Finite Group Databasebeta

← #26183115

Subgroups — #26183115

Order 12032.

954 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256804C211yesmaximal, characteristic
2#20252505C211yesmaximal, characteristic, complemented
3#20241858C211yesmaximal, characteristic, complemented
4#20241854C211yesmaximal, characteristic, complemented
5#20241849C211yesmaximal, characteristic, complemented
6#20241840C211yesmaximal, characteristic, complemented
7#20241832C211yesmaximal, characteristic, complemented
8#20241828C211yesmaximal, characteristic, complemented
9#20241823C211yesmaximal, characteristic, complemented
10#20241814C211yesmaximal, characteristic, complemented
11#20241806C211yesmaximal, characteristic, complemented
12#20241802C211yesmaximal, characteristic, complemented
13#20241797C211yesmaximal, characteristic, complemented
14#20241788C211yesmaximal, characteristic, complemented
15C47×#2965C211yesmaximal, characteristic, complemented
16#15689751C411yescharacteristic
17#15689745—21no—
18#15689744C411yescharacteristic
19#15689744C411yescharacteristic
20#15689728C411yescharacteristic
21#15689728C411yescharacteristic
22#15689724—21no—
23#15689706—21no—
24#15689706—21no—
25#15689701C411yescharacteristic
26#15689692C411yescharacteristic
27#15689687C411yescharacteristic
28#15689673C2211yescharacteristic
29#15689673C2211yescharacteristic
30#15689670—21no—
31#15689660—21no—
32#15689657C2211yescharacteristic
33#15689657C2211yescharacteristic
34#15689632—21no—
35#15689632—21no—
36C4×#10625350C2211yescharacteristic
37C2×C4×D188C2211yescharacteristic
38#15689254—21no—
39#15689201—21no—
40#15689195—21no—
41#15689195—21no—
42#15689180C2211yescharacteristic
43#15689180C2211yescharacteristic, complemented
44#15689176C2211yescharacteristic, complemented
45#15689147C2211yescharacteristic
46#15689147C2211yescharacteristic, complemented
47C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
48#15688855C2211yescharacteristic, complemented
49#15688855C2211yescharacteristic, complemented
50#15688855C2211yescharacteristic, complemented
51#15688855C2211yescharacteristic, complemented
52#15688852C2211yescharacteristic
53#15688852C2211yescharacteristic
54#15688852C2211yescharacteristic
55#15688852C2211yescharacteristic
56#15688852C2211yescharacteristic
57#15688852C2211yescharacteristic
58#15688852C2211yescharacteristic
59#15688852C2211yescharacteristic
60#15688852C2211yescharacteristic, complemented
61#15688852C2211yescharacteristic, complemented
62#15688852C2211yescharacteristic, complemented
63#15688852C2211yescharacteristic, complemented
64C4×#41×C47C2211yescharacteristic
65C47×#446—21no—
66C47×#436—21no—
67C47×#435—21no—
68C47×#435—21no—
69C47×#431C2211yescharacteristic
70C47×#431C2211yescharacteristic, complemented
71C47×#431C2211yescharacteristic, complemented
72C4×M16×C47C2211yescharacteristic
73C4×M16×C47C2211yescharacteristic, complemented
74C2×C4×C8×C47C2211yescharacteristic, complemented
75C2×#10625350—21no—
76C2×#10625350—21no—
77C2×#10625350C2×C411yescharacteristic
78C22×D188C2×C411yescharacteristic
79C22×C4×D47—21no—
80C2×#10625329—21no—
81C2×#10625329—21no—
82C22×C47⋊C8—21no—
83#13094024C2×C411yescharacteristic
84#13094024C2×C411yescharacteristic
85#13094023—21no—
86#13094021C2×C411yescharacteristic
87#13094021C2×C411yescharacteristic
88#13094020—21no—
89#13094019—21no—
90#13094019—21no—
91#13094018—21no—
92#13094018—21no—
93#13094016C2×C411yescharacteristic
94#13094016C2×C411yescharacteristic
95#13094015—21no—
96#13094013—21no—
97#13094012—21no—
98#13094012—21no—
99#13094012C2×C411yescharacteristic
100#13094012C2×C411yescharacteristic
101#13094010—21no—
102#13094010—21no—
103#13094009—21no—
104#13094009—21no—
105#13094009—21no—
106#13094009—21no—
107#13094007—21no—
108#13094007—21no—
109#13094006—21no—
110#13094006—21no—
111#13094003C2×C411yescharacteristic
112#13094003C2×C411yescharacteristic
113#13094002—21no—
114#13094002—21no—
115#13094001—21no—
116#13094001—21no—
117#13094000—21no—
118#13093999—21no—
119#13093999—21no—
120#13093998—21no—
121#13093998—21no—
122#13093998C2×C411yescharacteristic
123#13093998C2×C411yescharacteristic
124#13093998C2×C411yescharacteristic
125#13093998C2×C411yescharacteristic
126#13093998C2×C411yescharacteristic
127#13093998C2×C411yescharacteristic
128#13093997—21no—
129#13093997—21no—
130#13093997—21no—
131#13093997—21no—
132#13093996—21no—
133#13093996—21no—
134#13093995—21no—
135#13093994—21no—
136#13093994—21no—
137#13093992—21no—
138#13093992—21no—
139C4×Dic94C2×C411yescharacteristic
140C4×Dic94C2311yescharacteristic
141C4×D188—21no—
142C4×D188—21no—
143C4×D188—21no—
144C4×D188—21no—
145C4×D188C2×C411yescharacteristic
146C4×D188C2×C411yescharacteristic
147C4×D188C2×C411yescharacteristic
148C4×D188C2311yescharacteristic
149C4×D188C2311yescharacteristic
150C4×D188C2311yescharacteristic
151C4×C22⋊D47—21no—
152C4×C22⋊D47—21no—
153C4×C22⋊D47—21no—
154C4×C22⋊D47—21no—
155#13093983C2×C411yescharacteristic
156#13093981—21no—
157#13093981—21no—
158#13093981—21no—
159C2×C4⋊Dic47C2×C411yescharacteristic
160C2×(C2×D47)⋊C4—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
206C23×D47—21no—
207#41×C47—42no—
208C2×Q8×C47C22⋊C411yescharacteristic
209C2×D4×C47C22⋊C411yescharacteristic
210C2×D4×C47C22⋊C411yescharacteristic
211C2×D4×C47C22⋊C411yescharacteristic
212C22×C4×C47C22×C411yescharacteristic
213C22×C4×C47C22×C411yescharacteristic
214C22×C4×C47C22×C411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2×D411yescharacteristic
221C2×C22⋊D47—21no—
222C2×C22⋊D47—21no—
223C2×C22⋊D47—21no—
224C2×C22⋊D47—21no—
225C2×C22⋊D47—21no—
226C2×C22⋊D47—21no—
227C2×C22⋊D47—21no—
228C22×Dic47—21no—
229#10625350—42no—
230#10625350—81no—
231#10625350—81no—
232#10625350—81no—
233#10625350—81no—
234C2×D188—21no—
235C2×D188—21no—
236C2×D188—21no—
237C2×D188—21no—
238C2×D188—21no—
239C2×D188—42no—
240C2×D188C22×C411yescharacteristic
241C2×D188C22×C411yescharacteristic
242C2×D188C22×C411yescharacteristic
243C2×C4×D47—21no—
244C2×C4×D47—21no—
245C2×C4×D47—21no—
246C2×C4×D47—21no—
247C2×C4×D47—21no—
248C2×C4×D47—21no—
249C2×C4×D47—21no—
250C2×C4×D47—81no—
251C2×C4×D47—81no—
252C2×Dic94—21no—
253C2×Dic94—21no—
254C2×Dic94C22×C411yescharacteristic
255M16×C47—42no—
256M16×C47—42no—
257C2×C8×C47—21no—
258C2×C8×C47—21no—
259C2×C8×C47—21no—
260C2×C8×C47—21no—
261C2×C8×C47—42no—
262C4⋊C4×C47C22⋊C411yescharacteristic
263C4⋊C4×C47C22⋊C411yescharacteristic
264C4⋊C4×C47C22⋊C411yescharacteristic
265C4⋊C4×C47C22⋊C411yescharacteristic
266C4⋊C4×C47C22⋊C411yescharacteristic
267C4⋊C4×C47C22⋊C411yescharacteristic
268C22⋊C4×C47C22⋊C411yescharacteristic
269C22⋊C4×C47C22⋊C411yescharacteristic
270C22⋊C4×C47C22⋊C411yescharacteristic
271C22⋊C4×C47C22⋊C411yescharacteristic
272C22⋊C4×C47C22⋊C411yescharacteristic
273C22⋊C4×C47C22⋊C411yescharacteristic
274C42×C47C22×C411yescharacteristic
275C42×C47C22×C411yescharacteristic
276C42×C47C22×C411yescharacteristic
277C42×C47C2×D411yescharacteristic
278C42×C47C2×D411yescharacteristic
279C42×C47C2×D411yescharacteristic
280C42×C47C2×D411yescharacteristic
281C42×C47C2×D411yescharacteristic
282C42×C47C2×D411yescharacteristic
283C42×C47C2411yescharacteristic
284C22⋊Dic47—21no—
285C22⋊Dic47—21no—
286C22⋊Dic47—21no—
287(C2×D47)⋊C4—21no—
288(C2×D47)⋊C4—21no—
289(C2×D47)⋊C4—21no—
290(C2×D47)⋊C4—21no—
291(C2×D47)⋊C4—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—
298(C2×D47)⋊C4—21no—
299(C2×D47)⋊C4—21no—
300(C2×D47)⋊C4—21no—
301(C2×D47)⋊C4—21no—
302(C2×D47)⋊C4—21no—
303C4⋊Dic47—21no—
304C4⋊Dic47—21no—
305C4⋊Dic47—21no—
306C4⋊Dic47C22×C411yescharacteristic
307C4⋊Dic47C22×C411yescharacteristic
308C4⋊Dic47C22×C411yescharacteristic
309C4⋊Dic47C22×C411yescharacteristic
310Dic47⋊C4—21no—
311Dic47⋊C4—21no—
312Dic47⋊C4—21no—
313Dic47⋊C4—21no—
314Dic47⋊C4—21no—
315Dic47⋊C4—21no—
316Dic47⋊C4—21no—
317Dic47⋊C4—21no—
318C4×Dic47—21no—
319C4×Dic47—21no—
320C4×Dic47—21no—
321#10625329—81no—
322#10625329—81no—
323C2×C47⋊C8—21no—
324C2×C47⋊C8—21no—
325C2×C47⋊C8—21no—
326C2×C47⋊C8—21no—
327C2×C47⋊C8—81no—
328C23×C47C2×C22⋊C411yescharacteristic
329C23×C47C2×C22⋊C411yescharacteristic
330C23×C47C2×C22⋊C411yescharacteristic
331C22×D47—21no—
332C22×D47—21no—
333C22×D47—21no—
334C22×D47—42no—
335C22×D47—81no—
336C22×D47—81no—
337Q8×C47—41no—
338D4×C47—41no—
339D4×C47—41no—
340D4×C47—41no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—21no—
345C2×C4×C47—21no—
346C2×C4×C47—21no—
347C2×C4×C47—21no—
348C2×C4×C47—21no—
349C2×C4×C47—21no—
350C2×C4×C47—41no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47C2×C22⋊C411yescharacteristic
354C2×C4×C47C2×C22⋊C411yescharacteristic
355C2×C4×C47C2×C22⋊C411yescharacteristic
356C2×C4×C47C2×C22⋊C411yescharacteristic
357C2×C4×C47C2×C22⋊C411yescharacteristic
358C2×C4×C47C2×C22⋊C411yescharacteristic
359C2×C4×C47C2×C22⋊C411yescharacteristic
360C2×C4×C47C2×C22⋊C411yescharacteristic
361C2×C4×C47C2×C22⋊C411yescharacteristic
362C2×C4×C47C23×C411yescharacteristic
363C2×C4×C47C22×D411yescharacteristic
364C2×C4×C47C22×D411yescharacteristic
365C22⋊D47—42no—
366C22⋊D47—81no—
367C22⋊D47—81no—
368C22⋊D47—81no—
369C22⋊D47—81no—
370C22⋊D47—81no—
371C22⋊D47—81no—
372C2×Dic47—21no—
373C2×Dic47—21no—
374C2×Dic47—21no—
375C2×Dic47—21no—
376C2×Dic47—21no—
377C2×Dic47—81no—
378D188—22no—
379D188—22no—
380D188—22no—
381D188—42no—
382D188—81no—
383D188—81no—
384D188—81no—
385D188—81no—
386C4×D47—42no—
387C4×D47—41no—
388C4×D47—41no—
389C4×D47—41no—
390C4×D47—41no—
391C4×D47—41no—
392C4×D47—41no—
393C4×D47—81no—
394C4×D47—81no—
395C4×D47—81no—
396Dic94—22no—
397Dic94—81no—
398Dic94—81no—
399C8×C47—22no—
400C8×C47—41no—
401C8×C47—41no—
402C8×C47—41no—
403C47⋊C8—41no—
404C47⋊C8—41no—
405C47⋊C8—41no—
406C47⋊C8—41no—
407#17505—471nomaximal, Sylow
408C22×C47—21no—
409C22×C47—21no—
410C22×C47—21no—
411C22×C47—21no—
412C22×C47—21no—
413C22×C47—21no—
414C22×C47—21no—
415C22×C47—21no—
416C22×C47—21no—
417C22×C47C22×C22⋊C411yescharacteristic
418C2×D47—41no—
419C2×D47—41no—
420C2×D47—41no—
421C2×D47—41no—
422C2×D47—41no—
423C2×D47—41no—
424C2×D47—41no—
425C2×D47—41no—
426C2×D47—41no—
427C2×D47—84no—
428C4×C47—21no—
429C4×C47—21no—
430C4×C47—21no—
431C4×C47—21no—
432C4×C47—21no—
433C4×C47—21no—
434C4×C47—21no—
435C4×C47—21no—
436C4×C47—21no—
437C4×C47—21no—
438C4×C47#56812yes—
439C4×C47#57611yescharacteristic
440C4×C47#57711yescharacteristic
441Dic47—41no—
442Dic47—41no—
443Dic47—41no—
444Dic47—41no—
445Dic47—41no—
446#3460—471no—
447#2989—471no—
448#2965D4711yescharacteristic, complemented
449#1496—471no—
450#1495—471no—
451#1494—471no—
452#1492—471no—
453#1490—471no—
454#1489—471no—
455#1488—471no—
456#1486—471no—
457#1484—471no—
458#1483—471no—
459#1482—471no—
460#1480—471no—
461C2×C47—41no—
462C2×C47—41no—
463C2×C47—41no—
464C2×C47#287911yescharacteristic
465C2×C47#289711yescharacteristic
466C2×C47#290111yescharacteristic
467D47—81no—
468D47—81no—
469D47—81no—
470#544—471no—
471#542—471no—
472#542—471no—
473#542—941no—
474#540—471no—
475#540—471no—
476#540—941no—
477#538—941no—
478#538—941no—
479#537—471no—
480#535—471no—
481#535—471no—
482#532—471no—
483#532—471no—
484#532—941no—
485#529—471no—
486#529—471no—
487#529—941no—
488#525—941no—
489#525—941no—
490C4×#41—471no—
491C4×#41C2×D4711yescharacteristic
492C2×C4×D4—471no—
493#446—21no—
494#446—941no—
495#436—21no—
496#436—941no—
497#435—21no—
498#435—21no—
499#435—941no—
500#435—941no—
501#432—471no—
502#432—471no—
503#431—471no—
504#431C2×D4711yescharacteristic
505#431C2×D4711yescharacteristic, complemented
506#431C2×D4711yescharacteristic, complemented
507#423—471no—
508#423—471no—
509C2×C4⋊C8—471no—
510C4×M16C2×D4711yescharacteristic
511C4×M16C2×D4711yescharacteristic, complemented
512C2×C4×C8C2×D4711yescharacteristic, complemented
513Q8⋊C8—471no—
514Q8⋊C8—471no—
515Q8⋊C8—471no—
516Q8⋊C8—471no—
517D4⋊C8—471no—
518D4⋊C8—471no—
519D4⋊C8—471no—
520D4⋊C8—471no—
521D4⋊C8—471no—
522D4⋊C8—471no—
523D4⋊C8—471no—
524D4⋊C8—471no—
525D4⋊C8—471no—
526D4⋊C8—471no—
527D4⋊C8—471no—
528D4⋊C8—471no—
529C47#1750511yescharacteristic, complemented, Sylow
530C2×#41—471no—
531C2×#41—941no—
532C2×#41—941no—
533C2×#41C4×D4711yescharacteristic
534C22×D4—471no—
535C23×C4—941no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—941no—
539C2×M16—941no—
540C22×C8—21no—
541C22×C8—941no—
542C4⋊Q8—471no—
543C4⋊Q8—471no—
544C4⋊Q8—941no—
545#127—471no—
546#127—471no—
547#127—941no—
548#126—941no—
549#126—941no—
550#126—941no—
551#126—941no—
552#125—471no—
553#125—471no—
554#125—941no—
555#124—471no—
556#124—471no—
557#124—941no—
558#124—941no—
559#124—941no—
560#124—941no—
561#124—941no—
562#123—941no—
563#123—941no—
564#123—941no—
565#123—941no—
566#123—941no—
567#123—941no—
568#123—941no—
569#123—941no—
570C22⋊Q8—471no—
571C22⋊Q8—471no—
572C22⋊Q8—941no—
573C22⋊Q8—941no—
574C22⋊Q8—941no—
575C22⋊Q8—941no—
576C22⋊Q8—941no—
577#121—471no—
578#121—471no—
579#121—471no—
580#121—471no—
581#121—471no—
582#121—471no—
583#121—941no—
584#121—941no—
585#121—941no—
586#121—941no—
587#121—941no—
588#121—941no—
589#121—941no—
590#121—941no—
591#121—941no—
592#121—941no—
593#121—941no—
594#120—941no—
595#120—941no—
596#120—941no—
597#120—941no—
598C4×Q8—471no—
599C4×Q8—471no—
600C4×Q8D18811yescharacteristic
601C4×Q8C22⋊D4711yescharacteristic
602C4×D4—471no—
603C4×D4—471no—
604C4×D4—471no—
605C4×D4—471no—
606C4×D4—471no—
607C4×D4—471no—
608C4×D4—941no—
609C4×D4—941no—
610C4×D4—941no—
611C4×D4—941no—
612C4×D4—941no—
613C4×D4—941no—
614C4×D4—941no—
615C4×D4—941no—
616C4×D4D18811yescharacteristic
617C4×D4D18811yescharacteristic
618C4×D4D18811yescharacteristic
619C4×D4C22⋊D4711yescharacteristic
620C4×D4C22⋊D4711yescharacteristic
621C4×D4C22⋊D4711yescharacteristic
622#117—471no—
623#117—941no—
624#117—941no—
625#117—941no—
626#117C4×D4711yescharacteristic
627#117C4×D4711yescharacteristic
628#117C4×D4711yescharacteristic
629C2×C4⋊C4—471no—
630C2×C22⋊C4—941no—
631C2×C42—941no—
632C2×C42C22×D4711yescharacteristic
633C2×C42C22×D4711yescharacteristic
634C2×C42C22×D4711yescharacteristic
635C4⋊C8—21no—
636C4⋊C8—21no—
637C4⋊C8—21no—
638C4⋊C8—471no—
639C4⋊C8—471no—
640C4⋊C8—471no—
641C4⋊C8—471no—
642C4⋊C8—941no—
643C4⋊C8—941no—
644C4⋊C8—941no—
645C22⋊C8—21no—
646C22⋊C8—21no—
647C22⋊C8—21no—
648C22⋊C8—941no—
649C22⋊C8—941no—
650C22⋊C8—941no—
651#97—21no—
652#97—21no—
653#97—941no—
654#97—941no—
655C4×C8—21no—
656C4×C8—941no—
657C4×C8C22×D4711yescharacteristic
658C4×C8C22×D4711yescharacteristic
659C4×C8C22×D4711yescharacteristic
660C4×C8C22×D4711yescharacteristic
661C24—941no—
662#41—42no—
663#41—3761no—
664#41—3761no—
665#41—3761no—
666#41—3761no—
667#41—1882no—
668C2×Q8—471no—
669C2×Q8—941no—
670C2×Q8—941no—
671C2×Q8(C2×D47)⋊C411yescharacteristic
672C2×D4—471no—
673C2×D4—471no—
674C2×D4—471no—
675C2×D4—941no—
676C2×D4—941no—
677C2×D4—941no—
678C2×D4—941no—
679C2×D4—941no—
680C2×D4—941no—
681C2×D4—941no—
682C2×D4—941no—
683C2×D4—941no—
684C2×D4—941no—
685C2×D4—941no—
686C2×D4—941no—
687C2×D4—1882no—
688C2×D4(C2×D47)⋊C411yescharacteristic
689C2×D4(C2×D47)⋊C411yescharacteristic
690C2×D4(C2×D47)⋊C411yescharacteristic
691C22×C4—941no—
692C22×C4—941no—
693C22×C4—941no—
694C22×C4—941no—
695C22×C4—941no—
696C22×C4—941no—
697C22×C4—941no—
698C22×C4—941no—
699C22×C4—3761no—
700C22×C4—3761no—
701C22×C4C2×C4×D4711yescharacteristic
702C22×C4C2×C4×D4711yescharacteristic
703C22×C4C2×C4×D4711yescharacteristic
704C22×C4C2×D18811yescharacteristic
705C22×C4C2×D18811yescharacteristic
706C22×C4C2×D18811yescharacteristic
707C22×C4C2×C22⋊D4711yescharacteristic
708C22×C4C2×C22⋊D4711yescharacteristic
709C22×C4C2×C22⋊D4711yescharacteristic
710M16—42no—
711M16—42no—
712M16—3761no—
713M16—3761no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—42no—
719C2×C8—941no—
720C2×C8—941no—
721C2×C8—941no—
722C2×C8—941no—
723C2×C8—3761no—
724C4⋊C4—471no—
725C4⋊C4—471no—
726C4⋊C4—471no—
727C4⋊C4—471no—
728C4⋊C4—941no—
729C4⋊C4—941no—
730C4⋊C4—941no—
731C4⋊C4—941no—
732C4⋊C4—941no—
733C4⋊C4—941no—
734C4⋊C4—941no—
735C4⋊C4—941no—
736C4⋊C4—941no—
737C4⋊C4—941no—
738C4⋊C4—941no—
739C4⋊C4(C2×D47)⋊C411yescharacteristic
740C4⋊C4(C2×D47)⋊C411yescharacteristic
741C4⋊C4(C2×D47)⋊C411yescharacteristic
742C4⋊C4(C2×D47)⋊C411yescharacteristic
743C4⋊C4(C2×D47)⋊C411yescharacteristic
744C4⋊C4(C2×D47)⋊C411yescharacteristic
745C22⋊C4—941no—
746C22⋊C4—941no—
747C22⋊C4—941no—
748C22⋊C4—941no—
749C22⋊C4—941no—
750C22⋊C4—941no—
751C22⋊C4—941no—
752C22⋊C4—941no—
753C22⋊C4—941no—
754C22⋊C4—941no—
755C22⋊C4—941no—
756C22⋊C4—941no—
757C22⋊C4—941no—
758C22⋊C4—941no—
759C22⋊C4—941no—
760C22⋊C4—941no—
761C22⋊C4—941no—
762C22⋊C4—941no—
763C22⋊C4—941no—
764C22⋊C4(C2×D47)⋊C411yescharacteristic
765C22⋊C4(C2×D47)⋊C411yescharacteristic
766C22⋊C4(C2×D47)⋊C411yescharacteristic
767C22⋊C4(C2×D47)⋊C411yescharacteristic
768C22⋊C4(C2×D47)⋊C411yescharacteristic
769C22⋊C4(C2×D47)⋊C411yescharacteristic
770C42—941no—
771C42—941no—
772C42—941no—
773C42C2×C4×D4711yescharacteristic
774C42C2×C4×D4711yescharacteristic
775C42C2×C4×D4711yescharacteristic
776C42C2×D18811yescharacteristic
777C42C2×D18811yescharacteristic
778C42C2×D18811yescharacteristic
779C42C2×C22⋊D4711yescharacteristic
780C42C2×C22⋊D4711yescharacteristic
781C42C2×C22⋊D4711yescharacteristic
782C42C23×D4711yescharacteristic
783C23—941no—
784C23—941no—
785C23—941no—
786C23—3761no—
787C23—3761no—
788C23—1882no—
789C23C2×(C2×D47)⋊C411yescharacteristic
790C23C2×(C2×D47)⋊C411yescharacteristic
791C23C2×(C2×D47)⋊C411yescharacteristic
792Q8—41no—
793Q8—942no—
794Q8—3761no—
795Q8—3761no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—942no—
800D4—942no—
801D4—942no—
802D4—3761no—
803D4—3761no—
804D4—3761no—
805D4—3761no—
806D4—3761no—
807D4—3761no—
808D4—3761no—
809D4—3761no—
810D4—3761no—
811D4—3761no—
812D4—1882no—
813D4—1882no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—941no—
827C2×C4—941no—
828C2×C4—941no—
829C2×C4—941no—
830C2×C4—941no—
831C2×C4—3761no—
832C2×C4—3761no—
833C2×C4—3761no—
834C2×C4—3761no—
835C2×C4—1882no—
836C2×C4—1881no—
837C2×C4—1881no—
838C2×C4—1881no—
839C2×C4—1881no—
840C2×C4—1881no—
841C2×C4—1881no—
842C2×C4C2×(C2×D47)⋊C411yescharacteristic
843C2×C4C2×(C2×D47)⋊C411yescharacteristic
844C2×C4C2×(C2×D47)⋊C411yescharacteristic
845C2×C4C2×(C2×D47)⋊C411yescharacteristic
846C2×C4C2×(C2×D47)⋊C411yescharacteristic
847C2×C4C2×(C2×D47)⋊C411yescharacteristic
848C2×C4C2×(C2×D47)⋊C411yescharacteristic
849C2×C4C2×(C2×D47)⋊C411yescharacteristic
850C2×C4C2×(C2×D47)⋊C411yescharacteristic
851C2×C4C22×C4×D4711yescharacteristic
852C2×C4C22×C22⋊D4711yescharacteristic
853C2×C4C22×D18811yescharacteristic
854C8—22no—
855C8—41no—
856C8—41no—
857C8—41no—
858C8—1881no—
859C8—1881no—
860C8—1881no—
861C8—1881no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—3764no—
872C22—1881no—
873C22—1881no—
874C22—1881no—
875C22—1881no—
876C22—1881no—
877C22—1881no—
878C22—1881no—
879C22—1881no—
880C22—1881no—
881C22C22×(C2×D47)⋊C411yescharacteristic
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—21no—
890C4—21no—
891C4—21no—
892C4—1881no—
893C4—1881no—
894C4—1881no—
895C4—1881no—
896C4—1881no—
897C4#1568988912yes—
898C4#1568992811yescharacteristic
899C4#1568993511yescharacteristic
900C2—41no—
901C2—41no—
902C2—41no—
903C2—3761no—
904C2—3761no—
905C2—3761no—
906C2#2025183211yescharacteristic
907C2#2025191511yescharacteristic
908C2#2025193611yescharacteristic
subgroupG/H
centerC2×C4C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2965C2
socleC22×C47C22×C22⋊C4
prime radical#20256804C2
cosocleC42×C47C24
hypercenter#2965D47
hypocenterC47#17505
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. #20241858C2semidirect
4. #20241854C2semidirect
5. #20241849C2semidirect
6. #20241840C2semidirect
7. #20241832C2semidirect
8. #20241828C2semidirect
9. #20241823C2semidirect
10. #20241814C2semidirect
11. #20241806C2semidirect
12. #20241802C2semidirect
13. #20241797C2semidirect
14. #20241788C2semidirect
15. C47×#2965C2semidirect
43. #15689180C22semidirect
44. #15689176C22semidirect
46. #15689147C22semidirect
47. C2×C4⋊(C47⋊C8)C22semidirect
48. #15688855C22semidirect
49. #15688855C22semidirect
50. #15688855C22semidirect
51. #15688855C22semidirect
60. #15688852C22semidirect
61. #15688852C22semidirect
62. #15688852C22semidirect
63. #15688852C22semidirect
70. C47×#431C22semidirect
71. C47×#431C22semidirect
73. C4×M16×C47C22semidirect
74. C2×C4×C8×C47C22semidirect
448. #2965D47semidirect
505. #431C2×D47semidirect
506. #431C2×D47semidirect
511. C4×M16C2×D47semidirect
512. C2×C4×C8C2×D47semidirect
529. C47#17505semidirect

Maximal subgroups

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

subgroupindex
#202568042
#202525052
#202418582
#202418542
#202418492
#202418402
#202418322
#202418282
#202418232
#202418142
#202418062
#202418022
#202417972
#202417882
C47×#29652
#1750547