—716no—
1110C2×D4C23×D7112yes—
1111C2×D4C23×D7111yescharacteristic
1112C22×C4—2846no—
1113C22×C4—713no—
1114C22×C4—713no—
1115C22×C4—713no—
1116C22×C4—7112no—
1117C22×C4—716no—
1118C22×C4—713no—
1119C22×C4—711no—
1120C22×C4—713no—
1121C22×C4—711no—
1122C22×C4—711no—
1123C22×C4—713no—
1124C22×C4—713no—
1125C22×C4—713no—
1126C22×C4—713no—
1127C22×C4—713no—
1128C22×C4—7112no—
1129C22×C4—716no—
1130C22×C4—711no—
1131C22×C4—711no—
1132C22×C4—716no—
1133C22×C4—14212no—
1134C22×C4—1424no—
1135C22×C4C23×D7113yes—
1136C22×C4C23×D7116yes—
1137C22×C4C23×D7112yes—
1138C22×C4C23×D7113yes—
1139C22×C4C23×D7116yes—
1140C22×C4C23×D7111yescharacteristic
1141C4⋊C4—716no—
1142C4⋊C4—716no—
1143C4⋊C4—716no—
1144C4⋊C4—716no—
1145C4⋊C4—716no—
1146C4⋊C4—716no—
1147C4⋊C4—716no—
1148C4⋊C4—712no—
1149C4⋊C4—712no—
1150C4⋊C4—716no—
1151C4⋊C4—716no—
1152C4⋊C4—716no—
1153C4⋊C4—7112no—
1154C4⋊C4—716no—
1155C4⋊C4—716no—
1156C4⋊C4—7112no—
1157C4⋊C4—713no—
1158C4⋊C4—713no—
1159C4⋊C4—716no—
1160C4⋊C4—716no—
1161C4⋊C4—716no—
1162C4⋊C4—716no—
1163C4⋊C4—716no—
1164C4⋊C4—711no—
1165C4⋊C4—711no—
1166C4⋊C4—716no—
1167C4⋊C4—716no—
1168C4⋊C4C23×D7113yes—
1169C4⋊C4C23×D7113yes—
1170C4⋊C4C23×D7116yes—
1171C4⋊C4C23×D7116yes—
1172C4⋊C4C23×D71112yes—
1173C4⋊C4C23×D7116yes—
1174C4⋊C4C23×D71112yes—
1175C4⋊C4C23×D7113yes—
1176C4⋊C4C23×D7113yes—
1177C4⋊C4C23×D7116yes—
1178C4⋊C4C23×D7116yes—
1179C22⋊C4—716no—
1180C22⋊C4—712no—
1181C22⋊C4—712no—
1182C22⋊C4—712no—
1183C22⋊C4—716no—
1184C22⋊C4—716no—
1185C22⋊C4—716no—
1186C22⋊C4—712no—
1187C22⋊C4—712no—
1188C22⋊C4—716no—
1189C22⋊C4—7112no—
1190C22⋊C4—716no—
1191C22⋊C4—716no—
1192C22⋊C4—716no—
1193C22⋊C4—7112no—
1194C22⋊C4—7112no—
1195C22⋊C4—716no—
1196C22⋊C4—7112no—
1197C22⋊C4—716no—
1198C22⋊C4C23×D7116yes—
1199C22⋊C4C23×D7116yes—
1200C22⋊C4C23×D7116yes—
1201C42—713no—
1202C42—713no—
1203C42—713no—
1204C42—713no—
1205C42—713no—
1206C42—713no—
1207C42—713no—
1208C42—713no—
1209C42—713no—
1210C42—713no—
1211C42—7112no—
1212C42—716no—
1213C42—7112no—
1214C42—716no—
1215C42—713no—
1216C42—713no—
1217C42—712no—
1218C42C23×D7113yes—
1219C42C23×D7113yes—
1220C42C23×D7116yes—
1221C42C23×D7116yes—
1222C42C23×D7113yes—
1223C42C23×D7113yes—
1224C42C23×D7116yes—
1225C23—711no—
1226C23—711no—
1227C23—716no—
1228C23—1422no—
1229C23—1422no—
1230C23—1422no—
1231C23C24×D7112yes—
1232C23C24×D7111yescharacteristic
1233Q8—26no—
1234Q8—212no—
1235Q8—22no—
1236Q8—46no—
1237Q8—2846no—
1238Q8—7112no—
1239Q8—14212no—
1240Q8—14212no—
1241Q8—1426no—
1242Q8—1426no—
1243Q8#41×D7114yes—
1244D4—24no—
1245D4—22no—
1246D4—2846no—
1247D4—2846no—
1248D4—14212no—
1249D4—14212no—
1250D4—14212no—
1251D4—1424no—
1252D4—1424no—
1253D4—14212no—
1254D4—14212no—
1255D4—1426no—
1256C2×C4—26no—
1257C2×C4—212no—
1258C2×C4—24no—
1259C2×C4—43no—
1260C2×C4—46no—
1261C2×C4—2843no—
1262C2×C4—2843no—
1263C2×C4—2846no—
1264C2×C4—28412no—
1265C2×C4—2843no—
1266C2×C4—713no—
1267C2×C4—7112no—
1268C2×C4—711no—
1269C2×C4—711no—
1270C2×C4—713no—
1271C2×C4—716no—
1272C2×C4—713no—
1273C2×C4—712no—
1274C2×C4—712no—
1275C2×C4—713no—
1276C2×C4—1426no—
1277C2×C4—14224no—
1278C2×C4—1426no—
1279C2×C4—1426no—
1280C2×C4—1426no—
1281C2×C4—1426no—
1282C2×C4—1422no—
1283C2×C4—1426no—
1284C2×C4—14212no—
1285C2×C4—1422no—
1286C2×C4—1422no—
1287C2×C4—1422no—
1288C2×C4—1422no—
1289C2×C4—14212no—
1290C2×C4#1455617614yescomplemented
1291C2×C4C24×D7113yes—
1292C2×C4C24×D7113yes—
1293C2×C4C24×D7116yes—
1294C2×C4C24×D7116yes—
1295C2×C4C24×D7113yes—
1296C2×C4C24×D7112yes—
1297C2×C4C24×D7113yes—
1298C2×C4C24×D7111yescharacteristic
1299C2×C4C24×D7111yescharacteristic
1300C22—21no—
1301C22—21no—
1302C22—22no—
1303C22—22no—
1304C22—22no—
1305C22—712no—
1306C22—712no—
1307C22—1428no—
1308C22—1426no—
1309C22—1426no—
1310C22—1426no—
1311C22—1421no—
1312C22—1421no—
1313C22—1421no—
1314C22—1421no—
1315C22C2×#1455617612yes—
1316C22C25×D7111yescharacteristic
1317C4—26no—
1318C4—23no—
1319C4—22no—
1320C4—23no—
1321C4—26no—
1322C4—23no—
1323C4—716no—
1324C4—1422no—
1325C4—1423no—
1326C4—1421no—
1327C4—1421no—
1328C4—1426no—
1329C4—1423no—
1330C4—1422no—
1331C4—1423no—
1332C4C2×#41×D7116yes—
1333C4C2×#1455617612yes—
1334C4C2×#1455617612yes—
1335C2—22no—
1336C2—42no—
1337C2—2846no—
1338C2—1422no—
1339C2—1422no—
1340C2C22×#41×D7111yescharacteristic
1341C2C22×#1455617611yescharacteristic
1342C2#585×D7111yescharacteristic
subgroupG/H
centerC2×C4C24×D71
commutator, socle, cosocleC22×C71C26
FrattiniC22C25×D71
FittingQ8×#41×C71C2
hypercenterQ8×#41D71
hypocenterC71#62788
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. #22602433C2semidirect
2. #22602431C2semidirect
3. #22602426C2semidirect
4. #22602424C2semidirect
5. #22602334C2semidirect
6. #22602330C2semidirect
7. #22602206C2semidirect
8. #22602203C2semidirect
9. #22602149C2semidirect
10. #22602110C2semidirect
11. #22602048C2semidirect
12. #22601990C2semidirect
13. #22601958C2semidirect
14. #22601957C2semidirect
15. #22601935C2semidirect
16. #22601933C2semidirect
17. #22601918C2semidirect
18. #22601771C2semidirect
19. #22601637C2semidirect
20. #22601633C2semidirect
21. C4×#14556176C2semidirect
22. C2×C4×Q8×D71C2semidirect
23. Q8×#41×C71C2semidirect
26. #17986734C22semidirect
27. #17986734C22semidirect
28. #17986732C22semidirect
29. #17986729C22semidirect
30. #17986728C22semidirect
31. #17986727C22semidirect
32. #17986726C22semidirect
33. #17986725C22semidirect
34. #17986724C22semidirect
35. #17986724C22semidirect
36. #17986723C22semidirect
37. #17986722C22semidirect
38. #17986721C22semidirect
39. #17986721C22semidirect
40. #17986720C22semidirect
41. #17986719C22semidirect
42. #17986710C22semidirect
44. #17986705C22semidirect
50. #17986684C22semidirect
52. #17986683C22semidirect
54. #17986681C22semidirect
55. #17986671C22semidirect
56. #17986670C22semidirect
58. #17986664C22semidirect
63. #17986660C22semidirect
65. #17986659C22semidirect
71. #17986623C22semidirect
72. #17986622C22semidirect
73. #17986619C22semidirect
74. #17986610C22semidirect
75. #17986609C22semidirect
76. #17986608C22semidirect
86. #17986553C22semidirect
87. #17986553C22semidirect
99. #17986536C22semidirect
104. #17986533C22semidirect
111. #17986527C22semidirect
119. #17986481C22semidirect
121. #17986480C22semidirect
122. #17986477C22semidirect
124. #17986475C22semidirect
127. C4×#11765866C22semidirect
131. C4×#11765865C22semidirect
144. C4×Q8×D71C22semidirect
147. Q82×C71C22semidirect
148. #557×C71C22semidirect
150. #554×C71C22semidirect
152. D4×Q8×C71C22semidirect
154. #533×C71C22semidirect
157. C2×C4×Q8×C71C22semidirect
419. Q8×D71#41semidirect
573. C2×C4×C712−1+4semidirect
689. Q8×#41D71semidirect
695. C71#62788semidirect
702. Q82C2×D71semidirect
709. #557C2×D71semidirect
721. #554C2×D71semidirect
738. D4×Q8C2×D71semidirect
768. #533C2×D71semidirect
827. C2×C4×Q8C2×D71semidirect
1290. C2×C4#14556176semidirect

Maximal subgroups

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

subgroupindex
#226024332
#226024312
#226024262
#226024242
#226023342
#226023302
#226022062
#226022032
#226021492
#226021102
#226020482
#226019902
#226019582
#226019572
#226019352
#226019332
#226019182
#226017712
#226016372
#226016332
C4×#145561762
C2×C4×Q8×D712
Q8×#41×C712
#6278871