Finite Group Databasebeta

← #26004891

Subgroups — #26004891

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#19148706C214yesmaximal, complemented
2#19148696C214yesmaximal, complemented
3#19148606C214yesmaximal, complemented
4#19148595C214yesmaximal, complemented
5#19148440C216yesmaximal, complemented
6#19148401C211yesmaximal, characteristic, complemented
7#19148362C211yesmaximal, characteristic, complemented
8#19148308C216yesmaximal, complemented
9#19148254C211yesmaximal, characteristic, complemented
10#19148250C211yesmaximal, characteristic, complemented
11#19148221C214yesmaximal, complemented
12#19148212C214yesmaximal, complemented
13#19148193C214yesmaximal, complemented
14#19148190C214yesmaximal, complemented
15#19148011C216yesmaximal, complemented
16#19147888C216yesmaximal, complemented
17C4×#13063373C211yesmaximal, characteristic, complemented
18C2×C4×#10621902C211yesmaximal, characteristic, complemented
19C4×2−1+4×C43C211yesmaximal, characteristic, complemented
20C2×#13063373C2211yescharacteristic
21C22×#10621902C2211yescharacteristic
22#14583634C22112yescomplemented
23#14583632C22112yescomplemented
24Q8×Dic86C2214yescomplemented
25#14583628C2214yescomplemented
26#14583625C2214yescomplemented
27#14583625C2214yescomplemented
28#14583622C22112yescomplemented
29#14583621C22112yescomplemented
30#14583617C22112yescomplemented
31#14583614C22112yescomplemented
32#14583612C22112yescomplemented
33#14583612C22112yescomplemented
34#14583599C22112yescomplemented
35#14583597C22112yescomplemented
36#14583597C22112yescomplemented
37#14583593C22112yescomplemented
38#14583590C22112yescomplemented
39#14583584C22112yescomplemented
40#14583571C2214yes—
41#14583571C2214yes—
42#14583570C22112yescomplemented
43#14583568C2214yes—
44#14583568C2214yes—
45#14583568C2214yescomplemented
46Q8×C22⋊D43C2214yescomplemented
47#14583561C2214yes—
48#14583561C2214yes—
49#14583560C2214yes—
50#14583560C2214yes—
51#14583560C2214yescomplemented
52#14583556C2214yescomplemented
53#14583550C22112yescomplemented
54#14583527C2216yes—
55#14583521C22112yescomplemented
56#14583520C22112yescomplemented
57#14583504C22112yescomplemented
58#14583500C22112yescomplemented
59#14583482C22124yes—
60#14583477C2216yes—
61#14583468C2216yes—
62#14583463C2216yes—
63#14583453C2216yescomplemented
64#14583453C2216yescomplemented
65#14583452C2216yes—
66#14583449C22112yescomplemented
67#14583446C2216yescomplemented
68#14583446C2216yescomplemented
69#14583446C22112yescomplemented
70#14583445C2216yes—
71#14583436C2216yescomplemented
72#14583436C2216yescomplemented
73#14583436C22112yescomplemented
74#14583433C22112yescomplemented
75#14583431C2216yescomplemented
76#14583431C2216yescomplemented
77#14583429C22112yes—
78#14583429C2214yes—
79#14583427C22112yescomplemented
80#14583427C22112yescomplemented
81#14583411C2216yes—
82#14583408C22112yes—
83#14583408C22112yes—
84#14583406C2216yes—
85#14583381C2214yescomplemented
86#14583380C2216yes—
87#14583377C2211yescharacteristic
88#14583375C2214yescomplemented
89C4×#10621902C2214yes—
90C4×#10621902C2214yes—
91C4×#10621902C2214yes—
92C4×#10621902C2214yes—
93C4×#10621902C2214yescomplemented
94C4×#10621898C2216yes—
95C4×#10621898C22112yescomplemented
96C4×#10621898C22112yescomplemented
97C2×Q8×Dic43C2211yescharacteristic
98C4×Q8×D43C2214yescomplemented
99C2×C4×D172C2213yes—
100C2×#13063287C2213yes—
101C2×#13063283C2213yes—
102C2×C42×D43C2213yes—
103C2×2−1+4×C43C2211yescharacteristic
104C43×#520C2216yes—
105C43×#520C2214yescomplemented
106C43×#519C2211yescharacteristic
107C43×#519C2214yescomplemented
108C4×#41×C43C2216yes—
109C4×#41×C43C2214yescomplemented
110C2×C4×Q8×C43C2211yescharacteristic
111C2×C4×Q8×C43C2214yescomplemented
112#13063373—28no—
113C2×#10621902—28no—
114C2×#10621902C2314yes—
115C2×#10621902C2314yes—
116C2×#10621902C2314yes—
117C2×#10621898C2316yes—
118C2×#10621898C23112yes—
119C2×#10621898C23112yes—
120C2×Q8×D43C2314yes—
121C22×D172C2313yes—
122C22×C4×D43C2313yes—
123C22×C4×D43C2313yes—
124C22×C4×D43C2313yes—
125#13063325C23112yes—
126#13063324C2316yes—
127#13063324C23112yes—
128#13063324C2316yes—
129#13063323C2316yes—
130#13063322C23112yes—
131#13063321C23112yes—
132#13063321C2316yes—
133#13063320C23124yes—
134#13063320C23112yes—
135#13063320C2314yes—
136#13063319C23124yes—
137#13063318C23112yes—
138#13063318C2314yes—
139#13063317C23112yes—
140#13063316C23112yes—
141#13063316C2316yes—
142#13063316C2316yes—
143#13063315C23112yes—
144#13063315C2314yes—
145#13063314C23112yes—
146#13063314C2316yes—
147#13063313C23112yes—
148#13063313C23124yes—
149#13063312C2316yes—
150#13063311C23112yes—
151#13063311C23124yes—
152#13063311C2314yes—
153#13063310C23124yes—
154#13063310C23112yes—
155#13063310C23112yes—
156#13063309C2314yes—
157#13063308C23124yes—
158#13063307C23112yes—
159#13063307C23112yes—
160#13063306C2314yes—
161#13063305C2316yes—
162#13063305C2316yes—
163#13063304C23112yes—
164#13063303C23112yes—
165#13063303C23112yes—
166#13063302C2314yes—
167#13063302C23112yes—
168#13063301C2316yes—
169#13063301C2316yes—
170#13063301C23112yes—
171#13063300C23112yes—
172#13063300C23112yes—
173#13063300C2316yes—
174#13063300C2316yes—
175#13063299C23112yes—
176#13063299C23112yes—
177#13063299C23112yes—
178#13063299C23124yes—
179#13063298C23112yes—
180#13063298C23124yes—
181#13063298C23112yes—
182#13063297C2314yes—
183#13063297C23112yes—
184#13063296C23112yes—
185#13063296C2316yes—
186#13063296C2316yes—
187#13063295C23112yes—
188#13063293C23112yes—
189Q8×Dic43C2314yes—
190Q8×Dic43C2314yes—
191Q8×Dic43C2314yes—
192Q8×Dic43C2314yes—
193C4×Dic86C23112yes—
194C4×Dic86C23112yes—
195C4×Dic86C2316yes—
196C4×Dic86C2316yes—
197C4×Dic86C2314yes—
198C4×Dic86C23112yes—
199#13063290C23112yes—
200C4×D172C23112yes—
201C4×D172C23112yes—
202C4×D172C23112yes—
203C4×D172C23112yes—
204C4×D172C23112yes—
205C4×D172C2316yes—
206C4×D172C2316yes—
207C4×D172C23112yes—
208#13063287C23112yes—
209#13063287C23112yes—
210#13063287C23112yes—
211C4×C22⋊D43C23112yes—
212C4×C22⋊D43C23112yes—
213C4×C22⋊D43C23112yes—
214C4×C22⋊D43C23112yes—
215C4×C22⋊D43C23112yes—
216C4×C22⋊D43C23112yes—
217C4×C22⋊D43C2314yes—
218C4×C22⋊D43C23112yes—
219C4×C22⋊D43C2314yes—
220C4×C22⋊D43C23112yes—
221#13063284C23112yes—
222#13063284C2316yes—
223#13063284C2314yes—
224#13063283C23112yes—
225#13063283C23112yes—
226#13063283C23112yes—
227#13063282C23112yes—
228#13063282C23112yes—
229#13063282C23112yes—
230#13063282C2314yes—
231#13063282C23112yes—
232C2×C4⋊Dic43C2313yes—
233C4⋊C4×D43C23112yes—
234C2×(C2×D43)⋊C4C2316yes—
235C2×C4×Dic43C2311yescharacteristic
236C2×C4×Dic43C2313yes—
237C2×C4×Dic43C2313yes—
238C42×D43C2316yes—
239C42×D43C2316yes—
240C42×D43C2316yes—
241C42×D43C2316yes—
242C42×D43C23112yes—
2432−1+4×C43—28no—
244C2×#41×C43C2314yes—
245C2×#41×C43C2316yes—
246C22×Q8×C43C2314yes—
247C22×Q8×C43C2311yescharacteristic
248C4×Q8×C43C2314yes—
249C4×Q8×C43C2314yes—
250C4×Q8×C43C2314yes—
251C4×Q8×C43C2314yes—
252C4×Q8×C43C2316yes—
253C4×Q8×C43C23112yes—
254C4×Q8×C43C2316yes—
255C4×D4×C43C23112yes—
256C4×D4×C43C2314yes—
257C4×D4×C43C2316yes—
258C4×D4×C43C23112yes—
259C4×D4×C43C2316yes—
260#117×C43C2316yes—
261#117×C43C23112yes—
262#117×C43C23112yes—
263C2×C4⋊C4×C43C2313yes—
264C2×C4⋊C4×C43C23112yes—
265C2×C42×C43C2313yes—
266C2×C42×C43C23112yes—
267C23×D43C2413yes—
268#41×C43—216no—
269#41×C43—224no—
270C2×Q8×C43—216no—
271C2×Q8×C43#4118yescomplemented
272C2×Q8×C43C2416yes—
273C2×Q8×C43C2414yes—
274C2×D4×C43C2414yes—
275C2×D4×C43C2416yes—
276C22×C4×C43C2411yescharacteristic
277C22×C4×C43C2414yes—
278C22×C4×C43C24112yes—
279C22×C4×C43C2413yes—
280C22×C4×C43C24112yes—
281C22×C4×C43C2413yes—
282C2×C22⋊D43C2414yes—
283C2×C22⋊D43C2414yes—
284C2×C22⋊D43C24112yes—
285C2×C22⋊D43C24112yes—
286C2×C22⋊D43C24112yes—
287C22×Dic43C2411yescharacteristic
288C22×Dic43C2411yescharacteristic
289C22×Dic43C2413yes—
290#10621902—216no—
291#10621902—216no—
292#10621902—216no—
293Q8×D43—216no—
294#10621898—224no—
295#10621898—424no—
296#10621898—424no—
297C2×D172—212no—
298C2×D172C24112yes—
299C2×D172C2416yes—
300C2×D172C24112yes—
301C2×D172C24112yes—
302C2×C4×D43—212no—
303C2×C4×D43—46no—
304C2×C4×D43—46no—
305C2×C4×D43C2414yes—
306C2×C4×D43C2416yes—
307C2×C4×D43C2416yes—
308C2×C4×D43C2416yes—
309C2×C4×D43C2416yes—
310C2×C4×D43C24112yes—
311C2×C4×D43C2416yes—
312C2×C4×D43C2416yes—
313C2×C4×D43C24112yes—
314C2×Dic86C2416yes—
315C2×Dic86C2414yes—
316C2×Dic86C24112yes—
317C4⋊C4×C43C24112yes—
318C4⋊C4×C43C2416yes—
319C4⋊C4×C43C24112yes—
320C4⋊C4×C43C2416yes—
321C4⋊C4×C43C2414yes—
322C22⋊C4×C43C2414yes—
323C22⋊C4×C43C2414yes—
324C22⋊C4×C43C24112yes—
325C42×C43C2416yes—
326C42×C43C2414yes—
327C42×C43C2416yes—
328C42×C43C24112yes—
329C42×C43C24112yes—
330C22⋊Dic43C2414yes—
331C22⋊Dic43C2414yes—
332C22⋊Dic43C2414yes—
333C22⋊Dic43C2414yes—
334C22⋊Dic43C24112yes—
335(C2×D43)⋊C4C24124yes—
336(C2×D43)⋊C4C2414yes—
337(C2×D43)⋊C4C2414yes—
338(C2×D43)⋊C4C24112yes—
339(C2×D43)⋊C4C2414yes—
340(C2×D43)⋊C4C2414yes—
341(C2×D43)⋊C4C24112yes—
342(C2×D43)⋊C4C24112yes—
343(C2×D43)⋊C4C24112yes—
344(C2×D43)⋊C4C24112yes—
345(C2×D43)⋊C4C24112yes—
346C4⋊Dic43C2416yes—
347C4⋊Dic43C24112yes—
348C4⋊Dic43C2416yes—
349C4⋊Dic43C2414yes—
350C4⋊Dic43C2414yes—
351C4⋊Dic43C2414yes—
352C4⋊Dic43C24112yes—
353Dic43⋊C4C24112yes—
354Dic43⋊C4C2414yes—
355Dic43⋊C4C2414yes—
356Dic43⋊C4C2414yes—
357Dic43⋊C4C2414yes—
358Dic43⋊C4C2414yes—
359Dic43⋊C4C2414yes—
360Dic43⋊C4C24112yes—
361Dic43⋊C4C24112yes—
362Dic43⋊C4C24112yes—
363C4×Dic43C2411yescharacteristic
364C4×Dic43C2411yescharacteristic
365C4×Dic43C2411yescharacteristic
366C4×Dic43C2411yescharacteristic
367C4×Dic43C2414yes—
368C4×Dic43C2416yes—
369C4×Dic43C2416yes—
370C4×Dic43C2416yes—
371C4×Dic43C2416yes—
372C4×Dic43C24112yes—
373C4×Dic43C24112yes—
374C23×C43C2514yes—
375C23×C43C2511yescharacteristic
376C22×D43—26no—
377C22×D43—43no—
378C22×D43—43no—
379C22×D43C2516yes—
380C22×D43C2514yes—
381Q8×C43—212no—
382Q8×C43C2×#41116yes—
383D4×C43—28no—
384D4×C43—212no—
385C2×C4×C43—224no—
386C2×C4×C43—22no—
387C2×C4×C43—28no—
388C2×C4×C43—43no—
389C2×C4×C43—412no—
390C2×C4×C43C2×#41112yes—
391C2×C4×C43C2516yes—
392C2×C4×C43C2511yescharacteristic
393C2×C4×C43C2514yes—
394C2×C4×C43C2514yes—
395C2×C4×C43C2514yes—
396C2×C4×C43C2516yes—
397C2×C4×C43C2511yescharacteristic
398C22⋊D43—28no—
399C22⋊D43—28no—
400C22⋊D43—412no—
401C22⋊D43—412no—
402C22⋊D43—412no—
403C2×Dic43—22no—
404C2×Dic43—22no—
405C2×Dic43—43no—
406C2×Dic43C2511yescharacteristic
407C2×Dic43C2511yescharacteristic
408C2×Dic43C2511yescharacteristic
409C2×Dic43C2514yes—
410C2×Dic43C2514yes—
411C2×Dic43C2514yes—
412C2×Dic43C2516yes—
413C2×Dic43C2511yescharacteristic
414D172—224no—
415D172—212no—
416D172—412no—
417D172—412no—
418C4×D43—212no—
419C4×D43—212no—
420C4×D43—224no—
421C4×D43—212no—
422C4×D43—28no—
423C4×D43—212no—
424C4×D43—46no—
425C4×D43—46no—
426C4×D43—412no—
427Dic86—212no—
428Dic86—28no—
429Dic86—412no—
430#62793—431nomaximal, Sylow
431C22×C43—21no—
432C22×C43—21no—
433C22×C43—24no—
434C22×C43—24no—
435C22×C43—24no—
436C22×C43C22×#4112yes—
437C22×C43C2611yescharacteristic
438C2×D43—26no—
439C2×D43—24no—
440C2×D43—26no—
441C2×D43—26no—
442C2×D43—24no—
443C2×D43—24no—
444C2×D43—412no—
445C4×C43—24no—
446C4×C43—24no—
447C4×C43—24no—
448C4×C43—26no—
449C4×C43—21no—
450C4×C43C22×#41112yes—
451C4×C43#58512yes—
452Dic43—24no—
453Dic43—21no—
454Dic43—21no—
455Dic43—24no—
456Dic43—24no—
457Dic43—26no—
458Dic43—21no—
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#3487—431no—
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+4D4311yescharacteristic, complemented
478C2×C4×#41—431no—
479C2×C43—22no—
480C2×C43—44no—
481C2×C43C23×#4111yescharacteristic
482C2×C43C2×#58511yescharacteristic
483C2×C43C2×#58511yescharacteristic
484D43—44no—
485D43—46no—
486C2×2−1+4—431no—
487C2×2−1+4C2×D4311yescharacteristic
488C22×#41—431no—
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—434no—
511#550—434no—
512#550—4312no—
513D4×Q8—434no—
514#548—434no—
515#548—434no—
516#548—434no—
517#548—434no—
518#548—434no—
519#548—434no—
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#535—436no—
530#533—436no—
531#533—436no—
532#533—436no—
533#532—436no—
534#532—436no—
535#532—436no—
536#532—4312no—
537#532—4312no—
538#529—436no—
539#529—436no—
540#529—4312no—
541#529—434no—
542#529—4312no—
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#525—436no—
552#520—434no—
553#520—436no—
554#520C2×D4316yes—
555#520C2×D4314yescomplemented
556#519—431no—
557#519—434no—
558#519C2×D4311yescharacteristic
559#519C2×D4314yescomplemented
560C4×#41—434no—
561C4×#41—434no—
562C4×#41—434no—
563C4×#41—434no—
564C4×#41—434no—
565C4×#41—436no—
566C4×#41—4312no—
567C4×#41—4312no—
568C4×#41C2×D4316yes—
569C4×#41C2×D4314yescomplemented
570C2×C4×Q8—431no—
571C2×C4×Q8—434no—
572C2×C4×Q8C2×D4311yescharacteristic
573C2×C4×Q8C2×D4314yescomplemented
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—434no—
582C2×#41—434no—
583C2×#41—434no—
584C2×#41—436no—
585C2×#41—4312no—
586C2×#41—4312no—
587C2×#41—868no—
588C2×#41C22×D4316yes—
589C2×#41C22×D4314yes—
590C22×Q8—434no—
591C22×Q8C22×D4314yes—
592C22×Q8C22×D4311yescharacteristic
593C22×D4—433no—
594C23×C4—433no—
595C23×C4—433no—
596C23×C4—433no—
597C4⋊Q8—436no—
598C4⋊Q8—436no—
599C4⋊Q8—436no—
600C4⋊Q8—4312no—
601C4⋊Q8—4312no—
602#127—436no—
603#127—4312no—
604#127—4312no—
605#126—434no—
606#126—4312no—
607#126—4324no—
608#126—434no—
609#126—4312no—
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—4312no—
619#124—436no—
620#124—434no—
621#124—4312no—
622#124—4324no—
623#124—4312no—
624#124—4324no—
625#123—434no—
626#123—4324no—
627#123—4312no—
628#123—4312no—
629#123—4324no—
630#123—434no—
631#123—4312no—
632#123—4312no—
633C22⋊Q8—436no—
634C22⋊Q8—436no—
635C22⋊Q8—4312no—
636C22⋊Q8—4312no—
637C22⋊Q8—4312no—
638C22⋊Q8—4312no—
639C22⋊Q8—436no—
640C22⋊Q8—436no—
641C22⋊Q8—434no—
642C22⋊Q8—4312no—
643#121—434no—
644#121—4312no—
645#121—436no—
646#121—436no—
647#121—4312no—
648#121—4312no—
649#121—4312no—
650#121—4312no—
651#121—4324no—
652#121—436no—
653#121—436no—
654#121—4312no—
655#121—4312no—
656#121—4312no—
657#121—4312no—
658#121—4324no—
659#120—4312no—
660#120—4312no—
661C4×Q8—434no—
662C4×Q8—434no—
663C4×Q8—434no—
664C4×Q8—434no—
665C4×Q8—4312no—
666C4×Q8—436no—
667C4×Q8—434no—
668C4×Q8—436no—
669C4×Q8—4312no—
670C4×Q8—4312no—
671C4×Q8—4312no—
672C4×Q8C22×D4314yes—
673C4×Q8C22×D4314yes—
674C4×Q8C22×D4316yes—
675C4×Q8C22×D4314yes—
676C4×Q8C22×D43112yes—
677C4×Q8C22×D4316yes—
678C4×Q8C22×D4314yes—
679C4×D4—434no—
680C4×D4—434no—
681C4×D4—4312no—
682C4×D4—4312no—
683C4×D4—4312no—
684C4×D4—4312no—
685C4×D4—4312no—
686C4×D4—4312no—
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—4312no—
697C4×D4—4312no—
698C4×D4—4312no—
699C4×D4—4312no—
700C4×D4C22×D4314yes—
701C4×D4C22×D4316yes—
702C4×D4C22×D43112yes—
703C4×D4C22×D4316yes—
704C4×D4C22×D43112yes—
705#117—434no—
706#117—436no—
707#117—4312no—
708#117—4312no—
709#117—4312no—
710#117—4312no—
711#117—434no—
712#117—4312no—
713#117—4312no—
714#117—4312no—
715#117—4312no—
716#117C22×D4316yes—
717#117C22×D43112yes—
718#117C22×D43112yes—
719C2×C4⋊C4—433no—
720C2×C4⋊C4—4312no—
721C2×C4⋊C4C22×D4313yes—
722C2×C4⋊C4C22×D43112yes—
723C2×C22⋊C4—436no—
724C2×C42—433no—
725C2×C42—433no—
726C2×C42—431no—
727C2×C42—4312no—
728C2×C42—436no—
729C2×C42—436no—
730C2×C42—436no—
731C2×C42—436no—
732C2×C42C22×D4313yes—
733C2×C42C22×D43112yes—
734C24—433no—
735#41—216no—
736#41—224no—
737#41—8616no—
738#41—8616no—
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#1062189818yescomplemented
749C2×Q8C23×D4316yes—
750C2×Q8C23×D4314yes—
751C2×D4—434no—
752C2×D4—434no—
753C2×D4—4312no—
754C2×D4—4312no—
755C2×D4—4312no—
756C2×D4—4312no—
757C2×D4—436no—
758C2×D4—4312no—
759C2×D4—4312no—
760C2×D4—8612no—
761C2×D4C23×D4314yes—
762C2×D4C23×D4316yes—
763C22×C4—431no—
764C22×C4—431no—
765C22×C4—433no—
766C22×C4—436no—
767C22×C4—436no—
768C22×C4—436no—
769C22×C4—4312no—
770C22×C4—434no—
771C22×C4—436no—
772C22×C4—436no—
773C22×C4—436no—
774C22×C4—4312no—
775C22×C4—8612no—
776C22×C4—1726no—
777C22×C4—1726no—
778C22×C4C23×D43112yes—
779C22×C4C23×D4311yescharacteristic
780C22×C4C23×D4314yes—
781C22×C4C23×D4313yes—
782C22×C4C23×D43112yes—
783C22×C4C23×D4313yes—
784C4⋊C4—436no—
785C4⋊C4—4312no—
786C4⋊C4—4312no—
787C4⋊C4—434no—
788C4⋊C4—434no—
789C4⋊C4—434no—
790C4⋊C4—434no—
791C4⋊C4—436no—
792C4⋊C4—434no—
793C4⋊C4—434no—
794C4⋊C4—434no—
795C4⋊C4—434no—
796C4⋊C4—434no—
797C4⋊C4—4312no—
798C4⋊C4—4312no—
799C4⋊C4—4312no—
800C4⋊C4—4312no—
801C4⋊C4C23×D43112yes—
802C4⋊C4C23×D4316yes—
803C4⋊C4C23×D43112yes—
804C4⋊C4C23×D4316yes—
805C4⋊C4C23×D4314yes—
806C22⋊C4—434no—
807C22⋊C4—434no—
808C22⋊C4—434no—
809C22⋊C4—434no—
810C22⋊C4—4312no—
811C22⋊C4—4324no—
812C22⋊C4—434no—
813C22⋊C4—434no—
814C22⋊C4—4312no—
815C22⋊C4—434no—
816C22⋊C4—434no—
817C22⋊C4—4312no—
818C22⋊C4—4312no—
819C22⋊C4—4312no—
820C22⋊C4—4312no—
821C22⋊C4—4312no—
822C22⋊C4C23×D4314yes—
823C22⋊C4C23×D4314yes—
824C22⋊C4C23×D43112yes—
825C42—431no—
826C42—431no—
827C42—436no—
828C42—436no—
829C42—436no—
830C42—436no—
831C42—4312no—
832C42—4312no—
833C42—431no—
834C42—431no—
835C42—434no—
836C42C23×D4316yes—
837C42C23×D43112yes—
838C42C23×D43112yes—
839C42C23×D4316yes—
840C42C23×D4314yes—
841C23—436no—
842C23—434no—
843C23—866no—
844C23—1723no—
845C23—1723no—
846C23C24×D4314yes—
847C23C24×D4311yescharacteristic
848Q8—212no—
849Q8—868no—
850Q8—8612no—
851Q8—17212no—
852Q8C2×#10621898116yes—
853D4—28no—
854D4—212no—
855D4—868no—
856D4—868no—
857D4—8624no—
858D4—8612no—
859D4—17212no—
860D4—17212no—
861D4—17212no—
862D4—17212no—
863D4—17212no—
864C2×C4—224no—
865C2×C4—22no—
866C2×C4—28no—
867C2×C4—43no—
868C2×C4—412no—
869C2×C4—431no—
870C2×C4—431no—
871C2×C4—431no—
872C2×C4—431no—
873C2×C4—434no—
874C2×C4—434no—
875C2×C4—436no—
876C2×C4—434no—
877C2×C4—8612no—
878C2×C4—862no—
879C2×C4—862no—
880C2×C4—8612no—
881C2×C4—8612no—
882C2×C4—8624no—
883C2×C4—8612no—
884C2×C4—868no—
885C2×C4—1726no—
886C2×C4—1726no—
887C2×C4—17212no—
888C2×C4—1723no—
889C2×C4C2×#10621898112yes—
890C2×C4C24×D4316yes—
891C2×C4C24×D4311yescharacteristic
892C2×C4C24×D4314yes—
893C2×C4C24×D4314yes—
894C2×C4C24×D4314yes—
895C2×C4C24×D4316yes—
896C2×C4C24×D4311yescharacteristic
897C22—21no—
898C22—21no—
899C22—24no—
900C22—24no—
901C22—24no—
902C22—864no—
903C22—866no—
904C22—866no—
905C22—864no—
906C22—866no—
907C22—864no—
908C22—17212no—
909C22C22×#1062189812yes—
910C22C25×D4311yescharacteristic
911C4—24no—
912C4—26no—
913C4—24no—
914C4—21no—
915C4—24no—
916C4—432no—
917C4—861no—
918C4—861no—
919C4—864no—
920C4—861no—
921C4—864no—
922C4—866no—
923C4—864no—
924C4C22×#10621898112yes—
925C4#1458373612yes—
926C2—22no—
927C2—44no—
928C2—1726no—
929C2—1724no—
930C2C23×#1062189811yescharacteristic
931C2#585×D4311yescharacteristic
932C2C2×#1458373611yescharacteristic
subgroupG/H
centerC2×C4C24×D43
commutator, socle, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC4×2−1+4×C43C2
hypercenterC4×2−1+4D43
hypocenterC43#62793
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. #19148706C2semidirect
2. #19148696C2semidirect
3. #19148606C2semidirect
4. #19148595C2semidirect
5. #19148440C2semidirect
6. #19148401C2semidirect
7. #19148362C2semidirect
8. #19148308C2semidirect
9. #19148254C2semidirect
10. #19148250C2semidirect
11. #19148221C2semidirect
12. #19148212C2semidirect
13. #19148193C2semidirect
14. #19148190C2semidirect
15. #19148011C2semidirect
16. #19147888C2semidirect
17. C4×#13063373C2semidirect
18. C2×C4×#10621902C2semidirect
19. C4×2−1+4×C43C2semidirect
22. #14583634C22semidirect
23. #14583632C22semidirect
24. Q8×Dic86C22semidirect
25. #14583628C22semidirect
26. #14583625C22semidirect
27. #14583625C22semidirect
28. #14583622C22semidirect
29. #14583621C22semidirect
30. #14583617C22semidirect
31. #14583614C22semidirect
32. #14583612C22semidirect
33. #14583612C22semidirect
34. #14583599C22semidirect
35. #14583597C22semidirect
36. #14583597C22semidirect
37. #14583593C22semidirect
38. #14583590C22semidirect
39. #14583584C22semidirect
42. #14583570C22semidirect
45. #14583568C22semidirect
46. Q8×C22⋊D43C22semidirect
51. #14583560C22semidirect
52. #14583556C22semidirect
53. #14583550C22semidirect
55. #14583521C22semidirect
56. #14583520C22semidirect
57. #14583504C22semidirect
58. #14583500C22semidirect
63. #14583453C22semidirect
64. #14583453C22semidirect
66. #14583449C22semidirect
67. #14583446C22semidirect
68. #14583446C22semidirect
69. #14583446C22semidirect
71. #14583436C22semidirect
72. #14583436C22semidirect
73. #14583436C22semidirect
74. #14583433C22semidirect
75. #14583431C22semidirect
76. #14583431C22semidirect
79. #14583427C22semidirect
80. #14583427C22semidirect
85. #14583381C22semidirect
88. #14583375C22semidirect
93. C4×#10621902C22semidirect
95. C4×#10621898C22semidirect
96. C4×#10621898C22semidirect
98. C4×Q8×D43C22semidirect
105. C43×#520C22semidirect
107. C43×#519C22semidirect
109. C4×#41×C43C22semidirect
111. C2×C4×Q8×C43C22semidirect
271. C2×Q8×C43#41semidirect
477. C4×2−1+4D43semidirect
555. #520C2×D43semidirect
559. #519C2×D43semidirect
569. C4×#41C2×D43semidirect
573. C2×C4×Q8C2×D43semidirect
578. C43#62793semidirect
748. C2×Q8#10621898semidirect

Maximal subgroups

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

subgroupindex
#191487062
#191486962
#191486062
#191485952
#191484402
#191484012
#191483622
#191483082
#191482542
#191482502
#191482212
#191482122
#191481932
#191481902
#191480112
#191478882
C4×#130633732
C2×C4×#106219022
C4×2−1+4×C432
#6279343