Finite Group Databasebeta

← #26183130

Subgroups — #26183130

Order 12032.

890 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
1#20256815C211yesmaximal, characteristic
2#20252505C211yesmaximal, characteristic, complemented
3#20241862C211yesmaximal, characteristic, complemented
4#20241854C211yesmaximal, characteristic, complemented
5#20241849C211yesmaximal, characteristic, complemented
6#20241844C211yesmaximal, characteristic, complemented
7#20241836C211yesmaximal, characteristic, complemented
8#20241828C211yesmaximal, characteristic, complemented
9#20241823C211yesmaximal, characteristic, complemented
10#20241818C211yesmaximal, characteristic, complemented
11#20241810C211yesmaximal, characteristic, complemented
12#20241802C211yesmaximal, characteristic, complemented
13#20241797C211yesmaximal, characteristic, complemented
14#20241792C211yesmaximal, characteristic, complemented
15C47×#2965C211yesmaximal, characteristic, complemented
16#15689751C411yescharacteristic
17#15689744C411yescharacteristic
18#15689744C411yescharacteristic
19#15689738—21no—
20#15689735C411yescharacteristic
21#15689735C411yescharacteristic
22#15689731—21no—
23#15689715—21no—
24#15689715—21no—
25#15689701C411yescharacteristic
26#15689699C411yescharacteristic
27#15689694C411yescharacteristic
28#15689680C2211yescharacteristic
29#15689680C2211yescharacteristic
30#15689677—21no—
31#15689657C2211yescharacteristic
32#15689657C2211yescharacteristic
33#15689655—21no—
34#15689653—21no—
35#15689653—21no—
36C4×#10625350C2211yescharacteristic
37C2×C4×Dic94C2211yescharacteristic
38#15689254—21no—
39#15689201—21no—
40#15689195—21no—
41#15689195—21no—
42#15689180C2211yescharacteristic
43#15689180C2211yescharacteristic
44#15689176C2211yescharacteristic
45#15689147C2211yescharacteristic
46#15689147C2211yescharacteristic
47C2×C4⋊(C47⋊C8)C2211yescharacteristic
48#15688855C2211yescharacteristic
49#15688855C2211yescharacteristic
50#15688855C2211yescharacteristic
51#15688855C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688855C2211yescharacteristic
54#15688855C2211yescharacteristic
55#15688855C2211yescharacteristic
56#15688855C2211yescharacteristic
57#15688855C2211yescharacteristic
58#15688855C2211yescharacteristic
59#15688855C2211yescharacteristic
60#15688852C2211yescharacteristic
61#15688852C2211yescharacteristic
62#15688852C2211yescharacteristic
63#15688852C2211yescharacteristic
64C4×#41×C47C2211yescharacteristic
65C47×#446—21no—
66C47×#436—21no—
67C47×#435—21no—
68C47×#435—21no—
69C47×#431C2211yescharacteristic
70C47×#431C2211yescharacteristic
71C47×#431C2211yescharacteristic
72C4×M16×C47C2211yescharacteristic
73C4×M16×C47C2211yescharacteristic
74C2×C4×C8×C47C2211yescharacteristic
75C2×#10625350C2×C411yescharacteristic
76C22×Dic94C2×C411yescharacteristic
77C2×#10625329—21no—
78C2×#10625329—21no—
79C22×C47⋊C8—21no—
80#13094024C2×C411yescharacteristic
81#13094024C2×C411yescharacteristic
82#13094024C2×C411yescharacteristic
83#13094024C2×C411yescharacteristic
84#13094023—21no—
85#13094022—21no—
86#13094019—21no—
87#13094019—21no—
88#13094018—21no—
89#13094018—21no—
90#13094017—21no—
91#13094017—21no—
92#13094017—21no—
93#13094017—21no—
94#13094016—21no—
95#13094016—21no—
96#13094016C2×C411yescharacteristic
97#13094016C2×C411yescharacteristic
98#13094015—21no—
99#13094014—21no—
100#13094014—21no—
101#13094014—21no—
102#13094014—21no—
103#13094012C2×C411yescharacteristic
104#13094012C2×C411yescharacteristic
105#13094011—21no—
106#13094010—21no—
107#13094010—21no—
108#13094008—21no—
109#13094008—21no—
110#13094007—21no—
111#13094007—21no—
112#13094006—21no—
113#13094006—21no—
114#13094005—21no—
115#13094005—21no—
116#13094004—21no—
117#13094004—21no—
118#13094003—21no—
119#13094003—21no—
120#13094003C2×C411yescharacteristic
121#13094003C2×C411yescharacteristic
122#13094003C2×C411yescharacteristic
123#13094003C2×C411yescharacteristic
124#13094003C2×C411yescharacteristic
125#13094003C2×C411yescharacteristic
126#13094002—21no—
127#13094002—21no—
128#13094001—21no—
129#13094001—21no—
130#13094000—21no—
131#13093998C2×C411yescharacteristic
132#13093998C2×C411yescharacteristic
133#13093996—21no—
134#13093996—21no—
135#13093995—21no—
136C4×Dic94—21no—
137C4×Dic94—21no—
138C4×Dic94—21no—
139C4×Dic94—21no—
140C4×Dic94C2×C411yescharacteristic
141C4×Dic94C2×C411yescharacteristic
142C4×Dic94C2×C411yescharacteristic
143C4×Dic94C2311yescharacteristic
144C4×Dic94C2311yescharacteristic
145C4×Dic94C2311yescharacteristic
146C4×D188C2×C411yescharacteristic
147C4×D188C2311yescharacteristic
148C4×C22⋊D47—21no—
149C4×C22⋊D47—21no—
150C4×C22⋊D47—21no—
151C4×C22⋊D47—21no—
152#13093983—21no—
153#13093983—21no—
154#13093983C2×C411yescharacteristic
155#13093981—21no—
156#13093981—21no—
157#13093981—21no—
158C2×C4⋊Dic47C2×C411yescharacteristic
159C2×Dic47⋊C4—21no—
160C2×C4×Dic47—21no—
161C42×D47—21no—
162C4⋊(C47⋊C8)—21no—
163C4⋊(C47⋊C8)—21no—
164C4⋊(C47⋊C8)—21no—
165C4⋊(C47⋊C8)C2311yescharacteristic
166C4⋊(C47⋊C8)C2311yescharacteristic
167C4⋊(C47⋊C8)C2311yescharacteristic
168C4⋊(C47⋊C8)C2311yescharacteristic
169C22⋊(C47⋊C8)—21no—
170C22⋊(C47⋊C8)—21no—
171C22⋊(C47⋊C8)—21no—
172#13093935—21no—
173#13093935—21no—
174C4×C47⋊C8—21no—
175C2×#41×C47C2×C411yescharacteristic
176C2×M16×C47—21no—
177C2×M16×C47—21no—
178C22×C8×C47—21no—
179C4×Q8×C47D411yescharacteristic
180C4×Q8×C47D411yescharacteristic
181C4×D4×C47D411yescharacteristic
182C4×D4×C47D411yescharacteristic
183C4×D4×C47D411yescharacteristic
184C4×D4×C47D411yescharacteristic
185C4×D4×C47D411yescharacteristic
186C4×D4×C47D411yescharacteristic
187#117×C47C2×C411yescharacteristic
188#117×C47C2×C411yescharacteristic
189#117×C47C2×C411yescharacteristic
190C2×C42×C47C2311yescharacteristic
191C2×C42×C47C2311yescharacteristic
192C2×C42×C47C2311yescharacteristic
193C4⋊C8×C47—21no—
194C4⋊C8×C47—21no—
195C4⋊C8×C47—21no—
196C22⋊C8×C47—21no—
197C22⋊C8×C47—21no—
198C22⋊C8×C47—21no—
199#97×C47—21no—
200#97×C47—21no—
201C4×C8×C47—21no—
202C4×C8×C47C2311yescharacteristic
203C4×C8×C47C2311yescharacteristic
204C4×C8×C47C2311yescharacteristic
205C4×C8×C47C2311yescharacteristic
206#41×C47—42no—
207C2×Q8×C47C22⋊C411yescharacteristic
208C2×D4×C47C22⋊C411yescharacteristic
209C2×D4×C47C22⋊C411yescharacteristic
210C2×D4×C47C22⋊C411yescharacteristic
211C22×C4×C47C22×C411yescharacteristic
212C22×C4×C47C22×C411yescharacteristic
213C22×C4×C47C22×C411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D411yescharacteristic
220C2×C22⋊D47—21no—
221C2×C22⋊D47—21no—
222C2×C22⋊D47—21no—
223C22×Dic47—21no—
224C22×Dic47—21no—
225#10625350—42no—
226C2×D188C22×C411yescharacteristic
227C2×C4×D47—21no—
228C2×C4×D47—21no—
229C2×C4×D47—21no—
230C2×Dic94—21no—
231C2×Dic94—21no—
232C2×Dic94—21no—
233C2×Dic94—42no—
234C2×Dic94C22×C411yescharacteristic
235C2×Dic94C22×C411yescharacteristic
236C2×Dic94C22×C411yescharacteristic
237M16×C47—42no—
238M16×C47—42no—
239C2×C8×C47—21no—
240C2×C8×C47—21no—
241C2×C8×C47—21no—
242C2×C8×C47—21no—
243C2×C8×C47—42no—
244C4⋊C4×C47C22⋊C411yescharacteristic
245C4⋊C4×C47C22⋊C411yescharacteristic
246C4⋊C4×C47C22⋊C411yescharacteristic
247C4⋊C4×C47C22⋊C411yescharacteristic
248C4⋊C4×C47C22⋊C411yescharacteristic
249C4⋊C4×C47C22⋊C411yescharacteristic
250C22⋊C4×C47C22⋊C411yescharacteristic
251C22⋊C4×C47C22⋊C411yescharacteristic
252C22⋊C4×C47C22⋊C411yescharacteristic
253C22⋊C4×C47C22⋊C411yescharacteristic
254C22⋊C4×C47C22⋊C411yescharacteristic
255C22⋊C4×C47C22⋊C411yescharacteristic
256C42×C47C22×C411yescharacteristic
257C42×C47C22×C411yescharacteristic
258C42×C47C22×C411yescharacteristic
259C42×C47C2×D411yescharacteristic
260C42×C47C2×D411yescharacteristic
261C42×C47C2×D411yescharacteristic
262C42×C47C2×D411yescharacteristic
263C42×C47C2×D411yescharacteristic
264C42×C47C2×D411yescharacteristic
265C42×C47C2411yescharacteristic
266C22⋊Dic47—21no—
267C22⋊Dic47—21no—
268C22⋊Dic47—21no—
269C22⋊Dic47—21no—
270C22⋊Dic47—21no—
271C22⋊Dic47—21no—
272C22⋊Dic47—21no—
273(C2×D47)⋊C4—21no—
274(C2×D47)⋊C4—21no—
275(C2×D47)⋊C4—21no—
276(C2×D47)⋊C4—21no—
277(C2×D47)⋊C4—21no—
278(C2×D47)⋊C4—21no—
279(C2×D47)⋊C4—21no—
280(C2×D47)⋊C4—21no—
281C4⋊Dic47—21no—
282C4⋊Dic47—21no—
283C4⋊Dic47—21no—
284C4⋊Dic47—21no—
285C4⋊Dic47—21no—
286C4⋊Dic47—21no—
287C4⋊Dic47—21no—
288C4⋊Dic47C22×C411yescharacteristic
289C4⋊Dic47C22×C411yescharacteristic
290C4⋊Dic47C22×C411yescharacteristic
291C4⋊Dic47C22×C411yescharacteristic
292Dic47⋊C4—21no—
293Dic47⋊C4—21no—
294Dic47⋊C4—21no—
295Dic47⋊C4—21no—
296Dic47⋊C4—21no—
297Dic47⋊C4—21no—
298Dic47⋊C4—21no—
299Dic47⋊C4—21no—
300Dic47⋊C4—21no—
301Dic47⋊C4—21no—
302Dic47⋊C4—21no—
303Dic47⋊C4—21no—
304Dic47⋊C4—21no—
305Dic47⋊C4—21no—
306Dic47⋊C4—21no—
307Dic47⋊C4—21no—
308C4×Dic47—21no—
309C4×Dic47—21no—
310C4×Dic47—21no—
311C4×Dic47—21no—
312C4×Dic47—21no—
313C4×Dic47—21no—
314C4×Dic47—21no—
315#10625329—81no—
316#10625329—81no—
317C2×C47⋊C8—21no—
318C2×C47⋊C8—21no—
319C2×C47⋊C8—21no—
320C2×C47⋊C8—21no—
321C2×C47⋊C8—81no—
322C23×C47C2×C22⋊C411yescharacteristic
323C23×C47C2×C22⋊C411yescharacteristic
324C23×C47C2×C22⋊C411yescharacteristic
325C22×D47—21no—
326Q8×C47—41no—
327D4×C47—41no—
328D4×C47—41no—
329D4×C47—41no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—21no—
334C2×C4×C47—21no—
335C2×C4×C47—21no—
336C2×C4×C47—21no—
337C2×C4×C47—21no—
338C2×C4×C47—21no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47C2×C22⋊C411yescharacteristic
343C2×C4×C47C2×C22⋊C411yescharacteristic
344C2×C4×C47C2×C22⋊C411yescharacteristic
345C2×C4×C47C2×C22⋊C411yescharacteristic
346C2×C4×C47C2×C22⋊C411yescharacteristic
347C2×C4×C47C2×C22⋊C411yescharacteristic
348C2×C4×C47C2×C22⋊C411yescharacteristic
349C2×C4×C47C2×C22⋊C411yescharacteristic
350C2×C4×C47C2×C22⋊C411yescharacteristic
351C2×C4×C47C23×C411yescharacteristic
352C2×C4×C47C22×D411yescharacteristic
353C2×C4×C47C22×D411yescharacteristic
354C22⋊D47—42no—
355C22⋊D47—81no—
356C22⋊D47—81no—
357C2×Dic47—21no—
358C2×Dic47—21no—
359C2×Dic47—21no—
360C2×Dic47—21no—
361C2×Dic47—21no—
362C2×Dic47—21no—
363C2×Dic47—21no—
364C2×Dic47—42no—
365C2×Dic47—81no—
366D188—22no—
367C4×D47—42no—
368C4×D47—41no—
369C4×D47—41no—
370C4×D47—81no—
371Dic94—22no—
372Dic94—22no—
373Dic94—22no—
374Dic94—42no—
375Dic94—81no—
376Dic94—81no—
377C8×C47—22no—
378C8×C47—41no—
379C8×C47—41no—
380C8×C47—41no—
381C47⋊C8—41no—
382C47⋊C8—41no—
383C47⋊C8—41no—
384C47⋊C8—41no—
385#17506—471nomaximal, Sylow
386C22×C47—21no—
387C22×C47—21no—
388C22×C47—21no—
389C22×C47—21no—
390C22×C47—21no—
391C22×C47—21no—
392C22×C47—21no—
393C22×C47—21no—
394C22×C47—21no—
395C22×C47C22×C22⋊C411yescharacteristic
396C2×D47—41no—
397C2×D47—41no—
398C2×D47—41no—
399C4×C47—21no—
400C4×C47—21no—
401C4×C47—21no—
402C4×C47—21no—
403C4×C47—21no—
404C4×C47—21no—
405C4×C47—21no—
406C4×C47—21no—
407C4×C47—21no—
408C4×C47—21no—
409C4×C47#56812yes—
410C4×C47#57711yescharacteristic
411C4×C47#57811yescharacteristic
412Dic47—41no—
413Dic47—41no—
414Dic47—41no—
415Dic47—41no—
416Dic47—41no—
417Dic47—41no—
418Dic47—41no—
419#3461—471no—
420#2989—471no—
421#2965D4711yescharacteristic, complemented
422#1497—471no—
423#1495—471no—
424#1494—471no—
425#1493—471no—
426#1491—471no—
427#1489—471no—
428#1488—471no—
429#1487—471no—
430#1485—471no—
431#1483—471no—
432#1482—471no—
433#1481—471no—
434C2×C47—41no—
435C2×C47—41no—
436C2×C47—41no—
437C2×C47#287911yescharacteristic
438C2×C47#289811yescharacteristic
439C2×C47#290111yescharacteristic
440D47—81no—
441#544—471no—
442#542—471no—
443#542—471no—
444#542—941no—
445#541—471no—
446#541—471no—
447#541—941no—
448#539—941no—
449#539—941no—
450#537—471no—
451#536—471no—
452#536—471no—
453#533—471no—
454#533—471no—
455#533—941no—
456#529—471no—
457#529—471no—
458#529—941no—
459#529—941no—
460#529—941no—
461C4×#41—471no—
462C4×#41C2×D4711yescharacteristic
463C2×C4×Q8—471no—
464#446—21no—
465#446—941no—
466#436—21no—
467#436—941no—
468#435—21no—
469#435—21no—
470#435—941no—
471#435—941no—
472#432—471no—
473#432—471no—
474#431—471no—
475#431C2×D4711yescharacteristic
476#431C2×D4711yescharacteristic
477#431C2×D4711yescharacteristic
478#423—471no—
479#423—471no—
480C2×C4⋊C8—471no—
481C4×M16C2×D4711yescharacteristic
482C4×M16C2×D4711yescharacteristic
483C2×C4×C8C2×D4711yescharacteristic
484Q8⋊C8—471no—
485Q8⋊C8—471no—
486Q8⋊C8—471no—
487Q8⋊C8—471no—
488Q8⋊C8—471no—
489Q8⋊C8—471no—
490Q8⋊C8—471no—
491Q8⋊C8—471no—
492Q8⋊C8—471no—
493Q8⋊C8—471no—
494Q8⋊C8—471no—
495Q8⋊C8—471no—
496D4⋊C8—471no—
497D4⋊C8—471no—
498D4⋊C8—471no—
499D4⋊C8—471no—
500C47#1750611yescharacteristic, complemented, Sylow
501C2×#41—471no—
502C2×#41C4×D4711yescharacteristic
503C22×Q8—471no—
504C2×M16—21no—
505C2×M16—21no—
506C2×M16—941no—
507C2×M16—941no—
508C22×C8—21no—
509C22×C8—941no—
510C4⋊Q8—471no—
511C4⋊Q8—471no—
512C4⋊Q8—471no—
513C4⋊Q8—471no—
514C4⋊Q8—941no—
515C4⋊Q8—941no—
516#126—941no—
517#126—941no—
518#126—941no—
519#126—941no—
520#126—941no—
521#126—941no—
522#126—941no—
523#126—941no—
524#125—471no—
525#125—471no—
526#125—941no—
527#125—941no—
528#125—941no—
529#125—941no—
530#125—941no—
531#125—941no—
532#125—941no—
533#124—471no—
534#124—471no—
535#124—941no—
536#124—941no—
537#124—941no—
538#123—941no—
539#123—941no—
540#123—941no—
541#123—941no—
542#123—941no—
543#123—941no—
544#123—941no—
545#123—941no—
546C22⋊Q8—471no—
547C22⋊Q8—471no—
548C22⋊Q8—471no—
549C22⋊Q8—471no—
550C22⋊Q8—471no—
551C22⋊Q8—471no—
552C22⋊Q8—941no—
553C22⋊Q8—941no—
554C22⋊Q8—941no—
555C22⋊Q8—941no—
556C22⋊Q8—941no—
557C22⋊Q8—941no—
558C22⋊Q8—941no—
559C22⋊Q8—941no—
560C22⋊Q8—941no—
561#121—471no—
562#121—471no—
563#121—941no—
564#121—941no—
565#121—941no—
566C4×Q8—471no—
567C4×Q8—471no—
568C4×Q8—471no—
569C4×Q8—471no—
570C4×Q8—471no—
571C4×Q8—471no—
572C4×Q8—941no—
573C4×Q8—941no—
574C4×Q8—941no—
575C4×Q8—941no—
576C4×Q8D18811yescharacteristic
577C4×Q8C22⋊D4711yescharacteristic
578C4×D4—471no—
579C4×D4—471no—
580C4×D4—941no—
581C4×D4—941no—
582C4×D4—941no—
583C4×D4—941no—
584C4×D4D18811yescharacteristic
585C4×D4D18811yescharacteristic
586C4×D4D18811yescharacteristic
587C4×D4C22⋊D4711yescharacteristic
588C4×D4C22⋊D4711yescharacteristic
589C4×D4C22⋊D4711yescharacteristic
590#117—471no—
591#117—941no—
592#117—941no—
593#117—941no—
594#117—941no—
595#117—941no—
596#117C4×D4711yescharacteristic
597#117C4×D4711yescharacteristic
598#117C4×D4711yescharacteristic
599C2×C4⋊C4—471no—
600C2×C4⋊C4—941no—
601C2×C42—941no—
602C2×C42—941no—
603C2×C42C22×D4711yescharacteristic
604C2×C42C22×D4711yescharacteristic
605C2×C42C22×D4711yescharacteristic
606C4⋊C8—21no—
607C4⋊C8—21no—
608C4⋊C8—21no—
609C4⋊C8—471no—
610C4⋊C8—471no—
611C4⋊C8—471no—
612C4⋊C8—471no—
613C4⋊C8—941no—
614C4⋊C8—941no—
615C4⋊C8—941no—
616C22⋊C8—21no—
617C22⋊C8—21no—
618C22⋊C8—21no—
619C22⋊C8—941no—
620C22⋊C8—941no—
621C22⋊C8—941no—
622#97—21no—
623#97—21no—
624#97—941no—
625#97—941no—
626C4×C8—21no—
627C4×C8—941no—
628C4×C8C22×D4711yescharacteristic
629C4×C8C22×D4711yescharacteristic
630C4×C8C22×D4711yescharacteristic
631C4×C8C22×D4711yescharacteristic
632#41—42no—
633#41—1882no—
634C2×Q8—471no—
635C2×Q8—471no—
636C2×Q8—471no—
637C2×Q8—941no—
638C2×Q8—941no—
639C2×Q8—941no—
640C2×Q8—1882no—
641C2×Q8(C2×D47)⋊C411yescharacteristic
642C2×D4—471no—
643C2×D4—941no—
644C2×D4—941no—
645C2×D4—941no—
646C2×D4(C2×D47)⋊C411yescharacteristic
647C2×D4(C2×D47)⋊C411yescharacteristic
648C2×D4(C2×D47)⋊C411yescharacteristic
649C22×C4—941no—
650C22×C4—941no—
651C22×C4—941no—
652C22×C4—941no—
653C22×C4—941no—
654C22×C4C2×C4×D4711yescharacteristic
655C22×C4C2×C4×D4711yescharacteristic
656C22×C4C2×C4×D4711yescharacteristic
657C22×C4C2×D18811yescharacteristic
658C22×C4C2×D18811yescharacteristic
659C22×C4C2×D18811yescharacteristic
660C22×C4C2×C22⋊D4711yescharacteristic
661C22×C4C2×C22⋊D4711yescharacteristic
662C22×C4C2×C22⋊D4711yescharacteristic
663M16—42no—
664M16—42no—
665M16—3761no—
666M16—3761no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—42no—
672C2×C8—941no—
673C2×C8—941no—
674C2×C8—941no—
675C2×C8—941no—
676C2×C8—3761no—
677C4⋊C4—471no—
678C4⋊C4—471no—
679C4⋊C4—471no—
680C4⋊C4—471no—
681C4⋊C4—941no—
682C4⋊C4—941no—
683C4⋊C4—941no—
684C4⋊C4—941no—
685C4⋊C4—941no—
686C4⋊C4—941no—
687C4⋊C4—941no—
688C4⋊C4—941no—
689C4⋊C4—941no—
690C4⋊C4—941no—
691C4⋊C4—941no—
692C4⋊C4—941no—
693C4⋊C4—941no—
694C4⋊C4—941no—
695C4⋊C4—941no—
696C4⋊C4—941no—
697C4⋊C4—941no—
698C4⋊C4—941no—
699C4⋊C4—941no—
700C4⋊C4—941no—
701C4⋊C4—941no—
702C4⋊C4—941no—
703C4⋊C4—941no—
704C4⋊C4(C2×D47)⋊C411yescharacteristic
705C4⋊C4(C2×D47)⋊C411yescharacteristic
706C4⋊C4(C2×D47)⋊C411yescharacteristic
707C4⋊C4(C2×D47)⋊C411yescharacteristic
708C4⋊C4(C2×D47)⋊C411yescharacteristic
709C4⋊C4(C2×D47)⋊C411yescharacteristic
710C22⋊C4—941no—
711C22⋊C4—941no—
712C22⋊C4—941no—
713C22⋊C4—941no—
714C22⋊C4—941no—
715C22⋊C4—941no—
716C22⋊C4—941no—
717C22⋊C4—941no—
718C22⋊C4—941no—
719C22⋊C4—941no—
720C22⋊C4—941no—
721C22⋊C4—941no—
722C22⋊C4—941no—
723C22⋊C4—941no—
724C22⋊C4—941no—
725C22⋊C4(C2×D47)⋊C411yescharacteristic
726C22⋊C4(C2×D47)⋊C411yescharacteristic
727C22⋊C4(C2×D47)⋊C411yescharacteristic
728C22⋊C4(C2×D47)⋊C411yescharacteristic
729C22⋊C4(C2×D47)⋊C411yescharacteristic
730C22⋊C4(C2×D47)⋊C411yescharacteristic
731C42—941no—
732C42—941no—
733C42—941no—
734C42—941no—
735C42—941no—
736C42—941no—
737C42—941no—
738C42C2×C4×D4711yescharacteristic
739C42C2×C4×D4711yescharacteristic
740C42C2×C4×D4711yescharacteristic
741C42C2×D18811yescharacteristic
742C42C2×D18811yescharacteristic
743C42C2×D18811yescharacteristic
744C42C2×C22⋊D4711yescharacteristic
745C42C2×C22⋊D4711yescharacteristic
746C42C2×C22⋊D4711yescharacteristic
747C42C23×D4711yescharacteristic
748C23—941no—
749C23C2×(C2×D47)⋊C411yescharacteristic
750C23C2×(C2×D47)⋊C411yescharacteristic
751C23C2×(C2×D47)⋊C411yescharacteristic
752Q8—41no—
753Q8—942no—
754Q8—942no—
755Q8—942no—
756Q8—3761no—
757Q8—3761no—
758Q8—1882no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—942no—
763D4—3761no—
764D4—3761no—
765D4—1882no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—941no—
779C2×C4—941no—
780C2×C4—941no—
781C2×C4—941no—
782C2×C4—941no—
783C2×C4—941no—
784C2×C4—941no—
785C2×C4—3761no—
786C2×C4—3761no—
787C2×C4—1882no—
788C2×C4—1882no—
789C2×C4—1881no—
790C2×C4—1881no—
791C2×C4C2×(C2×D47)⋊C411yescharacteristic
792C2×C4C2×(C2×D47)⋊C411yescharacteristic
793C2×C4C2×(C2×D47)⋊C411yescharacteristic
794C2×C4C2×(C2×D47)⋊C411yescharacteristic
795C2×C4C2×(C2×D47)⋊C411yescharacteristic
796C2×C4C2×(C2×D47)⋊C411yescharacteristic
797C2×C4C2×(C2×D47)⋊C411yescharacteristic
798C2×C4C2×(C2×D47)⋊C411yescharacteristic
799C2×C4C2×(C2×D47)⋊C411yescharacteristic
800C2×C4C22×C4×D4711yescharacteristic
801C2×C4C22×C22⋊D4711yescharacteristic
802C2×C4C22×D18811yescharacteristic
803C8—22no—
804C8—41no—
805C8—41no—
806C8—41no—
807C8—1881no—
808C8—1881no—
809C8—1881no—
810C8—1881no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—1881no—
821C22—1881no—
822C22—1881no—
823C22C22×(C2×D47)⋊C411yescharacteristic
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—1881no—
835C4—1881no—
836C4—1881no—
837C4—1881no—
838C4—1881no—
839C4—1881no—
840C4—1881no—
841C4#1568988912yes—
842C4#1568993511yescharacteristic
843C4#1568994011yescharacteristic
844C2—41no—
845C2—41no—
846C2—41no—
847C2—3761no—
848C2#2025183211yescharacteristic
849C2#2025192211yescharacteristic
850C2#2025193611yescharacteristic
subgroupG/H
centerC2×C4C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2965C2
socleC22×C47C22×C22⋊C4
prime radical#15689701C4
cosocleC42×C47C24
hypercenter#2965D47
hypocenterC47#17506
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2965

Complements

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

NH ≅ G/Ntype
2. #20252505C2semidirect
3. #20241862C2semidirect
4. #20241854C2semidirect
5. #20241849C2semidirect
6. #20241844C2semidirect
7. #20241836C2semidirect
8. #20241828C2semidirect
9. #20241823C2semidirect
10. #20241818C2semidirect
11. #20241810C2semidirect
12. #20241802C2semidirect
13. #20241797C2semidirect
14. #20241792C2semidirect
15. C47×#2965C2semidirect
421. #2965D47semidirect
500. C47#17506semidirect

Maximal subgroups

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

subgroupindex
#202568152
#202525052
#202418622
#202418542
#202418492
#202418442
#202418362
#202418282
#202418232
#202418182
#202418102
#202418022
#202417972
#202417922
C47×#29652
#1750647