Finite Group Databasebeta

← #26183814

Subgroups — #26183814

Order 12032.

996 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257437C211yesmaximal, characteristic
2#20252423C211yesmaximal, characteristic, complemented
3#20241963C211yesmaximal, characteristic, complemented
4#20241959C211yesmaximal, characteristic, complemented
5#20241951C211yesmaximal, characteristic, complemented
6#20241942C211yesmaximal, characteristic, complemented
7#20241938C211yesmaximal, characteristic, complemented
8#20241929C211yesmaximal, characteristic, complemented
9#20241924C211yesmaximal, characteristic, complemented
10#20241920C211yesmaximal, characteristic, complemented
11#20241907C211yesmaximal, characteristic, complemented
12#20241890C211yesmaximal, characteristic, complemented
13#20241877C211yesmaximal, characteristic, complemented
14C2×#15688859C211yesmaximal, characteristic, complemented
15C47×#2318C211yesmaximal, characteristic, complemented
16#15689843C411yescharacteristic, complemented
17#15689828—21no—
18#15689813C411yescharacteristic, complemented
19#15689813C411yescharacteristic, complemented
20#15689799—21no—
21#15689799—21no—
22D4×Dic94C411yescharacteristic, complemented
23#15689782C411yescharacteristic, complemented
24#15689782C411yescharacteristic, complemented
25#15689778C411yescharacteristic, complemented
26#15689777C411yescharacteristic, complemented
27#15689767—21no—
28#15689738—21no—
29#15689715—21no—
30#15689715—21no—
31#15689680C2211yescharacteristic
32#15689657C2211yescharacteristic
33#15689634C2211yescharacteristic
34#15689634C2211yescharacteristic
35C2×#13094003C2211yescharacteristic
36C2×#13094003C2211yescharacteristic
37#15689602—21no—
38#15689201—21no—
39#15689195—21no—
40#15689195—21no—
41D4×C47⋊C8—21no—
42#15689180C2211yescharacteristic
43#15689176C2211yescharacteristic
44#15689087C2211yescharacteristic
45#15689087C2211yescharacteristic
46C2×C22⋊(C47⋊C8)C2211yescharacteristic
47C2×C22⋊(C47⋊C8)C2211yescharacteristic
48#15688859C2211yescharacteristic
49#15688859C2211yescharacteristic
50#15688859C2211yescharacteristic
51#15688859C2211yescharacteristic
52#15688859C2211yescharacteristic
53#15688859C2211yescharacteristic
54#15688859C2211yescharacteristic
55#15688859C2211yescharacteristic
56#15688859C2211yescharacteristic
57#15688859C2211yescharacteristic
58#15688859C2211yescharacteristic
59#15688859C2211yescharacteristic
60#15688856C2211yescharacteristic
61#15688856C2211yescharacteristic
62#15688856C2211yescharacteristic
63#15688856C2211yescharacteristic
64C2×C4×D4×C47C2211yescharacteristic
65C47×#388—21no—
66C47×#387—21no—
67C47×#386—21no—
68C47×#385—21no—
69C47×#383C2211yescharacteristic
70C47×#382C2211yescharacteristic
71C47×#381C2211yescharacteristic
72C47×#380C2211yescharacteristic
73C4×C22⋊C4×C47C2211yescharacteristic
74C2×#95×C47C2211yescharacteristic
75C2×#10625350C2×C411yescharacteristic
76C2×#10625350C2×C411yescharacteristic, complemented
77C2×#10625352—21no—
78C22×Dic94C2×C411yescharacteristic
79C22×Dic94C2×C411yescharacteristic, complemented
80C2×#10625329—21no—
81C2×#10625329—21no—
82C22×C47⋊C8—21no—
83C22×C47⋊C8—21no—
84#13094024C2×C411yescharacteristic, complemented
85#13094024C2×C411yescharacteristic, complemented
86#13094023—21no—
87#13094018—21no—
88#13094017—21no—
89#13094017—21no—
90#13094017—21no—
91#13094017—21no—
92#13094016—21no—
93#13094016C2×C411yescharacteristic, complemented
94#13094014—21no—
95#13094014—21no—
96#13094012C2×C411yescharacteristic, complemented
97#13094011—21no—
98#13094010—21no—
99#13094010—21no—
100#13094008—21no—
101#13094008—21no—
102#13094007—21no—
103#13094007—21no—
104#13094007—21no—
105#13094006—21no—
106#13094006—21no—
107#13094005—21no—
108#13094005—21no—
109#13094004—21no—
110#13094003—21no—
111#13094003—21no—
112#13094003—21no—
113#13094003—21no—
114#13094003—21no—
115#13094003C2×C411yescharacteristic
116#13094003C2×C411yescharacteristic
117#13094003C2×C411yescharacteristic
118#13094003C2×C411yescharacteristic, complemented
119#13094003C2×C411yescharacteristic, complemented
120#13094003C2×C411yescharacteristic, complemented
121#13094003C2311yescharacteristic
122#13094003C2311yescharacteristic
123#13094003C2311yescharacteristic
124#13094002—21no—
125#13094002—21no—
126#13094001—21no—
127#13094001—21no—
128#13093998C2×C411yescharacteristic
129#13093998C2×C411yescharacteristic, complemented
130#13093998C2311yescharacteristic
131#13093996—21no—
132#13093996—21no—
133#13093995—21no—
134#13093993—21no—
135#13093993—21no—
136C4×Dic94—21no—
137C4×Dic94C2×C411yescharacteristic, complemented
138C4×Dic94C2×C411yescharacteristic, complemented
139C4×Dic94C2×C411yescharacteristic, complemented
140#13093989—21no—
141C4×D188C2×C411yescharacteristic, complemented
142D4×Dic47—21no—
143C4×C22⋊D47—21no—
144C4×C22⋊D47—21no—
145C4×C22⋊D47—21no—
146C4×C22⋊D47—21no—
147C4×C22⋊D47—21no—
148(C22⋊D47)⋊C4—21no—
149(C22⋊D47)⋊C4—21no—
150#13093983—21no—
151#13093983C2×C411yescharacteristic
152#13093983C2×C411yescharacteristic, complemented
153#13093981—21no—
154#13093980—21no—
155#13093980—21no—
156C2×C4⋊Dic47C2×C411yescharacteristic
157C2×C4⋊Dic47C2×C411yescharacteristic, complemented
158C2×Dic47⋊C4—21no—
159C2×Dic47⋊C4—21no—
160C4⋊C4×D47—21no—
161C2×C22⋊Dic47—21no—
162C2×C22⋊Dic47—21no—
163C4⋊(C47⋊C8)—21no—
164C4⋊(C47⋊C8)—21no—
165C22⋊(C47⋊C8)—21no—
166C22⋊(C47⋊C8)—21no—
167C22⋊(C47⋊C8)—21no—
168C22⋊(C47⋊C8)—21no—
169C22⋊(C47⋊C8)C2311yescharacteristic
170C22⋊(C47⋊C8)C2311yescharacteristic
171C22⋊(C47⋊C8)C2311yescharacteristic
172C22⋊(C47⋊C8)C2311yescharacteristic
173#13093935—21no—
174C4×C47⋊C8—21no—
175C22×D4×C47D411yescharacteristic
176C23×C4×C47—21no—
177C23×C4×C47C2311yescharacteristic
178C23×C4×C47C2311yescharacteristic
179C4×D4×C47C2×C411yescharacteristic
180C4×D4×C47C2×C411yescharacteristic
181C4×D4×C47C2×C411yescharacteristic
182C4×D4×C47C2×C411yescharacteristic
183C4×D4×C47D411yescharacteristic
184C4×D4×C47D411yescharacteristic
185C4×D4×C47D411yescharacteristic
186C4×D4×C47D411yescharacteristic
187C2×C4⋊C4×C47—21no—
188C2×C4⋊C4×C47—21no—
189C2×C4⋊C4×C47D411yescharacteristic
190C2×C22⋊C4×C47—21no—
191C2×C22⋊C4×C47—21no—
192C2×C22⋊C4×C47—21no—
193C2×C22⋊C4×C47D411yescharacteristic
194C2×C22⋊C4×C47D411yescharacteristic
195C2×C42×C47—21no—
196C2×C42×C47C2311yescharacteristic
197#95×C47—21no—
198#95×C47—21no—
199#95×C47—21no—
200#95×C47—21no—
201#95×C47—21no—
202#95×C47C2311yescharacteristic
203#95×C47C2311yescharacteristic
204#95×C47C2311yescharacteristic
205#95×C47C2311yescharacteristic
206C24×C47C2×D411yescharacteristic
207C24×C47C2×D411yescharacteristic
208C2×D4×C47—42no—
209C2×D4×C47C22⋊C411yescharacteristic
210C2×D4×C47C22⋊C411yescharacteristic
211C2×D4×C47C22⋊C411yescharacteristic
212C2×D4×C47C22⋊C411yescharacteristic
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—42no—
218C22×C4×C47—81no—
219C22×C4×C47—81no—
220C22×C4×C47—81no—
221C22×C4×C47—81no—
222C22×C4×C47C22×C411yescharacteristic
223C22×C4×C47C22×C411yescharacteristic
224C22×C4×C47C22×C411yescharacteristic
225C22×C4×C47C22×C411yescharacteristic
226C22×C4×C47C2×D411yescharacteristic
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2×D411yescharacteristic
230C22×C4×C47C2×D411yescharacteristic
231C22×C4×C47C2×D411yescharacteristic
232C22×C4×C47C2×D411yescharacteristic
233C22×C4×C47C2×D411yescharacteristic
234C22×C4×C47C2411yescharacteristic
235C2×C22⋊D47—21no—
236C2×C22⋊D47—21no—
237C2×C22⋊D47—21no—
238C2×C22⋊D47—21no—
239C2×C22⋊D47—21no—
240C22×Dic47—21no—
241C22×Dic47—21no—
242C22×Dic47—21no—
243C22×Dic47—21no—
244#10625352—44no—
245#10625350—81no—
246#10625350—81no—
247C2×D188C22×C411yescharacteristic
248C2×C4×D47—21no—
249C2×C4×D47—21no—
250C2×C4×D47—21no—
251C2×Dic94—21no—
252C2×Dic94—21no—
253C2×Dic94—21no—
254C2×Dic94—81no—
255C2×Dic94—81no—
256C2×Dic94C22×C411yescharacteristic
257C2×Dic94C22×C411yescharacteristic
258C2×Dic94C22×C411yescharacteristic
259C4⋊C4×C47—81no—
260C4⋊C4×C47—81no—
261C4⋊C4×C47C22⋊C411yescharacteristic
262C4⋊C4×C47C22⋊C411yescharacteristic
263C4⋊C4×C47C22⋊C411yescharacteristic
264C4⋊C4×C47C22⋊C411yescharacteristic
265C22⋊C4×C47—42no—
266C22⋊C4×C47—81no—
267C22⋊C4×C47—81no—
268C22⋊C4×C47C22⋊C411yescharacteristic
269C22⋊C4×C47C22⋊C411yescharacteristic
270C22⋊C4×C47C22⋊C411yescharacteristic
271C22⋊C4×C47C22⋊C411yescharacteristic
272C22⋊C4×C47C22⋊C411yescharacteristic
273C22⋊C4×C47C22⋊C411yescharacteristic
274C22⋊C4×C47C22⋊C411yescharacteristic
275C22⋊C4×C47C22⋊C411yescharacteristic
276C42×C47—81no—
277C42×C47C22×C411yescharacteristic
278C42×C47C22×C411yescharacteristic
279C42×C47C2×D411yescharacteristic
280C42×C47C2×D411yescharacteristic
281C22⋊Dic47—21no—
282C22⋊Dic47—21no—
283C22⋊Dic47—21no—
284C22⋊Dic47—21no—
285C22⋊Dic47—21no—
286C22⋊Dic47—21no—
287C22⋊Dic47—21no—
288C22⋊Dic47—21no—
289C22⋊Dic47—21no—
290C22⋊Dic47—21no—
291C22⋊Dic47—21no—
292(C2×D47)⋊C4—21no—
293(C2×D47)⋊C4—21no—
294(C2×D47)⋊C4—21no—
295(C2×D47)⋊C4—21no—
296(C2×D47)⋊C4—21no—
297(C2×D47)⋊C4—21no—
298C4⋊Dic47—21no—
299C4⋊Dic47—21no—
300C4⋊Dic47—21no—
301C4⋊Dic47—21no—
302C4⋊Dic47—21no—
303C4⋊Dic47C22×C411yescharacteristic
304C4⋊Dic47C22×C411yescharacteristic
305C4⋊Dic47C22×C411yescharacteristic
306C4⋊Dic47C22×C411yescharacteristic
307Dic47⋊C4—21no—
308Dic47⋊C4—21no—
309Dic47⋊C4—21no—
310Dic47⋊C4—21no—
311Dic47⋊C4—21no—
312Dic47⋊C4—21no—
313Dic47⋊C4—21no—
314Dic47⋊C4—21no—
315Dic47⋊C4—21no—
316Dic47⋊C4—21no—
317Dic47⋊C4—21no—
318Dic47⋊C4—21no—
319Dic47⋊C4—21no—
320Dic47⋊C4—21no—
321C4×Dic47—21no—
322C4×Dic47—21no—
323C4×Dic47—21no—
324C4×Dic47—21no—
325C4×Dic47—21no—
326#10625329—81no—
327#10625329—81no—
328C2×C47⋊C8—21no—
329C2×C47⋊C8—21no—
330C2×C47⋊C8—21no—
331C2×C47⋊C8—21no—
332C2×C47⋊C8—81no—
333C2×C47⋊C8—81no—
334C23×C47—21no—
335C23×C47—21no—
336C23×C47—22no—
337C23×C47—21no—
338C23×C47—21no—
339C23×C47—41no—
340C23×C47—41no—
341C23×C47—41no—
342C23×C47C2×C22⋊C411yescharacteristic
343C23×C47C2×C22⋊C411yescharacteristic
344C23×C47C2×C22⋊C411yescharacteristic
345C23×C47C2×C22⋊C411yescharacteristic
346C23×C47C22×D411yescharacteristic
347C22×D47—21no—
348D4×C47—22no—
349D4×C47—22no—
350D4×C47—41no—
351D4×C47—41no—
352C2×C4×C47—21no—
353C2×C4×C47—21no—
354C2×C4×C47—41no—
355C2×C4×C47—41no—
356C2×C4×C47—41no—
357C2×C4×C47—41no—
358C2×C4×C47—41no—
359C2×C4×C47—41no—
360C2×C4×C47—41no—
361C2×C4×C47—41no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
364C2×C4×C47—41no—
365C2×C4×C47—41no—
366C2×C4×C47—41no—
367C2×C4×C47—41no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47—41no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47—84no—
379C2×C4×C47C2×C22⋊C411yescharacteristic
380C2×C4×C47C2×C22⋊C411yescharacteristic
381C2×C4×C47C2×C22⋊C411yescharacteristic
382C2×C4×C47C2×C22⋊C411yescharacteristic
383C2×C4×C47C2×C22⋊C411yescharacteristic
384C2×C4×C47C2×C22⋊C411yescharacteristic
385C2×C4×C47C2×C22⋊C411yescharacteristic
386C2×C4×C47C2×C22⋊C411yescharacteristic
387C2×C4×C47C23×C411yescharacteristic
388C2×C4×C47C22×D411yescharacteristic
389C22⋊D47—42no—
390C22⋊D47—41no—
391C22⋊D47—41no—
392C22⋊D47—42no—
393C22⋊D47—81no—
394C22⋊D47—81no—
395C2×Dic47—21no—
396C2×Dic47—21no—
397C2×Dic47—21no—
398C2×Dic47—21no—
399C2×Dic47—21no—
400C2×Dic47—21no—
401C2×Dic47—21no—
402C2×Dic47—42no—
403C2×Dic47—42no—
404C2×Dic47—81no—
405C2×Dic47—81no—
406D188—41no—
407C4×D47—42no—
408C4×D47—81no—
409C4×D47—81no—
410Dic94—42no—
411Dic94—41no—
412Dic94—41no—
413Dic94—41no—
414Dic94—81no—
415Dic94—81no—
416C47⋊C8—41no—
417C47⋊C8—41no—
418C47⋊C8—41no—
419C47⋊C8—41no—
420#17598—471nomaximal, Sylow
421C22×C47—21no—
422C22×C47—21no—
423C22×C47—21no—
424C22×C47—21no—
425C22×C47—21no—
426C22×C47—21no—
427C22×C47—21no—
428C22×C47—21no—
429C22×C47—21no—
430C22×C47—21no—
431C22×C47—21no—
432C22×C47—21no—
433C22×C47—21no—
434C22×C47—42no—
435C22×C47—42no—
436C22×C47—81no—
437C22×C47—81no—
438C22×C47#42112yes—
439C22×C47C22×C22⋊C411yescharacteristic
440C22×C47#57711yescharacteristic
441C22×C47#57811yescharacteristic
442C2×D47—41no—
443C2×D47—41no—
444C2×D47—41no—
445C4×C47—21no—
446C4×C47—21no—
447C4×C47—21no—
448C4×C47—21no—
449C4×C47—21no—
450C4×C47—21no—
451C4×C47—21no—
452C4×C47—21no—
453C4×C47—21no—
454C4×C47—21no—
455C4×C47—81no—
456C4×C47—81no—
457C4×C47—81no—
458C4×C47—81no—
459Dic47—41no—
460Dic47—41no—
461Dic47—41no—
462Dic47—41no—
463Dic47—41no—
464Dic47—41no—
465Dic47—41no—
466#3520—471no—
467#2974—471no—
468#2318D4711yescharacteristic, complemented
469#1521—471no—
470#1520—471no—
471#1518—471no—
472#1516—471no—
473#1515—471no—
474#1513—471no—
475#1512—471no—
476#1511—471no—
477#1508—471no—
478#1504—471no—
479#1501—471no—
480C2×#328—471no—
481C2×C47—21no—
482C2×C47—21no—
483C2×C47—22no—
484C2×C47—41no—
485C2×C47—41no—
486C2×C47—41no—
487C2×C47#288311yescharacteristic
488C2×C47#289811yescharacteristic
489C2×C47C2×#42111yescharacteristic
490D47—81no—
491#556—471no—
492#554—941no—
493#552—471no—
494#552—471no—
495#551—941no—
496#551—941no—
497D4×Q8—471no—
498#548—471no—
499#548—471no—
500#547—471no—
501#547—471no—
502#546—941no—
503#542—941no—
504#539—941no—
505#539—941no—
506#533—471no—
507#529—471no—
508#525—471no—
509#525—471no—
510C2×C22⋊Q8—471no—
511C2×C22⋊Q8—471no—
512#520—941no—
513C2×C4×D4C2×D4711yescharacteristic
514#436—941no—
515#435—941no—
516#435—941no—
517C8×D4—941no—
518#432—471no—
519#431—471no—
520#407—471no—
521#407—471no—
522C2×C22⋊C8—471no—
523C2×C22⋊C8—471no—
524#388—21no—
525#387—21no—
526#386—21no—
527#385—21no—
528#383C2×D4711yescharacteristic
529#382C2×D4711yescharacteristic
530#381C2×D4711yescharacteristic
531#380C2×D4711yescharacteristic
532C4×C22⋊C4C2×D4711yescharacteristic
533C2×#95C2×D4711yescharacteristic
534#328—471no—
535#328—471no—
536#328—471no—
537#328—471no—
538#328—471no—
539#328—471no—
540#328—471no—
541#328—471no—
542#328—471no—
543#328—471no—
544#328—471no—
545#328—471no—
546#327—471no—
547#327—471no—
548#327—471no—
549#327—471no—
550C47#1759811yescharacteristic, complemented, Sylow
551C2×#41—471no—
552C2×#41—471no—
553C2×#41—941no—
554C22×Q8—471no—
555C22×Q8—471no—
556C22×D4C22⋊D4711yescharacteristic
557C23×C4—21no—
558C23×C4C22×D4711yescharacteristic
559C23×C4C22×D4711yescharacteristic
560C2×M16—941no—
561C2×M16—941no—
562C22×C8—941no—
563C22×C8—941no—
564C4⋊Q8—471no—
565C4⋊Q8—471no—
566C4⋊Q8—941no—
567#126—941no—
568#126—941no—
569#126—941no—
570#126—941no—
571#126—941no—
572#125—471no—
573#125—941no—
574#125—941no—
575#125—941no—
576#124—471no—
577#124—941no—
578#124—941no—
579#124—941no—
580#123—941no—
581#123—941no—
582#123—941no—
583#123—941no—
584#123—941no—
585#123—941no—
586#123—941no—
587#123—941no—
588#123—941no—
589C22⋊Q8—471no—
590C22⋊Q8—471no—
591C22⋊Q8—471no—
592C22⋊Q8—471no—
593C22⋊Q8—471no—
594C22⋊Q8—471no—
595C22⋊Q8—471no—
596C22⋊Q8—471no—
597C22⋊Q8—471no—
598C22⋊Q8—941no—
599C22⋊Q8—941no—
600C22⋊Q8—941no—
601C22⋊Q8—941no—
602C22⋊Q8—941no—
603C22⋊Q8—941no—
604C22⋊Q8—941no—
605C22⋊Q8—941no—
606C22⋊Q8—941no—
607C22⋊Q8—941no—
608#121—471no—
609#121—471no—
610#121—471no—
611#121—941no—
612#121—941no—
613#121—941no—
614#120—941no—
615#120—941no—
616C4×Q8—471no—
617C4×Q8—471no—
618C4×Q8—471no—
619C4×Q8—941no—
620C4×Q8—941no—
621C4×D4—471no—
622C4×D4—941no—
623C4×D4—941no—
624C4×D4—941no—
625C4×D4—941no—
626C4×D4—941no—
627C4×D4—941no—
628C4×D4—941no—
629C4×D4—941no—
630C4×D4C4×D4711yescharacteristic
631C4×D4C4×D4711yescharacteristic
632C4×D4C4×D4711yescharacteristic
633C4×D4C4×D4711yescharacteristic
634C4×D4D18811yescharacteristic
635C4×D4D18811yescharacteristic
636C4×D4D18811yescharacteristic
637C4×D4D18811yescharacteristic
638#117—471no—
639#117—471no—
640#117—941no—
641#117—941no—
642#117—941no—
643#117—941no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—471no—
647C2×C4⋊C4—471no—
648C2×C4⋊C4—941no—
649C2×C4⋊C4—941no—
650C2×C4⋊C4—941no—
651C2×C4⋊C4C22⋊D4711yescharacteristic
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—941no—
656C2×C22⋊C4—941no—
657C2×C22⋊C4C22⋊D4711yescharacteristic
658C2×C22⋊C4C22⋊D4711yescharacteristic
659C2×C42—21no—
660C2×C42C22×D4711yescharacteristic
661C4⋊C8—941no—
662C4⋊C8—941no—
663C22⋊C8—471no—
664C22⋊C8—471no—
665C22⋊C8—471no—
666C22⋊C8—471no—
667C22⋊C8—941no—
668C22⋊C8—941no—
669C22⋊C8—941no—
670C22⋊C8—941no—
671#97—941no—
672C4×C8—941no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95C22×D4711yescharacteristic
679#95C22×D4711yescharacteristic
680#95C22×D4711yescharacteristic
681#95C22×D4711yescharacteristic
682C24C2×C22⋊D4711yescharacteristic
683C24C2×C22⋊D4711yescharacteristic
684#41—3761no—
685#41—3761no—
686#41—1884no—
687C2×Q8—471no—
688C2×Q8—471no—
689C2×Q8—471no—
690C2×Q8—941no—
691C2×Q8—941no—
692C2×Q8—941no—
693C2×Q8—3761no—
694C2×Q8—3761no—
695C2×D4—42no—
696C2×D4—471no—
697C2×D4—941no—
698C2×D4—941no—
699C2×D4—941no—
700C2×D4—941no—
701C2×D4—941no—
702C2×D4(C2×D47)⋊C411yescharacteristic
703C2×D4(C2×D47)⋊C411yescharacteristic
704C2×D4(C2×D47)⋊C411yescharacteristic
705C2×D4(C2×D47)⋊C411yescharacteristic
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—42no—
711C22×C4—81no—
712C22×C4—81no—
713C22×C4—81no—
714C22×C4—81no—
715C22×C4—941no—
716C22×C4—941no—
717C22×C4—941no—
718C22×C4—941no—
719C22×C4—941no—
720C22×C4—941no—
721C22×C4—941no—
722C22×C4C2×C4×D4711yescharacteristic
723C22×C4C2×C4×D4711yescharacteristic
724C22×C4C2×C4×D4711yescharacteristic
725C22×C4C2×C4×D4711yescharacteristic
726C22×C4C2×D18811yescharacteristic
727C22×C4C2×D18811yescharacteristic
728C22×C4C2×D18811yescharacteristic
729C22×C4C2×D18811yescharacteristic
730C22×C4C2×C22⋊D4711yescharacteristic
731C22×C4C2×C22⋊D4711yescharacteristic
732C22×C4C2×C22⋊D4711yescharacteristic
733C22×C4C2×C22⋊D4711yescharacteristic
734C22×C4C23×D4711yescharacteristic
735M16—3761no—
736M16—3761no—
737C2×C8—941no—
738C2×C8—941no—
739C2×C8—941no—
740C2×C8—941no—
741C2×C8—3761no—
742C2×C8—3761no—
743C4⋊C4—81no—
744C4⋊C4—81no—
745C4⋊C4—471no—
746C4⋊C4—471no—
747C4⋊C4—471no—
748C4⋊C4—471no—
749C4⋊C4—941no—
750C4⋊C4—941no—
751C4⋊C4—941no—
752C4⋊C4—941no—
753C4⋊C4—941no—
754C4⋊C4—941no—
755C4⋊C4—941no—
756C4⋊C4—941no—
757C4⋊C4—941no—
758C4⋊C4—941no—
759C4⋊C4—941no—
760C4⋊C4—941no—
761C4⋊C4—941no—
762C4⋊C4—941no—
763C4⋊C4—941no—
764C4⋊C4—941no—
765C4⋊C4—941no—
766C4⋊C4—941no—
767C4⋊C4—941no—
768C4⋊C4(C2×D47)⋊C411yescharacteristic
769C4⋊C4(C2×D47)⋊C411yescharacteristic
770C4⋊C4(C2×D47)⋊C411yescharacteristic
771C4⋊C4(C2×D47)⋊C411yescharacteristic
772C22⋊C4—42no—
773C22⋊C4—81no—
774C22⋊C4—81no—
775C22⋊C4—941no—
776C22⋊C4—941no—
777C22⋊C4—941no—
778C22⋊C4—941no—
779C22⋊C4—941no—
780C22⋊C4—941no—
781C22⋊C4—941no—
782C22⋊C4—941no—
783C22⋊C4—941no—
784C22⋊C4—941no—
785C22⋊C4—941no—
786C22⋊C4—941no—
787C22⋊C4—941no—
788C22⋊C4—941no—
789C22⋊C4—941no—
790C22⋊C4—941no—
791C22⋊C4—941no—
792C22⋊C4(C2×D47)⋊C411yescharacteristic
793C22⋊C4(C2×D47)⋊C411yescharacteristic
794C22⋊C4(C2×D47)⋊C411yescharacteristic
795C22⋊C4(C2×D47)⋊C411yescharacteristic
796C22⋊C4(C2×D47)⋊C411yescharacteristic
797C22⋊C4(C2×D47)⋊C411yescharacteristic
798C22⋊C4(C2×D47)⋊C411yescharacteristic
799C22⋊C4(C2×D47)⋊C411yescharacteristic
800C42—81no—
801C42—941no—
802C42—941no—
803C42—941no—
804C42—941no—
805C42—941no—
806C42C2×C4×D4711yescharacteristic
807C42C2×C4×D4711yescharacteristic
808C42C2×D18811yescharacteristic
809C42C2×D18811yescharacteristic
810C23—22no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—941no—
819C23C2×(C2×D47)⋊C411yescharacteristic
820C23C2×(C2×D47)⋊C411yescharacteristic
821C23C2×(C2×D47)⋊C411yescharacteristic
822C23C2×(C2×D47)⋊C411yescharacteristic
823C23C22×C22⋊D4711yescharacteristic
824Q8—3761no—
825Q8—3761no—
826Q8—1881no—
827Q8—1881no—
828Q8—1881no—
829Q8—1882no—
830D4—22no—
831D4—22no—
832D4—41no—
833D4—41no—
834D4—3761no—
835D4—3761no—
836D4—1881no—
837D4—1882no—
838D4—1882no—
839D4—1881no—
840D4—1881no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—84no—
868C2×C4—941no—
869C2×C4—941no—
870C2×C4—941no—
871C2×C4—941no—
872C2×C4—941no—
873C2×C4—941no—
874C2×C4—941no—
875C2×C4—3761no—
876C2×C4—3761no—
877C2×C4—3761no—
878C2×C4—3761no—
879C2×C4—1882no—
880C2×C4—1882no—
881C2×C4—1882no—
882C2×C4C2×(C2×D47)⋊C411yescharacteristic
883C2×C4C2×(C2×D47)⋊C411yescharacteristic
884C2×C4C2×(C2×D47)⋊C411yescharacteristic
885C2×C4C2×(C2×D47)⋊C411yescharacteristic
886C2×C4C2×(C2×D47)⋊C411yescharacteristic
887C2×C4C2×(C2×D47)⋊C411yescharacteristic
888C2×C4C2×(C2×D47)⋊C411yescharacteristic
889C2×C4C2×(C2×D47)⋊C411yescharacteristic
890C2×C4C22×C4×D4711yescharacteristic
891C2×C4C22×D18811yescharacteristic
892C8—1881no—
893C8—1881no—
894C8—1881no—
895C8—1881no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—42no—
910C22—42no—
911C22—81no—
912C22—81no—
913C22—1881no—
914C22—1881no—
915C22—1881no—
916C22#1568914112yes—
917C22C22×(C2×D47)⋊C411yescharacteristic
918C22#1568993411yescharacteristic
919C22#1568993811yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C4—1881no—
935C4—1881no—
936C4—1881no—
937C4—1881no—
938C4—1881no—
939C4—1881no—
940C4—1881no—
941C2—21no—
942C2—21no—
943C2—22no—
944C2—41no—
945C2—41no—
946C2—41no—
947C2—3761no—
948C2#2025184811yescharacteristic
949C2#2025191811yescharacteristic
950C2C2×#1568914111yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2318C2
socleC22×C47C22×C22⋊C4
prime radical#20257437C2
cosocleC22×C4×C47C24
hypercenter#2318D47
hypocenterC47#17598
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #20252423C2semidirect
3. #20241963C2semidirect
4. #20241959C2semidirect
5. #20241951C2semidirect
6. #20241942C2semidirect
7. #20241938C2semidirect
8. #20241929C2semidirect
9. #20241924C2semidirect
10. #20241920C2semidirect
11. #20241907C2semidirect
12. #20241890C2semidirect
13. #20241877C2semidirect
14. C2×#15688859C2semidirect
15. C47×#2318C2semidirect
16. #15689843C4semidirect
18. #15689813C4semidirect
19. #15689813C4semidirect
22. D4×Dic94C4semidirect
23. #15689782C4semidirect
24. #15689782C4semidirect
25. #15689778C4semidirect
26. #15689777C4semidirect
76. C2×#10625350C2×C4semidirect
79. C22×Dic94C2×C4semidirect
84. #13094024C2×C4semidirect
85. #13094024C2×C4semidirect
93. #13094016C2×C4semidirect
96. #13094012C2×C4semidirect
118. #13094003C2×C4semidirect
119. #13094003C2×C4semidirect
120. #13094003C2×C4semidirect
129. #13093998C2×C4semidirect
137. C4×Dic94C2×C4semidirect
138. C4×Dic94C2×C4semidirect
139. C4×Dic94C2×C4semidirect
141. C4×D188C2×C4semidirect
152. #13093983C2×C4semidirect
157. C2×C4⋊Dic47C2×C4semidirect
468. #2318D47semidirect
550. C47#17598semidirect

Maximal subgroups

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

subgroupindex
#202574372
#202524232
#202419632
#202419592
#202419512
#202419422
#202419382
#202419292
#202419242
#202419202
#202419072
#202418902
#202418772
C2×#156888592
C47×#23182
#1759847