Finite Group Databasebeta

← C2×#19144700 #25964773

Subgroups — C2×#19144700 #25964773

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×#14583431C211yesmaximal, characteristic, complemented
2C2×C4×#10621900C211yesmaximal, characteristic, complemented
3#19144700C2116yesmaximal, direct product factor
4C2×#14583243C211yesmaximal, characteristic, complemented
5C2×#14583222C211yesmaximal, characteristic, complemented
6C2×#14583209C211yesmaximal, characteristic, complemented
7C2×#14583201C211yesmaximal, characteristic, complemented
8C2×#14583120C211yesmaximal, characteristic, complemented
9C2×#14583112C211yesmaximal, characteristic, complemented
10C2×#14583062C211yesmaximal, characteristic, complemented
11C2×#14583041C211yesmaximal, characteristic
12C2×#14583007C211yesmaximal, characteristic, complemented
13C2×#14582999C211yesmaximal, characteristic, complemented
14C2×#14582999C211yesmaximal, characteristic, complemented
15C2×#14582954C211yesmaximal, characteristic, complemented
16C2×C43×#442C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21#14583431—24no—
22#14583431C2218yescomplemented
23C2×#13063318—21no—
24C2×#13063316C2211yescharacteristic
25C2×#13063312C2211yescharacteristic
26C2×#13063307—21no—
27C2×#13063305C2211yescharacteristic
28C2×#13063296C2211yescharacteristic
29C4×#10621900—24no—
30C4×#10621900C2218yescomplemented
31C2×C4×Dic86C2211yescharacteristic
32C2×C4×Dic86C2211yescharacteristic
33C2×#13063290C2211yescharacteristic
34C2×D4×Dic43C2211yescharacteristic
35C2×C4×C22⋊D43—21no—
36C2×C4×C22⋊D43—21no—
37C2×(C22⋊D43)⋊C4—21no—
38C2×#13063284—21no—
39C2×#13063283C2211yescharacteristic
40C2×#13063281—21no—
41C22×C4×Dic43—21no—
42C2×C42×D43C2211yescharacteristic
43#14583243C2218yescomplemented
44#14583222C2218yescomplemented
45#14583209C2218yescomplemented
46#14583201C2218yescomplemented
47#14583120C2218yescomplemented
48#14583112C2218yescomplemented
49#14583062C2218yescomplemented
50#14583041C2218yes—
51#14583007C2218yescomplemented
52#14582999C2218yescomplemented
53#14582999C2218yescomplemented
54#14582954C2218yescomplemented
55C2×#13063258C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063257C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063236C2211yescharacteristic
69C22×D8×C43C2211yescharacteristic
70C2×C4×D4×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C43×#442C2218yescomplemented
73C2×#106×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C2×#10621900—24no—
78C2×#10621900—22no—
79C2×#10621900—24no—
80C2×#10621900C2314yes—
81C22×Dic86C2311yescharacteristic
82C22×Dic86C2311yescharacteristic
83C22×C22⋊D43—21no—
84C22×C22⋊D43—21no—
85C23×Dic43—21no—
86C23×Dic43—21no—
87C22×C4×D43D411yescharacteristic
88C22×C4×D43D411yescharacteristic
89C22×C4×D43C2311yescharacteristic
90C2×Dic172—24no—
91C2×Dic172C2314yes—
92C2×#10621883—24no—
93C2×#10621883—24no—
94C2×#10621883C2314yes—
95C2×#10621883C2314yes—
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98#13063318—28no—
99#13063316—22no—
100#13063316C2314yes—
101#13063312—22no—
102#13063312C2314yes—
103#13063307—28no—
104#13063305—22no—
105#13063305C2314yes—
106#13063296—22no—
107#13063296C2314yes—
108C4×Dic86—22no—
109C4×Dic86—22no—
110C4×Dic86C2314yes—
111C4×Dic86C2314yes—
112#13063290—22no—
113#13063290C2314yes—
114D4×Dic43—22no—
115D4×Dic43C2314yes—
116C4×C22⋊D43—28no—
117C4×C22⋊D43—28no—
118(C22⋊D43)⋊C4—28no—
119#13063284—28no—
120#13063283—22no—
121#13063283C2314yes—
122#13063281—28no—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43—21no—
125C2×C4⋊Dic43C2311yescharacteristic
126C2×C4⋊Dic43C2311yescharacteristic
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×C22⋊Dic43—21no—
132C2×C22⋊Dic43—21no—
133C2×C22⋊Dic43—21no—
134C2×C22⋊Dic43—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×C4×Dic43—21no—
138C2×C4×Dic43—21no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43—21no—
141C2×C4×Dic43—28no—
142C2×C4×Dic43D411yescharacteristic
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43C2311yescharacteristic
145C42×D43D414yes—
146C42×D43C2314yes—
147#13063258C2314yes—
148#13063258C2314yes—
149#13063257C2314yes—
150Dic43⋊C8C2314yes—
151Dic43⋊C8C2314yes—
152#13063250C2314yes—
153#13063250C2314yes—
154#13063248C2314yes—
155#13063248C2314yes—
156#13063246C2314yes—
157#13063246C2314yes—
158(C2×D43)⋊C8C2314yes—
159(C2×D43)⋊C8C2314yes—
160#13063236C2314yes—
161C22×D4×C43C2311yescharacteristic
162C22×D4×C43C2311yescharacteristic
163C23×C4×C43—21no—
164C23×C4×C43—21no—
165C2×D8×C43—24no—
166C2×D8×C43C2314yes—
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C4×D4×C43—22no—
170C4×D4×C43—22no—
171C4×D4×C43C2314yes—
172C4×D4×C43C2314yes—
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43—21no—
177C2×C42×C43C2311yescharacteristic
178#106×C43C2314yes—
179#102×C43C2314yes—
180#102×C43C2314yes—
181#97×C43C2314yes—
182C24×C43—21no—
183C24×C43—21no—
184C23×D43C2×D411yescharacteristic
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—22no—
188C2×D4×C43—22no—
189C2×D4×C43—22no—
190C2×D4×C43#4114yes—
191C2×D4×C43C2412yes—
192C2×D4×C43C2412yes—
193C22×C4×C43—24no—
194C22×C4×C43—24no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—44no—
198C22×C4×C43—44no—
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—28no—
203C2×C22⋊D43—24no—
204C2×C22⋊D43—24no—
205C2×C22⋊D43—44no—
206C22×Dic43—28no—
207C22×Dic43—24no—
208C22×Dic43—24no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—44no—
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217#10621900—216no—
218#10621900—28no—
219#10621900—28no—
220C2×C4×D43—22no—
221C2×C4×D43—22no—
222C2×C4×D43—42no—
223C2×C4×D43—42no—
224C2×C4×D43C2×D412yes—
225C2×C4×D43C2×D414yes—
226C2×C4×D43C2×D414yes—
227C2×C4×D43C2412yes—
228C2×Dic86—21no—
229C2×Dic86—22no—
230C2×Dic86—22no—
231C2×Dic86—22no—
232C2×Dic86—21no—
233C2×Dic86#4114yes—
234C2×Dic86C2412yes—
235C2×Dic86C2412yes—
236D8×C43—28no—
237C2×C8×C43—22no—
238C2×C8×C43—22no—
239C2×C8×C43C2412yes—
240C2×C8×C43C2412yes—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43C2412yes—
244C4⋊C4×C43C2412yes—
245C22⋊C4×C43—24no—
246C22⋊C4×C43—24no—
247C42×C43C2×D412yes—
248C42×C43C2412yes—
249C22⋊Dic43—24no—
250C22⋊Dic43—24no—
251C22⋊Dic43—24no—
252C22⋊Dic43—24no—
253#10621883—28no—
254#10621883—28no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—24no—
260C4⋊Dic43—24no—
261C4⋊Dic43C2412yes—
262C4⋊Dic43C2412yes—
263Dic43⋊C4—24no—
264Dic43⋊C4—24no—
265Dic43⋊C4—24no—
266Dic43⋊C4—24no—
267C4×Dic43—24no—
268C4×Dic43—24no—
269C4×Dic43—24no—
270C4×Dic43—24no—
271C4×Dic43C2×D412yes—
272C4×Dic43C2×D414yes—
273C4×Dic43C2×D414yes—
274C4×Dic43C2412yes—
275C2×C43⋊C8—22no—
276C2×C43⋊C8—22no—
277C2×C43⋊C8C2412yes—
278C2×C43⋊C8C2412yes—
279Dic172—28no—
280C23×C43—24no—
281C23×C43—22no—
282C23×C43—22no—
283C23×C43—42no—
284C23×C43—42no—
285C23×C43—42no—
286C23×C43—42no—
287C23×C43—42no—
288C23×C43C22×D411yescharacteristic
289C22×D43—22no—
290C22×D43—22no—
291C22×D43—22no—
292C22×D43C22×D412yes—
293D4×C43—24no—
294D4×C43—22no—
295D4×C43—22no—
296D4×C43—22no—
297D4×C43—42no—
298D4×C43C2×#4114yes—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—48no—
304C2×C4×C43—48no—
305C2×C4×C43—42no—
306C2×C4×C43—42no—
307C2×C4×C43C22×D412yes—
308C2×C4×C43C22×D412yes—
309C2×C4×C43C22×D411yescharacteristic
310C2×C4×C43C2×#4112yes—
311C2×C4×C43C2×#4112yes—
312C2×C4×C43C2511yescharacteristic
313C22⋊D43—216no—
314C22⋊D43—48no—
315C2×Dic43—216no—
316C2×Dic43—24no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—48no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43C22×D412yes—
329C2×Dic43C22×D412yes—
330C2×Dic43C22×D412yes—
331C4×D43—24no—
332C4×D43—22no—
333C4×D43—22no—
334C4×D43—44no—
335C4×D43—44no—
336Dic86—24no—
337Dic86—22no—
338Dic86—22no—
339Dic86—22no—
340Dic86—42no—
341Dic86C2×#4114yes—
342C8×C43—22no—
343C8×C43—22no—
344C43⋊C8—22no—
345C43⋊C8—22no—
346C2×#3111—431nomaximal, Sylow
347C22×C43—24no—
348C22×C43—48no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—84no—
355C22×C43#52512yes—
356C22×C43#57512yes—
357C22×C43#57512yes—
358C22×C43C23×D411yescharacteristic
359C2×D43—22no—
360C2×D43—22no—
361C2×D43—22no—
362C2×D43—44no—
363C4×C43—22no—
364C4×C43—22no—
365C4×C43—42no—
366C4×C43—42no—
367C4×C43#52512yes—
368C4×C43C22×#4111yescharacteristic
369C4×C43C22×#4111yescharacteristic
370Dic43—24no—
371Dic43—22no—
372Dic43—22no—
373Dic43—22no—
374Dic43—42no—
375Dic43—42no—
376Dic43—42no—
377C2×#529—431no—
378C2×C4×#41—431no—
379#3111—4316no—
380C2×#485—431no—
381C2×#482—431no—
382C2×#479—431no—
383C2×#478—431no—
384C2×#464—431no—
385C2×#463—431no—
386C2×#452—431no—
387C2×#449—431no—
388C2×#442D4311yescharacteristic, complemented
389C2×#441—431no—
390C2×#440—431no—
391C2×#440—431no—
392C2×#432—431no—
393C2×C43—44no—
394C2×C43—82no—
395C2×C43#311114yescomplemented
396C2×C43C2×#52511yescharacteristic
397C2×C43C2×#57511yescharacteristic
398C2×C43C2×#57511yescharacteristic
399D43—42no—
400C22×#41—431no—
401C22×Q16—431no—
402C22×SD16—431no—
403C22×SD16—431no—
404C22×D8C2×D4311yescharacteristic
405#529—438no—
406#529—864no—
407C2×#126—861no—
408C2×#125—431no—
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×Q8—431no—
418C2×C4×D4—431no—
419C2×C4×D4—861no—
420C2×C4×D4—861no—
421C2×C4×D4—861no—
422C2×C4×D4C2×D4311yescharacteristic
423C2×C4×D4C2×D4311yescharacteristic
424C2×#117—431no—
425C2×#117—861no—
426C2×#117—861no—
427C22×C42—431no—
428C22×C42—861no—
429#485—438no—
430#482—438no—
431#479—438no—
432#478—438no—
433#464—438no—
434#463—438no—
435#452—438no—
436#449—438no—
437#442C2×D4318yescomplemented
438#441—438no—
439#440—438no—
440#440—438no—
441#432—438no—
442C2×#107—431no—
443C2×#107—431no—
444C2×#106—431no—
445C2×#106C2×D4311yescharacteristic
446C2×C4⋊C8—431no—
447C2×C4⋊C8—431no—
448C2×#103—431no—
449C2×#103—431no—
450C2×#103—431no—
451C2×#103—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102C2×D4311yescharacteristic
455C2×#102C2×D4311yescharacteristic
456C2×C22⋊C8—431no—
457C2×C22⋊C8—431no—
458C2×#97—431no—
459C2×#97C2×D4311yescharacteristic
460C43C2×#311111yescharacteristic, complemented, Sylow
461C2×#41—434no—
462C2×#41—862no—
463C2×#41—864no—
464C2×#41—864no—
465C22×Q8—431no—
466C22×Q8—431no—
467C22×D4—861no—
468C22×D4—861no—
469C22×D4C22×D4311yescharacteristic
470C22×D4C22×D4311yescharacteristic
471C23×C4—21no—
472C23×C4—21no—
473C23×C4—431no—
474C23×C4—431no—
475C23×C4—431no—
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—24no—
485C2×D8C22×D4314yes—
486C22×C8—431no—
487C22×C8—431no—
488C22×C8C22×D4311yescharacteristic
489C22×C8C22×D4311yescharacteristic
490#126—868no—
491#125—434no—
492#125—862no—
493#124—434no—
494#124—862no—
495#123—868no—
496C22⋊Q8—434no—
497C22⋊Q8—862no—
498#121—434no—
499#121—862no—
500C4×Q8—434no—
501C4×Q8—434no—
502C4×Q8—434no—
503C4×Q8—862no—
504C4×Q8—862no—
505C4×Q8—862no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—434no—
509C4×D4—862no—
510C4×D4—868no—
511C4×D4—868no—
512C4×D4—868no—
513C4×D4C22×D4314yes—
514C4×D4C22×D4314yes—
515#117—434no—
516#117—868no—
517#117—868no—
518#117—862no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4—861no—
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C4⋊C4C22×D4311yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
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—431no—
538C2×C42—431no—
539C2×C42—431no—
540C2×C42—434no—
541C2×C42—434no—
542C2×C42—868no—
543C2×C42—861no—
544C2×C42—861no—
545C2×C42—861no—
546C2×C42—861no—
547C2×C42C22×D4311yescharacteristic
548#107—434no—
549#107—434no—
550#106—434no—
551#106C22×D4314yes—
552C4⋊C8—434no—
553C4⋊C8—434no—
554#103—434no—
555#103—434no—
556#103—434no—
557#103—434no—
558#102—434no—
559#102—434no—
560#102C22×D4314yes—
561#102C22×D4314yes—
562C22⋊C8—434no—
563C22⋊C8—434no—
564#97—434no—
565#97C22×D4314yes—
566C24—21no—
567C24—21no—
568C24—431no—
569#41—868no—
570#41—8616no—
571#41—868no—
572C2×Q8—434no—
573C2×Q8—432no—
574C2×Q8—432no—
575C2×Q8—861no—
576C2×Q8—861no—
577C2×Q8—862no—
578C2×Q8—862no—
579C2×Q8—862no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—864no—
586C2×D4—868no—
587C2×D4—864no—
588C2×D4—1724no—
589C2×D4#1062189814yes—
590C2×D4C23×D4312yes—
591C2×D4C23×D4312yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—431no—
599C22×C4—431no—
600C22×C4—431no—
601C22×C4—432no—
602C22×C4—432no—
603C22×C4—434no—
604C22×C4—434no—
605C22×C4—864no—
606C22×C4—864no—
607C22×C4—868no—
608C22×C4—861no—
609C22×C4—862no—
610C22×C4—862no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—1722no—
615C22×C4—1722no—
616C22×C4—1724no—
617C22×C4D4×D4311yescharacteristic
618C22×C4D4×D4311yescharacteristic
619C22×C4C23×D4311yescharacteristic
620Q16—868no—
621SD16—868no—
622SD16—868no—
623D8—28no—
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—21no—
633C4⋊C4—21no—
634C4⋊C4—432no—
635C4⋊C4—432no—
636C4⋊C4—864no—
637C4⋊C4—864no—
638C4⋊C4—864no—
639C4⋊C4—864no—
640C4⋊C4—861no—
641C4⋊C4—861no—
642C4⋊C4—864no—
643C4⋊C4—864no—
644C4⋊C4C23×D4312yes—
645C4⋊C4C23×D4312yes—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—864no—
649C22⋊C4—864no—
650C22⋊C4—864no—
651C22⋊C4—864no—
652C22⋊C4—864no—
653C22⋊C4—864no—
654C42—434no—
655C42—434no—
656C42—432no—
657C42—432no—
658C42—864no—
659C42—864no—
660C42—864no—
661C42—864no—
662C42D4×D4312yes—
663C42C23×D4312yes—
664C23—24no—
665C23—22no—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—432no—
673C23—862no—
674C23—862no—
675C23—862no—
676C23C2×D4×D4311yescharacteristic
677Q8—434no—
678Q8—864no—
679Q8—862no—
680Q8—862no—
681Q8—862no—
682Q8—1722no—
683D4—24no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—42no—
688D4—8616no—
689D4—1728no—
690D4C2×#1062189814yes—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—48no—
696C2×C4—48no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—432no—
700C2×C4—432no—
701C2×C4—432no—
702C2×C4—8616no—
703C2×C4—862no—
704C2×C4—864no—
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—862no—
714C2×C4—1724no—
715C2×C4—1724no—
716C2×C4—1728no—
717C2×C4—1722no—
718C2×C4—1722no—
719C2×C4—1722no—
720C2×C4C2×D4×D4312yes—
721C2×C4C2×D4×D4312yes—
722C2×C4C2×D4×D4311yescharacteristic
723C2×C4#41×D4312yes—
724C2×C4C2×#1062189812yes—
725C2×C4C24×D4311yescharacteristic
726C8—22no—
727C8—22no—
728C8—862no—
729C8—862no—
730C22—24no—
731C22—42no—
732C22—42no—
733C22—48no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—862no—
739C22—862no—
740C22—862no—
741C22—1724no—
742C22#1458340812yes—
743C22#1458369512yes—
744C22#1458369512yes—
745C22C22×D4×D4311yescharacteristic
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—862no—
751C4—862no—
752C4—862no—
753C4—864no—
754C4—1722no—
755C4—1722no—
756C4—1722no—
757C4#1458340812yes—
758C4C2×#41×D4311yescharacteristic
759C4C22×#1062189811yescharacteristic
760C2—44no—
761C2—82no—
762C2—1722no—
763C2#1914470014yesdirect product factor
764C2C2×#1458340811yescharacteristic
765C2C2×#1458369511yescharacteristic
766C2C2×#1458369511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#442C2
socleC23×C43C22×D4
prime radicalC2×#14583041C2
hypercenterC2×#442D43
hypocenterC43C2×#3111
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#14583431C2semidirect
2. C2×C4×#10621900C2semidirect
3. #19144700C2direct (N × H)
4. C2×#14583243C2semidirect
5. C2×#14583222C2semidirect
6. C2×#14583209C2semidirect
7. C2×#14583201C2semidirect
8. C2×#14583120C2semidirect
9. C2×#14583112C2semidirect
10. C2×#14583062C2semidirect
12. C2×#14583007C2semidirect
13. C2×#14582999C2semidirect
14. C2×#14582999C2semidirect
15. C2×#14582954C2semidirect
16. C2×C43×#442C2semidirect
22. #14583431C22semidirect
30. C4×#10621900C22semidirect
43. #14583243C22semidirect
44. #14583222C22semidirect
45. #14583209C22semidirect
46. #14583201C22semidirect
47. #14583120C22semidirect
48. #14583112C22semidirect
49. #14583062C22semidirect
51. #14583007C22semidirect
52. #14582999C22semidirect
53. #14582999C22semidirect
54. #14582954C22semidirect
72. C43×#442C22semidirect
388. C2×#442D43semidirect
395. C2×C43#3111semidirect
437. #442C2×D43semidirect
460. C43C2×#3111semidirect
763. C2#19144700direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834312
C2×C4×#106219002
#191447002
C2×#145832432
C2×#145832222
C2×#145832092
C2×#145832012
C2×#145831202
C2×#145831122
C2×#145830622
C2×#145830412
C2×#145830072
C2×#145829992
C2×#145829542
C2×C43×#4422
C2×#311143