Finite Group Databasebeta

← C2×#19146651 #25973208

Subgroups — C2×#19146651 #25973208

Order 11008.

2094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583590C211yesmaximal, characteristic
2C2×Q8×D172C211yesmaximal, characteristic
3#19146651C2116yesmaximal, direct product factor
4C2×#14583268C211yesmaximal, characteristic, complemented
5C2×#14583243C211yesmaximal, characteristic, complemented
6C2×#14583231C211yesmaximal, characteristic, complemented
7C2×#14583206C211yesmaximal, characteristic, complemented
8C2×#14583156C211yesmaximal, characteristic, complemented
9C2×#14583139C211yesmaximal, characteristic, complemented
10C2×#14583109C211yesmaximal, characteristic, complemented
11C2×#14583053C211yesmaximal, characteristic, complemented
12C2×#14583053C211yesmaximal, characteristic, complemented
13C2×#14582972C211yesmaximal, characteristic
14C2×#14582906C211yesmaximal, characteristic, complemented
15C2×#103×D43C211yesmaximal, characteristic, complemented
16C2×C43×#441C211yesmaximal, characteristic, complemented
17C22×Q8×D43C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621885C2211yescharacteristic
21C22×#10621872C2211yescharacteristic
22C22×C8×D43C2211yescharacteristic
23#14583590—24no—
24#14583590C2218yes—
25Q8×D172—24no—
26Q8×D172C2218yes—
27C2×#13063325—21no—
28C2×#13063325C2211yescharacteristic
29C2×#13063319—21no—
30C2×#13063317C2211yescharacteristic
31C2×#13063315—21no—
32C2×#13063310—21no—
33C2×#13063305—21no—
34C2×#13063305—21no—
35C2×#13063305C2211yescharacteristic
36C2×#13063305C2211yescharacteristic
37C2×#13063301C2211yescharacteristic
38C2×#13063301C2211yescharacteristic
39C2×C4×D172—21no—
40C2×C4×D172C2211yescharacteristic
41C2×#13063283C2211yescharacteristic
42C2×#13063282—21no—
43C2×C4⋊C4×D43C2211yescharacteristic
44#14583268C2218yescomplemented
45#14583243C2218yescomplemented
46#14583231C2218yescomplemented
47#14583206C2218yescomplemented
48#14583156C2218yescomplemented
49#14583139C2218yescomplemented
50#14583109C2218yescomplemented
51#14583053C2218yescomplemented
52#14583053C2218yescomplemented
53#14582972C2218yes—
54C2×#13063258C2211yescharacteristic
55C2×#13063256C2211yescharacteristic
56C2×C4⋊(C43⋊C8)C2211yescharacteristic
57#14582906C2218yescomplemented
58C2×#13063250C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063249C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063248C2211yescharacteristic
66#103×D43C2218yescomplemented
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C2×C4×Q8×C43C2211yescharacteristic
72C43×#441C2218yescomplemented
73C2×#106×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86—21no—
79C22×Dic86C2311yescharacteristic
80C22×Dic86C2311yescharacteristic
81C2×Q8×D43—22no—
82C2×Q8×D43—22no—
83C2×Q8×D43—24no—
84C2×Q8×D43—24no—
85C2×Q8×D43—42no—
86C2×Q8×D43—42no—
87C2×Q8×D43C2314yes—
88C2×Q8×D43C2314yes—
89C22×D172D411yescharacteristic
90C22×C4×D43—21no—
91C22×C4×D43—21no—
92C22×C4×D43—21no—
93C22×C4×D43C2311yescharacteristic
94C22×C4×D43C2311yescharacteristic
95C2×#10621885—42no—
96C2×#10621885—42no—
97C2×#10621885C2314yes—
98C2×#10621885C2314yes—
99C2×#10621872—42no—
100C2×#10621872C2314yes—
101C22×C43⋊C8C2311yescharacteristic
102C22×C43⋊C8C2311yescharacteristic
103C2×C8×D43—42no—
104C2×C8×D43C2314yes—
105#13063325—22no—
106#13063325—28no—
107#13063325C2314yes—
108#13063319—28no—
109#13063317—22no—
110#13063317C2314yes—
111#13063315—28no—
112#13063310—28no—
113#13063305—22no—
114#13063305—22no—
115#13063305—28no—
116#13063305—28no—
117#13063305C2314yes—
118#13063305C2314yes—
119#13063301—22no—
120#13063301—22no—
121#13063301C2314yes—
122#13063301C2314yes—
123C4×D172—28no—
124C4×D172D414yes—
125C4×D172C2314yes—
126#13063283—22no—
127#13063283C2314yes—
128#13063282—28no—
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43—21no—
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43—21no—
133C2×C4⋊Dic43D411yescharacteristic
134C2×C4⋊Dic43C2311yescharacteristic
135C2×C4⋊Dic43C2311yescharacteristic
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C4⋊C4×D43—22no—
142C4⋊C4×D43C2314yes—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4D411yescharacteristic
149C2×(C2×D43)⋊C4D411yescharacteristic
150C2×C4×Dic43—21no—
151#13063258C2314yes—
152#13063256C2314yes—
153C4⋊(C43⋊C8)C2314yes—
154#13063250C2314yes—
155#13063250C2314yes—
156#13063250C2314yes—
157#13063250C2314yes—
158#13063249C2314yes—
159#13063249C2314yes—
160#13063248C2314yes—
161#13063248C2314yes—
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yes—
164C22×Q8×C43C2311yescharacteristic
165C22×Q8×C43C2311yescharacteristic
166C2×Q16×C43—24no—
167C2×Q16×C43C2314yes—
168C22×C8×C43C2311yescharacteristic
169C22×C8×C43C2311yescharacteristic
170C4×Q8×C43—22no—
171C4×Q8×C43—22no—
172C4×Q8×C43C2314yes—
173C4×Q8×C43C2314yes—
174C2×C4⋊C4×C43—21no—
175C2×C4⋊C4×C43—21no—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C42×C43—21no—
179C2×C42×C43—21no—
180C2×C42×C43C2311yescharacteristic
181#106×C43C2314yes—
182#103×C43C2314yes—
183#103×C43C2314yes—
184#97×C43C2314yes—
185C23×D43C2×D411yescharacteristic
186C23×D43C2×D411yescharacteristic
187C2×Q8×C43—21no—
188C2×Q8×C43—21no—
189C2×Q8×C43—22no—
190C2×Q8×C43—22no—
191C2×Q8×C43—22no—
192C2×Q8×C43#4114yes—
193C2×Q8×C43C2412yes—
194C2×Q8×C43C2412yes—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208Q8×D43—28no—
209Q8×D43—28no—
210Q8×D43—44no—
211Q8×D43—44no—
212Q8×D43—48no—
213Q8×D43—48no—
214C2×D172—24no—
215C2×D172C2×D414yes—
216C2×C4×D43—22no—
217C2×C4×D43—22no—
218C2×C4×D43—22no—
219C2×C4×D43—22no—
220C2×C4×D43—24no—
221C2×C4×D43—24no—
222C2×C4×D43—24no—
223C2×C4×D43—44no—
224C2×C4×D43—44no—
225C2×C4×D43—44no—
226C2×C4×D43C2×D412yes—
227C2×C4×D43C2×D412yes—
228C2×C4×D43C2412yes—
229C2×C4×D43C2412yes—
230C2×Dic86—22no—
231C2×Dic86—22no—
232C2×Dic86—22no—
233C2×Dic86—22no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86—24no—
237C2×Dic86—24no—
238C2×Dic86—44no—
239C2×Dic86—44no—
240C2×Dic86C2412yes—
241C2×Dic86C2412yes—
242Q16×C43—28no—
243C2×C8×C43—22no—
244C2×C8×C43—22no—
245C2×C8×C43C2412yes—
246C2×C8×C43C2412yes—
247C4⋊C4×C43—24no—
248C4⋊C4×C43—24no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43C2412yes—
252C4⋊C4×C43C2412yes—
253C42×C43—24no—
254C42×C43—24no—
255C42×C43C2×D412yes—
256C42×C43C2412yes—
257#10621885—44no—
258#10621885—44no—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4C2×D414yes—
265(C2×D43)⋊C4C2×D414yes—
266C4⋊Dic43—21no—
267C4⋊Dic43—24no—
268C4⋊Dic43—24no—
269C4⋊Dic43—21no—
270C4⋊Dic43—24no—
271C4⋊Dic43—24no—
272C4⋊Dic43C2×D414yes—
273C4⋊Dic43C2412yes—
274C4⋊Dic43C2412yes—
275Dic43⋊C4—24no—
276Dic43⋊C4—24no—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4—24no—
280C4×Dic43—24no—
281C2×C43⋊C8—22no—
282C2×C43⋊C8—22no—
283C2×C43⋊C8C2412yes—
284C2×C43⋊C8C2412yes—
285#10621872—44no—
286C8×D43—44no—
287C23×C43C22×D411yescharacteristic
288C22×D43—22no—
289C22×D43—22no—
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—22no—
293C22×D43#13714yes—
294C22×D43C22×D412yes—
295C22×D43C22×D412yes—
296Q8×C43—24no—
297Q8×C43—22no—
298Q8×C43—22no—
299Q8×C43—22no—
300Q8×C43—42no—
301Q8×C43C2×#4114yes—
302C2×C4×C43—24no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—42no—
310C2×C4×C43—42no—
311C2×C4×C43—42no—
312C2×C4×C43C22×D412yes—
313C2×C4×C43C22×D412yes—
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C2×#4112yes—
316C2×C4×C43H(5,𝔽2)12yes—
317C2×C4×C43C2511yescharacteristic
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43C22×D412yes—
329C2×Dic43C22×D412yes—
330D172—28no—
331C4×D43—24no—
332C4×D43—24no—
333C4×D43—22no—
334C4×D43—22no—
335C4×D43—22no—
336C4×D43—22no—
337C4×D43—48no—
338C4×D43—48no—
339C4×D43—48no—
340Dic86—22no—
341Dic86—22no—
342Dic86—22no—
343Dic86—22no—
344Dic86—48no—
345Dic86—48no—
346Dic86—42no—
347Dic86—42no—
348C8×C43—22no—
349C8×C43—22no—
350C43⋊C8—22no—
351C43⋊C8—22no—
352C2×#3312—431nomaximal, Sylow
353C22×C43#54612yes—
354C22×C43C2×#13712yes—
355C22×C43#57812yes—
356C22×C43C23×D411yescharacteristic
357C2×D43—22no—
358C2×D43—28no—
359C2×D43—22no—
360C2×D43—22no—
361C2×D43—22no—
362C2×D43—22no—
363C2×D43—44no—
364C2×D43C2×#13714yes—
365C4×C43—24no—
366C4×C43—22no—
367C4×C43—22no—
368C4×C43—42no—
369C4×C43—42no—
370C4×C43—42no—
371C4×C43#54612yes—
372C4×C43C22×#4111yescharacteristic
373C4×C43C2×H(5,𝔽2)11yescharacteristic
374Dic43—22no—
375Dic43—22no—
376Dic43—42no—
377Dic43—42no—
378Dic43—42no—
379Dic43—42no—
380C2×#552—431no—
381C2×D4×Q8—431no—
382#3312—4316no—
383C2×#491—431no—
384C2×#485—431no—
385C2×#483—431no—
386C2×#479—431no—
387C2×#470—431no—
388C2×#467—431no—
389C2×#462—431no—
390C2×#451—431no—
391C2×#451—431no—
392C2×#441D4311yescharacteristic, complemented
393C2×#435—431no—
394C2×#419—431no—
395C22×#103—431no—
396C2×C43#331214yescomplemented
397C2×C43C2×#54611yescharacteristic
398C2×C43C22×#13711yescharacteristic
399C2×C43C2×#57811yescharacteristic
400D43—24no—
401D43—42no—
402C23×Q8—431no—
403C23×Q8—431no—
404C22×Q16—431no—
405C22×Q16—431no—
406C22×Q16C2×D4311yescharacteristic
407C22×M16—431no—
408C23×C8—431no—
409#552—438no—
410#552—864no—
411D4×Q8—438no—
412D4×Q8—864no—
413C2×C4⋊Q8—431no—
414C2×C4⋊Q8—861no—
415C2×#126—861no—
416C2×#125—431no—
417C2×#125—861no—
418C2×#123—861no—
419C2×C22⋊Q8—431no—
420C2×C22⋊Q8—431no—
421C2×C22⋊Q8—431no—
422C2×C22⋊Q8—431no—
423C2×C22⋊Q8—861no—
424C2×C22⋊Q8—861no—
425C2×C4×Q8C2×D4311yescharacteristic
426C2×C4×Q8C2×D4311yescharacteristic
427C2×C4×D4—431no—
428C2×C4×D4—861no—
429C2×#117—431no—
430C2×#117—861no—
431C22×C4⋊C4—431no—
432#491—438no—
433#485—438no—
434#483—438no—
435#479—438no—
436#470—438no—
437#467—438no—
438#462—438no—
439#451—438no—
440#451—438no—
441#441C2×D4318yescomplemented
442#435—438no—
443C2×#107—431no—
444C2×#106—431no—
445C2×#106C2×D4311yescharacteristic
446C2×C4⋊C8—431no—
447#419—438no—
448C2×#103—431no—
449C2×#103—431no—
450C2×#103—431no—
451C2×#103—431no—
452C2×#103—431no—
453C2×#103—431no—
454C2×#103—431no—
455C2×#103—431no—
456C2×#103—438no—
457C2×#103C2×D4311yescharacteristic
458C2×#103C2×D4311yescharacteristic
459C2×C22⋊C8—431no—
460C2×C22⋊C8—431no—
461C2×#97C2×D4311yescharacteristic
462C43C2×#331211yescharacteristic, complemented, Sylow
463C22×Q8—434no—
464C22×Q8—434no—
465C22×Q8—431no—
466C22×Q8—431no—
467C22×Q8—861no—
468C22×Q8—861no—
469C22×Q8—862no—
470C22×Q8—862no—
471C22×Q8—864no—
472C22×Q8—864no—
473C22×Q8—1722no—
474C22×Q8—1722no—
475C22×Q8C22×D4311yescharacteristic
476C22×Q8C22×D4311yescharacteristic
477C22×D4—431no—
478C23×C4—431no—
479C23×C4—431no—
480C23×C4—861no—
481C23×C4—861no—
482C23×C4—861no—
483C2×Q16—24no—
484C2×Q16—434no—
485C2×Q16—434no—
486C2×Q16—1722no—
487C2×Q16—1722no—
488C2×Q16C22×D4314yes—
489C2×M16—434no—
490C2×M16—1722no—
491C22×C8—431no—
492C22×C8—431no—
493C22×C8—434no—
494C22×C8—1722no—
495C22×C8C22×D4311yescharacteristic
496C22×C8C22×D4311yescharacteristic
497C4⋊Q8—434no—
498C4⋊Q8—868no—
499C4⋊Q8—862no—
500#126—868no—
501#125—434no—
502#125—868no—
503#125—862no—
504#123—868no—
505C22⋊Q8—434no—
506C22⋊Q8—434no—
507C22⋊Q8—434no—
508C22⋊Q8—434no—
509C22⋊Q8—868no—
510C22⋊Q8—868no—
511C22⋊Q8—862no—
512C22⋊Q8—862no—
513C22⋊Q8—862no—
514C22⋊Q8—862no—
515C4×Q8—22no—
516C4×Q8—22no—
517C4×Q8C22×D4314yes—
518C4×Q8C22×D4314yes—
519C4×D4—434no—
520C4×D4—434no—
521C4×D4—868no—
522#117—434no—
523#117—868no—
524#117—862no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—431no—
528C2×C4⋊C4—431no—
529C2×C4⋊C4—431no—
530C2×C4⋊C4—434no—
531C2×C4⋊C4—862no—
532C2×C4⋊C4—861no—
533C2×C4⋊C4—861no—
534C2×C4⋊C4—861no—
535C2×C4⋊C4—861no—
536C2×C4⋊C4—861no—
537C2×C4⋊C4—861no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4C22×D4311yescharacteristic
542C2×C4⋊C4C22×D4311yescharacteristic
543C2×C22⋊C4—431no—
544C2×C22⋊C4—431no—
545C2×C22⋊C4—861no—
546C2×C22⋊C4—861no—
547C2×C22⋊C4—861no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C42—21no—
551C2×C42—21no—
552C2×C42—861no—
553C2×C42C22×D4311yescharacteristic
554#107—434no—
555#106—434no—
556#106C22×D4314yes—
557C4⋊C8—434no—
558#103—434no—
559#103—434no—
560#103—434no—
561#103—434no—
562#103—434no—
563#103—434no—
564#103—434no—
565#103—434no—
566#103C22×D4314yes—
567#103C22×D4314yes—
568C22⋊C8—434no—
569C22⋊C8—434no—
570#97C22×D4314yes—
571C24—431no—
572C24—431no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—432no—
579C2×Q8—432no—
580C2×Q8—864no—
581C2×Q8—864no—
582C2×Q8—861no—
583C2×Q8—861no—
584C2×Q8—868no—
585C2×Q8—868no—
586C2×Q8—862no—
587C2×Q8—862no—
588C2×Q8—862no—
589C2×Q8—862no—
590C2×Q8—1724no—
591C2×Q8—1724no—
592C2×Q8—1724no—
593C2×Q8—1724no—
594C2×Q8—1728no—
595C2×Q8—1728no—
596C2×Q8#1062189814yes—
597C2×Q8C23×D4312yes—
598C2×Q8C23×D4312yes—
599C2×D4—434no—
600C2×D4—864no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—431no—
606C22×C4—431no—
607C22×C4—432no—
608C22×C4—432no—
609C22×C4—432no—
610C22×C4—432no—
611C22×C4—864no—
612C22×C4—864no—
613C22×C4—864no—
614C22×C4—862no—
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—862no—
618C22×C4—861no—
619C22×C4—861no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—1724no—
623C22×C4—1724no—
624C22×C4—1724no—
625C22×C4D4×D4311yescharacteristic
626C22×C4D4×D4311yescharacteristic
627C22×C4C23×D4311yescharacteristic
628Q16—28no—
629Q16—1724no—
630Q16—1724no—
631M16—1724no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—432no—
635C2×C8—432no—
636C2×C8—862no—
637C2×C8—862no—
638C2×C8—1724no—
639C2×C8C23×D4312yes—
640C2×C8C23×D4312yes—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—434no—
646C4⋊C4—432no—
647C4⋊C4—432no—
648C4⋊C4—864no—
649C4⋊C4—864no—
650C4⋊C4—864no—
651C4⋊C4—864no—
652C4⋊C4—864no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—864no—
656C4⋊C4—864no—
657C4⋊C4—864no—
658C4⋊C4—864no—
659C4⋊C4C23×D4312yes—
660C4⋊C4C23×D4312yes—
661C22⋊C4—434no—
662C22⋊C4—434no—
663C22⋊C4—864no—
664C22⋊C4—864no—
665C22⋊C4—864no—
666C22⋊C4—864no—
667C22⋊C4—864no—
668C42—24no—
669C42—24no—
670C42—864no—
671C42D4×D4312yes—
672C42C23×D4312yes—
673C23—434no—
674C23—432no—
675C23—432no—
676C23—862no—
677C23—862no—
678C23—862no—
679C23—862no—
680C23—862no—
681C23C2×D4×D4311yescharacteristic
682Q8—22no—
683Q8—24no—
684Q8—22no—
685Q8—22no—
686Q8—42no—
687Q8—862no—
688Q8—862no—
689Q8—862no—
690Q8—862no—
691Q8—1728no—
692Q8—1728no—
693Q8—1722no—
694Q8—1722no—
695Q8C2×#1062189814yes—
696D4—868no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—432no—
708C2×C4—432no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—864no—
716C2×C4—864no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—862no—
721C2×C4—1728no—
722C2×C4—1728no—
723C2×C4—1728no—
724C2×C4—1722no—
725C2×C4—1722no—
726C2×C4—1722no—
727C2×C4—1722no—
728C2×C4C2×D4×D4312yes—
729C2×C4C2×D4×D4312yes—
730C2×C4C2×D4×D4311yescharacteristic
731C2×C4C2×#1062189812yes—
732C2×C4#1306337112yes—
733C2×C4C24×D4311yescharacteristic
734C8—22no—
735C8—22no—
736C8—862no—
737C8—862no—
738C22—434no—
739C22—862no—
740C22—862no—
741C22—868no—
742C22—862no—
743C22—862no—
744C22—862no—
745C22—1724no—
746C22#1458354512yes—
747C22#137×D4312yes—
748C22#1458371512yes—
749C22C22×D4×D4311yescharacteristic
750C4—24no—
751C4—22no—
752C4—22no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—862no—
757C4—862no—
758C4—1722no—
759C4—1722no—
760C4—1722no—
761C4—1722no—
762C4#1458354512yes—
763C4C22×#1062189811yescharacteristic
764C4C2×#1306337111yescharacteristic
765C2—864no—
766C2—1722no—
767C2#1914665114yesdirect product factor
768C2C2×#1458354511yescharacteristic
769C2C2×#137×D4311yescharacteristic
770C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#441C2
socleC23×C43C22×D4
prime radicalC22×D172D4
hypercenterC2×#441D43
hypocenterC43C2×#3312
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. #19146651C2direct (N × H)
4. C2×#14583268C2semidirect
5. C2×#14583243C2semidirect
6. C2×#14583231C2semidirect
7. C2×#14583206C2semidirect
8. C2×#14583156C2semidirect
9. C2×#14583139C2semidirect
10. C2×#14583109C2semidirect
11. C2×#14583053C2semidirect
12. C2×#14583053C2semidirect
14. C2×#14582906C2semidirect
15. C2×#103×D43C2semidirect
16. C2×C43×#441C2semidirect
44. #14583268C22semidirect
45. #14583243C22semidirect
46. #14583231C22semidirect
47. #14583206C22semidirect
48. #14583156C22semidirect
49. #14583139C22semidirect
50. #14583109C22semidirect
51. #14583053C22semidirect
52. #14583053C22semidirect
57. #14582906C22semidirect
66. #103×D43C22semidirect
72. C43×#441C22semidirect
392. C2×#441D43semidirect
396. C2×C43#3312semidirect
441. #441C2×D43semidirect
462. C43C2×#3312semidirect
767. C2#19146651direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835902
C2×Q8×D1722
#191466512
C2×#145832682
C2×#145832432
C2×#145832312
C2×#145832062
C2×#145831562
C2×#145831392
C2×#145831092
C2×#145830532
C2×#145829722
C2×#145829062
C2×#103×D432
C2×C43×#4412
C2×#331243