Finite Group Databasebeta

← C2×#19144568 #25964441

Subgroups — C2×#19144568 #25964441

Order 11008.

2234 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583478C211yesmaximal, characteristic
2C2×#14583380C211yesmaximal, characteristic, complemented
3#19144568C2116yesmaximal, direct product factor
4C2×#14583236C211yesmaximal, characteristic, complemented
5C2×#14583234C211yesmaximal, characteristic, complemented
6C2×#14583242C211yesmaximal, characteristic, complemented
7C2×#14583241C211yesmaximal, characteristic, complemented
8C2×#14583222C211yesmaximal, characteristic, complemented
9C2×#14583220C211yesmaximal, characteristic, complemented
10C2×#14583211C211yesmaximal, characteristic, complemented
11C2×#14582940C211yesmaximal, characteristic, complemented
12C2×#107×D43C211yesmaximal, characteristic, complemented
13C2×#14582897C211yesmaximal, characteristic, complemented
14C2×#14582892C211yesmaximal, characteristic, complemented
15C2×#14582864C211yesmaximal, characteristic, complemented
16C2×C43×#480C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621900C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21#14583478—24no—
22#14583478C2218yes—
23C2×#13063305C2211yescharacteristic
24C2×#13063304C2211yescharacteristic
25C2×#13063302—21no—
26C2×#13063298—21no—
27C2×#13063297—21no—
28C2×#13063296—21no—
29C2×#13063296C2211yescharacteristic
30#14583380—24no—
31#14583380C2218yescomplemented
32C2×#13063290—21no—
33C2×#13063287—21no—
34C2×C4×C22⋊D43—21no—
35C2×C4×C22⋊D43—21no—
36C2×#13063284C2211yescharacteristic
37C2×#13063283C2211yescharacteristic
38C2×#13063283C2211yescharacteristic
39C2×C4⋊C4×D43C2211yescharacteristic
40C2×C4⋊C4×D43C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic
42#14583242C2218yescomplemented
43#14583241C2218yescomplemented
44#14583236C2218yescomplemented
45#14583234C2218yescomplemented
46#14583222C2218yescomplemented
47#14583220C2218yescomplemented
48#14583211C2218yescomplemented
49#14582940C2218yescomplemented
50C2×#13063259C2211yescharacteristic
51C2×#13063258C2211yescharacteristic
52C2×#13063258C2211yescharacteristic
53C2×#13063258C2211yescharacteristic
54#107×D43C2218yescomplemented
55C2×#13063257C2211yescharacteristic
56C2×#13063256C2211yescharacteristic
57#14582897C2218yescomplemented
58#14582892C2218yescomplemented
59C2×#13063250C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65#14582864C2218yescomplemented
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C2×#121×C43C2211yescharacteristic
70C22×C4⋊C4×C43C2211yescharacteristic
71C43×#480C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#107×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621898—24no—
78C2×#10621898—24no—
79C2×#10621898D414yes—
80C2×#10621898C2314yes—
81C2×#10621900—22no—
82C2×#10621900—24no—
83C2×#10621900—24no—
84C2×#10621900C2314yes—
85C22×Dic86D411yescharacteristic
86C22×Dic86C2311yescharacteristic
87C22×D172D411yescharacteristic
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C22×C22⋊D43D411yescharacteristic
91C22×C22⋊D43D411yescharacteristic
92C23×Dic43—21no—
93C22×C4×D43—21no—
94C22×C4×D43—21no—
95C22×C4×D43—21no—
96C22×C4×D43C2311yescharacteristic
97C22×C4×D43C2311yescharacteristic
98C2×#10621872—24no—
99C2×#10621872C2314yes—
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2311yescharacteristic
102C2×C8×D43—24no—
103C2×C8×D43C2314yes—
104#13063305—22no—
105#13063305C2314yes—
106#13063304—22no—
107#13063304C2314yes—
108#13063302—28no—
109#13063298—28no—
110#13063297—28no—
111#13063296—28no—
112#13063296—22no—
113#13063296C2314yes—
114#13063290—28no—
115#13063287—28no—
116C4×C22⋊D43—28no—
117C4×C22⋊D43—28no—
118#13063284—22no—
119#13063284C2314yes—
120#13063283—22no—
121#13063283—22no—
122#13063283C2314yes—
123#13063283C2314yes—
124C2×C4⋊Dic43—21no—
125C2×C4⋊Dic43C2311yescharacteristic
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C4⋊C4×D43—22no—
133C4⋊C4×D43—22no—
134C4⋊C4×D43—22no—
135C4⋊C4×D43C2314yes—
136C4⋊C4×D43C2314yes—
137C4⋊C4×D43C2314yes—
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43—21no—
140C2×C22⋊Dic43—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43—21no—
147#13063259C2314yes—
148#13063258C2314yes—
149#13063258C2314yes—
150#13063258C2314yes—
151#13063257C2314yes—
152#13063256C2314yes—
153#13063250C2314yes—
154#13063250C2314yes—
155#13063248C2314yes—
156#13063248C2314yes—
157#13063246C2314yes—
158#13063246C2314yes—
159C22⋊(C43⋊C8)C2314yes—
160(C2×D43)⋊C8C2314yes—
161(C2×D43)⋊C8C2314yes—
162C22×D4×C43—21no—
163C22×D4×C43C2311yescharacteristic
164C23×C4×C43—21no—
165C23×C4×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168#121×C43—22no—
169#121×C43C2314yes—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—22no—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2314yes—
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C22⋊C4×C43—21no—
177#107×C43C2314yes—
178#107×C43C2314yes—
179#102×C43C2314yes—
180#102×C43C2314yes—
181C22⋊C8×C43C2314yes—
182C24×C43—21no—
183C24×C43C2×D411yescharacteristic
184C23×D43C2×D411yescharacteristic
185C23×D43C2×D411yescharacteristic
186C2×D4×C43—21no—
187C2×D4×C43—24no—
188C2×D4×C43—22no—
189C2×D4×C43—22no—
190C2×D4×C43—82no—
191C2×D4×C43C2412yes—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—24no—
198C22×C4×C43—82no—
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D412yes—
201C22×C4×C43C2412yes—
202C22×C4×C43C2411yescharacteristic
203C2×C22⋊D43—24no—
204C2×C22⋊D43—24no—
205C2×C22⋊D43—24no—
206C2×C22⋊D43—24no—
207C2×C22⋊D43—44no—
208C2×C22⋊D43—82no—
209C2×C22⋊D43C2×D414yes—
210C2×C22⋊D43C2×D414yes—
211C22×Dic43—24no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—44no—
217C22×Dic43C2×D411yescharacteristic
218C22×Dic43C2×D411yescharacteristic
219#10621900—28no—
220#10621900—28no—
221#10621900—48no—
222#10621898—216no—
223#10621898—28no—
224#10621898—28no—
225C2×D172—24no—
226C2×D172C2×D414yes—
227C2×C4×D43—22no—
228C2×C4×D43—22no—
229C2×C4×D43—24no—
230C2×C4×D43—24no—
231C2×C4×D43—24no—
232C2×C4×D43—82no—
233C2×C4×D43—82no—
234C2×C4×D43—82no—
235C2×C4×D43C2×D412yes—
236C2×C4×D43C2×D412yes—
237C2×C4×D43#4114yes—
238C2×C4×D43#4114yes—
239C2×C4×D43C2412yes—
240C2×C4×D43C2412yes—
241C2×Dic86—24no—
242C2×Dic86—22no—
243C2×Dic86—22no—
244C2×Dic86—21no—
245C2×Dic86C2×D414yes—
246C2×Dic86C2412yes—
247C2×C8×C43—22no—
248C2×C8×C43—22no—
249C2×C8×C43C2412yes—
250C2×C8×C43C2412yes—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—24no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43C2412yes—
256C4⋊C4×C43C2412yes—
257C4⋊C4×C43C2412yes—
258C22⋊C4×C43—24no—
259C22⋊Dic43—24no—
260C22⋊Dic43—24no—
261C22⋊Dic43—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4—24no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—24no—
269C4⋊Dic43C2412yes—
270C4⋊Dic43C2412yes—
271C4⋊Dic43C2412yes—
272Dic43⋊C4—24no—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275Dic43⋊C4—24no—
276C4×Dic43—24no—
277C4×Dic43—24no—
278C4×Dic43—24no—
279C2×C43⋊C8—22no—
280C2×C43⋊C8—22no—
281C2×C43⋊C8C2412yes—
282C2×C43⋊C8C2412yes—
283#10621872—28no—
284C8×D43—28no—
285C23×C43—22no—
286C23×C43—22no—
287C23×C43—22no—
288C23×C43—22no—
289C23×C43—42no—
290C23×C43—42no—
291C23×C43—42no—
292C23×C43C22×D412yes—
293C23×C43C22×D411yescharacteristic
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43#12314yes—
300C22×D43C22×D412yes—
301C22×D43C22×D412yes—
302D4×C43—22no—
303D4×C43—22no—
304D4×C43—42no—
305D4×C43—84no—
306C2×C4×C43—22no—
307C2×C4×C43—24no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—42no—
314C2×C4×C43—42no—
315C2×C4×C43—42no—
316C2×C4×C43—84no—
317C2×C4×C43C22×D412yes—
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C2×#4112yes—
320C2×C4×C43C2×#4112yes—
321C2×C4×C43C2511yescharacteristic
322C22⋊D43—28no—
323C22⋊D43—28no—
324C22⋊D43—48no—
325C22⋊D43—84no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—42no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43—42no—
335C2×Dic43—48no—
336C2×Dic43#12314yes—
337C2×Dic43C22×D412yes—
338C2×Dic43C22×D412yes—
339D172—28no—
340C4×D43—24no—
341C4×D43—22no—
342C4×D43—22no—
343C4×D43—84no—
344C4×D43—84no—
345C4×D43—84no—
346C4×D43#12318yes—
347C4×D43C2×#4114yes—
348C4×D43C2×#4114yes—
349Dic86—28no—
350Dic86—22no—
351Dic86—22no—
352Dic86—42no—
353C8×C43—22no—
354C8×C43—22no—
355C43⋊C8—22no—
356C43⋊C8—22no—
357C2×#3098—431nomaximal, Sylow
358C22×C43—22no—
359C22×C43—22no—
360C22×C43—22no—
361C22×C43—44no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—84no—
366C22×C43C2×#12312yes—
367C22×C43#57612yes—
368C22×C43#57812yes—
369C22×C43C23×D411yescharacteristic
370C2×D43—28no—
371C2×D43—22no—
372C2×D43—22no—
373C2×D43—22no—
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—44no—
377C2×D43C2×#12314yes—
378C4×C43—22no—
379C4×C43—42no—
380C4×C43—42no—
381C4×C43—42no—
382C4×C43C2×#12312yes—
383C4×C43C22×#4111yescharacteristic
384C4×C43C22×#4111yescharacteristic
385Dic43—22no—
386Dic43—42no—
387Dic43—42no—
388Dic43—42no—
389Dic43—42no—
390Dic43C2×#12314yes—
391C2×#537—431no—
392C2×#520—431no—
393#3098—4316no—
394C2×#484—431no—
395C2×#484—431no—
396C2×#485—431no—
397C2×#485—431no—
398C2×#482—431no—
399C2×#482—431no—
400C2×#480—431no—
401C2×#480D4311yescharacteristic, complemented
402C2×#428—431no—
403C22×#107—431no—
404C2×#417—431no—
405C2×#416—431no—
406C2×#408—431no—
407C2×C43—42no—
408C2×C43—82no—
409C2×C43#309814yescomplemented
410C2×C43C22×#12311yescharacteristic
411C2×C43C2×#57611yescharacteristic
412C2×C43C2×#57811yescharacteristic
413D43—24no—
414D43—42no—
415C22×#41—431no—
416C22×#41—431no—
417C22×M16—431no—
418C23×C8—431no—
419#537—438no—
420#537—864no—
421C2×C22⋊Q8—431no—
422C2×C22⋊Q8—431no—
423C2×C22⋊Q8—861no—
424C2×#121—431no—
425C2×#121—861no—
426C2×#121—861no—
427C2×#121—861no—
428C2×#121C2×D4311yescharacteristic
429#520—438no—
430#520—864no—
431C2×C4×Q8—861no—
432C2×C4×D4—861no—
433C2×C4×D4—861no—
434C2×C4×D4—861no—
435C2×#117—431no—
436C2×#117—431no—
437C2×#117—431no—
438C22×C4⋊C4—431no—
439C22×C4⋊C4—431no—
440C22×C4⋊C4—431no—
441C22×C4⋊C4C2×D4311yescharacteristic
442#485—438no—
443#485—438no—
444#484—438no—
445#484—438no—
446#482—438no—
447#482—438no—
448#480—438no—
449#480C2×D4318yescomplemented
450#428—438no—
451C2×#107—431no—
452C2×#107—431no—
453C2×#107—431no—
454C2×#107—431no—
455C2×#107—438no—
456C2×#107C2×D4311yescharacteristic
457C2×#107C2×D4311yescharacteristic
458C2×#106—431no—
459C2×#106—431no—
460#417—438no—
461#416—438no—
462C2×#103—431no—
463C2×#103—431no—
464C2×#103—431no—
465C2×#103—431no—
466C2×#102—431no—
467C2×#102—431no—
468C2×#102C2×D4311yescharacteristic
469C2×#102C2×D4311yescharacteristic
470#408—438no—
471C2×C22⋊C8—431no—
472C2×C22⋊C8—431no—
473C2×C22⋊C8—431no—
474C2×C22⋊C8C2×D4311yescharacteristic
475C43C2×#309811yescharacteristic, complemented, Sylow
476C2×#41—434no—
477C2×#41—434no—
478C2×#41—434no—
479C2×#41—864no—
480C2×#41—864no—
481C2×#41—862no—
482C2×#41—864no—
483C2×#41—864no—
484C22×Q8—431no—
485C22×Q8—431no—
486C22×D4—21no—
487C22×D4—431no—
488C22×D4—431no—
489C22×D4—431no—
490C22×D4—861no—
491C22×D4—861no—
492C22×D4C22×D4311yescharacteristic
493C23×C4—21no—
494C23×C4—431no—
495C23×C4—431no—
496C23×C4—861no—
497C23×C4—861no—
498C23×C4—861no—
499C23×C4—861no—
500C23×C4C22×D4311yescharacteristic
501C2×M16—434no—
502C2×M16—864no—
503C22×C8—431no—
504C22×C8—431no—
505C22×C8—434no—
506C22×C8—864no—
507C22×C8C22×D4311yescharacteristic
508C22×C8C22×D4311yescharacteristic
509C22⋊Q8—434no—
510C22⋊Q8—434no—
511C22⋊Q8—868no—
512C22⋊Q8—862no—
513C22⋊Q8—862no—
514#121—22no—
515#121—434no—
516#121—868no—
517#121—862no—
518#121—868no—
519#121—868no—
520#121C22×D4314yes—
521C4×Q8—868no—
522C4×D4—868no—
523C4×D4—868no—
524C4×D4—868no—
525#117—434no—
526#117—434no—
527#117—434no—
528#117—862no—
529#117—862no—
530#117—862no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—431no—
534C2×C4⋊C4—431no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—434no—
537C2×C4⋊C4—434no—
538C2×C4⋊C4—434no—
539C2×C4⋊C4—862no—
540C2×C4⋊C4—862no—
541C2×C4⋊C4—862no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4—861no—
545C2×C4⋊C4—861no—
546C2×C4⋊C4—861no—
547C2×C4⋊C4C22×D4311yescharacteristic
548C2×C4⋊C4C22×D4311yescharacteristic
549C2×C4⋊C4C22×D4311yescharacteristic
550C2×C4⋊C4C22×D4314yes—
551C2×C22⋊C4—21no—
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—861no—
559C2×C42—861no—
560C2×C42—861no—
561#107—434no—
562#107—434no—
563#107—434no—
564#107—434no—
565#107C22×D4314yes—
566#107C22×D4314yes—
567#106—434no—
568#106—434no—
569#103—434no—
570#103—434no—
571#103—434no—
572#103—434no—
573#102—434no—
574#102—434no—
575#102C22×D4314yes—
576#102C22×D4314yes—
577C22⋊C8—434no—
578C22⋊C8—434no—
579C22⋊C8—434no—
580C22⋊C8C22×D4314yes—
581C24—21no—
582C24—431no—
583C24—431no—
584C24D4×D4311yescharacteristic
585#41—8616no—
586#41—868no—
587#41—868no—
588#41—868no—
589#41—868no—
590#41—1728no—
591C2×Q8—434no—
592C2×Q8—432no—
593C2×Q8—864no—
594C2×Q8—861no—
595C2×Q8—862no—
596C2×Q8—862no—
597C2×D4—24no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—82no—
602C2×D4—434no—
603C2×D4—434no—
604C2×D4—434no—
605C2×D4—864no—
606C2×D4—864no—
607C2×D4—864no—
608C2×D4—864no—
609C2×D4—864no—
610C2×D4—3442no—
611C2×D4—1724no—
612C2×D4C23×D4312yes—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—24no—
619C22×C4—82no—
620C22×C4—431no—
621C22×C4—432no—
622C22×C4—434no—
623C22×C4—434no—
624C22×C4—432no—
625C22×C4—431no—
626C22×C4—432no—
627C22×C4—432no—
628C22×C4—864no—
629C22×C4—864no—
630C22×C4—864no—
631C22×C4—864no—
632C22×C4—862no—
633C22×C4—862no—
634C22×C4—861no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—3442no—
639C22×C4—3442no—
640C22×C4—3442no—
641C22×C4—1724no—
642C22×C4D4×D4312yes—
643C22×C4D4×D4311yescharacteristic
644C22×C4C23×D4312yes—
645C22×C4C23×D4311yescharacteristic
646M16—868no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—432no—
650C2×C8—432no—
651C2×C8—868no—
652C2×C8—862no—
653C2×C8—862no—
654C2×C8C23×D4312yes—
655C2×C8C23×D4312yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—24no—
659C4⋊C4—21no—
660C4⋊C4—432no—
661C4⋊C4—432no—
662C4⋊C4—432no—
663C4⋊C4—864no—
664C4⋊C4—864no—
665C4⋊C4—864no—
666C4⋊C4—864no—
667C4⋊C4—861no—
668C4⋊C4—861no—
669C4⋊C4—861no—
670C4⋊C4—864no—
671C4⋊C4C23×D4312yes—
672C4⋊C4C23×D4312yes—
673C4⋊C4C23×D4312yes—
674C22⋊C4—24no—
675C22⋊C4—864no—
676C22⋊C4—864no—
677C22⋊C4—864no—
678C22⋊C4—864no—
679C22⋊C4—864no—
680C22⋊C4—864no—
681C42—864no—
682C42—864no—
683C42—864no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—434no—
692C23—432no—
693C23—432no—
694C23—862no—
695C23—862no—
696C23—862no—
697C23—862no—
698C23—862no—
699C23C2×D4×D4312yes—
700C23C2×D4×D4311yescharacteristic
701Q8—868no—
702Q8—862no—
703Q8—862no—
704Q8—1722no—
705D4—22no—
706D4—22no—
707D4—42no—
708D4—84no—
709D4—868no—
710D4—868no—
711D4—868no—
712D4—3444no—
713D4—1728no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—84no—
725C2×C4—434no—
726C2×C4—432no—
727C2×C4—438no—
728C2×C4—434no—
729C2×C4—434no—
730C2×C4—432no—
731C2×C4—862no—
732C2×C4—864no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—3444no—
740C2×C4—3444no—
741C2×C4—3444no—
742C2×C4—1728no—
743C2×C4—1722no—
744C2×C4—1722no—
745C2×C4—1722no—
746C2×C4—1722no—
747C2×C4C2×D4×D4312yes—
748C2×C4C2×D4×D4311yescharacteristic
749C2×C4#41×D4312yes—
750C2×C4#41×D4312yes—
751C2×C4C24×D4311yescharacteristic
752C8—22no—
753C8—22no—
754C8—862no—
755C8—862no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—44no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—84no—
764C22—434no—
765C22—862no—
766C22—862no—
767C22—868no—
768C22—862no—
769C22—862no—
770C22—862no—
771C22—1724no—
772C22#123×D4312yes—
773C22#1458370012yes—
774C22#1458371512yes—
775C22C22×D4×D4311yescharacteristic
776C4—22no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—434no—
781C4—862no—
782C4—1722no—
783C4—1722no—
784C4—1722no—
785C4—1722no—
786C4#123×D4312yes—
787C4C2×#41×D4311yescharacteristic
788C4C2×#41×D4311yescharacteristic
789C2—42no—
790C2—82no—
791C2—864no—
792C2—1722no—
793C2#1914456814yesdirect product factor
794C2C2×#123×D4311yescharacteristic
795C2C2×#1458370011yescharacteristic
796C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#480C2
socleC23×C43C22×D4
prime radicalC2×#14583478C2
hypercenterC2×#480D43
hypocenterC43C2×#3098
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. C2×#14583380C2semidirect
3. #19144568C2direct (N × H)
4. C2×#14583236C2semidirect
5. C2×#14583234C2semidirect
6. C2×#14583242C2semidirect
7. C2×#14583241C2semidirect
8. C2×#14583222C2semidirect
9. C2×#14583220C2semidirect
10. C2×#14583211C2semidirect
11. C2×#14582940C2semidirect
12. C2×#107×D43C2semidirect
13. C2×#14582897C2semidirect
14. C2×#14582892C2semidirect
15. C2×#14582864C2semidirect
16. C2×C43×#480C2semidirect
31. #14583380C22semidirect
42. #14583242C22semidirect
43. #14583241C22semidirect
44. #14583236C22semidirect
45. #14583234C22semidirect
46. #14583222C22semidirect
47. #14583220C22semidirect
48. #14583211C22semidirect
49. #14582940C22semidirect
54. #107×D43C22semidirect
57. #14582897C22semidirect
58. #14582892C22semidirect
65. #14582864C22semidirect
71. C43×#480C22semidirect
401. C2×#480D43semidirect
409. C2×C43#3098semidirect
449. #480C2×D43semidirect
475. C43C2×#3098semidirect
793. C2#19144568direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834782
C2×#145833802
#191445682
C2×#145832362
C2×#145832342
C2×#145832422
C2×#145832412
C2×#145832222
C2×#145832202
C2×#145832112
C2×#145829402
C2×#107×D432
C2×#145828972
C2×#145828922
C2×#145828642
C2×C43×#4802
C2×#309843