Finite Group Databasebeta

← #25969349

Subgroups — #25969349

Order 11008.

1736 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148407C211yesmaximal, characteristic, complemented
2#19148011C211yesmaximal, characteristic
3#19145900C214yesmaximal, complemented
4#19145853C214yesmaximal, complemented
5#19145820C212yesmaximal, complemented
6#19145792C212yesmaximal, complemented
7#19145778C212yesmaximal, complemented
8#19145722C212yesmaximal, complemented
9#19145127C212yesmaximal, complemented
10#19144953C212yesmaximal, complemented
11#19144582C212yesmaximal, complemented
12#19144556C212yesmaximal, complemented
13#19144410C211yesmaximal, characteristic, complemented
14#19144388C211yesmaximal, characteristic, complemented
15C2×#14583190C211yesmaximal, characteristic, complemented
16#19143260C211yesmaximal, characteristic, complemented
17C43×#3076C211yesmaximal, characteristic, complemented
18Q8×Dic86—21no—
19#14583627—21no—
20#14583609—21no—
21#14583607—22no—
22Q8×D172—21no—
23#14583562—22no—
24#14583529C2214yescomplemented
25#14583527C2212yes—
26#14583527C2211yescharacteristic
27#14583521C2212yes—
28#14583520—21no—
29#14583504—21no—
30#14583500C2212yes—
31#14583482—22no—
32#14583477C2211yescharacteristic
33#14583468C2211yescharacteristic
34#14583463C2211yescharacteristic
35#14583454C2212yescomplemented
36#14583449—21no—
37#14583446C2212yes—
38C2×#13063325C2211yescharacteristic
39C4⋊Q8×D43C2212yescomplemented
40#14583436C2212yes—
41#14583433—21no—
42#14583408—22no—
43#14583379C2212yes—
44C4×#10621898C2211yescharacteristic
45C2×C4×D172C2211yescharacteristic
46#14583307C2214yescomplemented
47#14583307C2214yescomplemented
48#14583299C2214yescomplemented
49#14583296C2214yescomplemented
50#14583262C2214yes—
51#14583260C2214yes—
52#14583255C2214yes—
53#14583244C2214yes—
54#14583238C2214yescomplemented
55#14583228C2214yescomplemented
56#14583226C2214yes—
57#14583225C2214yes—
58#14583222C2214yescomplemented
59#14583219C2214yes—
60#14583216C2214yescomplemented
61#14583214C2214yes—
62#14583196C2214yes—
63#14583194C2212yescomplemented
64#14583190C2212yes—
65#14583190C2212yes—
66#14583190C2214yes—
67#14583189C2212yescomplemented
68#14583186C2212yes—
69#14583184C2212yescomplemented
70#14583179C2212yescomplemented
71#14583176C2212yes—
72#14582959C2214yescomplemented
73#14582955C2212yescomplemented
74#14582951C2212yescomplemented
75#14582942C2212yes—
76#14582942C2212yes—
77C2×#13063257C2212yes—
78#14582923C2211yescharacteristic
79#14582903C2212yes—
80#14582900C2212yes—
81C2×#13063247C2212yes—
82#14582865C2212yes—
83#14582854C2212yes—
84C43×#533C2211yescharacteristic
85C4×#41×C43C2211yescharacteristic
86C43×#479C2212yescomplemented
87C43×#478C2212yescomplemented
88C43×#477C2211yescharacteristic, complemented
89C43×#476C2211yescharacteristic, complemented
90C43×#475C2211yescharacteristic, complemented
91C43×#474C2211yescharacteristic, complemented
92C43×#427C2212yes—
93C2×C4⋊C8×C43C2211yescharacteristic
94C43×#416C2212yes—
95C2×#10621898—22no—
96C2×#10621898C2311yescharacteristic
97C22×Dic86—21no—
98C2×Q8×D43—22no—
99C22×D172C2311yescharacteristic
100C22×C4×D43—21no—
101C2×#10621877C2312yes—
102#13063325—21no—
103#13063325—21no—
104#13063325—22no—
105#13063325—21no—
106#13063325C2312yes—
107#13063325C2312yes—
108#13063324—24no—
109#13063324—22no—
110#13063324C2312yes—
111#13063324C2314yes—
112#13063323—22no—
113#13063322—21no—
114#13063321C2312yes—
115#13063320—22no—
116#13063319—22no—
117#13063317—22no—
118#13063317—21no—
119#13063316C2312yes—
120#13063316C2314yes—
121#13063315—24no—
122#13063314C2312yes—
123#13063313—21no—
124#13063313—22no—
125#13063311—22no—
126#13063310—22no—
127#13063310—22no—
128#13063308—22no—
129#13063307—22no—
130#13063305—22no—
131#13063305—24no—
132#13063304—21no—
133#13063303—24no—
134#13063303—22no—
135#13063302—24no—
136#13063302—22no—
137#13063301—22no—
138#13063301C2312yes—
139#13063300C2312yes—
140#13063300C2312yes—
141#13063299—21no—
142#13063299—22no—
143#13063299—21no—
144#13063299—21no—
145#13063298—22no—
146#13063298—22no—
147#13063297—22no—
148#13063296C2312yes—
149#13063295—22no—
150#13063293—22no—
151Q8×Dic43—22no—
152C4×Dic86—22no—
153C4×Dic86D411yescharacteristic
154C4×Dic86D411yescharacteristic
155#13063290—22no—
156C4×D172—22no—
157C4×D172—22no—
158C4×D172—21no—
159C4×D172—21no—
160C4×D172D411yescharacteristic
161C4×D172D411yescharacteristic
162C4×D172C2312yes—
163C4×D172C2312yes—
164C4×C22⋊D43—22no—
165C4×C22⋊D43D412yes—
166C4×C22⋊D43D412yes—
167(C22⋊D43)⋊C4—24no—
168#13063284C2311yescharacteristic
169#13063283C2314yes—
170#13063282—22no—
171#13063282C2312yes—
172C2×C4⋊Dic43—21no—
173C2×C4⋊Dic43C2311yescharacteristic
174C2×C4⋊Dic43C2312yes—
175C4⋊C4×D43—22no—
176C4⋊C4×D43C2314yes—
177C2×(C2×D43)⋊C4—21no—
178C42×D43C2312yes—
179#13063258C2314yes—
180#13063258C2314yes—
181#13063257C2314yes—
182#13063257C2314yes—
183#13063256C2314yes—
184#13063256C2314yes—
185C4⋊(C43⋊C8)C2312yes—
186C4⋊(C43⋊C8)C2312yes—
187#13063249C2314yes—
188#13063247C2314yes—
189#13063247C2314yes—
190#13063246C2314yes—
191#13063245C2314yes—
192#13063245C2314yes—
193(C2×D43)⋊C8C2314yes—
194(C2×D43)⋊C8C2314yes—
195#13063235C2314yes—
196C8×Dic43C2314yes—
197C2×#41×C43C2311yescharacteristic
198C22×C8×C43C2312yes—
199C4⋊Q8×C43C2311yescharacteristic
200C4⋊Q8×C43C2311yescharacteristic
201#125×C43C2312yes—
202C22⋊Q8×C43—21no—
203C22⋊Q8×C43—21no—
204C4×Q8×C43—21no—
205C4×Q8×C43—21no—
206C4×Q8×C43C2311yescharacteristic
207C4×Q8×C43C2311yescharacteristic
208C4×D4×C43—21no—
209C4×D4×C43—21no—
210C4×D4×C43C2311yescharacteristic
211C4×D4×C43C2311yescharacteristic
212#117×C43—21no—
213#117×C43C2311yescharacteristic
214#117×C43C2312yes—
215C2×C42×C43—21no—
216C2×C42×C43C2311yescharacteristic
217#107×C43C2312yes—
218#107×C43C2312yes—
219#106×C43C2312yes—
220#106×C43C2312yes—
221C4⋊C8×C43C2311yescharacteristic
222C4⋊C8×C43C2311yescharacteristic
223C4⋊C8×C43C2312yes—
224#103×C43C2312yes—
225#103×C43C2312yes—
226#102×C43C2312yes—
227#102×C43C2312yes—
228C23×D43—21no—
229#41×C43—22no—
230#41×C43—22no—
231C2×Q8×C43—21no—
232C2×Q8×C43—21no—
233C2×Q8×C43C2411yescharacteristic
234C2×D4×C43—21no—
235C2×D4×C43C2411yescharacteristic
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43C2×D411yescharacteristic
240C22×C4×C43C2×D411yescharacteristic
241C22×C4×C43C2411yescharacteristic
242C2×C22⋊D43—22no—
243C2×C22⋊D43—22no—
244C2×C22⋊D43—22no—
245C2×C22⋊D43C2×D412yes—
246C22×Dic43—21no—
247C22×Dic43—22no—
248Q8×D43—84no—
249#10621898—22no—
250#10621898—22no—
251#10621898—84no—
252C2×D172—21no—
253C2×D172—22no—
254C2×D172—22no—
255C2×D172—22no—
256C2×D172—22no—
257C2×D172C2×D411yescharacteristic
258C2×D172C2412yes—
259C2×C4×D43—22no—
260C2×C4×D43—22no—
261C2×C4×D43—24no—
262C2×C4×D43—82no—
263C2×C4×D43C2×D412yes—
264C2×C4×D43C2×D412yes—
265C2×C4×D43C2412yes—
266C2×Dic86—22no—
267C2×Dic86—22no—
268C2×Dic86—22no—
269C2×Dic86—24no—
270C2×Dic86—82no—
271C2×Dic86C2×D411yescharacteristic
272C2×C8×C43—24no—
273C2×C8×C43C2412yes—
274C2×C8×C43C2412yes—
275C4⋊C4×C43—21no—
276C4⋊C4×C43—21no—
277C4⋊C4×C43—22no—
278C4⋊C4×C43—22no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43—21no—
281C4⋊C4×C43C2412yes—
282C4⋊C4×C43C2412yes—
283C4⋊C4×C43C2411yescharacteristic
284C4⋊C4×C43C2411yescharacteristic
285C22⋊C4×C43—21no—
286C22⋊C4×C43—21no—
287C22⋊C4×C43—21no—
288C22⋊C4×C43—22no—
289C42×C43—21no—
290C42×C43—21no—
291C42×C43—21no—
292C42×C43—22no—
293C42×C43C2×D411yescharacteristic
294C42×C43C2×D411yescharacteristic
295C42×C43C2411yescharacteristic
296C42×C43C2411yescharacteristic
297C22⋊Dic43—22no—
298C22⋊Dic43C2×D412yes—
299(C2×D43)⋊C4—22no—
300(C2×D43)⋊C4—22no—
301(C2×D43)⋊C4—22no—
302(C2×D43)⋊C4—22no—
303(C2×D43)⋊C4—22no—
304(C2×D43)⋊C4—22no—
305(C2×D43)⋊C4—24no—
306(C2×D43)⋊C4—22no—
307(C2×D43)⋊C4C2×D412yes—
308(C2×D43)⋊C4C2×D412yes—
309C4⋊Dic43—22no—
310C4⋊Dic43—22no—
311C4⋊Dic43—21no—
312C4⋊Dic43—22no—
313C4⋊Dic43—22no—
314C4⋊Dic43—24no—
315C4⋊Dic43C2×D411yescharacteristic
316C4⋊Dic43C2×D411yescharacteristic
317C4⋊Dic43C2414yes—
318C4⋊Dic43C2412yes—
319Dic43⋊C4—24no—
320Dic43⋊C4—24no—
321Dic43⋊C4—22no—
322Dic43⋊C4—22no—
323Dic43⋊C4—22no—
324Dic43⋊C4—24no—
325Dic43⋊C4C2×D412yes—
326Dic43⋊C4C2×D412yes—
327C4×Dic43—24no—
328C4×Dic43C2×D412yes—
329C4×Dic43C2×D412yes—
330C4×Dic43C2412yes—
331#10621877—24no—
332C2×C43⋊C8C2414yes—
333C23×C43—21no—
334C23×C43C22×D411yescharacteristic
335C22×D43—22no—
336C22×D43—42no—
337C22×D43—81no—
338C22×D43—81no—
339C22×D43C22×D412yes—
340Q8×C43—21no—
341Q8×C43—21no—
342Q8×C43—42no—
343Q8×C43—42no—
344D4×C43—21no—
345D4×C43—21no—
346D4×C43—42no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—41no—
354C2×C4×C43—42no—
355C2×C4×C43—42no—
356C2×C4×C43—81no—
357C2×C4×C43C22×D411yescharacteristic
358C2×C4×C43C22×D411yescharacteristic
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C22×D411yescharacteristic
361C2×C4×C43C22×D411yescharacteristic
362C2×C4×C432−1+412yes—
363C2×C4×C432−1+412yes—
364C2×C4×C43C2511yescharacteristic
365C22⋊D43—24no—
366C22⋊D43—82no—
367C22⋊D43—82no—
368C22⋊D43—82no—
369C2×Dic43—24no—
370C2×Dic43—22no—
371C2×Dic43—82no—
372C2×Dic43—81no—
373C2×Dic43C22×D412yes—
374C2×Dic43C22×D412yes—
375C2×Dic43C22×D412yes—
376D172—22no—
377D172—22no—
378D172—22no—
379D172—42no—
380D172—82no—
381D172—82no—
382C4×D43—24no—
383C4×D43—22no—
384C4×D43—22no—
385C4×D43—42no—
386C4×D43—44no—
387C4×D43—82no—
388C4×D43—84no—
389Dic86—22no—
390Dic86—44no—
391Dic86—82no—
392Dic86—84no—
393Dic86—82no—
394C8×C43—22no—
395C8×C43—22no—
396C43⋊C8—24no—
397#60892—431nomaximal, Sylow
398C22×C43—21no—
399C22×C43—21no—
400C22×C43—41no—
401C22×C43—41no—
402C22×C43—41no—
403C22×C43#53612yes—
404C22×C43C23×D411yescharacteristic
405C2×D43—22no—
406C2×D43—22no—
407C2×D43—22no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—84no—
412C4×C43—21no—
413C4×C43—21no—
414C4×C43—21no—
415C4×C43—42no—
416C4×C43—41no—
417C4×C43—41no—
418C4×C43—41no—
419C4×C43—42no—
420C4×C43#53612yes—
421C4×C43#57712yes—
422C4×C43C2×2−1+411yescharacteristic
423C4×C43C2×2−1+411yescharacteristic
424Dic43—22no—
425Dic43—22no—
426Dic43—22no—
427Dic43—44no—
428Dic43—42no—
429#3503—431no—
430#3460—431no—
431#3244—434no—
432#3241—434no—
433#3238—432no—
434#3235—432no—
435#3233—432no—
436#3227—432no—
437#3163—432no—
438#3136—432no—
439#3099—432no—
440#3096—432no—
441#3079—431no—
442#3077—431no—
443#3076D4311yescharacteristic, complemented
444C2×#476—431no—
445#2925—431no—
446C2×C43—22no—
447C2×C43—81no—
448C2×C43C2×#53611yescharacteristic
449C2×C43C2×#57711yescharacteristic
450C2×C43#358511yescharacteristic
451D43—42no—
452D43—82no—
453Q82—861no—
454#557—861no—
455#554—861no—
456#554—862no—
457D4×Q8—861no—
458D4×Q8—862no—
459#544—434no—
460#544—432no—
461#544—431no—
462#542—432no—
463#542—861no—
464#540—432no—
465#540—861no—
466#538—862no—
467#537—431no—
468#535—431no—
469#535—431no—
470#533—432no—
471#533C2×D4311yescharacteristic
472#532—432no—
473#532—861no—
474C2×C4⋊Q8—432no—
475C2×C4⋊Q8—431no—
476#529—432no—
477#529—861no—
478#525—862no—
479#520—432no—
480C4×#41—431no—
481C4×#41C2×D4311yescharacteristic
482C2×C4×D4—431no—
483#501—434no—
484#501—434no—
485#499—434no—
486#498—434no—
487#490—434no—
488#489—434no—
489#488—434no—
490#486—434no—
491#485—434no—
492#483—434no—
493#482—434no—
494#482—434no—
495#482—434no—
496#481—434no—
497#481—434no—
498#480—434no—
499#479C2×D4312yescomplemented
500#478—434no—
501#478C2×D4312yescomplemented
502#477—432no—
503#477C2×D4311yescharacteristic, complemented
504#476—432no—
505#476—432no—
506#476—432no—
507#476—432no—
508#476—434no—
509#476C2×D4311yescharacteristic, complemented
510#475—432no—
511#475C2×D4311yescharacteristic, complemented
512#474—432no—
513#474—432no—
514#474C2×D4311yescharacteristic, complemented
515#433—434no—
516#432—432no—
517#431—432no—
518#428—432no—
519#428—432no—
520#427C2×D4312yes—
521C2×#106—432no—
522#423—431no—
523C2×C4⋊C8C2×D4311yescharacteristic
524#418—432no—
525#417—432no—
526#416C2×D4312yes—
527C2×#102—432no—
528#408—432no—
529#405—432no—
530C43#6089211yescharacteristic, complemented, Sylow
531C2×#41—431no—
532C2×#41—862no—
533C2×#41C22×D4311yescharacteristic
534C22×Q8—862no—
535C22×Q8—861no—
536C22×D4—431no—
537C23×C4—861no—
538C2×M16—432no—
539C22×C8C22×D4312yes—
540C4⋊Q8—434no—
541C4⋊Q8—432no—
542C4⋊Q8—432no—
543C4⋊Q8—432no—
544C4⋊Q8—861no—
545C4⋊Q8—862no—
546C4⋊Q8—862no—
547C4⋊Q8—862no—
548C4⋊Q8—864no—
549C4⋊Q8—861no—
550C4⋊Q8—861no—
551C4⋊Q8C22×D4311yescharacteristic
552C4⋊Q8C22×D4311yescharacteristic
553#127—432no—
554#127—861no—
555#126—862no—
556#126—862no—
557#125—432no—
558#125—434no—
559#125—861no—
560#125—862no—
561#125—864no—
562#125C22×D4312yes—
563#124—432no—
564#124—862no—
565#124—861no—
566#124—862no—
567#123—862no—
568#123—862no—
569#123—862no—
570#123—862no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—432no—
574C22⋊Q8—862no—
575C22⋊Q8—864no—
576C22⋊Q8—864no—
577C22⋊Q8—864no—
578C22⋊Q8—862no—
579C22⋊Q8—862no—
580C22⋊Q8—861no—
581C22⋊Q8—862no—
582#121—432no—
583#121—432no—
584#121—432no—
585#121—862no—
586#121—862no—
587#121—862no—
588#121—861no—
589#121—861no—
590#121—861no—
591#121—862no—
592#120—862no—
593#120—862no—
594C4×Q8—21no—
595C4×Q8—21no—
596C4×Q8—431no—
597C4×Q8—431no—
598C4×Q8—862no—
599C4×Q8—862no—
600C4×Q8—862no—
601C4×Q8C22×D4311yescharacteristic
602C4×Q8C22×D4311yescharacteristic
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—432no—
606C4×D4—432no—
607C4×D4—431no—
608C4×D4—431no—
609C4×D4—432no—
610C4×D4—432no—
611C4×D4—862no—
612C4×D4—862no—
613C4×D4—862no—
614C4×D4—864no—
615C4×D4—861no—
616C4×D4—861no—
617C4×D4C22×D4311yescharacteristic
618C4×D4C22×D4311yescharacteristic
619#117—21no—
620#117—431no—
621#117—432no—
622#117—434no—
623#117—862no—
624#117C22×D4311yescharacteristic
625#117C22×D4312yes—
626C2×C4⋊C4—431no—
627C2×C4⋊C4—432no—
628C2×C4⋊C4—434no—
629C2×C4⋊C4—862no—
630C2×C4⋊C4—861no—
631C2×C22⋊C4—861no—
632C2×C42—21no—
633C2×C42—432no—
634C2×C42C22×D4311yescharacteristic
635#107—434no—
636#107—434no—
637#107C22×D4312yes—
638#107C22×D4312yes—
639#106—434no—
640#106—434no—
641#106—434no—
642#106—434no—
643#106C22×D4312yes—
644#106C22×D4312yes—
645C4⋊C8—432no—
646C4⋊C8—432no—
647C4⋊C8C22×D4311yescharacteristic
648C4⋊C8C22×D4311yescharacteristic
649C4⋊C8C22×D4312yes—
650#103—434no—
651#103C22×D4312yes—
652#103C22×D4312yes—
653#102—434no—
654#102—434no—
655#102—434no—
656#102—434no—
657#102—434no—
658#102C22×D4312yes—
659#102C22×D4312yes—
660C22⋊C8—434no—
661C22⋊C8—434no—
662#97—434no—
663C4×C8—434no—
664C24—861no—
665#41—22no—
666#41—22no—
667#41—862no—
668#41—862no—
669#41—3444no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—431no—
673C2×Q8—862no—
674C2×Q8—864no—
675C2×Q8—862no—
676C2×Q8—862no—
677C2×Q8—3442no—
678C2×Q8—3444no—
679C2×Q8C23×D4311yescharacteristic
680C2×D4—21no—
681C2×D4—432no—
682C2×D4—431no—
683C2×D4—432no—
684C2×D4—862no—
685C2×D4—862no—
686C2×D4—862no—
687C2×D4—862no—
688C2×D4—862no—
689C2×D4—861no—
690C2×D4—862no—
691C2×D4—862no—
692C2×D4C23×D4311yescharacteristic
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—432no—
697C22×C4—432no—
698C22×C4—432no—
699C22×C4—864no—
700C22×C4—861no—
701C22×C4—862no—
702C22×C4—862no—
703C22×C4—862no—
704C22×C4—3442no—
705C22×C4D4×D4311yescharacteristic
706C22×C4D4×D4311yescharacteristic
707C22×C4C23×D4311yescharacteristic
708M16—864no—
709C2×C8—24no—
710C2×C8—434no—
711C2×C8C23×D4312yes—
712C2×C8C23×D4312yes—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—431no—
720C4⋊C4—431no—
721C4⋊C4—432no—
722C4⋊C4—432no—
723C4⋊C4—434no—
724C4⋊C4—432no—
725C4⋊C4—864no—
726C4⋊C4—864no—
727C4⋊C4—862no—
728C4⋊C4—862no—
729C4⋊C4—862no—
730C4⋊C4—862no—
731C4⋊C4—864no—
732C4⋊C4—864no—
733C4⋊C4—861no—
734C4⋊C4—862no—
735C4⋊C4—862no—
736C4⋊C4—862no—
737C4⋊C4C23×D4312yes—
738C4⋊C4C23×D4312yes—
739C4⋊C4C23×D4311yescharacteristic
740C4⋊C4C23×D4311yescharacteristic
741C22⋊C4—21no—
742C22⋊C4—22no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—432no—
746C22⋊C4—432no—
747C22⋊C4—432no—
748C22⋊C4—862no—
749C22⋊C4—862no—
750C22⋊C4—862no—
751C22⋊C4—862no—
752C22⋊C4—864no—
753C22⋊C4—862no—
754C22⋊C4—862no—
755C22⋊C4—862no—
756C22⋊C4—862no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—22no—
761C42—432no—
762C42—432no—
763C42—432no—
764C42—864no—
765C42D4×D4311yescharacteristic
766C42D4×D4311yescharacteristic
767C42C23×D4311yescharacteristic
768C42C23×D4311yescharacteristic
769C23—21no—
770C23—432no—
771C23—862no—
772C23—3441no—
773C23—3441no—
774C23—1722no—
775C23C2×D4×D4311yescharacteristic
776Q8—21no—
777Q8—21no—
778Q8—42no—
779Q8—42no—
780Q8—862no—
781Q8—3442no—
782Q8—3444no—
783Q8—3442no—
784Q8—1724no—
785D4—21no—
786D4—21no—
787D4—42no—
788D4—864no—
789D4—862no—
790D4—862no—
791D4—862no—
792D4—3442no—
793D4—3442no—
794D4—3442no—
795D4—3442no—
796D4—3442no—
797D4—1722no—
798C2×C4—22no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—81no—
808C2×C4—432no—
809C2×C4—432no—
810C2×C4—432no—
811C2×C4—864no—
812C2×C4—862no—
813C2×C4—862no—
814C2×C4—864no—
815C2×C4—862no—
816C2×C4—3442no—
817C2×C4—3444no—
818C2×C4—3441no—
819C2×C4—3442no—
820C2×C4—1722no—
821C2×C4—1724no—
822C2×C4C2×D4×D4311yescharacteristic
823C2×C4C2×D4×D4311yescharacteristic
824C2×C4C2×D4×D4311yescharacteristic
825C2×C4C2×D4×D4311yescharacteristic
826C2×C4C2×D4×D4311yescharacteristic
827C2×C4#1306337212yes—
828C2×C4#1306337312yes—
829C2×C4C24×D4311yescharacteristic
830C8—22no—
831C8—22no—
832C8—864no—
833C22—21no—
834C22—21no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—862no—
839C22—862no—
840C22—862no—
841C22—3444no—
842C22—1722no—
843C22—1722no—
844C22—1722no—
845C22#1458347212yes—
846C22C22×D4×D4311yescharacteristic
847C4—21no—
848C4—21no—
849C4—21no—
850C4—41no—
851C4—42no—
852C4—41no—
853C4—42no—
854C4—41no—
855C4—862no—
856C4—862no—
857C4—862no—
858C4—1722no—
859C4—1724no—
860C4#1458347212yes—
861C4#1458370612yes—
862C4C2×#1306337211yescharacteristic
863C4C2×#1306337311yescharacteristic
864C2—22no—
865C2—81no—
866C2—3442no—
867C2—1722no—
868C2C2×#1458347211yescharacteristic
869C2C2×#1458370611yescharacteristic
870C2#1914937211yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3076C2
socleC22×C43C23×D4
prime radical#19148011C2
hypercenter#3076D43
hypocenterC43#60892
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
1. #19148407C2semidirect
3. #19145900C2semidirect
4. #19145853C2semidirect
5. #19145820C2semidirect
6. #19145792C2semidirect
7. #19145778C2semidirect
8. #19145722C2semidirect
9. #19145127C2semidirect
10. #19144953C2semidirect
11. #19144582C2semidirect
12. #19144556C2semidirect
13. #19144410C2semidirect
14. #19144388C2semidirect
15. C2×#14583190C2semidirect
16. #19143260C2semidirect
17. C43×#3076C2semidirect
24. #14583529C22semidirect
35. #14583454C22semidirect
39. C4⋊Q8×D43C22semidirect
46. #14583307C22semidirect
47. #14583307C22semidirect
48. #14583299C22semidirect
49. #14583296C22semidirect
54. #14583238C22semidirect
55. #14583228C22semidirect
58. #14583222C22semidirect
60. #14583216C22semidirect
63. #14583194C22semidirect
67. #14583189C22semidirect
69. #14583184C22semidirect
70. #14583179C22semidirect
72. #14582959C22semidirect
73. #14582955C22semidirect
74. #14582951C22semidirect
86. C43×#479C22semidirect
87. C43×#478C22semidirect
88. C43×#477C22semidirect
89. C43×#476C22semidirect
90. C43×#475C22semidirect
91. C43×#474C22semidirect
443. #3076D43semidirect
499. #479C2×D43semidirect
501. #478C2×D43semidirect
503. #477C2×D43semidirect
509. #476C2×D43semidirect
511. #475C2×D43semidirect
514. #474C2×D43semidirect
530. C43#60892semidirect

Maximal subgroups

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

subgroupindex
#191484072
#191480112
#191459002
#191458532
#191458202
#191457922
#191457782
#191457222
#191451272
#191449532
#191445822
#191445562
#191444102
#191443882
C2×#145831902
#191432602
C43×#30762
#6089243