Finite Group Databasebeta

← #26004822

Subgroups — #26004822

Order 11008.

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#19148682C214yesmaximal, complemented
2#19148671C214yesmaximal, complemented
3#19148589C214yesmaximal, complemented
4#19148577C214yesmaximal, complemented
5#19148459C216yesmaximal, complemented
6#19148401C211yesmaximal, characteristic, complemented
7#19148362C211yesmaximal, characteristic, complemented
8#19148301C216yesmaximal, complemented
9#19148246C211yesmaximal, characteristic, complemented
10#19148216C214yesmaximal, complemented
11#19148211C214yesmaximal, complemented
12#19148185C214yesmaximal, complemented
13Q8×#10621900C214yesmaximal, complemented
14#19148019C216yesmaximal, complemented
15#19147887C216yesmaximal, complemented
162−1+4×Dic43C211yesmaximal, characteristic, complemented
17#19147804C211yesmaximal, characteristic, complemented
18C22×Q8×Dic43C211yesmaximal, characteristic, complemented
19C43×#3486C211yesmaximal, characteristic, complemented
20C2×#13063373C2211yescharacteristic
21#14583631C22112yescomplemented
22Q8×Dic86C2214yescomplemented
23#14583628C2214yescomplemented
24#14583625C2214yescomplemented
25#14583625C2214yescomplemented
26#14583624C22112yescomplemented
27#14583623C22112yescomplemented
28#14583620C22112yescomplemented
29#14583618C22112yescomplemented
30#14583607C22112yes—
31#14583607C22112yescomplemented
32#14583606C22112yes—
33#14583601C22112yes—
34#14583595C22112yes—
35#14583591C22112yes—
36#14583591C22112yescomplemented
37#14583589C22112yes—
38#14583583C22112yescomplemented
39#14583568C2214yescomplemented
40Q8×C22⋊D43C2214yes—
41Q8×C22⋊D43C2214yes—
42Q8×C22⋊D43C2214yescomplemented
43#14583560C2214yes—
44#14583560C2214yes—
45#14583560C2214yescomplemented
46#14583556C2214yescomplemented
47#14583553C22112yes—
48#14583549C22112yes—
49#14583527C2216yes—
50#14583522C22112yescomplemented
51#14583518C22112yescomplemented
52#14583510C22112yescomplemented
53#14583509C22112yescomplemented
54#14583493C22124yes—
55#14583477C2216yes—
56#14583473C2216yes—
57#14583454C22112yescomplemented
58#14583452C2216yes—
59#14583451C2216yes—
60#14583451C2216yes—
61#14583451C22112yescomplemented
62#14583445C2216yes—
63#14583444C2216yes—
64#14583444C2216yes—
65#14583435C2216yes—
66#14583435C2216yes—
67#14583435C22112yescomplemented
68#14583430C2216yes—
69#14583430C2216yes—
70#14583429C22112yes—
71#14583429C22112yes—
72#14583428C22112yescomplemented
73#14583426C22112yes—
74#14583426C22112yes—
75#14583410C2216yes—
76#14583405C22112yes—
77#14583405C2214yes—
78#14583382C2216yes—
79#14583382C2214yescomplemented
80#14583381C2214yescomplemented
81#14583379C2216yes—
82#14583377C2211yescharacteristic
83#14583377C2214yescomplemented
84#14583375C2214yescomplemented
85#41×Dic43C2216yes—
86#41×Dic43C2214yescomplemented
87C4×#10621902C2214yescomplemented
88#14583367C2216yes—
89C4×#10621900C22112yes—
90C4×#10621900C22112yes—
91C2×Q8×Dic43C2211yescharacteristic
92C2×Q8×Dic43C2214yes—
93C2×Q8×Dic43C2211yescharacteristic
94C2×Q8×Dic43C2214yes—
95C2×Q8×Dic43C2214yes—
96C2×Q8×Dic43C2213yes—
97C2×Q8×Dic43C2214yes—
98C2×Q8×Dic43C2213yes—
99C2×Q8×Dic43C2214yescomplemented
100C4×Q8×D43C2214yescomplemented
101C22×C4⋊Dic43C2213yes—
102C22×C4×Dic43C2213yes—
103C2×2−1+4×C43C2211yescharacteristic
104C23×Q8×C43C2211yescharacteristic
105D4×Q8×C43C2214yes—
106D4×Q8×C43C2214yes—
107C43×#548C2214yes—
108C43×#548C2214yes—
109C43×#536C2216yes—
110C43×#525C2216yes—
111C43×#519C2211yescharacteristic
112#13063373—28no—
113C2×#10621902C2314yes—
114C2×#10621898C2316yes—
115C2×#10621900C2314yes—
116C2×#10621900C23112yes—
117C2×Q8×D43C2314yes—
118C23×Dic43C2311yescharacteristic
119C23×Dic43C2313yes—
120#13063325C23112yes—
121#13063324C23112yes—
122#13063324C2316yes—
123#13063324C2316yes—
124#13063323C23112yes—
125#13063323C2316yes—
126#13063321C2316yes—
127#13063320C23124yes—
128#13063320C23112yes—
129#13063320C23112yes—
130#13063318C23112yes—
131#13063318C23124yes—
132#13063318C23112yes—
133#13063317C23112yes—
134#13063316C2316yes—
135#13063316C23124yes—
136#13063316C23112yes—
137#13063316C2316yes—
138#13063315C23124yes—
139#13063315C23112yes—
140#13063315C23112yes—
141#13063314C23112yes—
142#13063314C2316yes—
143#13063312C2316yes—
144#13063311C23112yes—
145#13063311C23112yes—
146#13063309C23112yes—
147#13063309C23124yes—
148#13063309C2314yes—
149#13063308C23112yes—
150#13063307C23124yes—
151#13063306C23112yes—
152#13063306C2314yes—
153#13063305C23124yes—
154#13063304C23112yes—
155#13063304C2316yes—
156#13063304C2316yes—
157#13063302C23112yes—
158#13063302C23124yes—
159#13063302C2314yes—
160#13063302C23112yes—
161#13063302C2314yes—
162#13063301C23112yes—
163#13063301C23112yes—
164#13063301C23112yes—
165#13063299C2316yes—
166#13063299C23112yes—
167#13063299C2316yes—
168#13063297C23112yes—
169#13063297C2314yes—
170#13063297C23112yes—
171#13063297C2314yes—
172#13063296C23112yes—
173#13063294C2314yes—
174Q8×Dic43C2314yes—
175Q8×Dic43C2314yes—
176Q8×Dic43C2314yes—
177Q8×Dic43C2314yes—
178Q8×Dic43C23112yes—
179Q8×Dic43C23112yes—
180Q8×Dic43C23112yes—
181Q8×Dic43C2314yes—
182Q8×Dic43C2314yes—
183Q8×Dic43C23112yes—
184Q8×Dic43C23112yes—
185Q8×Dic43C2316yes—
186Q8×Dic43C2316yes—
187C4×Dic86C23112yes—
188C4×Dic86C23112yes—
189C4×Dic86C23112yes—
190#13063290C2316yes—
191#13063290C23112yes—
192#13063290C23112yes—
193#13063290C2316yes—
194C4×D172C23112yes—
195D4×Dic43C23112yes—
196D4×Dic43C23112yes—
197D4×Dic43C2314yes—
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#13063284C2316yes—
216#13063284C23112yes—
217#13063283C23112yes—
218#13063283C23112yes—
219#13063283C23112yes—
220#13063282C23112yes—
221#13063281C23112yes—
222#13063281C23112yes—
223#13063281C2314yes—
224#13063281C23112yes—
225C2×C4⋊Dic43C23112yes—
226C2×C4⋊Dic43C23112yes—
227C2×C4⋊Dic43C23112yes—
228C2×C4⋊Dic43C2313yes—
229C2×C4⋊Dic43C2313yes—
230C2×C4⋊Dic43C2316yes—
231C4⋊C4×D43C23112yes—
232C2×C4×Dic43C2316yes—
233C2×C4×Dic43C2316yes—
234C2×C4×Dic43C2313yes—
235C2×C4×Dic43C2313yes—
236C2×C4×Dic43C2313yes—
237C2×C4×Dic43C2316yes—
238C2×C4×Dic43C2316yes—
239C2×C4×Dic43C2313yes—
240C2×C4×Dic43C23112yes—
241C42×D43C23112yes—
2422−1+4×C43—28no—
243C2×#41×C43C2314yes—
244C2×#41×C43C2316yes—
245C22×Q8×C43—28no—
246C22×Q8×C43C2314yes—
247C22×Q8×C43C2314yes—
248C22×Q8×C43C2314yes—
249C22×Q8×C43C2313yes—
250C22×Q8×C43C2311yescharacteristic
251C23×C4×C43C2313yes—
252C4⋊Q8×C43C23112yes—
253#124×C43C23112yes—
254#123×C43C23112yes—
255C22⋊Q8×C43C2316yes—
256C22⋊Q8×C43C2316yes—
257C22⋊Q8×C43C23112yes—
258C22⋊Q8×C43C23112yes—
259#121×C43C2316yes—
260#121×C43C2316yes—
261#120×C43C2314yes—
262C4×Q8×C43C2314yes—
263C4×Q8×C43C2314yes—
264C4×D4×C43C23112yes—
265C4×D4×C43C23112yes—
266#117×C43C2316yes—
267C24×C43C2411yescharacteristic
268#41×C43—216no—
269#41×C43—224no—
270C2×Q8×C43—216no—
271C2×Q8×C43—216no—
272C2×Q8×C43—216no—
273C2×Q8×C43—212no—
274C2×Q8×C43#4118yescomplemented
275C2×Q8×C43C24112yes—
276C2×Q8×C43C2416yes—
277C2×Q8×C43C2414yes—
278C2×D4×C43C2414yes—
279C2×D4×C43C2414yes—
280C2×D4×C43C2414yes—
281C2×D4×C43C2416yes—
282C22×C4×C43—212no—
283C22×C4×C43C2416yes—
284C22×C4×C43C2416yes—
285C22×C4×C43C24112yes—
286C22×C4×C43C2413yes—
287C22×C4×C43C2413yes—
288C2×C22⋊D43C2414yes—
289C2×C22⋊D43C2414yes—
290C2×C22⋊D43C2414yes—
291C2×C22⋊D43C2414yes—
292C2×C22⋊D43C24112yes—
293C22×Dic43—24no—
294C22×Dic43—46no—
295C22×Dic43C2411yescharacteristic
296C22×Dic43C2411yescharacteristic
297C22×Dic43C2411yescharacteristic
298C22×Dic43C2411yescharacteristic
299C22×Dic43C2411yescharacteristic
300C22×Dic43C2414yes—
301C22×Dic43C2416yes—
302C22×Dic43C2413yes—
303C22×Dic43C2416yes—
304C22×Dic43C2413yes—
305C22×Dic43C24112yes—
306C22×Dic43C2411yescharacteristic
307#10621902—216no—
308Q8×D43—216no—
309#10621900—216no—
310#10621900—424no—
311#10621898—224no—
312C2×D172C2416yes—
313C2×C4×D43C2414yes—
314C2×C4×D43C24112yes—
315C2×C4×D43C24112yes—
316C2×Dic86C2414yes—
317C2×Dic86C2416yes—
318C2×Dic86C24112yes—
319C4⋊C4×C43C2416yes—
320C4⋊C4×C43C2416yes—
321C4⋊C4×C43C24112yes—
322C4⋊C4×C43C24112yes—
323C22⋊C4×C43C2414yes—
324C22⋊C4×C43C2414yes—
325C22⋊C4×C43C2414yes—
326C22⋊C4×C43C24112yes—
327C22⋊C4×C43C24112yes—
328C42×C43C24112yes—
329C22⋊Dic43C2414yes—
330C22⋊Dic43C2414yes—
331C22⋊Dic43C2414yes—
332C22⋊Dic43C24112yes—
333C22⋊Dic43C2414yes—
334C22⋊Dic43C24112yes—
335C22⋊Dic43C2414yes—
336(C2×D43)⋊C4C2414yes—
337(C2×D43)⋊C4C24112yes—
338(C2×D43)⋊C4C2414yes—
339(C2×D43)⋊C4C24112yes—
340(C2×D43)⋊C4C24112yes—
341(C2×D43)⋊C4C24112yes—
342C4⋊Dic43C24112yes—
343C4⋊Dic43C24112yes—
344C4⋊Dic43C24124yes—
345C4⋊Dic43C2416yes—
346C4⋊Dic43C24112yes—
347C4⋊Dic43C2414yes—
348C4⋊Dic43C24112yes—
349C4⋊Dic43C2416yes—
350C4⋊Dic43C2414yes—
351Dic43⋊C4C24112yes—
352Dic43⋊C4C2414yes—
353Dic43⋊C4C2414yes—
354Dic43⋊C4C24112yes—
355Dic43⋊C4C24112yes—
356Dic43⋊C4C2414yes—
357Dic43⋊C4C24112yes—
358Dic43⋊C4C24112yes—
359Dic43⋊C4C24112yes—
360Dic43⋊C4C2414yes—
361C4×Dic43C2414yes—
362C4×Dic43C2416yes—
363C4×Dic43C24112yes—
364C4×Dic43C2416yes—
365C4×Dic43C2416yes—
366C4×Dic43C2414yes—
367C4×Dic43C2416yes—
368C4×Dic43C2416yes—
369C4×Dic43C2416yes—
370C4×Dic43C2416yes—
371C4×Dic43C2416yes—
372C4×Dic43C24112yes—
373C4×Dic43C24112yes—
374C23×C43—22no—
375C23×C43—22no—
376C23×C43—22no—
377C23×C43C2514yes—
378C23×C43C2511yescharacteristic
379C23×C43C2511yescharacteristic
380C23×C43C2511yescharacteristic
381C22×D43C2514yes—
382Q8×C43—224no—
383Q8×C43—212no—
384Q8×C43C2×#41116yes—
385D4×C43—28no—
386D4×C43—28no—
387D4×C43—28no—
388D4×C43—212no—
389C2×C4×C43—26no—
390C2×C4×C43—212no—
391C2×C4×C43—212no—
392C2×C4×C43—224no—
393C2×C4×C43C2×#41112yes—
394C2×C4×C43C2516yes—
395C2×C4×C43C2514yes—
396C2×C4×C43C2514yes—
397C2×C4×C43C2514yes—
398C2×C4×C43C2516yes—
399C22⋊D43—28no—
400C22⋊D43—28no—
401C22⋊D43—28no—
402C22⋊D43—28no—
403C22⋊D43—412no—
404C2×Dic43—22no—
405C2×Dic43—212no—
406C2×Dic43—28no—
407C2×Dic43—22no—
408C2×Dic43—22no—
409C2×Dic43—22no—
410C2×Dic43—22no—
411C2×Dic43—412no—
412C2×Dic43—43no—
413C2×Dic43—46no—
414C2×Dic43—43no—
415C2×Dic432−1+414yescomplemented
416C2×Dic43C2511yescharacteristic
417C2×Dic43C2511yescharacteristic
418C2×Dic43C2516yes—
419C2×Dic43C2514yes—
420C2×Dic43C2514yes—
421C2×Dic43C2516yes—
422C2×Dic43C2514yes—
423C2×Dic43C2511yescharacteristic
424C2×Dic43C2511yescharacteristic
425D172—212no—
426C4×D43—224no—
427C4×D43—28no—
428C4×D43—412no—
429Dic86—212no—
430Dic86—28no—
431Dic86—412no—
432#62788—431nomaximal, Sylow
433C22×C43—28no—
434C22×C43—21no—
435C22×C43—21no—
436C22×C43—21no—
437C22×C43—21no—
438C22×C43—21no—
439C22×C43—21no—
440C22×C43—24no—
441C22×C43—24no—
442C22×C43—24no—
443C22×C43C22×#4112yes—
444C22×C43C2×2−1+412yes—
445C22×C43#58512yes—
446C22×C43C2611yescharacteristic
447C2×D43—24no—
448C2×D43—24no—
449C2×D43—24no—
450C4×C43—24no—
451C4×C43—26no—
452C4×C43—24no—
453C4×C43—24no—
454C4×C43C22×#41112yes—
455Dic43—24no—
456Dic43—24no—
457Dic43—21no—
458Dic43—21no—
459Dic43—24no—
460Dic43—26no—
461Dic43—26no—
462Dic43C2×2−1+412yes—
463Dic43C2×2−1+412yes—
464#3523—434no—
465#3522—434no—
466#3516—434no—
467#3516—434no—
468#3507—436no—
469#3502—431no—
470#3497—431no—
471#3492—436no—
472#3486—431no—
473#3486D4311yescharacteristic, complemented
474#3482—434no—
475#3482—434no—
476#3480—434no—
477Q8×#41—434no—
478#3461—436no—
479#3444—436no—
480C4×2−1+4—431no—
481C4×2−1+4—431no—
482C22×C4×Q8—431no—
483C2×C43—22no—
484C2×C43—22no—
485C2×C43—22no—
486C2×C43—44no—
487C2×C43C23×#4111yescharacteristic
488C2×C43C22×2−1+411yescharacteristic
489C2×C43C2×#58511yescharacteristic
490D43—44no—
491C2×2−1+4—431no—
492C2×2−1+4C2×D4311yescharacteristic
493C23×Q8C2×D4311yescharacteristic
494#559—4312no—
495Q82—434no—
496#557—4312no—
497#557—434no—
498#557—434no—
499#557—434no—
500#556—4312no—
501#556—4312no—
502#556—4312no—
503#554—4312no—
504#554—4312no—
505#554—4312no—
506#553—4312no—
507#553—4312no—
508#552—4312no—
509#552—4312no—
510#552—4312no—
511#552—4312no—
512#550—434no—
513D4×Q8—434no—
514D4×Q8—434no—
515D4×Q8—434no—
516D4×Q8C2×D4314yes—
517D4×Q8C2×D4314yes—
518#548—434no—
519#548—434no—
520#548—434no—
521#548—434no—
522#548C2×D4314yes—
523#548C2×D4314yes—
524#547—4312no—
525#547—4312no—
526#544—436no—
527#542—4312no—
528#542—4312no—
529#541—4312no—
530#541—4312no—
531#539—4324no—
532#537—436no—
533#536—436no—
534#536C2×D4316yes—
535#533—4312no—
536#533—436no—
537#533—436no—
538#533—4312no—
539#533—436no—
540#532—436no—
541#532—436no—
542#532—436no—
543#529—4312no—
544#529—4312no—
545#529—4312no—
546#529—436no—
547#529—436no—
548#529—4312no—
549#529—436no—
550#529—436no—
551#529—4312no—
552#529—4312no—
553#525—436no—
554#525—434no—
555#525—4312no—
556#525C2×D4316yes—
557#520—436no—
558#520—434no—
559#520—434no—
560#520—436no—
561#519—431no—
562#519—434no—
563#519—434no—
564#519C2×D4311yescharacteristic
565C4×#41—436no—
566C4×#41—434no—
567C4×#41—434no—
568C4×#41—4312no—
569C4×#41—4312no—
570C4×#41—436no—
571C2×C4×Q8—431no—
572C2×C4×Q8—433no—
573C2×C4×Q8—434no—
574C2×C4×Q8—434no—
575C2×C4×Q8—431no—
576C2×C4×Q8—433no—
577C2×C4×Q8—434no—
578C2×C4×Q8—434no—
579C2×C4×Q8—434no—
580C2×C4×Q8—434no—
581C22×C4⋊C4—433no—
582C22×C42—433no—
583C43#6278811yescharacteristic, complemented, Sylow
5842−1+4—28no—
5852−1+4—868no—
586C2×#41—434no—
587C2×#41—434no—
588C2×#41—4312no—
589C2×#41—436no—
590C2×#41C22×D4316yes—
591C2×#41C22×D4314yes—
592C22×Q8—28no—
593C22×Q8—434no—
594C22×Q8C22×D4313yes—
595C22×Q8C22×D4314yes—
596C22×Q8C22×D4314yes—
597C22×Q8C22×D4314yes—
598C22×Q8C22×D4311yescharacteristic
599C23×C4—431no—
600C23×C4—433no—
601C23×C4C22×D4313yes—
602C4⋊Q8—436no—
603C4⋊Q8—4312no—
604C4⋊Q8—436no—
605C4⋊Q8—436no—
606C4⋊Q8—4312no—
607C4⋊Q8—4312no—
608C4⋊Q8C22×D43112yes—
609#127—436no—
610#126—4312no—
611#126—4312no—
612#126—4324no—
613#126—4312no—
614#126—4312no—
615#126—4324no—
616#125—4312no—
617#125—436no—
618#125—436no—
619#125—4312no—
620#125—4312no—
621#125—4324no—
622#125—4324no—
623#125—4312no—
624#124—436no—
625#124—4312no—
626#124—436no—
627#124—4312no—
628#124—4312no—
629#124C22×D43112yes—
630#123—434no—
631#123—4312no—
632#123—4312no—
633#123—434no—
634#123—4312no—
635#123—4324no—
636#123—4324no—
637#123C22×D43112yes—
638C22⋊Q8—4312no—
639C22⋊Q8—4312no—
640C22⋊Q8—4312no—
641C22⋊Q8—436no—
642C22⋊Q8—436no—
643C22⋊Q8—4312no—
644C22⋊Q8—4324no—
645C22⋊Q8—434no—
646C22⋊Q8—434no—
647C22⋊Q8—4312no—
648C22⋊Q8—4312no—
649C22⋊Q8—4324no—
650C22⋊Q8C22×D4316yes—
651C22⋊Q8C22×D4316yes—
652C22⋊Q8C22×D43112yes—
653C22⋊Q8C22×D43112yes—
654#121—434no—
655#121—434no—
656#121—4312no—
657#121—4312no—
658#121—4312no—
659#121—436no—
660#121—436no—
661#121—4312no—
662#121C22×D4316yes—
663#121C22×D4316yes—
664#120—434no—
665#120C22×D4314yes—
666C4×Q8—434no—
667C4×Q8—434no—
668C4×Q8—4312no—
669C4×Q8—4312no—
670C4×Q8—434no—
671C4×Q8—434no—
672C4×Q8—4312no—
673C4×Q8—4312no—
674C4×Q8—436no—
675C4×Q8—434no—
676C4×Q8—4312no—
677C4×Q8—436no—
678C4×Q8—434no—
679C4×Q8—436no—
680C4×Q8—436no—
681C4×Q8—4312no—
682C4×Q8—4312no—
683C4×Q8—4312no—
684C4×Q8—4312no—
685C4×Q8—4312no—
686C4×Q8C22×D4314yes—
687C4×Q8C22×D4314yes—
688C4×D4—434no—
689C4×D4—434no—
690C4×D4—436no—
691C4×D4—4312no—
692C4×D4—436no—
693C4×D4—4312no—
694C4×D4—4312no—
695C4×D4—4312no—
696C4×D4—4312no—
697C4×D4—4312no—
698C4×D4—4312no—
699C4×D4—436no—
700C4×D4—436no—
701C4×D4—434no—
702C4×D4—434no—
703C4×D4—4312no—
704C4×D4—4312no—
705C4×D4—4312no—
706C4×D4—4312no—
707C4×D4—4312no—
708C4×D4C22×D43112yes—
709C4×D4C22×D43112yes—
710#117—436no—
711#117—4312no—
712#117—4312no—
713#117—4312no—
714#117—4312no—
715#117—4312no—
716#117—434no—
717#117—4312no—
718#117—4312no—
719#117—4312no—
720#117—4312no—
721#117C22×D4316yes—
722C2×C4⋊C4—433no—
723C2×C4⋊C4—433no—
724C2×C4⋊C4—436no—
725C2×C4⋊C4—4312no—
726C2×C4⋊C4—4312no—
727C2×C4⋊C4—4312no—
728C2×C4⋊C4—4312no—
729C2×C42—433no—
730C2×C42—436no—
731C2×C42—436no—
732C2×C42—433no—
733C2×C42—436no—
734C2×C42—433no—
735C2×C42—436no—
736C2×C42—433no—
737C2×C42—4312no—
738C2×C42—4312no—
739C24C23×D4311yescharacteristic
740#41—216no—
741#41—224no—
742#41—8616no—
743#41—8616no—
744#41—8624no—
745#41—17224no—
746C2×Q8—216no—
747C2×Q8—216no—
748C2×Q8—216no—
749C2×Q8—212no—
750C2×Q8—434no—
751C2×Q8—436no—
752C2×Q8—4312no—
753C2×Q8—8616no—
754C2×Q8#1062190018yescomplemented
755C2×Q8C23×D43112yes—
756C2×Q8C23×D4316yes—
757C2×Q8C23×D4314yes—
758C2×D4—434no—
759C2×D4—434no—
760C2×D4—434no—
761C2×D4—434no—
762C2×D4—4312no—
763C2×D4—436no—
764C2×D4C23×D4314yes—
765C2×D4C23×D4316yes—
766C2×D4C23×D4314yes—
767C2×D4C23×D4314yes—
768C22×C4—212no—
769C22×C4—431no—
770C22×C4—431no—
771C22×C4—431no—
772C22×C4—431no—
773C22×C4—431no—
774C22×C4—431no—
775C22×C4—434no—
776C22×C4—436no—
777C22×C4—433no—
778C22×C4—436no—
779C22×C4—433no—
780C22×C4—4312no—
781C22×C4—434no—
782C22×C4—4312no—
783C22×C4—4312no—
784C22×C4—864no—
785C22×C4—1726no—
786C22×C4C23×D4316yes—
787C22×C4C23×D4316yes—
788C22×C4C23×D4313yes—
789C22×C4C23×D43112yes—
790C22×C4C23×D4313yes—
791C4⋊C4—4312no—
792C4⋊C4—4312no—
793C4⋊C4—4324no—
794C4⋊C4—436no—
795C4⋊C4—4312no—
796C4⋊C4—4312no—
797C4⋊C4—436no—
798C4⋊C4—434no—
799C4⋊C4—434no—
800C4⋊C4—434no—
801C4⋊C4—434no—
802C4⋊C4—434no—
803C4⋊C4—434no—
804C4⋊C4—4312no—
805C4⋊C4—4312no—
806C4⋊C4—4312no—
807C4⋊C4—4312no—
808C4⋊C4—4312no—
809C4⋊C4—4312no—
810C4⋊C4C23×D4316yes—
811C4⋊C4C23×D4316yes—
812C4⋊C4C23×D43112yes—
813C4⋊C4C23×D43112yes—
814C22⋊C4—434no—
815C22⋊C4—434no—
816C22⋊C4—4312no—
817C22⋊C4—434no—
818C22⋊C4—434no—
819C22⋊C4—434no—
820C22⋊C4—4312no—
821C22⋊C4—4312no—
822C22⋊C4—434no—
823C22⋊C4—434no—
824C22⋊C4—4312no—
825C22⋊C4—4312no—
826C22⋊C4—4312no—
827C22⋊C4C23×D4314yes—
828C22⋊C4C23×D4314yes—
829C22⋊C4C23×D43112yes—
830C22⋊C4C23×D43112yes—
831C22⋊C4C23×D4314yes—
832C42—436no—
833C42—434no—
834C42—434no—
835C42—436no—
836C42—436no—
837C42—436no—
838C42—436no—
839C42—436no—
840C42—436no—
841C42—436no—
842C42—4312no—
843C42—4312no—
844C42—4312no—
845C42C23×D43112yes—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—434no—
850C23C24×D4314yes—
851C23C24×D4311yescharacteristic
852C23C24×D4311yescharacteristic
853C23C24×D4311yescharacteristic
854Q8—224no—
855Q8—212no—
856Q8—868no—
857Q8—8612no—
858Q8—17212no—
859Q8C2×#10621900116yes—
860D4—28no—
861D4—28no—
862D4—28no—
863D4—212no—
864D4—868no—
865D4—868no—
866D4—868no—
867D4—868no—
868D4—8612no—
869D4—17212no—
870C2×C4—26no—
871C2×C4—212no—
872C2×C4—212no—
873C2×C4—224no—
874C2×C4—434no—
875C2×C4—431no—
876C2×C4—431no—
877C2×C4—431no—
878C2×C4—431no—
879C2×C4—436no—
880C2×C4—434no—
881C2×C4—434no—
882C2×C4—434no—
883C2×C4—436no—
884C2×C4—868no—
885C2×C4—862no—
886C2×C4—862no—
887C2×C4—862no—
888C2×C4—862no—
889C2×C4—868no—
890C2×C4—862no—
891C2×C4—8612no—
892C2×C4—8624no—
893C2×C4—17212no—
894C2×C4—1723no—
895C2×C4—1726no—
896C2×C4—1723no—
897C2×C4—17212no—
898C2×C4C2×#10621900112yes—
899C2×C4C24×D4316yes—
900C2×C4C24×D4314yes—
901C2×C4C24×D4314yes—
902C2×C4C24×D4314yes—
903C2×C4C24×D4316yes—
904C22—28no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—24no—
912C22—24no—
913C22—24no—
914C22—864no—
915C22—864no—
916C22—864no—
917C22C22×#1062190012yes—
918C222−1+4×D4312yes—
919C22#1458373612yes—
920C22C25×D4311yescharacteristic
921C4—24no—
922C4—26no—
923C4—24no—
924C4—24no—
925C4—432no—
926C4—432no—
927C4—864no—
928C4—861no—
929C4—861no—
930C4—864no—
931C4—866no—
932C4—866no—
933C4—864no—
934C4C22×#10621900112yes—
935C2—22no—
936C2—22no—
937C2—22no—
938C2—44no—
939C2—1724no—
940C2C23×#1062190011yescharacteristic
941C2C2×2−1+4×D4311yescharacteristic
942C2C2×#1458373611yescharacteristic
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3486C2
hypercenter#3486D43
hypocenterC43#62788
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3486

Complements

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

NH ≅ G/Ntype
1. #19148682C2semidirect
2. #19148671C2semidirect
3. #19148589C2semidirect
4. #19148577C2semidirect
5. #19148459C2semidirect
6. #19148401C2semidirect
7. #19148362C2semidirect
8. #19148301C2semidirect
9. #19148246C2semidirect
10. #19148216C2semidirect
11. #19148211C2semidirect
12. #19148185C2semidirect
13. Q8×#10621900C2semidirect
14. #19148019C2semidirect
15. #19147887C2semidirect
16. 2−1+4×Dic43C2semidirect
17. #19147804C2semidirect
18. C22×Q8×Dic43C2semidirect
19. C43×#3486C2semidirect
21. #14583631C22semidirect
22. Q8×Dic86C22semidirect
23. #14583628C22semidirect
24. #14583625C22semidirect
25. #14583625C22semidirect
26. #14583624C22semidirect
27. #14583623C22semidirect
28. #14583620C22semidirect
29. #14583618C22semidirect
31. #14583607C22semidirect
36. #14583591C22semidirect
38. #14583583C22semidirect
39. #14583568C22semidirect
42. Q8×C22⋊D43C22semidirect
45. #14583560C22semidirect
46. #14583556C22semidirect
50. #14583522C22semidirect
51. #14583518C22semidirect
52. #14583510C22semidirect
53. #14583509C22semidirect
57. #14583454C22semidirect
61. #14583451C22semidirect
67. #14583435C22semidirect
72. #14583428C22semidirect
79. #14583382C22semidirect
80. #14583381C22semidirect
83. #14583377C22semidirect
84. #14583375C22semidirect
86. #41×Dic43C22semidirect
87. C4×#10621902C22semidirect
99. C2×Q8×Dic43C22semidirect
100. C4×Q8×D43C22semidirect
274. C2×Q8×C43#41semidirect
415. C2×Dic432−1+4semidirect
473. #3486D43semidirect
583. C43#62788semidirect
754. C2×Q8#10621900semidirect

Maximal subgroups

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

subgroupindex
#191486822
#191486712
#191485892
#191485772
#191484592
#191484012
#191483622
#191483012
#191482462
#191482162
#191482112
#191481852
Q8×#106219002
#191480192
#191478872
2−1+4×Dic432
#191478042
C22×Q8×Dic432
C43×#34862
#6278843