Finite Group Databasebeta

← #27088544

Subgroups — #27088544

Order 12032.

2006 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256684C211yesmaximal, characteristic
2#20254618C214yesmaximal, complemented
3#20254609C214yesmaximal, complemented
4#20254539C212yesmaximal, complemented
5#20254532C212yesmaximal, complemented
6#20254516C212yesmaximal, complemented
7#20254509C212yesmaximal, complemented
8#20253930C212yesmaximal, complemented
9#20253784C212yesmaximal, complemented
10#20253311C214yesmaximal, complemented
11#20253197C214yesmaximal, complemented
12#20252021C211yesmaximal, characteristic, complemented
13C22×C4⋊Q8×C47C211yesmaximal, characteristic, complemented
14#15689680C2211yescharacteristic
15#15689680C2211yescharacteristic
16#15689680C2211yescharacteristic
17#15689673C2211yescharacteristic
18#15689673C2211yescharacteristic
19#15689673C2211yescharacteristic
20#15689657—21no—
21#15689657—21no—
22#15689657—21no—
23#15689657—21no—
24#15689657C2212yes—
25#15689657C2212yes—
26#15689634—21no—
27#15689634—21no—
28#15689634C2212yes—
29C4×#10625350—21no—
30C4×#10625350—21no—
31C4×#10625350C2212yes—
32#15689529C2218yescomplemented
33#15689526C2214yescomplemented
34#15689519C2214yescomplemented
35#15689485C2218yescomplemented
36#15689475C2214yescomplemented
37#15689471C2214yescomplemented
38#15689458C2218yes—
39#15689453C2218yes—
40#15689441C2218yes—
41#15689436C2218yes—
42#15689415C2218yescomplemented
43#15689410C2218yescomplemented
44#15689405C2218yescomplemented
45#15689400C2218yescomplemented
46#15689180C2212yes—
47#15689180C2212yes—
48#15689176C2212yes—
49#15689176C2212yes—
50#15689163C2218yes—
51#15689147C2212yes—
52#15689122C2218yes—
53#15689087C2212yes—
54C4×#10625329C2212yes—
55C23×Q8×C47—21no—
56C2×C4⋊Q8×C47—21no—
57C2×C4⋊Q8×C47—21no—
58C2×C4⋊Q8×C47—21no—
59C2×C4⋊Q8×C47—21no—
60C2×C4⋊Q8×C47—21no—
61C2×C4⋊Q8×C47—21no—
62C2×C4⋊Q8×C47C2212yes—
63C2×C4⋊Q8×C47C2212yes—
64C2×C4⋊Q8×C47C2212yes—
65C2×C4⋊Q8×C47C2212yes—
66C2×C4⋊Q8×C47C2212yes—
67C2×C4⋊Q8×C47C2212yes—
68C22×C4⋊C4×C47—21no—
69C22×C4⋊C4×C47C2212yes—
70C22×C42×C47C2211yescharacteristic
71C2×#10625350—21no—
72C2×#10625350—21no—
73C2×#10625350C2312yes—
74C2×#10625329C2314yes—
75#13094024C2311yescharacteristic
76#13094024C2311yescharacteristic
77#13094024C2311yescharacteristic
78#13094021C2311yescharacteristic
79#13094018—22no—
80#13094018—22no—
81#13094016—21no—
82#13094016—21no—
83#13094016C2312yes—
84#13094012—21no—
85#13094012—21no—
86#13094012C2312yes—
87#13094007—22no—
88#13094007—22no—
89#13094007—22no—
90#13094003—21no—
91#13094003—21no—
92#13094003—21no—
93#13094003—21no—
94#13094003C2312yes—
95#13094003C2312yes—
96#13093998—21no—
97#13093998—21no—
98#13093998—21no—
99#13093998—21no—
100#13093998C2312yes—
101#13093998C2312yes—
102#13093993—22no—
103C4×Dic94—21no—
104C4×Dic94—21no—
105C4×Dic94—21no—
106C4×Dic94—21no—
107C4×Dic94C2312yes—
108C4×Dic94C2312yes—
109C4×D188—21no—
110C4×D188—21no—
111C4×D188—21no—
112C4×D188—21no—
113C4×D188C2312yes—
114C4×D188C2312yes—
115C4×C22⋊D47—22no—
116C4×C22⋊D47—22no—
117C4×C22⋊D47—22no—
118C4×C22⋊D47—22no—
119C4×C22⋊D47—22no—
120C4×C22⋊D47—22no—
121#13093983—21no—
122#13093983—21no—
123#13093983C2312yes—
124#13093981—22no—
125#13093981—22no—
126#13093981—22no—
127C42×D47—22no—
128#13093957C23116yes—
129#13093955C23116yes—
130C4⋊(C47⋊C8)C2314yes—
131C4⋊(C47⋊C8)C2314yes—
132#13093947C23116yes—
133#13093944C23116yes—
134C22⋊(C47⋊C8)C2314yes—
135C22⋊(C47⋊C8)C2314yes—
136#13093935C2314yes—
137C4×C47⋊C8C2314yes—
138C22×Q8×C47—22no—
139C22×Q8×C47—22no—
140C22×Q8×C47—22no—
141C22×Q8×C47—22no—
142C22×Q8×C47—22no—
143C22×Q8×C47—22no—
144C22×Q8×C47—48no—
145C23×C4×C47—22no—
146C23×C4×C47D411yescharacteristic
147C23×C4×C47D411yescharacteristic
148C23×C4×C47C2311yescharacteristic
149C4⋊Q8×C47—22no—
150C4⋊Q8×C47—22no—
151C4⋊Q8×C47—22no—
152C4⋊Q8×C47—22no—
153C4⋊Q8×C47—22no—
154C4⋊Q8×C47—22no—
155C4⋊Q8×C47—22no—
156C4⋊Q8×C47—22no—
157C4⋊Q8×C47—22no—
158C4⋊Q8×C47—22no—
159C4⋊Q8×C47—22no—
160C4⋊Q8×C47—22no—
161C4⋊Q8×C47C2314yes—
162C4⋊Q8×C47C2314yes—
163C4⋊Q8×C47C2314yes—
164C4⋊Q8×C47C2314yes—
165C2×C4⋊C4×C47—22no—
166C2×C4⋊C4×C47—22no—
167C2×C4⋊C4×C47—22no—
168C2×C4⋊C4×C47—22no—
169C2×C4⋊C4×C47—22no—
170C2×C4⋊C4×C47—22no—
171C2×C4⋊C4×C47—22no—
172C2×C4⋊C4×C47—22no—
173C2×C4⋊C4×C47—22no—
174C2×C4⋊C4×C47C2314yes—
175C2×C4⋊C4×C47C2314yes—
176C2×C4⋊C4×C47C2314yes—
177C2×C42×C47D411yescharacteristic
178C2×C42×C47D411yescharacteristic
179C2×C42×C47D411yescharacteristic
180C2×C42×C47D411yescharacteristic
181C2×C42×C47D411yescharacteristic
182C2×C42×C47D411yescharacteristic
183C2×C42×C47C2311yescharacteristic
184C2×C42×C47C2311yescharacteristic
185C2×C42×C47C2311yescharacteristic
186C2×C42×C47C2311yescharacteristic
187C2×C42×C47C2311yescharacteristic
188C2×C42×C47C2311yescharacteristic
189C24×C47C2×D411yescharacteristic
190C2×Q8×C47—24no—
191C2×Q8×C47—24no—
192C2×Q8×C47—24no—
193C2×Q8×C47—24no—
194C2×Q8×C47—48no—
195C2×Q8×C47—48no—
196C2×Q8×C47—48no—
197C2×Q8×C47—48no—
198C2×Q8×C47—48no—
199C2×Q8×C47—48no—
200C22×C4×C47—24no—
201C22×C4×C47—24no—
202C22×C4×C47—24no—
203C22×C4×C47—24no—
204C22×C4×C47—24no—
205C22×C4×C47—24no—
206C22×C4×C47—48no—
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2×D411yescharacteristic
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2411yescharacteristic
223C22×C4×C47C2411yescharacteristic
224C22×C4×C47C2411yescharacteristic
225C2×C22⋊D47—22no—
226C2×C22⋊D47—22no—
227C2×C22⋊D47—22no—
228#10625350—28no—
229#10625350—44no—
230#10625350—44no—
231C2×D188—21no—
232C2×D188—21no—
233C2×D188C2412yes—
234C2×C4×D47—22no—
235C2×C4×D47—22no—
236C2×C4×D47—22no—
237C2×Dic94—21no—
238C2×Dic94—21no—
239C2×Dic94C2412yes—
240C4⋊C4×C47—24no—
241C4⋊C4×C47—24no—
242C4⋊C4×C47—24no—
243C4⋊C4×C47—24no—
244C4⋊C4×C47—24no—
245C4⋊C4×C47—24no—
246C4⋊C4×C47—24no—
247C4⋊C4×C47C2418yes—
248C42×C47C2×D411yescharacteristic
249C42×C47C2×D411yescharacteristic
250C42×C47C2×D411yescharacteristic
251C42×C47C2×D411yescharacteristic
252C42×C47C2×D411yescharacteristic
253C42×C47C2×D411yescharacteristic
254C42×C47C2×D411yescharacteristic
255C42×C47C2×D411yescharacteristic
256C42×C47C2×D411yescharacteristic
257C42×C47C2×D411yescharacteristic
258C42×C47C2×D411yescharacteristic
259C42×C47C2×D411yescharacteristic
260C42×C47C2411yescharacteristic
261C42×C47C2411yescharacteristic
262C42×C47C2411yescharacteristic
263C42×C47C2411yescharacteristic
264C22⋊Dic47—22no—
265C22⋊Dic47—22no—
266C22⋊Dic47—22no—
267(C2×D47)⋊C4—22no—
268(C2×D47)⋊C4—22no—
269(C2×D47)⋊C4—22no—
270(C2×D47)⋊C4—22no—
271(C2×D47)⋊C4—22no—
272(C2×D47)⋊C4—22no—
273C4⋊Dic47—21no—
274C4⋊Dic47—21no—
275C4⋊Dic47—21no—
276C4⋊Dic47—21no—
277C4⋊Dic47C2412yes—
278C4⋊Dic47C2412yes—
279Dic47⋊C4—22no—
280Dic47⋊C4—22no—
281Dic47⋊C4—22no—
282Dic47⋊C4—22no—
283Dic47⋊C4—22no—
284Dic47⋊C4—22no—
285C4×Dic47—22no—
286C4×Dic47—22no—
287C4×Dic47—22no—
288#10625329—28no—
289C2×C47⋊C8C2418yes—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47C22×D411yescharacteristic
294C23×C47C22×D411yescharacteristic
295C23×C47C22×D411yescharacteristic
296C22×D47—22no—
297Q8×C47—48no—
298Q8×C47—48no—
299Q8×C47—48no—
300Q8×C47—48no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—28no—
317C2×C4×C47—48no—
318C2×C4×C47—48no—
319C2×C4×C47—48no—
320C2×C4×C47AGL(1,ℤ/8)14yes—
321C2×C4×C47#13714yes—
322C2×C4×C47C22×D411yescharacteristic
323C2×C4×C47C22×D411yescharacteristic
324C2×C4×C47C22×D411yescharacteristic
325C2×C4×C47C22×D411yescharacteristic
326C2×C4×C47C22×D411yescharacteristic
327C2×C4×C47C22×D411yescharacteristic
328C2×C4×C47C22×D411yescharacteristic
329C2×C4×C47C22×D411yescharacteristic
330C2×C4×C47C22×D411yescharacteristic
331C2×C4×C47C22×D411yescharacteristic
332C2×C4×C47C22×D411yescharacteristic
333C2×C4×C472−1+414yes—
334C2×C4×C47C2511yescharacteristic
335C22⋊D47—44no—
336C22⋊D47—44no—
337C22⋊D47—44no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341D188—24no—
342D188—42no—
343D188—42no—
344C4×D47—44no—
345C4×D47—44no—
346C4×D47—44no—
347Dic94—24no—
348Dic94—42no—
349Dic94—42no—
350C47⋊C8—28no—
351#60860—471nomaximal, Sylow
352C22×C47—28no—
353C22×C47—21no—
354C22×C47—21no—
355C22×C47—21no—
356C22×C47—21no—
357C22×C47—21no—
358C22×C47—21no—
359C22×C47#53612yes—
360C22×C47C2×AGL(1,ℤ/8)12yes—
361C22×C47C2×#13712yes—
362C22×C47C23×D411yescharacteristic
363C2×D47—42no—
364C2×D47—42no—
365C2×D47—42no—
366C4×C47—21no—
367C4×C47—21no—
368C4×C47—21no—
369C4×C47—21no—
370C4×C47—21no—
371C4×C47—21no—
372C4×C47—48no—
373C4×C47#53612yes—
374C4×C47C2×AGL(1,ℤ/8)12yes—
375C4×C47C2×AGL(1,ℤ/8)12yes—
376C4×C47C2×#13712yes—
377C4×C47C2×#13712yes—
378C4×C47C2×2−1+412yes—
379Dic47—42no—
380Dic47—42no—
381Dic47—42no—
382#3444—471no—
383C22×C4⋊Q8D4711yescharacteristic, complemented
384#3239—474no—
385#3238—474no—
386#3230—472no—
387#3229—472no—
388#3227—472no—
389#3226—472no—
390#3165—472no—
391#3141—472no—
392#3092—474no—
393#3079—474no—
394#2920—471no—
395C2×C47—22no—
396C2×C47—22no—
397C2×C47—22no—
398C2×C47C2×#53611yescharacteristic
399C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
400C2×C47C22×#13711yescharacteristic
401D47—82no—
402C23×Q8—21no—
403#533—471no—
404#533—471no—
405#533—471no—
406#532—471no—
407#532—471no—
408#532—471no—
409C2×C4⋊Q8—21no—
410C2×C4⋊Q8—21no—
411C2×C4⋊Q8—21no—
412C2×C4⋊Q8—21no—
413C2×C4⋊Q8—21no—
414C2×C4⋊Q8—21no—
415C2×C4⋊Q8C2×D4712yes—
416C2×C4⋊Q8C2×D4712yes—
417C2×C4⋊Q8C2×D4712yes—
418C2×C4⋊Q8C2×D4712yes—
419C2×C4⋊Q8C2×D4712yes—
420C2×C4⋊Q8C2×D4712yes—
421#529—472no—
422#529—472no—
423#529—941no—
424#529—941no—
425#529—941no—
426#529—941no—
427#525—472no—
428#525—941no—
429#525—941no—
430C4×#41—472no—
431C4×#41—941no—
432C4×#41—941no—
433C22×C4⋊C4—21no—
434C22×C4⋊C4C2×D4712yes—
435C22×C42C2×D4711yescharacteristic
436#501—478no—
437#500—474no—
438#498—474no—
439#489—478no—
440#487—474no—
441#486—474no—
442#484—478no—
443#483—478no—
444#481—478no—
445#480—478no—
446#477—478no—
447#476—478no—
448#475—478no—
449#474—478no—
450#432—472no—
451#432—472no—
452#431—472no—
453#431—472no—
454#428—478no—
455#423—472no—
456#417—478no—
457#407—472no—
458C4×M16—472no—
459C47#6086011yescharacteristic, complemented, Sylow
460C2×#41—472no—
461C2×#41—941no—
462C2×#41—941no—
463C22×Q8—22no—
464C22×Q8—22no—
465C22×Q8—22no—
466C22×Q8—22no—
467C22×Q8—22no—
468C22×Q8—22no—
469C22×Q8—48no—
470C23×C4—22no—
471C23×C4C22⋊D4711yescharacteristic
472C23×C4C22⋊D4711yescharacteristic
473C23×C4C22×D4711yescharacteristic
474C2×M16—474no—
475C4⋊Q8—22no—
476C4⋊Q8—22no—
477C4⋊Q8—22no—
478C4⋊Q8—22no—
479C4⋊Q8—22no—
480C4⋊Q8—22no—
481C4⋊Q8—22no—
482C4⋊Q8—22no—
483C4⋊Q8—22no—
484C4⋊Q8—22no—
485C4⋊Q8—22no—
486C4⋊Q8—22no—
487C4⋊Q8—471no—
488C4⋊Q8—471no—
489C4⋊Q8—471no—
490C4⋊Q8C22×D4714yes—
491C4⋊Q8C22×D4714yes—
492C4⋊Q8C22×D4714yes—
493C4⋊Q8C22×D4714yes—
494#127—471no—
495#126—942no—
496#126—942no—
497#125—472no—
498#125—941no—
499#125—941no—
500#124—472no—
501#124—941no—
502#124—941no—
503#123—942no—
504#123—942no—
505#123—942no—
506C22⋊Q8—472no—
507C22⋊Q8—472no—
508C22⋊Q8—941no—
509C22⋊Q8—941no—
510C22⋊Q8—941no—
511C22⋊Q8—941no—
512#121—472no—
513#121—472no—
514#121—941no—
515#121—941no—
516#121—941no—
517#121—941no—
518#120—942no—
519C4×Q8—472no—
520C4×Q8—472no—
521C4×Q8—941no—
522C4×Q8—941no—
523C4×Q8—941no—
524C4×Q8—941no—
525C4×D4—472no—
526C4×D4—472no—
527C4×D4—942no—
528C4×D4—942no—
529C4×D4—942no—
530C4×D4—942no—
531C4×D4—942no—
532C4×D4—942no—
533C4×D4—941no—
534C4×D4—941no—
535C4×D4—941no—
536C4×D4—941no—
537#117—472no—
538#117—941no—
539#117—941no—
540#117—942no—
541#117—942no—
542#117—942no—
543C2×C4⋊C4—22no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—22no—
552C2×C4⋊C4C22×D4714yes—
553C2×C4⋊C4C22×D4714yes—
554C2×C4⋊C4C22×D4714yes—
555C2×C42—942no—
556C2×C42C22⋊D4711yescharacteristic
557C2×C42C22⋊D4711yescharacteristic
558C2×C42C22⋊D4711yescharacteristic
559C2×C42C22⋊D4711yescharacteristic
560C2×C42C22⋊D4711yescharacteristic
561C2×C42C22⋊D4711yescharacteristic
562C2×C42C22×D4711yescharacteristic
563C2×C42C22×D4711yescharacteristic
564C2×C42C22×D4711yescharacteristic
565C2×C42C22×D4711yescharacteristic
566C2×C42C22×D4711yescharacteristic
567C2×C42C22×D4711yescharacteristic
568#107—4716no—
569#106—4716no—
570C4⋊C8—474no—
571C4⋊C8—474no—
572#103—4716no—
573#102—4716no—
574C22⋊C8—474no—
575C22⋊C8—474no—
576#97—474no—
577C4×C8—474no—
578C24C2×C22⋊D4711yescharacteristic
579#41—948no—
580#41—1884no—
581#41—1884no—
582C2×Q8—24no—
583C2×Q8—24no—
584C2×Q8—24no—
585C2×Q8—24no—
586C2×Q8—48no—
587C2×Q8—48no—
588C2×Q8—48no—
589C2×Q8—48no—
590C2×Q8—48no—
591C2×Q8—48no—
592C2×Q8—472no—
593C2×Q8—941no—
594C2×Q8—941no—
595C2×D4—472no—
596C2×D4—942no—
597C2×D4—942no—
598C2×D4—942no—
599C2×D4—941no—
600C2×D4—941no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—48no—
608C22×C4—942no—
609C22×C4—942no—
610C22×C4—942no—
611C22×C4C2×C22⋊D4711yescharacteristic
612C22×C4C2×C22⋊D4711yescharacteristic
613C22×C4C2×C22⋊D4711yescharacteristic
614C22×C4C2×C22⋊D4711yescharacteristic
615C22×C4C2×C22⋊D4711yescharacteristic
616C22×C4C2×C22⋊D4711yescharacteristic
617C22×C4C2×C22⋊D4711yescharacteristic
618C22×C4C2×C22⋊D4711yescharacteristic
619C22×C4C2×C22⋊D4711yescharacteristic
620C22×C4C2×C22⋊D4711yescharacteristic
621C22×C4C2×C22⋊D4711yescharacteristic
622C22×C4C2×C22⋊D4711yescharacteristic
623C22×C4C2×C22⋊D4711yescharacteristic
624C22×C4C2×C22⋊D4711yescharacteristic
625C22×C4C2×C22⋊D4711yescharacteristic
626C22×C4C23×D4711yescharacteristic
627C22×C4C23×D4711yescharacteristic
628C22×C4C23×D4711yescharacteristic
629M16—948no—
630C2×C8—478no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—472no—
639C4⋊C4—472no—
640C4⋊C4—942no—
641C4⋊C4—942no—
642C4⋊C4—942no—
643C4⋊C4—942no—
644C4⋊C4—942no—
645C4⋊C4—942no—
646C4⋊C4—941no—
647C4⋊C4—941no—
648C4⋊C4—941no—
649C4⋊C4—941no—
650C4⋊C4C23×D4718yes—
651C22⋊C4—942no—
652C22⋊C4—942no—
653C22⋊C4—942no—
654C22⋊C4—942no—
655C22⋊C4—942no—
656C22⋊C4—942no—
657C22⋊C4—942no—
658C22⋊C4—942no—
659C22⋊C4—942no—
660C42—942no—
661C42—942no—
662C42—942no—
663C42C2×C22⋊D4711yescharacteristic
664C42C2×C22⋊D4711yescharacteristic
665C42C2×C22⋊D4711yescharacteristic
666C42C2×C22⋊D4711yescharacteristic
667C42C2×C22⋊D4711yescharacteristic
668C42C2×C22⋊D4711yescharacteristic
669C42C2×C22⋊D4711yescharacteristic
670C42C2×C22⋊D4711yescharacteristic
671C42C2×C22⋊D4711yescharacteristic
672C42C2×C22⋊D4711yescharacteristic
673C42C2×C22⋊D4711yescharacteristic
674C42C2×C22⋊D4711yescharacteristic
675C42C23×D4711yescharacteristic
676C42C23×D4711yescharacteristic
677C42C23×D4711yescharacteristic
678C42C23×D4711yescharacteristic
679C23—22no—
680C23—22no—
681C23—22no—
682C23—942no—
683C23C22×C22⋊D4711yescharacteristic
684C23C22×C22⋊D4711yescharacteristic
685C23C22×C22⋊D4711yescharacteristic
686Q8—48no—
687Q8—48no—
688Q8—48no—
689Q8—48no—
690Q8—944no—
691Q8—1882no—
692Q8—1882no—
693D4—944no—
694D4—1884no—
695D4—1884no—
696D4—1884no—
697D4—1882no—
698D4—1882no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—28no—
715C2×C4—48no—
716C2×C4—48no—
717C2×C4—48no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—1884no—
722C2×C4—1884no—
723C2×C4—1884no—
724C2×C4#1309405014yes—
725C2×C4#1309405514yes—
726C2×C4C22×C22⋊D4711yescharacteristic
727C2×C4C22×C22⋊D4711yescharacteristic
728C2×C4C22×C22⋊D4711yescharacteristic
729C2×C4C22×C22⋊D4711yescharacteristic
730C2×C4C22×C22⋊D4711yescharacteristic
731C2×C4C22×C22⋊D4711yescharacteristic
732C2×C4C22×C22⋊D4711yescharacteristic
733C2×C4C22×C22⋊D4711yescharacteristic
734C2×C4C22×C22⋊D4711yescharacteristic
735C2×C4C22×C22⋊D4711yescharacteristic
736C2×C4C22×C22⋊D4711yescharacteristic
737C2×C4#1309407214yes—
738C2×C4C24×D4711yescharacteristic
739C8—948no—
740C22—28no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—1882no—
748C22—1882no—
749C22—1882no—
750C22#1568969712yes—
751C22C2×#1309405012yes—
752C22C2×#1309405512yes—
753C22C23×C22⋊D4711yescharacteristic
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—48no—
761C4—1882no—
762C4—1882no—
763C4—1882no—
764C4#1568969712yes—
765C4C2×#1309405012yes—
766C4C2×#1309405012yes—
767C4C2×#1309405512yes—
768C4C2×#1309405512yes—
769C4C2×#1309407212yes—
770C2—22no—
771C2—22no—
772C2—22no—
773C2—3762no—
774C2C2×#1568969711yescharacteristic
775C2C22×#1309405011yescharacteristic
776C2C22×#1309405511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC22×C4⋊Q8×C47C2
socleC22×C47C23×D4
prime radical#20256684C2
hypercenterC22×C4⋊Q8D47
hypocenterC47#60860
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C42 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #20254618C2semidirect
3. #20254609C2semidirect
4. #20254539C2semidirect
5. #20254532C2semidirect
6. #20254516C2semidirect
7. #20254509C2semidirect
8. #20253930C2semidirect
9. #20253784C2semidirect
10. #20253311C2semidirect
11. #20253197C2semidirect
12. #20252021C2semidirect
13. C22×C4⋊Q8×C47C2semidirect
32. #15689529C22semidirect
33. #15689526C22semidirect
34. #15689519C22semidirect
35. #15689485C22semidirect
36. #15689475C22semidirect
37. #15689471C22semidirect
42. #15689415C22semidirect
43. #15689410C22semidirect
44. #15689405C22semidirect
45. #15689400C22semidirect
383. C22×C4⋊Q8D47semidirect
459. C47#60860semidirect

Maximal subgroups

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

subgroupindex
#202566842
#202546182
#202546092
#202545392
#202545322
#202545162
#202545092
#202539302
#202537842
#202533112
#202531972
#202520212
C22×C4⋊Q8×C472
#6086047