Finite Group Databasebeta

← C2×#19145280 #25966483

Subgroups — C2×#19145280 #25966483

Order 11008.

2034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583520C211yesmaximal, characteristic, complemented
2#19145280C2116yesmaximal, direct product factor
3C2×#14583309C211yesmaximal, characteristic, complemented
4C2×#14583286C211yesmaximal, characteristic, complemented
5C2×#14583256C211yesmaximal, characteristic, complemented
6C2×#14583245C211yesmaximal, characteristic, complemented
7C2×#14583150C211yesmaximal, characteristic, complemented
8C2×#14583143C211yesmaximal, characteristic, complemented
9C2×#14583133C211yesmaximal, characteristic, complemented
10C2×#14583126C211yesmaximal, characteristic, complemented
11C2×#14583009C211yesmaximal, characteristic, complemented
12C2×#14582999C211yesmaximal, characteristic, complemented
13C2×C4×#10621883C211yesmaximal, characteristic, complemented
14C2×C4×#10621882C211yesmaximal, characteristic, complemented
15C2×#14582855C211yesmaximal, characteristic, complemented
16C2×C43×#540C211yesmaximal, characteristic, complemented
17C22×#10621883C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C22×#10621882C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21C22×#10621877C2211yescharacteristic
22C23×C43⋊C8C2211yescharacteristic
23#14583520—24no—
24#14583520C2218yescomplemented
25C2×#13063325C2211yescharacteristic
26C2×#13063320—21no—
27C2×#13063313C2211yescharacteristic
28C2×#13063311—21no—
29C2×#13063307—21no—
30C2×#13063304C2211yescharacteristic
31C2×#13063303—21no—
32C2×#13063299C2211yescharacteristic
33C2×C4×Dic86C2211yescharacteristic
34C2×C4×D172C2211yescharacteristic
35#14583309C2218yescomplemented
36#14583286C2218yescomplemented
37#14583256C2218yescomplemented
38#14583245C2218yescomplemented
39#14583150C2218yescomplemented
40#14583143C2218yescomplemented
41#14583133C2218yescomplemented
42#14583126C2218yescomplemented
43#14583009C2218yescomplemented
44#14582999C2218yescomplemented
45C4×#10621883C2218yescomplemented
46C4×#10621882C2218yescomplemented
47C2×#13063258C2211yescharacteristic
48C2×#13063258C2211yescharacteristic
49C2×#13063256C2211yescharacteristic
50C2×#13063256C2211yescharacteristic
51C2×#13063248C2211yescharacteristic
52C2×#13063248C2211yescharacteristic
53C2×#13063246C2211yescharacteristic
54C2×#13063246C2211yescharacteristic
55C2×#13063246C2211yescharacteristic
56C2×#13063246C2211yescharacteristic
57C2×#13063245C2211yescharacteristic
58C2×#13063245C2211yescharacteristic
59#14582855C2218yescomplemented
60C2×#13063236C2211yescharacteristic
61C2×#13063236C2211yescharacteristic
62C2×C4×C43⋊C8C2211yescharacteristic
63C2×C4×C43⋊C8C2211yescharacteristic
64C43×#540—24no—
65C43×#540C2218yescomplemented
66C2×#127×C43C2211yescharacteristic
67C2×#125×C43C2211yescharacteristic
68C2×#123×C43—21no—
69C2×#123×C43—21no—
70C2×#121×C43—21no—
71C2×#121×C43—21no—
72C2×#121×C43C2211yescharacteristic
73C2×#121×C43C2211yescharacteristic
74C2×C4×D4×C43C2211yescharacteristic
75C2×C4×D4×C43C2211yescharacteristic
76C2×#117×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C22×D172C2311yescharacteristic
80C22×C22⋊D43—21no—
81C22×C4×D43—21no—
82C2×#10621883—24no—
83C2×#10621883—24no—
84C2×#10621883C2314yes—
85C2×#10621883C2314yes—
86C2×#10621882—24no—
87C2×#10621882—24no—
88C2×#10621882C2314yes—
89C2×#10621882C2314yes—
90C2×#10621877—24no—
91C2×#10621877C2314yes—
92C22×C43⋊C8—24no—
93C22×C43⋊C8C2311yescharacteristic
94C22×C43⋊C8C2311yescharacteristic
95C22×C43⋊C8C2314yes—
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98#13063325—22no—
99#13063325C2314yes—
100#13063320—28no—
101#13063313—22no—
102#13063313C2314yes—
103#13063311—28no—
104#13063307—28no—
105#13063304—22no—
106#13063304C2314yes—
107#13063303—28no—
108#13063299—22no—
109#13063299C2314yes—
110C4×Dic86—22no—
111C4×Dic86C2314yes—
112C4×D172—22no—
113C4×D172C2314yes—
114C2×C4⋊Dic43—21no—
115C2×C4⋊Dic43C2311yescharacteristic
116C2×C4⋊Dic43C2311yescharacteristic
117C2×Dic43⋊C4—21no—
118C2×Dic43⋊C4—21no—
119C2×C22⋊Dic43—21no—
120C2×(C2×D43)⋊C4—21no—
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4—21no—
123C2×(C2×D43)⋊C4—21no—
124C2×C4×Dic43—21no—
125#13063258C2314yes—
126#13063258C2314yes—
127#13063256C2314yes—
128#13063256C2314yes—
129#13063248C2314yes—
130#13063248C2314yes—
131#13063246C2314yes—
132#13063246C2314yes—
133#13063246C2314yes—
134#13063246C2314yes—
135#13063245C2314yes—
136#13063245C2314yes—
137#13063236C2314yes—
138#13063236C2314yes—
139C4×C43⋊C8C2314yes—
140C4×C43⋊C8C2314yes—
141C22×D4×C43—21no—
142C22×D4×C43—21no—
143C22×D4×C43—21no—
144C22×D4×C43—21no—
145C22×D4×C43C2311yescharacteristic
146C22×D4×C43C2311yescharacteristic
147C23×C4×C43—21no—
148C23×C4×C43—21no—
149C23×C4×C43C2311yescharacteristic
150#127×C43—22no—
151#127×C43C2314yes—
152#125×C43—22no—
153#125×C43C2314yes—
154#123×C43—28no—
155#123×C43—28no—
156#121×C43—22no—
157#121×C43—22no—
158#121×C43—28no—
159#121×C43—28no—
160#121×C43C2314yes—
161#121×C43C2314yes—
162C4×D4×C43—22no—
163C4×D4×C43—22no—
164C4×D4×C43C2314yes—
165C4×D4×C43C2314yes—
166#117×C43D414yes—
167#117×C43C2314yes—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43D411yescharacteristic
171C2×C4⋊C4×C43D411yescharacteristic
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43—21no—
177C2×C22⋊C4×C43—21no—
178C2×C22⋊C4×C43D411yescharacteristic
179C2×C22⋊C4×C43D411yescharacteristic
180C2×C42×C43C2311yescharacteristic
181C2×C42×C43C2311yescharacteristic
182C24×C43—21no—
183C24×C43—21no—
184C24×C43C2×D411yescharacteristic
185C23×D43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—24no—
189C2×D4×C43—24no—
190C2×D4×C43—24no—
191C2×D4×C43—24no—
192C2×D4×C43—22no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43—22no—
196C2×D4×C43—82no—
197C2×D4×C43—82no—
198C2×D4×C43—82no—
199C2×D4×C43—82no—
200C2×D4×C43C2412yes—
201C2×D4×C43C2412yes—
202C22×C4×C43—22no—
203C22×C4×C43—22no—
204C22×C4×C43—24no—
205C22×C4×C43—24no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—82no—
209C22×C4×C43—82no—
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D412yes—
216C22×C4×C43C2412yes—
217C22×C4×C43C2411yescharacteristic
218C2×C22⋊D43—24no—
219C2×C22⋊D43—82no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C2×D172—21no—
224C2×D172—22no—
225C2×D172—22no—
226C2×D172C2412yes—
227C2×C4×D43—24no—
228C2×C4×D43—82no—
229C2×Dic86—22no—
230C2×Dic86—22no—
231C2×Dic86—21no—
232C2×Dic86—24no—
233C2×Dic86—82no—
234C2×Dic86C2412yes—
235C4⋊C4×C43—24no—
236C4⋊C4×C43—24no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43C2×D414yes—
240C4⋊C4×C43C2×D414yes—
241C4⋊C4×C43C2412yes—
242C4⋊C4×C43C2412yes—
243C22⋊C4×C43—24no—
244C22⋊C4×C43—24no—
245C22⋊C4×C43—24no—
246C22⋊C4×C43—24no—
247C22⋊C4×C43C2×D414yes—
248C22⋊C4×C43C2×D414yes—
249C42×C43C2×D412yes—
250C42×C43C2×D412yes—
251C42×C43C2412yes—
252C42×C43C2412yes—
253C22⋊Dic43—24no—
254#10621883—28no—
255#10621883—28no—
256#10621882—28no—
257#10621882—28no—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—24no—
262C4⋊Dic43—24no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43C2412yes—
266C4⋊Dic43C2412yes—
267Dic43⋊C4—24no—
268Dic43⋊C4—24no—
269C4×Dic43—24no—
270#10621877—28no—
271C2×C43⋊C8—22no—
272C2×C43⋊C8—22no—
273C2×C43⋊C8—28no—
274C2×C43⋊C8#4114yes—
275C2×C43⋊C8#4114yes—
276C2×C43⋊C8C2412yes—
277C2×C43⋊C8C2412yes—
278C2×C43⋊C8C2412yes—
279C2×C43⋊C8C2412yes—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—22no—
283C23×C43—22no—
284C23×C43—22no—
285C23×C43—42no—
286C23×C43—42no—
287C23×C43—42no—
288C23×C43—42no—
289C23×C43—42no—
290C23×C43—42no—
291C23×C43C22×D412yes—
292C23×C43C22×D411yescharacteristic
293C22×D43—22no—
294C22×D43—42no—
295C22×D43—42no—
296C22×D43—42no—
297D4×C43—22no—
298D4×C43—22no—
299D4×C43—22no—
300D4×C43—22no—
301D4×C43—42no—
302D4×C43—42no—
303D4×C43—84no—
304D4×C43—84no—
305D4×C43—84no—
306D4×C43—84no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—24no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—42no—
318C2×C4×C43—42no—
319C2×C4×C43—84no—
320C2×C4×C43—84no—
321C2×C4×C43C22×D412yes—
322C2×C4×C43C22×D412yes—
323C2×C4×C43C22×D412yes—
324C2×C4×C43C22×D412yes—
325C2×C4×C43C22×D412yes—
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43C2×#4112yes—
328C2×C4×C43C2×#4112yes—
329C2×C4×C43C2511yescharacteristic
330C22⋊D43—84no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337D172—22no—
338D172—22no—
339D172—42no—
340C4×D43—84no—
341Dic86—22no—
342Dic86—22no—
343Dic86—42no—
344Dic86—84no—
345C43⋊C8—22no—
346C43⋊C8—22no—
347C43⋊C8C2×#4114yes—
348C43⋊C8C2×#4114yes—
349C2×#3179—431nomaximal, Sylow
350C22×C43—22no—
351C22×C43—22no—
352C22×C43—22no—
353C22×C43—44no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—84no—
361C22×C43—84no—
362C22×C43#53212yes—
363C22×C43#57612yes—
364C22×C43#57712yes—
365C22×C43C23×D411yescharacteristic
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—42no—
369C2×D43—84no—
370C4×C43—22no—
371C4×C43—22no—
372C4×C43—22no—
373C4×C43—22no—
374C4×C43—22no—
375C4×C43—42no—
376C4×C43—42no—
377C4×C43#53212yes—
378C4×C43C22×#4111yescharacteristic
379C4×C43C22×#4111yescharacteristic
380Dic43—42no—
381Dic43—42no—
382Dic43—42no—
383C2×#542—431no—
384C2×#540D4311yescharacteristic, complemented
385#3179—4316no—
386C2×#501—431no—
387C2×#496—431no—
388C2×#488—431no—
389C2×#486—431no—
390C2×#469—431no—
391C2×#468—431no—
392C2×#466—431no—
393C2×#465—431no—
394C2×#442—431no—
395C2×#440—431no—
396C2×C4×SD16—431no—
397C2×C4×D8—431no—
398C2×#405—431no—
399C2×C43—42no—
400C2×C43—82no—
401C2×C43—82no—
402C2×C43#317914yescomplemented
403C2×C43C2×#53211yescharacteristic
404C2×C43C2×#57611yescharacteristic
405C2×C43C2×#57711yescharacteristic
406D43—82no—
407C22×SD16—431no—
408C22×SD16—431no—
409C22×D8—431no—
410C22×D8—431no—
411C22×M16—431no—
412C23×C8—431no—
413#542—438no—
414#542—864no—
415#540—24no—
416#540C2×D4318yescomplemented
417C2×C4⋊Q8—431no—
418C2×#127C2×D4311yescharacteristic
419C2×#126—861no—
420C2×#125C2×D4311yescharacteristic
421C2×#124—431no—
422C2×#124—861no—
423C2×#123—21no—
424C2×#123—21no—
425C2×#123—861no—
426C2×C22⋊Q8—431no—
427C2×C22⋊Q8—861no—
428C2×#121—21no—
429C2×#121—21no—
430C2×#121—431no—
431C2×#121C2×D4311yescharacteristic
432C2×#121C2×D4311yescharacteristic
433C2×C4×Q8—431no—
434C2×C4×D4—431no—
435C2×C4×D4C2×D4311yescharacteristic
436C2×C4×D4C2×D4311yescharacteristic
437C2×#117C2×D4311yescharacteristic
438#501—438no—
439#496—438no—
440#488—438no—
441#486—438no—
442#469—438no—
443#468—438no—
444#466—438no—
445#465—438no—
446#442—438no—
447#440—438no—
448C4×SD16—438no—
449C4×D8—438no—
450C2×#107—431no—
451C2×#107—431no—
452C2×#106—431no—
453C2×#106—431no—
454C2×#103—431no—
455C2×#103—431no—
456C2×#102—431no—
457C2×#102—431no—
458C2×#102—431no—
459C2×#102—431no—
460C2×#102—431no—
461C2×#102—431no—
462#405—438no—
463C2×#97—431no—
464C2×#97—431no—
465C2×C4×C8—431no—
466C2×C4×C8—431no—
467C43C2×#317911yescharacteristic, complemented, Sylow
468C22×Q8—431no—
469C22×Q8—861no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—431no—
475C22×D4—861no—
476C22×D4C22×D4311yescharacteristic
477C22×D4C22×D4311yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—861no—
481C23×C4C22×D4311yescharacteristic
482C2×SD16—434no—
483C2×SD16—434no—
484C2×SD16—864no—
485C2×SD16—864no—
486C2×D8—434no—
487C2×D8—434no—
488C2×D8—864no—
489C2×D8—864no—
490C2×M16—434no—
491C2×M16—864no—
492C22×C8—431no—
493C22×C8—431no—
494C22×C8—431no—
495C22×C8—434no—
496C22×C8—431no—
497C22×C8—864no—
498C4⋊Q8—434no—
499C4⋊Q8—862no—
500#127—22no—
501#127C22×D4314yes—
502#126—868no—
503#125—22no—
504#125C22×D4314yes—
505#124—434no—
506#124—868no—
507#124—862no—
508#123—28no—
509#123—28no—
510#123—868no—
511C22⋊Q8—434no—
512C22⋊Q8—862no—
513C22⋊Q8—868no—
514#121—22no—
515#121—22no—
516#121—28no—
517#121—28no—
518#121—434no—
519#121—862no—
520#121C22×D4314yes—
521#121C22×D4314yes—
522C4×Q8—434no—
523C4×Q8—862no—
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—434no—
527C4×D4—862no—
528C4×D4C22×D4314yes—
529C4×D4C22×D4314yes—
530#117C22⋊D4314yes—
531#117C22×D4314yes—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—431no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—861no—
537C2×C4⋊C4—861no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4C22⋊D4311yescharacteristic
540C2×C4⋊C4C22⋊D4311yescharacteristic
541C2×C4⋊C4C22×D4311yescharacteristic
542C2×C4⋊C4C22×D4311yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—861no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4C22⋊D4311yescharacteristic
553C2×C22⋊C4C22⋊D4311yescharacteristic
554C2×C42—861no—
555C2×C42C22×D4311yescharacteristic
556C2×C42C22×D4311yescharacteristic
557#107—434no—
558#107—434no—
559#106—434no—
560#106—434no—
561#103—434no—
562#103—434no—
563#102—434no—
564#102—434no—
565#102—434no—
566#102—434no—
567#102—434no—
568#102—434no—
569#97—434no—
570#97—434no—
571C4×C8—434no—
572C4×C8—434no—
573C24—21no—
574C24—21no—
575C24—861no—
576C24C2×C22⋊D4311yescharacteristic
577C2×Q8—432no—
578C2×Q8—864no—
579C2×Q8—861no—
580C2×Q8—862no—
581C2×Q8—862no—
582C2×Q8—3442no—
583C2×D4—24no—
584C2×D4—24no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—24no—
588C2×D4—24no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—82no—
594C2×D4—82no—
595C2×D4—82no—
596C2×D4—82no—
597C2×D4—432no—
598C2×D4—864no—
599C2×D4—861no—
600C2×D4—862no—
601C2×D4—862no—
602C2×D4—3442no—
603C2×D4C23×D4312yes—
604C2×D4C23×D4312yes—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4—861no—
616C22×C4—864no—
617C22×C4—3442no—
618C22×C4C2×C22⋊D4312yes—
619C22×C4C2×C22⋊D4311yescharacteristic
620C22×C4C2×C22⋊D4311yescharacteristic
621C22×C4C2×C22⋊D4311yescharacteristic
622C22×C4C2×C22⋊D4311yescharacteristic
623C22×C4C2×C22⋊D4311yescharacteristic
624C22×C4C23×D4312yes—
625C22×C4C23×D4311yescharacteristic
626SD16—868no—
627SD16—868no—
628D8—868no—
629D8—868no—
630M16—868no—
631C2×C8—434no—
632C2×C8—434no—
633C2×C8—432no—
634C2×C8—432no—
635C2×C8—432no—
636C2×C8—432no—
637C2×C8—868no—
638C2×C8—862no—
639C2×C8—862no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—432no—
645C4⋊C4—432no—
646C4⋊C4—861no—
647C4⋊C4—861no—
648C4⋊C4—864no—
649C4⋊C4—864no—
650C4⋊C4—864no—
651C4⋊C4C2×C22⋊D4314yes—
652C4⋊C4C2×C22⋊D4314yes—
653C4⋊C4C23×D4312yes—
654C4⋊C4C23×D4312yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—864no—
660C22⋊C4—864no—
661C22⋊C4—864no—
662C22⋊C4—864no—
663C22⋊C4—864no—
664C22⋊C4C2×C22⋊D4314yes—
665C22⋊C4C2×C22⋊D4314yes—
666C42—864no—
667C42C2×C22⋊D4312yes—
668C42C2×C22⋊D4312yes—
669C42C23×D4312yes—
670C42C23×D4312yes—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—862no—
683C23—1722no—
684C23—1722no—
685C23—1722no—
686C23C22×C22⋊D4312yes—
687C23C22×C22⋊D4311yescharacteristic
688Q8—862no—
689Q8—862no—
690Q8—3444no—
691Q8—1722no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—42no—
697D4—42no—
698D4—84no—
699D4—84no—
700D4—84no—
701D4—84no—
702D4—862no—
703D4—862no—
704D4—3444no—
705D4—1722no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—84no—
719C2×C4—84no—
720C2×C4—862no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—3444no—
724C2×C4—1722no—
725C2×C4—1722no—
726C2×C4—1722no—
727C2×C4C22×C22⋊D4312yes—
728C2×C4C22×C22⋊D4312yes—
729C2×C4C22×C22⋊D4312yes—
730C2×C4C22×C22⋊D4312yes—
731C2×C4C22×C22⋊D4312yes—
732C2×C4C22×C22⋊D4311yescharacteristic
733C2×C4#41×D4312yes—
734C2×C4#41×D4312yes—
735C2×C4C24×D4311yescharacteristic
736C8—434no—
737C8—434no—
738C8—862no—
739C8—862no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—84no—
751C22—84no—
752C22—3444no—
753C22—1722no—
754C22—1722no—
755C22—1722no—
756C22#1458344512yes—
757C22#1458370212yes—
758C22#1458371012yes—
759C22C23×C22⋊D4311yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—42no—
766C4—42no—
767C4—1722no—
768C4—1722no—
769C4—1722no—
770C4#1458344512yes—
771C4C2×#41×D4311yescharacteristic
772C4C2×#41×D4311yescharacteristic
773C2—42no—
774C2—82no—
775C2—82no—
776C2—3442no—
777C2#1914528014yesdirect product factor
778C2C2×#1458344511yescharacteristic
779C2C2×#1458370211yescharacteristic
780C2C2×#1458371011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#540C2
socleC23×C43C22×D4
hypercenterC2×#540D43
hypocenterC43C2×#3179
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#14583520C2semidirect
2. #19145280C2direct (N × H)
3. C2×#14583309C2semidirect
4. C2×#14583286C2semidirect
5. C2×#14583256C2semidirect
6. C2×#14583245C2semidirect
7. C2×#14583150C2semidirect
8. C2×#14583143C2semidirect
9. C2×#14583133C2semidirect
10. C2×#14583126C2semidirect
11. C2×#14583009C2semidirect
12. C2×#14582999C2semidirect
13. C2×C4×#10621883C2semidirect
14. C2×C4×#10621882C2semidirect
15. C2×#14582855C2semidirect
16. C2×C43×#540C2semidirect
24. #14583520C22semidirect
35. #14583309C22semidirect
36. #14583286C22semidirect
37. #14583256C22semidirect
38. #14583245C22semidirect
39. #14583150C22semidirect
40. #14583143C22semidirect
41. #14583133C22semidirect
42. #14583126C22semidirect
43. #14583009C22semidirect
44. #14582999C22semidirect
45. C4×#10621883C22semidirect
46. C4×#10621882C22semidirect
59. #14582855C22semidirect
65. C43×#540C22semidirect
384. C2×#540D43semidirect
402. C2×C43#3179semidirect
416. #540C2×D43semidirect
467. C43C2×#3179semidirect
777. C2#19145280direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835202
#191452802
C2×#145833092
C2×#145832862
C2×#145832562
C2×#145832452
C2×#145831502
C2×#145831432
C2×#145831332
C2×#145831262
C2×#145830092
C2×#145829992
C2×C4×#106218832
C2×C4×#106218822
C2×#145828552
C2×C43×#5402
C2×#317943