Finite Group Databasebeta

← #26004885

Subgroups — #26004885

Order 11008.

7190 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148705C214yesmaximal, complemented
2#19148693C214yesmaximal, complemented
3#19148603C214yesmaximal, complemented
4#19148592C214yesmaximal, complemented
5#19148446C216yesmaximal, complemented
6#19148401C211yesmaximal, characteristic, complemented
7#19148362C211yesmaximal, characteristic, complemented
8#19148312C216yesmaximal, complemented
9#19148253C211yesmaximal, characteristic, complemented
10#19148218C214yesmaximal, complemented
11#19148211C214yesmaximal, complemented
12#19148194C214yesmaximal, complemented
13#19148185C214yesmaximal, complemented
14#19148008C216yesmaximal, complemented
15#19147887C216yesmaximal, complemented
162−1+4×Dic43C211yesmaximal, characteristic, complemented
17#19147804C211yesmaximal, characteristic, complemented
18C2×#41×Dic43C211yesmaximal, characteristic, complemented
19C43×#3487C211yesmaximal, characteristic, complemented
20C2×#13063373C2211yescharacteristic
21#14583635C22112yescomplemented
22#14583631C22112yescomplemented
23Q8×Dic86C2214yescomplemented
24#14583628C2214yescomplemented
25#14583625C2214yescomplemented
26#14583625C2214yescomplemented
27#14583620C22112yescomplemented
28#14583619C22112yescomplemented
29#14583618C22112yescomplemented
30#14583614C22112yescomplemented
31#14583613C22112yescomplemented
32#14583613C22112yescomplemented
33#14583601C22112yescomplemented
34#14583596C22112yescomplemented
35#14583596C22112yescomplemented
36#14583595C22112yescomplemented
37#14583589C22112yescomplemented
38#14583583C22112yescomplemented
39#14583569C22112yescomplemented
40#14583568C2214yes—
41#14583568C2214yes—
42#14583568C2214yescomplemented
43Q8×C22⋊D43C2214yescomplemented
44#14583560C2214yescomplemented
45#14583556C2214yes—
46#14583556C2214yes—
47#14583556C2214yescomplemented
48#14583549C22112yescomplemented
49#14583527C2216yes—
50#14583518C22112yescomplemented
51#14583516C22112yescomplemented
52#14583503C22112yescomplemented
53#14583502C22112yescomplemented
54#14583484C22124yes—
55#14583477C2216yes—
56#14583466C2216yes—
57#14583452C2216yes—
58#14583451C2216yescomplemented
59#14583451C2216yescomplemented
60#14583447C22112yescomplemented
61#14583445C2216yes—
62#14583444C2216yescomplemented
63#14583444C2216yescomplemented
64#14583444C22112yescomplemented
65#14583435C2216yescomplemented
66#14583435C2216yescomplemented
67#14583430C2216yescomplemented
68#14583430C2216yescomplemented
69#14583430C22112yescomplemented
70#14583429C22112yescomplemented
71#14583429C22112yescomplemented
72#14583428C22112yescomplemented
73#14583426C22112yes—
74#14583426C2214yes—
75#14583410C2216yes—
76#14583405C22112yes—
77#14583405C22112yes—
78#14583382C2216yes—
79#14583382C2214yescomplemented
80#14583381C2214yescomplemented
81#14583379C2216yes—
82#14583377C2211yescharacteristic
83#14583377C2214yescomplemented
84#14583375C2214yescomplemented
85#41×Dic43C2214yes—
86#41×Dic43C2214yes—
87#41×Dic43C2214yes—
88#41×Dic43C2214yes—
89#41×Dic43C2216yes—
90#41×Dic43C2214yescomplemented
91C4×#10621902C2214yescomplemented
92#14583367C2216yes—
93C4×#10621900C22112yescomplemented
94C4×#10621900C22112yescomplemented
95C2×Q8×Dic43C2211yescharacteristic
96C2×Q8×Dic43C2211yescharacteristic
97C2×Q8×Dic43C2214yescomplemented
98C4×Q8×D43C2214yescomplemented
99C2×D4×Dic43C2213yes—
100C2×D4×Dic43C2213yes—
101C2×#13063284C2213yes—
102C22×C4×Dic43C2213yes—
103C2×2−1+4×C43C2211yescharacteristic
104C22×#41×C43C2211yescharacteristic
105C43×#550C2214yes—
106C43×#550C2214yes—
107C43×#548C2214yes—
108C43×#548C2214yes—
109C43×#535C2216yes—
110C43×#525C2216yes—
111C43×#519C2211yescharacteristic
112#13063373—28no—
113C2×#10621902C2314yes—
114C2×#10621898C2316yes—
115C2×#10621900C23112yes—
116C2×#10621900C23112yes—
117C2×Q8×D43C2314yes—
118C23×Dic43C2313yes—
119C23×Dic43C2313yes—
120#13063325C23112yes—
121#13063324C2316yes—
122#13063324C23112yes—
123#13063324C2316yes—
124#13063323C2316yes—
125#13063321C23112yes—
126#13063321C2316yes—
127#13063320C23112yes—
128#13063320C2314yes—
129#13063318C23124yes—
130#13063318C23124yes—
131#13063318C23112yes—
132#13063318C2314yes—
133#13063317C23112yes—
134#13063316C23112yes—
135#13063316C2316yes—
136#13063316C2316yes—
137#13063315C23112yes—
138#13063315C2314yes—
139#13063314C2316yes—
140#13063312C23112yes—
141#13063312C2316yes—
142#13063312C23124yes—
143#13063311C23112yes—
144#13063311C23124yes—
145#13063311C2314yes—
146#13063309C23112yes—
147#13063309C23112yes—
148#13063308C2314yes—
149#13063307C23124yes—
150#13063306C23124yes—
151#13063306C23112yes—
152#13063306C23112yes—
153#13063304C2316yes—
154#13063304C2316yes—
155#13063304C23112yes—
156#13063302C23112yes—
157#13063302C2314yes—
158#13063302C23112yes—
159#13063302C23112yes—
160#13063301C23112yes—
161#13063299C23112yes—
162#13063299C2316yes—
163#13063299C2316yes—
164#13063297C23112yes—
165#13063297C23124yes—
166#13063297C2314yes—
167#13063297C23112yes—
168#13063297C23112yes—
169#13063296C23112yes—
170#13063296C23112yes—
171#13063296C23112yes—
172#13063296C23124yes—
173#13063294C23112yes—
174Q8×Dic43C2314yes—
175Q8×Dic43C2314yes—
176Q8×Dic43C2314yes—
177Q8×Dic43C2314yes—
178Q8×Dic43C23112yes—
179Q8×Dic43C2314yes—
180Q8×Dic43C2314yes—
181Q8×Dic43C2316yes—
182Q8×Dic43C2316yes—
183C4×Dic86C23112yes—
184C4×Dic86C23112yes—
185C4×Dic86C23112yes—
186#13063290C2316yes—
187#13063290C23112yes—
188#13063290C2314yes—
189#13063290C2316yes—
190C4×D172C23112yes—
191D4×Dic43C23112yes—
192D4×Dic43C23112yes—
193D4×Dic43C23112yes—
194D4×Dic43C23112yes—
195D4×Dic43C23112yes—
196D4×Dic43C23112yes—
197D4×Dic43C23112yes—
198D4×Dic43C2314yes—
199D4×Dic43C2316yes—
200D4×Dic43C23112yes—
201D4×Dic43C2316yes—
202#13063287C2316yes—
203#13063287C2316yes—
204C4×C22⋊D43C23112yes—
205C4×C22⋊D43C23112yes—
206C4×C22⋊D43C23112yes—
207C4×C22⋊D43C23112yes—
208(C22⋊D43)⋊C4C23112yes—
209(C22⋊D43)⋊C4C23112yes—
210(C22⋊D43)⋊C4C2314yes—
211(C22⋊D43)⋊C4C23112yes—
212(C22⋊D43)⋊C4C2314yes—
213(C22⋊D43)⋊C4C23112yes—
214#13063284C23112yes—
215#13063284C23112yes—
216#13063284C23112yes—
217#13063284C2316yes—
218#13063284C23112yes—
219#13063283C23112yes—
220#13063283C23112yes—
221#13063283C2314yes—
222#13063282C23112yes—
223#13063281C23112yes—
224#13063281C23112yes—
225#13063281C2314yes—
226#13063281C23112yes—
227C2×C4⋊Dic43C23112yes—
228C2×C4⋊Dic43C2313yes—
229C2×C4⋊Dic43C2313yes—
230C4⋊C4×D43C23112yes—
231C2×C22⋊Dic43C2316yes—
232C2×C4×Dic43C2311yescharacteristic
233C2×C4×Dic43C2313yes—
234C2×C4×Dic43C2313yes—
235C2×C4×Dic43C2313yes—
236C2×C4×Dic43C2316yes—
237C2×C4×Dic43C2316yes—
238C2×C4×Dic43C2316yes—
239C2×C4×Dic43C2316yes—
240C2×C4×Dic43C23112yes—
241C42×D43C23112yes—
2422−1+4×C43—28no—
243C2×#41×C43—28no—
244C2×#41×C43C2314yes—
245C2×#41×C43C2314yes—
246C2×#41×C43C2314yes—
247C2×#41×C43C2316yes—
248C22×Q8×C43C2314yes—
249C22×Q8×C43C2311yescharacteristic
250C22×D4×C43C2313yes—
251C23×C4×C43C2313yes—
252#127×C43C23112yes—
253#124×C43C23112yes—
254#123×C43C2314yes—
255C22⋊Q8×C43C2316yes—
256C22⋊Q8×C43C2316yes—
257#121×C43C2316yes—
258#121×C43C2316yes—
259#121×C43C23112yes—
260#121×C43C23112yes—
261#120×C43C23112yes—
262C4×Q8×C43C2314yes—
263C4×Q8×C43C2314yes—
264C4×D4×C43C23112yes—
265C4×D4×C43C23112yes—
266#117×C43C2316yes—
267C24×C43C2413yes—
268#41×C43—216no—
269#41×C43—216no—
270#41×C43—216no—
271#41×C43—224no—
272C2×Q8×C43—216no—
273C2×Q8×C43#4118yescomplemented
274C2×Q8×C43C2416yes—
275C2×Q8×C43C2414yes—
276C2×D4×C43—212no—
277C2×D4×C43C2414yes—
278C2×D4×C43C24112yes—
279C2×D4×C43C2416yes—
280C2×D4×C43C24112yes—
281C2×D4×C43C24112yes—
282C22×C4×C43—212no—
283C22×C4×C43C24112yes—
284C22×C4×C43C2416yes—
285C22×C4×C43C2416yes—
286C22×C4×C43C2411yescharacteristic
287C22×C4×C43C2413yes—
288C2×C22⋊D43C2414yes—
289C2×C22⋊D43C2414yes—
290C2×C22⋊D43C24112yes—
291C2×C22⋊D43C24112yes—
292C2×C22⋊D43C24112yes—
293C22×Dic43—46no—
294C22×Dic43—46no—
295C22×Dic43C2411yescharacteristic
296C22×Dic43C2411yescharacteristic
297C22×Dic43C2414yes—
298C22×Dic43C2416yes—
299C22×Dic43C2416yes—
300C22×Dic43C2413yes—
301C22×Dic43C2413yes—
302C22×Dic43C2416yes—
303C22×Dic43C2416yes—
304C22×Dic43C24112yes—
305#10621902—216no—
306Q8×D43—216no—
307#10621900—424no—
308#10621900—424no—
309#10621898—224no—
310C2×D172C2416yes—
311C2×C4×D43C2414yes—
312C2×C4×D43C24112yes—
313C2×C4×D43C24112yes—
314C2×Dic86C2416yes—
315C2×Dic86C2414yes—
316C2×Dic86C24112yes—
317C4⋊C4×C43C2416yes—
318C4⋊C4×C43C2416yes—
319C4⋊C4×C43C2414yes—
320C4⋊C4×C43C2414yes—
321C22⋊C4×C43C2414yes—
322C22⋊C4×C43C2414yes—
323C22⋊C4×C43C2414yes—
324C22⋊C4×C43C24112yes—
325C22⋊C4×C43C24112yes—
326C42×C43C24112yes—
327C22⋊Dic43C24124yes—
328C22⋊Dic43C2414yes—
329C22⋊Dic43C24112yes—
330C22⋊Dic43C24112yes—
331C22⋊Dic43C24112yes—
332C22⋊Dic43C2414yes—
333C22⋊Dic43C24112yes—
334C22⋊Dic43C2414yes—
335(C2×D43)⋊C4C2414yes—
336(C2×D43)⋊C4C24112yes—
337(C2×D43)⋊C4C2414yes—
338(C2×D43)⋊C4C2414yes—
339(C2×D43)⋊C4C2414yes—
340(C2×D43)⋊C4C24112yes—
341C4⋊Dic43C24112yes—
342C4⋊Dic43C2416yes—
343C4⋊Dic43C24112yes—
344C4⋊Dic43C24112yes—
345C4⋊Dic43C2414yes—
346C4⋊Dic43C24112yes—
347C4⋊Dic43C2416yes—
348C4⋊Dic43C2414yes—
349Dic43⋊C4C24112yes—
350Dic43⋊C4C2414yes—
351Dic43⋊C4C2414yes—
352Dic43⋊C4C2414yes—
353Dic43⋊C4C2414yes—
354Dic43⋊C4C24112yes—
355Dic43⋊C4C24112yes—
356Dic43⋊C4C2414yes—
357Dic43⋊C4C24112yes—
358Dic43⋊C4C2414yes—
359C4×Dic43C2414yes—
360C4×Dic43C2416yes—
361C4×Dic43C24112yes—
362C4×Dic43C2411yescharacteristic
363C4×Dic43C2411yescharacteristic
364C4×Dic43C2411yescharacteristic
365C4×Dic43C2411yescharacteristic
366C4×Dic43C2414yes—
367C4×Dic43C2416yes—
368C4×Dic43C2416yes—
369C4×Dic43C2416yes—
370C4×Dic43C2416yes—
371C4×Dic43C2416yes—
372C4×Dic43C24112yes—
373C4×Dic43C24112yes—
374C23×C43—26no—
375C23×C43—43no—
376C23×C43—43no—
377C23×C43C2516yes—
378C23×C43C2514yes—
379C23×C43C2511yescharacteristic
380C22×D43C2514yes—
381Q8×C43—212no—
382Q8×C43C2×#41116yes—
383D4×C43—28no—
384D4×C43—224no—
385D4×C43—212no—
386D4×C43—412no—
387D4×C43—412no—
388C2×C4×C43—22no—
389C2×C4×C43—212no—
390C2×C4×C43—212no—
391C2×C4×C43—224no—
392C2×C4×C43C2×#41112yes—
393C2×C4×C43C2511yescharacteristic
394C2×C4×C43C2511yescharacteristic
395C2×C4×C43C2514yes—
396C2×C4×C43C2514yes—
397C2×C4×C43C2514yes—
398C2×C4×C43C2516yes—
399C22⋊D43—28no—
400C22⋊D43—28no—
401C22⋊D43—412no—
402C22⋊D43—412no—
403C22⋊D43—412no—
404C2×Dic43—28no—
405C2×Dic43—212no—
406C2×Dic43—212no—
407C2×Dic43—22no—
408C2×Dic43—22no—
409C2×Dic43—412no—
410C2×Dic43—43no—
411C2×Dic43—46no—
412C2×Dic43—43no—
413C2×Dic43—46no—
414C2×Dic43C2511yescharacteristic
415C2×Dic43C2511yescharacteristic
416C2×Dic43C2516yes—
417C2×Dic43C2514yes—
418C2×Dic43C2514yes—
419C2×Dic43C2514yes—
420C2×Dic43C2516yes—
421C2×Dic43C2511yescharacteristic
422C2×Dic43C2511yescharacteristic
423D172—212no—
424C4×D43—224no—
425C4×D43—28no—
426C4×D43—412no—
427Dic86—212no—
428Dic86—28no—
429Dic86—412no—
430#62793—431nomaximal, Sylow
431C22×C43—21no—
432C22×C43—21no—
433C22×C43—26no—
434C22×C43—24no—
435C22×C43—26no—
436C22×C43—26no—
437C22×C43—24no—
438C22×C43—24no—
439C22×C43—412no—
440C22×C43C22×#4112yes—
441C22×C43C2611yescharacteristic
442C2×D43—24no—
443C2×D43—24no—
444C2×D43—24no—
445C4×C43—21no—
446C4×C43—21no—
447C4×C43—24no—
448C4×C43—24no—
449C4×C43—24no—
450C4×C43C22×#41112yes—
451Dic43—24no—
452Dic43—24no—
453Dic43—24no—
454Dic43—26no—
455Dic43—26no—
456Dic43—21no—
457Dic43—21no—
458Dic43#58512yes—
459Dic43#58512yes—
460#3524—434no—
461#3524—434no—
462#3518—434no—
463#3517—434no—
464#3506—436no—
465#3502—431no—
466#3497—431no—
467#3493—436no—
468#3487—431no—
469#3487D4311yescharacteristic, complemented
470#3483—434no—
471#3482—434no—
472#3480—434no—
473#3480—434no—
474#3460—436no—
475#3444—436no—
476C4×2−1+4—431no—
477C4×2−1+4—431no—
478C2×C4×#41—431no—
479C2×C43—22no—
480C2×C43—44no—
481C2×C43—46no—
482C2×C43C23×#4111yescharacteristic
483C2×C43C2×#58511yescharacteristic
484C2×C43C2×#58511yescharacteristic
485D43—44no—
486C2×2−1+4—431no—
487C2×2−1+4C2×D4311yescharacteristic
488C22×#41C2×D4311yescharacteristic
489#559—4312no—
490#559—4312no—
491Q82—434no—
492#557—434no—
493#557—434no—
494#557—434no—
495#556—4312no—
496#556—4312no—
497#556—4312no—
498#555—4312no—
499#555—4312no—
500#555—4312no—
501#553—4312no—
502#553—4312no—
503#553—4312no—
504#553—4312no—
505#552—4312no—
506#552—4312no—
507#550—434no—
508#550—434no—
509#550—434no—
510#550—4312no—
511#550C2×D4314yes—
512#550C2×D4314yes—
513D4×Q8—434no—
514#548—434no—
515#548—434no—
516#548—434no—
517#548—434no—
518#548C2×D4314yes—
519#548C2×D4314yes—
520#547—4312no—
521#544—436no—
522#542—4312no—
523#542—4312no—
524#540—4312no—
525#540—4312no—
526#538—4324no—
527#537—436no—
528#535—436no—
529#535C2×D4316yes—
530#533—436no—
531#533—436no—
532#533—436no—
533#532—436no—
534#532—4312no—
535#532—436no—
536#532—436no—
537#532—4312no—
538#529—4312no—
539#529—434no—
540#529—4312no—
541#529—436no—
542#529—436no—
543#529—436no—
544#529—436no—
545#529—4312no—
546#529—4312no—
547#529—4312no—
548#525—436no—
549#525—4312no—
550#525—4312no—
551#525C2×D4316yes—
552#520—436no—
553#520—434no—
554#520—434no—
555#520—436no—
556#519—431no—
557#519—434no—
558#519—434no—
559#519C2×D4311yescharacteristic
560C4×#41—434no—
561C4×#41—434no—
562C4×#41—434no—
563C4×#41—434no—
564C4×#41—436no—
565C4×#41—434no—
566C4×#41—434no—
567C4×#41—4312no—
568C4×#41—4312no—
569C4×#41—436no—
570C2×C4×Q8—431no—
571C2×C4×Q8—431no—
572C2×C4×Q8—434no—
573C2×C4×Q8—434no—
574C2×C4×D4—433no—
575C2×C4×D4—433no—
576C2×#117—433no—
577C22×C42—433no—
578C43#6279311yescharacteristic, complemented, Sylow
5792−1+4—28no—
5802−1+4—868no—
581C2×#41—28no—
582C2×#41—434no—
583C2×#41—4312no—
584C2×#41—4312no—
585C2×#41—436no—
586C2×#41C22×D4314yes—
587C2×#41C22×D4314yes—
588C2×#41C22×D4316yes—
589C2×#41C22×D4314yes—
590C22×Q8—434no—
591C22×Q8C22×D4314yes—
592C22×Q8C22×D4311yescharacteristic
593C22×D4C22×D4313yes—
594C23×C4—433no—
595C23×C4—433no—
596C23×C4C22×D4313yes—
597C4⋊Q8—436no—
598C4⋊Q8—436no—
599C4⋊Q8—436no—
600C4⋊Q8—4312no—
601C4⋊Q8—4312no—
602#127—436no—
603#127—4312no—
604#127C22×D43112yes—
605#126—434no—
606#126—4312no—
607#126—434no—
608#126—4312no—
609#126—4324no—
610#126—4324no—
611#125—434no—
612#125—4312no—
613#125—436no—
614#125—436no—
615#125—4312no—
616#125—4312no—
617#124—436no—
618#124—436no—
619#124—4312no—
620#124—4324no—
621#124—434no—
622#124—4312no—
623#124—4324no—
624#124C22×D43112yes—
625#123—4312no—
626#123—4312no—
627#123—4324no—
628#123—434no—
629#123—4312no—
630#123—4312no—
631#123—4324no—
632#123C22×D4314yes—
633C22⋊Q8—4312no—
634C22⋊Q8—436no—
635C22⋊Q8—436no—
636C22⋊Q8—4312no—
637C22⋊Q8—434no—
638C22⋊Q8—4312no—
639C22⋊Q8—4312no—
640C22⋊Q8—4312no—
641C22⋊Q8C22×D4316yes—
642C22⋊Q8C22×D4316yes—
643#121—434no—
644#121—4312no—
645#121—4312no—
646#121—4312no—
647#121—4312no—
648#121—4312no—
649#121—4312no—
650#121—4324no—
651#121—4324no—
652#121—436no—
653#121—436no—
654#121—4312no—
655#121C22×D4316yes—
656#121C22×D4316yes—
657#121C22×D43112yes—
658#121C22×D43112yes—
659#120—4312no—
660#120C22×D43112yes—
661C4×Q8—434no—
662C4×Q8—436no—
663C4×Q8—434no—
664C4×Q8—434no—
665C4×Q8—434no—
666C4×Q8—434no—
667C4×Q8—4312no—
668C4×Q8—436no—
669C4×Q8—434no—
670C4×Q8—436no—
671C4×Q8—434no—
672C4×Q8—436no—
673C4×Q8—4312no—
674C4×Q8—4312no—
675C4×Q8—4312no—
676C4×Q8—4312no—
677C4×Q8C22×D4314yes—
678C4×Q8C22×D4314yes—
679C4×D4—4312no—
680C4×D4—4312no—
681C4×D4—4312no—
682C4×D4—4312no—
683C4×D4—434no—
684C4×D4—436no—
685C4×D4—4312no—
686C4×D4—436no—
687C4×D4—4312no—
688C4×D4—4312no—
689C4×D4—4312no—
690C4×D4—4312no—
691C4×D4—4312no—
692C4×D4—4312no—
693C4×D4—4312no—
694C4×D4—436no—
695C4×D4—436no—
696C4×D4—434no—
697C4×D4—434no—
698C4×D4—4312no—
699C4×D4—4312no—
700C4×D4—4312no—
701C4×D4—4312no—
702C4×D4—4312no—
703C4×D4C22×D43112yes—
704C4×D4C22×D43112yes—
705#117—4312no—
706#117—4312no—
707#117—436no—
708#117—4312no—
709#117—4312no—
710#117—434no—
711#117—4312no—
712#117—4312no—
713#117—434no—
714#117—4312no—
715#117—4312no—
716#117—4312no—
717#117—4312no—
718#117C22×D4316yes—
719C2×C4⋊C4—433no—
720C2×C4⋊C4—433no—
721C2×C4⋊C4—4312no—
722C2×C4⋊C4—4312no—
723C2×C22⋊C4—436no—
724C2×C42—433no—
725C2×C42—433no—
726C2×C42—433no—
727C2×C42—4312no—
728C2×C42—436no—
729C2×C42—436no—
730C2×C42—436no—
731C2×C42—436no—
732C2×C42—431no—
733C2×C42—4312no—
734C24C23×D4313yes—
735#41—216no—
736#41—216no—
737#41—216no—
738#41—224no—
739#41—8616no—
740#41—8624no—
741#41—17224no—
742#41—17224no—
743C2×Q8—216no—
744C2×Q8—436no—
745C2×Q8—434no—
746C2×Q8—4312no—
747C2×Q8—8616no—
748C2×Q8#1062190018yescomplemented
749C2×Q8C23×D4316yes—
750C2×Q8C23×D4314yes—
751C2×D4—212no—
752C2×D4—434no—
753C2×D4—434no—
754C2×D4—4312no—
755C2×D4—4312no—
756C2×D4—4312no—
757C2×D4—436no—
758C2×D4C23×D4314yes—
759C2×D4C23×D43112yes—
760C2×D4C23×D4316yes—
761C2×D4C23×D43112yes—
762C2×D4C23×D43112yes—
763C22×C4—212no—
764C22×C4—431no—
765C22×C4—431no—
766C22×C4—434no—
767C22×C4—436no—
768C22×C4—436no—
769C22×C4—433no—
770C22×C4—433no—
771C22×C4—436no—
772C22×C4—436no—
773C22×C4—4312no—
774C22×C4—434no—
775C22×C4—4312no—
776C22×C4—4312no—
777C22×C4—1726no—
778C22×C4—1726no—
779C22×C4C23×D4311yescharacteristic
780C22×C4C23×D4316yes—
781C22×C4C23×D4316yes—
782C22×C4C23×D43112yes—
783C22×C4C23×D4313yes—
784C4⋊C4—4312no—
785C4⋊C4—436no—
786C4⋊C4—4312no—
787C4⋊C4—4312no—
788C4⋊C4—4312no—
789C4⋊C4—434no—
790C4⋊C4—434no—
791C4⋊C4—434no—
792C4⋊C4—436no—
793C4⋊C4—434no—
794C4⋊C4—434no—
795C4⋊C4—434no—
796C4⋊C4—434no—
797C4⋊C4—434no—
798C4⋊C4—4312no—
799C4⋊C4—4312no—
800C4⋊C4—4312no—
801C4⋊C4—4312no—
802C4⋊C4C23×D4316yes—
803C4⋊C4C23×D4314yes—
804C4⋊C4C23×D4316yes—
805C4⋊C4C23×D4314yes—
806C22⋊C4—4324no—
807C22⋊C4—434no—
808C22⋊C4—434no—
809C22⋊C4—4312no—
810C22⋊C4—434no—
811C22⋊C4—4312no—
812C22⋊C4—4312no—
813C22⋊C4—4312no—
814C22⋊C4—434no—
815C22⋊C4—4312no—
816C22⋊C4—434no—
817C22⋊C4—434no—
818C22⋊C4—434no—
819C22⋊C4—4312no—
820C22⋊C4C23×D4314yes—
821C22⋊C4C23×D4314yes—
822C22⋊C4C23×D43112yes—
823C22⋊C4C23×D43112yes—
824C22⋊C4C23×D4314yes—
825C42—431no—
826C42—431no—
827C42—436no—
828C42—431no—
829C42—431no—
830C42—436no—
831C42—434no—
832C42—434no—
833C42—436no—
834C42—436no—
835C42—436no—
836C42—436no—
837C42—4312no—
838C42—4312no—
839C42—4312no—
840C42C23×D43112yes—
841C23—26no—
842C23—43no—
843C23—43no—
844C23—434no—
845C23C24×D4316yes—
846C23C24×D4314yes—
847C23C24×D4311yescharacteristic
848Q8—212no—
849Q8—868no—
850Q8—8612no—
851Q8—17212no—
852Q8C2×#10621900116yes—
853D4—28no—
854D4—224no—
855D4—212no—
856D4—412no—
857D4—412no—
858D4—868no—
859D4—868no—
860D4—8612no—
861D4—17212no—
862D4—17212no—
863D4—17212no—
864C2×C4—22no—
865C2×C4—212no—
866C2×C4—212no—
867C2×C4—224no—
868C2×C4—431no—
869C2×C4—431no—
870C2×C4—431no—
871C2×C4—436no—
872C2×C4—431no—
873C2×C4—434no—
874C2×C4—434no—
875C2×C4—436no—
876C2×C4—434no—
877C2×C4—868no—
878C2×C4—862no—
879C2×C4—862no—
880C2×C4—8612no—
881C2×C4—8612no—
882C2×C4—868no—
883C2×C4—8624no—
884C2×C4—17212no—
885C2×C4—1723no—
886C2×C4—1726no—
887C2×C4—1726no—
888C2×C4—1723no—
889C2×C4—17212no—
890C2×C4C2×#10621900112yes—
891C2×C4C24×D4311yescharacteristic
892C2×C4C24×D4311yescharacteristic
893C2×C4C24×D4314yes—
894C2×C4C24×D4314yes—
895C2×C4C24×D4314yes—
896C2×C4C24×D4316yes—
897C22—21no—
898C22—21no—
899C22—24no—
900C22—26no—
901C22—26no—
902C22—26no—
903C22—24no—
904C22—24no—
905C22—412no—
906C22—864no—
907C22—864no—
908C22—864no—
909C22C22×#1062190012yes—
910C22C25×D4311yescharacteristic
911C4—21no—
912C4—21no—
913C4—24no—
914C4—24no—
915C4—24no—
916C4—432no—
917C4—432no—
918C4—864no—
919C4—861no—
920C4—861no—
921C4—866no—
922C4—866no—
923C4—864no—
924C4—864no—
925C4C22×#10621900112yes—
926C2—22no—
927C2—46no—
928C2—44no—
929C2—1724no—
930C2C23×#1062190011yescharacteristic
931C2#585×D4311yescharacteristic
932C2#585×D4311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3487C2
hypercenter#3487D43
hypocenterC43#62793
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3487

Complements

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

NH ≅ G/Ntype
1. #19148705C2semidirect
2. #19148693C2semidirect
3. #19148603C2semidirect
4. #19148592C2semidirect
5. #19148446C2semidirect
6. #19148401C2semidirect
7. #19148362C2semidirect
8. #19148312C2semidirect
9. #19148253C2semidirect
10. #19148218C2semidirect
11. #19148211C2semidirect
12. #19148194C2semidirect
13. #19148185C2semidirect
14. #19148008C2semidirect
15. #19147887C2semidirect
16. 2−1+4×Dic43C2semidirect
17. #19147804C2semidirect
18. C2×#41×Dic43C2semidirect
19. C43×#3487C2semidirect
21. #14583635C22semidirect
22. #14583631C22semidirect
23. Q8×Dic86C22semidirect
24. #14583628C22semidirect
25. #14583625C22semidirect
26. #14583625C22semidirect
27. #14583620C22semidirect
28. #14583619C22semidirect
29. #14583618C22semidirect
30. #14583614C22semidirect
31. #14583613C22semidirect
32. #14583613C22semidirect
33. #14583601C22semidirect
34. #14583596C22semidirect
35. #14583596C22semidirect
36. #14583595C22semidirect
37. #14583589C22semidirect
38. #14583583C22semidirect
39. #14583569C22semidirect
42. #14583568C22semidirect
43. Q8×C22⋊D43C22semidirect
44. #14583560C22semidirect
47. #14583556C22semidirect
48. #14583549C22semidirect
50. #14583518C22semidirect
51. #14583516C22semidirect
52. #14583503C22semidirect
53. #14583502C22semidirect
58. #14583451C22semidirect
59. #14583451C22semidirect
60. #14583447C22semidirect
62. #14583444C22semidirect
63. #14583444C22semidirect
64. #14583444C22semidirect
65. #14583435C22semidirect
66. #14583435C22semidirect
67. #14583430C22semidirect
68. #14583430C22semidirect
69. #14583430C22semidirect
70. #14583429C22semidirect
71. #14583429C22semidirect
72. #14583428C22semidirect
79. #14583382C22semidirect
80. #14583381C22semidirect
83. #14583377C22semidirect
84. #14583375C22semidirect
90. #41×Dic43C22semidirect
91. C4×#10621902C22semidirect
93. C4×#10621900C22semidirect
94. C4×#10621900C22semidirect
97. C2×Q8×Dic43C22semidirect
98. C4×Q8×D43C22semidirect
273. C2×Q8×C43#41semidirect
469. #3487D43semidirect
578. C43#62793semidirect
748. C2×Q8#10621900semidirect

Maximal subgroups

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

subgroupindex
#191487052
#191486932
#191486032
#191485922
#191484462
#191484012
#191483622
#191483122
#191482532
#191482182
#191482112
#191481942
#191481852
#191480082
#191478872
2−1+4×Dic432
#191478042
C2×#41×Dic432
C43×#34872
#6279343