Finite Group Databasebeta

← C2×#19146489 #25973011

Subgroups — C2×#19146489 #25973011

Order 11008.

2146 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×#14583590C211yesmaximal, characteristic, complemented
2C2×#14583557C211yesmaximal, characteristic
3#19146489C2116yesmaximal, direct product factor
4C2×#14583253C211yesmaximal, characteristic, complemented
5C2×#14583238C211yesmaximal, characteristic, complemented
6C2×#14583211C211yesmaximal, characteristic, complemented
7C2×#14583207C211yesmaximal, characteristic, complemented
8C2×#14583137C211yesmaximal, characteristic, complemented
9C2×#14583125C211yesmaximal, characteristic, complemented
10C2×#14583058C211yesmaximal, characteristic, complemented
11C2×#14583053C211yesmaximal, characteristic, complemented
12C2×C4×#10621885C211yesmaximal, characteristic, complemented
13C2×#14582964C211yesmaximal, characteristic, complemented
14C2×#14582892C211yesmaximal, characteristic, complemented
15C2×#103×D43C211yesmaximal, characteristic, complemented
16C2×C43×#464C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21C22×C8×D43C2211yescharacteristic
22#14583590—24no—
23#14583590C2218yescomplemented
24#14583557—24no—
25#14583557C2218yes—
26C2×#13063319—21no—
27C2×#13063317C2211yescharacteristic
28C2×#13063315—21no—
29C2×#13063311—21no—
30C2×#13063310—21no—
31C2×#13063302—21no—
32C2×#13063301C2211yescharacteristic
33C2×#13063301C2211yescharacteristic
34C2×#13063301C2211yescharacteristic
35C2×#13063298—21no—
36C2×#13063296C2211yescharacteristic
37C2×C4×Dic86C2211yescharacteristic
38C2×C4×D172C2211yescharacteristic
39C2×(C22⋊D43)⋊C4—21no—
40C2×#13063283C2211yescharacteristic
41C2×#13063282—21no—
42C2×C4⋊C4×D43C2211yescharacteristic
43#14583253C2218yescomplemented
44#14583238C2218yescomplemented
45#14583211C2218yescomplemented
46#14583207C2218yescomplemented
47#14583137C2218yescomplemented
48#14583125C2218yescomplemented
49#14583058C2218yescomplemented
50#14583053C2218yescomplemented
51C4×#10621885C2218yescomplemented
52#14582964C2218yescomplemented
53C2×#13063259C2211yescharacteristic
54C2×#13063258C2211yescharacteristic
55C2×#13063257C2211yescharacteristic
56#14582892C2218yescomplemented
57C2×#13063250C2211yescharacteristic
58C2×#13063250C2211yescharacteristic
59C2×#13063249C2211yescharacteristic
60C2×#13063249C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63#103×D43C2218yescomplemented
64C2×#13063246C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C4×C43⋊C8C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C2×#124×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C43×#464C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C2×#10621900—22no—
78C2×#10621900—24no—
79C2×#10621900—42no—
80C2×#10621900C2314yes—
81C22×Dic86—21no—
82C22×Dic86C2311yescharacteristic
83C2×Q8×D43—22no—
84C2×Q8×D43—24no—
85C2×Q8×D43—42no—
86C2×Q8×D43C2314yes—
87C22×D172D411yescharacteristic
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C23×Dic43—21no—
91C22×C4×D43—21no—
92C22×C4×D43—21no—
93C22×C4×D43C2311yescharacteristic
94C22×C4×D43C2311yescharacteristic
95C2×#10621885—24no—
96C2×#10621885C2314yes—
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99C2×C8×D43—42no—
100C2×C8×D43—42no—
101C2×C8×D43C2314yes—
102C2×C8×D43C2314yes—
103#13063319—28no—
104#13063317—22no—
105#13063317C2314yes—
106#13063315—28no—
107#13063311—28no—
108#13063310—28no—
109#13063302—28no—
110#13063301—22no—
111#13063301—22no—
112#13063301—22no—
113#13063301C2314yes—
114#13063301C2314yes—
115#13063301C2314yes—
116#13063298—28no—
117#13063296—22no—
118#13063296C2314yes—
119C4×Dic86—22no—
120C4×Dic86C2314yes—
121C4×D172D414yes—
122C4×D172C2314yes—
123(C22⋊D43)⋊C4—28no—
124#13063283—22no—
125#13063283C2314yes—
126#13063282—28no—
127C2×C4⋊Dic43D411yescharacteristic
128C2×C4⋊Dic43C2311yescharacteristic
129C2×C4⋊Dic43C2311yescharacteristic
130C2×C4⋊Dic43C2311yescharacteristic
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C4⋊C4×D43—22no—
139C4⋊C4×D43C2314yes—
140C2×C22⋊Dic43—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4D411yescharacteristic
146C2×(C2×D43)⋊C4D411yescharacteristic
147C2×C4×Dic43—21no—
148C2×C4×Dic43—21no—
149#13063259C2314yes—
150#13063258C2314yes—
151#13063257C2314yes—
152#13063250C2314yes—
153#13063250C2314yes—
154#13063249C2314yes—
155#13063249C2314yes—
156#13063249C2314yes—
157#13063248C2314yes—
158#13063246C2314yes—
159#13063246C2314yes—
160(C2×D43)⋊C8C2314yes—
161(C2×D43)⋊C8C2314yes—
162C4×C43⋊C8C2314yes—
163C22×Q8×C43C2311yescharacteristic
164C22×Q8×C43C2311yescharacteristic
165C22×D4×C43C2311yescharacteristic
166C2×Q16×C43—42no—
167C2×Q16×C43C2314yes—
168C2×SD16×C43—42no—
169C2×SD16×C43C2314yes—
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172#124×C43—22no—
173#124×C43C2314yes—
174C4×Q8×C43—22no—
175C4×Q8×C43C2314yes—
176C2×C4⋊C4×C43—21no—
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C42×C43—21no—
181C2×C42×C43C2311yescharacteristic
182C4⋊C8×C43C2314yes—
183#103×C43C2314yes—
184#102×C43C2314yes—
185C24×C43—21no—
186C23×D43C2×D411yescharacteristic
187C23×D43C2×D411yescharacteristic
188C2×Q8×C43—21no—
189C2×Q8×C43—21no—
190C2×Q8×C43—22no—
191C2×Q8×C43—22no—
192C2×Q8×C43—22no—
193C2×Q8×C43—22no—
194C2×Q8×C43C2412yes—
195C2×Q8×C43C2412yes—
196C2×D4×C43—21no—
197C2×D4×C43—22no—
198C2×D4×C43—22no—
199C2×D4×C43C2412yes—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2411yescharacteristic
206C2×C22⋊D43—24no—
207C2×C22⋊D43—24no—
208C2×C22⋊D43—44no—
209C2×C22⋊D43—44no—
210C22×Dic43—24no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—44no—
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218Q8×D43—28no—
219Q8×D43—44no—
220Q8×D43—48no—
221#10621900—28no—
222#10621900—44no—
223#10621900—48no—
224C2×D172—24no—
225C2×D172C2×D414yes—
226C2×C4×D43—22no—
227C2×C4×D43—22no—
228C2×C4×D43—22no—
229C2×C4×D43—22no—
230C2×C4×D43—24no—
231C2×C4×D43—24no—
232C2×C4×D43—44no—
233C2×C4×D43—44no—
234C2×C4×D43C2×D412yes—
235C2×C4×D43C2×D412yes—
236C2×C4×D43C2412yes—
237C2×C4×D43C2412yes—
238C2×Dic86—21no—
239C2×Dic86—22no—
240C2×Dic86—24no—
241C2×Dic86—44no—
242C2×Dic86#4114yes—
243C2×Dic86C2412yes—
244Q16×C43—44no—
245SD16×C43—44no—
246C2×C8×C43—22no—
247C2×C8×C43—22no—
248C2×C8×C43C2412yes—
249C2×C8×C43C2412yes—
250C4⋊C4×C43—24no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43C2412yes—
253C22⋊C4×C43—24no—
254C22⋊C4×C43—24no—
255C42×C43—24no—
256C42×C43C2×D412yes—
257C42×C43C2412yes—
258C22⋊Dic43—24no—
259#10621885—28no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4C2×D414yes—
265(C2×D43)⋊C4C2×D414yes—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43C2×D414yes—
270C4⋊Dic43C2412yes—
271C4⋊Dic43C2412yes—
272C4⋊Dic43C2412yes—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275Dic43⋊C4—24no—
276Dic43⋊C4—24no—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4—24no—
280C4×Dic43—24no—
281C4×Dic43—24no—
282C2×C43⋊C8—22no—
283C2×C43⋊C8—22no—
284C2×C43⋊C8C2412yes—
285C2×C43⋊C8C2412yes—
286C8×D43—44no—
287C8×D43—44no—
288C23×C43—22no—
289C23×C43—42no—
290C23×C43—42no—
291C23×C43—42no—
292C23×C43C22×D411yescharacteristic
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43#13514yes—
299C22×D43C22×D412yes—
300C22×D43C22×D412yes—
301Q8×C43—22no—
302Q8×C43—22no—
303Q8×C43—22no—
304Q8×C43—22no—
305Q8×C43—42no—
306Q8×C43—42no—
307D4×C43—22no—
308D4×C43—22no—
309D4×C43—42no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43C22×D412yes—
319C2×C4×C43C22×D412yes—
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C2×#4112yes—
322C2×C4×C43H(5,𝔽2)12yes—
323C2×C4×C43C2511yescharacteristic
324C22⋊D43—48no—
325C22⋊D43—48no—
326C2×Dic43—24no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—48no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43C22×D412yes—
338C2×Dic43C22×D412yes—
339D172—28no—
340C4×D43—24no—
341C4×D43—24no—
342C4×D43—22no—
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—22no—
346C4×D43—48no—
347C4×D43—48no—
348Dic86—24no—
349Dic86—22no—
350Dic86—48no—
351Dic86C2×#4114yes—
352C8×C43—22no—
353C8×C43—22no—
354C43⋊C8—22no—
355C43⋊C8—22no—
356C2×#3300—431nomaximal, Sylow
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—84no—
361C22×C43#54612yes—
362C22×C43C2×#13512yes—
363C22×C43#57812yes—
364C22×C43C23×D411yescharacteristic
365C2×D43—22no—
366C2×D43—28no—
367C2×D43—22no—
368C2×D43—22no—
369C2×D43—22no—
370C2×D43—22no—
371C2×D43—44no—
372C2×D43C2×#13514yes—
373C4×C43—22no—
374C4×C43—22no—
375C4×C43—42no—
376C4×C43—42no—
377C4×C43—42no—
378C4×C43#54612yes—
379C4×C43C22×#4111yescharacteristic
380C4×C43C2×H(5,𝔽2)11yescharacteristic
381Dic43—24no—
382Dic43—22no—
383Dic43—22no—
384Dic43—42no—
385Dic43—42no—
386Dic43—42no—
387C2×#552—431no—
388C2×#548—431no—
389#3300—4316no—
390C2×#488—431no—
391C2×#485—431no—
392C2×#480—431no—
393C2×#479—431no—
394C2×#467—431no—
395C2×#465—431no—
396C2×#464D4311yescharacteristic, complemented
397C2×#452—431no—
398C2×#451—431no—
399C2×C4×Q16—431no—
400C2×C8×D4—431no—
401C2×#416—431no—
402C22×#103—431no—
403C2×C43—82no—
404C2×C43#330014yescomplemented
405C2×C43C2×#54611yescharacteristic
406C2×C43C22×#13511yescharacteristic
407C2×C43C2×#57811yescharacteristic
408D43—24no—
409D43—42no—
410C22×#41—431no—
411C23×Q8—431no—
412C22×Q16—431no—
413C22×Q16C2×D4311yescharacteristic
414C22×SD16C2×D4311yescharacteristic
415C23×C8—431no—
416C23×C8—431no—
417#552—438no—
418#552—864no—
419#548—438no—
420#548—864no—
421C2×#126—861no—
422C2×#125—431no—
423C2×#125—861no—
424C2×#124—861no—
425C2×#124C2×D4311yescharacteristic
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×Q8C2×D4311yescharacteristic
435C2×C4×D4—431no—
436C2×C4×D4—861no—
437C2×#117—431no—
438C2×#117—861no—
439C22×C4⋊C4—431no—
440#488—438no—
441#485—438no—
442#480—438no—
443#479—438no—
444#467—438no—
445#465—438no—
446#464C2×D4318yescomplemented
447#452—438no—
448#451—438no—
449C4×Q16—438no—
450C8×D4—438no—
451C2×#107—431no—
452C2×#107—431no—
453C2×#106—431no—
454C2×C4⋊C8C2×D4311yescharacteristic
455#416—438no—
456C2×#103—431no—
457C2×#103—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#103—431no—
461C2×#103—431no—
462C2×#103—438no—
463C2×#103C2×D4311yescharacteristic
464C2×#102—431no—
465C2×#102—431no—
466C2×#102C2×D4311yescharacteristic
467C2×C22⋊C8—431no—
468C2×C22⋊C8—431no—
469C2×C4×C8—431no—
470C43C2×#330011yescharacteristic, complemented, Sylow
471C2×#41—434no—
472C2×#41—862no—
473C2×#41—864no—
474C2×#41—1722no—
475C22×Q8—434no—
476C22×Q8—431no—
477C22×Q8—861no—
478C22×Q8—862no—
479C22×Q8—864no—
480C22×Q8—1722no—
481C22×Q8C22×D4311yescharacteristic
482C22×Q8C22×D4311yescharacteristic
483C22×D4—431no—
484C22×D4—861no—
485C22×D4—861no—
486C22×D4C22×D4311yescharacteristic
487C23×C4—431no—
488C23×C4—431no—
489C23×C4—861no—
490C23×C4—861no—
491C23×C4—861no—
492C2×Q16—42no—
493C2×Q16—434no—
494C2×Q16—864no—
495C2×Q16C22×D4314yes—
496C2×SD16—42no—
497C2×SD16C22×D4314yes—
498C22×C8—431no—
499C22×C8—431no—
500C22×C8—434no—
501C22×C8—434no—
502C22×C8—1722no—
503C22×C8—1722no—
504C22×C8C22×D4311yescharacteristic
505C22×C8C22×D4311yescharacteristic
506#126—868no—
507#125—434no—
508#125—868no—
509#125—862no—
510#124—22no—
511#124—868no—
512#124C22×D4314yes—
513#123—868no—
514C22⋊Q8—434no—
515C22⋊Q8—434no—
516C22⋊Q8—434no—
517C22⋊Q8—868no—
518C22⋊Q8—862no—
519C22⋊Q8—862no—
520C22⋊Q8—862no—
521#121—434no—
522#121—868no—
523#121—862no—
524C4×Q8—22no—
525C4×Q8—434no—
526C4×Q8—862no—
527C4×Q8C22×D4314yes—
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—431no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—434no—
540C2×C4⋊C4—862no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4—861no—
545C2×C4⋊C4—861no—
546C2×C4⋊C4—861no—
547C2×C4⋊C4—861no—
548C2×C4⋊C4C22×D4311yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—431no—
552C2×C22⋊C4—431no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C42—21no—
559C2×C42—861no—
560C2×C42—861no—
561C2×C42C22×D4311yescharacteristic
562#107—434no—
563#107—434no—
564#106—434no—
565C4⋊C8C22×D4314yes—
566#103—434no—
567#103—434no—
568#103—434no—
569#103—434no—
570#103—434no—
571#103—434no—
572#103C22×D4314yes—
573#102—434no—
574#102—434no—
575#102C22×D4314yes—
576C22⋊C8—434no—
577C22⋊C8—434no—
578C4×C8—434no—
579C24—21no—
580C24—431no—
581C24—431no—
582#41—868no—
583#41—1724no—
584#41—1728no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—434no—
592C2×Q8—432no—
593C2×Q8—864no—
594C2×Q8—861no—
595C2×Q8—862no—
596C2×Q8—868no—
597C2×Q8—1724no—
598C2×Q8—1724no—
599C2×Q8—1728no—
600C2×Q8C23×D4312yes—
601C2×Q8C23×D4312yes—
602C2×D4—21no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—434no—
606C2×D4—864no—
607C2×D4—864no—
608C2×D4—864no—
609C2×D4—1724no—
610C2×D4—1724no—
611C2×D4C23×D4312yes—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—432no—
618C22×C4—432no—
619C22×C4—432no—
620C22×C4—432no—
621C22×C4—864no—
622C22×C4—864no—
623C22×C4—864no—
624C22×C4—861no—
625C22×C4—862no—
626C22×C4—862no—
627C22×C4—862no—
628C22×C4—862no—
629C22×C4—861no—
630C22×C4—861no—
631C22×C4—861no—
632C22×C4—1724no—
633C22×C4—1724no—
634C22×C4—1724no—
635C22×C4D4×D4311yescharacteristic
636C22×C4D4×D4311yescharacteristic
637C22×C4C23×D4311yescharacteristic
638Q16—44no—
639Q16—868no—
640SD16—44no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—432no—
644C2×C8—432no—
645C2×C8—862no—
646C2×C8—862no—
647C2×C8—1724no—
648C2×C8—1724no—
649C2×C8C23×D4312yes—
650C2×C8C23×D4312yes—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—434no—
654C4⋊C4—432no—
655C4⋊C4—432no—
656C4⋊C4—432no—
657C4⋊C4—864no—
658C4⋊C4—864no—
659C4⋊C4—864no—
660C4⋊C4—864no—
661C4⋊C4—861no—
662C4⋊C4—861no—
663C4⋊C4—861no—
664C4⋊C4—864no—
665C4⋊C4—864no—
666C4⋊C4—864no—
667C4⋊C4C23×D4312yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—434no—
671C22⋊C4—434no—
672C22⋊C4—864no—
673C22⋊C4—864no—
674C22⋊C4—864no—
675C22⋊C4—864no—
676C22⋊C4—864no—
677C42—24no—
678C42—864no—
679C42—864no—
680C42D4×D4312yes—
681C42C23×D4312yes—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—434no—
687C23—432no—
688C23—432no—
689C23—862no—
690C23—862no—
691C23—862no—
692C23—862no—
693C23—862no—
694C23C2×D4×D4311yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—42no—
701Q8—434no—
702Q8—862no—
703Q8—864no—
704Q8—1728no—
705D4—22no—
706D4—22no—
707D4—42no—
708D4—868no—
709D4—1728no—
710D4—1728no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—432no—
720C2×C4—432no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—864no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—864no—
730C2×C4—864no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—1728no—
735C2×C4—1728no—
736C2×C4—1728no—
737C2×C4—1722no—
738C2×C4—1722no—
739C2×C4—1722no—
740C2×C4C2×D4×D4312yes—
741C2×C4C2×D4×D4312yes—
742C2×C4C2×D4×D4311yescharacteristic
743C2×C4#41×D4312yes—
744C2×C4#1306337012yes—
745C2×C4C24×D4311yescharacteristic
746C8—22no—
747C8—22no—
748C8—862no—
749C8—862no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—84no—
754C22—434no—
755C22—862no—
756C22—862no—
757C22—868no—
758C22—862no—
759C22—862no—
760C22—862no—
761C22—1724no—
762C22#1458354612yes—
763C22#135×D4312yes—
764C22#1458371512yes—
765C22C22×D4×D4311yescharacteristic
766C4—22no—
767C4—22no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—862no—
772C4—862no—
773C4—864no—
774C4—1722no—
775C4—1722no—
776C4—1722no—
777C4#1458354612yes—
778C4C2×#41×D4311yescharacteristic
779C4C2×#1306337011yescharacteristic
780C2—82no—
781C2—864no—
782C2—1722no—
783C2#1914648914yesdirect product factor
784C2C2×#1458354611yescharacteristic
785C2C2×#135×D4311yescharacteristic
786C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
prime radicalC2×#14583557C2
hypercenterC2×#464D43
hypocenterC43C2×#3300
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#14583590C2semidirect
3. #19146489C2direct (N × H)
4. C2×#14583253C2semidirect
5. C2×#14583238C2semidirect
6. C2×#14583211C2semidirect
7. C2×#14583207C2semidirect
8. C2×#14583137C2semidirect
9. C2×#14583125C2semidirect
10. C2×#14583058C2semidirect
11. C2×#14583053C2semidirect
12. C2×C4×#10621885C2semidirect
13. C2×#14582964C2semidirect
14. C2×#14582892C2semidirect
15. C2×#103×D43C2semidirect
16. C2×C43×#464C2semidirect
23. #14583590C22semidirect
43. #14583253C22semidirect
44. #14583238C22semidirect
45. #14583211C22semidirect
46. #14583207C22semidirect
47. #14583137C22semidirect
48. #14583125C22semidirect
49. #14583058C22semidirect
50. #14583053C22semidirect
51. C4×#10621885C22semidirect
52. #14582964C22semidirect
56. #14582892C22semidirect
63. #103×D43C22semidirect
73. C43×#464C22semidirect
396. C2×#464D43semidirect
404. C2×C43#3300semidirect
446. #464C2×D43semidirect
470. C43C2×#3300semidirect
783. C2#19146489direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835902
C2×#145835572
#191464892
C2×#145832532
C2×#145832382
C2×#145832112
C2×#145832072
C2×#145831372
C2×#145831252
C2×#145830582
C2×#145830532
C2×C4×#106218852
C2×#145829642
C2×#145828922
C2×#103×D432
C2×C43×#4642
C2×#330043