Finite Group Databasebeta

← C2×#19144715 #25964789

Subgroups — C2×#19144715 #25964789

Order 11008.

2398 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×#14583446C211yesmaximal, characteristic
2C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
3#19144715C2116yesmaximal, direct product factor
4C2×#14583214C211yesmaximal, characteristic, complemented
5C2×#14583211C211yesmaximal, characteristic, complemented
6C2×#14583193C211yesmaximal, characteristic, complemented
7C2×#14583192C211yesmaximal, characteristic, complemented
8C2×#14583098C211yesmaximal, characteristic, complemented
9C2×#14583097C211yesmaximal, characteristic, complemented
10C2×#14583039C211yesmaximal, characteristic, complemented
11C2×#14583036C211yesmaximal, characteristic, complemented
12C2×#14583001C211yesmaximal, characteristic, complemented
13C2×#14582999C211yesmaximal, characteristic, complemented
14C2×#14582997C211yesmaximal, characteristic, complemented
15C2×#14582954C211yesmaximal, characteristic, complemented
16C2×C43×#440C211yesmaximal, characteristic, complemented
17C22×#10621898—21no—
18C22×Q8×D43C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C22×#10621884C2211yescharacteristic
22#14583446—24no—
23#14583446C2218yes—
24C2×#13063324C2211yescharacteristic
25C2×#13063321C2211yescharacteristic
26C2×#13063311—21no—
27C2×#13063300C2211yescharacteristic
28C2×#13063298—21no—
29C2×#13063296C2211yescharacteristic
30C2×Q8×Dic43C2211yescharacteristic
31C2×C4×Dic86—21no—
32C2×C4×Dic86C2211yescharacteristic
33C2×#13063290—21no—
34C2×#13063290C2211yescharacteristic
35C4×Q8×D43—24no—
36C4×Q8×D43C2218yescomplemented
37C2×C4×D172C2211yescharacteristic
38C2×C4×C22⋊D43—21no—
39C2×C4⋊C4×D43—21no—
40C2×C4⋊C4×D43C2211yescharacteristic
41C2×C42×D43—21no—
42C2×C42×D43C2211yescharacteristic
43#14583214C2218yescomplemented
44#14583211C2218yescomplemented
45#14583193C2218yescomplemented
46#14583192C2218yescomplemented
47#14583098C2218yescomplemented
48#14583097C2218yescomplemented
49#14583039C2218yescomplemented
50#14583036C2218yescomplemented
51#14583001C2218yescomplemented
52#14582999C2218yescomplemented
53#14582997C2218yescomplemented
54#14582954C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063258C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063236C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C43×#440C2218yescomplemented
73C2×#107×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C2×#10621898—28no—
78C2×#10621898—48no—
79C22×Dic86—21no—
80C22×Dic86—21no—
81C22×Dic86C2311yescharacteristic
82C2×Q8×D43—24no—
83C2×Q8×D43—22no—
84C2×Q8×D43—24no—
85C2×Q8×D43C2314yes—
86C22×D172—21no—
87C22×D172C2311yescharacteristic
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C22×C4×D43—21no—
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C22×C4×D43D411yescharacteristic
95C22×C4×D43D411yescharacteristic
96C22×C4×D43C2311yescharacteristic
97C2×#10621873—24no—
98C2×#10621873C2314yes—
99C2×#10621883—24no—
100C2×#10621883C2314yes—
101C2×#10621884—24no—
102C2×#10621884C2314yes—
103C22×C43⋊C8C2311yescharacteristic
104C22×C43⋊C8C2311yescharacteristic
105#13063324—22no—
106#13063324C2314yes—
107#13063321—22no—
108#13063321C2314yes—
109#13063311—28no—
110#13063300—22no—
111#13063300C2314yes—
112#13063298—28no—
113#13063296—22no—
114#13063296C2314yes—
115Q8×Dic43—22no—
116Q8×Dic43C2314yes—
117C4×Dic86—22no—
118C4×Dic86—28no—
119C4×Dic86C2314yes—
120#13063290—22no—
121#13063290—28no—
122#13063290C2314yes—
123C4×D172—22no—
124C4×D172C2314yes—
125C4×C22⋊D43—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—
133C4⋊C4×D43—28no—
134C4⋊C4×D43—22no—
135C4⋊C4×D43C2314yes—
136C2×C22⋊Dic43—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43—21no—
141C2×C4×Dic43—21no—
142C2×C4×Dic43D411yescharacteristic
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43C2311yescharacteristic
145C42×D43—28no—
146C42×D43D414yes—
147C42×D43C2314yes—
148#13063259C2314yes—
149#13063258C2314yes—
150#13063258C2314yes—
151Dic43⋊C8C2314yes—
152Dic43⋊C8C2314yes—
153#13063250C2314yes—
154#13063249C2314yes—
155#13063248C2314yes—
156#13063247C2314yes—
157#13063246C2314yes—
158#13063245C2314yes—
159(C2×D43)⋊C8C2314yes—
160(C2×D43)⋊C8C2314yes—
161#13063236C2314yes—
162C22×Q8×C43C2311yescharacteristic
163C22×D4×C43C2311yescharacteristic
164C23×C4×C43—21no—
165C2×SD16×C43—24no—
166C2×SD16×C43C2314yes—
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C4×Q8×C43—22no—
170C4×Q8×C43C2314yes—
171C4×D4×C43—22no—
172C4×D4×C43C2314yes—
173C2×C4⋊C4×C43—21no—
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C22⋊C4×C43—21no—
177C2×C42×C43—21no—
178C2×C42×C43C2311yescharacteristic
179#107×C43C2314yes—
180#103×C43C2314yes—
181#102×C43C2314yes—
182#97×C43C2314yes—
183C24×C43—21no—
184C23×D43—21no—
185C23×D43C2×D411yescharacteristic
186C2×Q8×C43—21no—
187C2×Q8×C43—22no—
188C2×Q8×C43#4114yescomplemented
189C2×Q8×C43C2412yes—
190C2×D4×C43—21no—
191C2×D4×C43—22no—
192C2×D4×C43—22no—
193C2×D4×C43C2412yes—
194C22×C4×C43—24no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—44no—
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—24no—
203C2×C22⋊D43—24no—
204C2×C22⋊D43—24no—
205C2×C22⋊D43—44no—
206C2×C22⋊D43—44no—
207C2×C22⋊D43—44no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213C22×Dic43C2×D411yescharacteristic
214Q8×D43—216no—
215Q8×D43—28no—
216Q8×D43—28no—
217#10621898—432no—
218C2×D172—21no—
219C2×D172—24no—
220C2×D172—22no—
221C2×D172—22no—
222C2×D172—44no—
223C2×D172C2412yes—
224C2×C4×D43—28no—
225C2×C4×D43—22no—
226C2×C4×D43—22no—
227C2×C4×D43—24no—
228C2×C4×D43—24no—
229C2×C4×D43—24no—
230C2×C4×D43—24no—
231C2×C4×D43—24no—
232C2×C4×D43—44no—
233C2×C4×D43—44no—
234C2×C4×D43C2×D414yes—
235C2×C4×D43C2×D412yes—
236C2×C4×D43C2×D414yes—
237C2×C4×D43C2412yes—
238C2×Dic86—28no—
239C2×Dic86—21no—
240C2×Dic86—22no—
241C2×Dic86—24no—
242C2×Dic86—24no—
243C2×Dic86—44no—
244C2×Dic86#4114yescomplemented
245C2×Dic86C2412yes—
246SD16×C43—28no—
247C2×C8×C43—22no—
248C2×C8×C43—22no—
249C2×C8×C43C2412yes—
250C2×C8×C43C2412yes—
251C4⋊C4×C43—24no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43C2412yes—
255C4⋊C4×C43C2412yes—
256C22⋊C4×C43—24no—
257C42×C43—24no—
258C42×C43C2×D412yes—
259C42×C43C2412yes—
260C22⋊Dic43—24no—
261#10621884—28no—
262#10621883—28no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4—24no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—24no—
268C4⋊Dic43C2412yes—
269C4⋊Dic43C2412yes—
270Dic43⋊C4—24no—
271Dic43⋊C4—24no—
272Dic43⋊C4—24no—
273Dic43⋊C4—24no—
274C4×Dic43—24no—
275C4×Dic43—24no—
276C4×Dic43—24no—
277C4×Dic43C2×D412yes—
278C4×Dic43C2×D414yes—
279C4×Dic43C2×D414yes—
280C4×Dic43C2412yes—
281C2×C43⋊C8—22no—
282C2×C43⋊C8—22no—
283C2×C43⋊C8C2412yes—
284C2×C43⋊C8C2412yes—
285#10621873—28no—
286C23×C43—22no—
287C23×C43—42no—
288C23×C43—42no—
289C23×C43—42no—
290C23×C43C22×D411yescharacteristic
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—42no—
295C22×D43—42no—
296C22×D43—42no—
297C22×D43AGL(1,ℤ/8)14yes—
298C22×D43C22×D412yes—
299Q8×C43—24no—
300Q8×C43—22no—
301Q8×C43C2×#4114yescomplemented
302D4×C43—22no—
303D4×C43—22no—
304D4×C43—42no—
305C2×C4×C43—24no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—48no—
312C2×C4×C43—42no—
313C2×C4×C43—42no—
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—48no—
321C22⋊D43—48no—
322C22⋊D43—48no—
323C2×Dic43—22no—
324C2×Dic43—24no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—42no—
330C2×Dic43—42no—
331C2×Dic43#13714yes—
332C2×Dic43C22×D412yes—
333C2×Dic43C22×D412yes—
334C2×Dic43C22×D412yes—
335D172—22no—
336D172—22no—
337D172—48no—
338D172—42no—
339C4×D43—216no—
340C4×D43—28no—
341C4×D43—24no—
342C4×D43—22no—
343C4×D43—22no—
344C4×D43—28no—
345C4×D43—48no—
346C4×D43—48no—
347Dic86—216no—
348Dic86—24no—
349Dic86—22no—
350Dic86—48no—
351Dic86C2×#4114yescomplemented
352C8×C43—22no—
353C8×C43—22no—
354C43⋊C8—22no—
355C43⋊C8—22no—
356C2×#3112—431nomaximal, Sylow
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—84no—
361C22×C43#52512yes—
362C22×C43C2×AGL(1,ℤ/8)12yes—
363C22×C43C2×#13712yes—
364C22×C43C23×D411yescharacteristic
365C2×D43—28no—
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—42no—
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—84no—
372C2×D43C2×AGL(1,ℤ/8)14yes—
373C4×C43—24no—
374C4×C43—22no—
375C4×C43—22no—
376C4×C43—42no—
377C4×C43—42no—
378C4×C43#52512yes—
379C4×C43C22×#4111yescharacteristic
380C4×C43C22×#4111yescharacteristic
381Dic43—22no—
382Dic43—24no—
383Dic43—22no—
384Dic43—42no—
385Dic43—42no—
386Dic43C2×#13714yes—
387C2×#532—431no—
388C22×C4×Q8—431no—
389#3112—4316no—
390C2×#480—431no—
391C2×#480—431no—
392C2×#477—431no—
393C2×#477—431no—
394C2×#460—431no—
395C2×#460—431no—
396C2×#448—431no—
397C2×#448—431no—
398C2×#440—431no—
399C2×#440—431no—
400C2×#440—431no—
401C2×#440D4311yescharacteristic, complemented
402C2×#432—431no—
403C2×C43—82no—
404C2×C43#311214yescomplemented
405C2×C43C2×#52511yescharacteristic
406C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
407C2×C43C22×#13711yescharacteristic
408D43—24no—
409D43—82no—
410C22×#41—861no—
411C23×Q8—431no—
412C22×SD16—431no—
413C22×SD16—431no—
414C22×SD16—431no—
415C22×SD16C2×D4311yescharacteristic
416#532—438no—
417#532—864no—
418C2×C4⋊Q8—431no—
419C2×#127—431no—
420C2×#124—861no—
421C2×#121—431no—
422C2×#121—431no—
423C2×#121—861no—
424C2×C4×Q8—431no—
425C2×C4×Q8—438no—
426C2×C4×Q8—431no—
427C2×C4×Q8—431no—
428C2×C4×Q8—861no—
429C2×C4×Q8—861no—
430C2×C4×Q8—864no—
431C2×C4×Q8C2×D4311yescharacteristic
432C2×C4×D4—431no—
433C2×C4×D4—861no—
434C2×C4×D4C2×D4311yescharacteristic
435C22×C4⋊C4—431no—
436C22×C4⋊C4—861no—
437C22×C42—431no—
438C22×C42—861no—
439#480—438no—
440#480—438no—
441#477—438no—
442#477—438no—
443#460—438no—
444#460—438no—
445#448—438no—
446#448—438no—
447#440—438no—
448#440—438no—
449#440—438no—
450#440C2×D4318yescomplemented
451#432—438no—
452C2×#107—431no—
453C2×#107—431no—
454C2×#107—431no—
455C2×#107C2×D4311yescharacteristic
456C2×C4⋊C8—431no—
457C2×C4⋊C8—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#103—431no—
461C2×#103C2×D4311yescharacteristic
462C2×#102—431no—
463C2×#102—431no—
464C2×#102—431no—
465C2×#102C2×D4311yescharacteristic
466C2×C22⋊C8—431no—
467C2×C22⋊C8—431no—
468C2×#97—431no—
469C2×#97C2×D4311yescharacteristic
470C43C2×#311211yescharacteristic, complemented, Sylow
471C2×#41—868no—
472C2×#41—1728no—
473C22×Q8—434no—
474C22×Q8—431no—
475C22×Q8—861no—
476C22×Q8—861no—
477C22×Q8—862no—
478C22×Q8—864no—
479C22×Q8—864no—
480C22×Q8C22×D4311yescharacteristic
481C22×D4—431no—
482C22×D4—861no—
483C22×D4—861no—
484C22×D4—861no—
485C22×D4—861no—
486C22×D4C22×D4311yescharacteristic
487C23×C4—21no—
488C23×C4—431no—
489C23×C4—431no—
490C23×C4—431no—
491C23×C4—861no—
492C23×C4—861no—
493C23×C4—861no—
494C2×SD16—24no—
495C2×SD16—434no—
496C2×SD16—434no—
497C2×SD16—434no—
498C2×SD16—864no—
499C2×SD16—864no—
500C2×SD16—864no—
501C2×SD16C22×D4314yes—
502C22×C8—431no—
503C22×C8—431no—
504C22×C8C22×D4311yescharacteristic
505C22×C8C22×D4311yescharacteristic
506C4⋊Q8—434no—
507C4⋊Q8—862no—
508#127—434no—
509#127—862no—
510#124—868no—
511#121—434no—
512#121—434no—
513#121—868no—
514#121—862no—
515#121—862no—
516C4×Q8—22no—
517C4×Q8—434no—
518C4×Q8—434no—
519C4×Q8—434no—
520C4×Q8—868no—
521C4×Q8—868no—
522C4×Q8—862no—
523C4×Q8—862no—
524C4×Q8—862no—
525C4×Q8C22×D4314yes—
526C4×D4—22no—
527C4×D4—434no—
528C4×D4—868no—
529C4×D4—862no—
530C4×D4C22×D4314yes—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—431no—
533C2×C4⋊C4—431no—
534C2×C4⋊C4—434no—
535C2×C4⋊C4—862no—
536C2×C4⋊C4—868no—
537C2×C4⋊C4—861no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4C22×D4311yescharacteristic
543C2×C4⋊C4C22×D4311yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—861no—
546C2×C22⋊C4—861no—
547C2×C22⋊C4—861no—
548C2×C42—21no—
549C2×C42—431no—
550C2×C42—431no—
551C2×C42—431no—
552C2×C42—434no—
553C2×C42—434no—
554C2×C42—868no—
555C2×C42—861no—
556C2×C42—861no—
557C2×C42—861no—
558C2×C42C22×D4311yescharacteristic
559#107—434no—
560#107—434no—
561#107—434no—
562#107C22×D4314yes—
563C4⋊C8—434no—
564C4⋊C8—434no—
565#103—434no—
566#103—434no—
567#103—434no—
568#103C22×D4314yes—
569#102—434no—
570#102—434no—
571#102—434no—
572#102C22×D4314yes—
573C22⋊C8—434no—
574C22⋊C8—434no—
575#97—434no—
576#97C22×D4314yes—
577C24—21no—
578C24—431no—
579C24—861no—
580#41—17232no—
581C2×Q8—21no—
582C2×Q8—22no—
583C2×Q8—434no—
584C2×Q8—432no—
585C2×Q8—864no—
586C2×Q8—864no—
587C2×Q8—868no—
588C2×Q8—868no—
589C2×Q8—8616no—
590C2×Q8—868no—
591C2×Q8—861no—
592C2×Q8—862no—
593C2×Q8—1724no—
594C2×Q8#1062189814yescomplemented
595C2×Q8C23×D4312yes—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—432no—
600C2×D4—864no—
601C2×D4—864no—
602C2×D4—864no—
603C2×D4—864no—
604C2×D4—861no—
605C2×D4—862no—
606C2×D4—862no—
607C2×D4—1724no—
608C2×D4—1724no—
609C2×D4—1724no—
610C2×D4—1724no—
611C2×D4C23×D4312yes—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—44no—
617C22×C4—431no—
618C22×C4—431no—
619C22×C4—431no—
620C22×C4—434no—
621C22×C4—434no—
622C22×C4—432no—
623C22×C4—432no—
624C22×C4—864no—
625C22×C4—864no—
626C22×C4—864no—
627C22×C4—868no—
628C22×C4—864no—
629C22×C4—861no—
630C22×C4—862no—
631C22×C4—862no—
632C22×C4—861no—
633C22×C4—861no—
634C22×C4—864no—
635C22×C4—1724no—
636C22×C4—1724no—
637C22×C4D4×D4311yescharacteristic
638C22×C4D4×D4311yescharacteristic
639C22×C4C23×D4311yescharacteristic
640SD16—28no—
641SD16—868no—
642SD16—868no—
643SD16—868no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—432no—
647C2×C8—432no—
648C2×C8—862no—
649C2×C8—862no—
650C2×C8C23×D4312yes—
651C2×C8C23×D4312yes—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
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—864no—
664C4⋊C4C23×D4312yes—
665C4⋊C4C23×D4312yes—
666C22⋊C4—24no—
667C22⋊C4—864no—
668C22⋊C4—864no—
669C22⋊C4—864no—
670C42—24no—
671C42—434no—
672C42—434no—
673C42—432no—
674C42—432no—
675C42—864no—
676C42—864no—
677C42—864no—
678C42D4×D4312yes—
679C42C23×D4312yes—
680C23—22no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—434no—
685C23—432no—
686C23—862no—
687C23—862no—
688C23—862no—
689C23—1722no—
690C23—1722no—
691C23—1722no—
692C23C2×D4×D4311yescharacteristic
693Q8—24no—
694Q8—22no—
695Q8—434no—
696Q8—8616no—
697Q8—864no—
698Q8—862no—
699Q8—1728no—
700Q8C2×#1062189814yescomplemented
701D4—22no—
702D4—22no—
703D4—42no—
704D4—862no—
705D4—862no—
706D4—1728no—
707D4—1728no—
708D4—1728no—
709D4—1728no—
710D4—1722no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—434no—
721C2×C4—432no—
722C2×C4—432no—
723C2×C4—432no—
724C2×C4—868no—
725C2×C4—868no—
726C2×C4—8616no—
727C2×C4—862no—
728C2×C4—864no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—864no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—1728no—
737C2×C4—1728no—
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—42no—
751C22—42no—
752C22—42no—
753C22—84no—
754C22—434no—
755C22—868no—
756C22—862no—
757C22—862no—
758C22—3444no—
759C22—1722no—
760C22—1722no—
761C22—1722no—
762C22#1458340812yes—
763C22AGL(1,ℤ/8)×D4312yes—
764C22#137×D4312yes—
765C22C22×D4×D4311yescharacteristic
766C4—22no—
767C4—22no—
768C4—24no—
769C4—42no—
770C4—42no—
771C4—434no—
772C4—862no—
773C4—862no—
774C4—864no—
775C4—1722no—
776C4—1722no—
777C4#1458340812yes—
778C4C2×#41×D4311yescharacteristic
779C4C22×#1062189811yescharacteristic
780C2—82no—
781C2—864no—
782C2—3442no—
783C2#1914471514yesdirect product factor
784C2C2×#1458340811yescharacteristic
785C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
786C2C2×#137×D4311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#440C2
socleC23×C43C22×D4
prime radicalC2×#14583446C2
hypercenterC2×#440D43
hypocenterC43C2×#3112
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D43C2semidirect
3. #19144715C2direct (N × H)
4. C2×#14583214C2semidirect
5. C2×#14583211C2semidirect
6. C2×#14583193C2semidirect
7. C2×#14583192C2semidirect
8. C2×#14583098C2semidirect
9. C2×#14583097C2semidirect
10. C2×#14583039C2semidirect
11. C2×#14583036C2semidirect
12. C2×#14583001C2semidirect
13. C2×#14582999C2semidirect
14. C2×#14582997C2semidirect
15. C2×#14582954C2semidirect
16. C2×C43×#440C2semidirect
36. C4×Q8×D43C22semidirect
43. #14583214C22semidirect
44. #14583211C22semidirect
45. #14583193C22semidirect
46. #14583192C22semidirect
47. #14583098C22semidirect
48. #14583097C22semidirect
49. #14583039C22semidirect
50. #14583036C22semidirect
51. #14583001C22semidirect
52. #14582999C22semidirect
53. #14582997C22semidirect
54. #14582954C22semidirect
72. C43×#440C22semidirect
188. C2×Q8×C43#41semidirect
244. C2×Dic86#41semidirect
301. Q8×C43C2×#41semidirect
351. Dic86C2×#41semidirect
401. C2×#440D43semidirect
404. C2×C43#3112semidirect
450. #440C2×D43semidirect
470. C43C2×#3112semidirect
594. C2×Q8#10621898semidirect
700. Q8C2×#10621898semidirect
783. C2#19144715direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834462
C2×C4×Q8×D432
#191447152
C2×#145832142
C2×#145832112
C2×#145831932
C2×#145831922
C2×#145830982
C2×#145830972
C2×#145830392
C2×#145830362
C2×#145830012
C2×#145829992
C2×#145829972
C2×#145829542
C2×C43×#4402
C2×#311243