Finite Group Databasebeta

← C2×#20255724 #27093221

Subgroups — C2×#20255724 #27093221

Order 12032.

2210 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689828C211yesmaximal, characteristic, complemented
2C2×#15689791C211yesmaximal, characteristic
3#20255724C2116yesmaximal, direct product factor
4C2×#15689468C211yesmaximal, characteristic, complemented
5C2×#15689438C211yesmaximal, characteristic, complemented
6C2×#15689417C211yesmaximal, characteristic, complemented
7C2×#15689370C211yesmaximal, characteristic, complemented
8C2×#15689367C211yesmaximal, characteristic, complemented
9C2×#15689322C211yesmaximal, characteristic, complemented
10C2×#15689287C211yesmaximal, characteristic, complemented
11C2×#15689286C211yesmaximal, characteristic, complemented
12C2×#15689217C211yesmaximal, characteristic, complemented
13C2×#15689198C211yesmaximal, characteristic, complemented
14C2×#15689122C211yesmaximal, characteristic, complemented
15C2×#15689121C211yesmaximal, characteristic, complemented
16C2×C47×#480C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×#10625352C2211yescharacteristic
19C22×Dic188C2211yescharacteristic
20C22×#10625325C2211yescharacteristic
21C22×#10625335C2211yescharacteristic
22C22×#10625329C2211yescharacteristic
23C22×#10625324C2211yescharacteristic
24#15689828—24no—
25#15689828C2218yescomplemented
26#15689791—24no—
27#15689791C2218yes—
28C2×#13094023C2211yescharacteristic
29C2×#13094020—21no—
30C2×#13094020C2211yescharacteristic
31C2×#13094014—21no—
32C2×#13094004C2211yescharacteristic
33C2×#13094003—21no—
34C2×#13094003C2211yescharacteristic
35C2×#13094002—21no—
36C2×#13093999C2211yescharacteristic
37C2×#13093997—21no—
38C2×#13093996—21no—
39C2×#13093989C2211yescharacteristic
40C2×#13093989C2211yescharacteristic
41C2×C4×C22⋊D47—21no—
42C2×C4×C22⋊D47C2211yescharacteristic
43C2×(C22⋊D47)⋊C4—21no—
44C2×C4⋊C4×D47C2211yescharacteristic
45#15689468C2218yescomplemented
46#15689438C2218yescomplemented
47#15689417C2218yescomplemented
48#15689370C2218yescomplemented
49#15689367C2218yescomplemented
50#15689322C2218yescomplemented
51#15689287C2218yescomplemented
52#15689286C2218yescomplemented
53#15689217C2218yescomplemented
54#15689198C2218yescomplemented
55C2×#13093957C2211yescharacteristic
56C2×Dic47⋊C8C2211yescharacteristic
57#15689122C2218yescomplemented
58#15689121C2218yescomplemented
59C2×#13093949C2211yescharacteristic
60C2×#13093947C2211yescharacteristic
61C2×#13093947C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×#121×C47C2211yescharacteristic
70C22×C4⋊C4×C47C2211yescharacteristic
71C47×#480C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#107×C47C2211yescharacteristic
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C2×#10625350—22no—
78C2×#10625350—24no—
79C2×#10625350—42no—
80C2×#10625350C2314yes—
81C2×#10625352—22no—
82C2×#10625352—24no—
83C2×#10625352—42no—
84C2×#10625352C2314yes—
85C22×Dic94—21no—
86C22×Dic94C2311yescharacteristic
87C22×Dic94C2311yescharacteristic
88C22×D188—21no—
89C22×D188C2311yescharacteristic
90C22×C22⋊D47—21no—
91C22×C22⋊D47—21no—
92C22×C22⋊D47—21no—
93C22×C22⋊D47—21no—
94C22×C22⋊D47D411yescharacteristic
95C23×Dic47—21no—
96C22×C4×D47—21no—
97C22×C4×D47—21no—
98C22×C4×D47C2311yescharacteristic
99C2×Dic188—24no—
100C2×Dic188C2314yes—
101C2×#10625325—42no—
102C2×#10625325C2314yes—
103C2×#10625335—42no—
104C2×#10625335C2314yes—
105C2×#10625329—42no—
106C2×#10625329C2314yes—
107C2×#10625324—42no—
108C2×#10625324C2314yes—
109C22×C47⋊C8C2311yescharacteristic
110C22×C47⋊C8C2311yescharacteristic
111#13094023—22no—
112#13094023C2314yes—
113#13094020—28no—
114#13094020—22no—
115#13094020C2314yes—
116#13094014—28no—
117#13094004—22no—
118#13094004C2314yes—
119#13094003—22no—
120#13094003—28no—
121#13094003C2314yes—
122#13094002—28no—
123#13093999—22no—
124#13093999C2314yes—
125#13093997—28no—
126#13093996—28no—
127#13093989—22no—
128#13093989—22no—
129#13093989C2314yes—
130#13093989C2314yes—
131C4×C22⋊D47—28no—
132C4×C22⋊D47D414yes—
133C4×C22⋊D47C2314yes—
134(C22⋊D47)⋊C4—28no—
135C2×C4⋊Dic47—21no—
136C2×C4⋊Dic47C2311yescharacteristic
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4—21no—
140C2×Dic47⋊C4—21no—
141C2×Dic47⋊C4—21no—
142C2×Dic47⋊C4D411yescharacteristic
143C4⋊C4×D47—22no—
144C4⋊C4×D47C2314yes—
145C2×C22⋊Dic47—21no—
146C2×C22⋊Dic47D411yescharacteristic
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4—21no—
149C2×(C2×D47)⋊C4D411yescharacteristic
150C2×C4×Dic47—21no—
151C2×C4×Dic47—21no—
152C2×C4×Dic47C2311yescharacteristic
153#13093957C2314yes—
154Dic47⋊C8C2314yes—
155#13093949C2314yes—
156#13093947C2314yes—
157#13093947C2314yes—
158#13093947C2314yes—
159#13093946C2314yes—
160#13093945C2314yes—
161#13093944C2314yes—
162#13093944C2314yes—
163(C2×D47)⋊C8C2314yes—
164C8×Dic47C2314yes—
165C22×D4×C47—21no—
166C22×D4×C47C2311yescharacteristic
167C23×C4×C47—21no—
168C23×C4×C47C2311yescharacteristic
169C22×C8×C47C2311yescharacteristic
170C22×C8×C47C2311yescharacteristic
171#121×C47—22no—
172#121×C47C2314yes—
173C2×C4⋊C4×C47—22no—
174C2×C4⋊C4×C47—21no—
175C2×C4⋊C4×C47C2314yes—
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C22⋊C4×C47—21no—
180#107×C47C2314yes—
181#107×C47C2314yes—
182#102×C47C2314yes—
183#102×C47C2314yes—
184C22⋊C8×C47C2314yes—
185C24×C47—21no—
186C24×C47C2×D411yescharacteristic
187C23×D47—21no—
188C23×D47C2×D411yescharacteristic
189C2×D4×C47—24no—
190C2×D4×C47—21no—
191C2×D4×C47—22no—
192C2×D4×C47—22no—
193C2×D4×C47—82no—
194C2×D4×C47C2412yes—
195C22×C4×C47—22no—
196C22×C4×C47—22no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—24no—
201C22×C4×C47—82no—
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D412yes—
204C22×C4×C47C2412yes—
205C22×C4×C47C2411yescharacteristic
206C2×C22⋊D47—24no—
207C2×C22⋊D47—24no—
208C2×C22⋊D47—24no—
209C2×C22⋊D47—24no—
210C2×C22⋊D47—24no—
211C2×C22⋊D47—44no—
212C2×C22⋊D47—44no—
213C2×C22⋊D47—44no—
214C2×C22⋊D47—82no—
215C2×C22⋊D47C2×D414yes—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47—21no—
219C22×Dic47—24no—
220C22×Dic47—44no—
221C22×Dic47C2×D411yescharacteristic
222C22×Dic47C2×D411yescharacteristic
223C22×Dic47C2×D411yescharacteristic
224#10625352—28no—
225#10625352—44no—
226#10625352—48no—
227#10625350—28no—
228#10625350—44no—
229#10625350—48no—
230C2×D188—22no—
231C2×D188—22no—
232C2×D188—21no—
233C2×D188—24no—
234C2×D188—82no—
235C2×D188C2412yes—
236C2×C4×D47—22no—
237C2×C4×D47—22no—
238C2×C4×D47—24no—
239C2×C4×D47—24no—
240C2×C4×D47—44no—
241C2×C4×D47—82no—
242C2×C4×D47C2×D412yes—
243C2×C4×D47C2412yes—
244C2×Dic94—21no—
245C2×Dic94—22no—
246C2×Dic94—22no—
247C2×Dic94—22no—
248C2×Dic94—21no—
249C2×Dic94—24no—
250C2×Dic94—82no—
251C2×Dic94#4114yes—
252C2×Dic94C2412yes—
253C2×Dic94C2412yes—
254C2×C8×C47—22no—
255C2×C8×C47—22no—
256C2×C8×C47C2412yes—
257C2×C8×C47C2412yes—
258C4⋊C4×C47—21no—
259C4⋊C4×C47—24no—
260C4⋊C4×C47—21no—
261C4⋊C4×C47—21no—
262C4⋊C4×C47C2412yes—
263C4⋊C4×C47C2412yes—
264C4⋊C4×C47C2412yes—
265C22⋊C4×C47—24no—
266C22⋊Dic47—24no—
267C22⋊Dic47C2×D414yes—
268#10625335—44no—
269(C2×D47)⋊C4—24no—
270(C2×D47)⋊C4—24no—
271(C2×D47)⋊C4C2×D414yes—
272C4⋊Dic47—21no—
273C4⋊Dic47—24no—
274C4⋊Dic47C2412yes—
275Dic47⋊C4—24no—
276Dic47⋊C4—24no—
277Dic47⋊C4—24no—
278Dic47⋊C4—24no—
279Dic47⋊C4—24no—
280Dic47⋊C4C2×D414yes—
281C4×Dic47—24no—
282C4×Dic47—24no—
283C4×Dic47C2×D412yes—
284C4×Dic47C2412yes—
285#10625329—44no—
286C2×C47⋊C8—22no—
287C2×C47⋊C8—22no—
288C2×C47⋊C8C2412yes—
289C2×C47⋊C8C2412yes—
290Dic188—28no—
291#10625325—44no—
292#10625324—44no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—42no—
298C23×C47—42no—
299C23×C47—42no—
300C23×C47C22×D412yes—
301C23×C47C22×D411yescharacteristic
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—42no—
307C22×D47—42no—
308C22×D47—42no—
309C22×D47C22×D412yes—
310D4×C47—22no—
311D4×C47—22no—
312D4×C47—42no—
313D4×C47—84no—
314C2×C4×C47—22no—
315C2×C4×C47—24no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—42no—
322C2×C4×C47—42no—
323C2×C4×C47—42no—
324C2×C4×C47—84no—
325C2×C4×C47C22×D412yes—
326C2×C4×C47C22×D411yescharacteristic
327C2×C4×C47C2×#4112yes—
328C2×C4×C47H(5,𝔽2)12yes—
329C2×C4×C47C2511yescharacteristic
330C22⋊D47—28no—
331C22⋊D47—48no—
332C22⋊D47—48no—
333C22⋊D47—48no—
334C22⋊D47—84no—
335C2×Dic47—24no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—48no—
342C2×Dic47—42no—
343C2×Dic47—42no—
344C2×Dic47#13714yes—
345C2×Dic47C22×D412yes—
346C2×Dic47C22×D412yes—
347C2×Dic47C22×D412yes—
348D188—22no—
349D188—22no—
350D188—42no—
351D188—84no—
352C4×D47—24no—
353C4×D47—22no—
354C4×D47—22no—
355C4×D47—48no—
356C4×D47—84no—
357Dic94—24no—
358Dic94—22no—
359Dic94—22no—
360Dic94—22no—
361Dic94—42no—
362Dic94—84no—
363Dic94C2×#4114yes—
364C8×C47—22no—
365C8×C47—22no—
366C47⋊C8—22no—
367C47⋊C8—22no—
368C2×#3333—471nomaximal, Sylow
369C22×C47—22no—
370C22×C47—22no—
371C22×C47—22no—
372C22×C47—44no—
373C22×C47—42no—
374C22×C47—42no—
375C22×C47—42no—
376C22×C47—84no—
377C22×C47#54612yes—
378C22×C47C2×#13712yes—
379C22×C47#57612yes—
380C22×C47C23×D411yescharacteristic
381C2×D47—22no—
382C2×D47—22no—
383C2×D47—22no—
384C2×D47—44no—
385C2×D47—42no—
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—84no—
389C4×C47—22no—
390C4×C47—42no—
391C4×C47—42no—
392C4×C47—42no—
393C4×C47#54612yes—
394C4×C47C22×#4111yescharacteristic
395C4×C47C2×H(5,𝔽2)11yescharacteristic
396Dic47—24no—
397Dic47—22no—
398Dic47—22no—
399Dic47—42no—
400Dic47—42no—
401Dic47C2×#13714yes—
402C2×#554—471no—
403C2×#550—471no—
404#3333—4716no—
405C2×#486—471no—
406C2×#480—471no—
407C2×#480D4711yescharacteristic, complemented
408C2×#477—471no—
409C2×#468—471no—
410C2×#468—471no—
411C2×#460—471no—
412C2×#452—471no—
413C2×#452—471no—
414C2×C4×Q16—471no—
415C2×#436—471no—
416C2×#417—471no—
417C2×#417—471no—
418C2×C47—42no—
419C2×C47—82no—
420C2×C47#333314yescomplemented
421C2×C47C2×#54611yescharacteristic
422C2×C47C22×#13711yescharacteristic
423C2×C47C2×#57611yescharacteristic
424D47—42no—
425D47—82no—
426C22×#41—471no—
427C22×#41—471no—
428C22×Q16—471no—
429C22×SD16—471no—
430C22×SD16—471no—
431C22×M16—471no—
432C22×M16—471no—
433#554—478no—
434#554—944no—
435#550—478no—
436#550—944no—
437C2×C4⋊Q8—471no—
438C2×#127—471no—
439C2×#127—941no—
440C2×#125—941no—
441C2×C22⋊Q8—471no—
442C2×C22⋊Q8—471no—
443C2×C22⋊Q8—941no—
444C2×C22⋊Q8—941no—
445C2×#121—471no—
446C2×#121—941no—
447C2×#121—941no—
448C2×#121C2×D4711yescharacteristic
449C2×C4×Q8—471no—
450C2×C4×Q8—471no—
451C2×C4×D4—471no—
452C2×C4×D4—941no—
453C2×C4×D4—941no—
454C22×C4⋊C4—471no—
455C22×C4⋊C4C2×D4711yescharacteristic
456#486—478no—
457#480—478no—
458#480C2×D4718yescomplemented
459#477—478no—
460#468—478no—
461#468—478no—
462#460—478no—
463#452—478no—
464#452—478no—
465C4×Q16—478no—
466#436—478no—
467C2×#107—471no—
468C2×#107C2×D4711yescharacteristic
469C2×#107C2×D4711yescharacteristic
470C2×C4⋊C8—471no—
471#417—478no—
472#417—478no—
473C2×#103—471no—
474C2×#103—471no—
475C2×#103—471no—
476C2×#103—471no—
477C2×#102—471no—
478C2×#102—471no—
479C2×#102—471no—
480C2×#102—471no—
481C2×#102C2×D4711yescharacteristic
482C2×#102C2×D4711yescharacteristic
483C2×C22⋊C8—471no—
484C2×C22⋊C8C2×D4711yescharacteristic
485C2×C4×C8—471no—
486C47C2×#333311yescharacteristic, complemented, Sylow
487C2×#41—474no—
488C2×#41—474no—
489C2×#41—944no—
490C2×#41—942no—
491C2×#41—942no—
492C2×#41—944no—
493C2×#41—1882no—
494C2×#41—1882no—
495C22×Q8—471no—
496C22×Q8—471no—
497C22×Q8—941no—
498C22×D4—21no—
499C22×D4—471no—
500C22×D4—471no—
501C22×D4—941no—
502C22×D4—941no—
503C22×D4—941no—
504C22×D4—941no—
505C22×D4—941no—
506C22×D4C22×D4711yescharacteristic
507C23×C4—21no—
508C23×C4—471no—
509C23×C4—941no—
510C23×C4—941no—
511C23×C4—941no—
512C23×C4C22×D4711yescharacteristic
513C2×Q16—474no—
514C2×Q16—944no—
515C2×SD16—474no—
516C2×SD16—474no—
517C2×SD16—1882no—
518C2×SD16—1882no—
519C2×M16—474no—
520C2×M16—474no—
521C2×M16—1882no—
522C2×M16—1882no—
523C22×C8—471no—
524C22×C8—471no—
525C22×C8C22×D4711yescharacteristic
526C22×C8C22×D4711yescharacteristic
527C4⋊Q8—474no—
528C4⋊Q8—942no—
529#127—474no—
530#127—942no—
531#127—948no—
532#125—948no—
533C22⋊Q8—474no—
534C22⋊Q8—474no—
535C22⋊Q8—948no—
536C22⋊Q8—948no—
537C22⋊Q8—942no—
538C22⋊Q8—942no—
539#121—22no—
540#121—474no—
541#121—948no—
542#121—948no—
543#121—942no—
544#121C22×D4714yes—
545C4×Q8—474no—
546C4×Q8—474no—
547C4×Q8—942no—
548C4×Q8—942no—
549C4×D4—474no—
550C4×D4—474no—
551C4×D4—948no—
552C4×D4—948no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—471no—
556C2×C4⋊C4—471no—
557C2×C4⋊C4—474no—
558C2×C4⋊C4—942no—
559C2×C4⋊C4—941no—
560C2×C4⋊C4—941no—
561C2×C4⋊C4—941no—
562C2×C4⋊C4—941no—
563C2×C4⋊C4—941no—
564C2×C4⋊C4—941no—
565C2×C4⋊C4C22×D4711yescharacteristic
566C2×C4⋊C4C22×D4711yescharacteristic
567C2×C4⋊C4C22×D4714yes—
568C2×C4⋊C4C22×D4711yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—471no—
571C2×C22⋊C4—471no—
572C2×C22⋊C4—941no—
573C2×C22⋊C4—941no—
574C2×C22⋊C4—941no—
575C2×C42—471no—
576C2×C42—941no—
577C2×C42—941no—
578#107—474no—
579#107C22×D4714yes—
580#107C22×D4714yes—
581C4⋊C8—474no—
582#103—474no—
583#103—474no—
584#103—474no—
585#103—474no—
586#102—474no—
587#102—474no—
588#102—474no—
589#102—474no—
590#102C22×D4714yes—
591#102C22×D4714yes—
592C22⋊C8—474no—
593C22⋊C8C22×D4714yes—
594C4×C8—474no—
595C24—21no—
596C24—471no—
597C24—941no—
598C24D4×D4711yescharacteristic
599#41—948no—
600#41—948no—
601#41—1884no—
602#41—1888no—
603#41—1884no—
604#41—1888no—
605C2×Q8—474no—
606C2×Q8—472no—
607C2×Q8—472no—
608C2×Q8—944no—
609C2×Q8—941no—
610C2×Q8—941no—
611C2×Q8—942no—
612C2×Q8—942no—
613C2×Q8—942no—
614C2×Q8—3762no—
615C2×D4—24no—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—82no—
620C2×D4—474no—
621C2×D4—472no—
622C2×D4—944no—
623C2×D4—944no—
624C2×D4—944no—
625C2×D4—944no—
626C2×D4—944no—
627C2×D4—944no—
628C2×D4—941no—
629C2×D4—942no—
630C2×D4—942no—
631C2×D4—3762no—
632C2×D4—3762no—
633C2×D4—1884no—
634C2×D4—1884no—
635C2×D4—1884no—
636C2×D4C23×D4712yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—82no—
644C22×C4—471no—
645C22×C4—471no—
646C22×C4—471no—
647C22×C4—472no—
648C22×C4—472no—
649C22×C4—944no—
650C22×C4—944no—
651C22×C4—941no—
652C22×C4—942no—
653C22×C4—942no—
654C22×C4—941no—
655C22×C4—941no—
656C22×C4—944no—
657C22×C4—3762no—
658C22×C4—1884no—
659C22×C4—1884no—
660C22×C4D4×D4712yes—
661C22×C4D4×D4711yescharacteristic
662C22×C4C23×D4712yes—
663C22×C4C23×D4711yescharacteristic
664Q16—948no—
665SD16—1884no—
666SD16—1884no—
667M16—1884no—
668M16—1884no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—472no—
672C2×C8—472no—
673C2×C8—942no—
674C2×C8—942no—
675C2×C8C23×D4712yes—
676C2×C8C23×D4712yes—
677C4⋊C4—21no—
678C4⋊C4—24no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—474no—
682C4⋊C4—472no—
683C4⋊C4—944no—
684C4⋊C4—944no—
685C4⋊C4—944no—
686C4⋊C4—944no—
687C4⋊C4—944no—
688C4⋊C4—944no—
689C4⋊C4—941no—
690C4⋊C4C23×D4712yes—
691C4⋊C4C23×D4712yes—
692C4⋊C4C23×D4712yes—
693C22⋊C4—24no—
694C22⋊C4—474no—
695C22⋊C4—474no—
696C22⋊C4—944no—
697C22⋊C4—944no—
698C22⋊C4—944no—
699C42—472no—
700C42—472no—
701C42—944no—
702C42—944no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—472no—
711C23—942no—
712C23—942no—
713C23—942no—
714C23—942no—
715C23—1882no—
716C23—1882no—
717C23—1882no—
718C23C2×D4×D4712yes—
719C23C2×D4×D4711yescharacteristic
720Q8—474no—
721Q8—944no—
722Q8—942no—
723Q8—942no—
724Q8—942no—
725Q8—3764no—
726Q8—1882no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—84no—
731D4—948no—
732D4—942no—
733D4—942no—
734D4—3764no—
735D4—3764no—
736D4—1888no—
737D4—1888no—
738D4—1888no—
739D4—1882no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—84no—
751C2×C4—474no—
752C2×C4—472no—
753C2×C4—472no—
754C2×C4—472no—
755C2×C4—942no—
756C2×C4—944no—
757C2×C4—942no—
758C2×C4—942no—
759C2×C4—944no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—3764no—
765C2×C4—1888no—
766C2×C4—1888no—
767C2×C4—1882no—
768C2×C4—1882no—
769C2×C4C2×D4×D4712yes—
770C2×C4C2×D4×D4711yescharacteristic
771C2×C4#41×D4712yes—
772C2×C4#1309407012yes—
773C2×C4C24×D4711yescharacteristic
774C8—22no—
775C8—22no—
776C8—942no—
777C8—942no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—84no—
786C22—942no—
787C22—942no—
788C22—942no—
789C22—3764no—
790C22—1882no—
791C22—1882no—
792C22—1882no—
793C22—1884no—
794C22#1568976512yes—
795C22#137×D4712yes—
796C22#1568992412yes—
797C22C22×D4×D4711yescharacteristic
798C4—22no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—474no—
803C4—942no—
804C4—944no—
805C4—942no—
806C4—1882no—
807C4—1882no—
808C4#1568976512yes—
809C4C2×#41×D4711yescharacteristic
810C4C2×#1309407011yescharacteristic
811C2—42no—
812C2—82no—
813C2—3762no—
814C2—1882no—
815C2#2025572414yesdirect product factor
816C2C2×#1568976511yescharacteristic
817C2C2×#137×D4711yescharacteristic
818C2C2×#1568992411yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#480C2
socleC23×C47C22×D4
prime radicalC2×#15689791C2
hypercenterC2×#480D47
hypocenterC47C2×#3333
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#15689828C2semidirect
3. #20255724C2direct (N × H)
4. C2×#15689468C2semidirect
5. C2×#15689438C2semidirect
6. C2×#15689417C2semidirect
7. C2×#15689370C2semidirect
8. C2×#15689367C2semidirect
9. C2×#15689322C2semidirect
10. C2×#15689287C2semidirect
11. C2×#15689286C2semidirect
12. C2×#15689217C2semidirect
13. C2×#15689198C2semidirect
14. C2×#15689122C2semidirect
15. C2×#15689121C2semidirect
16. C2×C47×#480C2semidirect
25. #15689828C22semidirect
45. #15689468C22semidirect
46. #15689438C22semidirect
47. #15689417C22semidirect
48. #15689370C22semidirect
49. #15689367C22semidirect
50. #15689322C22semidirect
51. #15689287C22semidirect
52. #15689286C22semidirect
53. #15689217C22semidirect
54. #15689198C22semidirect
57. #15689122C22semidirect
58. #15689121C22semidirect
71. C47×#480C22semidirect
407. C2×#480D47semidirect
420. C2×C47#3333semidirect
458. #480C2×D47semidirect
486. C47C2×#3333semidirect
815. C2#20255724direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898282
C2×#156897912
#202557242
C2×#156894682
C2×#156894382
C2×#156894172
C2×#156893702
C2×#156893672
C2×#156893222
C2×#156892872
C2×#156892862
C2×#156892172
C2×#156891982
C2×#156891222
C2×#156891212
C2×C47×#4802
C2×#333347