Finite Group Databasebeta

← #32905677

Subgroups — #32905677

Order 18176.

7094 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602427C214yesmaximal, complemented
2#22602416C214yesmaximal, complemented
3#22602334C214yesmaximal, complemented
4#22602322C214yesmaximal, complemented
5#22602204C216yesmaximal, complemented
6#22602146C211yesmaximal, characteristic, complemented
7#22602107C211yesmaximal, characteristic, complemented
8#22602046C216yesmaximal, complemented
9#22601991C211yesmaximal, characteristic, complemented
10#22601961C214yesmaximal, complemented
11#22601956C214yesmaximal, complemented
12#22601930C214yesmaximal, complemented
13Q8×#11765864C214yesmaximal, complemented
14#22601764C216yesmaximal, complemented
15#22601632C216yesmaximal, complemented
162−1+4×Dic71C211yesmaximal, characteristic, complemented
17#22601549C211yesmaximal, characteristic, complemented
18C22×Q8×Dic71C211yesmaximal, characteristic, complemented
19C71×#3486C211yesmaximal, characteristic, complemented
20C2×#14556176C2211yescharacteristic
21#17986731C22112yescomplemented
22Q8×Dic142C2214yescomplemented
23#17986728C2214yescomplemented
24#17986725C2214yescomplemented
25#17986725C2214yescomplemented
26#17986724C22112yescomplemented
27#17986723C22112yescomplemented
28#17986720C22112yescomplemented
29#17986718C22112yescomplemented
30#17986707C22112yes—
31#17986707C22112yescomplemented
32#17986706C22112yes—
33#17986701C22112yes—
34#17986695C22112yes—
35#17986691C22112yes—
36#17986691C22112yescomplemented
37#17986689C22112yes—
38#17986683C22112yescomplemented
39#17986668C2214yescomplemented
40Q8×C22⋊D71C2214yes—
41Q8×C22⋊D71C2214yes—
42Q8×C22⋊D71C2214yescomplemented
43#17986660C2214yes—
44#17986660C2214yes—
45#17986660C2214yescomplemented
46#17986656C2214yescomplemented
47#17986653C22112yes—
48#17986649C22112yes—
49#17986627C2216yes—
50#17986622C22112yescomplemented
51#17986618C22112yescomplemented
52#17986610C22112yescomplemented
53#17986609C22112yescomplemented
54#17986593C22124yes—
55#17986577C2216yes—
56#17986573C2216yes—
57#17986554C22112yescomplemented
58#17986552C2216yes—
59#17986551C2216yes—
60#17986551C2216yes—
61#17986551C22112yescomplemented
62#17986545C2216yes—
63#17986544C2216yes—
64#17986544C2216yes—
65#17986535C2216yes—
66#17986535C2216yes—
67#17986535C22112yescomplemented
68#17986530C2216yes—
69#17986530C2216yes—
70#17986529C22112yes—
71#17986529C22112yes—
72#17986528C22112yescomplemented
73#17986526C22112yes—
74#17986526C22112yes—
75#17986510C2216yes—
76#17986505C22112yes—
77#17986505C2214yes—
78#17986482C2216yes—
79#17986482C2214yescomplemented
80#17986481C2214yescomplemented
81#17986479C2216yes—
82#17986477C2211yescharacteristic
83#17986477C2214yescomplemented
84#17986475C2214yescomplemented
85#41×Dic71C2216yes—
86#41×Dic71C2214yescomplemented
87C4×#11765866C2214yescomplemented
88#17986467C2216yes—
89C4×#11765864C22112yes—
90C4×#11765864C22112yes—
91C2×Q8×Dic71C2213yes—
92C2×Q8×Dic71C2211yescharacteristic
93C2×Q8×Dic71C2214yes—
94C2×Q8×Dic71C2211yescharacteristic
95C2×Q8×Dic71C2214yes—
96C2×Q8×Dic71C2214yes—
97C2×Q8×Dic71C2213yes—
98C2×Q8×Dic71C2214yes—
99C2×Q8×Dic71C2214yescomplemented
100C4×Q8×D71C2214yescomplemented
101C22×C4⋊Dic71C2213yes—
102C22×C4×Dic71C2213yes—
103C2×2−1+4×C71C2211yescharacteristic
104C23×Q8×C71C2211yescharacteristic
105D4×Q8×C71C2214yes—
106D4×Q8×C71C2214yes—
107#548×C71C2214yes—
108#548×C71C2214yes—
109#536×C71C2216yes—
110#525×C71C2216yes—
111#519×C71C2211yescharacteristic
112#14556176—28no—
113C2×#11765866C2314yes—
114C2×#11765865C2316yes—
115C2×#11765864C2314yes—
116C2×#11765864C23112yes—
117C2×Q8×D71C2314yes—
118C23×Dic71C2311yescharacteristic
119C23×Dic71C2313yes—
120#14556128C23112yes—
121#14556127C23112yes—
122#14556127C2316yes—
123#14556127C2316yes—
124#14556126C23112yes—
125#14556126C2316yes—
126#14556124C2316yes—
127#14556123C23124yes—
128#14556123C23112yes—
129#14556123C23112yes—
130#14556121C23124yes—
131#14556121C23112yes—
132#14556121C23112yes—
133#14556120C23112yes—
134#14556119C23124yes—
135#14556119C23112yes—
136#14556119C2316yes—
137#14556119C2316yes—
138#14556118C23124yes—
139#14556118C23112yes—
140#14556118C23112yes—
141#14556117C23112yes—
142#14556117C2316yes—
143#14556115C2316yes—
144#14556114C23112yes—
145#14556114C23112yes—
146#14556112C23124yes—
147#14556112C23112yes—
148#14556112C2314yes—
149#14556111C23112yes—
150#14556110C23124yes—
151#14556109C23112yes—
152#14556109C2314yes—
153#14556108C23124yes—
154#14556107C23112yes—
155#14556107C2316yes—
156#14556107C2316yes—
157#14556105C23112yes—
158#14556105C23124yes—
159#14556105C23112yes—
160#14556105C2314yes—
161#14556105C2314yes—
162#14556104C23112yes—
163#14556104C23112yes—
164#14556104C23112yes—
165#14556102C23112yes—
166#14556102C2316yes—
167#14556102C2316yes—
168#14556100C23112yes—
169#14556100C23112yes—
170#14556100C2314yes—
171#14556100C2314yes—
172#14556099C23112yes—
173#14556097C2314yes—
174Q8×Dic71C23112yes—
175Q8×Dic71C2316yes—
176Q8×Dic71C2314yes—
177Q8×Dic71C2314yes—
178Q8×Dic71C2314yes—
179Q8×Dic71C2314yes—
180Q8×Dic71C23112yes—
181Q8×Dic71C23112yes—
182Q8×Dic71C23112yes—
183Q8×Dic71C2314yes—
184Q8×Dic71C2314yes—
185Q8×Dic71C23112yes—
186Q8×Dic71C2316yes—
187C4×Dic142C23112yes—
188C4×Dic142C23112yes—
189C4×Dic142C23112yes—
190#14556093C2316yes—
191#14556093C2316yes—
192#14556093C23112yes—
193#14556093C23112yes—
194C4×D284C23112yes—
195D4×Dic71C23112yes—
196D4×Dic71C2316yes—
197D4×Dic71C23112yes—
198D4×Dic71C23112yes—
199D4×Dic71C2314yes—
200D4×Dic71C2314yes—
201D4×Dic71C2316yes—
202#14556090C2316yes—
203#14556090C2316yes—
204C4×C22⋊D71C23112yes—
205C4×C22⋊D71C23112yes—
206C4×C22⋊D71C23112yes—
207C4×C22⋊D71C23112yes—
208(C22⋊D71)⋊C4C23112yes—
209(C22⋊D71)⋊C4C23112yes—
210(C22⋊D71)⋊C4C23112yes—
211(C22⋊D71)⋊C4C2314yes—
212(C22⋊D71)⋊C4C23112yes—
213(C22⋊D71)⋊C4C2314yes—
214#14556087C2316yes—
215#14556087C23112yes—
216#14556087C23112yes—
217#14556086C23112yes—
218#14556086C23112yes—
219#14556086C23112yes—
220#14556085C23112yes—
221#14556084C23112yes—
222#14556084C23112yes—
223#14556084C2314yes—
224#14556084C23112yes—
225C2×C4⋊Dic71C2313yes—
226C2×C4⋊Dic71C2316yes—
227C2×C4⋊Dic71C23112yes—
228C2×C4⋊Dic71C23112yes—
229C2×C4⋊Dic71C23112yes—
230C2×C4⋊Dic71C2313yes—
231C4⋊C4×D71C23112yes—
232C2×C4×Dic71C2316yes—
233C2×C4×Dic71C2316yes—
234C2×C4×Dic71C2313yes—
235C2×C4×Dic71C2313yes—
236C2×C4×Dic71C2313yes—
237C2×C4×Dic71C2316yes—
238C2×C4×Dic71C2316yes—
239C2×C4×Dic71C2313yes—
240C2×C4×Dic71C23112yes—
241C42×D71C23112yes—
2422−1+4×C71—28no—
243C2×#41×C71C2316yes—
244C2×#41×C71C2314yes—
245C22×Q8×C71—28no—
246C22×Q8×C71C2313yes—
247C22×Q8×C71C2314yes—
248C22×Q8×C71C2314yes—
249C22×Q8×C71C2314yes—
250C22×Q8×C71C2311yescharacteristic
251C23×C4×C71C2313yes—
252C4⋊Q8×C71C23112yes—
253#124×C71C23112yes—
254#123×C71C23112yes—
255C22⋊Q8×C71C23112yes—
256C22⋊Q8×C71C23112yes—
257C22⋊Q8×C71C2316yes—
258C22⋊Q8×C71C2316yes—
259#121×C71C2316yes—
260#121×C71C2316yes—
261#120×C71C2314yes—
262C4×Q8×C71C2314yes—
263C4×Q8×C71C2314yes—
264C4×D4×C71C23112yes—
265C4×D4×C71C23112yes—
266#117×C71C2316yes—
267#11765866—216no—
268#11765865—224no—
269#11765864—216no—
270#11765864—424no—
271C2×Dic142C2416yes—
272C2×Dic142C2414yes—
273C2×Dic142C24112yes—
274Q8×D71—216no—
275C2×D284C2416yes—
276C2×C22⋊D71C2414yes—
277C2×C22⋊D71C2414yes—
278C2×C22⋊D71C2414yes—
279C2×C22⋊D71C2414yes—
280C2×C22⋊D71C24112yes—
281C22×Dic71—24no—
282C22×Dic71—46no—
283C22×Dic71C2416yes—
284C22×Dic71C2411yescharacteristic
285C22×Dic71C2411yescharacteristic
286C22×Dic71C2411yescharacteristic
287C22×Dic71C2411yescharacteristic
288C22×Dic71C2411yescharacteristic
289C22×Dic71C2414yes—
290C22×Dic71C2413yes—
291C22×Dic71C2416yes—
292C22×Dic71C2413yes—
293C22×Dic71C24112yes—
294C22×Dic71C2411yescharacteristic
295C2×C4×D71C24112yes—
296C2×C4×D71C2414yes—
297C2×C4×D71C24112yes—
298C4⋊Dic71C24112yes—
299C4⋊Dic71C24112yes—
300C4⋊Dic71C24124yes—
301C4⋊Dic71C2416yes—
302C4⋊Dic71C24112yes—
303C4⋊Dic71C2414yes—
304C4⋊Dic71C24112yes—
305C4⋊Dic71C2416yes—
306C4⋊Dic71C2414yes—
307Dic71⋊C4C24112yes—
308Dic71⋊C4C2414yes—
309Dic71⋊C4C2414yes—
310Dic71⋊C4C24112yes—
311Dic71⋊C4C24112yes—
312Dic71⋊C4C2414yes—
313Dic71⋊C4C24112yes—
314Dic71⋊C4C24112yes—
315Dic71⋊C4C24112yes—
316Dic71⋊C4C2414yes—
317C22⋊Dic71C2414yes—
318C22⋊Dic71C2414yes—
319C22⋊Dic71C2414yes—
320C22⋊Dic71C24112yes—
321C22⋊Dic71C2414yes—
322C22⋊Dic71C24112yes—
323C22⋊Dic71C2414yes—
324(C2×D71)⋊C4C2414yes—
325(C2×D71)⋊C4C24112yes—
326(C2×D71)⋊C4C2414yes—
327(C2×D71)⋊C4C24112yes—
328(C2×D71)⋊C4C24112yes—
329(C2×D71)⋊C4C24112yes—
330C4×Dic71C2414yes—
331C4×Dic71C2416yes—
332C4×Dic71C24112yes—
333C4×Dic71C2416yes—
334C4×Dic71C2416yes—
335C4×Dic71C2414yes—
336C4×Dic71C2416yes—
337C4×Dic71C2416yes—
338C4×Dic71C2416yes—
339C4×Dic71C2416yes—
340C4×Dic71C2416yes—
341C4×Dic71C24112yes—
342C4×Dic71C24112yes—
343C24×C71C2411yescharacteristic
344#41×C71—216no—
345#41×C71—224no—
346C2×Q8×C71—216no—
347C2×Q8×C71—216no—
348C2×Q8×C71—216no—
349C2×Q8×C71—212no—
350C2×Q8×C71#4118yescomplemented
351C2×Q8×C71C24112yes—
352C2×Q8×C71C2416yes—
353C2×Q8×C71C2414yes—
354C2×D4×C71C2414yes—
355C2×D4×C71C2414yes—
356C2×D4×C71C2414yes—
357C2×D4×C71C2416yes—
358C22×C4×C71—212no—
359C22×C4×C71C2416yes—
360C22×C4×C71C2416yes—
361C22×C4×C71C24112yes—
362C22×C4×C71C2413yes—
363C22×C4×C71C2413yes—
364C4⋊C4×C71C2416yes—
365C4⋊C4×C71C2416yes—
366C4⋊C4×C71C24112yes—
367C4⋊C4×C71C24112yes—
368C22⋊C4×C71C2414yes—
369C22⋊C4×C71C2414yes—
370C22⋊C4×C71C2414yes—
371C22⋊C4×C71C24112yes—
372C22⋊C4×C71C24112yes—
373C42×C71C24112yes—
374C23×C71—22no—
375C23×C71—22no—
376C23×C71—22no—
377C23×C71C2514yes—
378C23×C71C2511yescharacteristic
379C23×C71C2511yescharacteristic
380C23×C71C2511yescharacteristic
381C22×D71C2514yes—
382Q8×C71—224no—
383Q8×C71—212no—
384Q8×C71C2×#41116yes—
385D4×C71—28no—
386D4×C71—28no—
387D4×C71—28no—
388D4×C71—212no—
389C2×C4×C71—26no—
390C2×C4×C71—212no—
391C2×C4×C71—212no—
392C2×C4×C71—224no—
393C2×C4×C71C2×#41112yes—
394C2×C4×C71C2514yes—
395C2×C4×C71C2514yes—
396C2×C4×C71C2516yes—
397C2×C4×C71C2514yes—
398C2×C4×C71C2516yes—
399C22⋊D71—28no—
400C22⋊D71—28no—
401C22⋊D71—28no—
402C22⋊D71—28no—
403C22⋊D71—412no—
404C2×Dic71—22no—
405C2×Dic71—212no—
406C2×Dic71—22no—
407C2×Dic71—22no—
408C2×Dic71—22no—
409C2×Dic71—22no—
410C2×Dic71—28no—
411C2×Dic71—43no—
412C2×Dic71—46no—
413C2×Dic71—43no—
414C2×Dic71—412no—
415C2×Dic712−1+414yescomplemented
416C2×Dic71C2511yescharacteristic
417C2×Dic71C2511yescharacteristic
418C2×Dic71C2516yes—
419C2×Dic71C2514yes—
420C2×Dic71C2514yes—
421C2×Dic71C2516yes—
422C2×Dic71C2514yes—
423C2×Dic71C2511yescharacteristic
424C2×Dic71C2511yescharacteristic
425D284—212no—
426C4×D71—224no—
427C4×D71—28no—
428C4×D71—412no—
429Dic142—212no—
430Dic142—28no—
431Dic142—412no—
432C22×C71—28no—
433C22×C71—21no—
434C22×C71—21no—
435C22×C71—21no—
436C22×C71—21no—
437C22×C71—21no—
438C22×C71—21no—
439C22×C71—24no—
440C22×C71—24no—
441C22×C71—24no—
442C22×C71C22×#4112yes—
443C22×C71C2×2−1+412yes—
444C22×C71#58512yes—
445C22×C71C2611yescharacteristic
446C2×D71—24no—
447C2×D71—24no—
448C2×D71—24no—
449C4×C71—24no—
450C4×C71—26no—
451C4×C71—24no—
452C4×C71—24no—
453C4×C71C22×#41112yes—
454Dic71—24no—
455Dic71—24no—
456Dic71—21no—
457Dic71—21no—
458Dic71—24no—
459Dic71—26no—
460Dic71—26no—
461Dic71C2×2−1+412yes—
462Dic71C2×2−1+412yes—
463#62788—711nomaximal, Sylow
464C2×C71—22no—
465C2×C71—22no—
466C2×C71—22no—
467C2×C71—44no—
468C2×C71C23×#4111yescharacteristic
469C2×C71C22×2−1+411yescharacteristic
470C2×C71C2×#58511yescharacteristic
471D71—44no—
472#3523—714no—
473#3522—714no—
474#3516—714no—
475#3516—714no—
476#3507—716no—
477#3502—711no—
478#3497—711no—
479#3492—716no—
480#3486—711no—
481#3486D7111yescharacteristic, complemented
482#3482—714no—
483#3482—714no—
484#3480—714no—
485Q8×#41—714no—
486#3461—716no—
487#3444—716no—
488C4×2−1+4—711no—
489C4×2−1+4—711no—
490C22×C4×Q8—711no—
491C71#6278811yescharacteristic, complemented, Sylow
492C2×2−1+4—711no—
493C2×2−1+4C2×D7111yescharacteristic
494C23×Q8C2×D7111yescharacteristic
495#559—7112no—
496Q82—714no—
497#557—7112no—
498#557—714no—
499#557—714no—
500#557—714no—
501#556—7112no—
502#556—7112no—
503#556—7112no—
504#554—7112no—
505#554—7112no—
506#554—7112no—
507#553—7112no—
508#553—7112no—
509#552—7112no—
510#552—7112no—
511#552—7112no—
512#552—7112no—
513#550—714no—
514D4×Q8—714no—
515D4×Q8—714no—
516D4×Q8—714no—
517D4×Q8C2×D7114yes—
518D4×Q8C2×D7114yes—
519#548—714no—
520#548—714no—
521#548—714no—
522#548—714no—
523#548C2×D7114yes—
524#548C2×D7114yes—
525#547—7112no—
526#547—7112no—
527#544—716no—
528#542—7112no—
529#542—7112no—
530#541—7112no—
531#541—7112no—
532#539—7124no—
533#537—716no—
534#536—716no—
535#536C2×D7116yes—
536#533—7112no—
537#533—716no—
538#533—716no—
539#533—7112no—
540#533—716no—
541#532—716no—
542#532—716no—
543#532—716no—
544#529—7112no—
545#529—7112no—
546#529—7112no—
547#529—716no—
548#529—716no—
549#529—7112no—
550#529—716no—
551#529—716no—
552#529—7112no—
553#529—7112no—
554#525—716no—
555#525—714no—
556#525—7112no—
557#525C2×D7116yes—
558#520—716no—
559#520—714no—
560#520—714no—
561#520—716no—
562#519—711no—
563#519—714no—
564#519—714no—
565#519C2×D7111yescharacteristic
566C4×#41—716no—
567C4×#41—714no—
568C4×#41—714no—
569C4×#41—7112no—
570C4×#41—7112no—
571C4×#41—716no—
572C2×C4×Q8—711no—
573C2×C4×Q8—713no—
574C2×C4×Q8—714no—
575C2×C4×Q8—714no—
576C2×C4×Q8—711no—
577C2×C4×Q8—713no—
578C2×C4×Q8—714no—
579C2×C4×Q8—714no—
580C2×C4×Q8—714no—
581C2×C4×Q8—714no—
582C22×C4⋊C4—713no—
583C22×C42—713no—
5842−1+4—28no—
5852−1+4—1428no—
586C2×#41—714no—
587C2×#41—7112no—
588C2×#41—714no—
589C2×#41—716no—
590C2×#41C22×D7116yes—
591C2×#41C22×D7114yes—
592C22×Q8—28no—
593C22×Q8—714no—
594C22×Q8C22×D7113yes—
595C22×Q8C22×D7114yes—
596C22×Q8C22×D7114yes—
597C22×Q8C22×D7114yes—
598C22×Q8C22×D7111yescharacteristic
599C23×C4—713no—
600C23×C4—711no—
601C23×C4C22×D7113yes—
602C4⋊Q8—716no—
603C4⋊Q8—7112no—
604C4⋊Q8—716no—
605C4⋊Q8—716no—
606C4⋊Q8—7112no—
607C4⋊Q8—7112no—
608C4⋊Q8C22×D71112yes—
609#127—716no—
610#126—7112no—
611#126—7112no—
612#126—7124no—
613#126—7112no—
614#126—7112no—
615#126—7124no—
616#125—7112no—
617#125—716no—
618#125—716no—
619#125—7112no—
620#125—7112no—
621#125—7124no—
622#125—7124no—
623#125—7112no—
624#124—716no—
625#124—7112no—
626#124—716no—
627#124—7112no—
628#124—7112no—
629#124C22×D71112yes—
630#123—714no—
631#123—7112no—
632#123—7112no—
633#123—714no—
634#123—7112no—
635#123—7124no—
636#123—7124no—
637#123C22×D71112yes—
638C22⋊Q8—7112no—
639C22⋊Q8—7112no—
640C22⋊Q8—7112no—
641C22⋊Q8—716no—
642C22⋊Q8—716no—
643C22⋊Q8—7112no—
644C22⋊Q8—7124no—
645C22⋊Q8—714no—
646C22⋊Q8—714no—
647C22⋊Q8—7112no—
648C22⋊Q8—7112no—
649C22⋊Q8—7124no—
650C22⋊Q8C22×D7116yes—
651C22⋊Q8C22×D7116yes—
652C22⋊Q8C22×D71112yes—
653C22⋊Q8C22×D71112yes—
654#121—714no—
655#121—714no—
656#121—7112no—
657#121—7112no—
658#121—7112no—
659#121—716no—
660#121—716no—
661#121—7112no—
662#121C22×D7116yes—
663#121C22×D7116yes—
664#120—714no—
665#120C22×D7114yes—
666C4×Q8—714no—
667C4×Q8—714no—
668C4×Q8—7112no—
669C4×Q8—7112no—
670C4×Q8—714no—
671C4×Q8—714no—
672C4×Q8—7112no—
673C4×Q8—7112no—
674C4×Q8—716no—
675C4×Q8—714no—
676C4×Q8—7112no—
677C4×Q8—716no—
678C4×Q8—714no—
679C4×Q8—716no—
680C4×Q8—716no—
681C4×Q8—7112no—
682C4×Q8—7112no—
683C4×Q8—7112no—
684C4×Q8—7112no—
685C4×Q8—7112no—
686C4×Q8C22×D7114yes—
687C4×Q8C22×D7114yes—
688C4×D4—714no—
689C4×D4—714no—
690C4×D4—716no—
691C4×D4—7112no—
692C4×D4—716no—
693C4×D4—7112no—
694C4×D4—7112no—
695C4×D4—7112no—
696C4×D4—7112no—
697C4×D4—7112no—
698C4×D4—7112no—
699C4×D4—716no—
700C4×D4—716no—
701C4×D4—714no—
702C4×D4—714no—
703C4×D4—7112no—
704C4×D4—7112no—
705C4×D4—7112no—
706C4×D4—7112no—
707C4×D4—7112no—
708C4×D4C22×D71112yes—
709C4×D4C22×D71112yes—
710#117—716no—
711#117—7112no—
712#117—7112no—
713#117—7112no—
714#117—7112no—
715#117—7112no—
716#117—714no—
717#117—7112no—
718#117—7112no—
719#117—7112no—
720#117—7112no—
721#117C22×D7116yes—
722C2×C4⋊C4—713no—
723C2×C4⋊C4—713no—
724C2×C4⋊C4—716no—
725C2×C4⋊C4—7112no—
726C2×C4⋊C4—7112no—
727C2×C4⋊C4—7112no—
728C2×C4⋊C4—7112no—
729C2×C42—713no—
730C2×C42—716no—
731C2×C42—716no—
732C2×C42—713no—
733C2×C42—716no—
734C2×C42—713no—
735C2×C42—716no—
736C2×C42—713no—
737C2×C42—7112no—
738C2×C42—7112no—
739C24C23×D7111yescharacteristic
740#41—216no—
741#41—224no—
742#41—28424no—
743#41—14216no—
744#41—14216no—
745#41—14224no—
746C2×Q8—216no—
747C2×Q8—216no—
748C2×Q8—216no—
749C2×Q8—212no—
750C2×Q8—7112no—
751C2×Q8—714no—
752C2×Q8—716no—
753C2×Q8—14216no—
754C2×Q8#1176586418yescomplemented
755C2×Q8C23×D71112yes—
756C2×Q8C23×D7116yes—
757C2×Q8C23×D7114yes—
758C2×D4—7112no—
759C2×D4—714no—
760C2×D4—714no—
761C2×D4—714no—
762C2×D4—714no—
763C2×D4—716no—
764C2×D4C23×D7114yes—
765C2×D4C23×D7116yes—
766C2×D4C23×D7114yes—
767C2×D4C23×D7114yes—
768C22×C4—212no—
769C22×C4—2846no—
770C22×C4—713no—
771C22×C4—716no—
772C22×C4—713no—
773C22×C4—7112no—
774C22×C4—7112no—
775C22×C4—711no—
776C22×C4—711no—
777C22×C4—711no—
778C22×C4—711no—
779C22×C4—711no—
780C22×C4—711no—
781C22×C4—714no—
782C22×C4—716no—
783C22×C4—714no—
784C22×C4—7112no—
785C22×C4—1424no—
786C22×C4C23×D7116yes—
787C22×C4C23×D7116yes—
788C22×C4C23×D7113yes—
789C22×C4C23×D71112yes—
790C22×C4C23×D7113yes—
791C4⋊C4—7112no—
792C4⋊C4—714no—
793C4⋊C4—714no—
794C4⋊C4—714no—
795C4⋊C4—714no—
796C4⋊C4—7112no—
797C4⋊C4—7112no—
798C4⋊C4—7112no—
799C4⋊C4—7112no—
800C4⋊C4—7112no—
801C4⋊C4—7112no—
802C4⋊C4—7112no—
803C4⋊C4—7124no—
804C4⋊C4—716no—
805C4⋊C4—7112no—
806C4⋊C4—716no—
807C4⋊C4—714no—
808C4⋊C4—714no—
809C4⋊C4—7112no—
810C4⋊C4C23×D7116yes—
811C4⋊C4C23×D7116yes—
812C4⋊C4C23×D71112yes—
813C4⋊C4C23×D71112yes—
814C22⋊C4—714no—
815C22⋊C4—714no—
816C22⋊C4—7112no—
817C22⋊C4—714no—
818C22⋊C4—714no—
819C22⋊C4—714no—
820C22⋊C4—7112no—
821C22⋊C4—7112no—
822C22⋊C4—714no—
823C22⋊C4—714no—
824C22⋊C4—7112no—
825C22⋊C4—7112no—
826C22⋊C4—7112no—
827C22⋊C4C23×D7114yes—
828C22⋊C4C23×D7114yes—
829C22⋊C4C23×D71112yes—
830C22⋊C4C23×D71112yes—
831C22⋊C4C23×D7114yes—
832C42—716no—
833C42—714no—
834C42—714no—
835C42—716no—
836C42—716no—
837C42—716no—
838C42—716no—
839C42—716no—
840C42—716no—
841C42—716no—
842C42—7112no—
843C42—7112no—
844C42—7112no—
845C42C23×D71112yes—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—714no—
850C23C24×D7114yes—
851C23C24×D7111yescharacteristic
852C23C24×D7111yescharacteristic
853C23C24×D7111yescharacteristic
854Q8—224no—
855Q8—212no—
856Q8—28412no—
857Q8—1428no—
858Q8—14212no—
859Q8C2×#11765864116yes—
860D4—28no—
861D4—28no—
862D4—28no—
863D4—212no—
864D4—28412no—
865D4—1428no—
866D4—1428no—
867D4—1428no—
868D4—1428no—
869D4—14212no—
870C2×C4—26no—
871C2×C4—212no—
872C2×C4—212no—
873C2×C4—224no—
874C2×C4—28412no—
875C2×C4—2843no—
876C2×C4—2846no—
877C2×C4—2843no—
878C2×C4—28412no—
879C2×C4—714no—
880C2×C4—711no—
881C2×C4—711no—
882C2×C4—711no—
883C2×C4—711no—
884C2×C4—716no—
885C2×C4—714no—
886C2×C4—714no—
887C2×C4—714no—
888C2×C4—716no—
889C2×C4—1428no—
890C2×C4—1422no—
891C2×C4—1422no—
892C2×C4—1422no—
893C2×C4—1422no—
894C2×C4—1428no—
895C2×C4—1422no—
896C2×C4—14212no—
897C2×C4—14224no—
898C2×C4C2×#11765864112yes—
899C2×C4C24×D7116yes—
900C2×C4C24×D7114yes—
901C2×C4C24×D7114yes—
902C2×C4C24×D7114yes—
903C2×C4C24×D7116yes—
904C22—28no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—24no—
912C22—24no—
913C22—24no—
914C22—1424no—
915C22—1424no—
916C22—1424no—
917C22C22×#1176586412yes—
918C222−1+4×D7112yes—
919C22#1798683612yes—
920C22C25×D7111yescharacteristic
921C4—24no—
922C4—26no—
923C4—24no—
924C4—24no—
925C4—712no—
926C4—712no—
927C4—1424no—
928C4—1421no—
929C4—1421no—
930C4—1424no—
931C4—1426no—
932C4—1424no—
933C4—1426no—
934C4C22×#11765864112yes—
935C2—22no—
936C2—22no—
937C2—22no—
938C2—44no—
939C2—2844no—
940C2C23×#1176586411yescharacteristic
941C2C2×2−1+4×D7111yescharacteristic
942C2C2×#1798683611yescharacteristic
subgroupG/H
center, FrattiniC22C25×D71
commutator, socle, cosocleC22×C71C26
FittingC71×#3486C2
hypercenter#3486D71
hypocenterC71#62788
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ #3486

Complements

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

NH ≅ G/Ntype
1. #22602427C2semidirect
2. #22602416C2semidirect
3. #22602334C2semidirect
4. #22602322C2semidirect
5. #22602204C2semidirect
6. #22602146C2semidirect
7. #22602107C2semidirect
8. #22602046C2semidirect
9. #22601991C2semidirect
10. #22601961C2semidirect
11. #22601956C2semidirect
12. #22601930C2semidirect
13. Q8×#11765864C2semidirect
14. #22601764C2semidirect
15. #22601632C2semidirect
16. 2−1+4×Dic71C2semidirect
17. #22601549C2semidirect
18. C22×Q8×Dic71C2semidirect
19. C71×#3486C2semidirect
21. #17986731C22semidirect
22. Q8×Dic142C22semidirect
23. #17986728C22semidirect
24. #17986725C22semidirect
25. #17986725C22semidirect
26. #17986724C22semidirect
27. #17986723C22semidirect
28. #17986720C22semidirect
29. #17986718C22semidirect
31. #17986707C22semidirect
36. #17986691C22semidirect
38. #17986683C22semidirect
39. #17986668C22semidirect
42. Q8×C22⋊D71C22semidirect
45. #17986660C22semidirect
46. #17986656C22semidirect
50. #17986622C22semidirect
51. #17986618C22semidirect
52. #17986610C22semidirect
53. #17986609C22semidirect
57. #17986554C22semidirect
61. #17986551C22semidirect
67. #17986535C22semidirect
72. #17986528C22semidirect
79. #17986482C22semidirect
80. #17986481C22semidirect
83. #17986477C22semidirect
84. #17986475C22semidirect
86. #41×Dic71C22semidirect
87. C4×#11765866C22semidirect
99. C2×Q8×Dic71C22semidirect
100. C4×Q8×D71C22semidirect
350. C2×Q8×C71#41semidirect
415. C2×Dic712−1+4semidirect
481. #3486D71semidirect
491. C71#62788semidirect
754. C2×Q8#11765864semidirect

Maximal subgroups

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

subgroupindex
#226024272
#226024162
#226023342
#226023222
#226022042
#226021462
#226021072
#226020462
#226019912
#226019612
#226019562
#226019302
Q8×#117658642
#226017642
#226016322
2−1+4×Dic712
#226015492
C22×Q8×Dic712
C71×#34862
#6278871