Finite Group Databasebeta

← #25961135

Subgroups — #25961135

Order 11008.

1962 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147887C211yesmaximal, characteristic
2#19143605C214yesmaximal, complemented
3#19143603C214yesmaximal, complemented
4#19143590C214yesmaximal, complemented
5#19143583C214yesmaximal, complemented
6#19143534C211yesmaximal, characteristic, complemented
7#19143533C211yesmaximal, characteristic, complemented
8#19143311C211yesmaximal, characteristic, complemented
9#19143310C211yesmaximal, characteristic, complemented
10#19143290C211yesmaximal, characteristic, complemented
11#19143289C211yesmaximal, characteristic, complemented
12#19143285C211yesmaximal, characteristic, complemented
13#19143245C211yesmaximal, characteristic, complemented
14#19143242C211yesmaximal, characteristic, complemented
15#19143224C211yesmaximal, characteristic, complemented
16#19143022C211yesmaximal, characteristic, complemented
17#19143021C211yesmaximal, characteristic, complemented
18C22×#13063235C211yesmaximal, characteristic, complemented
19C43×#2929C211yesmaximal, characteristic, complemented
20C2×#13063333C2211yescharacteristic
21C2×#13063332C2211yescharacteristic
22C2×#13063331C2211yescharacteristic
23C23×C43⋊C8C2211yescharacteristic
24#14583452C2211yescharacteristic
25#14583451C412yes—
26#14583445C2211yescharacteristic
27#14583444C412yes—
28#14583435C412yes—
29#14583430C412yes—
30#14583429C2214yes—
31#14583426C414yes—
32#14583410C2211yescharacteristic
33#14583405C414yes—
34#41×Dic43C2211yescharacteristic
35#14583367C2211yescharacteristic
36C4×#10621900C2214yes—
37C22×C4×Dic43C2211yescharacteristic
38#14583029C2214yescomplemented
39#14583028C2214yescomplemented
40#14583027C2214yescomplemented
41#14583026C2214yescomplemented
42#14582973C2214yescomplemented
43#14582971C2214yes—
44#14582970C2214yes—
45#14582970C2214yescomplemented
46#14582968C2214yescomplemented
47#14582967C2214yes—
48#14582967C2214yescomplemented
49D4×C43⋊C8C2214yes—
50C8×C22⋊D43C2214yes—
51(C22⋊D43)⋊C8C2214yes—
52#14582959C2214yescomplemented
53#14582957C2214yescomplemented
54#14582955C2214yescomplemented
55#14582953C2214yes—
56#14582953C2214yescomplemented
57#14582949C2214yes—
58#14582927C2211yescharacteristic
59#14582926C2211yescharacteristic
60#14582925C2211yescharacteristic
61#14582922C2211yescharacteristic
62#14582922C2211yescharacteristic
63#14582867C2211yescharacteristic
64#14582866C2211yescharacteristic
65#14582865C2211yescharacteristic
66#14582863C2211yescharacteristic
67#14582857C2211yescharacteristic
68#14582857C2212yescomplemented
69#14582856C2212yescomplemented
70#14582855C2211yescharacteristic
71#14582854C2211yescharacteristic
72#14582854C2212yescomplemented
73#14582853C2212yescomplemented
74M16×Dic43C2211yescharacteristic
75M16×Dic43C2211yescharacteristic
76M16×Dic43C2212yescomplemented
77C4×#10621872C2212yescomplemented
78C2×#13063235C2211yescharacteristic
79C2×#13063235C2211yescharacteristic
80C2×#13063235C2211yescharacteristic
81C2×#13063235C2211yescharacteristic
82C2×#13063235C2212yes—
83C2×#13063235C2212yes—
84C2×#13063235C2212yes—
85C2×#13063235C2212yes—
86C2×#13063235C2212yescomplemented
87#97×D43C2212yescomplemented
88C2×#131×C43C2211yescharacteristic
89C23×C8×C43C2211yescharacteristic
90C43×#525C2211yescharacteristic
91C43×#435C2214yes—
92C8×D4×C43C2214yes—
93C43×#424C2211yescharacteristic
94C43×#408C2211yescharacteristic
95C43×#407C2211yescharacteristic
96C43×#405C2211yescharacteristic
97C2×#10621898C2311yescharacteristic
98C2×#10621900C2×C414yes—
99C23×Dic43C2×C412yes—
100#13063333—24no—
101#13063332—24no—
102#13063331—24no—
103C2×#10621877C2311yescharacteristic
104C2×#10621877C2311yescharacteristic
105C2×#10621877C2312yes—
106C2×#10621872C2312yes—
107C2×#10621872C2312yes—
108C22×C43⋊C8—24no—
109C22×C43⋊C8C2311yescharacteristic
110C22×C43⋊C8C2312yes—
111C22×C43⋊C8C2312yes—
112C22×C43⋊C8C2312yes—
113C22×C43⋊C8C2311yescharacteristic
114C2×C8×D43C2312yes—
115C2×C8×D43C2312yes—
116#13063324C2×C412yes—
117#13063323C2×C411yescharacteristic
118#13063321C2×C411yescharacteristic
119#13063320C2×C414yes—
120#13063318C2×C414yes—
121#13063316C2×C412yes—
122#13063315C2×C414yes—
123#13063314C2×C411yescharacteristic
124#13063312C2×C411yescharacteristic
125#13063311C2×C414yes—
126#13063309C2×C414yes—
127#13063308C2×C412yes—
128#13063306C2×C414yes—
129#13063304C2×C412yes—
130#13063302C2×C414yes—
131#13063302C2×C414yes—
132#13063299C2×C412yes—
133#13063297C2×C414yes—
134#13063297C2×C414yes—
135#13063294C2×C412yes—
136Q8×Dic43C2×C412yes—
137C4×Dic86C2314yes—
138#13063290C2×C414yes—
139#13063290C2×C412yes—
140D4×Dic43C2×C414yes—
141D4×Dic43C2×C414yes—
142D4×Dic43C2×C412yes—
143#13063287C2×C412yes—
144C4×C22⋊D43C2314yes—
145C4×C22⋊D43C2314yes—
146(C22⋊D43)⋊C4C2×C414yes—
147(C22⋊D43)⋊C4C2×C414yes—
148(C22⋊D43)⋊C4C2×C414yes—
149#13063284C2311yescharacteristic
150#13063284C2312yes—
151#13063283C2×C414yes—
152#13063282C2312yes—
153#13063281C2×C414yes—
154#13063281C2×C414yes—
155C2×C4×Dic43C2×C412yes—
156C2×C4×Dic43C2×C412yes—
157C2×C4×Dic43C2×C412yes—
158C2×C4×Dic43C2311yescharacteristic
159C2×C4×Dic43C2312yes—
160C2×C4×Dic43C2312yes—
161C2×C4×Dic43C2311yescharacteristic
162C2×C4×Dic43C2312yes—
163C42×D43C2312yes—
164C4⋊(C43⋊C8)C2314yes—
165Dic43⋊C8C2314yes—
166Dic43⋊C8C2314yes—
167Dic43⋊C8C2314yes—
168Dic43⋊C8C2314yes—
169C22⋊(C43⋊C8)C2314yes—
170C22⋊(C43⋊C8)C2314yes—
171(C2×D43)⋊C8C2314yes—
172(C2×D43)⋊C8C2314yes—
173#13063236C2312yes—
174#13063235C2311yescharacteristic
175#13063235C2312yes—
176#13063235C2311yescharacteristic
177#13063235C2311yescharacteristic
178#13063235C2311yescharacteristic
179#13063235C2312yes—
180#13063235C2312yes—
181#13063235C2312yes—
182#13063235C2312yes—
183#13063235C2312yes—
184#13063235C2312yes—
185#13063235C2312yes—
186#13063235C2312yes—
187#13063235C2312yes—
188C4×C43⋊C8C2312yes—
189C8×Dic43C2312yes—
190C8×Dic43C2312yes—
191C8×Dic43C2312yes—
192C8×Dic43C2312yes—
193C2×#41×C43C2311yescharacteristic
194C23×C4×C43C2311yescharacteristic
195#131×C43—24no—
196C2×M16×C43C2311yescharacteristic
197C2×M16×C43C2311yescharacteristic
198C2×M16×C43C2312yes—
199C22×C8×C43—24no—
200C22×C8×C43C2311yescharacteristic
201C22×C8×C43C2312yes—
202C22×C8×C43C2312yes—
203C22×C8×C43C2312yes—
204C22×C8×C43C2311yescharacteristic
205#123×C43C2×C412yes—
206C22⋊Q8×C43C2×C412yes—
207#121×C43C2×C412yes—
208#120×C43C2×C412yes—
209C4×D4×C43C2314yes—
210#117×C43C2311yescharacteristic
211C4⋊C8×C43C2314yes—
212C22⋊C8×C43C2314yes—
213C22⋊C8×C43C2314yes—
214#97×C43C2312yes—
215C4×C8×C43C2312yes—
216C24×C43C22×C411yescharacteristic
217#41×C43—22no—
218#41×C43—22no—
219C2×Q8×C43C22×C411yescharacteristic
220C2×D4×C43C22×C414yes—
221C2×D4×C43C22×C412yes—
222C2×D4×C43C22×C411yescharacteristic
223C22×C4×C43—22no—
224C22×C4×C43—22no—
225C22×C4×C43C22×C412yes—
226C22×C4×C43C22×C411yescharacteristic
227C22×C4×C43C2412yes—
228C22×C4×C43C2412yes—
229C22×C4×C43C2411yescharacteristic
230C2×C22⋊D43C22×C412yes—
231C2×C22⋊D43C22×C414yes—
232C2×C22⋊D43C22×C414yes—
233C22×Dic43—44no—
234C22×Dic43C22×C412yes—
235C22×Dic43C22×C412yes—
236C22×Dic43C22×C412yes—
237C22×Dic43C22×C412yes—
238C22×Dic43C22×C412yes—
239C22×Dic43C22×C412yes—
240C22×Dic43C22×C414yes—
241#10621900—48no—
242#10621898—22no—
243#10621898—22no—
244C2×D172C22×C411yescharacteristic
245C2×C4×D43C22×C414yes—
246C2×C4×D43C2412yes—
247C2×Dic86C22×C411yescharacteristic
248C2×Dic86C22×C414yes—
249M16×C43—22no—
250M16×C43—22no—
251M16×C43—24no—
252C2×C8×C43—22no—
253C2×C8×C43—24no—
254C2×C8×C43—24no—
255C2×C8×C43—24no—
256C2×C8×C43#4114yescomplemented
257C2×C8×C43C2412yes—
258C2×C8×C43C2412yes—
259C2×C8×C43C2412yes—
260C2×C8×C43C2411yescharacteristic
261C2×C8×C43C2411yescharacteristic
262C4⋊C4×C43C22×C412yes—
263C4⋊C4×C43C22×C414yes—
264C22⋊C4×C43C22×C412yes—
265C22⋊C4×C43C22×C414yes—
266C22⋊C4×C43C22×C414yes—
267C42×C43C2412yes—
268C22⋊Dic43C22×C414yes—
269C22⋊Dic43C22×C414yes—
270C22⋊Dic43C22×C412yes—
271C22⋊Dic43C22×C414yes—
272(C2×D43)⋊C4C22×C414yes—
273(C2×D43)⋊C4C22×C414yes—
274(C2×D43)⋊C4C22×C414yes—
275C4⋊Dic43C22×C414yes—
276C4⋊Dic43C22×C412yes—
277C4⋊Dic43C22×C414yes—
278Dic43⋊C4C22×C414yes—
279Dic43⋊C4C22×C414yes—
280Dic43⋊C4C22×C414yes—
281Dic43⋊C4C22×C414yes—
282Dic43⋊C4C22×C414yes—
283C4×Dic43C22×C414yes—
284C4×Dic43C22×C412yes—
285C4×Dic43C22×C412yes—
286C4×Dic43C22×C412yes—
287C4×Dic43C22×C412yes—
288C4×Dic43C22×C411yescharacteristic
289C4×Dic43C22×C412yes—
290C4×Dic43C22×C411yescharacteristic
291C4×Dic43C22×C414yes—
292C4×Dic43C2411yescharacteristic
293C4×Dic43C2412yes—
294C4×Dic43C2411yescharacteristic
295C4×Dic43C2412yes—
296#10621877—22no—
297#10621877—22no—
298#10621877—24no—
299C2×C43⋊C8—22no—
300C2×C43⋊C8—24no—
301C2×C43⋊C8—24no—
302C2×C43⋊C8—24no—
303C2×C43⋊C8#4114yescomplemented
304C2×C43⋊C8C2412yes—
305C2×C43⋊C8C2412yes—
306C2×C43⋊C8C2412yes—
307C2×C43⋊C8C2411yescharacteristic
308C2×C43⋊C8C2411yescharacteristic
309#10621872—24no—
310#10621872—24no—
311C8×D43—24no—
312C8×D43—24no—
313C23×C43—22no—
314C23×C43—24no—
315C23×C43C23×C412yes—
316C23×C43C23×C411yescharacteristic
317C23×C43C23×C412yes—
318C22×D43C23×C412yes—
319Q8×C43—22no—
320D4×C43—24no—
321D4×C43—28no—
322D4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—24no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43C23×C412yes—
330C2×C4×C43C23×C412yes—
331C2×C4×C43C23×C414yes—
332C2×C4×C43C23×C411yescharacteristic
333C2×C4×C43C2×#4112yes—
334C2×C4×C43C2×#4112yes—
335C2×C4×C43C2511yescharacteristic
336C22⋊D43—24no—
337C22⋊D43—28no—
338C22⋊D43—44no—
339C2×Dic43—24no—
340C2×Dic43—24no—
341C2×Dic43—44no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43—42no—
346C2×Dic43C23×C412yes—
347C2×Dic43C23×C412yes—
348C2×Dic43C23×C412yes—
349C2×Dic43C23×C412yes—
350C2×Dic43C23×C412yes—
351C2×Dic43C23×C414yes—
352D172—22no—
353C4×D43—22no—
354C4×D43—22no—
355C4×D43—44no—
356Dic86—22no—
357Dic86—44no—
358C8×C43—22no—
359C8×C43—22no—
360C8×C43—22no—
361C8×C43C2×#4112yes—
362C8×C43C2×#4112yes—
363C43⋊C8—22no—
364C43⋊C8—22no—
365C43⋊C8—22no—
366C43⋊C8C2×#4112yes—
367C43⋊C8C2×#4112yes—
368#60207—431nomaximal, Sylow
369C22×C43—28no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—24no—
375C22×C43C4×#4112yes—
376C22×C43#56814yes—
377C22×C43C24×C411yescharacteristic
378C2×D43—22no—
379C2×D43—24no—
380C4×C43—22no—
381C4×C43—22no—
382C4×C43—24no—
383C4×C43C4×#4112yes—
384C4×C43C22×#4111yescharacteristic
385C4×C43C22×#4111yescharacteristic
386Dic43—22no—
387Dic43—22no—
388Dic43—24no—
389Dic43—22no—
390Dic43—22no—
391Dic43—22no—
392#3444—431no—
393#2970—434no—
394#2970—434no—
395#2968—434no—
396#2968—434no—
397#2961—431no—
398#2961—431no—
399#2932—431no—
400#2932—431no—
401#2929—431no—
402#2929—431no—
403#2929—431no—
404#2929D4311yescharacteristic, complemented
405#2923—431no—
406#2923—431no—
407#2920—431no—
408#2875—431no—
409#2875—431no—
410C22×#97—431no—
411C2×C43—22no—
412C2×C43—24no—
413C2×C43—42no—
414C2×C43C2×C4×#4111yescharacteristic
415C2×C43C2×#56812yes—
416D43—42no—
417C2×#131—431no—
418C2×#131—431no—
419C2×#131—431no—
420C2×#131C2×D4311yescharacteristic
421C23×C8—431no—
422C23×C8C2×D4311yescharacteristic
423#533—432no—
424#533—431no—
425#532—431no—
426#532—432no—
427#529—434no—
428#529—432no—
429#529—432no—
430#529—434no—
431#525—431no—
432#525—434no—
433#525C2×D4311yescharacteristic
434C4×#41—431no—
435C4×#41—434no—
436C4×#41—431no—
437C22×C42—431no—
438#446—434no—
439#446—434no—
440#446—434no—
441#446—434no—
442#435—434no—
443#435—434no—
444#435—434no—
445#435—434no—
446#435—434no—
447#435—434no—
448#435—434no—
449#435C2×D4314yes—
450C8×D4—434no—
451C8×D4—434no—
452C8×D4—434no—
453C8×D4C2×D4314yes—
454#433—434no—
455#433—434no—
456#432—434no—
457#432—434no—
458#432—434no—
459#431—434no—
460#424—431no—
461#424—431no—
462#424—431no—
463#424C2×D4311yescharacteristic
464#423—431no—
465#423—431no—
466#408—431no—
467#408—431no—
468#408—431no—
469#408C2×D4311yescharacteristic
470#407—431no—
471#407C2×D4311yescharacteristic
472#405—431no—
473#405—432no—
474#405—431no—
475#405—432no—
476#405—431no—
477#405—432no—
478#405—432no—
479#405C2×D4311yescharacteristic
480C4×M16—431no—
481C4×M16—431no—
482C4×M16—432no—
483C4×M16—432no—
484C2×#97—431no—
485C2×#97—431no—
486C2×#97—431no—
487C2×#97—431no—
488C2×#97—432no—
489C2×#97—432no—
490C2×#97—432no—
491C2×#97—432no—
492C2×#97—432no—
493C2×#97—432no—
494C43#6020711yescharacteristic, complemented, Sylow
495C2×#41—434no—
496C2×#41—431no—
497C2×#41C22×D4311yescharacteristic
498C23×C4—432no—
499C23×C4C22×D4311yescharacteristic
500#131—24no—
501#131—864no—
502#131—864no—
503#131—864no—
504C2×M16—431no—
505C2×M16—431no—
506C2×M16—432no—
507C2×M16—432no—
508C2×M16—432no—
509C2×M16C22×D4311yescharacteristic
510C2×M16C22×D4311yescharacteristic
511C2×M16C22×D4312yes—
512C22×C8—24no—
513C22×C8—431no—
514C22×C8—431no—
515C22×C8—432no—
516C22×C8—432no—
517C22×C8—432no—
518C22×C8—432no—
519C22×C8—432no—
520C22×C8—864no—
521C22×C8C22×D4311yescharacteristic
522C22×C8C22×D4312yes—
523C22×C8C22×D4312yes—
524C22×C8C22×D4312yes—
525C22×C8C22×D4311yescharacteristic
526C4⋊Q8—431no—
527C4⋊Q8—432no—
528#127—431no—
529#126—434no—
530#126—434no—
531#125—434no—
532#125—432no—
533#124—431no—
534#124—431no—
535#124—434no—
536#123—434no—
537#123—432no—
538#123—434no—
539#123C4×D4312yes—
540C22⋊Q8—432no—
541C22⋊Q8—434no—
542C22⋊Q8—434no—
543C22⋊Q8C4×D4312yes—
544#121—434no—
545#121—434no—
546#121—432no—
547#121C4×D4312yes—
548#120—432no—
549#120C4×D4312yes—
550C4×Q8—432no—
551C4×Q8—434no—
552C4×Q8—432no—
553C4×Q8—434no—
554C4×D4—434no—
555C4×D4—434no—
556C4×D4—432no—
557C4×D4—434no—
558C4×D4—434no—
559C4×D4—432no—
560C4×D4—434no—
561C4×D4—434no—
562C4×D4—434no—
563C4×D4C22×D4314yes—
564#117—431no—
565#117—432no—
566#117—434no—
567#117—434no—
568#117—434no—
569#117—432no—
570#117C22×D4311yescharacteristic
571C2×C42—432no—
572C2×C42—432no—
573C2×C42—432no—
574C2×C42—432no—
575C2×C42—431no—
576C2×C42—432no—
577C2×C42—432no—
578C2×C42—431no—
579C2×C42—432no—
580C4⋊C8—434no—
581C4⋊C8—434no—
582C4⋊C8—434no—
583C4⋊C8—434no—
584C4⋊C8—434no—
585C4⋊C8C22×D4314yes—
586C22⋊C8—434no—
587C22⋊C8—434no—
588C22⋊C8—434no—
589C22⋊C8—434no—
590C22⋊C8C22×D4314yes—
591C22⋊C8C22×D4314yes—
592#97—431no—
593#97—431no—
594#97—431no—
595#97—431no—
596#97—432no—
597#97—432no—
598#97—432no—
599#97—432no—
600#97—432no—
601#97—432no—
602#97—432no—
603#97—432no—
604#97—432no—
605#97—432no—
606#97—432no—
607#97C22×D4312yes—
608C4×C8—432no—
609C4×C8—432no—
610C4×C8—432no—
611C4×C8—432no—
612C4×C8—432no—
613C4×C8C22×D4312yes—
614C24C2×C4×D4311yescharacteristic
615#41—22no—
616#41—22no—
617#41—862no—
618#41—862no—
619#41—1728no—
620C2×Q8—431no—
621C2×Q8—434no—
622C2×Q8C2×C4×D4311yescharacteristic
623C2×D4—432no—
624C2×D4—434no—
625C2×D4—434no—
626C2×D4—431no—
627C2×D4C2×C4×D4312yes—
628C2×D4C2×C4×D4311yescharacteristic
629C2×D4C2×C4×D4314yes—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—432no—
633C22×C4—432no—
634C22×C4—432no—
635C22×C4—432no—
636C22×C4—432no—
637C22×C4—432no—
638C22×C4—434no—
639C22×C4—432no—
640C22×C4—434no—
641C22×C4—1724no—
642C22×C4C2×C4×D4312yes—
643C22×C4C2×C4×D4311yescharacteristic
644C22×C4C23×D4312yes—
645C22×C4C23×D4312yes—
646C22×C4C23×D4311yescharacteristic
647M16—22no—
648M16—22no—
649M16—24no—
650M16—864no—
651M16—864no—
652M16—862no—
653M16—862no—
654M16—864no—
655C2×C8—22no—
656C2×C8—24no—
657C2×C8—24no—
658C2×C8—24no—
659C2×C8—434no—
660C2×C8—431no—
661C2×C8—431no—
662C2×C8—432no—
663C2×C8—432no—
664C2×C8—432no—
665C2×C8—864no—
666C2×C8—864no—
667C2×C8—864no—
668C2×C8—864no—
669C2×C8—862no—
670C2×C8—864no—
671C2×C8#1062190014yescomplemented
672C2×C8C23×D4312yes—
673C2×C8C23×D4312yes—
674C2×C8C23×D4312yes—
675C2×C8C23×D4311yescharacteristic
676C2×C8C23×D4311yescharacteristic
677C4⋊C4—434no—
678C4⋊C4—434no—
679C4⋊C4—432no—
680C4⋊C4—434no—
681C4⋊C4—434no—
682C4⋊C4—434no—
683C4⋊C4—434no—
684C4⋊C4—434no—
685C4⋊C4C2×C4×D4314yes—
686C4⋊C4C2×C4×D4312yes—
687C22⋊C4—432no—
688C22⋊C4—434no—
689C22⋊C4—434no—
690C22⋊C4—434no—
691C22⋊C4—434no—
692C22⋊C4—434no—
693C22⋊C4—434no—
694C22⋊C4C2×C4×D4314yes—
695C22⋊C4C2×C4×D4314yes—
696C22⋊C4C2×C4×D4312yes—
697C42—432no—
698C42—432no—
699C42—432no—
700C42—431no—
701C42—432no—
702C42—432no—
703C42—431no—
704C42—434no—
705C42—434no—
706C42—431no—
707C42—432no—
708C42—431no—
709C42—432no—
710C42C23×D4312yes—
711C23—22no—
712C23—24no—
713C23—432no—
714C23C22×C4×D4312yes—
715C23C22×C4×D4311yescharacteristic
716C23C22×C4×D4312yes—
717Q8—22no—
718Q8—862no—
719Q8—1724no—
720D4—24no—
721D4—28no—
722D4—22no—
723D4—864no—
724D4—868no—
725D4—862no—
726D4—1724no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—432no—
734C2×C4—432no—
735C2×C4—432no—
736C2×C4—432no—
737C2×C4—434no—
738C2×C4—432no—
739C2×C4—864no—
740C2×C4—864no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—1724no—
744C2×C4—1722no—
745C2×C4—1722no—
746C2×C4—1722no—
747C2×C4—1722no—
748C2×C4—1724no—
749C2×C4C22×C4×D4312yes—
750C2×C4C22×C4×D4312yes—
751C2×C4C22×C4×D4314yes—
752C2×C4C22×C4×D4311yescharacteristic
753C2×C4#41×D4312yes—
754C2×C4C2×#1062190012yes—
755C2×C4C24×D4311yescharacteristic
756C8—22no—
757C8—22no—
758C8—22no—
759C8—432no—
760C8—432no—
761C8—862no—
762C8—862no—
763C8—862no—
764C8C2×#1062190012yes—
765C8C2×#1062190012yes—
766C22—28no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—24no—
771C22—22no—
772C22—864no—
773C22—862no—
774C22C4×#1062190012yes—
775C22#1458366414yes—
776C22C23×C4×D4311yescharacteristic
777C4—24no—
778C4—22no—
779C4—22no—
780C4—862no—
781C4—862no—
782C4—862no—
783C4—862no—
784C4—864no—
785C4—862no—
786C4C4×#1062190012yes—
787C4C2×#41×D4311yescharacteristic
788C4C22×#1062190011yescharacteristic
789C2—22no—
790C2—24no—
791C2—42no—
792C2—1722no—
793C2C2×C4×#1062190011yescharacteristic
794C2C2×#1458366412yes—
subgroupG/H
center, FrattiniC2×C4C24×D43
commutator, socleC22×C43C24×C4
FittingC43×#2929C2
prime radical#19147887C2
cosocleC2×C4×C43C25
hypercenter#2929D43
hypocenterC43#60207
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #2929

Complements

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

NH ≅ G/Ntype
2. #19143605C2semidirect
3. #19143603C2semidirect
4. #19143590C2semidirect
5. #19143583C2semidirect
6. #19143534C2semidirect
7. #19143533C2semidirect
8. #19143311C2semidirect
9. #19143310C2semidirect
10. #19143290C2semidirect
11. #19143289C2semidirect
12. #19143285C2semidirect
13. #19143245C2semidirect
14. #19143242C2semidirect
15. #19143224C2semidirect
16. #19143022C2semidirect
17. #19143021C2semidirect
18. C22×#13063235C2semidirect
19. C43×#2929C2semidirect
38. #14583029C22semidirect
39. #14583028C22semidirect
40. #14583027C22semidirect
41. #14583026C22semidirect
42. #14582973C22semidirect
45. #14582970C22semidirect
46. #14582968C22semidirect
48. #14582967C22semidirect
52. #14582959C22semidirect
53. #14582957C22semidirect
54. #14582955C22semidirect
56. #14582953C22semidirect
68. #14582857C22semidirect
69. #14582856C22semidirect
72. #14582854C22semidirect
73. #14582853C22semidirect
76. M16×Dic43C22semidirect
77. C4×#10621872C22semidirect
86. C2×#13063235C22semidirect
87. #97×D43C22semidirect
256. C2×C8×C43#41semidirect
303. C2×C43⋊C8#41semidirect
404. #2929D43semidirect
494. C43#60207semidirect
671. C2×C8#10621900semidirect

Maximal subgroups

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

subgroupindex
#191478872
#191436052
#191436032
#191435902
#191435832
#191435342
#191435332
#191433112
#191433102
#191432902
#191432892
#191432852
#191432452
#191432422
#191432242
#191430222
#191430212
C22×#130632352
C43×#29292
#6020743