Finite Group Databasebeta

← C2×#19146864 #25973467

Subgroups — C2×#19146864 #25973467

Order 11008.

2114 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583584C211yesmaximal, characteristic, complemented
2C2×#14583556C211yesmaximal, characteristic
3#19146864C2116yesmaximal, direct product factor
4C2×#14583252C211yesmaximal, characteristic, complemented
5C2×#14583234C211yesmaximal, characteristic, complemented
6C2×#14583222C211yesmaximal, characteristic, complemented
7C2×#14583204C211yesmaximal, characteristic, complemented
8C2×#14583157C211yesmaximal, characteristic, complemented
9C2×#14583144C211yesmaximal, characteristic, complemented
10C2×#14583120C211yesmaximal, characteristic, complemented
11C2×#14583061C211yesmaximal, characteristic, complemented
12C2×#14583056C211yesmaximal, characteristic, complemented
13C2×#14582991C211yesmaximal, characteristic, complemented
14C2×#14582975C211yesmaximal, characteristic, complemented
15C2×#14582906C211yesmaximal, characteristic, complemented
16C2×C43×#417C211yesmaximal, characteristic, complemented
17C22×Q8×D43C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C22×#10621872C2211yescharacteristic
22#14583584—24no—
23#14583584C2218yescomplemented
24#14583556—24no—
25#14583556C2218yes—
26C2×#13063320—21no—
27C2×#13063316C2211yescharacteristic
28C2×#13063315—21no—
29C2×#13063312—21no—
30C2×#13063312C2211yescharacteristic
31C2×#13063308—21no—
32C2×#13063305C2211yescharacteristic
33C2×#13063304—21no—
34C2×#13063304C2211yescharacteristic
35C2×#13063304C2211yescharacteristic
36C2×#13063296—21no—
37C2×#13063296C2211yescharacteristic
38C2×Q8×Dic43C2211yescharacteristic
39C2×#13063290C2211yescharacteristic
40C2×C4×C22⋊D43—21no—
41C2×C4×C22⋊D43C2211yescharacteristic
42C2×#13063284—21no—
43C2×#13063283C2211yescharacteristic
44#14583252C2218yescomplemented
45#14583234C2218yescomplemented
46#14583222C2218yescomplemented
47#14583204C2218yescomplemented
48#14583157C2218yescomplemented
49#14583144C2218yescomplemented
50#14583120C2218yescomplemented
51#14583061C2218yescomplemented
52#14583056C2218yescomplemented
53#14582991C2218yescomplemented
54#14582975C2218yescomplemented
55C2×#13063258C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063257C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59#14582906C2218yescomplemented
60C2×#13063250C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×#41×C43C2211yescharacteristic
70C22×M16×C43C2211yescharacteristic
71C22×C4⋊C4×C43C2211yescharacteristic
72C43×#417C2218yescomplemented
73C2×#103×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C22×Dic86C2311yescharacteristic
80C2×Q8×D43—22no—
81C2×Q8×D43—24no—
82C2×Q8×D43—42no—
83C2×Q8×D43C2314yes—
84C22×C22⋊D43—21no—
85C22×C22⋊D43D411yescharacteristic
86C22×C4×D43—21no—
87C22×C4×D43C2311yescharacteristic
88C2×Dic172—42no—
89C2×Dic172C2314yes—
90C2×#10621885—24no—
91C2×#10621885C2314yes—
92C2×#10621883—42no—
93C2×#10621883C2314yes—
94C2×#10621872—42no—
95C2×#10621872C2314yes—
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98#13063320—28no—
99#13063316—22no—
100#13063316C2314yes—
101#13063315—28no—
102#13063312—28no—
103#13063312—22no—
104#13063312C2314yes—
105#13063308—28no—
106#13063305—22no—
107#13063305C2314yes—
108#13063304—22no—
109#13063304—22no—
110#13063304—28no—
111#13063304C2314yes—
112#13063304C2314yes—
113#13063296—28no—
114#13063296—22no—
115#13063296C2314yes—
116Q8×Dic43—22no—
117Q8×Dic43C2314yes—
118#13063290—22no—
119#13063290C2314yes—
120C4×C22⋊D43—28no—
121C4×C22⋊D43D414yes—
122C4×C22⋊D43C2314yes—
123#13063284—28no—
124#13063283—22no—
125#13063283C2314yes—
126C2×C4⋊Dic43—21no—
127C2×C4⋊Dic43—21no—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43C2311yescharacteristic
130C2×C4⋊Dic43C2311yescharacteristic
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4D411yescharacteristic
136C2×C22⋊Dic43—21no—
137C2×C22⋊Dic43—21no—
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43—21no—
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43D411yescharacteristic
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4D411yescharacteristic
145C2×C4×Dic43—21no—
146C2×C4×Dic43—21no—
147C2×C4×Dic43—21no—
148C2×C4×Dic43C2311yescharacteristic
149#13063258C2314yes—
150#13063258C2314yes—
151#13063257C2314yes—
152Dic43⋊C8C2314yes—
153#13063250C2314yes—
154#13063250C2314yes—
155#13063249C2314yes—
156#13063248C2314yes—
157#13063248C2314yes—
158#13063246C2314yes—
159C22⋊(C43⋊C8)C2314yes—
160(C2×D43)⋊C8C2314yes—
161C8×Dic43C2314yes—
162C2×#41×C43—22no—
163C2×#41×C43—24no—
164C2×#41×C43—42no—
165C2×#41×C43C2314yes—
166C22×Q8×C43C2311yescharacteristic
167C22×D4×C43—21no—
168C22×D4×C43C2311yescharacteristic
169C23×C4×C43—21no—
170C23×C4×C43—21no—
171C23×C4×C43C2311yescharacteristic
172C2×M16×C43—42no—
173C2×M16×C43C2314yes—
174C22×C8×C43C2311yescharacteristic
175C22×C8×C43C2311yescharacteristic
176C2×C4⋊C4×C43—22no—
177C2×C4⋊C4×C43—21no—
178C2×C4⋊C4×C43C2314yes—
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C4⋊C4×C43C2311yescharacteristic
181#103×C43C2314yes—
182#103×C43C2314yes—
183#102×C43C2314yes—
184#102×C43C2314yes—
185C24×C43—21no—
186C24×C43C2×D411yescharacteristic
187C23×D43C2×D411yescharacteristic
188#41×C43—28no—
189#41×C43—44no—
190#41×C43—48no—
191C2×Q8×C43—21no—
192C2×Q8×C43—22no—
193C2×Q8×C43#4114yes—
194C2×Q8×C43C2412yes—
195C2×D4×C43—21no—
196C2×D4×C43—24no—
197C2×D4×C43—22no—
198C2×D4×C43—22no—
199C2×D4×C43—44no—
200C2×D4×C43C2412yes—
201C22×C4×C43—22no—
202C22×C4×C43—22no—
203C22×C4×C43—24no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—24no—
208C22×C4×C43—44no—
209C22×C4×C43—44no—
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D412yes—
212C22×C4×C43C2412yes—
213C22×C4×C43C2411yescharacteristic
214C2×C22⋊D43—24no—
215C2×C22⋊D43—42no—
216C2×C22⋊D43—44no—
217C2×C22⋊D43C2×D414yes—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43C2×D411yescharacteristic
223C22×Dic43C2×D411yescharacteristic
224C22×Dic43C2×D411yescharacteristic
225Q8×D43—28no—
226Q8×D43—44no—
227Q8×D43—48no—
228C2×C4×D43—22no—
229C2×C4×D43—22no—
230C2×C4×D43—24no—
231C2×C4×D43—44no—
232C2×C4×D43C2×D412yes—
233C2×C4×D43C2412yes—
234C2×Dic86—22no—
235C2×Dic86—22no—
236C2×Dic86—22no—
237C2×Dic86—22no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—24no—
241C2×Dic86—44no—
242C2×Dic86C2412yes—
243C2×Dic86C2412yes—
244M16×C43—44no—
245C2×C8×C43—22no—
246C2×C8×C43—22no—
247C2×C8×C43C2412yes—
248C2×C8×C43C2412yes—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—24no—
252C4⋊C4×C43C2412yes—
253C4⋊C4×C43C2412yes—
254C22⋊Dic43—24no—
255C22⋊Dic43—24no—
256C22⋊Dic43—24no—
257C22⋊Dic43—24no—
258C22⋊Dic43—24no—
259C22⋊Dic43C2×D414yes—
260#10621885—28no—
261#10621883—44no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4C2×D414yes—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—24no—
268C4⋊Dic43—24no—
269C4⋊Dic43—24no—
270C4⋊Dic43C2412yes—
271C4⋊Dic43C2412yes—
272Dic43⋊C4—24no—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275Dic43⋊C4—24no—
276Dic43⋊C4C2×D414yes—
277C4×Dic43—24no—
278C4×Dic43—24no—
279C4×Dic43—24no—
280C4×Dic43C2×D412yes—
281C4×Dic43C2412yes—
282C2×C43⋊C8—22no—
283C2×C43⋊C8—22no—
284C2×C43⋊C8C2412yes—
285C2×C43⋊C8C2412yes—
286Dic172—44no—
287#10621872—44no—
288C23×C43—22no—
289C23×C43—22no—
290C23×C43—22no—
291C23×C43—22no—
292C23×C43—42no—
293C23×C43—42no—
294C23×C43—42no—
295C23×C43C22×D412yes—
296C23×C43C22×D411yescharacteristic
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43C22×D412yes—
301Q8×C43—24no—
302Q8×C43—22no—
303Q8×C43C2×#4114yes—
304D4×C43—22no—
305D4×C43—22no—
306D4×C43—48no—
307D4×C43—42no—
308C2×C4×C43—24no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—24no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—48no—
317C2×C4×C43—48no—
318C2×C4×C43—42no—
319C2×C4×C43—42no—
320C2×C4×C43C22×D412yes—
321C2×C4×C43C22×D411yescharacteristic
322C2×C4×C43C2×#4112yes—
323C2×C4×C43H(5,𝔽2)12yes—
324C2×C4×C43C2511yescharacteristic
325C22⋊D43—44no—
326C22⋊D43—48no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—42no—
338C2×Dic43C22×D412yes—
339C2×Dic43C22×D412yes—
340C2×Dic43C22×D412yes—
341C4×D43—24no—
342C4×D43—22no—
343C4×D43—22no—
344C4×D43—48no—
345Dic86—22no—
346Dic86—22no—
347Dic86—22no—
348Dic86—22no—
349Dic86—48no—
350Dic86—42no—
351Dic86—42no—
352C8×C43—22no—
353C8×C43—22no—
354C43⋊C8—22no—
355C43⋊C8—22no—
356C2×#3327—431nomaximal, Sylow
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—22no—
360C22×C43—44no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—84no—
365C22×C43#54612yes—
366C22×C43#57512yes—
367C22×C43#57812yes—
368C22×C43C23×D411yescharacteristic
369C2×D43—22no—
370C2×D43—22no—
371C2×D43—22no—
372C2×D43—44no—
373C4×C43—24no—
374C4×C43—22no—
375C4×C43—42no—
376C4×C43—42no—
377C4×C43#54612yes—
378C4×C43C22×#4111yescharacteristic
379C4×C43C2×H(5,𝔽2)11yescharacteristic
380Dic43—22no—
381Dic43—22no—
382Dic43—22no—
383Dic43—42no—
384Dic43—42no—
385Dic43—42no—
386Dic43—42no—
387C2×#552—431no—
388C2×#548—431no—
389#3327—4316no—
390C2×#488—431no—
391C2×#484—431no—
392C2×#482—431no—
393C2×#479—431no—
394C2×#470—431no—
395C2×#468—431no—
396C2×#464—431no—
397C2×#452—431no—
398C2×#451—431no—
399C2×C4×Q16—431no—
400C2×#436—431no—
401C2×#417D4311yescharacteristic, complemented
402C2×#419—431no—
403C2×C43—42no—
404C2×C43—82no—
405C2×C43#332714yescomplemented
406C2×C43C2×#54611yescharacteristic
407C2×C43C2×#57511yescharacteristic
408C2×C43C2×#57811yescharacteristic
409D43—42no—
410C22×#41C2×D4311yescharacteristic
411C23×Q8—431no—
412C22×Q16—431no—
413C22×Q16—431no—
414C22×SD16—431no—
415C22×M16—431no—
416C22×M16C2×D4311yescharacteristic
417#552—438no—
418#552—864no—
419#548—438no—
420#548—864no—
421C2×#126—861no—
422C2×#125—431no—
423C2×#125—861no—
424C2×#124—431no—
425C2×#124—861no—
426C2×#123—861no—
427C2×C22⋊Q8—431no—
428C2×C22⋊Q8—431no—
429C2×C22⋊Q8—431no—
430C2×C22⋊Q8—861no—
431C2×#121—431no—
432C2×#121—861no—
433C2×C4×Q8—431no—
434C2×C4×Q8—431no—
435C2×C4×D4—431no—
436C2×C4×D4—861no—
437C2×#117—431no—
438C2×#117—861no—
439C22×C4⋊C4C2×D4311yescharacteristic
440#488—438no—
441#484—438no—
442#482—438no—
443#479—438no—
444#470—438no—
445#468—438no—
446#464—438no—
447#452—438no—
448#451—438no—
449C4×Q16—438no—
450#436—438no—
451C2×#107—431no—
452C2×#107—431no—
453C2×#106—431no—
454C2×C4⋊C8—431no—
455#419—438no—
456#417C2×D4318yescomplemented
457C2×#103—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#103—431no—
461C2×#103—431no—
462C2×#103C2×D4311yescharacteristic
463C2×#103C2×D4311yescharacteristic
464C2×#102—431no—
465C2×#102C2×D4311yescharacteristic
466C2×#102C2×D4311yescharacteristic
467C2×C22⋊C8—431no—
468C2×C22⋊C8—431no—
469C2×C4×C8—431no—
470C43C2×#332711yescharacteristic, complemented, Sylow
471C2×#41—22no—
472C2×#41—24no—
473C2×#41—42no—
474C2×#41C22×D4314yes—
475C22×Q8—434no—
476C22×Q8—431no—
477C22×Q8—431no—
478C22×Q8—861no—
479C22×Q8—862no—
480C22×Q8—864no—
481C22×Q8—1722no—
482C22×Q8C22×D4311yescharacteristic
483C22×D4—21no—
484C22×D4—431no—
485C22×D4—861no—
486C22×D4C22×D4311yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—431no—
490C23×C4—861no—
491C23×C4C22×D4311yescharacteristic
492C2×Q16—434no—
493C2×Q16—434no—
494C2×Q16—864no—
495C2×Q16—1722no—
496C2×SD16—434no—
497C2×SD16—1722no—
498C2×M16—42no—
499C2×M16—434no—
500C2×M16—1722no—
501C2×M16C22×D4314yes—
502C22×C8—431no—
503C22×C8—431no—
504C22×C8C22×D4311yescharacteristic
505C22×C8C22×D4311yescharacteristic
506#126—868no—
507#125—434no—
508#125—862no—
509#125—868no—
510#124—434no—
511#124—862no—
512#124—868no—
513#123—868no—
514C22⋊Q8—434no—
515C22⋊Q8—434no—
516C22⋊Q8—434no—
517C22⋊Q8—862no—
518C22⋊Q8—868no—
519C22⋊Q8—862no—
520C22⋊Q8—862no—
521#121—434no—
522#121—862no—
523#121—868no—
524C4×Q8—434no—
525C4×Q8—434no—
526C4×Q8—862no—
527C4×Q8—862no—
528C4×D4—434no—
529C4×D4—434no—
530C4×D4—868no—
531#117—434no—
532#117—868no—
533#117—862no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4—861no—
545C2×C4⋊C4—861no—
546C2×C4⋊C4C22×D4311yescharacteristic
547C2×C4⋊C4C22×D4311yescharacteristic
548C2×C4⋊C4C22×D4314yes—
549C2×C22⋊C4—431no—
550C2×C22⋊C4—431no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C42—431no—
559C2×C42—861no—
560C2×C42—861no—
561C2×C42—861no—
562#107—434no—
563#107—434no—
564#106—434no—
565C4⋊C8—434no—
566#103—434no—
567#103—434no—
568#103—434no—
569#103—434no—
570#103—434no—
571#103C22×D4314yes—
572#103C22×D4314yes—
573#102—434no—
574#102C22×D4314yes—
575#102C22×D4314yes—
576C22⋊C8—434no—
577C22⋊C8—434no—
578C4×C8—434no—
579C24—21no—
580C24—431no—
581C24D4×D4311yescharacteristic
582#41—28no—
583#41—44no—
584#41—48no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—432no—
588C2×Q8—432no—
589C2×Q8—864no—
590C2×Q8—861no—
591C2×Q8—861no—
592C2×Q8—868no—
593C2×Q8—862no—
594C2×Q8—862no—
595C2×Q8—862no—
596C2×Q8—862no—
597C2×Q8—1724no—
598C2×Q8—1724no—
599C2×Q8—1728no—
600C2×Q8#1062189814yes—
601C2×Q8C23×D4312yes—
602C2×D4—24no—
603C2×D4—21no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—44no—
607C2×D4—434no—
608C2×D4—864no—
609C2×D4—1722no—
610C2×D4—1724no—
611C2×D4C23×D4312yes—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—24no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—24no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—431no—
622C22×C4—431no—
623C22×C4—431no—
624C22×C4—432no—
625C22×C4—432no—
626C22×C4—864no—
627C22×C4—862no—
628C22×C4—862no—
629C22×C4—861no—
630C22×C4—861no—
631C22×C4—861no—
632C22×C4—861no—
633C22×C4—1724no—
634C22×C4D4×D4312yes—
635C22×C4D4×D4311yescharacteristic
636C22×C4C23×D4312yes—
637C22×C4C23×D4311yescharacteristic
638Q16—868no—
639Q16—1724no—
640SD16—1724no—
641M16—44no—
642M16—1724no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—432no—
646C2×C8—432no—
647C2×C8—862no—
648C2×C8—862no—
649C2×C8C23×D4312yes—
650C2×C8C23×D4312yes—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—24no—
654C4⋊C4—434no—
655C4⋊C4—432no—
656C4⋊C4—432no—
657C4⋊C4—864no—
658C4⋊C4—864no—
659C4⋊C4—864no—
660C4⋊C4—864no—
661C4⋊C4—864no—
662C4⋊C4—861no—
663C4⋊C4—861no—
664C4⋊C4—864no—
665C4⋊C4—864no—
666C4⋊C4C23×D4312yes—
667C4⋊C4C23×D4312yes—
668C22⋊C4—434no—
669C22⋊C4—434no—
670C22⋊C4—864no—
671C22⋊C4—864no—
672C22⋊C4—864no—
673C22⋊C4—864no—
674C22⋊C4—864no—
675C22⋊C4—864no—
676C22⋊C4—864no—
677C42—432no—
678C42—432no—
679C42—864no—
680C42—864no—
681C42—864no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—432no—
690C23—862no—
691C23—862no—
692C23—862no—
693C23C2×D4×D4312yes—
694C23C2×D4×D4311yescharacteristic
695Q8—22no—
696Q8—24no—
697Q8—862no—
698Q8—862no—
699Q8—862no—
700Q8—862no—
701Q8—1728no—
702Q8—1722no—
703Q8—1722no—
704Q8C2×#1062189814yes—
705D4—22no—
706D4—22no—
707D4—48no—
708D4—42no—
709D4—1724no—
710D4—1728no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—48no—
720C2×C4—48no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—432no—
724C2×C4—432no—
725C2×C4—432no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—864no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—1728no—
737C2×C4—1722no—
738C2×C4—1722no—
739C2×C4—1722no—
740C2×C4—1722no—
741C2×C4C2×D4×D4312yes—
742C2×C4C2×D4×D4311yescharacteristic
743C2×C4C2×#1062189812yes—
744C2×C4#1306337012yes—
745C2×C4C24×D4311yescharacteristic
746C8—22no—
747C8—22no—
748C8—862no—
749C8—862no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—84no—
758C22—862no—
759C22—862no—
760C22—862no—
761C22—1724no—
762C22#1458353912yes—
763C22#1458369512yes—
764C22#1458371512yes—
765C22C22×D4×D4311yescharacteristic
766C4—22no—
767C4—24no—
768C4—42no—
769C4—42no—
770C4—862no—
771C4—862no—
772C4—862no—
773C4—1722no—
774C4—1722no—
775C4—1722no—
776C4—1722no—
777C4#1458353912yes—
778C4C22×#1062189811yescharacteristic
779C4C2×#1306337011yescharacteristic
780C2—42no—
781C2—82no—
782C2—1722no—
783C2#1914686414yesdirect product factor
784C2C2×#1458353911yescharacteristic
785C2C2×#1458369511yescharacteristic
786C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#417C2
socleC23×C43C22×D4
prime radicalC2×#14583556C2
hypercenterC2×#417D43
hypocenterC43C2×#3327
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#14583584C2semidirect
3. #19146864C2direct (N × H)
4. C2×#14583252C2semidirect
5. C2×#14583234C2semidirect
6. C2×#14583222C2semidirect
7. C2×#14583204C2semidirect
8. C2×#14583157C2semidirect
9. C2×#14583144C2semidirect
10. C2×#14583120C2semidirect
11. C2×#14583061C2semidirect
12. C2×#14583056C2semidirect
13. C2×#14582991C2semidirect
14. C2×#14582975C2semidirect
15. C2×#14582906C2semidirect
16. C2×C43×#417C2semidirect
23. #14583584C22semidirect
44. #14583252C22semidirect
45. #14583234C22semidirect
46. #14583222C22semidirect
47. #14583204C22semidirect
48. #14583157C22semidirect
49. #14583144C22semidirect
50. #14583120C22semidirect
51. #14583061C22semidirect
52. #14583056C22semidirect
53. #14582991C22semidirect
54. #14582975C22semidirect
59. #14582906C22semidirect
72. C43×#417C22semidirect
401. C2×#417D43semidirect
405. C2×C43#3327semidirect
456. #417C2×D43semidirect
470. C43C2×#3327semidirect
783. C2#19146864direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835842
C2×#145835562
#191468642
C2×#145832522
C2×#145832342
C2×#145832222
C2×#145832042
C2×#145831572
C2×#145831442
C2×#145831202
C2×#145830612
C2×#145830562
C2×#145829912
C2×#145829752
C2×#145829062
C2×C43×#4172
C2×#332743