Finite Group Databasebeta

← C2×#19144790 #25964840

Subgroups — C2×#19144790 #25964840

Order 11008.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583500C211yesmaximal, characteristic, complemented
2C2×#14583378C211yesmaximal, characteristic, complemented
3#19144790C2116yesmaximal, direct product factor
4C2×#14583216C211yesmaximal, characteristic, complemented
5C2×#14583214C211yesmaximal, characteristic, complemented
6C2×#14583205C211yesmaximal, characteristic, complemented
7C2×#14583201C211yesmaximal, characteristic, complemented
8C2×#14583098C211yesmaximal, characteristic, complemented
9C2×#14583092C211yesmaximal, characteristic, complemented
10C2×#14583045C211yesmaximal, characteristic, complemented
11C2×#14583041C211yesmaximal, characteristic, complemented
12C2×#14583009C211yesmaximal, characteristic, complemented
13C2×#14582999C211yesmaximal, characteristic, complemented
14C2×C4×#10621873C211yesmaximal, characteristic, complemented
15C2×#14582958C211yesmaximal, characteristic, complemented
16C2×C4×D8×C43C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21#14583500—24no—
22#14583500C2218yescomplemented
23C2×#13063321C2211yescharacteristic
24C2×#13063316C2211yescharacteristic
25C2×#13063308—21no—
26C2×#13063307—21no—
27C2×#13063300C2211yescharacteristic
28C2×#13063299—21no—
29C2×#13063298—21no—
30C2×#13063296C2211yescharacteristic
31#14583378—24no—
32#14583378C2218yescomplemented
33C2×C4×Dic86C2211yescharacteristic
34C2×#13063290C2211yescharacteristic
35C2×C4×D172C2211yescharacteristic
36C2×D4×Dic43C2211yescharacteristic
37C2×C4×C22⋊D43—21no—
38C2×(C22⋊D43)⋊C4—21no—
39C2×#13063282C2211yescharacteristic
40C2×#13063281—21no—
41C22×Dic43⋊C4—21no—
42C2×C4⋊C4×D43C2211yescharacteristic
43#14583216C2218yescomplemented
44#14583214C2218yescomplemented
45#14583205C2218yescomplemented
46#14583201C2218yescomplemented
47#14583098C2218yescomplemented
48#14583092C2218yescomplemented
49#14583045C2218yescomplemented
50#14583041C2218yescomplemented
51#14583009C2218yescomplemented
52#14582999C2218yescomplemented
53C4×#10621873C2218yescomplemented
54#14582958C2218yescomplemented
55C2×#13063258C2211yescharacteristic
56C2×#13063257C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063236C2211yescharacteristic
69C22×D8×C43C2211yescharacteristic
70C2×C4×D4×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C4×D8×C43C2218yescomplemented
73C2×#107×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic
77C2×#10621900—24no—
78C2×#10621900—22no—
79C2×#10621900—24no—
80C2×#10621900C2314yes—
81C22×Dic86C2311yescharacteristic
82C22×D172—21no—
83C22×D172C2311yescharacteristic
84C22×C22⋊D43—21no—
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C23×Dic43—21no—
89C23×Dic43—21no—
90C22×C4×D43—21no—
91C22×C4×D43—21no—
92C22×C4×D43C2311yescharacteristic
93C2×#10621873—24no—
94C2×#10621873C2314yes—
95C2×#10621883—24no—
96C2×#10621883C2314yes—
97C2×#10621882—24no—
98C2×#10621882C2314yes—
99C22×C43⋊C8C2311yescharacteristic
100C22×C43⋊C8C2311yescharacteristic
101#13063321—22no—
102#13063321C2314yes—
103#13063316—22no—
104#13063316C2314yes—
105#13063308—28no—
106#13063307—28no—
107#13063300—22no—
108#13063300C2314yes—
109#13063299—28no—
110#13063298—28no—
111#13063296—22no—
112#13063296C2314yes—
113C4×Dic86—22no—
114C4×Dic86C2314yes—
115#13063290—22no—
116#13063290C2314yes—
117C4×D172—22no—
118C4×D172C2314yes—
119D4×Dic43—22no—
120D4×Dic43C2314yes—
121C4×C22⋊D43—28no—
122(C22⋊D43)⋊C4—28no—
123#13063282D414yes—
124#13063282C2314yes—
125#13063281—28no—
126C2×C4⋊Dic43—21no—
127C2×C4⋊Dic43C2311yescharacteristic
128C2×C4⋊Dic43C2311yescharacteristic
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—28no—
134C2×Dic43⋊C4D411yescharacteristic
135C2×Dic43⋊C4D411yescharacteristic
136C4⋊C4×D43—22no—
137C4⋊C4×D43C2314yes—
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4D411yescharacteristic
143C2×(C2×D43)⋊C4D411yescharacteristic
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43C2311yescharacteristic
147#13063258C2314yes—
148#13063257C2314yes—
149#13063256C2314yes—
150Dic43⋊C8C2314yes—
151Dic43⋊C8C2314yes—
152#13063250C2314yes—
153#13063248C2314yes—
154#13063247C2314yes—
155#13063246C2314yes—
156#13063246C2314yes—
157#13063245C2314yes—
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#107×C43C2314yes—
179#102×C43C2314yes—
180#102×C43C2314yes—
181C4×C8×C43C2314yes—
182C24×C43—21no—
183C24×C43—21no—
184C23×D43—21no—
185C23×D43C2×D411yescharacteristic
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—22no—
189C2×D4×C43—22no—
190C2×D4×C43—22no—
191C2×D4×C43#4114yes—
192C2×D4×C43C2412yes—
193C2×D4×C43C2412yes—
194C22×C4×C43—24no—
195C22×C4×C43—24no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—82no—
199C22×C4×C43—82no—
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2411yescharacteristic
203C2×C22⋊D43—28no—
204C2×C22⋊D43—24no—
205C2×C22⋊D43—24no—
206C2×C22⋊D43—24no—
207C2×C22⋊D43—24no—
208C2×C22⋊D43—82no—
209C2×C22⋊D43—82no—
210C2×C22⋊D43—82no—
211C22×Dic43—28no—
212C22×Dic43—24no—
213C22×Dic43—24no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—82no—
218C22×Dic43C2×D411yescharacteristic
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221#10621900—216no—
222#10621900—28no—
223#10621900—28no—
224C2×D172—21no—
225C2×D172—24no—
226C2×D172—22no—
227C2×D172—22no—
228C2×D172—82no—
229C2×D172C2412yes—
230C2×C4×D43—22no—
231C2×C4×D43—22no—
232C2×C4×D43—24no—
233C2×C4×D43—24no—
234C2×C4×D43—82no—
235C2×C4×D43—82no—
236C2×C4×D43C2×D412yes—
237C2×C4×D43C2412yes—
238C2×Dic86—21no—
239C2×Dic86—22no—
240C2×Dic86#4114yes—
241C2×Dic86C2412yes—
242D8×C43—28no—
243C2×C8×C43—22no—
244C2×C8×C43—22no—
245C2×C8×C43C2412yes—
246C2×C8×C43C2412yes—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43C2412yes—
250C4⋊C4×C43C2412yes—
251C22⋊C4×C43—24no—
252C22⋊C4×C43—24no—
253C42×C43C2×D412yes—
254C42×C43C2412yes—
255C22⋊Dic43—24no—
256C22⋊Dic43—24no—
257#10621883—28no—
258#10621882—28no—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4C2×D414yes—
262(C2×D43)⋊C4C2×D414yes—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—24no—
266C4⋊Dic43C2412yes—
267C4⋊Dic43C2412yes—
268Dic43⋊C4—24no—
269Dic43⋊C4—24no—
270Dic43⋊C4—24no—
271Dic43⋊C4—24no—
272Dic43⋊C4C2×D414yes—
273Dic43⋊C4C2×D414yes—
274C4×Dic43—24no—
275C4×Dic43—24no—
276C4×Dic43C2×D412yes—
277C4×Dic43C2412yes—
278C2×C43⋊C8—22no—
279C2×C43⋊C8—22no—
280C2×C43⋊C8C2412yes—
281C2×C43⋊C8C2412yes—
282#10621873—28no—
283C23×C43—24no—
284C23×C43—22no—
285C23×C43—22no—
286C23×C43—42no—
287C23×C43—42no—
288C23×C43—42no—
289C23×C43—42no—
290C23×C43—42no—
291C23×C43C22×D411yescharacteristic
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—42no—
297C22×D43—42no—
298C22×D43—42no—
299C22×D43C22×D412yes—
300D4×C43—24no—
301D4×C43—22no—
302D4×C43—22no—
303D4×C43—22no—
304D4×C43—42no—
305D4×C43C2×#4114yes—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—42no—
311C2×C4×C43—42no—
312C2×C4×C43—84no—
313C2×C4×C43—84no—
314C2×C4×C43C22×D412yes—
315C2×C4×C43C22×D412yes—
316C2×C4×C43C22×D411yescharacteristic
317C2×C4×C43C2×#4112yes—
318C2×C4×C43C2×#4112yes—
319C2×C4×C43C2511yescharacteristic
320C22⋊D43—216no—
321C22⋊D43—84no—
322C22⋊D43—84no—
323C22⋊D43—84no—
324C2×Dic43—216no—
325C2×Dic43—24no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43—84no—
335C2×Dic43C22×D412yes—
336C2×Dic43C22×D412yes—
337C2×Dic43C22×D412yes—
338D172—22no—
339D172—22no—
340D172—42no—
341D172—84no—
342C4×D43—24no—
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—84no—
346C4×D43—84no—
347Dic86—24no—
348Dic86—22no—
349Dic86C2×#4114yes—
350C8×C43—22no—
351C8×C43—22no—
352C43⋊C8—22no—
353C43⋊C8—22no—
354C2×#3119—431nomaximal, Sylow
355C22×C43—24no—
356C22×C43—48no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—84no—
363C22×C43#52512yes—
364C22×C43#57612yes—
365C22×C43#57712yes—
366C22×C43C23×D411yescharacteristic
367C2×D43—22no—
368C2×D43—22no—
369C2×D43—22no—
370C2×D43—44no—
371C2×D43—42no—
372C2×D43—42no—
373C2×D43—42no—
374C2×D43—84no—
375C4×C43—22no—
376C4×C43—22no—
377C4×C43—42no—
378C4×C43—42no—
379C4×C43#52512yes—
380C4×C43C22×#4111yescharacteristic
381C4×C43C22×#4111yescharacteristic
382Dic43—24no—
383Dic43—22no—
384Dic43—22no—
385Dic43—22no—
386Dic43—42no—
387Dic43—42no—
388C2×#540—431no—
389C2×#520—431no—
390#3119—4316no—
391C2×#481—431no—
392C2×#480—431no—
393C2×#479—431no—
394C2×#478—431no—
395C2×#460—431no—
396C2×#459—431no—
397C2×#449—431no—
398C2×#449—431no—
399C2×#442—431no—
400C2×#440—431no—
401C2×C4×SD16—431no—
402C2×C4×D8D4311yescharacteristic, complemented
403C2×#433—431no—
404C2×C43—44no—
405C2×C43—82no—
406C2×C43#311914yescomplemented
407C2×C43C2×#52511yescharacteristic
408C2×C43C2×#57611yescharacteristic
409C2×C43C2×#57711yescharacteristic
410D43—42no—
411D43—82no—
412C22×#41—431no—
413C22×SD16—431no—
414C22×SD16—431no—
415C22×D8—431no—
416C22×D8C2×D4311yescharacteristic
417#540—438no—
418#540—864no—
419C2×#127—431no—
420C2×#125—431no—
421C2×#123—861no—
422C2×#123—861no—
423C2×#121—431no—
424C2×#121—431no—
425C2×#121—861no—
426C2×#121—861no—
427#520—438no—
428#520—864no—
429C2×C4×Q8—431no—
430C2×C4×Q8—431no—
431C2×C4×D4—431no—
432C2×C4×D4—431no—
433C2×C4×D4—861no—
434C2×C4×D4—861no—
435C2×C4×D4C2×D4311yescharacteristic
436C2×C4×D4C2×D4311yescharacteristic
437C2×#117—431no—
438C2×#117—861no—
439C22×C4⋊C4—431no—
440C22×C4⋊C4—861no—
441#481—438no—
442#480—438no—
443#479—438no—
444#478—438no—
445#460—438no—
446#459—438no—
447#449—438no—
448#449—438no—
449#442—438no—
450#440—438no—
451C4×SD16—438no—
452C4×D8C2×D4318yescomplemented
453#433—438no—
454C2×#107—431no—
455C2×#107C2×D4311yescharacteristic
456C2×#106—431no—
457C2×#106—431no—
458C2×C4⋊C8—431no—
459C2×C4⋊C8—431no—
460C2×#103—431no—
461C2×#103—431no—
462C2×#102—431no—
463C2×#102—431no—
464C2×#102—431no—
465C2×#102—431no—
466C2×#102C2×D4311yescharacteristic
467C2×#102C2×D4311yescharacteristic
468C2×C22⋊C8—431no—
469C2×C22⋊C8—431no—
470C2×#97—431no—
471C2×C4×C8C2×D4311yescharacteristic
472C43C2×#311911yescharacteristic, complemented, Sylow
473C2×#41—434no—
474C2×#41—862no—
475C2×#41—864no—
476C2×#41—864no—
477C22×Q8—431no—
478C22×D4—431no—
479C22×D4—861no—
480C22×D4—861no—
481C22×D4—861no—
482C22×D4—861no—
483C22×D4—861no—
484C22×D4C22×D4311yescharacteristic
485C22×D4C22×D4311yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—431no—
489C23×C4—861no—
490C23×C4—861no—
491C23×C4—861no—
492C23×C4—861no—
493C2×SD16—434no—
494C2×SD16—434no—
495C2×SD16—864no—
496C2×SD16—864no—
497C2×D8—24no—
498C2×D8—434no—
499C2×D8—864no—
500C2×D8C22×D4314yes—
501C22×C8—431no—
502C22×C8—431no—
503C22×C8C22×D4311yescharacteristic
504C22×C8C22×D4311yescharacteristic
505#127—434no—
506#127—862no—
507#125—434no—
508#125—862no—
509#123—868no—
510#123—868no—
511#121—434no—
512#121—434no—
513#121—868no—
514#121—868no—
515#121—862no—
516#121—862no—
517C4×Q8—434no—
518C4×Q8—434no—
519C4×Q8—862no—
520C4×Q8—862no—
521C4×D4—22no—
522C4×D4—22no—
523C4×D4—434no—
524C4×D4—434no—
525C4×D4—862no—
526C4×D4—868no—
527C4×D4—868no—
528C4×D4—862no—
529C4×D4C22×D4314yes—
530C4×D4C22×D4314yes—
531#117—434no—
532#117—434no—
533#117—868no—
534C2×C4⋊C4—431no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—434no—
539C2×C4⋊C4—862no—
540C2×C4⋊C4—868no—
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×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—431no—
551C2×C22⋊C4—431no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C42—431no—
557C2×C42—861no—
558C2×C42—861no—
559C2×C42C22×D4311yescharacteristic
560#107—434no—
561#107C22×D4314yes—
562#106—434no—
563#106—434no—
564C4⋊C8—434no—
565C4⋊C8—434no—
566#103—434no—
567#103—434no—
568#102—434no—
569#102—434no—
570#102—434no—
571#102—434no—
572#102C22×D4314yes—
573#102C22×D4314yes—
574C22⋊C8—434no—
575C22⋊C8—434no—
576#97—434no—
577C4×C8C22×D4314yes—
578C24—21no—
579C24—21no—
580C24—431no—
581C24—861no—
582#41—868no—
583#41—8616no—
584#41—868no—
585C2×Q8—434no—
586C2×Q8—432no—
587C2×Q8—861no—
588C2×Q8—862no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—432no—
595C2×D4—864no—
596C2×D4—864no—
597C2×D4—864no—
598C2×D4—864no—
599C2×D4—868no—
600C2×D4—864no—
601C2×D4—861no—
602C2×D4—862no—
603C2×D4—862no—
604C2×D4—3442no—
605C2×D4—3442no—
606C2×D4—3442no—
607C2×D4—3442no—
608C2×D4#1062189814yes—
609C2×D4C23×D4312yes—
610C2×D4C23×D4312yes—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—24no—
614C22×C4—24no—
615C22×C4—82no—
616C22×C4—82no—
617C22×C4—431no—
618C22×C4—431no—
619C22×C4—431no—
620C22×C4—432no—
621C22×C4—432no—
622C22×C4—864no—
623C22×C4—864no—
624C22×C4—864no—
625C22×C4—868no—
626C22×C4—861no—
627C22×C4—862no—
628C22×C4—862no—
629C22×C4—861no—
630C22×C4—861no—
631C22×C4—864no—
632C22×C4—3442no—
633C22×C4—3442no—
634C22×C4—3442no—
635C22×C4D4×D4311yescharacteristic
636C22×C4D4×D4311yescharacteristic
637C22×C4C23×D4311yescharacteristic
638SD16—868no—
639SD16—868no—
640D8—28no—
641D8—868no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—432no—
645C2×C8—432no—
646C2×C8—862no—
647C2×C8—862no—
648C2×C8C23×D4312yes—
649C2×C8C23×D4312yes—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—434no—
653C4⋊C4—434no—
654C4⋊C4—432no—
655C4⋊C4—432no—
656C4⋊C4—864no—
657C4⋊C4—864no—
658C4⋊C4—864no—
659C4⋊C4—864no—
660C4⋊C4—861no—
661C4⋊C4—861no—
662C4⋊C4—864no—
663C4⋊C4C23×D4312yes—
664C4⋊C4C23×D4312yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—434no—
668C22⋊C4—434no—
669C22⋊C4—864no—
670C22⋊C4—864no—
671C22⋊C4—864no—
672C22⋊C4—864no—
673C42—432no—
674C42—432no—
675C42—864no—
676C42—864no—
677C42D4×D4312yes—
678C42C23×D4312yes—
679C23—24no—
680C23—22no—
681C23—22no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—432no—
688C23—862no—
689C23—862no—
690C23—862no—
691C23—862no—
692C23—1722no—
693C23—1722no—
694C23—1722no—
695C23C2×D4×D4311yescharacteristic
696Q8—434no—
697Q8—864no—
698Q8—862no—
699D4—24no—
700D4—22no—
701D4—22no—
702D4—22no—
703D4—42no—
704D4—8616no—
705D4—862no—
706D4—862no—
707D4—3444no—
708D4—3444no—
709D4—3444no—
710D4—3444no—
711D4—1722no—
712D4C2×#1062189814yes—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—84no—
720C2×C4—84no—
721C2×C4—432no—
722C2×C4—432no—
723C2×C4—432no—
724C2×C4—8616no—
725C2×C4—862no—
726C2×C4—864no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—864no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—3444no—
736C2×C4—3444no—
737C2×C4—3444no—
738C2×C4—1722no—
739C2×C4—1722no—
740C2×C4C2×D4×D4312yes—
741C2×C4C2×D4×D4312yes—
742C2×C4C2×D4×D4311yescharacteristic
743C2×C4#41×D4312yes—
744C2×C4C2×#1062189812yes—
745C2×C4C24×D4311yescharacteristic
746C8—22no—
747C8—22no—
748C8—862no—
749C8—862no—
750C22—24no—
751C22—42no—
752C22—42no—
753C22—48no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—84no—
758C22—862no—
759C22—862no—
760C22—862no—
761C22—3444no—
762C22—1722no—
763C22—1722no—
764C22—1722no—
765C22—1724no—
766C22#1458340812yes—
767C22#1458370012yes—
768C22#1458370612yes—
769C22C22×D4×D4311yescharacteristic
770C4—22no—
771C4—22no—
772C4—42no—
773C4—42no—
774C4—862no—
775C4—862no—
776C4—862no—
777C4—864no—
778C4—1722no—
779C4—1722no—
780C4#1458340812yes—
781C4C2×#41×D4311yescharacteristic
782C4C22×#1062189811yescharacteristic
783C2—44no—
784C2—82no—
785C2—3442no—
786C2—1722no—
787C2#1914479014yesdirect product factor
788C2C2×#1458340811yescharacteristic
789C2C2×#1458370011yescharacteristic
790C2C2×#1458370611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C4×D8×C43C2
socleC23×C43C22×D4
hypercenterC2×C4×D8D43
hypocenterC43C2×#3119
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#14583500C2semidirect
2. C2×#14583378C2semidirect
3. #19144790C2direct (N × H)
4. C2×#14583216C2semidirect
5. C2×#14583214C2semidirect
6. C2×#14583205C2semidirect
7. C2×#14583201C2semidirect
8. C2×#14583098C2semidirect
9. C2×#14583092C2semidirect
10. C2×#14583045C2semidirect
11. C2×#14583041C2semidirect
12. C2×#14583009C2semidirect
13. C2×#14582999C2semidirect
14. C2×C4×#10621873C2semidirect
15. C2×#14582958C2semidirect
16. C2×C4×D8×C43C2semidirect
22. #14583500C22semidirect
32. #14583378C22semidirect
43. #14583216C22semidirect
44. #14583214C22semidirect
45. #14583205C22semidirect
46. #14583201C22semidirect
47. #14583098C22semidirect
48. #14583092C22semidirect
49. #14583045C22semidirect
50. #14583041C22semidirect
51. #14583009C22semidirect
52. #14582999C22semidirect
53. C4×#10621873C22semidirect
54. #14582958C22semidirect
72. C4×D8×C43C22semidirect
402. C2×C4×D8D43semidirect
406. C2×C43#3119semidirect
452. C4×D8C2×D43semidirect
472. C43C2×#3119semidirect
787. C2#19144790direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835002
C2×#145833782
#191447902
C2×#145832162
C2×#145832142
C2×#145832052
C2×#145832012
C2×#145830982
C2×#145830922
C2×#145830452
C2×#145830412
C2×#145830092
C2×#145829992
C2×C4×#106218732
C2×#145829582
C2×C4×D8×C432
C2×#311943