Finite Group Databasebeta

← C2×#19144711 #25964784

Subgroups — C2×#19144711 #25964784

Order 11008.

2182 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583434C211yesmaximal, characteristic, complemented
2C2×C4×#10621902C211yesmaximal, characteristic, complemented
3#19144711C2116yesmaximal, direct product factor
4C2×#14583243C211yesmaximal, characteristic, complemented
5C2×#14583226C211yesmaximal, characteristic, complemented
6C2×#14583196C211yesmaximal, characteristic, complemented
7C2×#14583121C211yesmaximal, characteristic, complemented
8C2×#14583115C211yesmaximal, characteristic, complemented
9C2×#14583064C211yesmaximal, characteristic, complemented
10C2×#14583047C211yesmaximal, characteristic
11C2×#14583010C211yesmaximal, characteristic, complemented
12C2×#14583003C211yesmaximal, characteristic, complemented
13C2×#14583002C211yesmaximal, characteristic, complemented
14C2×#14582998C211yesmaximal, characteristic, complemented
15C2×#14582955C211yesmaximal, characteristic, complemented
16C2×C43×#479C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21C22×D344C2211yescharacteristic
22#14583434—24no—
23#14583434C2218yescomplemented
24C2×#13063320—21no—
25C2×#13063313C2211yescharacteristic
26C2×#13063310—21no—
27C2×#13063305C2211yescharacteristic
28C2×#13063300C2211yescharacteristic
29C4×#10621902—24no—
30C4×#10621902C2218yescomplemented
31C2×Q8×Dic43C2211yescharacteristic
32C2×#13063290C2211yescharacteristic
33C2×C4×D172—21no—
34C2×C4×D172C2211yescharacteristic
35C2×#13063287—21no—
36C2×#13063287—21no—
37C2×#13063287C2211yescharacteristic
38C2×#13063287C2211yescharacteristic
39C2×#13063283—21no—
40C2×#13063283—21no—
41C2×#13063283C2211yescharacteristic
42C2×C42×D43—21no—
43C2×C42×D43C2211yescharacteristic
44#14583243C2218yescomplemented
45#14583226C2218yescomplemented
46#14583196C2218yescomplemented
47#14583121C2218yescomplemented
48#14583115C2218yescomplemented
49#14583064C2218yescomplemented
50#14583047C2218yes—
51#14583010C2218yescomplemented
52#14583003C2218yescomplemented
53#14583002C2218yescomplemented
54#14582998C2218yescomplemented
55#14582955C2218yescomplemented
56C2×#13063258C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×C4⋊(C43⋊C8)C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063248C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063245C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×(C2×D43)⋊C8C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C2×#125×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C43×#479C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C2×#10621902—24no—
78C2×#10621902—24no—
79C2×#10621902—22no—
80C2×#10621902C2314yes—
81C22×Dic86C2311yescharacteristic
82C22×D172—21no—
83C22×D172—21no—
84C22×D172C2311yescharacteristic
85C22×D172C2311yescharacteristic
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89C22×C4×D43—21no—
90C22×C4×D43D411yescharacteristic
91C22×C4×D43D411yescharacteristic
92C22×C4×D43C2311yescharacteristic
93C2×#10621885—24no—
94C2×#10621885C2314yes—
95C2×#10621873—24no—
96C2×#10621873C2314yes—
97C2×#10621884—24no—
98C2×#10621884C2314yes—
99C2×D344—24no—
100C2×D344C2314yes—
101C22×C43⋊C8C2311yescharacteristic
102C22×C43⋊C8C2311yescharacteristic
103#13063320—28no—
104#13063313—22no—
105#13063313C2314yes—
106#13063310—28no—
107#13063305—22no—
108#13063305C2314yes—
109#13063300—22no—
110#13063300C2314yes—
111Q8×Dic43—22no—
112Q8×Dic43C2314yes—
113#13063290—22no—
114#13063290C2314yes—
115C4×D172—28no—
116C4×D172—22no—
117C4×D172C2314yes—
118#13063287—28no—
119#13063287—28no—
120#13063287—22no—
121#13063287—22no—
122#13063287C2314yes—
123#13063287C2314yes—
124#13063283—22no—
125#13063283—28no—
126#13063283—28no—
127#13063283C2314yes—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43C2311yescharacteristic
131C2×Dic43⋊C4—21no—
132C2×(C2×D43)⋊C4—21no—
133C2×(C2×D43)⋊C4—21no—
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×C4×Dic43—21no—
141C2×C4×Dic43—21no—
142C2×C4×Dic43—21no—
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43D411yescharacteristic
145C2×C4×Dic43C2311yescharacteristic
146C42×D43—28no—
147C42×D43D414yes—
148C42×D43C2314yes—
149#13063258C2314yes—
150#13063256C2314yes—
151C4⋊(C43⋊C8)C2314yes—
152#13063250C2314yes—
153#13063248C2314yes—
154#13063247C2314yes—
155#13063245C2314yes—
156#13063245C2314yes—
157#13063245C2314yes—
158(C2×D43)⋊C8C2314yes—
159(C2×D43)⋊C8C2314yes—
160#13063235C2314yes—
161#13063235C2314yes—
162C22×Q8×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165#125×C43—22no—
166#125×C43C2314yes—
167C4×Q8×C43—22no—
168C4×Q8×C43C2314yes—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C42×C43—21no—
176C2×C42×C43C2311yescharacteristic
177#107×C43C2314yes—
178#106×C43C2314yes—
179C4⋊C8×C43C2314yes—
180#103×C43C2314yes—
181#103×C43C2314yes—
182C23×D43—21no—
183C23×D43—21no—
184C23×D43C2×D411yescharacteristic
185C2×Q8×C43—21no—
186C2×Q8×C43—22no—
187C2×Q8×C43#4114yes—
188C2×Q8×C43C2412yes—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2411yescharacteristic
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43C2×D411yescharacteristic
199C22×Dic43C2×D411yescharacteristic
200C22×Dic43C2×D411yescharacteristic
201#10621902—216no—
202#10621902—28no—
203#10621902—28no—
204C2×D172—28no—
205C2×D172—21no—
206C2×D172—22no—
207C2×D172—21no—
208C2×D172—24no—
209C2×D172—24no—
210C2×D172—22no—
211C2×D172—22no—
212C2×D172—44no—
213C2×D172#4114yes—
214C2×D172C2412yes—
215C2×D172C2412yes—
216C2×C4×D43—28no—
217C2×C4×D43—22no—
218C2×C4×D43—22no—
219C2×C4×D43—24no—
220C2×C4×D43—24no—
221C2×C4×D43—24no—
222C2×C4×D43—24no—
223C2×C4×D43—42no—
224C2×C4×D43—42no—
225C2×C4×D43—44no—
226C2×C4×D43—44no—
227C2×C4×D43—44no—
228C2×C4×D43C2×D412yes—
229C2×C4×D43C2×D414yes—
230C2×C4×D43C2×D414yes—
231C2×C4×D43C2412yes—
232C2×Dic86—22no—
233C2×Dic86—22no—
234C2×Dic86—21no—
235C2×Dic86C2412yes—
236C2×C8×C43—22no—
237C2×C8×C43—22no—
238C2×C8×C43C2412yes—
239C2×C8×C43C2412yes—
240C4⋊C4×C43—24no—
241C4⋊C4×C43—24no—
242C4⋊C4×C43—24no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43C2412yes—
247C4⋊C4×C43C2412yes—
248C4⋊C4×C43C2412yes—
249C42×C43—24no—
250C42×C43C2×D412yes—
251C42×C43C2412yes—
252#10621885—28no—
253#10621884—28no—
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)⋊C4—24no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—24no—
262C4⋊Dic43—21no—
263C4⋊Dic43—24no—
264C4⋊Dic43—24no—
265C4⋊Dic43C2412yes—
266Dic43⋊C4—24no—
267C4×Dic43—24no—
268C4×Dic43—24no—
269C4×Dic43—24no—
270C4×Dic43C2×D414yes—
271C4×Dic43C2×D412yes—
272C4×Dic43C2×D414yes—
273C4×Dic43C2412yes—
274C2×C43⋊C8—22no—
275C2×C43⋊C8—22no—
276C2×C43⋊C8C2412yes—
277C2×C43⋊C8C2412yes—
278D344—28no—
279#10621873—28no—
280C23×C43C22×D411yescharacteristic
281C22×D43—22no—
282C22×D43—24no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—42no—
288C22×D43—42no—
289C22×D43—42no—
290C22×D43—42no—
291C22×D43—42no—
292C22×D43C22×D412yes—
293Q8×C43—24no—
294Q8×C43—22no—
295Q8×C43C2×#4114yes—
296C2×C4×C43—24no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—42no—
304C2×C4×C43—42no—
305C2×C4×C43—42no—
306C2×C4×C43C22×D412yes—
307C2×C4×C43C22×D412yes—
308C2×C4×C43C22×D411yescharacteristic
309C2×C4×C43C2×#4112yes—
310C2×C4×C43C2×#4112yes—
311C2×C4×C43C2511yescharacteristic
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43C22×D412yes—
320C2×Dic43C22×D412yes—
321C2×Dic43C22×D412yes—
322D172—216no—
323D172—24no—
324D172—22no—
325D172—22no—
326D172—22no—
327D172—48no—
328D172—42no—
329D172C2×#4114yes—
330C4×D43—216no—
331C4×D43—24no—
332C4×D43—22no—
333C4×D43—22no—
334C4×D43—44no—
335C4×D43—44no—
336C4×D43—48no—
337C4×D43—48no—
338C4×D43—48no—
339Dic86—22no—
340Dic86—22no—
341Dic86—42no—
342C8×C43—22no—
343C8×C43—22no—
344C43⋊C8—22no—
345C43⋊C8—22no—
346C2×#3111—431nomaximal, Sylow
347C22×C43#52512yes—
348C22×C43#57512yes—
349C22×C43#57512yes—
350C22×C43C23×D411yescharacteristic
351C2×D43—24no—
352C2×D43—22no—
353C2×D43—22no—
354C2×D43—22no—
355C2×D43—44no—
356C2×D43—48no—
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—42no—
361C2×D43—42no—
362C2×D43—84no—
363C4×C43—24no—
364C4×C43—22no—
365C4×C43—22no—
366C4×C43—42no—
367C4×C43—42no—
368C4×C43—42no—
369C4×C43#52512yes—
370C4×C43C22×#4111yescharacteristic
371C4×C43C22×#4111yescharacteristic
372Dic43—22no—
373Dic43—22no—
374Dic43—22no—
375Dic43—42no—
376Dic43—42no—
377C2×#529—431no—
378C2×C4×#41—431no—
379#3111—4316no—
380C2×#485—431no—
381C2×#482—431no—
382C2×#479D4311yescharacteristic, complemented
383C2×#478—431no—
384C2×#464—431no—
385C2×#463—431no—
386C2×#452—431no—
387C2×#449—431no—
388C2×#442—431no—
389C2×#441—431no—
390C2×#440—431no—
391C2×#440—431no—
392C2×#432—431no—
393C2×C43#311114yescomplemented
394C2×C43C2×#52511yescharacteristic
395C2×C43C2×#57511yescharacteristic
396C2×C43C2×#57511yescharacteristic
397D43—42no—
398D43—44no—
399D43—82no—
400C22×#41—431no—
401C22×Q16—431no—
402C22×SD16—431no—
403C22×SD16—431no—
404C22×D8—431no—
405#529—438no—
406#529—864no—
407C2×#126—861no—
408C2×#125C2×D4311yescharacteristic
409C2×#124—431no—
410C2×#123—861no—
411C2×C22⋊Q8—431no—
412C2×#121—431no—
413C4×#41—438no—
414C4×#41—864no—
415C2×C4×Q8—431no—
416C2×C4×Q8—431no—
417C2×C4×Q8C2×D4311yescharacteristic
418C2×C4×D4—431no—
419C2×C4×D4—431no—
420C2×C4×D4—431no—
421C2×C4×D4—861no—
422C2×C4×D4—861no—
423C2×C4×D4—861no—
424C2×#117—431no—
425C2×#117—861no—
426C2×#117—861no—
427C22×C42—431no—
428C22×C42—861no—
429#485—438no—
430#482—438no—
431#479C2×D4318yescomplemented
432#478—438no—
433#464—438no—
434#463—438no—
435#452—438no—
436#449—438no—
437#442—438no—
438#441—438no—
439#440—438no—
440#440—438no—
441#432—438no—
442C2×#107—431no—
443C2×#107C2×D4311yescharacteristic
444C2×#106—431no—
445C2×#106C2×D4311yescharacteristic
446C2×C4⋊C8—431no—
447C2×C4⋊C8C2×D4311yescharacteristic
448C2×#103—431no—
449C2×#103—431no—
450C2×#103C2×D4311yescharacteristic
451C2×#103C2×D4311yescharacteristic
452C2×#102—431no—
453C2×#102—431no—
454C2×#102—431no—
455C2×#102—431no—
456C2×C22⋊C8—431no—
457C2×C22⋊C8—431no—
458C2×#97—431no—
459C2×#97—431no—
460C43C2×#311111yescharacteristic, complemented, Sylow
461C2×#41—434no—
462C2×#41—862no—
463C2×#41—864no—
464C2×#41—864no—
465C22×Q8—431no—
466C22×Q8C22×D4311yescharacteristic
467C22×D4—431no—
468C22×D4—431no—
469C22×D4—861no—
470C22×D4—861no—
471C23×C4—431no—
472C23×C4—431no—
473C23×C4—431no—
474C23×C4—861no—
475C23×C4—861no—
476C23×C4—861no—
477C23×C4—861no—
478C2×Q16—434no—
479C2×Q16—864no—
480C2×SD16—434no—
481C2×SD16—434no—
482C2×SD16—864no—
483C2×SD16—864no—
484C2×D8—434no—
485C2×D8—864no—
486C22×C8—431no—
487C22×C8—431no—
488C22×C8C22×D4311yescharacteristic
489C22×C8C22×D4311yescharacteristic
490#126—868no—
491#125—22no—
492#125C22×D4314yes—
493#124—434no—
494#124—862no—
495#123—868no—
496C22⋊Q8—434no—
497C22⋊Q8—862no—
498#121—434no—
499#121—862no—
500C4×Q8—22no—
501C4×Q8—434no—
502C4×Q8—434no—
503C4×Q8—862no—
504C4×Q8—862no—
505C4×Q8C22×D4314yes—
506C4×D4—434no—
507C4×D4—434no—
508C4×D4—434no—
509C4×D4—868no—
510C4×D4—862no—
511C4×D4—862no—
512C4×D4—868no—
513C4×D4—868no—
514C4×D4—862no—
515#117—434no—
516#117—868no—
517#117—868no—
518#117—862no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C4⋊C4C22×D4311yescharacteristic
529C2×C22⋊C4—861no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C42—21no—
538C2×C42—431no—
539C2×C42—431no—
540C2×C42—431no—
541C2×C42—434no—
542C2×C42—434no—
543C2×C42—868no—
544C2×C42—861no—
545C2×C42—861no—
546C2×C42—861no—
547C2×C42C22×D4311yescharacteristic
548#107—434no—
549#107C22×D4314yes—
550#106—434no—
551#106C22×D4314yes—
552C4⋊C8—434no—
553C4⋊C8C22×D4314yes—
554#103—434no—
555#103—434no—
556#103C22×D4314yes—
557#103C22×D4314yes—
558#102—434no—
559#102—434no—
560#102—434no—
561#102—434no—
562C22⋊C8—434no—
563C22⋊C8—434no—
564#97—434no—
565#97—434no—
566C24—431no—
567C24—861no—
568C24—861no—
569#41—868no—
570#41—8616no—
571#41—868no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—432no—
575C2×Q8—861no—
576C2×Q8—862no—
577C2×Q8—862no—
578C2×Q8#1062190214yes—
579C2×Q8C23×D4312yes—
580C2×D4—434no—
581C2×D4—432no—
582C2×D4—432no—
583C2×D4—864no—
584C2×D4—868no—
585C2×D4—864no—
586C2×D4—861no—
587C2×D4—861no—
588C2×D4—862no—
589C2×D4—862no—
590C2×D4—862no—
591C2×D4—1724no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—431no—
597C22×C4—431no—
598C22×C4—431no—
599C22×C4—432no—
600C22×C4—432no—
601C22×C4—434no—
602C22×C4—434no—
603C22×C4—864no—
604C22×C4—864no—
605C22×C4—864no—
606C22×C4—868no—
607C22×C4—862no—
608C22×C4—862no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—864no—
612C22×C4—1722no—
613C22×C4—1722no—
614C22×C4—1724no—
615C22×C4—1724no—
616C22×C4—1724no—
617C22×C4D4×D4311yescharacteristic
618C22×C4D4×D4311yescharacteristic
619C22×C4C23×D4311yescharacteristic
620Q16—868no—
621SD16—868no—
622SD16—868no—
623D8—868no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—432no—
627C2×C8—432no—
628C2×C8—862no—
629C2×C8—862no—
630C2×C8C23×D4312yes—
631C2×C8C23×D4312yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—432no—
639C4⋊C4—864no—
640C4⋊C4—864no—
641C4⋊C4—864no—
642C4⋊C4—861no—
643C4⋊C4C23×D4312yes—
644C4⋊C4C23×D4312yes—
645C4⋊C4C23×D4312yes—
646C22⋊C4—864no—
647C22⋊C4—864no—
648C22⋊C4—864no—
649C22⋊C4—864no—
650C22⋊C4—864no—
651C22⋊C4—864no—
652C22⋊C4—864no—
653C22⋊C4—864no—
654C42—24no—
655C42—434no—
656C42—434no—
657C42—432no—
658C42—432no—
659C42—864no—
660C42—864no—
661C42—864no—
662C42D4×D4312yes—
663C42C23×D4312yes—
664C23—432no—
665C23—864no—
666C23—862no—
667C23—862no—
668C23—862no—
669C23—862no—
670C23—862no—
671C23—1722no—
672C23—1722no—
673C23—1722no—
674C23—1722no—
675C23—1722no—
676C23C2×D4×D4311yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—862no—
680Q8—862no—
681Q8—1722no—
682Q8C2×#1062190214yes—
683D4—434no—
684D4—8616no—
685D4—864no—
686D4—862no—
687D4—862no—
688D4—862no—
689D4—1728no—
690D4—1722no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—432no—
702C2×C4—432no—
703C2×C4—432no—
704C2×C4—8616no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—864no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—1724no—
714C2×C4—1724no—
715C2×C4—1728no—
716C2×C4—1728no—
717C2×C4—1728no—
718C2×C4—1722no—
719C2×C4—1722no—
720C2×C4C2×D4×D4312yes—
721C2×C4C2×D4×D4312yes—
722C2×C4C2×D4×D4311yescharacteristic
723C2×C4#41×D4312yes—
724C2×C4C2×#1062190212yes—
725C2×C4C24×D4311yescharacteristic
726C8—22no—
727C8—22no—
728C8—862no—
729C8—862no—
730C22—862no—
731C22—862no—
732C22—864no—
733C22—862no—
734C22—3444no—
735C22—1722no—
736C22—1722no—
737C22—1722no—
738C22—1724no—
739C22—1728no—
740C22—1722no—
741C22—1722no—
742C22#1458341212yes—
743C22#1458369612yes—
744C22#1458369812yes—
745C22C22×D4×D4311yescharacteristic
746C4—22no—
747C4—22no—
748C4—24no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—862no—
753C4—862no—
754C4—862no—
755C4—1722no—
756C4—1722no—
757C4#1458341212yes—
758C4C2×#41×D4311yescharacteristic
759C4C22×#1062190211yescharacteristic
760C2—3442no—
761C2—1722no—
762C2—1724no—
763C2#1914471114yesdirect product factor
764C2C2×#1458341211yescharacteristic
765C2C2×#1458369611yescharacteristic
766C2C2×#1458369811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#479C2
socleC23×C43C22×D4
prime radicalC2×#14583047C2
hypercenterC2×#479D43
hypocenterC43C2×#3111
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. C2×#14583434C2semidirect
2. C2×C4×#10621902C2semidirect
3. #19144711C2direct (N × H)
4. C2×#14583243C2semidirect
5. C2×#14583226C2semidirect
6. C2×#14583196C2semidirect
7. C2×#14583121C2semidirect
8. C2×#14583115C2semidirect
9. C2×#14583064C2semidirect
11. C2×#14583010C2semidirect
12. C2×#14583003C2semidirect
13. C2×#14583002C2semidirect
14. C2×#14582998C2semidirect
15. C2×#14582955C2semidirect
16. C2×C43×#479C2semidirect
23. #14583434C22semidirect
30. C4×#10621902C22semidirect
44. #14583243C22semidirect
45. #14583226C22semidirect
46. #14583196C22semidirect
47. #14583121C22semidirect
48. #14583115C22semidirect
49. #14583064C22semidirect
51. #14583010C22semidirect
52. #14583003C22semidirect
53. #14583002C22semidirect
54. #14582998C22semidirect
55. #14582955C22semidirect
71. C43×#479C22semidirect
382. C2×#479D43semidirect
393. C2×C43#3111semidirect
431. #479C2×D43semidirect
460. C43C2×#3111semidirect
763. C2#19144711direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834342
C2×C4×#106219022
#191447112
C2×#145832432
C2×#145832262
C2×#145831962
C2×#145831212
C2×#145831152
C2×#145830642
C2×#145830472
C2×#145830102
C2×#145830032
C2×#145830022
C2×#145829982
C2×#145829552
C2×C43×#4792
C2×#311143