Finite Group Databasebeta

← C2×#19146696 #25973256

Subgroups — C2×#19146696 #25973256

Order 11008.

2126 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×#14583590C211yesmaximal, characteristic, complemented
2C2×#14583553C211yesmaximal, characteristic
3#19146696C2116yesmaximal, direct product factor
4C2×#14583268C211yesmaximal, characteristic, complemented
5C2×#14583236C211yesmaximal, characteristic, complemented
6C2×#14583242C211yesmaximal, characteristic, complemented
7C2×#14583199C211yesmaximal, characteristic, complemented
8C2×#14583156C211yesmaximal, characteristic, complemented
9C2×#14583139C211yesmaximal, characteristic, complemented
10C2×#14583109C211yesmaximal, characteristic, complemented
11C2×#14583058C211yesmaximal, characteristic, complemented
12C2×#14583058C211yesmaximal, characteristic, complemented
13C2×#14582972C211yesmaximal, characteristic, complemented
14C2×#14582897C211yesmaximal, characteristic, complemented
15C2×#14582892C211yesmaximal, characteristic, complemented
16C2×C43×#440C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×#10621900C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621885C2211yescharacteristic
21C22×#10621872C2211yescharacteristic
22C22×C8×D43C2211yescharacteristic
23#14583590—24no—
24#14583590C2218yescomplemented
25#14583553—24no—
26#14583553C2218yes—
27C2×#13063325C2211yescharacteristic
28C2×#13063319—21no—
29C2×#13063317C2211yescharacteristic
30C2×#13063315—21no—
31C2×#13063310—21no—
32C2×#13063309—21no—
33C2×#13063309—21no—
34C2×#13063305C2211yescharacteristic
35C2×#13063305C2211yescharacteristic
36C2×#13063301C2211yescharacteristic
37C2×#13063301C2211yescharacteristic
38C2×#13063299—21no—
39C2×C4×D172C2211yescharacteristic
40C2×#13063283C2211yescharacteristic
41C2×#13063282—21no—
42C22×C4⋊Dic43—21no—
43C2×C4⋊C4×D43C2211yescharacteristic
44#14583268C2218yescomplemented
45#14583242C2218yescomplemented
46#14583236C2218yescomplemented
47#14583199C2218yescomplemented
48#14583156C2218yescomplemented
49#14583139C2218yescomplemented
50#14583109C2218yescomplemented
51#14583058C2218yescomplemented
52#14583058C2218yescomplemented
53#14582972C2218yescomplemented
54C2×#13063258C2211yescharacteristic
55C2×#13063256C2211yescharacteristic
56C2×C4⋊(C43⋊C8)C2211yescharacteristic
57#14582897C2218yescomplemented
58#14582892C2218yescomplemented
59C2×#13063250C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063250C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×#13063246C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
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×#10621900—24no—
78C2×#10621900—24no—
79C2×#10621900—22no—
80C2×#10621900—22no—
81C2×#10621900—42no—
82C2×#10621900—42no—
83C2×#10621900C2314yes—
84C2×#10621900C2314yes—
85C22×Dic86C2311yescharacteristic
86C22×Dic86C2311yescharacteristic
87C22×D172D411yescharacteristic
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C23×Dic43—21no—
91C23×Dic43—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#13063325C2314yes—
107#13063319—28no—
108#13063317—22no—
109#13063317C2314yes—
110#13063315—28no—
111#13063310—28no—
112#13063309—28no—
113#13063309—28no—
114#13063305—22no—
115#13063305—22no—
116#13063305C2314yes—
117#13063305C2314yes—
118#13063301—22no—
119#13063301—22no—
120#13063301C2314yes—
121#13063301C2314yes—
122#13063299—28no—
123C4×D172D414yes—
124C4×D172C2314yes—
125#13063283—22no—
126#13063283C2314yes—
127#13063282—28no—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43—21no—
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43—28no—
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#13063248C2314yes—
159#13063248C2314yes—
160#13063246C2314yes—
161#13063246C2314yes—
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yes—
164C22×Q8×C43C2311yescharacteristic
165C22×D4×C43C2311yescharacteristic
166C23×C4×C43—21no—
167C2×SD16×C43—24no—
168C2×SD16×C43C2314yes—
169C22×C8×C43C2311yescharacteristic
170C22×C8×C43C2311yescharacteristic
171C4×Q8×C43—22no—
172C4×Q8×C43C2314yes—
173C4×D4×C43—22no—
174C4×D4×C43C2314yes—
175C2×C4⋊C4×C43—21no—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C22⋊C4×C43—21no—
179C2×C42×C43—21no—
180C2×C42×C43C2311yescharacteristic
181#107×C43C2314yes—
182#103×C43C2314yes—
183#102×C43C2314yes—
184#97×C43C2314yes—
185C24×C43—21no—
186C23×D43C2×D411yescharacteristic
187C23×D43C2×D411yescharacteristic
188C2×Q8×C43—21no—
189C2×Q8×C43—22no—
190C2×Q8×C43—22no—
191C2×Q8×C43C2412yes—
192C2×D4×C43—21no—
193C2×D4×C43—22no—
194C2×D4×C43#4114yes—
195C2×D4×C43C2412yes—
196C22×C4×C43—24no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—44no—
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2411yescharacteristic
204C2×C22⋊D43—24no—
205C2×C22⋊D43—24no—
206C2×C22⋊D43—44no—
207C2×C22⋊D43—44no—
208C22×Dic43—24no—
209C22×Dic43—24no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—44no—
215C22×Dic43—44no—
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218#10621900—28no—
219#10621900—28no—
220#10621900—44no—
221#10621900—44no—
222#10621900—48no—
223#10621900—48no—
224C2×D172—42no—
225C2×D172C2×D414yes—
226C2×C4×D43—22no—
227C2×C4×D43—22no—
228C2×C4×D43—22no—
229C2×C4×D43—22no—
230C2×C4×D43—24no—
231C2×C4×D43—44no—
232C2×C4×D43C2×D412yes—
233C2×C4×D43C2×D412yes—
234C2×C4×D43C2412yes—
235C2×C4×D43C2412yes—
236C2×Dic86—22no—
237C2×Dic86—22no—
238C2×Dic86—22no—
239C2×Dic86—22no—
240C2×Dic86—21no—
241C2×Dic86—21no—
242C2×Dic86C2412yes—
243C2×Dic86C2412yes—
244SD16×C43—28no—
245C2×C8×C43—22no—
246C2×C8×C43—22no—
247C2×C8×C43C2412yes—
248C2×C8×C43C2412yes—
249C4⋊C4×C43—24no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43C2412yes—
253C4⋊C4×C43C2412yes—
254C22⋊C4×C43—24no—
255C42×C43—24no—
256C42×C43C2×D412yes—
257C42×C43C2412yes—
258#10621885—44no—
259#10621885—44no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4C2×D414yes—
266(C2×D43)⋊C4C2×D414yes—
267C4⋊Dic43—21no—
268C4⋊Dic43—24no—
269C4⋊Dic43—24no—
270C4⋊Dic43—21no—
271C4⋊Dic43—24no—
272C4⋊Dic43—24no—
273C4⋊Dic43C2×D414yes—
274C4⋊Dic43C2412yes—
275C4⋊Dic43C2412yes—
276Dic43⋊C4—24no—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4—24no—
280Dic43⋊C4—24no—
281C4×Dic43—24no—
282C2×C43⋊C8—22no—
283C2×C43⋊C8—22no—
284C2×C43⋊C8C2412yes—
285C2×C43⋊C8C2412yes—
286#10621872—44no—
287C8×D43—44no—
288C23×C43—24no—
289C23×C43—22no—
290C23×C43—42no—
291C23×C43—42no—
292C23×C43C22×D411yescharacteristic
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43C22×D412yes—
300C22×D43C22×D412yes—
301Q8×C43—22no—
302Q8×C43—22no—
303Q8×C43—42no—
304D4×C43—24no—
305D4×C43—22no—
306D4×C43C2×#4114yes—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—48no—
313C2×C4×C43—42no—
314C2×C4×C43—42no—
315C2×C4×C43—42no—
316C2×C4×C43C22×D412yes—
317C2×C4×C43C22×D412yes—
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C2×#4112yes—
320C2×C4×C43H(5,𝔽2)12yes—
321C2×C4×C43C2511yescharacteristic
322C22⋊D43—48no—
323C22⋊D43—48no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—48no—
331C2×Dic43—48no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43C22×D412yes—
337C2×Dic43C22×D412yes—
338D172—44no—
339C4×D43—24no—
340C4×D43—24no—
341C4×D43—22no—
342C4×D43—22no—
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—48no—
346Dic86—22no—
347Dic86—22no—
348Dic86—22no—
349Dic86—22no—
350Dic86—42no—
351Dic86—42no—
352C8×C43—22no—
353C8×C43—22no—
354C43⋊C8—22no—
355C43⋊C8—22no—
356C2×#3315—431nomaximal, Sylow
357C22×C43—24no—
358C22×C43—48no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43#54612yes—
362C22×C43#57512yes—
363C22×C43#57812yes—
364C22×C43C23×D411yescharacteristic
365C2×D43—22no—
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—22no—
369C2×D43—22no—
370C2×D43—22no—
371C2×D43—44no—
372C2×D43—44no—
373C4×C43—22no—
374C4×C43—22no—
375C4×C43—42no—
376C4×C43—42no—
377C4×C43—42no—
378C4×C43#54612yes—
379C4×C43C22×#4111yescharacteristic
380C4×C43C2×H(5,𝔽2)11yescharacteristic
381Dic43—22no—
382Dic43—22no—
383Dic43—42no—
384Dic43—42no—
385Dic43—42no—
386Dic43—42no—
387C2×#552—431no—
388C2×#547—431no—
389#3315—4316no—
390C2×#491—431no—
391C2×#484—431no—
392C2×#485—431no—
393C2×#478—431no—
394C2×#470—431no—
395C2×#467—431no—
396C2×#462—431no—
397C2×#452—431no—
398C2×#452—431no—
399C2×#440D4311yescharacteristic, complemented
400C2×#435—431no—
401C2×#417—431no—
402C2×#416—431no—
403C2×C43—44no—
404C2×C43#331514yescomplemented
405C2×C43C2×#54611yescharacteristic
406C2×C43C2×#57511yescharacteristic
407C2×C43C2×#57811yescharacteristic
408D43—42no—
409D43—42no—
410C22×#41—431no—
411C22×#41—431no—
412C22×Q16—431no—
413C22×Q16—431no—
414C22×SD16C2×D4311yescharacteristic
415C22×M16—431no—
416C23×C8—431no—
417#552—438no—
418#552—864no—
419#547—438no—
420#547—864no—
421C2×C4⋊Q8—431no—
422C2×#126—861no—
423C2×#125—431no—
424C2×#125—861no—
425C2×#123—861no—
426C2×#123—861no—
427C2×#123—861no—
428C2×C22⋊Q8—431no—
429C2×C22⋊Q8—431no—
430C2×C22⋊Q8—431no—
431C2×C22⋊Q8—431no—
432C2×#121—861no—
433C2×C4×Q8C2×D4311yescharacteristic
434C2×C4×D4—431no—
435C2×C4×D4C2×D4311yescharacteristic
436C2×#117—431no—
437C2×#117—861no—
438C22×C4⋊C4—431no—
439C22×C4⋊C4—861no—
440#491—438no—
441#485—438no—
442#484—438no—
443#478—438no—
444#470—438no—
445#467—438no—
446#462—438no—
447#452—438no—
448#452—438no—
449#440C2×D4318yescomplemented
450#435—438no—
451C2×#107—431no—
452C2×#107C2×D4311yescharacteristic
453C2×#106—431no—
454C2×C4⋊C8—431no—
455#417—438no—
456#416—438no—
457C2×#103—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#103—431no—
461C2×#103—431no—
462C2×#103—431no—
463C2×#103C2×D4311yescharacteristic
464C2×#102—431no—
465C2×#102—431no—
466C2×#102C2×D4311yescharacteristic
467C2×C22⋊C8—431no—
468C2×C22⋊C8—431no—
469C2×#97C2×D4311yescharacteristic
470C43C2×#331511yescharacteristic, complemented, Sylow
471C2×#41—434no—
472C2×#41—434no—
473C2×#41—862no—
474C2×#41—862no—
475C2×#41—864no—
476C2×#41—864no—
477C2×#41—1722no—
478C2×#41—1722no—
479C22×Q8—431no—
480C22×Q8—431no—
481C22×Q8C22×D4311yescharacteristic
482C22×D4—431no—
483C22×D4—861no—
484C22×D4—861no—
485C22×D4C22×D4311yescharacteristic
486C23×C4—21no—
487C23×C4—431no—
488C23×C4—431no—
489C23×C4—861no—
490C23×C4—861no—
491C23×C4—861no—
492C2×Q16—434no—
493C2×Q16—434no—
494C2×Q16—1722no—
495C2×Q16—1722no—
496C2×SD16—24no—
497C2×SD16C22×D4314yes—
498C2×M16—434no—
499C2×M16—1722no—
500C22×C8—431no—
501C22×C8—431no—
502C22×C8—434no—
503C22×C8—1722no—
504C22×C8C22×D4311yescharacteristic
505C22×C8C22×D4311yescharacteristic
506C4⋊Q8—434no—
507C4⋊Q8—862no—
508#126—868no—
509#125—434no—
510#125—868no—
511#125—862no—
512#123—868no—
513#123—868no—
514#123—868no—
515C22⋊Q8—434no—
516C22⋊Q8—434no—
517C22⋊Q8—434no—
518C22⋊Q8—434no—
519C22⋊Q8—862no—
520C22⋊Q8—862no—
521C22⋊Q8—862no—
522C22⋊Q8—862no—
523#121—868no—
524C4×Q8—22no—
525C4×Q8C22×D4314yes—
526C4×D4—22no—
527C4×D4—434no—
528C4×D4—434no—
529C4×D4C22×D4314yes—
530#117—434no—
531#117—868no—
532#117—862no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—431no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—434no—
538C2×C4⋊C4—862no—
539C2×C4⋊C4—868no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4—861no—
545C2×C4⋊C4—861no—
546C2×C4⋊C4—861no—
547C2×C4⋊C4—861no—
548C2×C4⋊C4—861no—
549C2×C4⋊C4C22×D4311yescharacteristic
550C2×C4⋊C4C22×D4311yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—431no—
553C2×C22⋊C4—431no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4—861no—
559C2×C42—21no—
560C2×C42—861no—
561C2×C42C22×D4311yescharacteristic
562#107—434no—
563#107C22×D4314yes—
564#106—434no—
565C4⋊C8—434no—
566#103—434no—
567#103—434no—
568#103—434no—
569#103—434no—
570#103—434no—
571#103—434no—
572#103C22×D4314yes—
573#102—434no—
574#102—434no—
575#102C22×D4314yes—
576C22⋊C8—434no—
577C22⋊C8—434no—
578#97C22×D4314yes—
579C24—21no—
580C24—431no—
581C24—431no—
582#41—868no—
583#41—868no—
584#41—1724no—
585#41—1724no—
586#41—1728no—
587#41—1728no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—432no—
592C2×Q8—432no—
593C2×Q8—861no—
594C2×Q8—861no—
595C2×Q8—862no—
596C2×Q8—862no—
597C2×Q8—862no—
598C2×Q8—862no—
599C2×Q8C23×D4312yes—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—434no—
603C2×D4—864no—
604C2×D4—864no—
605C2×D4—1722no—
606C2×D4—1724no—
607C2×D4—1724no—
608C2×D4#1062189814yes—
609C2×D4C23×D4312yes—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—24no—
614C22×C4—44no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—432no—
618C22×C4—432no—
619C22×C4—432no—
620C22×C4—432no—
621C22×C4—864no—
622C22×C4—864no—
623C22×C4—864no—
624C22×C4—862no—
625C22×C4—862no—
626C22×C4—862no—
627C22×C4—862no—
628C22×C4—861no—
629C22×C4—861no—
630C22×C4—861no—
631C22×C4—861no—
632C22×C4—1724no—
633C22×C4—1724no—
634C22×C4—1724no—
635C22×C4D4×D4311yescharacteristic
636C22×C4D4×D4311yescharacteristic
637C22×C4C23×D4311yescharacteristic
638Q16—1724no—
639Q16—1724no—
640SD16—28no—
641M16—1724no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—432no—
645C2×C8—432no—
646C2×C8—862no—
647C2×C8—862no—
648C2×C8—1724no—
649C2×C8C23×D4312yes—
650C2×C8C23×D4312yes—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—434no—
655C4⋊C4—432no—
656C4⋊C4—432no—
657C4⋊C4—864no—
658C4⋊C4—864no—
659C4⋊C4—864no—
660C4⋊C4—864no—
661C4⋊C4—864no—
662C4⋊C4—861no—
663C4⋊C4—861no—
664C4⋊C4—864no—
665C4⋊C4—864no—
666C4⋊C4—864no—
667C4⋊C4—864no—
668C4⋊C4C23×D4312yes—
669C4⋊C4C23×D4312yes—
670C22⋊C4—24no—
671C22⋊C4—434no—
672C22⋊C4—434no—
673C22⋊C4—864no—
674C22⋊C4—864no—
675C22⋊C4—864no—
676C22⋊C4—864no—
677C22⋊C4—864no—
678C42—24no—
679C42—864no—
680C42D4×D4312yes—
681C42C23×D4312yes—
682C23—22no—
683C23—24no—
684C23—42no—
685C23—42no—
686C23—432no—
687C23—432no—
688C23—862no—
689C23—862no—
690C23—862no—
691C23—862no—
692C23—862no—
693C23—862no—
694C23C2×D4×D4311yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—42no—
698Q8—862no—
699Q8—862no—
700Q8—862no—
701Q8—862no—
702Q8—1722no—
703Q8—1722no—
704D4—22no—
705D4—24no—
706D4—1724no—
707D4—1728no—
708D4—1728no—
709D4C2×#1062189814yes—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—48no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—432no—
720C2×C4—432no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—864no—
728C2×C4—864no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—1728no—
734C2×C4—1728no—
735C2×C4—1728no—
736C2×C4—1722no—
737C2×C4—1722no—
738C2×C4—1722no—
739C2×C4—1722no—
740C2×C4C2×D4×D4312yes—
741C2×C4C2×D4×D4312yes—
742C2×C4C2×D4×D4311yescharacteristic
743C2×C4C2×#1062189812yes—
744C2×C4#1306337112yes—
745C2×C4C24×D4311yescharacteristic
746C8—22no—
747C8—22no—
748C8—862no—
749C8—862no—
750C22—24no—
751C22—42no—
752C22—42no—
753C22—48no—
754C22—862no—
755C22—862no—
756C22—862no—
757C22—862no—
758C22—862no—
759C22—862no—
760C22—1724no—
761C22—1724no—
762C22#1458354512yes—
763C22#1458369512yes—
764C22#1458371512yes—
765C22C22×D4×D4311yescharacteristic
766C4—22no—
767C4—22no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—862no—
772C4—862no—
773C4—1722no—
774C4—1722no—
775C4—1722no—
776C4—1722no—
777C4#1458354512yes—
778C4C22×#1062189811yescharacteristic
779C4C2×#1306337111yescharacteristic
780C2—44no—
781C2—1722no—
782C2—1722no—
783C2#1914669614yesdirect product factor
784C2C2×#1458354511yescharacteristic
785C2C2×#1458369511yescharacteristic
786C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#440C2
socleC23×C43C22×D4
prime radicalC2×#14583553C2
hypercenterC2×#440D43
hypocenterC43C2×#3315
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
1. C2×#14583590C2semidirect
3. #19146696C2direct (N × H)
4. C2×#14583268C2semidirect
5. C2×#14583236C2semidirect
6. C2×#14583242C2semidirect
7. C2×#14583199C2semidirect
8. C2×#14583156C2semidirect
9. C2×#14583139C2semidirect
10. C2×#14583109C2semidirect
11. C2×#14583058C2semidirect
12. C2×#14583058C2semidirect
13. C2×#14582972C2semidirect
14. C2×#14582897C2semidirect
15. C2×#14582892C2semidirect
16. C2×C43×#440C2semidirect
24. #14583590C22semidirect
44. #14583268C22semidirect
45. #14583242C22semidirect
46. #14583236C22semidirect
47. #14583199C22semidirect
48. #14583156C22semidirect
49. #14583139C22semidirect
50. #14583109C22semidirect
51. #14583058C22semidirect
52. #14583058C22semidirect
53. #14582972C22semidirect
57. #14582897C22semidirect
58. #14582892C22semidirect
72. C43×#440C22semidirect
399. C2×#440D43semidirect
404. C2×C43#3315semidirect
449. #440C2×D43semidirect
470. C43C2×#3315semidirect
783. C2#19146696direct (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×#145835532
#191466962
C2×#145832682
C2×#145832362
C2×#145832422
C2×#145831992
C2×#145831562
C2×#145831392
C2×#145831092
C2×#145830582
C2×#145829722
C2×#145828972
C2×#145828922
C2×C43×#4402
C2×#331543