Finite Group Databasebeta

← #3499×D71 #32905860

Subgroups — #3499×D71 #32905860

Order 18176.

11126 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D71C212yesmaximal, complemented
2#22602125C211yesmaximal, characteristic, complemented
3#22602124C214yesmaximal, complemented
4#22602123C213yesmaximal, complemented
5#22602122C216yesmaximal, complemented
6#22602121C212yesmaximal, complemented
7#22602120C213yesmaximal, complemented
8#22602119C2112yesmaximal, complemented
9D4×Q8×D71C214yesmaximal, complemented
10#547×D71C2112yesmaximal, complemented
11#536×D71C216yesmaximal, complemented
12#532×D71C213yesmaximal, complemented
13C2×C4⋊Q8×D71C213yesmaximal, complemented
14C4×#41×D71C211yesmaximal, characteristic, complemented
15C71×#3499C211yesmaximal, characteristic, complemented
16C2×#14556176C2216yescomplemented
17C2×#14556176C2214yescomplemented
18C2×#14556175C22112yescomplemented
19C2×#14556175C2216yescomplemented
20C2×#14556175C2212yescomplemented
212−1+4×D71—232no—
22C2×#41×D71C22112yes—
23C2×#41×D71C2216yes—
24C2×#41×D71C2211yescharacteristic
25C22×Q8×D71C2214yes—
26C22×Q8×D71C2216yes—
27Q8×D284C2214yescomplemented
28D4×Dic142C22112yescomplemented
29#17986664C22112yescomplemented
30Q8×C22⋊D71C2218yescomplemented
31#17986662C22124yescomplemented
32#17986654C22112yescomplemented
33#17986653C22112yescomplemented
34#17986652C22112yescomplemented
35#17986651C22124yescomplemented
36#17986650C22124yescomplemented
37#17986649C22124yescomplemented
38#17986648C22124yescomplemented
39#17986647C22148yescomplemented
40#17986575C2216yescomplemented
41#17986574C22112yescomplemented
42#17986573C2216yescomplemented
43#17986572C22124yescomplemented
44#17986571C22124yescomplemented
45#17986570C2216yescomplemented
46#17986569C22112yescomplemented
47#17986550C2213yescomplemented
48#17986549C2213yescomplemented
49#17986548C2216yescomplemented
50#17986547C2213yescomplemented
51#17986546C22112yescomplemented
52#17986545C2216yescomplemented
53#17986544C22112yescomplemented
54C2×#14556128C2213yescomplemented
55C2×#14556127C22112yescomplemented
56C2×#14556126C2216yescomplemented
57C4⋊Q8×D71C22112yes—
58C4⋊Q8×D71C2213yes—
59C4⋊Q8×D71C2216yes—
60C4⋊Q8×D71C22112yescomplemented
61C4⋊Q8×D71C2216yescomplemented
62C4⋊Q8×D71C2216yescomplemented
63#127×D71C2211yescharacteristic
64#124×D71C2216yes—
65#123×D71C22124yes—
66C22⋊Q8×D71C22124yes—
67#121×D71C22112yes—
68#41×Dic71C2211yescharacteristic, complemented
69C4×#11765866C2212yescomplemented
70C4×#11765865C2213yescomplemented
71#17986467C2213yescomplemented
72C4×#11765864C2216yescomplemented
73C4×Q8×D71C2212yes—
74C4×D4×D71C2216yes—
75C4×D4×D71C22112yes—
76#117×D71C2213yes—
77C2×C4⋊C4×D71C22112yes—
78C2×C42×D71C2213yes—
79C2×2−1+4×C71C2212yescomplemented
80D4×Q8×C71C2214yescomplemented
81#547×C71C22112yescomplemented
82#536×C71C2216yescomplemented
83#532×C71C2213yescomplemented
84C2×C4⋊Q8×C71C2213yescomplemented
85C4×#41×C71C2211yescharacteristic, complemented
86#14556176—232no—
87#14556176—248no—
88#14556175—248no—
89#14556175—296no—
90#14556175—216no—
91C2×#11765866C2316yes—
92C2×#11765866C23112yes—
93C2×#11765866C2311yescharacteristic
94C2×#11765865C23112yes—
95C2×#11765865C2316yes—
96C2×#11765865C23124yes—
97C2×#11765865C23112yes—
98C2×#11765865C2313yes—
99C2×#11765864C2316yes—
100C2×#11765864C23112yes—
101C2×#11765864C23124yes—
102C2×#11765864C23112yes—
103C2×#11765864C2313yes—
104#41×D71—296no—
105#41×D71—248no—
106#41×D71D4116yescomplemented
107C22×Dic142C2316yes—
108C22×Dic142C23112yes—
109C22×Dic142C23112yes—
110C2×Q8×D71—232no—
111C2×Q8×D71—248no—
112C2×Q8×D71C23112yes—
113C2×Q8×D71C2316yes—
114C2×Q8×D71C23112yes—
115C2×Q8×D71C23112yes—
116C2×Q8×D71C23112yes—
117C2×Q8×D71C2314yes—
118C2×Q8×D71C2311yescharacteristic
119C2×D4×D71C23112yes—
120C2×D4×D71C2312yes—
121C2×D4×D71C2314yes—
122C2×D4×D71C2313yes—
123C22×C4×D71C23112yes—
124C22×C4×D71C23112yes—
125C22×C4×D71C2316yes—
126C22×C4×D71C2313yes—
127#14556128C2316yes—
128#14556128C23112yes—
129#14556128C2313yes—
130#14556127C23124yes—
131#14556127C23124yes—
132#14556127C23124yes—
133#14556127C23112yes—
134#14556126C23112yes—
135#14556126C23124yes—
136#14556126C2316yes—
137#14556125C2311yescharacteristic
138#14556124C2314yes—
139#14556124C2312yes—
140#14556117C2316yes—
141#14556116C2316yes—
142#14556115C2316yes—
143#14556114C23124yes—
144#14556113C23148yes—
145#14556112C23124yes—
146#14556111C23124yes—
147#14556110C23148yes—
148#14556109C23124yes—
149#14556108C23124yes—
150#14556107C23124yes—
151#14556106C23148yes—
152#14556105C23148yes—
153#14556104C23124yes—
154#14556103C23112yes—
155#14556102C23112yes—
156#14556101C23124yes—
157#14556100C23124yes—
158#14556099C23112yes—
159Q8×Dic71C2312yes—
160C4×Dic142C2316yes—
161#14556093C2316yes—
162C4×D284C2316yes—
163C4×D284C23112yes—
164D4×Dic71C2316yes—
165D4×Dic71C23112yes—
166#14556090C23112yes—
167#14556090C2316yes—
168C4×C22⋊D71C23124yes—
169C4×C22⋊D71C23112yes—
170(C22⋊D71)⋊C4C23112yes—
171(C22⋊D71)⋊C4C23124yes—
172#14556087C2313yes—
173#14556086C2316yes—
174#14556085C2316yes—
175#14556084C2316yes—
176C2×C4⋊Dic71C23112yes—
177C2×Dic71⋊C4C23124yes—
178C4⋊C4×D71C23124yes—
179C4⋊C4×D71C23124yes—
180C4⋊C4×D71C23112yes—
181C4⋊C4×D71C23124yes—
182C4⋊C4×D71C2316yes—
183C22⋊C4×D71C2316yes—
184C22⋊C4×D71C23124yes—
185C2×C4×Dic71C2316yes—
186C2×C4×Dic71C2313yes—
187C42×D71C2311yescharacteristic
188C42×D71C2313yes—
189C42×D71C2316yes—
190C42×D71C2316yes—
191C42×D71C2313yes—
192C42×D71C2313yes—
1932−1+4×C71—216no—
194C2×#41×C71C2316yes—
195C2×#41×C71C23112yes—
196C2×#41×C71C2311yescharacteristic
197C22×Q8×C71C2316yes—
198C22×Q8×C71C2314yes—
199C4⋊Q8×C71C2316yes—
200C4⋊Q8×C71C23112yes—
201C4⋊Q8×C71C2313yes—
202#127×C71C2311yescharacteristic
203#124×C71C2316yes—
204#123×C71C23124yes—
205C22⋊Q8×C71C23124yes—
206#121×C71C23112yes—
207C4×Q8×C71C2312yes—
208C4×D4×C71C2316yes—
209C4×D4×C71C23112yes—
210#117×C71C2313yes—
211C2×C4⋊C4×C71C23112yes—
212C2×C42×C71C2313yes—
213C23×D71C2414yes—
214C23×D71C2413yes—
215#11765866—248no—
216#11765866—224no—
217#11765866C2×D418yescomplemented
218#11765865—224no—
219#11765865—296no—
220#11765865—248no—
221#11765865—248no—
222#11765865C2×D4124yescomplemented
223#11765864—248no—
224#11765864—296no—
225#11765864—248no—
226#11765864—224no—
227#11765864C2×D4124yescomplemented
228C2×Dic142—224no—
229C2×Dic142—248no—
230C2×Dic142—248no—
231C2×Dic142C24124yes—
232C2×Dic142C24112yes—
233C2×Dic142C24112yes—
234C2×Dic142C2416yes—
235C2×Dic142C2413yes—
236Q8×D71—216no—
237Q8×D71—248no—
238Q8×D71—224no—
239Q8×D71—248no—
240Q8×D71—248no—
241Q8×D71—248no—
242Q8×D71C2×D418yes—
243C2×D284C24112yes—
244C2×D284C2412yes—
245C2×D284C2414yes—
246C2×D284C2413yes—
247C2×C22⋊D71C24112yes—
248C2×C22⋊D71C24112yes—
249C2×C22⋊D71C2414yes—
250C2×C22⋊D71C2418yes—
251C2×C22⋊D71C2416yes—
252D4×D71—248no—
253D4×D71—28no—
254D4×D71—216no—
255D4×D71C2×D4124yes—
256C22×Dic71C24112yes—
257C22×Dic71C24112yes—
258C22×Dic71C2416yes—
259C22×Dic71C2413yes—
260C2×C4×D71—248no—
261C2×C4×D71—248no—
262C2×C4×D71—224no—
263C2×C4×D71C2×D4124yes—
264C2×C4×D71C24112yes—
265C2×C4×D71C24124yes—
266C2×C4×D71C24112yes—
267C2×C4×D71C24112yes—
268C2×C4×D71C2416yes—
269C2×C4×D71C2416yes—
270C2×C4×D71C2416yes—
271C2×C4×D71C2413yes—
272C2×C4×D71C2411yescharacteristic
273C2×C4×D71C2413yes—
274C2×C4×D71C2413yes—
275C2×C4×D71C2412yes—
276C4⋊Dic71C24112yes—
277C4⋊Dic71C24124yes—
278C4⋊Dic71C2416yes—
279Dic71⋊C4C24124yes—
280Dic71⋊C4C24148yes—
281Dic71⋊C4C24112yes—
282C22⋊Dic71C2416yes—
283C22⋊Dic71C24124yes—
284(C2×D71)⋊C4C24112yes—
285(C2×D71)⋊C4C24124yes—
286(C2×D71)⋊C4C24124yes—
287C4×Dic71C2411yescharacteristic
288C4×Dic71C2412yes—
289C4×Dic71C2416yes—
290C4×Dic71C2413yes—
291C4×Dic71C2416yes—
292C4×Dic71C2416yes—
293C4×Dic71C2416yes—
294#41×C71—248no—
295#41×C71—224no—
296#41×C71C2×D418yescomplemented
297C2×Q8×C71—216no—
298C2×Q8×C71—224no—
299C2×Q8×C71C24112yes—
300C2×Q8×C71C2416yes—
301C2×Q8×C71C2411yescharacteristic
302C2×D4×C71C24112yes—
303C2×D4×C71C2412yes—
304C2×D4×C71C2414yes—
305C2×D4×C71C2413yes—
306C22×C4×C71C24112yes—
307C22×C4×C71C24112yes—
308C22×C4×C71C2416yes—
309C22×C4×C71C2413yes—
310C4⋊C4×C71C24112yes—
311C4⋊C4×C71C24124yes—
312C4⋊C4×C71C2416yes—
313C22⋊C4×C71C2416yes—
314C22⋊C4×C71C24124yes—
315C42×C71C2411yescharacteristic
316C42×C71C2413yes—
317C42×C71C2416yes—
318C23×C71C2514yes—
319C23×C71C2513yes—
320C22×D71—212no—
321C22×D71—28no—
322C22×D71—216no—
323C22×D71C22×D4112yes—
324C22×D71C2514yes—
325C22×D71C2513yes—
326C22×D71C2511yescharacteristic
327Q8×C71—212no—
328Q8×C71—224no—
329Q8×C71C22×D414yes—
330D4×C71—224no—
331D4×C71—24no—
332D4×C71—28no—
333D4×C71C22×D4112yes—
334C2×C4×C71—224no—
335C2×C4×C71—224no—
336C2×C4×C71—212no—
337C2×C4×C71C22×D4112yes—
338C2×C4×C71C2516yes—
339C2×C4×C71C25112yes—
340C2×C4×C71C2511yescharacteristic
341C2×C4×C71C2513yes—
342C2×C4×C71C2512yes—
343C22⋊D71—224no—
344C22⋊D71—224no—
345C22⋊D71—28no—
346C22⋊D71—216no—
347C22⋊D71C22×D4124yes—
348C2×Dic71—224no—
349C2×Dic71—224no—
350C2×Dic71—212no—
351C2×Dic71C22×D4112yes—
352C2×Dic71C2516yes—
353C2×Dic71C25112yes—
354C2×Dic71C2511yescharacteristic
355C2×Dic71C2513yes—
356C2×Dic71C2512yes—
357D284—224no—
358D284—24no—
359D284—28no—
360D284C22×D4112yes—
361C4×D71—224no—
362C4×D71—248no—
363C4×D71—212no—
364C4×D71—224no—
365C4×D71—212no—
366C4×D71—224no—
367C4×D71—212no—
368C4×D71C22×D4112yes—
369C4×D71C22×D414yes—
370C4×D71C22×D4112yes—
371C4×D71C22×D4112yes—
372C4×D712−1+418yescomplemented
373Dic142—212no—
374Dic142—224no—
375Dic142—224no—
376Dic142—248no—
377Dic142C22×D4112yes—
378C22×C71—26no—
379C22×C71—24no—
380C22×C71—28no—
381C22×C71C23×D416yes—
382C22×C71C2611yescharacteristic
383C2×D71—26no—
384C2×D71—224no—
385C2×D71—24no—
386C2×D71—28no—
387C2×D71—416no—
388C2×D71C23×D416yes—
389C2×D71C23×D412yes—
390C2×D71C2×2−1+414yes—
391C4×C71—212no—
392C4×C71—26no—
393C4×C71C23×D412yes—
394C4×C71C23×D416yes—
395C4×C71C2×2−1+414yescomplemented
396Dic71—212no—
397Dic71—26no—
398Dic71C23×D412yes—
399Dic71C23×D416yes—
400Dic71C2×2−1+414yescomplemented
401C2×#3499—711nomaximal, Sylow
402C2×C71—26no—
403C2×C71—44no—
404C2×C71C24×D411yescharacteristic
405C2×C71C22×2−1+412yes—
406D71—26no—
407D71—44no—
408D71#349914yesdirect product factor
409C22×2−1+4—712no—
410#3499—712no—
411#3499—714no—
412#3499—7112no—
413#3499—716no—
414#3499—713no—
415#3499—713no—
416#3499—711no—
417#3499D7111yescharacteristic, direct product factor
418C2×D4×Q8—714no—
419C2×#547—7112no—
420C2×#536—716no—
421C2×#532—713no—
422C22×C4⋊Q8—713no—
423C2×C4×#41—711no—
424C71C2×#349911yescharacteristic, complemented, Sylow
425C2×2−1+4—716no—
426C2×2−1+4—7112no—
427C2×2−1+4—712no—
428C2×2−1+4—714no—
429C2×2−1+4—716no—
430C2×2−1+4—14232no—
431C2×2−1+4C2×D7112yescomplemented
432C22×#41—711no—
433C22×#41—716no—
434C22×#41—7112no—
435C23×Q8—716no—
436C23×Q8—714no—
437D4×Q8—718no—
438D4×Q8—7112no—
439D4×Q8—7124no—
440D4×Q8—714no—
441D4×Q8—7112no—
442D4×Q8C2×D7114yescomplemented
443#547—7124no—
444#547—7112no—
445#547—7148no—
446#547—7124no—
447#547—7124no—
448#547—7112no—
449#547—7112no—
450#547—7124no—
451#547C2×D71112yescomplemented
452#536—716no—
453#536—716no—
454#536—7112no—
455#536—7112no—
456#536—7124no—
457#536—7124no—
458#536—716no—
459#536C2×D7116yescomplemented
460#532—716no—
461#532—713no—
462#532—713no—
463#532—716no—
464#532—7112no—
465#532—7112no—
466#532—713no—
467#532C2×D7113yescomplemented
468C2×C4⋊Q8—716no—
469C2×C4⋊Q8—713no—
470C2×C4⋊Q8—716no—
471C2×C4⋊Q8—7112no—
472C2×C4⋊Q8—716no—
473C2×C4⋊Q8—716no—
474C2×C4⋊Q8—7112no—
475C2×C4⋊Q8—7112no—
476C2×C4⋊Q8—713no—
477C2×C4⋊Q8C2×D7113yescomplemented
478C2×#127—711no—
479C2×#124—716no—
480C2×#123—7124no—
481C2×C22⋊Q8—7124no—
482C2×#121—7112no—
483C4×#41—711no—
484C4×#41—712no—
485C4×#41—716no—
486C4×#41—713no—
487C4×#41—713no—
488C4×#41C2×D7111yescharacteristic, complemented
489C2×C4×Q8—712no—
490C2×C4×D4—716no—
491C2×C4×D4—7112no—
492C2×#117—713no—
493C22×C4⋊C4—7112no—
494C22×C42—713no—
4952−1+4—216no—
4962−1+4—14232no—
4972−1+4—14248no—
4982−1+4—14296no—
4992−1+4—14248no—
5002−1+4—14216no—
501C2×#41—7116no—
502C2×#41—711no—
503C2×#41—716no—
504C2×#41—7112no—
505C2×#41—713no—
506C2×#41—7112no—
507C2×#41—716no—
508C2×#41—7112no—
509C2×#41—7124no—
510C2×#41—713no—
511C2×#41—7112no—
512C2×#41—716no—
513C2×#41—7112no—
514C2×#41—7124no—
515C2×#41—14248no—
516C2×#41—14296no—
517C2×#41C22×D7116yes—
518C2×#41C22×D71112yes—
519C2×#41C22×D7111yescharacteristic
520C22×Q8—711no—
521C22×Q8—7112no—
522C22×Q8—716no—
523C22×Q8—7112no—
524C22×Q8—7112no—
525C22×Q8—7112no—
526C22×Q8—714no—
527C22×Q8—7112no—
528C22×Q8—716no—
529C22×Q8—7112no—
530C22×Q8—14248no—
531C22×Q8—14232no—
532C22×Q8C22×D7116yes—
533C22×Q8C22×D7114yes—
534C22×D4—713no—
535C22×D4—714no—
536C22×D4—7112no—
537C22×D4—712no—
538C23×C4—713no—
539C23×C4—716no—
540C23×C4—7112no—
541C23×C4—7112no—
542C4⋊Q8—716no—
543C4⋊Q8—7112no—
544C4⋊Q8—7124no—
545C4⋊Q8—7112no—
546C4⋊Q8—7124no—
547C4⋊Q8—7124no—
548C4⋊Q8—7124no—
549C4⋊Q8—713no—
550C4⋊Q8—716no—
551C4⋊Q8—7112no—
552C4⋊Q8C22×D7113yes—
553C4⋊Q8C22×D7116yes—
554C4⋊Q8C22×D71112yes—
555#127—712no—
556#127—714no—
557#127—711no—
558#127C22×D7111yescharacteristic
559#124—716no—
560#124—716no—
561#124—7124no—
562#124—716no—
563#124C22×D7116yes—
564#123—7124no—
565#123—7124no—
566#123—7148no—
567#123—7148no—
568#123—7124no—
569#123C22×D71124yes—
570C22⋊Q8—7124no—
571C22⋊Q8—7124no—
572C22⋊Q8—7148no—
573C22⋊Q8—7124no—
574C22⋊Q8—7148no—
575C22⋊Q8C22×D71124yes—
576#121—7112no—
577#121—7124no—
578#121—7112no—
579#121—7112no—
580#121—7124no—
581#121C22×D71112yes—
582C4×Q8—712no—
583C4×Q8—716no—
584C4×Q8—716no—
585C4×Q8C22×D7112yes—
586C4×D4—716no—
587C4×D4—7112no—
588C4×D4—7112no—
589C4×D4—7124no—
590C4×D4—716no—
591C4×D4—7112no—
592C4×D4—7112no—
593C4×D4—7124no—
594C4×D4—716no—
595C4×D4—7112no—
596C4×D4C22×D7116yes—
597C4×D4C22×D71112yes—
598#117—713no—
599#117—716no—
600#117—716no—
601#117—716no—
602#117C22×D7113yes—
603C2×C4⋊C4—7124no—
604C2×C4⋊C4—7112no—
605C2×C4⋊C4—7112no—
606C2×C4⋊C4—7124no—
607C2×C4⋊C4—7124no—
608C2×C4⋊C4—7124no—
609C2×C4⋊C4—716no—
610C2×C4⋊C4C22×D71112yes—
611C2×C22⋊C4—716no—
612C2×C22⋊C4—7124no—
613C2×C42—716no—
614C2×C42—713no—
615C2×C42—713no—
616C2×C42—716no—
617C2×C42—716no—
618C2×C42—713no—
619C2×C42—713no—
620C2×C42—711no—
621C2×C42C22×D7113yes—
622C24—713no—
623C24—714no—
624#41—248no—
625#41—224no—
626#41—718no—
627#41—7124no—
628#41—7124no—
629#41—14248no—
630#41—14296no—
631#41—14248no—
632#41—14248no—
633#41—14224no—
634#41—14224no—
635#41—14296no—
636#41—14248no—
637#41—14248no—
638#41—14224no—
639#41D4×D7118yescomplemented
640C2×Q8—216no—
641C2×Q8—224no—
642C2×Q8—718no—
643C2×Q8—713no—
644C2×Q8—7124no—
645C2×Q8—7112no—
646C2×Q8—7112no—
647C2×Q8—716no—
648C2×Q8—14248no—
649C2×Q8—14248no—
650C2×Q8—14224no—
651C2×Q8—14248no—
652C2×Q8—14248no—
653C2×Q8—14248no—
654C2×Q8—14248no—
655C2×Q8—14216no—
656C2×Q8—14224no—
657C2×Q8C23×D71112yes—
658C2×Q8C23×D7116yes—
659C2×Q8C23×D7111yescharacteristic
660C2×D4—716no—
661C2×D4—7124no—
662C2×D4—718no—
663C2×D4—7112no—
664C2×D4—7112no—
665C2×D4—714no—
666C2×D4—713no—
667C2×D4—714no—
668C2×D4—7112no—
669C2×D4—712no—
670C2×D4—14216no—
671C2×D4—1428no—
672C2×D4—14248no—
673C2×D4C23×D7114yes—
674C2×D4C23×D71112yes—
675C2×D4C23×D7112yes—
676C2×D4C23×D7113yes—
677C22×C4—713no—
678C22×C4—7124no—
679C22×C4—712no—
680C22×C4—711no—
681C22×C4—713no—
682C22×C4—713no—
683C22×C4—713no—
684C22×C4—716no—
685C22×C4—7112no—
686C22×C4—7112no—
687C22×C4—716no—
688C22×C4—716no—
689C22×C4—716no—
690C22×C4—7112no—
691C22×C4—7124no—
692C22×C4—7112no—
693C22×C4—7112no—
694C22×C4—14224no—
695C22×C4—14248no—
696C22×C4—14248no—
697C22×C4C23×D7116yes—
698C22×C4C23×D71112yes—
699C22×C4C23×D71112yes—
700C22×C4C23×D7113yes—
701C4⋊C4—7124no—
702C4⋊C4—7148no—
703C4⋊C4—7112no—
704C4⋊C4—7112no—
705C4⋊C4—7124no—
706C4⋊C4—716no—
707C4⋊C4C23×D71112yes—
708C4⋊C4C23×D71124yes—
709C4⋊C4C23×D7116yes—
710C22⋊C4—716no—
711C22⋊C4—7124no—
712C22⋊C4—7112no—
713C22⋊C4—7124no—
714C22⋊C4—7124no—
715C22⋊C4C23×D7116yes—
716C22⋊C4C23×D71124yes—
717C42—711no—
718C42—712no—
719C42—716no—
720C42—713no—
721C42—716no—
722C42—716no—
723C42—716no—
724C42C23×D7111yescharacteristic
725C42C23×D7113yes—
726C42C23×D7116yes—
727C23—711no—
728C23—7112no—
729C23—713no—
730C23—714no—
731C23—1428no—
732C23—14216no—
733C23—14212no—
734C23C24×D7114yes—
735C23C24×D7113yes—
736Q8—224no—
737Q8—212no—
738Q8—7112no—
739Q8—14224no—
740Q8—14248no—
741Q8—14224no—
742Q8—14212no—
743Q8C2×D4×D7114yes—
744D4—224no—
745D4—24no—
746D4—28no—
747D4—7124no—
748D4—7112no—
749D4—14224no—
750D4—1428no—
751D4—14216no—
752D4—14224no—
753D4—14224no—
754D4—1424no—
755D4—1428no—
756D4C2×D4×D71112yes—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—212no—
760C2×C4—7112no—
761C2×C4—712no—
762C2×C4—711no—
763C2×C4—713no—
764C2×C4—714no—
765C2×C4—7112no—
766C2×C4—7112no—
767C2×C4—7112no—
768C2×C4—718no—
769C2×C4—716no—
770C2×C4—7112no—
771C2×C4—14224no—
772C2×C4—14212no—
773C2×C4—14224no—
774C2×C4—14248no—
775C2×C4—14212no—
776C2×C4—14224no—
777C2×C4—14212no—
778C2×C4—14224no—
779C2×C4—14224no—
780C2×C4—14212no—
781C2×C4C2×D4×D71112yes—
782C2×C4C24×D7116yes—
783C2×C4C24×D71112yes—
784C2×C4C24×D7111yescharacteristic
785C2×C4C24×D7113yes—
786C2×C4C24×D7112yes—
787C22—26no—
788C22—24no—
789C22—28no—
790C22—28416no—
791C22—712no—
792C22—714no—
793C22—716no—
794C22—14224no—
795C22—1424no—
796C22—1428no—
797C22—1426no—
798C22C22×D4×D7116yes—
799C22C25×D7111yescharacteristic
800C4—212no—
801C4—26no—
802C4—712no—
803C4—716no—
804C4—714no—
805C4—14212no—
806C4—1426no—
807C4C22×D4×D7116yes—
808C4C22×D4×D7112yes—
809C42−1+4×D7114yescomplemented
810C2—26no—
811C2—44no—
812C2—2844no—
813C2—714no—
814C2—1426no—
815C2C23×D4×D7111yescharacteristic
816C2C2×2−1+4×D7112yes—
subgroupG/H
center, FrattiniC22C25×D71
commutator, socle, cosocleC22×C71C26
FittingC71×#3499C2
hypercenter#3499D71
hypocenterC71C2×#3499
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D71C2semidirect
2. #22602125C2semidirect
3. #22602124C2semidirect
4. #22602123C2semidirect
5. #22602122C2semidirect
6. #22602121C2semidirect
7. #22602120C2semidirect
8. #22602119C2semidirect
9. D4×Q8×D71C2semidirect
10. #547×D71C2semidirect
11. #536×D71C2semidirect
12. #532×D71C2semidirect
13. C2×C4⋊Q8×D71C2semidirect
14. C4×#41×D71C2semidirect
15. C71×#3499C2semidirect
16. C2×#14556176C22semidirect
17. C2×#14556176C22semidirect
18. C2×#14556175C22semidirect
19. C2×#14556175C22semidirect
20. C2×#14556175C22semidirect
27. Q8×D284C22semidirect
28. D4×Dic142C22semidirect
29. #17986664C22semidirect
30. Q8×C22⋊D71C22semidirect
31. #17986662C22semidirect
32. #17986654C22semidirect
33. #17986653C22semidirect
34. #17986652C22semidirect
35. #17986651C22semidirect
36. #17986650C22semidirect
37. #17986649C22semidirect
38. #17986648C22semidirect
39. #17986647C22semidirect
40. #17986575C22semidirect
41. #17986574C22semidirect
42. #17986573C22semidirect
43. #17986572C22semidirect
44. #17986571C22semidirect
45. #17986570C22semidirect
46. #17986569C22semidirect
47. #17986550C22semidirect
48. #17986549C22semidirect
49. #17986548C22semidirect
50. #17986547C22semidirect
51. #17986546C22semidirect
52. #17986545C22semidirect
53. #17986544C22semidirect
54. C2×#14556128C22semidirect
55. C2×#14556127C22semidirect
56. C2×#14556126C22semidirect
60. C4⋊Q8×D71C22semidirect
61. C4⋊Q8×D71C22semidirect
62. C4⋊Q8×D71C22semidirect
68. #41×Dic71C22semidirect
69. C4×#11765866C22semidirect
70. C4×#11765865C22semidirect
71. #17986467C22semidirect
72. C4×#11765864C22semidirect
79. C2×2−1+4×C71C22semidirect
80. D4×Q8×C71C22semidirect
81. #547×C71C22semidirect
82. #536×C71C22semidirect
83. #532×C71C22semidirect
84. C2×C4⋊Q8×C71C22semidirect
85. C4×#41×C71C22semidirect
106. #41×D71D4semidirect
217. #11765866C2×D4semidirect
222. #11765865C2×D4semidirect
227. #11765864C2×D4semidirect
296. #41×C71C2×D4semidirect
372. C4×D712−1+4semidirect
395. C4×C71C2×2−1+4semidirect
400. Dic71C2×2−1+4semidirect
408. D71#3499direct (N × H)
417. #3499D71direct (N × H)
424. C71C2×#3499semidirect
431. C2×2−1+4C2×D71semidirect
442. D4×Q8C2×D71semidirect
451. #547C2×D71semidirect
459. #536C2×D71semidirect
467. #532C2×D71semidirect
477. C2×C4⋊Q8C2×D71semidirect
488. C4×#41C2×D71semidirect
639. #41D4×D71semidirect
809. C42−1+4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D712
#226021252
#226021242
#226021232
#226021222
#226021212
#226021202
#226021192
D4×Q8×D712
#547×D712
#536×D712
#532×D712
C2×C4⋊Q8×D712
C4×#41×D712
C71×#34992
C2×#349971