Finite Group Databasebeta

← #25112091

Subgroups — #25112091

Order 11008.

1478 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583552C211yesmaximal, characteristic
2C2×#14582972C211yesmaximal, characteristic, complemented
3C2×#14582899C211yesmaximal, characteristic, complemented
4C2×#14582894C211yesmaximal, characteristic, complemented
5#19137521C211yesmaximal, characteristic, complemented
6#19135519C211yesmaximal, characteristic, complemented
7#19135025C211yesmaximal, characteristic, complemented
8#19135015C211yesmaximal, characteristic, complemented
9#19134904C211yesmaximal, characteristic, complemented
10#19134899C211yesmaximal, characteristic, complemented
11#19134602C211yesmaximal, characteristic, complemented
12#19134534C211yesmaximal, characteristic, complemented
13#19134534C211yesmaximal, characteristic, complemented
14#19134421C211yesmaximal, characteristic, complemented
15C43×#1960C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×#10621902C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#14583552—24no—
21#14583552C418yescomplemented
22C2×#13063310—21no—
23C2×#13063310—21no—
24C2×#13063301C2211yescharacteristic
25C2×#13063301C2211yescharacteristic
26C2×#13063300—21no—
27C2×C4×D172C2211yescharacteristic
28C2×C4×D172C2211yescharacteristic
29C2×#13063283C2211yescharacteristic
30C2×C4⋊C4×D43—21no—
31C2×C4⋊C4×D43C2211yescharacteristic
32#14582972—24no—
33C2×C4⋊(C43⋊C8)C2211yescharacteristic
34#14582899—24no—
35#14582894—24no—
36C2×#13063249C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063247C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46#14582788—21no—
47#14582782—21no—
48#14582777—21no—
49#14582756C2211yescharacteristic
50#14582756C2211yescharacteristic
51C4×C4⋊Dic43C2211yescharacteristic
52#14582746—21no—
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55#14582661C2211yescharacteristic
56#14582661C2211yescharacteristic
57C2×C4⋊Q8×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#97×C43C2211yescharacteristic
63C43×#382C2211yescharacteristic
64C2×#10621902—22no—
65C2×#10621902—22no—
66C2×#10621902—22no—
67C2×#10621902—22no—
68C2×#10621902—22no—
69C2×#10621902—22no—
70C2×#10621902—41no—
71C2×#10621902—41no—
72C2×#10621902—41no—
73C2×#10621902—41no—
74C2×#10621902C2×C414yes—
75C2×#10621902C2×C414yescomplemented
76C22×D172—21no—
77C22×D172—21no—
78C22×D172D411yescharacteristic
79C22×D172C2311yescharacteristic
80C22×C4×D43—21no—
81C22×C4×D43—21no—
82C22×C4×D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43C2311yescharacteristic
85C22×C4×D43C2311yescharacteristic
86C2×#10621872—22no—
87C2×#10621872—22no—
88C2×#10621872—41no—
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C2×C8×D43—22no—
92C2×C8×D43—22no—
93C2×C8×D43—41no—
94#13063310—28no—
95#13063310—28no—
96#13063301—22no—
97#13063301—22no—
98#13063301C2×C414yes—
99#13063301C2×C414yescomplemented
100#13063300—28no—
101C4×D172—22no—
102C4×D172C2×C414yes—
103C4×D172C2×C414yescomplemented
104C4×D172D414yes—
105#13063283—22no—
106#13063283—41no—
107C2×C4⋊Dic43D411yescharacteristic
108C2×C4⋊Dic43C2311yescharacteristic
109C2×C4⋊Dic43C2311yescharacteristic
110C2×C4⋊Dic43C2311yescharacteristic
111C2×Dic43⋊C4—21no—
112C2×Dic43⋊C4—21no—
113C2×Dic43⋊C4—21no—
114C4⋊C4×D43—28no—
115C4⋊C4×D43—22no—
116C4⋊C4×D43—41no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4—21no—
120C2×(C2×D43)⋊C4—21no—
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4—21no—
123C2×(C2×D43)⋊C4D411yescharacteristic
124C2×(C2×D43)⋊C4D411yescharacteristic
125C2×C4×Dic43—21no—
126C2×C4×Dic43—21no—
127C4⋊(C43⋊C8)—22no—
128#13063249—22no—
129#13063249—22no—
130#13063249—41no—
131#13063249—41no—
132#13063247—22no—
133#13063247D414yescomplemented
134#13063245—22no—
135#13063245—22no—
136(C2×D43)⋊C8—22no—
137(C2×D43)⋊C8—22no—
138C43⋊#95—21no—
139C43⋊#95—21no—
140C43⋊#95—21no—
141C22×Q8×C43C2311yescharacteristic
142C22×Q8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144C22×C8×C43C2311yescharacteristic
145C4⋊Q8×C43—22no—
146C4⋊Q8×C43C2×C414yescomplemented
147C2×C4⋊C4×C43—21no—
148C2×C4⋊C4×C43—21no—
149C2×C4⋊C4×C43C2311yescharacteristic
150C2×C4⋊C4×C43C2311yescharacteristic
151C2×C42×C43C2311yescharacteristic
152#103×C43—22no—
153#103×C43—22no—
154#103×C43—41no—
155#103×C43—41no—
156#97×C43—22no—
157#95×C43—21no—
158#95×C43—21no—
159C23×D43—21no—
160C23×D43C2×D411yescharacteristic
161C23×D43C2×D411yescharacteristic
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43C22×C412yes—
173C2×Q8×C43C22×C412yes—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2411yescharacteristic
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186#10621902—28no—
187#10621902—28no—
188#10621902—44no—
189#10621902—44no—
190#10621902—44no—
191#10621902—44no—
192#10621902—44no—
193#10621902—44no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172—21no—
197C2×D172—24no—
198C2×D172—24no—
199C2×D172—41no—
200C2×D172—41no—
201C2×D172—42no—
202C2×D172—42no—
203C2×D172—42no—
204C2×D172—42no—
205C2×D172C22⋊C414yes—
206C2×D172C22×C412yes—
207C2×D172C2×D412yes—
208C2×D172#4112yes—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—21no—
212C2×C4×D43—21no—
213C2×C4×D43—21no—
214C2×C4×D43—21no—
215C2×C4×D43—21no—
216C2×C4×D43—21no—
217C2×C4×D43—24no—
218C2×C4×D43—24no—
219C2×C4×D43—24no—
220C2×C4×D43—42no—
221C2×C4×D43—42no—
222C2×C4×D43—42no—
223C2×C4×D43—42no—
224C2×C4×D43—42no—
225C2×C4×D43—42no—
226C2×C4×D43—42no—
227C2×C4×D43—42no—
228C2×C4×D43—81no—
229C2×C4×D43C22×C412yes—
230C2×C4×D43C22×C412yes—
231C2×C4×D43C2×D412yes—
232C2×C4×D43C2×D412yes—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43C2×D412yes—
239C4⋊C4×C43—24no—
240C4⋊C4×C43—24no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C42×C43C22×C412yes—
246C42×C43C2×D412yes—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—42no—
251(C2×D43)⋊C4—42no—
252(C2×D43)⋊C4—81no—
253(C2×D43)⋊C4C22⋊C414yes—
254(C2×D43)⋊C4C22⋊C414yes—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43C22⋊C414yes—
260C4⋊Dic43C22×C412yes—
261C4⋊Dic43C2×D412yes—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264Dic43⋊C4—42no—
265C4×Dic43—42no—
266C4×Dic43—81no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273#10621872—44no—
274C8×D43—44no—
275C23×C43C22×D411yescharacteristic
276C22×D43—22no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—22no—
280C22×D43—21no—
281C22×D43—21no—
282C22×D43—22no—
283C22×D43—21no—
284C22×D43—21no—
285C22×D43—21no—
286C22×D43—21no—
287C22×D43—21no—
288C22×D43—21no—
289C22×D43—21no—
290C22×D43—21no—
291C22×D43—41no—
292C22×D43—41no—
293C22×D43—41no—
294C22×D43—41no—
295C22×D43C2×C22⋊C412yes—
296C22×D43C2×C22⋊C412yes—
297Q8×C43—22no—
298Q8×C43—22no—
299Q8×C43—22no—
300Q8×C43—22no—
301Q8×C43—41no—
302Q8×C43—41no—
303Q8×C43—41no—
304Q8×C43—41no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43C2×C22⋊C412yes—
322C2×C4×C43C2×C22⋊C412yes—
323C2×C4×C43C23×C411yescharacteristic
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C2×#4111yescharacteristic
327C2×C4×C43H(5,𝔽2)11yescharacteristic
328C2×C4×C43H(5,𝔽2)11yescharacteristic
329C2×Dic43—21no—
330C2×Dic43—21no—
331C2×Dic43—21no—
332C2×Dic43—21no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43C2×C22⋊C412yes—
343C2×Dic43C2×C22⋊C412yes—
344D172—22no—
345D172—22no—
346D172—22no—
347D172—44no—
348D172—48no—
349D172—48no—
350D172C4×D414yes—
351C4×D43—22no—
352C4×D43—22no—
353C4×D43—22no—
354C4×D43—22no—
355C4×D43—22no—
356C4×D43—22no—
357C4×D43—22no—
358C4×D43—22no—
359C4×D43—48no—
360C4×D43—48no—
361C4×D43—48no—
362C4×D43—84no—
363C8×C43—22no—
364C8×C43—41no—
365C43⋊C8—41no—
366C43⋊C8—41no—
367#22420—431nomaximal, Sylow
368C22×C43C22×C22⋊C411yescharacteristic
369C22×C43D4211yescharacteristic
370C22×C43#54611yescharacteristic
371C22×C43#57511yescharacteristic
372C22×C43#57511yescharacteristic
373C22×C43#57711yescharacteristic
374C22×C43#57811yescharacteristic
375C2×D43—24no—
376C2×D43—22no—
377C2×D43—22no—
378C2×D43—22no—
379C2×D43—22no—
380C2×D43—22no—
381C2×D43—22no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—41no—
385C2×D43—41no—
386C2×D43—42no—
387C2×D43—41no—
388C2×D43—41no—
389C2×D43—42no—
390C2×D43—41no—
391C2×D43—41no—
392C2×D43—42no—
393C2×D43—41no—
394C2×D43—41no—
395C2×D43—42no—
396C4×C43—22no—
397C4×C43—22no—
398C4×C43—42no—
399C4×C43—42no—
400C4×C43—81no—
401C4×C43—81no—
402C4×C43C2×C4×D411yescharacteristic
403C4×C43#51811yescharacteristic
404C4×C43D4211yescharacteristic
405C4×C43#54611yescharacteristic
406Dic43—22no—
407Dic43—22no—
408Dic43—42no—
409Dic43—42no—
410Dic43—81no—
411C2×#547—431no—
412C2×#435—431no—
413C2×#417—431no—
414C2×#416—431no—
415#2352—431no—
416#1981—431no—
417#1960D4311yescharacteristic, complemented
418#1894—431no—
419#1892—431no—
420#1873—431no—
421#1872—431no—
422#1804—431no—
423#1788—431no—
424#1788—431no—
425#1762—431no—
426C2×C43D4×C22⋊C411yescharacteristic
427C2×C43#289611yescharacteristic
428C2×C43#289811yescharacteristic
429C2×C43#326711yescharacteristic
430C2×C43#326911yescharacteristic
431C2×C43#330711yescharacteristic
432C2×C43#331511yescharacteristic
433D43—42no—
434D43—42no—
435D43—44no—
436C22×#41—431no—
437C22×#41—431no—
438C22×M16—431no—
439C23×C8—431no—
440#547—438no—
441#547—864no—
442C2×C4⋊Q8C2×D4311yescharacteristic
443C2×#123—861no—
444C2×#123—861no—
445C2×C22⋊Q8—431no—
446C2×C22⋊Q8—431no—
447C2×#121—861no—
448C2×C4×D4—431no—
449C2×C4×D4—431no—
450C2×#117—431no—
451C22×C4⋊C4—431no—
452C22×C4⋊C4—861no—
453#435—864no—
454C2×C4⋊C8—431no—
455#417—864no—
456#416—864no—
457C2×#103—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#103—431no—
461C2×#103C2×D4311yescharacteristic
462C2×#103C2×D4311yescharacteristic
463C2×#103C2×D4311yescharacteristic
464C2×#103C2×D4311yescharacteristic
465C2×#102—431no—
466C2×#102—431no—
467C2×#102—431no—
468C2×#102—431no—
469C2×C22⋊C8—431no—
470C2×C22⋊C8—431no—
471C2×#97C2×D4311yescharacteristic
472#388—861no—
473#387—861no—
474#386—861no—
475#382C2×D4311yescharacteristic
476#380—431no—
477#380—431no—
478C4×C4⋊C4—431no—
479C4×C22⋊C4—861no—
480#340—431no—
481#340—431no—
482#340—431no—
483#340—431no—
484C43#2242011yescharacteristic, complemented, Sylow
485C2×#41—434no—
486C2×#41—434no—
487C2×#41—862no—
488C2×#41—862no—
489C2×#41—862no—
490C2×#41—862no—
491C2×#41—862no—
492C2×#41—862no—
493C2×#41—1721no—
494C2×#41—1721no—
495C2×#41—1721no—
496C2×#41—1721no—
497C22×Q8C22×D4311yescharacteristic
498C22×Q8C22×D4311yescharacteristic
499C22×D4—431no—
500C22×D4—431no—
501C22×D4—861no—
502C22×D4—861no—
503C23×C4—431no—
504C23×C4—431no—
505C23×C4—861no—
506C23×C4—861no—
507C23×C4—861no—
508C23×C4—861no—
509C2×M16—862no—
510C2×M16—862no—
511C2×M16—1721no—
512C22×C8—431no—
513C22×C8—431no—
514C22×C8—862no—
515C22×C8—862no—
516C22×C8—1721no—
517C22×C8C22×D4311yescharacteristic
518C22×C8C22×D4311yescharacteristic
519C4⋊Q8—22no—
520C4⋊Q8C4×D4314yescomplemented
521#123—868no—
522#123—868no—
523C22⋊Q8—434no—
524C22⋊Q8—434no—
525C22⋊Q8—862no—
526C22⋊Q8—862no—
527#121—868no—
528C4×D4—434no—
529C4×D4—434no—
530C4×D4—434no—
531C4×D4—862no—
532#117—862no—
533#117—1721no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—431no—
540C2×C4⋊C4—868no—
541C2×C4⋊C4—862no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4—861no—
545C2×C4⋊C4—1721no—
546C2×C4⋊C4C22×D4311yescharacteristic
547C2×C4⋊C4C22×D4311yescharacteristic
548C2×C22⋊C4—431no—
549C2×C22⋊C4—431no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C42—861no—
557C2×C42—861no—
558C2×C42C22×D4311yescharacteristic
559C4⋊C8—862no—
560#103—22no—
561#103—22no—
562#103—41no—
563#103—41no—
564#103—862no—
565#103—862no—
566#103—1721no—
567#103—1721no—
568#102—434no—
569#102—862no—
570#102—862no—
571#102—862no—
572C22⋊C8—862no—
573C22⋊C8—862no—
574#97—22no—
575#95—21no—
576#95—21no—
577#95—861no—
578#95—861no—
579#95—861no—
580C24—431no—
581C24—431no—
582C24—861no—
583#41—868no—
584#41—868no—
585#41—1724no—
586#41—1724no—
587#41—1724no—
588#41—1724no—
589#41—1724no—
590#41—1724no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×C4×D4312yes—
602C2×Q8C2×C4×D4312yes—
603C2×D4—434no—
604C2×D4—432no—
605C2×D4—432no—
606C2×D4—432no—
607C2×D4—864no—
608C2×D4—864no—
609C2×D4—861no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4—1721no—
613C2×D4—1721no—
614C2×D4—1722no—
615C2×D4—1722no—
616C2×D4—1722no—
617C2×D4—1722no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—431no—
623C22×C4—431no—
624C22×C4—432no—
625C22×C4—432no—
626C22×C4—432no—
627C22×C4—432no—
628C22×C4—864no—
629C22×C4—864no—
630C22×C4—861no—
631C22×C4—861no—
632C22×C4—861no—
633C22×C4—861no—
634C22×C4—861no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—861no—
639C22×C4—861no—
640C22×C4—864no—
641C22×C4—861no—
642C22×C4—3441no—
643C22×C4—1722no—
644C22×C4—1722no—
645C22×C4—1722no—
646C22×C4—1722no—
647C22×C4—1722no—
648C22×C4—1722no—
649C22×C4—1722no—
650C22×C4—1722no—
651C22×C4D4×D4311yescharacteristic
652C22×C4D4×D4311yescharacteristic
653C22×C4C23×D4311yescharacteristic
654M16—1724no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—861no—
661C2×C8—861no—
662C2×C8—861no—
663C2×C8—861no—
664C2×C8—861no—
665C2×C8—861no—
666C2×C8—1724no—
667C2×C8D4×D4312yes—
668C4⋊C4—24no—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—434no—
675C4⋊C4—432no—
676C4⋊C4—432no—
677C4⋊C4—864no—
678C4⋊C4—864no—
679C4⋊C4—861no—
680C4⋊C4—861no—
681C4⋊C4—861no—
682C4⋊C4—861no—
683C4⋊C4—1722no—
684C22⋊C4—434no—
685C22⋊C4—434no—
686C22⋊C4—864no—
687C22⋊C4—864no—
688C22⋊C4—864no—
689C22⋊C4—3441no—
690C22⋊C4—1722no—
691C22⋊C4—1722no—
692C42—3441no—
693C42—1722no—
694C42C2×C4×D4312yes—
695C42D4×D4312yes—
696C23—432no—
697C23—432no—
698C23—862no—
699C23—861no—
700C23—861no—
701C23—861no—
702C23—861no—
703C23—861no—
704C23—861no—
705C23—861no—
706C23—861no—
707C23—861no—
708C23—861no—
709C23—862no—
710C23—861no—
711C23—861no—
712C23—862no—
713C23—1721no—
714C23—1721no—
715C23—1721no—
716C23—1721no—
717C23C2×D4×D4311yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724Q8—41no—
725Q8—41no—
726D4—434no—
727D4—862no—
728D4—862no—
729D4—862no—
730D4—1724no—
731D4—1728no—
732D4—1728no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—432no—
750C2×C4—432no—
751C2×C4—861no—
752C2×C4—861no—
753C2×C4—861no—
754C2×C4—861no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—3444no—
766C2×C4—1728no—
767C2×C4—1728no—
768C2×C4—1728no—
769C2×C4—1721no—
770C2×C4—1721no—
771C2×C4—1721no—
772C2×C4—1721no—
773C2×C4—1721no—
774C2×C4—1721no—
775C2×C4—1721no—
776C2×C4C22⋊C4×D4312yes—
777C2×C4C22⋊C4×D4312yes—
778C2×C4C22×C4×D4311yescharacteristic
779C2×C4C2×D4×D4311yescharacteristic
780C2×C4C2×D4×D4311yescharacteristic
781C2×C4#41×D4311yescharacteristic
782C2×C4#1306337011yescharacteristic
783C2×C4#1306337111yescharacteristic
784C8—22no—
785C8—41no—
786C8—1721no—
787C8—1721no—
788C22—862no—
789C22—862no—
790C22—864no—
791C22—862no—
792C22—862no—
793C22—862no—
794C22—862no—
795C22—1721no—
796C22—1721no—
797C22—1722no—
798C22—1721no—
799C22—1721no—
800C22—1722no—
801C22—1721no—
802C22—1721no—
803C22—1722no—
804C22—1721no—
805C22—1721no—
806C22—1722no—
807C22—1722no—
808C22—1722no—
809C22C2×C22⋊C4×D4311yescharacteristic
810C22#1458353411yescharacteristic
811C22#1458354211yescharacteristic
812C22#1458369811yescharacteristic
813C22#1458369811yescharacteristic
814C22#1458370811yescharacteristic
815C22#1458371511yescharacteristic
816C4—22no—
817C4—22no—
818C4—42no—
819C4—42no—
820C4—81no—
821C4—81no—
822C4—862no—
823C4—862no—
824C4—3441no—
825C4—1722no—
826C4—1722no—
827C4C4×D4×D4311yescharacteristic
828C4#1458337111yescharacteristic
829C4#1458353311yescharacteristic
830C4#1458354611yescharacteristic
831C2—1722no—
832C2—1722no—
833C2—1724no—
834C2#1913741611yescharacteristic
835C2#1914311311yescharacteristic
836C2#1914312711yescharacteristic
837C2#1914611911yescharacteristic
838C2#1914614911yescharacteristic
839C2#1914657011yescharacteristic
840C2#1914669011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1960C2
socleC23×C43C22×D4
prime radicalC2×#14583552C2
cosocleC22×C4×C43C24
hypercenter#1960D43
hypocenterC43#22420
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
2. C2×#14582972C2semidirect
3. C2×#14582899C2semidirect
4. C2×#14582894C2semidirect
5. #19137521C2semidirect
6. #19135519C2semidirect
7. #19135025C2semidirect
8. #19135015C2semidirect
9. #19134904C2semidirect
10. #19134899C2semidirect
11. #19134602C2semidirect
12. #19134534C2semidirect
13. #19134534C2semidirect
14. #19134421C2semidirect
15. C43×#1960C2semidirect
21. #14583552C4semidirect
75. C2×#10621902C2×C4semidirect
99. #13063301C2×C4semidirect
103. C4×D172C2×C4semidirect
133. #13063247D4semidirect
146. C4⋊Q8×C43C2×C4semidirect
417. #1960D43semidirect
484. C43#22420semidirect
520. C4⋊Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835522
C2×#145829722
C2×#145828992
C2×#145828942
#191375212
#191355192
#191350252
#191350152
#191349042
#191348992
#191346022
#191345342
#191344212
C43×#19602
#2242043