Finite Group Databasebeta

← #25064096

Subgroups — #25064096

Order 11008.

1014 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147887C211yesmaximal, characteristic
2#19143224C211yesmaximal, characteristic, complemented
3#19136990C211yesmaximal, characteristic, complemented
4#19133171C212yesmaximal, complemented
5#19133169C212yesmaximal, complemented
6#19133139C211yesmaximal, characteristic, complemented
7#19133138C211yesmaximal, characteristic, complemented
8#19133136C211yesmaximal, characteristic, complemented
9#19133105C212yesmaximal, complemented
10#19133101C212yesmaximal, complemented
11C43×#1513C211yesmaximal, 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#14582766C2212yes—
42#14582764—21no—
43#14582760—21no—
44#14582759C2211yescharacteristic
45C4⋊C4×Dic43—21no—
46C22⋊C4×Dic43—21no—
47#14582744C2212yes—
48#14582637C2212yes—
49#14582636C2212yes—
50#14582635C2212yes—
51#14582634C2212yes—
52#14582633C2212yes—
53#14582632C2212yes—
54C43×#525C2211yescharacteristic
55C43×#407C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C43×#328C2212yes—
58C43×#327C2212yes—
59C2×#10621898C2×C411yescharacteristic
60C2×#10621900—21no—
61C2×#10621900—21no—
62C23×Dic43D411yescharacteristic
63C23×Dic43D411yescharacteristic
64C2×#10621877—21no—
65#13063324C2×C411yescharacteristic
66#13063324C2×C411yescharacteristic
67#13063323C2×C411yescharacteristic
68#13063321C2×C411yescharacteristic
69#13063320—21no—
70#13063320—21no—
71#13063318—21no—
72#13063318—21no—
73#13063316C2×C411yescharacteristic
74#13063316C2×C411yescharacteristic
75#13063315—21no—
76#13063315—21no—
77#13063314C2×C411yescharacteristic
78#13063312C2×C411yescharacteristic
79#13063311—21no—
80#13063311—21no—
81#13063309—21no—
82#13063309—21no—
83#13063308—21no—
84#13063306—21no—
85#13063306—21no—
86#13063304C2×C411yescharacteristic
87#13063304C2311yescharacteristic
88#13063302—21no—
89#13063302—21no—
90#13063302—21no—
91#13063302—21no—
92#13063299C2×C411yescharacteristic
93#13063299C2311yescharacteristic
94#13063297—21no—
95#13063297—21no—
96#13063297—21no—
97#13063297—21no—
98#13063294—21no—
99Q8×Dic43C2×C411yescharacteristic
100Q8×Dic43C2×C411yescharacteristic
101C4×Dic86—21no—
102C4×Dic86—21no—
103#13063290—21no—
104#13063290—21no—
105#13063290C2×C411yescharacteristic
106#13063290C2×C411yescharacteristic
107D4×Dic43—21no—
108D4×Dic43—21no—
109D4×Dic43—21no—
110D4×Dic43—21no—
111D4×Dic43C2×C411yescharacteristic
112D4×Dic43C2×C411yescharacteristic
113#13063287C2×C411yescharacteristic
114#13063287C2×C411yescharacteristic
115C4×C22⋊D43—21no—
116C4×C22⋊D43—21no—
117C4×C22⋊D43—21no—
118C4×C22⋊D43—21no—
119(C22⋊D43)⋊C4—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#13063284—21no—
126#13063284C2×C411yescharacteristic
127#13063283—21no—
128#13063283—21no—
129#13063282—21no—
130#13063281—21no—
131#13063281—21no—
132#13063281—21no—
133#13063281—21no—
134C2×C4⋊Dic43—21no—
135C2×C22⋊Dic43—21no—
136C2×C4×Dic43—21no—
137C2×C4×Dic43—22no—
138C2×C4×Dic43C2×C411yescharacteristic
139C2×C4×Dic43C2×C411yescharacteristic
140C2×C4×Dic43C2×C411yescharacteristic
141C2×C4×Dic43C2×C411yescharacteristic
142C2×C4×Dic43D411yescharacteristic
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43D411yescharacteristic
145C2×C4×Dic43D411yescharacteristic
146C2×C4×Dic43D411yescharacteristic
147C2×C4×Dic43D411yescharacteristic
148C2×C4×Dic43C2311yescharacteristic
149C2×C4×Dic43C2311yescharacteristic
150C42×D43—21no—
151Dic43⋊C8—22no—
152Dic43⋊C8—22no—
153C22⋊(C43⋊C8)—21no—
154C22⋊(C43⋊C8)C2312yes—
155#13063235—22no—
156C8×Dic43—22no—
157C43⋊#95—22no—
158C43⋊#95—22no—
159C43⋊#95—22no—
160C43⋊#95C2312yes—
161C2×#41×C43C2×C411yescharacteristic
162C23×C4×C43C2311yescharacteristic
163C2×M16×C43—21no—
164#123×C43—21no—
165C22⋊Q8×C43C2×C411yescharacteristic
166C22⋊Q8×C43C2311yescharacteristic
167#121×C43C2×C411yescharacteristic
168#121×C43C2311yescharacteristic
169#120×C43—21no—
170C4×D4×C43—21no—
171C4×D4×C43—21no—
172#117×C43C2×C411yescharacteristic
173C2×C4⋊C4×C43—21no—
174C2×C22⋊C4×C43—21no—
175C22⋊C8×C43—21no—
176C22⋊C8×C43C2312yes—
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×C43C22×C411yescharacteristic
189C22×C4×C43C22×C411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2411yescharacteristic
194C2×C22⋊D43—21no—
195C2×C22⋊D43—21no—
196C2×C22⋊D43—21no—
197C2×C22⋊D43—21no—
198C2×C22⋊D43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—22no—
202C22×Dic43—41no—
203C22×Dic43—41no—
204C22×Dic43—42no—
205C22×Dic43C22⋊C411yescharacteristic
206C22×Dic43C22⋊C411yescharacteristic
207C22×Dic43C22⋊C411yescharacteristic
208C22×Dic43C22⋊C411yescharacteristic
209C22×Dic43C22⋊C411yescharacteristic
210C22×Dic43C22⋊C411yescharacteristic
211C22×Dic43C22⋊C411yescharacteristic
212C22×Dic43C22⋊C411yescharacteristic
213C22×Dic43C2×D411yescharacteristic
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217#10621900—42no—
218#10621900—42no—
219#10621900—44no—
220#10621898—42no—
221C2×D172C22×C411yescharacteristic
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×Dic86—21no—
226C2×Dic86—21no—
227C2×Dic86C22×C411yescharacteristic
228M16×C43—42no—
229C2×C8×C43—22no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—42no—
233C4⋊C4×C43C22×C411yescharacteristic
234C4⋊C4×C43C22×C411yescharacteristic
235C22⋊C4×C43—21no—
236C22⋊C4×C43—21no—
237C22⋊C4×C43—21no—
238C22⋊C4×C43—21no—
239C22⋊C4×C43—21no—
240C22⋊C4×C43—42no—
241C42×C43—21no—
242C22⋊Dic43—21no—
243C22⋊Dic43—21no—
244C22⋊Dic43—21no—
245C22⋊Dic43—21no—
246C22⋊Dic43—21no—
247C22⋊Dic43—21no—
248C22⋊Dic43—21no—
249C22⋊Dic43—42no—
250(C2×D43)⋊C4—21no—
251(C2×D43)⋊C4—21no—
252(C2×D43)⋊C4—21no—
253(C2×D43)⋊C4—21no—
254(C2×D43)⋊C4—21no—
255(C2×D43)⋊C4—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—42no—
261C4⋊Dic43C22×C411yescharacteristic
262C4⋊Dic43C22×C411yescharacteristic
263Dic43⋊C4—21no—
264Dic43⋊C4—21no—
265Dic43⋊C4—21no—
266Dic43⋊C4—21no—
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—21no—
272Dic43⋊C4—21no—
273C4×Dic43—21no—
274C4×Dic43—21no—
275C4×Dic43—21no—
276C4×Dic43—21no—
277C4×Dic43—21no—
278C4×Dic43—44no—
279C4×Dic43C22⋊C411yescharacteristic
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×Dic43C2×D411yescharacteristic
292C4×Dic43C2×D411yescharacteristic
293C4×Dic43C2×D411yescharacteristic
294C4×Dic43C2×D411yescharacteristic
295#10621877—42no—
296C2×C43⋊C8—22no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43C2×C22⋊C411yescharacteristic
303C23×C43C2×C22⋊C411yescharacteristic
304C23×C43C22×D411yescharacteristic
305C22×D43—21no—
306Q8×C43—41no—
307D4×C43—41no—
308D4×C43—42no—
309D4×C43—42no—
310D4×C43—41no—
311D4×C43—41no—
312C2×C4×C43—22no—
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—42no—
322C2×C4×C43—42no—
323C2×C4×C43—42no—
324C2×C4×C43—42no—
325C2×C4×C43C2×C22⋊C411yescharacteristic
326C2×C4×C43C2×C22⋊C411yescharacteristic
327C2×C4×C43C23×C411yescharacteristic
328C2×C4×C43C22×D411yescharacteristic
329C22⋊D43—42no—
330C22⋊D43—42no—
331C22⋊D43—42no—
332C22⋊D43—41no—
333C22⋊D43—41no—
334C22⋊D43—42no—
335C2×Dic43—21no—
336C2×Dic43—21no—
337C2×Dic43—21no—
338C2×Dic43—21no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—21no—
343C2×Dic43—21no—
344C2×Dic43—21no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—42no—
353C2×Dic43—42no—
354C2×Dic43—42no—
355C2×Dic43—42no—
356C2×Dic43—42no—
357C2×Dic43C2×C22⋊C411yescharacteristic
358C2×Dic43C2×C22⋊C411yescharacteristic
359C2×Dic43C2×C22⋊C411yescharacteristic
360C2×Dic43C2×C22⋊C411yescharacteristic
361C2×Dic43C2×C22⋊C411yescharacteristic
362C2×Dic43C2×C22⋊C411yescharacteristic
363C2×Dic43C2×C22⋊C411yescharacteristic
364C2×Dic43C2×C22⋊C411yescharacteristic
365D172—41no—
366C4×D43—42no—
367C4×D43—42no—
368C4×D43—42no—
369Dic86—42no—
370Dic86—42no—
371Dic86—41no—
372C8×C43—42no—
373C43⋊C8—42no—
374#17594—431nomaximal, Sylow
375C22×C43—21no—
376C22×C43—21no—
377C22×C43—21no—
378C22×C43—21no—
379C22×C43—21no—
380C22×C43—21no—
381C22×C43—21no—
382C22×C43—21no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—41no—
388C22×C43C22×C22⋊C411yescharacteristic
389C22×C43#57511yescharacteristic
390C22×C43#57511yescharacteristic
391C2×D43—41no—
392C2×D43—41no—
393C2×D43—41no—
394C4×C43—21no—
395C4×C43—21no—
396C4×C43—21no—
397C4×C43—41no—
398C4×C43—41no—
399C4×C43—41no—
400C4×C43—82no—
401C4×C43#41012yes—
402Dic43—21no—
403Dic43—21no—
404Dic43—21no—
405Dic43—21no—
406Dic43—21no—
407Dic43—21no—
408Dic43—21no—
409Dic43—41no—
410Dic43—41no—
411Dic43—41no—
412Dic43—82no—
413Dic43#42112yes—
414#3444—431no—
415#2920—431no—
416#2283—431no—
417#1521—432no—
418#1521—432no—
419#1513—431no—
420#1513—431no—
421#1513—431no—
422#1513D4311yescharacteristic, complemented
423#1506—432no—
424#1505—432no—
425C2×C43—21no—
426C2×C43—21no—
427C2×C43—41no—
428C2×C43—41no—
429C2×C43—81no—
430C2×C43C2×#41011yescharacteristic
431C2×C43#289611yescharacteristic
432C2×C43C2×#42111yescharacteristic
433D43—81no—
434#533—431no—
435#533—431no—
436#533—431no—
437#532—431no—
438#532—431no—
439#532—431no—
440#529—431no—
441#529—431no—
442#529—431no—
443#529—431no—
444#529—861no—
445#529—861no—
446#529—861no—
447#529—861no—
448#525—431no—
449#525—861no—
450#525—861no—
451#525C2×D4311yescharacteristic
452C4×#41—431no—
453C4×#41—431no—
454C4×#41—861no—
455C4×#41—861no—
456C22×C42—431no—
457#432—432no—
458#432—861no—
459#431—432no—
460#431—861no—
461#423—861no—
462#407—431no—
463#407C2×D4311yescharacteristic
464C4×M16—861no—
465#383—432no—
466#382—861no—
467#381—861no—
468#380—431no—
469#380C2×D4311yescharacteristic
470C4×C4⋊C4—861no—
471C4×C22⋊C4—861no—
472#376—432no—
473#328—432no—
474#328—432no—
475#328—432no—
476#328C2×D4312yes—
477#327—432no—
478#327—432no—
479#327—432no—
480#327C2×D4312yes—
481C43#1759411yescharacteristic, complemented, Sylow
482C2×#41—431no—
483C2×#41—861no—
484C2×#41—861no—
485C2×#41C4×D4311yescharacteristic
486C23×C4—431no—
487C23×C4—431no—
488C23×C4C22×D4311yescharacteristic
489C2×M16—21no—
490C2×M16—861no—
491C4⋊Q8—431no—
492C4⋊Q8—431no—
493C4⋊Q8—431no—
494#127—431no—
495#126—861no—
496#126—861no—
497#126—861no—
498#126—861no—
499#125—431no—
500#125—431no—
501#125—861no—
502#125—861no—
503#124—431no—
504#124—431no—
505#124—861no—
506#124—861no—
507#123—21no—
508#123—861no—
509#123—861no—
510#123—861no—
511#123—861no—
512#123—861no—
513C22⋊Q8—431no—
514C22⋊Q8—431no—
515C22⋊Q8—861no—
516C22⋊Q8—861no—
517C22⋊Q8—861no—
518C22⋊Q8—861no—
519C22⋊Q8C4×D4311yescharacteristic
520C22⋊Q8C22×D4311yescharacteristic
521#121—431no—
522#121—431no—
523#121—861no—
524#121—861no—
525#121—861no—
526#121—861no—
527#121C4×D4311yescharacteristic
528#121C22×D4311yescharacteristic
529#120—21no—
530#120—861no—
531C4×Q8—431no—
532C4×Q8—431no—
533C4×Q8—431no—
534C4×Q8—431no—
535C4×Q8—861no—
536C4×Q8—861no—
537C4×Q8—861no—
538C4×Q8—861no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—431no—
542C4×D4—431no—
543C4×D4—431no—
544C4×D4—431no—
545C4×D4—861no—
546C4×D4—861no—
547C4×D4—861no—
548C4×D4—861no—
549C4×D4—861no—
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—
559#117—431no—
560#117—861no—
561#117—861no—
562#117—861no—
563#117—861no—
564#117—861no—
565#117—861no—
566#117—861no—
567#117—861no—
568#117C4×D4311yescharacteristic
569C2×C4⋊C4—21no—
570C2×C4⋊C4—861no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—861no—
573C2×C42—431no—
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—861no—
586C2×C42—861no—
587C2×C42—862no—
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—432no—
597#95—862no—
598#95—862no—
599#95—862no—
600#95C22×D4312yes—
601C24D4×D4311yescharacteristic
602#41—42no—
603#41—1722no—
604#41—1724no—
605#41—1722no—
606#41—1722no—
607C2×Q8—431no—
608C2×Q8—861no—
609C2×Q8—861no—
610C2×Q8C2×C4×D4311yescharacteristic
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—431no—
615C2×D4—861no—
616C2×D4—861no—
617C2×D4—861no—
618C2×D4—861no—
619C2×D4—861no—
620C2×D4C2×C4×D4311yescharacteristic
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—42no—
624C22×C4—431no—
625C22×C4—431no—
626C22×C4—431no—
627C22×C4—431no—
628C22×C4—431no—
629C22×C4—431no—
630C22×C4—431no—
631C22×C4—431no—
632C22×C4—431no—
633C22×C4—431no—
634C22×C4—431no—
635C22×C4—431no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—861no—
639C22×C4—861no—
640C22×C4—861no—
641C22×C4—862no—
642C22×C4—1722no—
643C22×C4—1721no—
644C22×C4—1721no—
645C22×C4C2×C4×D4311yescharacteristic
646C22×C4C2×C4×D4311yescharacteristic
647C22×C4D4×D4311yescharacteristic
648C22×C4D4×D4311yescharacteristic
649C22×C4D4×D4311yescharacteristic
650C22×C4C23×D4311yescharacteristic
651M16—42no—
652M16—1722no—
653C2×C8—22no—
654C2×C8—862no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—42no—
658C4⋊C4—431no—
659C4⋊C4—431no—
660C4⋊C4—861no—
661C4⋊C4—861no—
662C4⋊C4—861no—
663C4⋊C4—861no—
664C4⋊C4—861no—
665C4⋊C4—861no—
666C4⋊C4—861no—
667C4⋊C4—861no—
668C4⋊C4—861no—
669C4⋊C4—861no—
670C4⋊C4—861no—
671C4⋊C4—861no—
672C4⋊C4—861no—
673C4⋊C4—861no—
674C4⋊C4—1722no—
675C4⋊C4C2×C4×D4311yescharacteristic
676C4⋊C4C2×C4×D4311yescharacteristic
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—42no—
683C22⋊C4—861no—
684C22⋊C4—861no—
685C22⋊C4—861no—
686C22⋊C4—861no—
687C22⋊C4—861no—
688C22⋊C4—861no—
689C22⋊C4—861no—
690C22⋊C4—861no—
691C22⋊C4—861no—
692C22⋊C4—861no—
693C22⋊C4—861no—
694C22⋊C4—861no—
695C22⋊C4—861no—
696C22⋊C4—1722no—
697C42—21no—
698C42—431no—
699C42—431no—
700C42—431no—
701C42—431no—
702C42—431no—
703C42—431no—
704C42—431no—
705C42—431no—
706C42—431no—
707C42—431no—
708C42—431no—
709C42—431no—
710C42—431no—
711C42—431no—
712C42—431no—
713C42—431no—
714C42—861no—
715C42—861no—
716C42—861no—
717C42—861no—
718C42—861no—
719C42—1724no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—41no—
724C23—41no—
725C23—861no—
726C23C22⋊C4×D4311yescharacteristic
727C23C22⋊C4×D4311yescharacteristic
728C23C2×D4×D4311yescharacteristic
729Q8—41no—
730Q8—1721no—
731Q8—1722no—
732Q8—1722no—
733D4—41no—
734D4—42no—
735D4—42no—
736D4—41no—
737D4—41no—
738D4—1721no—
739D4—1722no—
740D4—1722no—
741D4—1722no—
742D4—1722no—
743D4—1721no—
744D4—1721no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—431no—
759C2×C4—431no—
760C2×C4—431no—
761C2×C4—431no—
762C2×C4—431no—
763C2×C4—431no—
764C2×C4—431no—
765C2×C4—431no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—861no—
770C2×C4—861no—
771C2×C4—861no—
772C2×C4—861no—
773C2×C4—861no—
774C2×C4—861no—
775C2×C4—861no—
776C2×C4—1722no—
777C2×C4—1722no—
778C2×C4—1721no—
779C2×C4—1721no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4—1722no—
786C2×C4—1722no—
787C2×C4—1722no—
788C2×C4—1722no—
789C2×C4—1722no—
790C2×C4—1722no—
791C2×C4C22⋊C4×D4311yescharacteristic
792C2×C4C22⋊C4×D4311yescharacteristic
793C2×C4C22×C4×D4311yescharacteristic
794C2×C4C2×D4×D4311yescharacteristic
795C8—42no—
796C8—1722no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—42no—
806C22—42no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—1721no—
811C22—1721no—
812C22—1721no—
813C22C2×C22⋊C4×D4311yescharacteristic
814C22#1458369511yescharacteristic
815C22#1458369811yescharacteristic
816C4—21no—
817C4—21no—
818C4—21no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—82no—
823C4—432no—
824C4—861no—
825C4—861no—
826C4—861no—
827C4—861no—
828C4—861no—
829C4—861no—
830C4—861no—
831C4—3442no—
832C4—1721no—
833C4—1721no—
834C4—1721no—
835C4#1458287112yes—
836C2—21no—
837C2—21no—
838C2—41no—
839C2—41no—
840C2—81no—
841C2—3441no—
842C2C2×#1458287111yescharacteristic
843C2#1914311111yescharacteristic
844C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1513C2
socleC22×C43C22×C22⋊C4
prime radical#19147887C2
cosocleC22×C4×C43C24
hypercenter#1513D43
hypocenterC43#17594
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1513

Complements

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

NH ≅ G/Ntype
2. #19143224C2semidirect
3. #19136990C2semidirect
4. #19133171C2semidirect
5. #19133169C2semidirect
6. #19133139C2semidirect
7. #19133138C2semidirect
8. #19133136C2semidirect
9. #19133105C2semidirect
10. #19133101C2semidirect
11. C43×#1513C2semidirect
12. #14583452C4semidirect
13. #14583451C4semidirect
15. #14583445C4semidirect
16. #14583444C4semidirect
18. #14583435C4semidirect
20. #14583430C4semidirect
29. #41×Dic43C4semidirect
30. #14583367C4semidirect
422. #1513D43semidirect
481. C43#17594semidirect

Maximal subgroups

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

subgroupindex
#191478872
#191432242
#191369902
#191331712
#191331692
#191331392
#191331382
#191331362
#191331052
#191331012
C43×#15132
#1759443