Finite Group Databasebeta

← C2×#19145276 #25966479

Subgroups — C2×#19145276 #25966479

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×#14583521C211yesmaximal, characteristic, complemented
2C2×#14583500C211yesmaximal, characteristic, complemented
3#19145276C2116yesmaximal, direct product factor
4C2×#14583307C211yesmaximal, characteristic, complemented
5C2×#14583285C211yesmaximal, characteristic, complemented
6C2×#14583255C211yesmaximal, characteristic, complemented
7C2×#14583244C211yesmaximal, characteristic, complemented
8C2×#14583151C211yesmaximal, characteristic, complemented
9C2×#14583148C211yesmaximal, characteristic, complemented
10C2×#14583136C211yesmaximal, characteristic, complemented
11C2×#14583125C211yesmaximal, characteristic, complemented
12C2×#14583012C211yesmaximal, characteristic, complemented
13C2×C4×#10621884C211yesmaximal, characteristic, complemented
14C2×C4×#10621882C211yesmaximal, characteristic, complemented
15C2×#14582856C211yesmaximal, characteristic, complemented
16C2×C43×#440C211yesmaximal, characteristic, complemented
17C22×#10621884C2211yescharacteristic
18C22×D344C2211yescharacteristic
19C22×#10621882C2211yescharacteristic
20C22×#10621872C2211yescharacteristic
21C22×C8×D43C2211yescharacteristic
22#14583521—24no—
23#14583521C2218yescomplemented
24#14583500—24no—
25#14583500C2218yescomplemented
26C2×#13063324C2211yescharacteristic
27C2×#13063321C2211yescharacteristic
28C2×#13063319—21no—
29C2×#13063316C2211yescharacteristic
30C2×#13063314C2211yescharacteristic
31C2×#13063313—21no—
32C2×#13063310—21no—
33C2×#13063308—21no—
34C2×#13063307—21no—
35C2×#13063303—21no—
36C2×#13063301C2211yescharacteristic
37C2×#13063300C2211yescharacteristic
38C2×#13063300C2211yescharacteristic
39C2×#13063299—21no—
40C2×#13063298—21no—
41C2×#13063296C2211yescharacteristic
42C2×C4×D172C2211yescharacteristic
43C2×C4×D172C2211yescharacteristic
44C2×#13063282C2211yescharacteristic
45#14583307C2218yescomplemented
46#14583285C2218yescomplemented
47#14583255C2218yescomplemented
48#14583244C2218yescomplemented
49#14583151C2218yescomplemented
50#14583148C2218yescomplemented
51#14583136C2218yescomplemented
52#14583125C2218yescomplemented
53#14583012C2218yescomplemented
54C4×#10621884C2218yescomplemented
55C4×#10621882C2218yescomplemented
56C2×#13063258C2211yescharacteristic
57C2×#13063257C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59C2×#13063249C2211yescharacteristic
60C2×#13063247C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063246C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65#14582856C2218yescomplemented
66C2×#13063235C2211yescharacteristic
67C2×C4×C43⋊C8C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C43×#440C2218yescomplemented
73C2×#107×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×D172—21no—
79C22×D172—21no—
80C22×D172C2311yescharacteristic
81C22×D172C2311yescharacteristic
82C22×C22⋊D43—21no—
83C22×C22⋊D43—21no—
84C22×C22⋊D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C22×C4×D43C2311yescharacteristic
88C2×#10621884—24no—
89C2×#10621884C2314yes—
90C2×D344—24no—
91C2×D344C2314yes—
92C2×#10621882—24no—
93C2×#10621882C2314yes—
94C2×#10621872—24no—
95C2×#10621872C2314yes—
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98C2×C8×D43—24no—
99C2×C8×D43C2314yes—
100#13063324—22no—
101#13063324C2314yes—
102#13063321—22no—
103#13063321C2314yes—
104#13063319—28no—
105#13063316—22no—
106#13063316C2314yes—
107#13063314—22no—
108#13063314C2314yes—
109#13063313—28no—
110#13063310—28no—
111#13063308—28no—
112#13063307—28no—
113#13063303—28no—
114#13063301—22no—
115#13063301C2314yes—
116#13063300—22no—
117#13063300—22no—
118#13063300C2314yes—
119#13063300C2314yes—
120#13063299—28no—
121#13063298—28no—
122#13063296—22no—
123#13063296C2314yes—
124C4×D172—22no—
125C4×D172—22no—
126C4×D172C2314yes—
127C4×D172C2314yes—
128#13063282D414yes—
129#13063282C2314yes—
130C2×C4⋊Dic43—21no—
131C2×C4⋊Dic43C2311yescharacteristic
132C2×C4⋊Dic43C2311yescharacteristic
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4D411yescharacteristic
137C2×Dic43⋊C4D411yescharacteristic
138C2×C22⋊Dic43—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4D411yescharacteristic
147C2×(C2×D43)⋊C4D411yescharacteristic
148C2×C4×Dic43C2311yescharacteristic
149#13063258C2314yes—
150#13063257C2314yes—
151#13063256C2314yes—
152#13063249C2314yes—
153#13063247C2314yes—
154#13063247C2314yes—
155#13063246C2314yes—
156#13063245C2314yes—
157#13063245C2314yes—
158#13063235C2314yes—
159C4×C43⋊C8C2314yes—
160C8×Dic43C2314yes—
161C22×Q8×C43C2311yescharacteristic
162C22×D4×C43C2311yescharacteristic
163C23×C4×C43—21no—
164C2×SD16×C43—24no—
165C2×SD16×C43C2314yes—
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C4×Q8×C43—22no—
169C4×Q8×C43C2314yes—
170C4×D4×C43—22no—
171C4×D4×C43C2314yes—
172C2×C4⋊C4×C43—21no—
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C22⋊C4×C43—21no—
176C2×C42×C43—21no—
177C2×C42×C43C2311yescharacteristic
178#107×C43C2314yes—
179#103×C43C2314yes—
180#102×C43C2314yes—
181#97×C43C2314yes—
182C24×C43—21no—
183C23×D43—21no—
184C23×D43—21no—
185C23×D43C2×D411yescharacteristic
186C2×Q8×C43—21no—
187C2×Q8×C43—22no—
188C2×Q8×C43—22no—
189C2×Q8×C43C2412yes—
190C2×D4×C43—21no—
191C2×D4×C43—22no—
192C2×D4×C43—22no—
193C2×D4×C43C2412yes—
194C22×C4×C43—24no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—82no—
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—24no—
203C2×C22⋊D43—24no—
204C2×C22⋊D43—24no—
205C2×C22⋊D43—82no—
206C2×C22⋊D43—82no—
207C2×C22⋊D43—82no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—24no—
216C2×D172—24no—
217C2×D172—22no—
218C2×D172—22no—
219C2×D172—22no—
220C2×D172—22no—
221C2×D172—82no—
222C2×D172—82no—
223C2×D172C2412yes—
224C2×D172C2412yes—
225C2×C4×D43—22no—
226C2×C4×D43—22no—
227C2×C4×D43—24no—
228C2×C4×D43—24no—
229C2×C4×D43—82no—
230C2×C4×D43—82no—
231C2×C4×D43C2×D412yes—
232C2×C4×D43C2412yes—
233C2×Dic86—24no—
234C2×Dic86—82no—
235SD16×C43—28no—
236C2×C8×C43—22no—
237C2×C8×C43#4114yes—
238C2×C8×C43C2412yes—
239C2×C8×C43C2412yes—
240C4⋊C4×C43—24no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43C2412yes—
244C4⋊C4×C43C2412yes—
245C22⋊C4×C43—24no—
246C42×C43—24no—
247C42×C43C2×D412yes—
248C42×C43C2412yes—
249C22⋊Dic43—24no—
250#10621884—28no—
251#10621882—28no—
252(C2×D43)⋊C4—24no—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4C2×D414yes—
260(C2×D43)⋊C4C2×D414yes—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—24no—
264C4⋊Dic43C2412yes—
265C4⋊Dic43C2412yes—
266Dic43⋊C4—24no—
267Dic43⋊C4—24no—
268Dic43⋊C4—24no—
269Dic43⋊C4C2×D414yes—
270Dic43⋊C4C2×D414yes—
271C4×Dic43C2×D412yes—
272C4×Dic43C2412yes—
273C2×C43⋊C8—22no—
274C2×C43⋊C8#4114yes—
275C2×C43⋊C8C2412yes—
276C2×C43⋊C8C2412yes—
277D344—28no—
278#10621872—28no—
279C8×D43—28no—
280C23×C43—22no—
281C23×C43—42no—
282C23×C43—42no—
283C23×C43—42no—
284C23×C43C22×D411yescharacteristic
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—22no—
289C22×D43—22no—
290C22×D43—42no—
291C22×D43—42no—
292C22×D43—42no—
293C22×D43—42no—
294C22×D43—42no—
295C22×D43—42no—
296C22×D43C22×D412yes—
297Q8×C43—22no—
298Q8×C43—22no—
299Q8×C43—42no—
300D4×C43—22no—
301D4×C43—22no—
302D4×C43—42no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—42no—
309C2×C4×C43—42no—
310C2×C4×C43—42no—
311C2×C4×C43—84no—
312C2×C4×C43C22×D412yes—
313C2×C4×C43C22×D412yes—
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C2×#4112yes—
316C2×C4×C43C2×#4112yes—
317C2×C4×C43C2511yescharacteristic
318C22⋊D43—84no—
319C22⋊D43—84no—
320C22⋊D43—84no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43C22×D412yes—
329C2×Dic43C22×D412yes—
330C2×Dic43C22×D412yes—
331D172—22no—
332D172—22no—
333D172—22no—
334D172—22no—
335D172—42no—
336D172—42no—
337D172—84no—
338D172—84no—
339C4×D43—24no—
340C4×D43—22no—
341C4×D43—22no—
342C4×D43—84no—
343C4×D43—84no—
344Dic86—84no—
345C8×C43—22no—
346C8×C43C2×#4114yes—
347C43⋊C8—22no—
348C43⋊C8C2×#4114yes—
349C2×#3179—431nomaximal, Sylow
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—84no—
354C22×C43#53212yes—
355C22×C43#57612yes—
356C22×C43#57712yes—
357C22×C43C23×D411yescharacteristic
358C2×D43—22no—
359C2×D43—22no—
360C2×D43—22no—
361C2×D43—44no—
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—42no—
365C2×D43—42no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—84no—
369C2×D43—84no—
370C4×C43—22no—
371C4×C43—22no—
372C4×C43—42no—
373C4×C43—42no—
374C4×C43—42no—
375C4×C43#53212yes—
376C4×C43C22×#4111yescharacteristic
377C4×C43C22×#4111yescharacteristic
378Dic43—22no—
379Dic43—22no—
380Dic43—22no—
381Dic43—42no—
382Dic43—42no—
383C2×#542—431no—
384C2×#540—431no—
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×#440D4311yescharacteristic, complemented
396C2×C4×SD16—431no—
397C2×C4×D8—431no—
398C2×#405—431no—
399C2×C43—82no—
400C2×C43#317914yescomplemented
401C2×C43C2×#53211yescharacteristic
402C2×C43C2×#57611yescharacteristic
403C2×C43C2×#57711yescharacteristic
404D43—42no—
405D43—82no—
406D43—82no—
407C22×SD16—431no—
408C22×SD16C2×D4311yescharacteristic
409C22×D8—431no—
410C22×D8—431no—
411C22×M16—431no—
412C23×C8—431no—
413#542—438no—
414#542—864no—
415#540—438no—
416#540—864no—
417C2×C4⋊Q8—431no—
418C2×#127—431no—
419C2×#126—861no—
420C2×#125—431no—
421C2×#124—431no—
422C2×#124—861no—
423C2×#123—861no—
424C2×#123—861no—
425C2×#123—861no—
426C2×C22⋊Q8—431no—
427C2×C22⋊Q8—861no—
428C2×#121—431no—
429C2×#121—431no—
430C2×#121—431no—
431C2×#121—861no—
432C2×#121—861no—
433C2×C4×Q8C2×D4311yescharacteristic
434C2×C4×D4—431no—
435C2×C4×D4—431no—
436C2×C4×D4C2×D4311yescharacteristic
437C2×#117—431no—
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#440C2×D4318yescomplemented
448C4×SD16—438no—
449C4×D8—438no—
450C2×#107—431no—
451C2×#107C2×D4311yescharacteristic
452C2×#106—431no—
453C2×#106—431no—
454C2×#103—431no—
455C2×#103C2×D4311yescharacteristic
456C2×#102—431no—
457C2×#102—431no—
458C2×#102—431no—
459C2×#102—431no—
460C2×#102—431no—
461C2×#102C2×D4311yescharacteristic
462#405—438no—
463C2×#97—431no—
464C2×#97C2×D4311yescharacteristic
465C2×C4×C8—431no—
466C2×C4×C8—431no—
467C43C2×#317911yescharacteristic, complemented, Sylow
468C22×Q8—861no—
469C22×Q8C22×D4311yescharacteristic
470C22×D4—431no—
471C22×D4—431no—
472C22×D4—861no—
473C22×D4—861no—
474C22×D4—861no—
475C22×D4—861no—
476C22×D4—861no—
477C22×D4C22×D4311yescharacteristic
478C23×C4—21no—
479C23×C4—431no—
480C23×C4—861no—
481C23×C4—861no—
482C2×SD16—24no—
483C2×SD16—434no—
484C2×SD16—864no—
485C2×SD16C22×D4314yes—
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—434no—
495C22×C8—864no—
496C22×C8C22×D4311yescharacteristic
497C22×C8C22×D4311yescharacteristic
498C4⋊Q8—434no—
499C4⋊Q8—862no—
500#127—434no—
501#127—862no—
502#126—868no—
503#125—434no—
504#125—862no—
505#124—434no—
506#124—868no—
507#124—862no—
508#123—868no—
509#123—868no—
510#123—868no—
511C22⋊Q8—434no—
512C22⋊Q8—868no—
513C22⋊Q8—862no—
514#121—434no—
515#121—434no—
516#121—434no—
517#121—868no—
518#121—868no—
519#121—862no—
520#121—862no—
521#121—862no—
522C4×Q8—22no—
523C4×Q8C22×D4314yes—
524C4×D4—22no—
525C4×D4—434no—
526C4×D4—434no—
527C4×D4—862no—
528C4×D4—862no—
529C4×D4C22×D4314yes—
530#117—434no—
531#117—434no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—431no—
534C2×C4⋊C4—431no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—861no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4C22×D4311yescharacteristic
542C2×C4⋊C4C22×D4311yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—431no—
545C2×C22⋊C4—431no—
546C2×C22⋊C4—861no—
547C2×C22⋊C4—861no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C42—21no—
555C2×C42—431no—
556C2×C42C22×D4311yescharacteristic
557#107—434no—
558#107C22×D4314yes—
559#106—434no—
560#106—434no—
561#103—434no—
562#103C22×D4314yes—
563#102—434no—
564#102—434no—
565#102—434no—
566#102—434no—
567#102—434no—
568#102C22×D4314yes—
569#97—434no—
570#97C22×D4314yes—
571C4×C8—434no—
572C4×C8—434no—
573C24—21no—
574C24—431no—
575C24—861no—
576C24—861no—
577C2×Q8—21no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—864no—
581C2×Q8—3442no—
582C2×Q8C23×D4312yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—432no—
587C2×D4—432no—
588C2×D4—864no—
589C2×D4—864no—
590C2×D4—864no—
591C2×D4—864no—
592C2×D4—864no—
593C2×D4—861no—
594C2×D4—861no—
595C2×D4—862no—
596C2×D4—862no—
597C2×D4—862no—
598C2×D4—862no—
599C2×D4—3442no—
600C2×D4—3442no—
601C2×D4—3442no—
602C2×D4—3442no—
603C2×D4—3442no—
604C2×D4C23×D4312yes—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—24no—
609C22×C4—82no—
610C22×C4—431no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—432no—
614C22×C4—432no—
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—861no—
618C22×C4—861no—
619C22×C4—864no—
620C22×C4—864no—
621C22×C4—3442no—
622C22×C4—3442no—
623C22×C4D4×D4311yescharacteristic
624C22×C4D4×D4311yescharacteristic
625C22×C4C23×D4311yescharacteristic
626SD16—28no—
627SD16—868no—
628D8—868no—
629D8—868no—
630M16—868no—
631C2×C8—22no—
632C2×C8—434no—
633C2×C8—432no—
634C2×C8—432no—
635C2×C8—862no—
636C2×C8—868no—
637C2×C8#1062189814yes—
638C2×C8C23×D4312yes—
639C2×C8C23×D4312yes—
640C4⋊C4—24no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—434no—
644C4⋊C4—434no—
645C4⋊C4—432no—
646C4⋊C4—432no—
647C4⋊C4—864no—
648C4⋊C4—864no—
649C4⋊C4—864no—
650C4⋊C4—864no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4C23×D4312yes—
654C4⋊C4C23×D4312yes—
655C22⋊C4—24no—
656C22⋊C4—434no—
657C22⋊C4—434no—
658C22⋊C4—864no—
659C22⋊C4—864no—
660C22⋊C4—864no—
661C22⋊C4—864no—
662C22⋊C4—864no—
663C22⋊C4—864no—
664C22⋊C4—864no—
665C22⋊C4—864no—
666C42—24no—
667C42—432no—
668C42—432no—
669C42D4×D4312yes—
670C42C23×D4312yes—
671C23—22no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—432no—
676C23—862no—
677C23—862no—
678C23—862no—
679C23—862no—
680C23—862no—
681C23—1722no—
682C23—1722no—
683C23—1722no—
684C23—1722no—
685C23—1722no—
686C23—1722no—
687C23C2×D4×D4311yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—3444no—
692D4—22no—
693D4—22no—
694D4—42no—
695D4—862no—
696D4—862no—
697D4—862no—
698D4—862no—
699D4—3444no—
700D4—3444no—
701D4—3444no—
702D4—3444no—
703D4—3444no—
704D4—1722no—
705D4—1722no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—84no—
715C2×C4—432no—
716C2×C4—432no—
717C2×C4—432no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—862no—
721C2×C4—864no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—3444no—
727C2×C4—3444no—
728C2×C4—1722no—
729C2×C4—1722no—
730C2×C4C2×D4×D4312yes—
731C2×C4C2×D4×D4312yes—
732C2×C4C2×D4×D4311yescharacteristic
733C2×C4#41×D4312yes—
734C2×C4C2×#1062189812yes—
735C2×C4C24×D4311yescharacteristic
736C8—22no—
737C8—434no—
738C8—862no—
739C8C2×#1062189814yes—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—84no—
744C22—862no—
745C22—862no—
746C22—862no—
747C22—3444no—
748C22—3444no—
749C22—1722no—
750C22—1722no—
751C22—1722no—
752C22—1722no—
753C22—1722no—
754C22—1722no—
755C22—1724no—
756C22#1458344612yes—
757C22#1458370312yes—
758C22#1458370812yes—
759C22C22×D4×D4311yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—42no—
764C4—42no—
765C4—862no—
766C4—862no—
767C4—862no—
768C4—1722no—
769C4—1722no—
770C4#1458344612yes—
771C4C2×#41×D4311yescharacteristic
772C4C22×#1062189811yescharacteristic
773C2—82no—
774C2—3442no—
775C2—3442no—
776C2—1722no—
777C2#1914527614yesdirect product factor
778C2C2×#1458344611yescharacteristic
779C2C2×#1458370311yescharacteristic
780C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#440C2
socleC23×C43C22×D4
hypercenterC2×#440D43
hypocenterC43C2×#3179
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#14583521C2semidirect
2. C2×#14583500C2semidirect
3. #19145276C2direct (N × H)
4. C2×#14583307C2semidirect
5. C2×#14583285C2semidirect
6. C2×#14583255C2semidirect
7. C2×#14583244C2semidirect
8. C2×#14583151C2semidirect
9. C2×#14583148C2semidirect
10. C2×#14583136C2semidirect
11. C2×#14583125C2semidirect
12. C2×#14583012C2semidirect
13. C2×C4×#10621884C2semidirect
14. C2×C4×#10621882C2semidirect
15. C2×#14582856C2semidirect
16. C2×C43×#440C2semidirect
23. #14583521C22semidirect
25. #14583500C22semidirect
45. #14583307C22semidirect
46. #14583285C22semidirect
47. #14583255C22semidirect
48. #14583244C22semidirect
49. #14583151C22semidirect
50. #14583148C22semidirect
51. #14583136C22semidirect
52. #14583125C22semidirect
53. #14583012C22semidirect
54. C4×#10621884C22semidirect
55. C4×#10621882C22semidirect
65. #14582856C22semidirect
72. C43×#440C22semidirect
395. C2×#440D43semidirect
400. C2×C43#3179semidirect
447. #440C2×D43semidirect
467. C43C2×#3179semidirect
777. C2#19145276direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835212
C2×#145835002
#191452762
C2×#145833072
C2×#145832852
C2×#145832552
C2×#145832442
C2×#145831512
C2×#145831482
C2×#145831362
C2×#145831252
C2×#145830122
C2×C4×#106218842
C2×C4×#106218822
C2×#145828562
C2×C43×#4402
C2×#317943