Finite Group Databasebeta

← C2×#20252858 #27083115

Subgroups — C2×#20252858 #27083115

Order 12032.

2810 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094056C211yesmaximal, characteristic, complemented
2C22×#13094053C211yesmaximal, characteristic, complemented
3C2×#15689672C211yesmaximal, characteristic
4C2×C4×Q8×D47C211yesmaximal, characteristic, complemented
5#20252858C2116yesmaximal, direct product factor
6C2×#15689346C211yesmaximal, characteristic, complemented
7C2×#15689345C211yesmaximal, characteristic, complemented
8C2×#15689342C211yesmaximal, characteristic, complemented
9C2×#15689332C211yesmaximal, characteristic, complemented
10C2×#15689331C211yesmaximal, characteristic, complemented
11C2×#15689322C211yesmaximal, characteristic, complemented
12C2×#15689321C211yesmaximal, characteristic, complemented
13C2×#15689145C211yesmaximal, characteristic, complemented
14C2×#15689123C211yesmaximal, characteristic, complemented
15C2×#15689121C211yesmaximal, characteristic, complemented
16C2×C47×#464C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625352C2211yescharacteristic
19C22×Q8×D47C2211yescharacteristic
20C2×#13094056—28no—
21C2×#13094056C2218yescomplemented
22C2×#13094053—28no—
23C2×#13094053C2218yescomplemented
24C22×Dic188C2211yescharacteristic
25C22×#10625337C2211yescharacteristic
26C22×#10625337C2211yescharacteristic
27C22×#10625325C2211yescharacteristic
28C22×#10625335C2211yescharacteristic
29C22×#10625336C2211yescharacteristic
30C22×#10625324C2211yescharacteristic
31C22×#10625324C2211yescharacteristic
32#15689672—24no—
33#15689672C2218yes—
34C2×#13094022C2211yescharacteristic
35C2×#13094020C2211yescharacteristic
36C2×#13094012C2211yescharacteristic
37C2×#13093997—21no—
38C2×#13093997—21no—
39C2×Q8×Dic47C2211yescharacteristic
40C2×C4×Dic94—21no—
41C2×C4×Dic94C2211yescharacteristic
42C2×#13093989—21no—
43C2×#13093989C2211yescharacteristic
44C4×Q8×D47—24no—
45C4×Q8×D47C2218yescomplemented
46C2×(C22⋊D47)⋊C4—21no—
47C2×(C22⋊D47)⋊C4—21no—
48C2×C4⋊C4×D47—21no—
49C2×C4⋊C4×D47C2211yescharacteristic
50C2×C42×D47—21no—
51C2×C42×D47C2211yescharacteristic
52#15689346C2218yescomplemented
53#15689345C2218yescomplemented
54#15689342C2218yescomplemented
55#15689332C2218yescomplemented
56#15689331C2218yescomplemented
57#15689322C2218yescomplemented
58#15689321C2218yescomplemented
59#15689145C2218yescomplemented
60C2×C4⋊(C47⋊C8)C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63#15689123C2218yescomplemented
64#15689121C2218yescomplemented
65C2×#13093949C2211yescharacteristic
66C2×#13093948C2211yescharacteristic
67C2×#13093947C2211yescharacteristic
68C2×#13093946C2211yescharacteristic
69C2×#13093945C2211yescharacteristic
70C2×#13093944C2211yescharacteristic
71C22×Q16×C47C2211yescharacteristic
72C22×SD16×C47C2211yescharacteristic
73C2×#124×C47C2211yescharacteristic
74C2×C4×Q8×C47C2211yescharacteristic
75C47×#464C2218yescomplemented
76C2×C4⋊C8×C47C2211yescharacteristic
77C2×#103×C47C2211yescharacteristic
78C2×#102×C47C2211yescharacteristic
79C2×#10625354—22no—
80C2×#10625354—24no—
81C2×#10625354—24no—
82C2×#10625354C2314yes—
83C2×#10625352—24no—
84C2×#10625352—22no—
85C2×#10625352—24no—
86C2×#10625352C2314yes—
87C22×Dic94—21no—
88C22×Dic94C2311yescharacteristic
89C22×Dic94C2311yescharacteristic
90C2×Q8×D47—22no—
91C2×Q8×D47—24no—
92C2×Q8×D47D418yescomplemented
93C2×Q8×D47C2314yes—
94C22×D188—21no—
95C22×D188C2311yescharacteristic
96C22×C22⋊D47—21no—
97C22×C22⋊D47—21no—
98C22×C22⋊D47—21no—
99C23×Dic47—21no—
100C22×C4×D47—21no—
101C22×C4×D47—21no—
102C22×C4×D47—21no—
103C22×C4×D47D411yescharacteristic
104C22×C4×D47D411yescharacteristic
105C22×C4×D47C2311yescharacteristic
106#13094056—232no—
107#13094053—232no—
108C2×Dic188—24no—
109C2×Dic188C2314yes—
110C2×#10625337—24no—
111C2×#10625337—24no—
112C2×#10625337C2314yes—
113C2×#10625337C2314yes—
114C2×#10625325—24no—
115C2×#10625325C2314yes—
116C2×#10625335—24no—
117C2×#10625335C2314yes—
118C2×#10625336—24no—
119C2×#10625336C2314yes—
120C2×#10625324—24no—
121C2×#10625324—24no—
122C2×#10625324C2314yes—
123C2×#10625324C2314yes—
124C22×C47⋊C8C2311yescharacteristic
125C22×C47⋊C8C2311yescharacteristic
126#13094022—22no—
127#13094022C2314yes—
128#13094020—22no—
129#13094020C2314yes—
130#13094012—22no—
131#13094012C2314yes—
132#13093997—28no—
133#13093997—28no—
134Q8×Dic47—22no—
135Q8×Dic47C2314yes—
136C4×Dic94—22no—
137C4×Dic94—28no—
138C4×Dic94C2314yes—
139#13093989—22no—
140#13093989—28no—
141#13093989C2314yes—
142(C22⋊D47)⋊C4—28no—
143(C22⋊D47)⋊C4—28no—
144C2×C4⋊Dic47—21no—
145C2×C4⋊Dic47C2311yescharacteristic
146C2×Dic47⋊C4—21no—
147C2×Dic47⋊C4—21no—
148C2×Dic47⋊C4—21no—
149C2×Dic47⋊C4—21no—
150C2×Dic47⋊C4—21no—
151C4⋊C4×D47—28no—
152C4⋊C4×D47—22no—
153C4⋊C4×D47C2314yes—
154C2×(C2×D47)⋊C4—21no—
155C2×(C2×D47)⋊C4—21no—
156C2×C4×Dic47—21no—
157C2×C4×Dic47—21no—
158C2×C4×Dic47—21no—
159C2×C4×Dic47D411yescharacteristic
160C2×C4×Dic47D411yescharacteristic
161C2×C4×Dic47C2311yescharacteristic
162C42×D47—28no—
163C42×D47D414yes—
164C42×D47C2314yes—
165C4⋊(C47⋊C8)C2314yes—
166Dic47⋊C8C2314yes—
167Dic47⋊C8C2314yes—
168#13093949C2314yes—
169#13093948C2314yes—
170#13093947C2314yes—
171#13093946C2314yes—
172#13093945C2314yes—
173#13093944C2314yes—
174C22×Q8×C47C2311yescharacteristic
175C22×Q8×C47C2311yescharacteristic
176C22×D4×C47C2311yescharacteristic
177C2×Q16×C47—24no—
178C2×Q16×C47C2314yes—
179C2×SD16×C47—24no—
180C2×SD16×C47C2314yes—
181C22×C8×C47C2311yescharacteristic
182C22×C8×C47C2311yescharacteristic
183#124×C47—22no—
184#124×C47C2314yes—
185C4×Q8×C47—22no—
186C4×Q8×C47C2314yes—
187C2×C4⋊C4×C47—21no—
188C2×C4⋊C4×C47C2311yescharacteristic
189C2×C22⋊C4×C47—21no—
190C2×C22⋊C4×C47—21no—
191C2×C42×C47—21no—
192C2×C42×C47C2311yescharacteristic
193C4⋊C8×C47C2314yes—
194#103×C47C2314yes—
195#102×C47C2314yes—
196C24×C47—21no—
197C23×D47—21no—
198C23×D47C2×D411yescharacteristic
199C2×Q8×C47—21no—
200C2×Q8×C47—21no—
201C2×Q8×C47—22no—
202C2×Q8×C47—22no—
203C2×Q8×C47—22no—
204C2×Q8×C47C2×D414yes—
205C2×Q8×C47C2412yes—
206C2×Q8×C47C2412yes—
207C2×D4×C47—22no—
208C2×D4×C47—21no—
209C2×D4×C47—22no—
210C2×D4×C47C2412yes—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2411yescharacteristic
217C2×C22⋊D47—24no—
218C2×C22⋊D47—24no—
219C2×C22⋊D47—24no—
220C2×C22⋊D47—44no—
221C2×C22⋊D47—44no—
222C2×C22⋊D47—44no—
223C22×Dic47—21no—
224C22×Dic47—21no—
225C22×Dic47—21no—
226C22×Dic47—24no—
227C22×Dic47—44no—
228C22×Dic47C2×D411yescharacteristic
229C22×Dic47C2×D411yescharacteristic
230C22×Dic47C2×D411yescharacteristic
231#10625354—28no—
232#10625354—28no—
233#10625354—48no—
234Q8×D47—216no—
235Q8×D47—28no—
236Q8×D47C2×D4116yescomplemented
237#10625352—28no—
238#10625352—28no—
239#10625352—48no—
240C2×D188—22no—
241C2×D188—22no—
242C2×D188—24no—
243C2×D188—21no—
244C2×D188—44no—
245C2×D188C2412yes—
246C2×C4×D47—28no—
247C2×C4×D47—24no—
248C2×C4×D47—24no—
249C2×C4×D47—24no—
250C2×C4×D47—24no—
251C2×C4×D47—42no—
252C2×C4×D47—44no—
253C2×C4×D47—44no—
254C2×C4×D47C2×D414yes—
255C2×C4×D47C2×D414yes—
256C2×C4×D47C2×D412yes—
257C2×C4×D47C2×D414yes—
258C2×C4×D47#4114yes—
259C2×C4×D47C2412yes—
260C2×Dic94—21no—
261C2×Dic94—22no—
262C2×Dic94—28no—
263C2×Dic94—24no—
264C2×Dic94—22no—
265C2×Dic94—22no—
266C2×Dic94—21no—
267C2×Dic94C2×D414yes—
268C2×Dic94C2412yes—
269C2×Dic94C2412yes—
270Q16×C47—28no—
271SD16×C47—28no—
272C2×C8×C47—22no—
273C2×C8×C47—22no—
274C2×C8×C47C2412yes—
275C2×C8×C47C2412yes—
276C4⋊C4×C47—24no—
277C4⋊C4×C47—21no—
278C4⋊C4×C47C2412yes—
279C22⋊C4×C47—24no—
280C22⋊C4×C47—24no—
281C42×C47—24no—
282C42×C47C2×D412yes—
283C42×C47C2412yes—
284#10625337—28no—
285#10625337—28no—
286#10625336—28no—
287#10625335—28no—
288(C2×D47)⋊C4—24no—
289(C2×D47)⋊C4—24no—
290C4⋊Dic47—21no—
291C4⋊Dic47—24no—
292C4⋊Dic47C2412yes—
293Dic47⋊C4—24no—
294Dic47⋊C4—24no—
295Dic47⋊C4—24no—
296Dic47⋊C4—24no—
297Dic47⋊C4—24no—
298C4×Dic47—24no—
299C4×Dic47—24no—
300C4×Dic47—24no—
301C4×Dic47C2×D412yes—
302C4×Dic47C2×D414yes—
303C4×Dic47C2×D414yes—
304C4×Dic47C2412yes—
305C2×C47⋊C8—22no—
306C2×C47⋊C8—22no—
307C2×C47⋊C8C2412yes—
308C2×C47⋊C8C2412yes—
309Dic188—28no—
310#10625325—28no—
311#10625324—28no—
312#10625324—28no—
313C23×C47—22no—
314C23×C47—42no—
315C23×C47—42no—
316C23×C47—42no—
317C23×C47C22×D411yescharacteristic
318C22×D47—22no—
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—42no—
322C22×D47—42no—
323C22×D47—42no—
324C22×D47#12114yes—
325C22×D47C22×D412yes—
326Q8×C47—24no—
327Q8×C47—22no—
328Q8×C47—22no—
329Q8×C47—22no—
330Q8×C47—42no—
331Q8×C47C22×D414yes—
332D4×C47—22no—
333D4×C47—22no—
334D4×C47—42no—
335C2×C4×C47—24no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—42no—
342C2×C4×C47—42no—
343C2×C4×C47C22×D412yes—
344C2×C4×C47C22×D412yes—
345C2×C4×C47C22×D411yescharacteristic
346C2×C4×C47C22×D412yes—
347C2×C4×C47C2×#4112yes—
348C2×C4×C47C2511yescharacteristic
349C22⋊D47—48no—
350C22⋊D47—48no—
351C22⋊D47—48no—
352C2×Dic47—24no—
353C2×Dic47—22no—
354C2×Dic47—22no—
355C2×Dic47—22no—
356C2×Dic47—22no—
357C2×Dic47—42no—
358C2×Dic47—42no—
359C2×Dic47—48no—
360C2×Dic47#12114yes—
361C2×Dic47#13714yescomplemented
362C2×Dic47C22×D412yes—
363C2×Dic47C22×D412yes—
364C2×Dic47C22×D412yes—
365D188—22no—
366D188—22no—
367D188—48no—
368D188—42no—
369C4×D47—216no—
370C4×D47—28no—
371C4×D47—44no—
372C4×D47—48no—
373C4×D47—48no—
374C4×D47#12118yes—
375C4×D47C22×D414yes—
376C4×D47C2×#4114yes—
377Dic94—24no—
378Dic94—22no—
379Dic94—216no—
380Dic94—22no—
381Dic94—22no—
382Dic94—42no—
383Dic94C22×D414yes—
384C8×C47—22no—
385C8×C47—22no—
386C47⋊C8—22no—
387C47⋊C8—22no—
388C2×#3037—471nomaximal, Sylow
389C22×C47—42no—
390C22×C47—42no—
391C22×C47—42no—
392C22×C47—84no—
393C22×C47C2×#12112yes—
394C22×C47C2×#13712yes—
395C22×C47#57512yes—
396C22×C47C23×D411yescharacteristic
397C2×D47—28no—
398C2×D47—22no—
399C2×D47—22no—
400C2×D47—42no—
401C2×D47—42no—
402C2×D47—42no—
403C2×D47—84no—
404C2×D47C2×#12114yes—
405C4×C47—24no—
406C4×C47—22no—
407C4×C47—22no—
408C4×C47—42no—
409C4×C47—42no—
410C4×C47C2×#12112yes—
411C4×C47C23×D411yescharacteristic
412C4×C47C22×#4111yescharacteristic
413Dic47—24no—
414Dic47—22no—
415Dic47—42no—
416Dic47—42no—
417Dic47C2×#12114yes—
418Dic47C2×#13714yescomplemented
419C22×#137—471no—
420C22×#137—471no—
421C2×#532—471no—
422C22×C4×Q8—471no—
423#3037—4716no—
424C2×#464—471no—
425C2×#464—471no—
426C2×#464—471no—
427C2×#464D4711yescharacteristic, complemented
428C2×#462—471no—
429C2×#462—471no—
430C2×#460—471no—
431C2×#460—471no—
432C2×#423—471no—
433C2×#417—471no—
434C2×#417—471no—
435C2×C47—82no—
436C2×C47#303714yescomplemented
437C2×C47C22×#12111yescharacteristic
438C2×C47C22×#13711yescharacteristic
439C2×C47C2×#57511yescharacteristic
440D47—24no—
441D47—82no—
442C22×#41—471no—
443C22×#41—471no—
444C23×Q8—471no—
445C2×#137—478no—
446C2×#137—478no—
447C2×#137—948no—
448C2×#137—948no—
449C22×Q16—471no—
450C22×Q16—471no—
451C22×Q16—471no—
452C22×Q16C2×D4711yescharacteristic
453C22×SD16—471no—
454C22×SD16—471no—
455C22×SD16—471no—
456C22×SD16C2×D4711yescharacteristic
457C22×M16—471no—
458C22×M16—471no—
459#532—478no—
460#532—944no—
461C2×C4⋊Q8—471no—
462C2×#127—471no—
463C2×#124—471no—
464C2×#124C2×D4711yescharacteristic
465C2×#121—941no—
466C2×#121—941no—
467C2×C4×Q8—471no—
468C2×C4×Q8—478no—
469C2×C4×Q8—471no—
470C2×C4×Q8—471no—
471C2×C4×Q8—941no—
472C2×C4×Q8—941no—
473C2×C4×Q8—944no—
474C2×C4×Q8C2×D4711yescharacteristic
475C2×C4×D4—941no—
476C2×C4×D4—941no—
477C22×C4⋊C4—471no—
478C22×C4⋊C4—941no—
479C22×C42—471no—
480C22×C42—941no—
481#464—478no—
482#464—478no—
483#464—478no—
484#464C2×D4718yescomplemented
485#462—478no—
486#462—478no—
487#460—478no—
488#460—478no—
489#423—478no—
490C2×C4⋊C8—471no—
491C2×C4⋊C8—471no—
492C2×C4⋊C8—471no—
493C2×C4⋊C8C2×D4711yescharacteristic
494#417—478no—
495#417—478no—
496C2×#103—471no—
497C2×#103—471no—
498C2×#103—471no—
499C2×#103C2×D4711yescharacteristic
500C2×#102—471no—
501C2×#102—471no—
502C2×#102—471no—
503C2×#102C2×D4711yescharacteristic
504C47C2×#303711yescharacteristic, complemented, Sylow
505C2×#41—474no—
506C2×#41—474no—
507C2×#41—942no—
508C2×#41—942no—
509C2×#41—944no—
510C2×#41—944no—
511C2×#41—944no—
512C2×#41—944no—
513C22×Q8—478no—
514C22×Q8—474no—
515C22×Q8—471no—
516C22×Q8—471no—
517C22×Q8—941no—
518C22×Q8—942no—
519C22×Q8—944no—
520C22×Q8C22×D4711yescharacteristic
521C22×Q8C22×D4711yescharacteristic
522C22×D4—471no—
523C22×D4—941no—
524C22×D4—941no—
525C22×D4—941no—
526C22×D4—941no—
527C22×D4C22×D4711yescharacteristic
528C23×C4—471no—
529C23×C4—471no—
530C23×C4—471no—
531C23×C4—941no—
532C23×C4—941no—
533C23×C4—941no—
534C23×C4—941no—
535#137—9432no—
536#137—9432no—
537C2×Q16—24no—
538C2×Q16—474no—
539C2×Q16—474no—
540C2×Q16—474no—
541C2×Q16—944no—
542C2×Q16—944no—
543C2×Q16—944no—
544C2×Q16C22×D4714yes—
545C2×SD16—24no—
546C2×SD16—474no—
547C2×SD16—474no—
548C2×SD16—474no—
549C2×SD16—944no—
550C2×SD16—944no—
551C2×SD16—944no—
552C2×SD16C22×D4714yes—
553C2×M16—474no—
554C2×M16—474no—
555C2×M16—944no—
556C2×M16—944no—
557C22×C8—471no—
558C22×C8—471no—
559C22×C8C22×D4711yescharacteristic
560C22×C8C22×D4711yescharacteristic
561C4⋊Q8—474no—
562C4⋊Q8—942no—
563#127—474no—
564#127—942no—
565#124—22no—
566#124—474no—
567#124—942no—
568#124C22×D4714yes—
569#121—948no—
570#121—948no—
571C4×Q8—22no—
572C4×Q8—474no—
573C4×Q8—474no—
574C4×Q8—474no—
575C4×Q8—948no—
576C4×Q8—948no—
577C4×Q8—942no—
578C4×Q8—942no—
579C4×Q8—942no—
580C4×Q8C22×D4714yes—
581C4×D4—948no—
582C4×D4—948no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—471no—
585C2×C4⋊C4—474no—
586C2×C4⋊C4—942no—
587C2×C4⋊C4—948no—
588C2×C4⋊C4—941no—
589C2×C4⋊C4—941no—
590C2×C4⋊C4—941no—
591C2×C4⋊C4—941no—
592C2×C4⋊C4—941no—
593C2×C4⋊C4—941no—
594C2×C4⋊C4C22×D4711yescharacteristic
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—941no—
598C2×C22⋊C4—941no—
599C2×C42—21no—
600C2×C42—471no—
601C2×C42—471no—
602C2×C42—471no—
603C2×C42—474no—
604C2×C42—474no—
605C2×C42—948no—
606C2×C42—941no—
607C2×C42—941no—
608C2×C42—941no—
609C2×C42C22×D4711yescharacteristic
610C4⋊C8—474no—
611C4⋊C8—474no—
612C4⋊C8—474no—
613C4⋊C8C22×D4714yes—
614#103—474no—
615#103—474no—
616#103—474no—
617#103C22×D4714yes—
618#102—474no—
619#102—474no—
620#102—474no—
621#102C22×D4714yes—
622C24—21no—
623C24—471no—
624C24—941no—
625#41—948no—
626#41—948no—
627#41—948no—
628#41—948no—
629#41—1888no—
630#41—1888no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—22no—
636C2×Q8—4716no—
637C2×Q8—474no—
638C2×Q8—472no—
639C2×Q8—472no—
640C2×Q8—944no—
641C2×Q8—948no—
642C2×Q8—9416no—
643C2×Q8—948no—
644C2×Q8—941no—
645C2×Q8—941no—
646C2×Q8—942no—
647C2×Q8—942no—
648C2×Q8—942no—
649C2×Q8D4×D4714yes—
650C2×Q8C23×D4712yes—
651C2×Q8C23×D4712yes—
652C2×D4—22no—
653C2×D4—21no—
654C2×D4—22no—
655C2×D4—472no—
656C2×D4—944no—
657C2×D4—944no—
658C2×D4—944no—
659C2×D4—944no—
660C2×D4—942no—
661C2×D4—941no—
662C2×D4—942no—
663C2×D4—1884no—
664C2×D4—1884no—
665C2×D4—1884no—
666C2×D4—1884no—
667C2×D4C23×D4712yes—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—471no—
672C22×C4—471no—
673C22×C4—472no—
674C22×C4—474no—
675C22×C4—474no—
676C22×C4—472no—
677C22×C4—471no—
678C22×C4—474no—
679C22×C4—474no—
680C22×C4—944no—
681C22×C4—944no—
682C22×C4—944no—
683C22×C4—948no—
684C22×C4—944no—
685C22×C4—944no—
686C22×C4—941no—
687C22×C4—941no—
688C22×C4—941no—
689C22×C4—1882no—
690C22×C4—1884no—
691C22×C4—1884no—
692C22×C4—1884no—
693C22×C4D4×D4711yescharacteristic
694C22×C4D4×D4711yescharacteristic
695C22×C4C23×D4711yescharacteristic
696Q16—28no—
697Q16—948no—
698Q16—948no—
699Q16—948no—
700SD16—28no—
701SD16—948no—
702SD16—948no—
703SD16—948no—
704M16—948no—
705M16—948no—
706C2×C8—22no—
707C2×C8—22no—
708C2×C8—472no—
709C2×C8—472no—
710C2×C8—942no—
711C2×C8—942no—
712C2×C8C23×D4712yes—
713C2×C8C23×D4712yes—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—472no—
717C4⋊C4—944no—
718C4⋊C4—944no—
719C4⋊C4—944no—
720C4⋊C4—944no—
721C4⋊C4—944no—
722C4⋊C4—944no—
723C4⋊C4—941no—
724C4⋊C4C23×D4712yes—
725C22⋊C4—24no—
726C22⋊C4—24no—
727C22⋊C4—944no—
728C22⋊C4—944no—
729C42—24no—
730C42—474no—
731C42—474no—
732C42—472no—
733C42—472no—
734C42—944no—
735C42—944no—
736C42—944no—
737C42D4×D4712yes—
738C42C23×D4712yes—
739C23—22no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—474no—
744C23—472no—
745C23—942no—
746C23—942no—
747C23—942no—
748C23—1882no—
749C23—1882no—
750C23—1882no—
751C23C2×D4×D4711yescharacteristic
752Q8—24no—
753Q8—22no—
754Q8—22no—
755Q8—22no—
756Q8—42no—
757Q8—474no—
758Q8—9416no—
759Q8—944no—
760Q8—942no—
761Q8—942no—
762Q8—942no—
763Q8—1882no—
764Q8C2×D4×D4714yes—
765D4—22no—
766D4—22no—
767D4—42no—
768D4—942no—
769D4—942no—
770D4—1888no—
771D4—1888no—
772D4—1888no—
773D4—1888no—
774D4—1882no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—474no—
784C2×C4—474no—
785C2×C4—472no—
786C2×C4—472no—
787C2×C4—478no—
788C2×C4—474no—
789C2×C4—474no—
790C2×C4—472no—
791C2×C4—948no—
792C2×C4—9416no—
793C2×C4—944no—
794C2×C4—942no—
795C2×C4—942no—
796C2×C4—942no—
797C2×C4—942no—
798C2×C4—1884no—
799C2×C4—1888no—
800C2×C4—1888no—
801C2×C4—1888no—
802C2×C4—1882no—
803C2×C4—1882no—
804C2×C4C2×D4×D4712yes—
805C2×C4C2×D4×D4712yes—
806C2×C4C2×D4×D4711yescharacteristic
807C2×C4C2×D4×D4712yes—
808C2×C4#41×D4712yes—
809C2×C4C24×D4711yescharacteristic
810C8—22no—
811C8—22no—
812C8—942no—
813C8—942no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—84no—
818C22—474no—
819C22—942no—
820C22—942no—
821C22—948no—
822C22—3764no—
823C22—1882no—
824C22—1882no—
825C22—1882no—
826C22#121×D4712yes—
827C22#137×D4712yes—
828C22#1568992012yes—
829C22C22×D4×D4711yescharacteristic
830C4—22no—
831C4—22no—
832C4—24no—
833C4—42no—
834C4—42no—
835C4—474no—
836C4—474no—
837C4—942no—
838C4—944no—
839C4—1882no—
840C4—1882no—
841C4#121×D4712yes—
842C4C22×D4×D4711yescharacteristic
843C4C2×#41×D4711yescharacteristic
844C2—82no—
845C2—944no—
846C2—3762no—
847C2#2025285814yesdirect product factor
848C2C2×#121×D4711yescharacteristic
849C2C2×#137×D4711yescharacteristic
850C2C2×#1568992011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#464C2
socleC23×C47C22×D4
prime radicalC2×#15689672C2
hypercenterC2×#464D47
hypocenterC47C2×#3037
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C22×#13094056C2semidirect
2. C22×#13094053C2semidirect
4. C2×C4×Q8×D47C2semidirect
5. #20252858C2direct (N × H)
6. C2×#15689346C2semidirect
7. C2×#15689345C2semidirect
8. C2×#15689342C2semidirect
9. C2×#15689332C2semidirect
10. C2×#15689331C2semidirect
11. C2×#15689322C2semidirect
12. C2×#15689321C2semidirect
13. C2×#15689145C2semidirect
14. C2×#15689123C2semidirect
15. C2×#15689121C2semidirect
16. C2×C47×#464C2semidirect
21. C2×#13094056C22semidirect
23. C2×#13094053C22semidirect
45. C4×Q8×D47C22semidirect
52. #15689346C22semidirect
53. #15689345C22semidirect
54. #15689342C22semidirect
55. #15689332C22semidirect
56. #15689331C22semidirect
57. #15689322C22semidirect
58. #15689321C22semidirect
59. #15689145C22semidirect
63. #15689123C22semidirect
64. #15689121C22semidirect
75. C47×#464C22semidirect
92. C2×Q8×D47D4semidirect
236. Q8×D47C2×D4semidirect
361. C2×Dic47#137semidirect
418. Dic47C2×#137semidirect
427. C2×#464D47semidirect
436. C2×C47#3037semidirect
484. #464C2×D47semidirect
504. C47C2×#3037semidirect
847. C2#20252858direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940562
C22×#130940532
C2×#156896722
C2×C4×Q8×D472
#202528582
C2×#156893462
C2×#156893452
C2×#156893422
C2×#156893322
C2×#156893312
C2×#156893222
C2×#156893212
C2×#156891452
C2×#156891232
C2×#156891212
C2×C47×#4642
C2×#303747