Finite Group Databasebeta

← C2×#20255515 #27092997

Subgroups — C2×#20255515 #27092997

Order 12032.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689808C211yesmaximal, characteristic, complemented
2C2×#15689792C211yesmaximal, characteristic
3#20255515C2116yesmaximal, direct product factor
4C2×#15689486C211yesmaximal, characteristic, complemented
5C2×#15689441C211yesmaximal, characteristic, complemented
6C2×#15689445C211yesmaximal, characteristic, complemented
7C2×#15689432C211yesmaximal, characteristic, complemented
8C2×#15689369C211yesmaximal, characteristic, complemented
9C2×#15689351C211yesmaximal, characteristic, complemented
10C2×#15689322C211yesmaximal, characteristic, complemented
11C2×#15689288C211yesmaximal, characteristic, complemented
12C2×#15689285C211yesmaximal, characteristic, complemented
13C2×#15689227C211yesmaximal, characteristic, complemented
14C2×#15689192C211yesmaximal, characteristic, complemented
15C2×#15689118C211yesmaximal, characteristic, complemented
16C2×C47×#417C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×#10625335C2211yescharacteristic
21C22×C8×D47C2211yescharacteristic
22#15689808—24no—
23#15689808C2218yescomplemented
24#15689792—24no—
25#15689792C2218yes—
26C2×#13094020—21no—
27C2×#13094020C2211yescharacteristic
28C2×#13094019—21no—
29C2×#13094015C2211yescharacteristic
30C2×#13094014—21no—
31C2×#13094007—21no—
32C2×#13094004C2211yescharacteristic
33C2×#13094003C2211yescharacteristic
34C2×#13093998—21no—
35C2×#13093998C2211yescharacteristic
36C2×#13093995—21no—
37C2×#13093995C2211yescharacteristic
38C2×Q8×Dic47C2211yescharacteristic
39C2×#13093989C2211yescharacteristic
40C2×C4×C22⋊D47—21no—
41C2×C4×C22⋊D47C2211yescharacteristic
42C2×#13093983—21no—
43C2×#13093982C2211yescharacteristic
44#15689486C2218yescomplemented
45#15689445C2218yescomplemented
46#15689441C2218yescomplemented
47#15689432C2218yescomplemented
48#15689369C2218yescomplemented
49#15689351C2218yescomplemented
50#15689322C2218yescomplemented
51#15689288C2218yescomplemented
52#15689285C2218yescomplemented
53#15689227C2218yescomplemented
54#15689192C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093955C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59#15689118C2218yescomplemented
60C2×#13093949C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093945C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69C22×#41×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic
71C22×C4⋊C4×C47C2211yescharacteristic
72C47×#417C2218yescomplemented
73C2×#103×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C2×#10625354—22no—
78C2×#10625354—24no—
79C2×#10625354—42no—
80C2×#10625354C2314yes—
81C22×Dic94C2311yescharacteristic
82C22×D188—21no—
83C22×D188C2311yescharacteristic
84C22×C22⋊D47—21no—
85C22×C22⋊D47—21no—
86C22×C22⋊D47—21no—
87C22×C22⋊D47—21no—
88C22×C22⋊D47D411yescharacteristic
89C22×C4×D47—21no—
90C22×C4×D47C2311yescharacteristic
91C2×#10625337—24no—
92C2×#10625337C2314yes—
93C2×#10625325—42no—
94C2×#10625325C2314yes—
95C2×#10625335—42no—
96C2×#10625335C2314yes—
97C22×C47⋊C8C2311yescharacteristic
98C22×C47⋊C8C2311yescharacteristic
99C2×C8×D47—42no—
100C2×C8×D47C2314yes—
101#13094020—28no—
102#13094020—22no—
103#13094020C2314yes—
104#13094019—28no—
105#13094015—22no—
106#13094015C2314yes—
107#13094014—28no—
108#13094007—28no—
109#13094004—22no—
110#13094004C2314yes—
111#13094003—22no—
112#13094003C2314yes—
113#13093998—22no—
114#13093998—28no—
115#13093998C2314yes—
116#13093995—22no—
117#13093995—28no—
118#13093995C2314yes—
119Q8×Dic47—22no—
120Q8×Dic47C2314yes—
121#13093989—22no—
122#13093989C2314yes—
123C4×C22⋊D47—28no—
124C4×C22⋊D47D414yes—
125C4×C22⋊D47C2314yes—
126#13093983—28no—
127#13093982—22no—
128#13093982C2314yes—
129C2×C4⋊Dic47—21no—
130C2×C4⋊Dic47—21no—
131C2×C4⋊Dic47—21no—
132C2×C4⋊Dic47C2311yescharacteristic
133C2×C4⋊Dic47C2311yescharacteristic
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4D411yescharacteristic
138C2×C22⋊Dic47—21no—
139C2×C22⋊Dic47—21no—
140C2×C22⋊Dic47D411yescharacteristic
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4D411yescharacteristic
145C2×C4×Dic47—21no—
146C2×C4×Dic47—21no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47C2311yescharacteristic
149#13093958C2314yes—
150#13093955C2314yes—
151#13093955C2314yes—
152Dic47⋊C8C2314yes—
153#13093949C2314yes—
154#13093948C2314yes—
155#13093946C2314yes—
156#13093945C2314yes—
157#13093944C2314yes—
158#13093944C2314yes—
159C22⋊(C47⋊C8)C2314yes—
160(C2×D47)⋊C8C2314yes—
161#13093934C2314yes—
162C2×#41×C47—22no—
163C2×#41×C47—24no—
164C2×#41×C47—42no—
165C2×#41×C47C2314yes—
166C22×Q8×C47C2311yescharacteristic
167C22×D4×C47—21no—
168C22×D4×C47C2311yescharacteristic
169C23×C4×C47—21no—
170C23×C4×C47—21no—
171C23×C4×C47C2311yescharacteristic
172C2×M16×C47—42no—
173C2×M16×C47C2314yes—
174C22×C8×C47C2311yescharacteristic
175C22×C8×C47C2311yescharacteristic
176C2×C4⋊C4×C47—22no—
177C2×C4⋊C4×C47—21no—
178C2×C4⋊C4×C47C2314yes—
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C4⋊C4×C47C2311yescharacteristic
181#103×C47C2314yes—
182#103×C47C2314yes—
183#102×C47C2314yes—
184#102×C47C2314yes—
185C24×C47—21no—
186C24×C47C2×D411yescharacteristic
187C23×D47—21no—
188C23×D47C2×D411yescharacteristic
189#41×C47—28no—
190#41×C47—44no—
191#41×C47—48no—
192C2×Q8×C47—21no—
193C2×Q8×C47—22no—
194C2×Q8×C47#4114yes—
195C2×Q8×C47C2412yes—
196C2×D4×C47—24no—
197C2×D4×C47—21no—
198C2×D4×C47—22no—
199C2×D4×C47—22no—
200C2×D4×C47—44no—
201C2×D4×C47C2412yes—
202C22×C4×C47—21no—
203C22×C4×C47—22no—
204C22×C4×C47—22no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—24no—
208C22×C4×C47—24no—
209C22×C4×C47—44no—
210C22×C4×C47—44no—
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D412yes—
213C22×C4×C47C2412yes—
214C22×C4×C47C2411yescharacteristic
215C2×C22⋊D47—24no—
216C2×C22⋊D47—24no—
217C2×C22⋊D47—24no—
218C2×C22⋊D47—24no—
219C2×C22⋊D47—42no—
220C2×C22⋊D47—44no—
221C2×C22⋊D47—82no—
222C2×C22⋊D47—82no—
223C2×C22⋊D47—82no—
224C2×C22⋊D47C2×D414yes—
225C22×Dic47—21no—
226C22×Dic47—21no—
227C22×Dic47—21no—
228C22×Dic47C2×D411yescharacteristic
229C22×Dic47C2×D411yescharacteristic
230C22×Dic47C2×D411yescharacteristic
231#10625354—28no—
232#10625354—44no—
233#10625354—48no—
234C2×D188—22no—
235C2×D188—22no—
236C2×D188—24no—
237C2×D188—21no—
238C2×D188—44no—
239C2×D188C2412yes—
240C2×C4×D47—22no—
241C2×C4×D47—22no—
242C2×C4×D47—24no—
243C2×C4×D47—44no—
244C2×C4×D47C2×D412yes—
245C2×C4×D47C2412yes—
246C2×Dic94—22no—
247C2×Dic94—22no—
248C2×Dic94—21no—
249C2×Dic94C2412yes—
250M16×C47—44no—
251C2×C8×C47—22no—
252C2×C8×C47—22no—
253C2×C8×C47C2412yes—
254C2×C8×C47C2412yes—
255C4⋊C4×C47—21no—
256C4⋊C4×C47—21no—
257C4⋊C4×C47—24no—
258C4⋊C4×C47C2412yes—
259C4⋊C4×C47C2412yes—
260C22⋊Dic47—24no—
261C22⋊Dic47—24no—
262C22⋊Dic47C2×D414yes—
263#10625337—28no—
264#10625335—44no—
265(C2×D47)⋊C4—24no—
266(C2×D47)⋊C4—24no—
267(C2×D47)⋊C4—24no—
268(C2×D47)⋊C4C2×D414yes—
269C4⋊Dic47—21no—
270C4⋊Dic47—21no—
271C4⋊Dic47—24no—
272C4⋊Dic47—24no—
273C4⋊Dic47—24no—
274C4⋊Dic47C2412yes—
275C4⋊Dic47C2412yes—
276Dic47⋊C4—24no—
277Dic47⋊C4—24no—
278Dic47⋊C4—24no—
279Dic47⋊C4C2×D414yes—
280C4×Dic47—24no—
281C4×Dic47—24no—
282C4×Dic47—24no—
283C4×Dic47C2×D412yes—
284C4×Dic47C2412yes—
285C2×C47⋊C8—22no—
286C2×C47⋊C8—22no—
287C2×C47⋊C8C2412yes—
288C2×C47⋊C8C2412yes—
289#10625325—44no—
290C8×D47—44no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—42no—
296C23×C47—42no—
297C23×C47—42no—
298C23×C47C22×D412yes—
299C23×C47C22×D411yescharacteristic
300C22×D47—22no—
301C22×D47—22no—
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—42no—
305C22×D47—42no—
306C22×D47—42no—
307C22×D47C22×D412yes—
308Q8×C47—24no—
309Q8×C47—22no—
310Q8×C47C2×#4114yes—
311D4×C47—22no—
312D4×C47—22no—
313D4×C47—48no—
314D4×C47—42no—
315C2×C4×C47—24no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—24no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—48no—
324C2×C4×C47—48no—
325C2×C4×C47—42no—
326C2×C4×C47—42no—
327C2×C4×C47C22×D412yes—
328C2×C4×C47C22×D411yescharacteristic
329C2×C4×C47C2×#4112yes—
330C2×C4×C47H(5,𝔽2)12yes—
331C2×C4×C47C2511yescharacteristic
332C22⋊D47—44no—
333C22⋊D47—48no—
334C22⋊D47—84no—
335C22⋊D47—84no—
336C22⋊D47—84no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—42no—
344C2×Dic47—42no—
345C2×Dic47—42no—
346C2×Dic47C22×D412yes—
347C2×Dic47C22×D412yes—
348C2×Dic47C22×D412yes—
349D188—22no—
350D188—22no—
351D188—48no—
352D188—42no—
353C4×D47—24no—
354C4×D47—22no—
355C4×D47—22no—
356C4×D47—48no—
357Dic94—22no—
358Dic94—22no—
359Dic94—42no—
360C8×C47—22no—
361C8×C47—22no—
362C47⋊C8—22no—
363C47⋊C8—22no—
364C2×#3317—471nomaximal, Sylow
365C22×C47—22no—
366C22×C47—22no—
367C22×C47—22no—
368C22×C47—44no—
369C22×C47—42no—
370C22×C47—42no—
371C22×C47—42no—
372C22×C47—84no—
373C22×C47#54612yes—
374C22×C47#57512yes—
375C22×C47#57712yes—
376C22×C47C23×D411yescharacteristic
377C2×D47—22no—
378C2×D47—22no—
379C2×D47—22no—
380C2×D47—44no—
381C2×D47—42no—
382C2×D47—42no—
383C2×D47—42no—
384C2×D47—84no—
385C4×C47—24no—
386C4×C47—22no—
387C4×C47—42no—
388C4×C47—42no—
389C4×C47#54612yes—
390C4×C47C22×#4111yescharacteristic
391C4×C47C2×H(5,𝔽2)11yescharacteristic
392Dic47—22no—
393Dic47—22no—
394Dic47—22no—
395Dic47—42no—
396Dic47—42no—
397Dic47—42no—
398C2×#552—471no—
399C2×#550—471no—
400#3317—4716no—
401C2×#490—471no—
402C2×#481—471no—
403C2×#482—471no—
404C2×#479—471no—
405C2×#468—471no—
406C2×#465—471no—
407C2×#460—471no—
408C2×#452—471no—
409C2×#452—471no—
410C2×#441—471no—
411C2×#435—471no—
412C2×#417D4711yescharacteristic, complemented
413C2×#416—471no—
414C2×C47—42no—
415C2×C47—82no—
416C2×C47#331714yescomplemented
417C2×C47C2×#54611yescharacteristic
418C2×C47C2×#57511yescharacteristic
419C2×C47C2×#57711yescharacteristic
420D47—42no—
421D47—82no—
422C22×#41—471no—
423C22×#41C2×D4711yescharacteristic
424C22×Q16—471no—
425C22×SD16—471no—
426C22×SD16—471no—
427C22×M16C2×D4711yescharacteristic
428C23×C8—471no—
429#552—478no—
430#552—944no—
431#550—478no—
432#550—944no—
433C2×#127—471no—
434C2×#127—941no—
435C2×#126—941no—
436C2×#125—471no—
437C2×#125—941no—
438C2×#123—941no—
439C2×C22⋊Q8—471no—
440C2×C22⋊Q8—471no—
441C2×#121—471no—
442C2×#121—471no—
443C2×#121—941no—
444C2×#121—941no—
445C2×C4×Q8—471no—
446C2×C4×Q8—471no—
447C2×C4×D4—471no—
448C2×C4×D4—941no—
449C2×#117—471no—
450C2×#117—941no—
451C22×C4⋊C4C2×D4711yescharacteristic
452#490—478no—
453#482—478no—
454#481—478no—
455#479—478no—
456#468—478no—
457#465—478no—
458#460—478no—
459#452—478no—
460#452—478no—
461#441—478no—
462#435—478no—
463C2×#107—471no—
464C2×#106—471no—
465C2×#106—471no—
466C2×C4⋊C8—471no—
467#417C2×D4718yescomplemented
468#416—478no—
469C2×#103—471no—
470C2×#103—471no—
471C2×#103C2×D4711yescharacteristic
472C2×#103C2×D4711yescharacteristic
473C2×#102—471no—
474C2×#102—471no—
475C2×#102—471no—
476C2×#102—471no—
477C2×#102C2×D4711yescharacteristic
478C2×#102C2×D4711yescharacteristic
479C2×C22⋊C8—471no—
480C2×C22⋊C8—471no—
481C2×#97—471no—
482C47C2×#331711yescharacteristic, complemented, Sylow
483C2×#41—22no—
484C2×#41—24no—
485C2×#41—42no—
486C2×#41—474no—
487C2×#41—942no—
488C2×#41—944no—
489C2×#41—1882no—
490C2×#41C22×D4714yes—
491C22×Q8—471no—
492C22×Q8C22×D4711yescharacteristic
493C22×D4—21no—
494C22×D4—471no—
495C22×D4—471no—
496C22×D4—941no—
497C22×D4—941no—
498C22×D4—941no—
499C22×D4—941no—
500C22×D4—941no—
501C22×D4C22×D4711yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—471no—
505C23×C4—941no—
506C23×C4C22×D4711yescharacteristic
507C2×Q16—474no—
508C2×Q16—944no—
509C2×SD16—474no—
510C2×SD16—474no—
511C2×SD16—1882no—
512C2×SD16—1882no—
513C2×M16—42no—
514C2×M16C22×D4714yes—
515C22×C8—471no—
516C22×C8—471no—
517C22×C8—474no—
518C22×C8—1882no—
519C22×C8C22×D4711yescharacteristic
520C22×C8C22×D4711yescharacteristic
521#127—474no—
522#127—942no—
523#127—948no—
524#126—948no—
525#125—474no—
526#125—942no—
527#125—948no—
528#123—948no—
529C22⋊Q8—474no—
530C22⋊Q8—474no—
531C22⋊Q8—942no—
532C22⋊Q8—942no—
533#121—474no—
534#121—474no—
535#121—948no—
536#121—948no—
537#121—942no—
538#121—942no—
539C4×Q8—474no—
540C4×Q8—474no—
541C4×Q8—942no—
542C4×Q8—942no—
543C4×D4—474no—
544C4×D4—474no—
545C4×D4—948no—
546#117—474no—
547#117—948no—
548#117—942no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—471no—
552C2×C4⋊C4—471no—
553C2×C4⋊C4—471no—
554C2×C4⋊C4—941no—
555C2×C4⋊C4—941no—
556C2×C4⋊C4—941no—
557C2×C4⋊C4—941no—
558C2×C4⋊C4—941no—
559C2×C4⋊C4—941no—
560C2×C4⋊C4C22×D4711yescharacteristic
561C2×C4⋊C4C22×D4711yescharacteristic
562C2×C4⋊C4C22×D4714yes—
563C2×C22⋊C4—471no—
564C2×C22⋊C4—471no—
565C2×C22⋊C4—941no—
566C2×C22⋊C4—941no—
567C2×C22⋊C4—941no—
568C2×C22⋊C4—941no—
569C2×C22⋊C4—941no—
570C2×C42—471no—
571C2×C42—941no—
572C2×C42—941no—
573C2×C42—941no—
574#107—474no—
575#106—474no—
576#106—474no—
577C4⋊C8—474no—
578#103—474no—
579#103—474no—
580#103C22×D4714yes—
581#103C22×D4714yes—
582#102—474no—
583#102—474no—
584#102—474no—
585#102—474no—
586#102C22×D4714yes—
587#102C22×D4714yes—
588C22⋊C8—474no—
589C22⋊C8—474no—
590#97—474no—
591C24—21no—
592C24—471no—
593C24—941no—
594C24D4×D4711yescharacteristic
595#41—28no—
596#41—44no—
597#41—48no—
598#41—948no—
599#41—1884no—
600#41—1888no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—472no—
604C2×Q8—941no—
605C2×Q8—942no—
606C2×Q8—942no—
607C2×Q8#1062535014yes—
608C2×Q8C23×D4712yes—
609C2×D4—24no—
610C2×D4—21no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—44no—
614C2×D4—474no—
615C2×D4—472no—
616C2×D4—944no—
617C2×D4—944no—
618C2×D4—944no—
619C2×D4—944no—
620C2×D4—944no—
621C2×D4—941no—
622C2×D4—942no—
623C2×D4—942no—
624C2×D4—3762no—
625C2×D4—3762no—
626C2×D4—3762no—
627C2×D4—1884no—
628C2×D4—1882no—
629C2×D4—1884no—
630C2×D4C23×D4712yes—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—24no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—24no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—471no—
641C22×C4—471no—
642C22×C4—471no—
643C22×C4—472no—
644C22×C4—472no—
645C22×C4—944no—
646C22×C4—942no—
647C22×C4—942no—
648C22×C4—941no—
649C22×C4—941no—
650C22×C4—941no—
651C22×C4—1884no—
652C22×C4D4×D4712yes—
653C22×C4D4×D4711yescharacteristic
654C22×C4C23×D4712yes—
655C22×C4C23×D4711yescharacteristic
656Q16—948no—
657SD16—1884no—
658SD16—1884no—
659M16—44no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—472no—
663C2×C8—472no—
664C2×C8—942no—
665C2×C8—942no—
666C2×C8—1884no—
667C2×C8C23×D4712yes—
668C2×C8C23×D4712yes—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—474no—
673C4⋊C4—472no—
674C4⋊C4—472no—
675C4⋊C4—944no—
676C4⋊C4—944no—
677C4⋊C4—944no—
678C4⋊C4—944no—
679C4⋊C4—944no—
680C4⋊C4—944no—
681C4⋊C4—941no—
682C4⋊C4—941no—
683C4⋊C4C23×D4712yes—
684C4⋊C4C23×D4712yes—
685C22⋊C4—474no—
686C22⋊C4—474no—
687C22⋊C4—944no—
688C22⋊C4—944no—
689C22⋊C4—944no—
690C22⋊C4—944no—
691C22⋊C4—944no—
692C42—472no—
693C42—472no—
694C42—944no—
695C42—944no—
696C42—944no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—472no—
705C23—942no—
706C23—942no—
707C23—942no—
708C23—942no—
709C23—1882no—
710C23—1882no—
711C23—1882no—
712C23C2×D4×D4712yes—
713C23C2×D4×D4711yescharacteristic
714Q8—24no—
715Q8—22no—
716Q8—942no—
717Q8—942no—
718Q8—1882no—
719Q8C2×#1062535014yes—
720D4—22no—
721D4—22no—
722D4—48no—
723D4—42no—
724D4—942no—
725D4—942no—
726D4—3764no—
727D4—3764no—
728D4—3764no—
729D4—1888no—
730D4—1884no—
731D4—1888no—
732D4—1882no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—48no—
742C2×C4—48no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—472no—
746C2×C4—472no—
747C2×C4—472no—
748C2×C4—942no—
749C2×C4—942no—
750C2×C4—942no—
751C2×C4—944no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—942no—
756C2×C4—942no—
757C2×C4—1888no—
758C2×C4—1882no—
759C2×C4—1882no—
760C2×C4—1882no—
761C2×C4C2×D4×D4712yes—
762C2×C4C2×D4×D4711yescharacteristic
763C2×C4C2×#1062535012yes—
764C2×C4#1309406912yes—
765C2×C4C24×D4711yescharacteristic
766C8—22no—
767C8—22no—
768C8—942no—
769C8—942no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—84no—
778C22—942no—
779C22—942no—
780C22—942no—
781C22—3764no—
782C22—1882no—
783C22—1882no—
784C22—1882no—
785C22—1884no—
786C22#1568976312yes—
787C22#1568991912yes—
788C22#1568993212yes—
789C22C22×D4×D4711yescharacteristic
790C4—22no—
791C4—24no—
792C4—42no—
793C4—42no—
794C4—942no—
795C4—942no—
796C4—942no—
797C4—1882no—
798C4—1882no—
799C4—1882no—
800C4#1568976312yes—
801C4C22×#1062535011yescharacteristic
802C4C2×#1309406911yescharacteristic
803C2—42no—
804C2—82no—
805C2—3762no—
806C2—1882no—
807C2#2025551514yesdirect product factor
808C2C2×#1568976311yescharacteristic
809C2C2×#1568991911yescharacteristic
810C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#417C2
socleC23×C47C22×D4
prime radicalC2×#15689792C2
hypercenterC2×#417D47
hypocenterC47C2×#3317
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#15689808C2semidirect
3. #20255515C2direct (N × H)
4. C2×#15689486C2semidirect
5. C2×#15689441C2semidirect
6. C2×#15689445C2semidirect
7. C2×#15689432C2semidirect
8. C2×#15689369C2semidirect
9. C2×#15689351C2semidirect
10. C2×#15689322C2semidirect
11. C2×#15689288C2semidirect
12. C2×#15689285C2semidirect
13. C2×#15689227C2semidirect
14. C2×#15689192C2semidirect
15. C2×#15689118C2semidirect
16. C2×C47×#417C2semidirect
23. #15689808C22semidirect
44. #15689486C22semidirect
45. #15689445C22semidirect
46. #15689441C22semidirect
47. #15689432C22semidirect
48. #15689369C22semidirect
49. #15689351C22semidirect
50. #15689322C22semidirect
51. #15689288C22semidirect
52. #15689285C22semidirect
53. #15689227C22semidirect
54. #15689192C22semidirect
59. #15689118C22semidirect
72. C47×#417C22semidirect
412. C2×#417D47semidirect
416. C2×C47#3317semidirect
467. #417C2×D47semidirect
482. C47C2×#3317semidirect
807. C2#20255515direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898082
C2×#156897922
#202555152
C2×#156894862
C2×#156894412
C2×#156894452
C2×#156894322
C2×#156893692
C2×#156893512
C2×#156893222
C2×#156892882
C2×#156892852
C2×#156892272
C2×#156891922
C2×#156891182
C2×C47×#4172
C2×#331747