Finite Group Databasebeta

← #25064090

Subgroups — #25064090

Order 11008.

1042 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147887C211yesmaximal, characteristic
2#19143224C211yesmaximal, characteristic, complemented
3C2×#14582766C211yesmaximal, characteristic, complemented
4#19133171C212yesmaximal, complemented
5#19133169C212yesmaximal, complemented
6#19133144C212yesmaximal, complemented
7#19133140C212yesmaximal, complemented
8#19133100C211yesmaximal, characteristic, complemented
9#19133099C211yesmaximal, characteristic, complemented
10#19133097C211yesmaximal, characteristic, complemented
11C43×#1504C211yesmaximal, characteristic, complemented
12#14583452C411yescharacteristic, complemented
13#14583451C411yescharacteristic, complemented
14#14583451C2211yescharacteristic
15#14583445C411yescharacteristic, complemented
16#14583444C411yescharacteristic, complemented
17#14583444C2211yescharacteristic
18#14583435C411yescharacteristic, complemented
19#14583435C2211yescharacteristic
20#14583430C411yescharacteristic, complemented
21#14583430C2211yescharacteristic
22#14583429—21no—
23#14583429—21no—
24#14583426—21no—
25#14583426—21no—
26#14583410C2211yescharacteristic
27#14583405—21no—
28#14583405—21no—
29#41×Dic43C411yescharacteristic, complemented
30#14583367C411yescharacteristic, complemented
31C4×#10621900—21no—
32C4×#10621900—21no—
33C22×C4×Dic43C2211yescharacteristic
34#14582953—21no—
35#14582953C2212yes—
36#14582949—21no—
37#14582949C2212yes—
38#14582922—21no—
39#14582863C2211yescharacteristic
40M16×Dic43—21no—
41#14582766—21no—
42#14582766—21no—
43#14582766C2212yes—
44#14582766C2212yes—
45C2×C43⋊#95—21no—
46C2×C43⋊#95—21no—
47C2×C43⋊#95C2211yescharacteristic
48#14582637C2212yes—
49#14582636C2212yes—
50#14582635C2212yes—
51#14582634C2212yes—
52#14582633C2212yes—
53#14582632C2212yes—
54C43×#525C2211yescharacteristic
55C43×#407C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C43×#328C2212yes—
58C43×#327C2212yes—
59C2×#10621898C2×C411yescharacteristic
60C2×#10621900—21no—
61C2×#10621900—21no—
62C23×Dic43—21no—
63C23×Dic43D411yescharacteristic
64C23×Dic43D411yescharacteristic
65C2×#10621877—21no—
66#13063324C2×C411yescharacteristic, complemented
67#13063324C2×C411yescharacteristic, complemented
68#13063323C2×C411yescharacteristic, complemented
69#13063321C2×C411yescharacteristic, complemented
70#13063320—21no—
71#13063320—21no—
72#13063318—21no—
73#13063318—21no—
74#13063316C2×C411yescharacteristic, complemented
75#13063316C2×C411yescharacteristic, complemented
76#13063315—21no—
77#13063315—21no—
78#13063314C2×C411yescharacteristic, complemented
79#13063312C2×C411yescharacteristic, complemented
80#13063311—21no—
81#13063311—21no—
82#13063309—21no—
83#13063309—21no—
84#13063308—21no—
85#13063306—21no—
86#13063306—21no—
87#13063304C2×C411yescharacteristic
88#13063304C2311yescharacteristic
89#13063302—21no—
90#13063302—21no—
91#13063302—21no—
92#13063302—21no—
93#13063299C2×C411yescharacteristic
94#13063299C2311yescharacteristic
95#13063297—21no—
96#13063297—21no—
97#13063297—21no—
98#13063297—21no—
99#13063294—21no—
100Q8×Dic43C2×C411yescharacteristic, complemented
101Q8×Dic43C2×C411yescharacteristic, complemented
102C4×Dic86—21no—
103C4×Dic86—21no—
104#13063290—21no—
105#13063290—21no—
106#13063290C2×C411yescharacteristic, complemented
107#13063290C2×C411yescharacteristic, complemented
108D4×Dic43—21no—
109D4×Dic43—21no—
110D4×Dic43—21no—
111D4×Dic43—21no—
112D4×Dic43C2×C411yescharacteristic, complemented
113D4×Dic43C2×C411yescharacteristic, complemented
114#13063287C2×C411yescharacteristic, complemented
115#13063287C2×C411yescharacteristic, complemented
116C4×C22⋊D43—21no—
117C4×C22⋊D43—21no—
118C4×C22⋊D43—21no—
119C4×C22⋊D43—21no—
120(C22⋊D43)⋊C4—21no—
121(C22⋊D43)⋊C4—21no—
122(C22⋊D43)⋊C4—21no—
123(C22⋊D43)⋊C4—21no—
124(C22⋊D43)⋊C4—21no—
125(C22⋊D43)⋊C4—21no—
126#13063284—21no—
127#13063284C2×C411yescharacteristic
128#13063283—21no—
129#13063283—21no—
130#13063282—21no—
131#13063281—21no—
132#13063281—21no—
133#13063281—21no—
134#13063281—21no—
135C2×C4×Dic43—21no—
136C2×C4×Dic43C2×C411yescharacteristic
137C2×C4×Dic43C2×C411yescharacteristic
138C2×C4×Dic43C2×C411yescharacteristic
139C2×C4×Dic43C2×C411yescharacteristic
140C2×C4×Dic43D411yescharacteristic
141C2×C4×Dic43D411yescharacteristic
142C2×C4×Dic43D411yescharacteristic
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43D411yescharacteristic
145C2×C4×Dic43D411yescharacteristic
146C2×C4×Dic43C2311yescharacteristic
147C2×C4×Dic43C2311yescharacteristic
148C42×D43—21no—
149Dic43⋊C8—22no—
150Dic43⋊C8—22no—
151C22⋊(C43⋊C8)—21no—
152C22⋊(C43⋊C8)C2312yes—
153#13063235—22no—
154C8×Dic43—22no—
155C43⋊#95—21no—
156C43⋊#95—22no—
157C43⋊#95—22no—
158C43⋊#95—22no—
159C43⋊#95—22no—
160C43⋊#95C2312yes—
161C2×#41×C43C2×C411yescharacteristic
162C23×C4×C43—21no—
163C23×C4×C43C2311yescharacteristic
164C2×M16×C43—21no—
165#123×C43—21no—
166C22⋊Q8×C43C2×C411yescharacteristic
167C22⋊Q8×C43C2311yescharacteristic
168#121×C43C2×C411yescharacteristic
169#121×C43C2311yescharacteristic
170#120×C43—21no—
171C4×D4×C43—21no—
172C4×D4×C43—21no—
173#117×C43C2×C411yescharacteristic
174C22⋊C8×C43—21no—
175C22⋊C8×C43C2312yes—
176#95×C43—21no—
177#95×C43C2312yes—
178C24×C43C2×D411yescharacteristic
179#41×C43—42no—
180C2×Q8×C43C22×C411yescharacteristic
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43C22×C411yescharacteristic
185C22×C4×C43—21no—
186C22×C4×C43—22no—
187C22×C4×C43—42no—
188C22×C4×C43—42no—
189C22×C4×C43—42no—
190C22×C4×C43—42no—
191C22×C4×C43C22×C411yescharacteristic
192C22×C4×C43C22×C411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2411yescharacteristic
197C2×C22⋊D43—21no—
198C2×C22⋊D43—21no—
199C2×C22⋊D43—21no—
200C2×C22⋊D43—21no—
201C2×C22⋊D43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—22no—
205C22×Dic43—41no—
206C22×Dic43—41no—
207C22×Dic43—42no—
208C22×Dic43—42no—
209C22×Dic43—42no—
210C22×Dic43—42no—
211C22×Dic43C22⋊C411yescharacteristic
212C22×Dic43C22⋊C411yescharacteristic
213C22×Dic43C22⋊C411yescharacteristic
214C22×Dic43C22⋊C411yescharacteristic
215C22×Dic43C22⋊C411yescharacteristic
216C22×Dic43C22⋊C411yescharacteristic
217C22×Dic43C22⋊C411yescharacteristic
218C22×Dic43C22⋊C411yescharacteristic
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222C22×Dic43C2×D411yescharacteristic
223#10621900—42no—
224#10621900—42no—
225#10621900—44no—
226#10621898—42no—
227C2×D172C22×C411yescharacteristic
228C2×C4×D43—21no—
229C2×C4×D43—21no—
230C2×C4×D43—21no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86C22×C411yescharacteristic
234M16×C43—42no—
235C2×C8×C43—22no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43C22×C411yescharacteristic
239C4⋊C4×C43C22×C411yescharacteristic
240C22⋊C4×C43—21no—
241C22⋊C4×C43—21no—
242C22⋊C4×C43—21no—
243C22⋊C4×C43—21no—
244C22⋊C4×C43—21no—
245C42×C43—21no—
246C22⋊Dic43—21no—
247C22⋊Dic43—21no—
248C22⋊Dic43—21no—
249C22⋊Dic43—21no—
250C22⋊Dic43—21no—
251C22⋊Dic43—21no—
252C22⋊Dic43—21no—
253(C2×D43)⋊C4—21no—
254(C2×D43)⋊C4—21no—
255(C2×D43)⋊C4—21no—
256(C2×D43)⋊C4—21no—
257(C2×D43)⋊C4—21no—
258(C2×D43)⋊C4—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43C22×C411yescharacteristic
264C4⋊Dic43C22×C411yescharacteristic
265Dic43⋊C4—21no—
266Dic43⋊C4—21no—
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—21no—
272Dic43⋊C4—21no—
273Dic43⋊C4—21no—
274Dic43⋊C4—21no—
275C4×Dic43—21no—
276C4×Dic43—21no—
277C4×Dic43—21no—
278C4×Dic43—21no—
279C4×Dic43—21no—
280C4×Dic43C22⋊C411yescharacteristic
281C4×Dic43C22⋊C411yescharacteristic
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22⋊C411yescharacteristic
284C4×Dic43C22⋊C411yescharacteristic
285C4×Dic43C22⋊C411yescharacteristic
286C4×Dic43C22⋊C411yescharacteristic
287C4×Dic43C22⋊C411yescharacteristic
288C4×Dic43C22×C411yescharacteristic
289C4×Dic43C22×C411yescharacteristic
290C4×Dic43C22×C411yescharacteristic
291C4×Dic43C22×C411yescharacteristic
292C4×Dic43C2×D411yescharacteristic
293C4×Dic43C2×D411yescharacteristic
294C4×Dic43C2×D411yescharacteristic
295C4×Dic43C2×D411yescharacteristic
296#10621877—42no—
297C2×C43⋊C8—22no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—22no—
301C23×C43—22no—
302C23×C43—21no—
303C23×C43C2×C22⋊C411yescharacteristic
304C23×C43C2×C22⋊C411yescharacteristic
305C23×C43C22×D411yescharacteristic
306C22×D43—21no—
307Q8×C43—41no—
308D4×C43—41no—
309D4×C43—41no—
310D4×C43—41no—
311D4×C43—42no—
312D4×C43—42no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—42no—
323C2×C4×C43—42no—
324C2×C4×C43—42no—
325C2×C4×C43—42no—
326C2×C4×C43—84no—
327C2×C4×C43C2×C22⋊C411yescharacteristic
328C2×C4×C43C2×C22⋊C411yescharacteristic
329C2×C4×C43C23×C411yescharacteristic
330C2×C4×C43C22×D411yescharacteristic
331C22⋊D43—42no—
332C22⋊D43—42no—
333C22⋊D43—41no—
334C22⋊D43—41no—
335C22⋊D43—42no—
336C22⋊D43—42no—
337C2×Dic43—21no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—21no—
344C2×Dic43—21no—
345C2×Dic43—21no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—42no—
355C2×Dic43—42no—
356C2×Dic43—42no—
357C2×Dic43—42no—
358C2×Dic43—42no—
359C2×Dic43—84no—
360C2×Dic43C2×C22⋊C411yescharacteristic
361C2×Dic43C2×C22⋊C411yescharacteristic
362C2×Dic43C2×C22⋊C411yescharacteristic
363C2×Dic43C2×C22⋊C411yescharacteristic
364C2×Dic43C2×C22⋊C411yescharacteristic
365C2×Dic43C2×C22⋊C411yescharacteristic
366C2×Dic43C2×C22⋊C411yescharacteristic
367C2×Dic43C2×C22⋊C411yescharacteristic
368D172—41no—
369C4×D43—42no—
370C4×D43—42no—
371C4×D43—42no—
372Dic86—42no—
373Dic86—42no—
374Dic86—41no—
375C8×C43—42no—
376C43⋊C8—42no—
377#17593—431nomaximal, Sylow
378C22×C43—24no—
379C22×C43—24no—
380C22×C43—21no—
381C22×C43—21no—
382C22×C43—21no—
383C22×C43—21no—
384C22×C43—21no—
385C22×C43—21no—
386C22×C43—41no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43#41012yes—
390C22×C43#42112yes—
391C22×C43C22×C22⋊C411yescharacteristic
392C22×C43#57511yescharacteristic
393C22×C43#57511yescharacteristic
394C2×D43—41no—
395C2×D43—41no—
396C2×D43—41no—
397C4×C43—21no—
398C4×C43—21no—
399C4×C43—21no—
400C4×C43—21no—
401C4×C43—41no—
402C4×C43—41no—
403C4×C43—41no—
404C4×C43—82no—
405Dic43—21no—
406Dic43—21no—
407Dic43—21no—
408Dic43—21no—
409Dic43—21no—
410Dic43—21no—
411Dic43—21no—
412Dic43—21no—
413Dic43—41no—
414Dic43—41no—
415Dic43—41no—
416Dic43—82no—
417#3444—431no—
418#2920—431no—
419C2×#383—431no—
420#1521—432no—
421#1521—432no—
422#1515—432no—
423#1514—432no—
424#1504—431no—
425#1504—431no—
426#1504—431no—
427#1504D4311yescharacteristic, complemented
428C2×C43—21no—
429C2×C43—21no—
430C2×C43—22no—
431C2×C43—22no—
432C2×C43—81no—
433C2×C43C2×#41011yescharacteristic
434C2×C43#289611yescharacteristic
435C2×C43C2×#42111yescharacteristic
436D43—81no—
437#533—431no—
438#533—431no—
439#533—431no—
440#532—431no—
441#532—431no—
442#532—431no—
443#529—431no—
444#529—431no—
445#529—431no—
446#529—431no—
447#529—861no—
448#529—861no—
449#529—861no—
450#529—861no—
451#525—431no—
452#525—861no—
453#525—861no—
454#525C2×D4311yescharacteristic
455C4×#41—431no—
456C4×#41—431no—
457C4×#41—861no—
458C4×#41—861no—
459C22×C42—431no—
460#432—432no—
461#432—861no—
462#431—432no—
463#431—861no—
464#423—861no—
465#407—431no—
466#407C2×D4311yescharacteristic
467C4×M16—861no—
468#383—432no—
469#383—432no—
470#383—861no—
471#383—861no—
472C2×#95—431no—
473C2×#95—861no—
474C2×#95—861no—
475C2×#95C2×D4311yescharacteristic
476#328—432no—
477#328—432no—
478#328—432no—
479#328C2×D4312yes—
480#327—432no—
481#327—432no—
482#327—432no—
483#327C2×D4312yes—
484C43#1759311yescharacteristic, complemented, Sylow
485C2×#41—431no—
486C2×#41—861no—
487C2×#41—861no—
488C2×#41C4×D4311yescharacteristic
489C23×C4—21no—
490C23×C4—431no—
491C23×C4—431no—
492C23×C4—861no—
493C23×C4C22×D4311yescharacteristic
494C2×M16—21no—
495C2×M16—861no—
496C4⋊Q8—431no—
497C4⋊Q8—431no—
498C4⋊Q8—431no—
499#127—431no—
500#126—861no—
501#126—861no—
502#126—861no—
503#126—861no—
504#125—431no—
505#125—431no—
506#125—861no—
507#125—861no—
508#124—431no—
509#124—431no—
510#124—861no—
511#124—861no—
512#123—21no—
513#123—861no—
514#123—861no—
515#123—861no—
516#123—861no—
517#123—861no—
518C22⋊Q8—431no—
519C22⋊Q8—431no—
520C22⋊Q8—861no—
521C22⋊Q8—861no—
522C22⋊Q8—861no—
523C22⋊Q8—861no—
524C22⋊Q8C4×D4311yescharacteristic
525C22⋊Q8C22×D4311yescharacteristic
526#121—431no—
527#121—431no—
528#121—861no—
529#121—861no—
530#121—861no—
531#121—861no—
532#121C4×D4311yescharacteristic
533#121C22×D4311yescharacteristic
534#120—21no—
535#120—861no—
536C4×Q8—431no—
537C4×Q8—431no—
538C4×Q8—431no—
539C4×Q8—431no—
540C4×Q8—861no—
541C4×Q8—861no—
542C4×Q8—861no—
543C4×Q8—861no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—431no—
547C4×D4—431no—
548C4×D4—431no—
549C4×D4—431no—
550C4×D4—861no—
551C4×D4—861no—
552C4×D4—861no—
553C4×D4—861no—
554C4×D4—861no—
555C4×D4—861no—
556C4×D4—861no—
557C4×D4—861no—
558C4×D4—861no—
559C4×D4—861no—
560C4×D4—861no—
561C4×D4—861no—
562C4×D4—861no—
563C4×D4—861no—
564#117—431no—
565#117—861no—
566#117—861no—
567#117—861no—
568#117—861no—
569#117—861no—
570#117—861no—
571#117—861no—
572#117—861no—
573#117C4×D4311yescharacteristic
574C2×C42—431no—
575C2×C42—431no—
576C2×C42—431no—
577C2×C42—431no—
578C2×C42—431no—
579C2×C42—431no—
580C2×C42—431no—
581C2×C42—431no—
582C2×C42—431no—
583C2×C42—431no—
584C2×C42—431no—
585C2×C42—431no—
586C2×C42—861no—
587C2×C42—861no—
588C4⋊C8—862no—
589C4⋊C8—862no—
590C22⋊C8—21no—
591C22⋊C8—432no—
592C22⋊C8—861no—
593C22⋊C8C22×D4312yes—
594#97—862no—
595C4×C8—862no—
596#95—21no—
597#95—432no—
598#95—862no—
599#95—862no—
600#95—862no—
601#95—862no—
602#95—861no—
603#95C22×D4312yes—
604C24D4×D4311yescharacteristic
605#41—42no—
606#41—1722no—
607#41—1724no—
608#41—1722no—
609#41—1722no—
610C2×Q8—431no—
611C2×Q8—861no—
612C2×Q8—861no—
613C2×Q8C2×C4×D4311yescharacteristic
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—431no—
618C2×D4—861no—
619C2×D4—861no—
620C2×D4—861no—
621C2×D4—861no—
622C2×D4—861no—
623C2×D4C2×C4×D4311yescharacteristic
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—431no—
631C22×C4—431no—
632C22×C4—431no—
633C22×C4—431no—
634C22×C4—431no—
635C22×C4—431no—
636C22×C4—431no—
637C22×C4—431no—
638C22×C4—431no—
639C22×C4—431no—
640C22×C4—431no—
641C22×C4—431no—
642C22×C4—861no—
643C22×C4—861no—
644C22×C4—861no—
645C22×C4—861no—
646C22×C4—861no—
647C22×C4—862no—
648C22×C4—1722no—
649C22×C4—1721no—
650C22×C4—1721no—
651C22×C4—1722no—
652C22×C4—1722no—
653C22×C4—1722no—
654C22×C4C2×C4×D4311yescharacteristic
655C22×C4C2×C4×D4311yescharacteristic
656C22×C4D4×D4311yescharacteristic
657C22×C4D4×D4311yescharacteristic
658C22×C4D4×D4311yescharacteristic
659C22×C4C23×D4311yescharacteristic
660M16—42no—
661M16—1722no—
662C2×C8—22no—
663C2×C8—862no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—431no—
667C4⋊C4—431no—
668C4⋊C4—861no—
669C4⋊C4—861no—
670C4⋊C4—861no—
671C4⋊C4—861no—
672C4⋊C4—861no—
673C4⋊C4—861no—
674C4⋊C4—861no—
675C4⋊C4—861no—
676C4⋊C4—861no—
677C4⋊C4—861no—
678C4⋊C4—861no—
679C4⋊C4—861no—
680C4⋊C4—861no—
681C4⋊C4—861no—
682C4⋊C4C2×C4×D4311yescharacteristic
683C4⋊C4C2×C4×D4311yescharacteristic
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—861no—
690C22⋊C4—861no—
691C22⋊C4—861no—
692C22⋊C4—861no—
693C22⋊C4—861no—
694C22⋊C4—861no—
695C22⋊C4—861no—
696C22⋊C4—861no—
697C22⋊C4—861no—
698C22⋊C4—861no—
699C22⋊C4—861no—
700C22⋊C4—861no—
701C22⋊C4—861no—
702C42—21no—
703C42—431no—
704C42—431no—
705C42—431no—
706C42—431no—
707C42—431no—
708C42—431no—
709C42—431no—
710C42—431no—
711C42—431no—
712C42—431no—
713C42—431no—
714C42—431no—
715C42—431no—
716C42—431no—
717C42—431no—
718C42—431no—
719C42—861no—
720C42—861no—
721C42—861no—
722C42—861no—
723C42—861no—
724C23—22no—
725C23—22no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—861no—
730C23C22⋊C4×D4311yescharacteristic
731C23C22⋊C4×D4311yescharacteristic
732C23C2×D4×D4311yescharacteristic
733Q8—41no—
734Q8—1721no—
735Q8—1722no—
736Q8—1722no—
737D4—41no—
738D4—42no—
739D4—42no—
740D4—41no—
741D4—41no—
742D4—1721no—
743D4—1722no—
744D4—1722no—
745D4—1722no—
746D4—1722no—
747D4—1721no—
748D4—1721no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—84no—
763C2×C4—431no—
764C2×C4—431no—
765C2×C4—431no—
766C2×C4—431no—
767C2×C4—431no—
768C2×C4—431no—
769C2×C4—431no—
770C2×C4—431no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—861no—
774C2×C4—861no—
775C2×C4—861no—
776C2×C4—861no—
777C2×C4—861no—
778C2×C4—861no—
779C2×C4—861no—
780C2×C4—3444no—
781C2×C4—1722no—
782C2×C4—1722no—
783C2×C4—1722no—
784C2×C4—1721no—
785C2×C4—1721no—
786C2×C4—1721no—
787C2×C4—1721no—
788C2×C4—1721no—
789C2×C4—1721no—
790C2×C4—1721no—
791C2×C4—1721no—
792C2×C4—1722no—
793C2×C4—1722no—
794C2×C4—1722no—
795C2×C4—1722no—
796C2×C4—1722no—
797C2×C4C22⋊C4×D4311yescharacteristic
798C2×C4C22⋊C4×D4311yescharacteristic
799C2×C4C22×C4×D4311yescharacteristic
800C2×C4C2×D4×D4311yescharacteristic
801C8—42no—
802C8—1722no—
803C22—24no—
804C22—24no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—1721no—
815C22—1721no—
816C22—1721no—
817C22#1458287112yes—
818C22#1458291412yes—
819C22C2×C22⋊C4×D4311yescharacteristic
820C22#1458369511yescharacteristic
821C22#1458369811yescharacteristic
822C4—21no—
823C4—21no—
824C4—21no—
825C4—21no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—82no—
830C4—861no—
831C4—861no—
832C4—861no—
833C4—861no—
834C4—861no—
835C4—861no—
836C4—861no—
837C4—861no—
838C4—3442no—
839C4—1721no—
840C4—1721no—
841C4—1721no—
842C2—21no—
843C2—21no—
844C2—22no—
845C2—22no—
846C2—81no—
847C2—3441no—
848C2C2×#1458287111yescharacteristic
849C2#1914311111yescharacteristic
850C2C2×#1458291411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1504C2
socleC22×C43C22×C22⋊C4
prime radical#19147887C2
cosocleC22×C4×C43C24
hypercenter#1504D43
hypocenterC43#17593
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1504

Complements

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

NH ≅ G/Ntype
2. #19143224C2semidirect
3. C2×#14582766C2semidirect
4. #19133171C2semidirect
5. #19133169C2semidirect
6. #19133144C2semidirect
7. #19133140C2semidirect
8. #19133100C2semidirect
9. #19133099C2semidirect
10. #19133097C2semidirect
11. C43×#1504C2semidirect
12. #14583452C4semidirect
13. #14583451C4semidirect
15. #14583445C4semidirect
16. #14583444C4semidirect
18. #14583435C4semidirect
20. #14583430C4semidirect
29. #41×Dic43C4semidirect
30. #14583367C4semidirect
66. #13063324C2×C4semidirect
67. #13063324C2×C4semidirect
68. #13063323C2×C4semidirect
69. #13063321C2×C4semidirect
74. #13063316C2×C4semidirect
75. #13063316C2×C4semidirect
78. #13063314C2×C4semidirect
79. #13063312C2×C4semidirect
100. Q8×Dic43C2×C4semidirect
101. Q8×Dic43C2×C4semidirect
106. #13063290C2×C4semidirect
107. #13063290C2×C4semidirect
112. D4×Dic43C2×C4semidirect
113. D4×Dic43C2×C4semidirect
114. #13063287C2×C4semidirect
115. #13063287C2×C4semidirect
427. #1504D43semidirect
484. C43#17593semidirect

Maximal subgroups

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

subgroupindex
#191478872
#191432242
C2×#145827662
#191331712
#191331692
#191331442
#191331402
#191331002
#191330992
#191330972
C43×#15042
#1759343