Finite Group Databasebeta

← #32905996

Subgroups — #32905996

Order 18176.

11346 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986834C212yesmaximal, complemented
2#22602132C216yesmaximal, complemented
3#22602128C212yesmaximal, complemented
4#22602125C211yesmaximal, characteristic, complemented
5#22602120C213yesmaximal, complemented
6#22602116C213yesmaximal, complemented
7#22602105C214yesmaximal, complemented
8#22602096C2112yesmaximal, complemented
9#22601830C214yesmaximal, complemented
10D4×#11765864C2112yesmaximal, complemented
11#22601671C216yesmaximal, complemented
12C2×#17986547C213yesmaximal, complemented
13#532×D71C213yesmaximal, complemented
14C4×#41×D71C211yesmaximal, characteristic, complemented
15C71×#3498C211yesmaximal, characteristic, complemented
16#17986834—232no—
17C2×#14556175C2214yescomplemented
18C2×#14556175C2216yescomplemented
19C2×#14556175C2212yescomplemented
20C2×#14556173C22112yescomplemented
21C2×#14556173C2216yescomplemented
22C22×#11765864C22112yescomplemented
23C22×#11765864C2216yescomplemented
24C2×#41×D71C2211yescharacteristic
25C2×#41×D71C2214yescomplemented
26C2×#41×D71C2216yescomplemented
27#17986669C22112yescomplemented
28Q8×D284C2214yescomplemented
29D4×Dic142C22112yescomplemented
30#17986656C2218yescomplemented
31#17986655C22124yescomplemented
32#17986654C22112yescomplemented
33#17986653C22112yescomplemented
34#17986649C22124yescomplemented
35#17986646C22124yescomplemented
36#17986643C22124yescomplemented
37#17986636C22148yescomplemented
38#17986634C22112yescomplemented
39D4×C22⋊D71C22124yescomplemented
40#17986578C22124yescomplemented
41#17986575C2216yescomplemented
42#17986570C2216yescomplemented
43#17986569C22112yescomplemented
44#17986566C2216yescomplemented
45#17986562C22112yescomplemented
46#17986559C22124yescomplemented
47#17986550C2211yescharacteristic, complemented
48#17986549C2213yescomplemented
49#17986548C2216yescomplemented
50#17986547C22112yescomplemented
51#17986547C22112yescomplemented
52#17986547C2216yescomplemented
53#17986547C2213yescomplemented
54#17986547C2216yescomplemented
55#17986547C2216yescomplemented
56#17986546C22112yescomplemented
57#17986545C2216yescomplemented
58#17986544C22112yescomplemented
59C2×#14556128C2213yescomplemented
60C4⋊Q8×D71C2213yescomplemented
61#127×D71C2213yescomplemented
62C2×#14556115C2216yescomplemented
63#124×D71C2216yescomplemented
64#17986509C22124yescomplemented
65#17986505C22124yescomplemented
66C2×#14556099C22112yescomplemented
67#121×D71C22112yescomplemented
68#41×Dic71C2211yescharacteristic, complemented
69C4×#11765866C2212yescomplemented
70C4×#11765865C2213yescomplemented
71#17986467C2213yescomplemented
72C4×#11765864C2216yescomplemented
73C4×Q8×D71C2212yescomplemented
74C2×D4×Dic71C22112yescomplemented
75C4×D4×D71C2216yescomplemented
76C4×D4×D71C22112yescomplemented
77#117×D71C2213yescomplemented
78C2×C42×D71C2213yescomplemented
79C2×H(5,𝔽2)×C71C2212yescomplemented
80#550×C71C2214yescomplemented
81D42×C71C22112yescomplemented
82#535×C71C2216yescomplemented
83#532×C71C2213yescomplemented
84C2×#127×C71C2213yescomplemented
85C4×#41×C71C2211yescharacteristic, complemented
86#14556175—248no—
87#14556175—232no—
88#14556175—216no—
89#14556173—248no—
90#14556173—296no—
91C2×#11765866C2312yes—
92C2×#11765866C2311yescharacteristic
93C2×#11765865C2316yes—
94C2×#11765865C23112yes—
95C2×#11765865C23112yes—
96C2×#11765865C2313yes—
97C2×#11765864—296no—
98C2×#11765864—248no—
99C2×#11765864C23112yes—
100C2×#11765864C23112yes—
101C2×#11765864C23112yes—
102C2×#11765864C2316yes—
103C2×#11765864C23112yes—
104C2×#11765864C23124yes—
105C2×#11765864C23112yes—
106C2×#11765864C23112yes—
107C2×#11765864C2313yes—
108#41×D71—232no—
109#41×D71—248no—
110#41×D71D4116yescomplemented
111C22×Dic142C2316yes—
112C22×Dic142C23112yes—
113C2×Q8×D71C2316yes—
114C2×Q8×D71C2314yes—
115C2×Q8×D71C2311yescharacteristic
116C22×C22⋊D71C23124yes—
117C22×C22⋊D71C23112yes—
118C2×D4×D71C2316yes—
119C2×D4×D71C23112yes—
120C2×D4×D71C23112yes—
121C2×D4×D71C23112yes—
122C2×D4×D71C2313yes—
123C23×Dic71C23112yes—
124C22×C4×D71C23112yes—
125C22×C4×D71C2316yes—
126C22×C4×D71C2313yes—
127#14556128C2316yes—
128#14556128C23112yes—
129#14556128C2313yes—
130#14556127C23112yes—
131#14556126C2316yes—
132#14556125C2311yescharacteristic
133#14556124C2316yes—
134#14556124C23112yes—
135#14556117C2312yes—
136#14556116C2316yes—
137#14556115C23112yes—
138#14556115C23124yes—
139#14556115C2316yes—
140#14556114C23124yes—
141#14556112C23124yes—
142#14556110C23148yes—
143#14556109C23124yes—
144#14556108C23124yes—
145#14556107C23124yes—
146#14556105C23148yes—
147#14556103C2314yes—
148#14556102C23112yes—
149#14556101C23124yes—
150#14556100C23148yes—
151#14556100C23124yes—
152#14556099C23124yes—
153#14556099C23124yes—
154#14556099C23124yes—
155#14556099C23124yes—
156#14556099C23112yes—
157#14556097C23124yes—
158#14556096C23148yes—
159Q8×Dic71C2312yes—
160C4×Dic142C2316yes—
161#14556093C2316yes—
162C4×D284C2316yes—
163C4×D284C23112yes—
164D4×Dic71C23124yes—
165D4×Dic71C23124yes—
166D4×Dic71C2316yes—
167D4×Dic71C23112yes—
168D4×Dic71C23124yes—
169#14556090C2316yes—
170#14556090C2314yes—
171C4×C22⋊D71C23112yes—
172C4×C22⋊D71C23124yes—
173(C22⋊D71)⋊C4C23112yes—
174(C22⋊D71)⋊C4C23124yes—
175#14556087C2313yes—
176#14556086C2316yes—
177#14556085C2316yes—
178#14556084C2316yes—
179C2×C4⋊Dic71C23112yes—
180C4⋊C4×D71C2316yes—
181C4⋊C4×D71C23112yes—
182C2×C22⋊Dic71C23124yes—
183C22⋊C4×D71C23124yes—
184C22⋊C4×D71C2316yes—
185C2×C4×Dic71C2316yes—
186C2×C4×Dic71C2313yes—
187C42×D71C2311yescharacteristic
188C42×D71C2313yes—
189C42×D71C2316yes—
190C42×D71C2316yes—
191C42×D71C2313yes—
192C42×D71C2313yes—
193H(5,𝔽2)×C71—216no—
194C2×#41×C71C2316yes—
195C2×#41×C71C2314yes—
196C2×#41×C71C2311yescharacteristic
197C22×D4×C71C2316yes—
198C22×D4×C71C23112yes—
199C22×D4×C71C23112yes—
200C4⋊Q8×C71C2311yescharacteristic
201#127×C71C2316yes—
202#127×C71C23112yes—
203#127×C71C2313yes—
204#124×C71C2316yes—
205#121×C71C23124yes—
206#121×C71C23112yes—
207#120×C71C23124yes—
208C4×Q8×C71C2312yes—
209C4×D4×C71C2316yes—
210C4×D4×C71C23112yes—
211#117×C71C2313yes—
212C2×C42×C71C2313yes—
213C23×D71C24112yes—
214C23×D71C2413yes—
215#11765866—28no—
216#11765866C2×D418yescomplemented
217#11765865—224no—
218#11765865—248no—
219#11765865—248no—
220#11765865C2×D4124yescomplemented
221#11765864—248no—
222#11765864—296no—
223#11765864—248no—
224#11765864—248no—
225#11765864—224no—
226#11765864—248no—
227#11765864—248no—
228#11765864—248no—
229#11765864C2×D4124yescomplemented
230C2×Dic142—224no—
231C2×Dic142—248no—
232C2×Dic142C24112yes—
233C2×Dic142C24112yes—
234C2×Dic142C2416yes—
235C2×Dic142C2413yes—
236Q8×D71—216no—
237Q8×D71—224no—
238Q8×D71C2×D418yescomplemented
239C2×D284C2414yes—
240C2×D284C2412yes—
241C2×D284C2414yes—
242C2×D284C2413yes—
243C2×C22⋊D71—248no—
244C2×C22⋊D71—296no—
245C2×C22⋊D71C24124yes—
246C2×C22⋊D71C24112yes—
247C2×C22⋊D71C24112yes—
248C2×C22⋊D71C24112yes—
249C2×C22⋊D71C24124yes—
250C2×C22⋊D71C2416yes—
251D4×D71—248no—
252D4×D71—248no—
253D4×D71—224no—
254D4×D71—424no—
255D4×D71C2×D4124yescomplemented
256C22×Dic71—248no—
257C22×Dic71C24112yes—
258C22×Dic71C24112yes—
259C22×Dic71C24124yes—
260C22×Dic71C2416yes—
261C22×Dic71C2413yes—
262C2×C4×D71—248no—
263C2×C4×D71—412no—
264C2×C4×D71C2×D4124yescomplemented
265C2×C4×D71C2414yes—
266C2×C4×D71C2412yes—
267C2×C4×D71C2416yes—
268C2×C4×D71C24112yes—
269C2×C4×D71C24112yes—
270C2×C4×D71C2416yes—
271C2×C4×D71C2416yes—
272C2×C4×D71C2413yes—
273C2×C4×D71C2411yescharacteristic
274C2×C4×D71C2413yes—
275C2×C4×D71C2413yes—
276C4⋊Dic71C24112yes—
277C4⋊Dic71C2416yes—
278C4⋊Dic71C24124yes—
279Dic71⋊C4C24112yes—
280Dic71⋊C4C24124yes—
281C22⋊Dic71C24124yes—
282C22⋊Dic71C2416yes—
283C22⋊Dic71C24148yes—
284(C2×D71)⋊C4C2418yes—
285(C2×D71)⋊C4C24112yes—
286(C2×D71)⋊C4C24124yes—
287C4×Dic71C2412yes—
288C4×Dic71C2411yescharacteristic
289C4×Dic71C2416yes—
290C4×Dic71C2413yes—
291C4×Dic71C2416yes—
292C4×Dic71C2416yes—
293C4×Dic71C2416yes—
294C24×C71C24112yes—
295#41×C71—216no—
296#41×C71—224no—
297#41×C71C2×D418yescomplemented
298C2×Q8×C71C2412yes—
299C2×Q8×C71C2411yescharacteristic
300C2×D4×C71—248no—
301C2×D4×C71—224no—
302C2×D4×C71—424no—
303C2×D4×C71C24112yes—
304C2×D4×C71C24112yes—
305C2×D4×C71C2416yes—
306C2×D4×C71C24112yes—
307C2×D4×C71C24124yes—
308C2×D4×C71C2413yes—
309C22×C4×C71C24112yes—
310C22×C4×C71C2416yes—
311C22×C4×C71C2413yes—
312C4⋊C4×C71C2416yes—
313C4⋊C4×C71C2414yes—
314C22⋊C4×C71C2416yes—
315C22⋊C4×C71C24124yes—
316C42×C71C2411yescharacteristic
317C42×C71C2413yes—
318C42×C71C2416yes—
319C23×C71—224no—
320C23×C71—424no—
321C23×C71C25112yes—
322C23×C71C2513yes—
323C22×D71—224no—
324C22×D71—46no—
325C22×D71—424no—
326C22×D71C22×D4112yes—
327C22×D71C2514yes—
328C22×D71C2513yes—
329C22×D71C2511yescharacteristic
330Q8×C71—24no—
331Q8×C71C22×D414yes—
332D4×C71—224no—
333D4×C71—212no—
334D4×C71—224no—
335D4×C71—224no—
336D4×C71—424no—
337D4×C71C22×D4112yes—
338C2×C4×C71—224no—
339C2×C4×C71—212no—
340C2×C4×C71C22×D4112yes—
341C2×C4×C71C2516yes—
342C2×C4×C71C2514yes—
343C2×C4×C71C2511yescharacteristic
344C2×C4×C71C2513yes—
345C2×C4×C71C2512yes—
346C22⋊D71—224no—
347C22⋊D71—248no—
348C22⋊D71—224no—
349C22⋊D71—224no—
350C22⋊D71—424no—
351C22⋊D71C22×D4124yes—
352C2×Dic71—224no—
353C2×Dic71—224no—
354C2×Dic71—248no—
355C2×Dic71—46no—
356C2×Dic71C22×D4112yes—
357C2×Dic71C2512yes—
358C2×Dic71C2516yes—
359C2×Dic71C25112yes—
360C2×Dic71C2511yescharacteristic
361C2×Dic71C2513yes—
362D284—28no—
363D284—24no—
364D284—28no—
365D284C22×D4112yes—
366C4×D71—224no—
367C4×D71—224no—
368C4×D71—24no—
369C4×D71—212no—
370C4×D71—28no—
371C4×D71—46no—
372C4×D71—46no—
373C4×D71C22×D4112yes—
374C4×D71C22×D414yes—
375C4×D71C22×D4112yes—
376C4×D71C22×D4112yes—
377Dic142—212no—
378Dic142—224no—
379Dic142—224no—
380Dic142C22×D4112yes—
381C22×C71—26no—
382C22×C71—212no—
383C22×C71—224no—
384C22×C71—824no—
385C22×C71C23×D416yes—
386C22×C71C2611yescharacteristic
387C2×D71—22no—
388C2×D71—26no—
389C2×D71—24no—
390C2×D71—28no—
391C2×D71—412no—
392C2×D71—824no—
393C2×D71C23×D416yes—
394C2×D71C23×D412yes—
395C4×C71—24no—
396C4×C71—26no—
397C4×C71C23×D412yes—
398C4×C71C23×D416yes—
399C4×C71#58514yescomplemented
400Dic71—212no—
401Dic71—22no—
402Dic71—26no—
403Dic71C23×D416yes—
404Dic71C23×D412yes—
405#62812—711nomaximal, Sylow
406C2×C71—26no—
407C2×C71—412no—
408C2×C71C24×D411yescharacteristic
409C2×C71C2×#58512yes—
410D71—22no—
411D71—26no—
412D71—44no—
413C2×#585—712no—
414#3500—712no—
415#3500—716no—
416#3499—713no—
417#3499—711no—
418#3498—713no—
419#3498D7111yescharacteristic, complemented
420#3497—714no—
421#3496—7112no—
422D4×#41—714no—
423D4×#41—7112no—
424#3449—716no—
425C2×#532—713no—
426C2×#532—713no—
427C2×C4×#41—711no—
428C71#6281211yescharacteristic, complemented, Sylow
429#585—14232no—
430C2×2−1+4—714no—
431C2×2−1+4—716no—
432C2×2−1+4—712no—
433C2×H(5,𝔽2)—7112no—
434C2×H(5,𝔽2)—716no—
435C2×H(5,𝔽2)C2×D7112yescomplemented
436C22×#41—711no—
437C22×#41—716no—
438C22×#41—714no—
439C22×#41—716no—
440C22×#41—7112no—
441#550—7112no—
442#550C2×D7114yescomplemented
443D4×Q8—714no—
444D4×Q8—7112no—
445#548—718no—
446#548—7124no—
447#547—7124no—
448#547—7112no—
449#547—7112no—
450#546—7124no—
451#546—7124no—
452#546—7148no—
453D42—7124no—
454D42—7112no—
455D42C2×D71112yescomplemented
456#537—7124no—
457#536—716no—
458#536—7112no—
459#536—716no—
460#535—716no—
461#535—7112no—
462#535C2×D7116yescomplemented
463#534—7124no—
464#532—716no—
465#532—711no—
466#532—713no—
467#532—716no—
468#532—7112no—
469#532—7112no—
470#532—716no—
471#532—716no—
472#532—716no—
473#532—7112no—
474#532—7112no—
475#532—713no—
476#532C2×D7113yescomplemented
477C2×C4⋊Q8—713no—
478C2×C4⋊Q8—713no—
479C2×#127—713no—
480C2×#127C2×D7113yescomplemented
481C2×#124—716no—
482C2×#124—716no—
483#525—7124no—
484#525—7124no—
485C2×#121—7112no—
486C2×#121—7112no—
487C4×#41—711no—
488C4×#41—712no—
489C4×#41—716no—
490C4×#41—713no—
491C4×#41—713no—
492C4×#41C2×D7111yescharacteristic, complemented
493C2×C4×Q8—712no—
494C2×C4×D4—7112no—
495C2×C4×D4—716no—
496C2×C4×D4—7112no—
497C2×#117—713no—
498C22×C42—713no—
4992−1+4—14232no—
5002−1+4—14248no—
5012−1+4—14216no—
502H(5,𝔽2)—216no—
503H(5,𝔽2)—14296no—
504H(5,𝔽2)—14248no—
505C2×#41—7116no—
506C2×#41—711no—
507C2×#41—712no—
508C2×#41—713no—
509C2×#41—7112no—
510C2×#41—7112no—
511C2×#41—716no—
512C2×#41—7112no—
513C2×#41—7112no—
514C2×#41—7112no—
515C2×#41—7124no—
516C2×#41—7112no—
517C2×#41—713no—
518C2×#41—716no—
519C2×#41—7112no—
520C2×#41—7112no—
521C2×#41—14248no—
522C2×#41—14248no—
523C2×#41—14296no—
524C2×#41—14232no—
525C2×#41C22×D7116yes—
526C2×#41C22×D7114yes—
527C2×#41C22×D7111yescharacteristic
528C22×Q8—711no—
529C22×Q8—716no—
530C22×Q8—714no—
531C22×Q8—716no—
532C22×Q8—7112no—
533C22×D4—7112no—
534C22×D4—713no—
535C22×D4—7112no—
536C22×D4—7124no—
537C22×D4—7112no—
538C22×D4—716no—
539C22×D4—7112no—
540C22×D4C22×D7116yes—
541C22×D4C22×D71112yes—
542C22×D4C22×D71112yes—
543C23×C4—716no—
544C23×C4—713no—
545C23×C4—7112no—
546C23×C4—7112no—
547C4⋊Q8—716no—
548C4⋊Q8—7112no—
549C4⋊Q8—713no—
550C4⋊Q8—716no—
551C4⋊Q8—7112no—
552C4⋊Q8C22×D7111yescharacteristic
553#127—716no—
554#127—7112no—
555#127—711no—
556#127C22×D7113yes—
557#127C22×D7116yes—
558#127C22×D71112yes—
559#124—712no—
560#124—716no—
561#124—7112no—
562#124—7124no—
563#124—7124no—
564#124—716no—
565#124C22×D7116yes—
566#123—7124no—
567#123—7148no—
568#123—7124no—
569C22⋊Q8—7124no—
570C22⋊Q8—7124no—
571C22⋊Q8—7148no—
572#121—7112no—
573#121—7124no—
574#121—7124no—
575#121—7124no—
576#121—7124no—
577#121—7124no—
578#121—7148no—
579#121—7112no—
580#121—714no—
581#121—7124no—
582#121C22×D71112yes—
583#121C22×D71124yes—
584#120—7124no—
585#120—7148no—
586#120C22×D71124yes—
587C4×Q8—712no—
588C4×Q8—716no—
589C4×Q8—716no—
590C4×Q8C22×D7112yes—
591C4×D4—7112no—
592C4×D4—716no—
593C4×D4—7124no—
594C4×D4—7124no—
595C4×D4—7124no—
596C4×D4—7112no—
597C4×D4—7124no—
598C4×D4—714no—
599C4×D4—716no—
600C4×D4—7112no—
601C4×D4—7124no—
602C4×D4—716no—
603C4×D4—7112no—
604C4×D4C22×D7116yes—
605C4×D4C22×D71112yes—
606#117—713no—
607#117—716no—
608#117—716no—
609#117—716no—
610#117C22×D7113yes—
611C2×C4⋊C4—7112no—
612C2×C4⋊C4—716no—
613C2×C4⋊C4—7112no—
614C2×C22⋊C4—7124no—
615C2×C22⋊C4—716no—
616C2×C22⋊C4—7124no—
617C2×C42—716no—
618C2×C42—713no—
619C2×C42—713no—
620C2×C42—716no—
621C2×C42—716no—
622C2×C42—713no—
623C2×C42—713no—
624C2×C42—711no—
625C2×C42C22×D7113yes—
626C24—713no—
627C24—7112no—
628C24C23×D71112yes—
629#41—216no—
630#41—224no—
631#41—718no—
632#41—7124no—
633#41—7124no—
634#41—14248no—
635#41—14248no—
636#41—14248no—
637#41—14224no—
638#41—14248no—
639#41—14248no—
640#41—14248no—
641#41—1428no—
642#41—14296no—
643#41—14248no—
644#41—14248no—
645#41—14224no—
646#41D4×D7118yescomplemented
647C2×Q8—718no—
648C2×Q8—713no—
649C2×Q8—7112no—
650C2×Q8—7112no—
651C2×Q8—716no—
652C2×Q8—14248no—
653C2×Q8—14224no—
654C2×Q8—14216no—
655C2×Q8—14224no—
656C2×Q8C23×D7112yes—
657C2×Q8C23×D7111yescharacteristic
658C2×D4—248no—
659C2×D4—224no—
660C2×D4—424no—
661C2×D4—28424no—
662C2×D4—7124no—
663C2×D4—716no—
664C2×D4—7124no—
665C2×D4—7124no—
666C2×D4—7112no—
667C2×D4—7112no—
668C2×D4—7112no—
669C2×D4—713no—
670C2×D4—714no—
671C2×D4—714no—
672C2×D4—712no—
673C2×D4—14224no—
674C2×D4—14248no—
675C2×D4—14248no—
676C2×D4—14296no—
677C2×D4—14248no—
678C2×D4C23×D71112yes—
679C2×D4C23×D71112yes—
680C2×D4C23×D71112yes—
681C2×D4C23×D7116yes—
682C2×D4C23×D71124yes—
683C2×D4C23×D7113yes—
684C22×C4—28412no—
685C22×C4—716no—
686C22×C4—716no—
687C22×C4—716no—
688C22×C4—713no—
689C22×C4—7124no—
690C22×C4—711no—
691C22×C4—713no—
692C22×C4—713no—
693C22×C4—713no—
694C22×C4—7112no—
695C22×C4—7112no—
696C22×C4—7124no—
697C22×C4—712no—
698C22×C4—716no—
699C22×C4—7112no—
700C22×C4—714no—
701C22×C4—7112no—
702C22×C4—14248no—
703C22×C4—14248no—
704C22×C4C23×D7116yes—
705C22×C4C23×D71112yes—
706C22×C4C23×D7113yes—
707C4⋊C4—7112no—
708C4⋊C4—7124no—
709C4⋊C4—7112no—
710C4⋊C4—716no—
711C4⋊C4—7124no—
712C4⋊C4C23×D7114yes—
713C4⋊C4C23×D7116yes—
714C22⋊C4—7124no—
715C22⋊C4—716no—
716C22⋊C4—7148no—
717C22⋊C4—718no—
718C22⋊C4—7112no—
719C22⋊C4—7124no—
720C22⋊C4C23×D7116yes—
721C22⋊C4C23×D71124yes—
722C42—712no—
723C42—711no—
724C42—716no—
725C42—713no—
726C42—716no—
727C42—716no—
728C42—716no—
729C42C23×D7111yescharacteristic
730C42C23×D7113yes—
731C42C23×D7116yes—
732C23—224no—
733C23—424no—
734C23—2846no—
735C23—28424no—
736C23—7112no—
737C23—713no—
738C23—711no—
739C23—714no—
740C23—14224no—
741C23C24×D71112yes—
742C23C24×D7113yes—
743Q8—24no—
744Q8—7112no—
745Q8—14224no—
746Q8—14224no—
747Q8—14212no—
748Q8C2×D4×D7114yes—
749D4—224no—
750D4—224no—
751D4—212no—
752D4—224no—
753D4—424no—
754D4—28424no—
755D4—7124no—
756D4—7112no—
757D4—1428no—
758D4—14224no—
759D4—14224no—
760D4—14248no—
761D4—14224no—
762D4—1424no—
763D4—1428no—
764D4C2×D4×D71112yes—
765C2×C4—224no—
766C2×C4—212no—
767C2×C4—2846no—
768C2×C4—2846no—
769C2×C4—2846no—
770C2×C4—7112no—
771C2×C4—711no—
772C2×C4—713no—
773C2×C4—714no—
774C2×C4—7112no—
775C2×C4—7112no—
776C2×C4—7112no—
777C2×C4—712no—
778C2×C4—716no—
779C2×C4—7112no—
780C2×C4—1428no—
781C2×C4—14224no—
782C2×C4—14224no—
783C2×C4—14248no—
784C2×C4—14224no—
785C2×C4—14224no—
786C2×C4—1424no—
787C2×C4—14212no—
788C2×C4C2×D4×D71112yes—
789C2×C4C24×D7116yes—
790C2×C4C24×D7114yes—
791C2×C4C24×D7111yescharacteristic
792C2×C4C24×D7113yes—
793C2×C4C24×D7112yes—
794C22—26no—
795C22—212no—
796C22—224no—
797C22—824no—
798C22—28412no—
799C22—56824no—
800C22—712no—
801C22—716no—
802C22—1424no—
803C22—1428no—
804C22—1422no—
805C22—1426no—
806C22C22×D4×D7116yes—
807C22C25×D7111yescharacteristic
808C4—24no—
809C4—26no—
810C4—712no—
811C4—716no—
812C4—14212no—
813C4—1422no—
814C4—1426no—
815C4C22×D4×D7116yes—
816C4C22×D4×D7112yes—
817C4#1798683414yescomplemented
818C2—26no—
819C2—412no—
820C2—2844no—
821C2—1422no—
822C2—1426no—
823C2C23×D4×D7111yescharacteristic
824C2C2×#1798683412yes—
subgroupG/H
center, FrattiniC22C25×D71
commutator, socle, cosocleC22×C71C26
FittingC71×#3498C2
hypercenter#3498D71
hypocenterC71#62812
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ #3498

Complements

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

NH ≅ G/Ntype
1. C2×#17986834C2semidirect
2. #22602132C2semidirect
3. #22602128C2semidirect
4. #22602125C2semidirect
5. #22602120C2semidirect
6. #22602116C2semidirect
7. #22602105C2semidirect
8. #22602096C2semidirect
9. #22601830C2semidirect
10. D4×#11765864C2semidirect
11. #22601671C2semidirect
12. C2×#17986547C2semidirect
13. #532×D71C2semidirect
14. C4×#41×D71C2semidirect
15. C71×#3498C2semidirect
17. C2×#14556175C22semidirect
18. C2×#14556175C22semidirect
19. C2×#14556175C22semidirect
20. C2×#14556173C22semidirect
21. C2×#14556173C22semidirect
22. C22×#11765864C22semidirect
23. C22×#11765864C22semidirect
25. C2×#41×D71C22semidirect
26. C2×#41×D71C22semidirect
27. #17986669C22semidirect
28. Q8×D284C22semidirect
29. D4×Dic142C22semidirect
30. #17986656C22semidirect
31. #17986655C22semidirect
32. #17986654C22semidirect
33. #17986653C22semidirect
34. #17986649C22semidirect
35. #17986646C22semidirect
36. #17986643C22semidirect
37. #17986636C22semidirect
38. #17986634C22semidirect
39. D4×C22⋊D71C22semidirect
40. #17986578C22semidirect
41. #17986575C22semidirect
42. #17986570C22semidirect
43. #17986569C22semidirect
44. #17986566C22semidirect
45. #17986562C22semidirect
46. #17986559C22semidirect
47. #17986550C22semidirect
48. #17986549C22semidirect
49. #17986548C22semidirect
50. #17986547C22semidirect
51. #17986547C22semidirect
52. #17986547C22semidirect
53. #17986547C22semidirect
54. #17986547C22semidirect
55. #17986547C22semidirect
56. #17986546C22semidirect
57. #17986545C22semidirect
58. #17986544C22semidirect
59. C2×#14556128C22semidirect
60. C4⋊Q8×D71C22semidirect
61. #127×D71C22semidirect
62. C2×#14556115C22semidirect
63. #124×D71C22semidirect
64. #17986509C22semidirect
65. #17986505C22semidirect
66. C2×#14556099C22semidirect
67. #121×D71C22semidirect
68. #41×Dic71C22semidirect
69. C4×#11765866C22semidirect
70. C4×#11765865C22semidirect
71. #17986467C22semidirect
72. C4×#11765864C22semidirect
73. C4×Q8×D71C22semidirect
74. C2×D4×Dic71C22semidirect
75. C4×D4×D71C22semidirect
76. C4×D4×D71C22semidirect
77. #117×D71C22semidirect
78. C2×C42×D71C22semidirect
79. C2×H(5,𝔽2)×C71C22semidirect
80. #550×C71C22semidirect
81. D42×C71C22semidirect
82. #535×C71C22semidirect
83. #532×C71C22semidirect
84. C2×#127×C71C22semidirect
85. C4×#41×C71C22semidirect
110. #41×D71D4semidirect
216. #11765866C2×D4semidirect
220. #11765865C2×D4semidirect
229. #11765864C2×D4semidirect
238. Q8×D71C2×D4semidirect
255. D4×D71C2×D4semidirect
264. C2×C4×D71C2×D4semidirect
297. #41×C71C2×D4semidirect
399. C4×C71#585semidirect
419. #3498D71semidirect
428. C71#62812semidirect
435. C2×H(5,𝔽2)C2×D71semidirect
442. #550C2×D71semidirect
455. D42C2×D71semidirect
462. #535C2×D71semidirect
476. #532C2×D71semidirect
480. C2×#127C2×D71semidirect
492. C4×#41C2×D71semidirect
646. #41D4×D71semidirect
817. C4#17986834semidirect

Maximal subgroups

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

subgroupindex
C2×#179868342
#226021322
#226021282
#226021252
#226021202
#226021162
#226021052
#226020962
#226018302
D4×#117658642
#226016712
C2×#179865472
#532×D712
C4×#41×D712
C71×#34982
#6281271