Finite Group Databasebeta

← #26183939

Subgroups — #26183939

Order 12032.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257140C211yesmaximal, characteristic
2#20252046C211yesmaximal, characteristic, complemented
3#20241963C211yesmaximal, characteristic, complemented
4#20241951C211yesmaximal, characteristic, complemented
5#20241942C211yesmaximal, characteristic
6#20241938C211yesmaximal, characteristic, complemented
7#20241924C211yesmaximal, characteristic, complemented
8#20241920C211yesmaximal, characteristic, complemented
9#20241911C211yesmaximal, characteristic, complemented
10#20241899C211yesmaximal, characteristic, complemented
11#20241890C211yesmaximal, characteristic
12#20241886C211yesmaximal, characteristic, complemented
13#20241872C211yesmaximal, characteristic, complemented
14C2×#15688859C211yesmaximal, characteristic, complemented
15C47×#2343C211yesmaximal, characteristic, complemented
16#15689841—21no—
17#15689828—21no—
18#15689812—21no—
19#15689808—21no—
20#15689806—21no—
21#15689806—21no—
22#15689799—21no—
23#15689799—21no—
24#15689751C411yescharacteristic, complemented
25#15689744C411yescharacteristic, complemented
26#15689744C411yescharacteristic, complemented
27#15689735C411yescharacteristic, complemented
28#15689735C411yescharacteristic, complemented
29#15689699C411yescharacteristic, complemented
30#15689680C2211yescharacteristic
31#15689680C2211yescharacteristic
32#15689657C2211yescharacteristic
33#15689657C2211yescharacteristic
34#15689634C2211yescharacteristic
35C2×#13094003C2211yescharacteristic
36#15689603C411yescharacteristic, complemented
37#15689600C411yescharacteristic, complemented
38#15689184—21no—
39#15689184—21no—
40#15689180C2211yescharacteristic
41#15689180C2211yescharacteristic
42#15689176C2211yescharacteristic
43#15689176C2211yescharacteristic
44#15689150—21no—
45#15689087C2211yescharacteristic
46C2×C22⋊(C47⋊C8)C2211yescharacteristic
47#15689079—21no—
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×#117×C47C2211yescharacteristic
65C47×#387—21no—
66C47×#387—21no—
67C47×#385—21no—
68C47×#383C2211yescharacteristic
69C47×#382C2211yescharacteristic
70C47×#381C2211yescharacteristic
71C4×C4⋊C4×C47C2211yescharacteristic
72C4×C22⋊C4×C47—21no—
73C47×#376C2211yescharacteristic
74C2×#95×C47C2211yescharacteristic
75C2×#10625350C2×C411yescharacteristic
76C22×Dic94C2×C411yescharacteristic
77C2×#10625329—21no—
78C22×C47⋊C8—21no—
79#13094024C2×C411yescharacteristic, complemented
80#13094024C2×C411yescharacteristic, complemented
81#13094024C2×C411yescharacteristic, complemented
82#13094024C2×C411yescharacteristic, complemented
83#13094023—21no—
84#13094019—21no—
85#13094019—21no—
86#13094018—21no—
87#13094018—21no—
88#13094017—21no—
89#13094017—21no—
90#13094017—21no—
91#13094017—21no—
92#13094016—21no—
93#13094016—21no—
94#13094016C2×C411yescharacteristic, complemented
95#13094016C2×C411yescharacteristic, complemented
96#13094015—21no—
97#13094014—21no—
98#13094014—21no—
99#13094014—21no—
100#13094014—21no—
101#13094012C2×C411yescharacteristic, complemented
102#13094012C2×C411yescharacteristic, complemented
103#13094010—21no—
104#13094010—21no—
105#13094008—21no—
106#13094008—21no—
107#13094007—21no—
108#13094007—21no—
109#13094007—21no—
110#13094006—21no—
111#13094006—21no—
112#13094004—21no—
113#13094004—21no—
114#13094003—21no—
115#13094003—21no—
116#13094003—21no—
117#13094003—21no—
118#13094003C2×C411yescharacteristic
119#13094003C2×C411yescharacteristic
120#13094003C2×C411yescharacteristic
121#13094003C2311yescharacteristic
122#13094003C2311yescharacteristic
123#13094003C2311yescharacteristic
124#13094002—21no—
125#13094002—21no—
126#13094001—21no—
127#13094001—21no—
128#13093998C2×C411yescharacteristic
129#13093998C2311yescharacteristic
130#13093993—21no—
131C4×Dic94—21no—
132C4×Dic94—21no—
133C4×Dic94C2×C411yescharacteristic, complemented
134C4×Dic94C2×C411yescharacteristic, complemented
135C4×Dic94C2×C411yescharacteristic, complemented
136C4×Dic94C2×C411yescharacteristic, complemented
137C4×Dic94C2×C411yescharacteristic, complemented
138C4×Dic94C2×C411yescharacteristic, complemented
139#13093989—21no—
140#13093989—21no—
141C4×D188C2×C411yescharacteristic, complemented
142C4×D188C2×C411yescharacteristic, complemented
143C4×C22⋊D47—21no—
144C4×C22⋊D47—21no—
145C4×C22⋊D47—21no—
146C4×C22⋊D47—21no—
147(C22⋊D47)⋊C4—21no—
148(C22⋊D47)⋊C4—21no—
149#13093983—21no—
150#13093983—21no—
151#13093983C2×C411yescharacteristic
152#13093982—21no—
153#13093981—21no—
154#13093981—21no—
155#13093980—21no—
156#13093980—21no—
157C2×C4⋊Dic47C2×C411yescharacteristic
158C2×Dic47⋊C4—21no—
159C4⋊C4×D47—21no—
160C2×C22⋊Dic47—21no—
161C4⋊(C47⋊C8)—21no—
162C4⋊(C47⋊C8)—21no—
163C4⋊(C47⋊C8)—21no—
164C4⋊(C47⋊C8)—21no—
165C22⋊(C47⋊C8)—21no—
166C22⋊(C47⋊C8)—21no—
167C22⋊(C47⋊C8)C2311yescharacteristic
168C22⋊(C47⋊C8)C2311yescharacteristic
169C22⋊(C47⋊C8)C2311yescharacteristic
170C22⋊(C47⋊C8)C2311yescharacteristic
171#13093935—21no—
172#13093935—21no—
173C4×C47⋊C8—21no—
174C4×C47⋊C8—21no—
175C23×C4×C47—21no—
176C23×C4×C47C2311yescharacteristic
177#117×C47C2×C411yescharacteristic
178#117×C47C2×C411yescharacteristic
179#117×C47C2×C411yescharacteristic
180#117×C47C2×C411yescharacteristic
181#117×C47D411yescharacteristic
182#117×C47D411yescharacteristic
183#117×C47D411yescharacteristic
184#117×C47D411yescharacteristic
185C2×C4⋊C4×C47—21no—
186C2×C4⋊C4×C47—21no—
187C2×C4⋊C4×C47D411yescharacteristic
188C2×C4⋊C4×C47D411yescharacteristic
189C2×C22⋊C4×C47—21no—
190C2×C22⋊C4×C47D411yescharacteristic
191C2×C22⋊C4×C47D411yescharacteristic
192C2×C42×C47—21no—
193C2×C42×C47—21no—
194C2×C42×C47C2311yescharacteristic
195C2×C42×C47C2311yescharacteristic
196#95×C47—21no—
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
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—42no—
212C22×C4×C47—42no—
213C22×C4×C47—42no—
214C22×C4×C47—81no—
215C22×C4×C47C22×C411yescharacteristic
216C22×C4×C47C22×C411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2×D411yescharacteristic
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2411yescharacteristic
225C2×C22⋊D47—21no—
226C2×C22⋊D47—21no—
227C2×C22⋊D47—21no—
228C22×Dic47—21no—
229C22×Dic47—21no—
230#10625350—42no—
231C2×D188C22×C411yescharacteristic
232C2×C4×D47—21no—
233C2×C4×D47—21no—
234C2×C4×D47—21no—
235C2×Dic94—21no—
236C2×Dic94—21no—
237C2×Dic94—21no—
238C2×Dic94—42no—
239C2×Dic94C22×C411yescharacteristic
240C2×Dic94C22×C411yescharacteristic
241C2×Dic94C22×C411yescharacteristic
242C4⋊C4×C47—42no—
243C4⋊C4×C47—81no—
244C4⋊C4×C47C22⋊C411yescharacteristic
245C4⋊C4×C47C22⋊C411yescharacteristic
246C4⋊C4×C47C22⋊C411yescharacteristic
247C4⋊C4×C47C22⋊C411yescharacteristic
248C4⋊C4×C47C22⋊C411yescharacteristic
249C4⋊C4×C47C22⋊C411yescharacteristic
250C4⋊C4×C47C22⋊C411yescharacteristic
251C4⋊C4×C47C22⋊C411yescharacteristic
252C22⋊C4×C47—42no—
253C22⋊C4×C47C22⋊C411yescharacteristic
254C22⋊C4×C47C22⋊C411yescharacteristic
255C22⋊C4×C47C22⋊C411yescharacteristic
256C22⋊C4×C47C22⋊C411yescharacteristic
257C22⋊C4×C47C22⋊C411yescharacteristic
258C22⋊C4×C47C22⋊C411yescharacteristic
259C22⋊C4×C47C22⋊C411yescharacteristic
260C22⋊C4×C47C22⋊C411yescharacteristic
261C42×C47—42no—
262C42×C47—81no—
263C42×C47C22×C411yescharacteristic
264C42×C47C22×C411yescharacteristic
265C42×C47C22×C411yescharacteristic
266C42×C47C22×C411yescharacteristic
267C42×C47C2×D411yescharacteristic
268C42×C47C2×D411yescharacteristic
269C42×C47C2×D411yescharacteristic
270C42×C47C2×D411yescharacteristic
271C22⋊Dic47—21no—
272C22⋊Dic47—21no—
273C22⋊Dic47—21no—
274C22⋊Dic47—21no—
275C22⋊Dic47—21no—
276C22⋊Dic47—21no—
277C22⋊Dic47—21no—
278(C2×D47)⋊C4—21no—
279(C2×D47)⋊C4—21no—
280(C2×D47)⋊C4—21no—
281(C2×D47)⋊C4—21no—
282(C2×D47)⋊C4—21no—
283(C2×D47)⋊C4—21no—
284(C2×D47)⋊C4—21no—
285(C2×D47)⋊C4—21no—
286C4⋊Dic47—21no—
287C4⋊Dic47—21no—
288C4⋊Dic47—21no—
289C4⋊Dic47—21no—
290C4⋊Dic47—21no—
291C4⋊Dic47—21no—
292C4⋊Dic47—21no—
293C4⋊Dic47C22×C411yescharacteristic
294C4⋊Dic47C22×C411yescharacteristic
295C4⋊Dic47C22×C411yescharacteristic
296C4⋊Dic47C22×C411yescharacteristic
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—
308Dic47⋊C4—21no—
309Dic47⋊C4—21no—
310Dic47⋊C4—21no—
311Dic47⋊C4—21no—
312Dic47⋊C4—21no—
313C4×Dic47—21no—
314C4×Dic47—21no—
315C4×Dic47—21no—
316C4×Dic47—21no—
317C4×Dic47—21no—
318C4×Dic47—21no—
319C4×Dic47—21no—
320#10625329—42no—
321C2×C47⋊C8—21no—
322C2×C47⋊C8—21no—
323C2×C47⋊C8—21no—
324C2×C47⋊C8—21no—
325C2×C47⋊C8—42no—
326C23×C47—21no—
327C23×C47—21no—
328C23×C47—22no—
329C23×C47—41no—
330C23×C47C2×C22⋊C411yescharacteristic
331C23×C47C2×C22⋊C411yescharacteristic
332C23×C47C22×D411yescharacteristic
333C22×D47—21no—
334C2×C4×C47—21no—
335C2×C4×C47—21no—
336C2×C4×C47—21no—
337C2×C4×C47—21no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—41no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47—41no—
354C2×C4×C47—41no—
355C2×C4×C47—41no—
356C2×C4×C47—41no—
357C2×C4×C47—41no—
358C2×C4×C47—84no—
359C2×C4×C47C2×C22⋊C411yescharacteristic
360C2×C4×C47C2×C22⋊C411yescharacteristic
361C2×C4×C47C2×C22⋊C411yescharacteristic
362C2×C4×C47C2×C22⋊C411yescharacteristic
363C2×C4×C47C2×C22⋊C411yescharacteristic
364C2×C4×C47C2×C22⋊C411yescharacteristic
365C2×C4×C47C2×C22⋊C411yescharacteristic
366C2×C4×C47C2×C22⋊C411yescharacteristic
367C2×C4×C47C2×C22⋊C411yescharacteristic
368C2×C4×C47C2×C22⋊C411yescharacteristic
369C2×C4×C47C23×C411yescharacteristic
370C2×C4×C47C22×D411yescharacteristic
371C22⋊D47—41no—
372C22⋊D47—41no—
373C22⋊D47—42no—
374C22⋊D47—81no—
375C2×Dic47—21no—
376C2×Dic47—21no—
377C2×Dic47—21no—
378C2×Dic47—21no—
379C2×Dic47—21no—
380C2×Dic47—21no—
381C2×Dic47—21no—
382C2×Dic47—42no—
383C2×Dic47—81no—
384D188—41no—
385C4×D47—42no—
386C4×D47—81no—
387C4×D47—81no—
388Dic94—42no—
389Dic94—41no—
390Dic94—41no—
391Dic94—41no—
392Dic94—81no—
393Dic94—81no—
394C47⋊C8—41no—
395C47⋊C8—41no—
396C47⋊C8—41no—
397C47⋊C8—41no—
398#17609—471nomaximal, Sylow
399C22×C47—21no—
400C22×C47—21no—
401C22×C47—21no—
402C22×C47—21no—
403C22×C47—21no—
404C22×C47—21no—
405C22×C47—21no—
406C22×C47—42no—
407C22×C47—42no—
408C22×C47#41012yes—
409C22×C47C22×C22⋊C411yescharacteristic
410C22×C47#57711yescharacteristic
411C22×C47#57811yescharacteristic
412C2×D47—41no—
413C2×D47—41no—
414C2×D47—41no—
415C4×C47—21no—
416C4×C47—21no—
417C4×C47—21no—
418C4×C47—21no—
419C4×C47—21no—
420C4×C47—21no—
421C4×C47—21no—
422C4×C47—21no—
423C4×C47—21no—
424C4×C47—21no—
425C4×C47—21no—
426C4×C47—21no—
427C4×C47—42no—
428C4×C47—81no—
429C4×C47—81no—
430C4×C47—81no—
431Dic47—41no—
432Dic47—41no—
433Dic47—41no—
434Dic47—41no—
435Dic47—41no—
436Dic47—41no—
437Dic47—41no—
438#3495—471no—
439#2924—471no—
440#2343D4711yescharacteristic, complemented
441#1521—471no—
442#1518—471no—
443#1516—471no—
444#1515—471no—
445#1512—471no—
446#1511—471no—
447#1509—471no—
448#1506—471no—
449#1504—471no—
450#1503—471no—
451#1500—471no—
452C2×#328—471no—
453C2×C47—21no—
454C2×C47—21no—
455C2×C47—22no—
456C2×C47—41no—
457C2×C47C2×#41011yescharacteristic
458C2×C47#289811yescharacteristic
459C2×C47#290111yescharacteristic
460D47—81no—
461#556—941no—
462#554—941no—
463#552—941no—
464#552—941no—
465#552—941no—
466#552—941no—
467#551—941no—
468#551—941no—
469#544—471no—
470#542—471no—
471#542—471no—
472#541—471no—
473#541—471no—
474#536—471no—
475#533—471no—
476#533—471no—
477#529—471no—
478#529—471no—
479#525—471no—
480C2×C22⋊Q8—471no—
481#520—471no—
482#519—471no—
483C2×#117C2×D4711yescharacteristic
484#433—941no—
485#433—941no—
486#432—471no—
487#432—471no—
488#431—471no—
489#431—471no—
490#424—941no—
491#407—471no—
492C2×C22⋊C8—471no—
493#405—941no—
494#387—21no—
495#387—21no—
496#385—21no—
497#383C2×D4711yescharacteristic
498#382C2×D4711yescharacteristic
499#381C2×D4711yescharacteristic
500C4×C4⋊C4C2×D4711yescharacteristic
501C4×C22⋊C4—21no—
502#376C2×D4711yescharacteristic
503C2×#95C2×D4711yescharacteristic
504#328—471no—
505#328—471no—
506#328—471no—
507#328—471no—
508#328—471no—
509#328—471no—
510#328—471no—
511#328—471no—
512#328—471no—
513#328—471no—
514#328—471no—
515#328—471no—
516#327—471no—
517#327—471no—
518#327—471no—
519#327—471no—
520C47#1760911yescharacteristic, complemented, Sylow
521C2×#41—471no—
522C22×Q8—471no—
523C23×C4—21no—
524C23×C4C22×D4711yescharacteristic
525C2×M16—941no—
526C22×C8—941no—
527C4⋊Q8—471no—
528C4⋊Q8—471no—
529C4⋊Q8—471no—
530C4⋊Q8—471no—
531C4⋊Q8—941no—
532#126—941no—
533#126—941no—
534#126—941no—
535#126—941no—
536#126—941no—
537#126—941no—
538#126—941no—
539#126—941no—
540#125—471no—
541#125—471no—
542#125—941no—
543#125—941no—
544#125—941no—
545#125—941no—
546#125—941no—
547#125—941no—
548#125—941no—
549#124—471no—
550#124—471no—
551#124—941no—
552#124—941no—
553#123—941no—
554#123—941no—
555#123—941no—
556#123—941no—
557#123—941no—
558#123—941no—
559#123—941no—
560C22⋊Q8—471no—
561C22⋊Q8—471no—
562C22⋊Q8—471no—
563C22⋊Q8—471no—
564C22⋊Q8—471no—
565C22⋊Q8—471no—
566C22⋊Q8—941no—
567C22⋊Q8—941no—
568C22⋊Q8—941no—
569C22⋊Q8—941no—
570C22⋊Q8—941no—
571C22⋊Q8—941no—
572C22⋊Q8—941no—
573C22⋊Q8—941no—
574C22⋊Q8—941no—
575C22⋊Q8—941no—
576#121—471no—
577#121—471no—
578#120—941no—
579C4×Q8—471no—
580C4×Q8—471no—
581C4×Q8—471no—
582C4×Q8—471no—
583C4×Q8—471no—
584C4×Q8—471no—
585C4×Q8—941no—
586C4×Q8—941no—
587C4×Q8—941no—
588C4×Q8—941no—
589C4×D4—471no—
590C4×D4—471no—
591C4×D4—941no—
592C4×D4—941no—
593C4×D4—941no—
594C4×D4—941no—
595C4×D4—941no—
596C4×D4—941no—
597#117—471no—
598#117—941no—
599#117—941no—
600#117—941no—
601#117—941no—
602#117—941no—
603#117—941no—
604#117—941no—
605#117C4×D4711yescharacteristic
606#117C4×D4711yescharacteristic
607#117C4×D4711yescharacteristic
608#117C4×D4711yescharacteristic
609#117D18811yescharacteristic
610#117D18811yescharacteristic
611#117D18811yescharacteristic
612#117D18811yescharacteristic
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—471no—
616C2×C4⋊C4—941no—
617C2×C4⋊C4—941no—
618C2×C4⋊C4C22⋊D4711yescharacteristic
619C2×C4⋊C4C22⋊D4711yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—941no—
622C2×C22⋊C4C22⋊D4711yescharacteristic
623C2×C22⋊C4C22⋊D4711yescharacteristic
624C2×C42—21no—
625C2×C42—21no—
626C2×C42C22×D4711yescharacteristic
627C2×C42C22×D4711yescharacteristic
628C4⋊C8—941no—
629C4⋊C8—941no—
630C4⋊C8—941no—
631C4⋊C8—941no—
632C22⋊C8—471no—
633C22⋊C8—471no—
634C22⋊C8—471no—
635C22⋊C8—471no—
636C22⋊C8—941no—
637C22⋊C8—941no—
638#97—941no—
639#97—941no—
640C4×C8—941no—
641C4×C8—941no—
642#95—21no—
643#95—21no—
644#95—21no—
645#95—21no—
646#95—21no—
647#95—21no—
648#95C22×D4711yescharacteristic
649#95C22×D4711yescharacteristic
650#95C22×D4711yescharacteristic
651#95C22×D4711yescharacteristic
652C24C2×C22⋊D4711yescharacteristic
653#41—1882no—
654C2×Q8—471no—
655C2×Q8—471no—
656C2×Q8—471no—
657C2×Q8—941no—
658C2×Q8—941no—
659C2×Q8—941no—
660C2×Q8—1882no—
661C2×D4—471no—
662C2×D4—941no—
663C2×D4—941no—
664C2×D4—941no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—81no—
673C22×C4—941no—
674C22×C4—941no—
675C22×C4—941no—
676C22×C4—941no—
677C22×C4—941no—
678C22×C4C2×C4×D4711yescharacteristic
679C22×C4C2×C4×D4711yescharacteristic
680C22×C4C2×D18811yescharacteristic
681C22×C4C2×D18811yescharacteristic
682C22×C4C2×C22⋊D4711yescharacteristic
683C22×C4C2×C22⋊D4711yescharacteristic
684C22×C4C2×C22⋊D4711yescharacteristic
685C22×C4C2×C22⋊D4711yescharacteristic
686C22×C4C2×C22⋊D4711yescharacteristic
687C22×C4C23×D4711yescharacteristic
688M16—1882no—
689C2×C8—941no—
690C2×C8—941no—
691C2×C8—941no—
692C2×C8—941no—
693C2×C8—1882no—
694C4⋊C4—42no—
695C4⋊C4—81no—
696C4⋊C4—471no—
697C4⋊C4—471no—
698C4⋊C4—471no—
699C4⋊C4—471no—
700C4⋊C4—941no—
701C4⋊C4—941no—
702C4⋊C4—941no—
703C4⋊C4—941no—
704C4⋊C4—941no—
705C4⋊C4—941no—
706C4⋊C4—941no—
707C4⋊C4—941no—
708C4⋊C4—941no—
709C4⋊C4—941no—
710C4⋊C4—941no—
711C4⋊C4—941no—
712C4⋊C4—941no—
713C4⋊C4—941no—
714C4⋊C4—941no—
715C4⋊C4—941no—
716C4⋊C4—941no—
717C4⋊C4—941no—
718C4⋊C4—941no—
719C4⋊C4—941no—
720C4⋊C4—941no—
721C4⋊C4—941no—
722C4⋊C4—941no—
723C4⋊C4(C2×D47)⋊C411yescharacteristic
724C4⋊C4(C2×D47)⋊C411yescharacteristic
725C4⋊C4(C2×D47)⋊C411yescharacteristic
726C4⋊C4(C2×D47)⋊C411yescharacteristic
727C4⋊C4(C2×D47)⋊C411yescharacteristic
728C4⋊C4(C2×D47)⋊C411yescharacteristic
729C4⋊C4(C2×D47)⋊C411yescharacteristic
730C4⋊C4(C2×D47)⋊C411yescharacteristic
731C22⋊C4—42no—
732C22⋊C4—941no—
733C22⋊C4—941no—
734C22⋊C4—941no—
735C22⋊C4—941no—
736C22⋊C4—941no—
737C22⋊C4—941no—
738C22⋊C4—941no—
739C22⋊C4—941no—
740C22⋊C4—941no—
741C22⋊C4—941no—
742C22⋊C4—941no—
743C22⋊C4—941no—
744C22⋊C4—941no—
745C22⋊C4—941no—
746C22⋊C4—941no—
747C22⋊C4(C2×D47)⋊C411yescharacteristic
748C22⋊C4(C2×D47)⋊C411yescharacteristic
749C22⋊C4(C2×D47)⋊C411yescharacteristic
750C22⋊C4(C2×D47)⋊C411yescharacteristic
751C22⋊C4(C2×D47)⋊C411yescharacteristic
752C22⋊C4(C2×D47)⋊C411yescharacteristic
753C22⋊C4(C2×D47)⋊C411yescharacteristic
754C22⋊C4(C2×D47)⋊C411yescharacteristic
755C42—42no—
756C42—81no—
757C42—941no—
758C42—941no—
759C42—941no—
760C42—941no—
761C42—941no—
762C42—941no—
763C42—941no—
764C42C2×C4×D4711yescharacteristic
765C42C2×C4×D4711yescharacteristic
766C42C2×C4×D4711yescharacteristic
767C42C2×C4×D4711yescharacteristic
768C42C2×D18811yescharacteristic
769C42C2×D18811yescharacteristic
770C42C2×D18811yescharacteristic
771C42C2×D18811yescharacteristic
772C23—22no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—941no—
777C23C2×(C2×D47)⋊C411yescharacteristic
778C23C2×(C2×D47)⋊C411yescharacteristic
779C23C22×C22⋊D4711yescharacteristic
780Q8—3761no—
781Q8—3761no—
782Q8—1881no—
783Q8—1881no—
784Q8—1881no—
785Q8—1882no—
786D4—3761no—
787D4—1881no—
788D4—1882no—
789D4—1881no—
790D4—1881no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—84no—
816C2×C4—941no—
817C2×C4—941no—
818C2×C4—941no—
819C2×C4—941no—
820C2×C4—941no—
821C2×C4—941no—
822C2×C4—941no—
823C2×C4—3761no—
824C2×C4—3761no—
825C2×C4—3761no—
826C2×C4—1882no—
827C2×C4—1882no—
828C2×C4C2×(C2×D47)⋊C411yescharacteristic
829C2×C4C2×(C2×D47)⋊C411yescharacteristic
830C2×C4C2×(C2×D47)⋊C411yescharacteristic
831C2×C4C2×(C2×D47)⋊C411yescharacteristic
832C2×C4C2×(C2×D47)⋊C411yescharacteristic
833C2×C4C2×(C2×D47)⋊C411yescharacteristic
834C2×C4C2×(C2×D47)⋊C411yescharacteristic
835C2×C4C2×(C2×D47)⋊C411yescharacteristic
836C2×C4C2×(C2×D47)⋊C411yescharacteristic
837C2×C4C2×(C2×D47)⋊C411yescharacteristic
838C2×C4C22×C4×D4711yescharacteristic
839C2×C4C22×D18811yescharacteristic
840C8—1881no—
841C8—1881no—
842C8—1881no—
843C8—1881no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—42no—
852C22—42no—
853C22—1881no—
854C22—1881no—
855C22—1881no—
856C22#1568909612yes—
857C22C22×(C2×D47)⋊C411yescharacteristic
858C22#1568993411yescharacteristic
859C22#1568993811yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—42no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4—1881no—
877C4—1881no—
878C4—1881no—
879C4—1881no—
880C4—1881no—
881C4—1881no—
882C4—1881no—
883C2—21no—
884C2—21no—
885C2—22no—
886C2—41no—
887C2—3761no—
888C2C2×#1568909611yescharacteristic
889C2#2025191811yescharacteristic
890C2#2025193611yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2343C2
socleC22×C47C22×C22⋊C4
prime radical#15689634C22
cosocleC22×C4×C47C24
hypercenter#2343D47
hypocenterC47#17609
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2343

Complements

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

NH ≅ G/Ntype
2. #20252046C2semidirect
3. #20241963C2semidirect
4. #20241951C2semidirect
6. #20241938C2semidirect
7. #20241924C2semidirect
8. #20241920C2semidirect
9. #20241911C2semidirect
10. #20241899C2semidirect
12. #20241886C2semidirect
13. #20241872C2semidirect
14. C2×#15688859C2semidirect
15. C47×#2343C2semidirect
24. #15689751C4semidirect
25. #15689744C4semidirect
26. #15689744C4semidirect
27. #15689735C4semidirect
28. #15689735C4semidirect
29. #15689699C4semidirect
36. #15689603C4semidirect
37. #15689600C4semidirect
79. #13094024C2×C4semidirect
80. #13094024C2×C4semidirect
81. #13094024C2×C4semidirect
82. #13094024C2×C4semidirect
94. #13094016C2×C4semidirect
95. #13094016C2×C4semidirect
101. #13094012C2×C4semidirect
102. #13094012C2×C4semidirect
133. C4×Dic94C2×C4semidirect
134. C4×Dic94C2×C4semidirect
135. C4×Dic94C2×C4semidirect
136. C4×Dic94C2×C4semidirect
137. C4×Dic94C2×C4semidirect
138. C4×Dic94C2×C4semidirect
141. C4×D188C2×C4semidirect
142. C4×D188C2×C4semidirect
440. #2343D47semidirect
520. C47#17609semidirect

Maximal subgroups

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

subgroupindex
#202571402
#202520462
#202419632
#202419512
#202419422
#202419382
#202419242
#202419202
#202419112
#202418992
#202418902
#202418862
#202418722
C2×#156888592
C47×#23432
#1760947