Finite Group Databasebeta

← #26183195

Subgroups — #26183195

Order 12032.

958 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256952C211yesmaximal, characteristic
2#20252355C211yesmaximal, characteristic, complemented
3#20241860C211yesmaximal, characteristic, complemented
4#20241851C211yesmaximal, characteristic, complemented
5#20241846C211yesmaximal, characteristic, complemented
6#20241830C211yesmaximal, characteristic, complemented
7#20241825C211yesmaximal, characteristic, complemented
8#20241820C211yesmaximal, characteristic, complemented
9#20241808C211yesmaximal, characteristic, complemented
10#20241799C211yesmaximal, characteristic, complemented
11#20241794C211yesmaximal, characteristic, complemented
12#20241778C211yesmaximal, characteristic, complemented
13#20241773C211yesmaximal, characteristic, complemented
14#20241768C211yesmaximal, characteristic, complemented
15C47×#2925C211yesmaximal, characteristic, complemented
16#15689846C411yescharacteristic
17#15689838C411yescharacteristic
18#15689833C411yescharacteristic
19#15689823—21no—
20#15689814—21no—
21#15689813C411yescharacteristic
22#15689813C411yescharacteristic
23#15689802—21no—
24#15689802—21no—
25#15689778C411yescharacteristic
26#15689769C411yescharacteristic
27#15689769C411yescharacteristic
28#15689680C2211yescharacteristic
29#15689657C2211yescharacteristic
30#15689657C2211yescharacteristic
31#15689651—21no—
32#15689651—21no—
33#15689630—21no—
34C4×#10625350C2211yescharacteristic
35C4×#10625350C2211yescharacteristic
36C2×C4×D188C2211yescharacteristic
37#117×D47—21no—
38#15689254—21no—
39#15689201—21no—
40#15689195—21no—
41#15689195—21no—
42#15689176C2211yescharacteristic
43#15689176C2211yescharacteristic, complemented
44#15689176C2211yescharacteristic, complemented
45C4×#10625329C2211yescharacteristic
46C4×#10625329C2211yescharacteristic, complemented
47C2×C4×C47⋊C8C2211yescharacteristic, complemented
48#15688853C2211yescharacteristic, complemented
49#15688853C2211yescharacteristic, complemented
50#15688853C2211yescharacteristic, complemented
51#15688853C2211yescharacteristic, complemented
52#15688853C2211yescharacteristic, complemented
53#15688853C2211yescharacteristic, complemented
54#15688853C2211yescharacteristic, complemented
55#15688853C2211yescharacteristic, complemented
56#15688850C2211yescharacteristic
57#15688850C2211yescharacteristic
58#15688850C2211yescharacteristic
59#15688850C2211yescharacteristic
60#15688850C2211yescharacteristic
61#15688850C2211yescharacteristic
62#15688850C2211yescharacteristic
63#15688850C2211yescharacteristic
64C4×#41×C47C2211yescharacteristic
65C47×#433—21no—
66C47×#433—21no—
67C47×#432C2211yescharacteristic
68C47×#432C2211yescharacteristic, complemented
69C47×#431C2211yescharacteristic
70C47×#431C2211yescharacteristic, complemented
71C47×#423C2211yescharacteristic, complemented
72C2×C4⋊C8×C47C2211yescharacteristic, complemented
73C47×#408—21no—
74C47×#405—21no—
75C2×#10625350C2×C411yescharacteristic
76C2×#10625350C2×C411yescharacteristic
77C22×D188C2×C411yescharacteristic
78C22×C4×D47—21no—
79C2×#10625329—21no—
80C2×#10625329—21no—
81C22×C47⋊C8—21no—
82#13094024C2×C411yescharacteristic
83#13094024C2×C411yescharacteristic
84#13094019—21no—
85#13094019—21no—
86#13094018—21no—
87#13094018—21no—
88#13094017—21no—
89#13094017—21no—
90#13094016—21no—
91#13094016C2×C411yescharacteristic
92#13094016C2×C411yescharacteristic
93#13094014—21no—
94#13094014—21no—
95#13094012C2×C411yescharacteristic
96#13094012C2×C411yescharacteristic
97#13094010—21no—
98#13094010—21no—
99#13094009—21no—
100#13094009—21no—
101#13094007—21no—
102#13094007—21no—
103#13094006—21no—
104#13094006—21no—
105#13094005—21no—
106#13094005—21no—
107#13094003—21no—
108#13094003C2×C411yescharacteristic
109#13094003C2×C411yescharacteristic
110#13094003C2×C411yescharacteristic
111#13094003C2×C411yescharacteristic
112#13094002—21no—
113#13094002—21no—
114#13094000—21no—
115#13094000—21no—
116#13093998C2×C411yescharacteristic
117#13093998C2×C411yescharacteristic
118#13093997—21no—
119#13093997—21no—
120#13093995—21no—
121#13093995—21no—
122#13093992—21no—
123#13093992—21no—
124C4×Dic94—21no—
125C4×Dic94C2×C411yescharacteristic
126C4×Dic94C2×C411yescharacteristic
127C4×Dic94C2311yescharacteristic
128C4×Dic94C2311yescharacteristic
129C4×D188—21no—
130C4×D188—21no—
131C4×D188C2×C411yescharacteristic
132C4×D188C2×C411yescharacteristic
133C4×D188C2×C411yescharacteristic
134C4×D188C2×C411yescharacteristic
135C4×D188C2311yescharacteristic
136C4×D188C2311yescharacteristic
137C4×C22⋊D47—21no—
138C4×C22⋊D47—21no—
139C4×C22⋊D47—21no—
140C4×C22⋊D47—21no—
141C4×C22⋊D47—21no—
142C4×C22⋊D47—21no—
143#13093983—21no—
144#13093983C2×C411yescharacteristic
145#13093983C2×C411yescharacteristic
146#13093982—21no—
147#13093982—21no—
148#13093981—21no—
149#13093981—21no—
150#13093981—21no—
151#13093981—21no—
152#13093980—21no—
153#13093980—21no—
154C2×C4⋊Dic47C2×C411yescharacteristic
155C4⋊C4×D47—21no—
156C4⋊C4×D47—21no—
157C2×(C2×D47)⋊C4—21no—
158C22⋊C4×D47—21no—
159C22⋊C4×D47—21no—
160C42×D47—21no—
161C42×D47—21no—
162C4⋊(C47⋊C8)—21no—
163C4⋊(C47⋊C8)—21no—
164C4⋊(C47⋊C8)—21no—
165C22⋊(C47⋊C8)—21no—
166C22⋊(C47⋊C8)—21no—
167C22⋊(C47⋊C8)—21no—
168#13093935—21no—
169#13093935—21no—
170C4×C47⋊C8—21no—
171C4×C47⋊C8C2311yescharacteristic
172C4×C47⋊C8C2311yescharacteristic
173C4×C47⋊C8C2311yescharacteristic
174C4×C47⋊C8C2311yescharacteristic
175C2×#41×C47D411yescharacteristic
176C2×M16×C47—21no—
177C22×C8×C47—21no—
178C4×Q8×C47C2×C411yescharacteristic
179C4×Q8×C47D411yescharacteristic
180C4×D4×C47C2×C411yescharacteristic
181C4×D4×C47C2×C411yescharacteristic
182C4×D4×C47C2×C411yescharacteristic
183C4×D4×C47D411yescharacteristic
184C4×D4×C47D411yescharacteristic
185C4×D4×C47D411yescharacteristic
186#117×C47D411yescharacteristic
187#117×C47D411yescharacteristic
188#117×C47D411yescharacteristic
189C2×C42×C47C2311yescharacteristic
190C2×C42×C47C2311yescharacteristic
191C2×C42×C47C2311yescharacteristic
192C4⋊C8×C47—21no—
193C4⋊C8×C47—21no—
194C4⋊C8×C47C2311yescharacteristic
195C4⋊C8×C47C2311yescharacteristic
196C4⋊C8×C47C2311yescharacteristic
197C4⋊C8×C47C2311yescharacteristic
198C22⋊C8×C47—21no—
199C22⋊C8×C47—21no—
200C22⋊C8×C47—21no—
201C22⋊C8×C47—21no—
202#97×C47—21no—
203#97×C47—21no—
204C4×C8×C47—21no—
205C4×C8×C47—21no—
206C23×D47—21no—
207#41×C47—41no—
208#41×C47—41no—
209C2×Q8×C47C22⋊C411yescharacteristic
210C2×D4×C47C22⋊C411yescharacteristic
211C2×D4×C47C22⋊C411yescharacteristic
212C2×D4×C47C22⋊C411yescharacteristic
213C22×C4×C47C22×C411yescharacteristic
214C22×C4×C47C22×C411yescharacteristic
215C22×C4×C47C22×C411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2×D411yescharacteristic
221C22×C4×C47C2×D411yescharacteristic
222C2×C22⋊D47—21no—
223C2×C22⋊D47—21no—
224C2×C22⋊D47—21no—
225C2×C22⋊D47—21no—
226C22×Dic47—21no—
227#10625350—22no—
228#10625350—22no—
229#10625350—41no—
230#10625350—41no—
231C2×D188—22no—
232C2×D188—21no—
233C2×D188—41no—
234C2×D188C22×C411yescharacteristic
235C2×D188C22×C411yescharacteristic
236C2×C4×D47—21no—
237C2×C4×D47—21no—
238C2×C4×D47—21no—
239C2×C4×D47—21no—
240C2×C4×D47—21no—
241C2×C4×D47—21no—
242C2×C4×D47—21no—
243C2×C4×D47—21no—
244C2×C4×D47—42no—
245C2×C4×D47—42no—
246C2×Dic94—21no—
247C2×Dic94C22×C411yescharacteristic
248C2×Dic94C22×C411yescharacteristic
249M16×C47—42no—
250C2×C8×C47—21no—
251C2×C8×C47—21no—
252C2×C8×C47—21no—
253C2×C8×C47—21no—
254C2×C8×C47—42no—
255C4⋊C4×C47C22⋊C411yescharacteristic
256C4⋊C4×C47C22⋊C411yescharacteristic
257C4⋊C4×C47C22⋊C411yescharacteristic
258C4⋊C4×C47C22⋊C411yescharacteristic
259C4⋊C4×C47C22⋊C411yescharacteristic
260C4⋊C4×C47C22⋊C411yescharacteristic
261C22⋊C4×C47C22⋊C411yescharacteristic
262C22⋊C4×C47C22⋊C411yescharacteristic
263C22⋊C4×C47C22⋊C411yescharacteristic
264C22⋊C4×C47C22⋊C411yescharacteristic
265C22⋊C4×C47C22⋊C411yescharacteristic
266C22⋊C4×C47C22⋊C411yescharacteristic
267C42×C47C22×C411yescharacteristic
268C42×C47C22×C411yescharacteristic
269C42×C47C22×C411yescharacteristic
270C42×C47C2×D411yescharacteristic
271C42×C47C2×D411yescharacteristic
272C42×C47C2×D411yescharacteristic
273C42×C47C2×D411yescharacteristic
274C42×C47C2×D411yescharacteristic
275C42×C47C2×D411yescharacteristic
276C42×C47C2411yescharacteristic
277C22⋊Dic47—21no—
278C22⋊Dic47—21no—
279C22⋊Dic47—21no—
280C22⋊Dic47—21no—
281C22⋊Dic47—21no—
282C22⋊Dic47—21no—
283(C2×D47)⋊C4—21no—
284(C2×D47)⋊C4—21no—
285(C2×D47)⋊C4—21no—
286(C2×D47)⋊C4—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—
295C4⋊Dic47—21no—
296C4⋊Dic47—21no—
297C4⋊Dic47—21no—
298C4⋊Dic47—21no—
299C4⋊Dic47C22×C411yescharacteristic
300C4⋊Dic47C22×C411yescharacteristic
301C4⋊Dic47C22×C411yescharacteristic
302C4⋊Dic47C22×C411yescharacteristic
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—
313Dic47⋊C4—21no—
314Dic47⋊C4—21no—
315C4×Dic47—21no—
316C4×Dic47—21no—
317C4×Dic47—21no—
318C4×Dic47—21no—
319C4×Dic47—21no—
320C4×Dic47—21no—
321#10625329—42no—
322#10625329—42no—
323C2×C47⋊C8—21no—
324C2×C47⋊C8—21no—
325C2×C47⋊C8—21no—
326C2×C47⋊C8—21no—
327C2×C47⋊C8—42no—
328C23×C47C2×C22⋊C411yescharacteristic
329C23×C47C2×C22⋊C411yescharacteristic
330C23×C47C2×C22⋊C411yescharacteristic
331C22×D47—21no—
332C22×D47—21no—
333C22×D47—42no—
334C22×D47—42no—
335C22×D47—81no—
336Q8×C47—41no—
337D4×C47—41no—
338D4×C47—41no—
339D4×C47—41no—
340C2×C4×C47—21no—
341C2×C4×C47—21no—
342C2×C4×C47—21no—
343C2×C4×C47—21no—
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—21no—
351C2×C4×C47—21no—
352C2×C4×C47—41no—
353C2×C4×C47—41no—
354C2×C4×C47—41no—
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×C47C2×C22⋊C411yescharacteristic
363C2×C4×C47C2×C22⋊C411yescharacteristic
364C2×C4×C47C23×C411yescharacteristic
365C2×C4×C47C22×D411yescharacteristic
366C2×C4×C47C22×D411yescharacteristic
367C22⋊D47—42no—
368C22⋊D47—42no—
369C22⋊D47—81no—
370C22⋊D47—81no—
371C2×Dic47—21no—
372C2×Dic47—21no—
373C2×Dic47—21no—
374C2×Dic47—21no—
375C2×Dic47—21no—
376C2×Dic47—21no—
377C2×Dic47—42no—
378D188—21no—
379D188—21no—
380D188—21no—
381D188—42no—
382D188#13112yes—
383C4×D47—42no—
384C4×D47—42no—
385C4×D47—42no—
386C4×D47—42no—
387C4×D47—41no—
388C4×D47—41no—
389C4×D47—41no—
390C4×D47—41no—
391C4×D47—81no—
392C4×D47—81no—
393Dic94—21no—
394Dic94—21no—
395Dic94—21no—
396Dic94—21no—
397Dic94—81no—
398C8×C47—41no—
399C8×C47—41no—
400C8×C47—41no—
401C8×C47—41no—
402C47⋊C8—22no—
403C47⋊C8—41no—
404C47⋊C8—41no—
405C47⋊C8—41no—
406#17513—471nomaximal, Sylow
407C22×C47—21no—
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×C47C22×C22⋊C411yescharacteristic
417C2×D47—22no—
418C2×D47—41no—
419C2×D47—41no—
420C2×D47—41no—
421C2×D47—41no—
422C2×D47—41no—
423C2×D47—84no—
424C4×C47—21no—
425C4×C47—21no—
426C4×C47—21no—
427C4×C47—21no—
428C4×C47—21no—
429C4×C47—21no—
430C4×C47—21no—
431C4×C47—21no—
432C4×C47—21no—
433C4×C47—21no—
434C4×C47C2×#13111yescharacteristic
435C4×C47#56811yescharacteristic
436C4×C47#57511yescharacteristic
437C4×C47#57511yescharacteristic
438Dic47—41no—
439Dic47—41no—
440Dic47—41no—
441Dic47—41no—
442Dic47—41no—
443Dic47—41no—
444#3475—471no—
445#2965—471no—
446#2925D4711yescharacteristic, complemented
447#1497—471no—
448#1495—471no—
449#1494—471no—
450#1490—471no—
451#1489—471no—
452#1488—471no—
453#1485—471no—
454#1483—471no—
455#1482—471no—
456#1478—471no—
457#1477—471no—
458#1476—471no—
459C2×C47—41no—
460C2×C47—41no—
461C2×C47—41no—
462C2×C47#288011yescharacteristic
463C2×C47#289611yescharacteristic
464C2×C47#290111yescharacteristic
465D47—42no—
466D47—81no—
467#556—471no—
468#555—471no—
469#554—471no—
470#553—941no—
471#552—471no—
472#552—471no—
473#552—941no—
474#551—941no—
475#551—941no—
476#547—471no—
477#546—471no—
478#546—471no—
479#533—471no—
480#529—471no—
481#529—471no—
482#529—941no—
483#529—941no—
484#525—941no—
485C4×#41—471no—
486C4×#41—471no—
487C4×#41C2×D4711yescharacteristic
488C2×C4×D4—471no—
489C2×#117—941no—
490#446—941no—
491#436—941no—
492#435—941no—
493#435—941no—
494#433—21no—
495#433—21no—
496#432C2×D4711yescharacteristic
497#432C2×D4711yescharacteristic, complemented
498#431—471no—
499#431—471no—
500#431—471no—
501#431C2×D4711yescharacteristic
502#431C2×D4711yescharacteristic, complemented
503#423C2×D4711yescharacteristic, complemented
504C2×C4⋊C8C2×D4711yescharacteristic, complemented
505#408—21no—
506#405—21no—
507C4×M16—471no—
508C4×M16—471no—
509C2×C4×C8—471no—
510Q8⋊C8—471no—
511Q8⋊C8—471no—
512Q8⋊C8—471no—
513Q8⋊C8—471no—
514Q8⋊C8—471no—
515Q8⋊C8—471no—
516Q8⋊C8—471no—
517Q8⋊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—
526C47#1751311yescharacteristic, complemented, Sylow
527C2×#41—471no—
528C2×#41—471no—
529C2×#41C22⋊D4711yescharacteristic
530C22×D4—471no—
531C23×C4—941no—
532C2×M16—21no—
533C2×M16—941no—
534C2×M16—941no—
535C22×C8—21no—
536C22×C8—941no—
537C4⋊Q8—471no—
538C4⋊Q8—471no—
539#126—941no—
540#126—941no—
541#126—941no—
542#126—941no—
543#126—941no—
544#126—941no—
545#125—471no—
546#125—471no—
547#125—941no—
548#125—941no—
549#125—941no—
550#124—471no—
551#124—471no—
552#124—941no—
553#124—941no—
554#123—941no—
555#123—941no—
556#123—941no—
557#123—941no—
558#123—941no—
559#123—941no—
560#123—941no—
561#123—941no—
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—
571#121—471no—
572#121—471no—
573#121—941no—
574#121—941no—
575#121—941no—
576#121—941no—
577#120—941no—
578#120—941no—
579C4×Q8—471no—
580C4×Q8—471no—
581C4×Q8—471no—
582C4×Q8—471no—
583C4×Q8—941no—
584C4×Q8C4×D4711yescharacteristic
585C4×Q8D18811yescharacteristic
586C4×D4—471no—
587C4×D4—471no—
588C4×D4—471no—
589C4×D4—471no—
590C4×D4—471no—
591C4×D4—471no—
592C4×D4—941no—
593C4×D4—941no—
594C4×D4—941no—
595C4×D4—941no—
596C4×D4—941no—
597C4×D4—941no—
598C4×D4—941no—
599C4×D4—941no—
600C4×D4C4×D4711yescharacteristic
601C4×D4C4×D4711yescharacteristic
602C4×D4C4×D4711yescharacteristic
603C4×D4D18811yescharacteristic
604C4×D4D18811yescharacteristic
605C4×D4D18811yescharacteristic
606#117—471no—
607#117—471no—
608#117—941no—
609#117—941no—
610#117—941no—
611#117—941no—
612#117—941no—
613#117—941no—
614#117—941no—
615#117—941no—
616#117—941no—
617#117C22⋊D4711yescharacteristic
618#117C22⋊D4711yescharacteristic
619#117C22⋊D4711yescharacteristic
620C2×C4⋊C4—471no—
621C2×C4⋊C4—941no—
622C2×C4⋊C4—941no—
623C2×C22⋊C4—941no—
624C2×C22⋊C4—941no—
625C2×C22⋊C4—941no—
626C2×C42—941no—
627C2×C42—941no—
628C2×C42C22×D4711yescharacteristic
629C2×C42C22×D4711yescharacteristic
630C2×C42C22×D4711yescharacteristic
631C4⋊C8—21no—
632C4⋊C8—21no—
633C4⋊C8—941no—
634C4⋊C8—941no—
635C4⋊C8—941no—
636C4⋊C8C22×D4711yescharacteristic
637C4⋊C8C22×D4711yescharacteristic
638C4⋊C8C22×D4711yescharacteristic
639C4⋊C8C22×D4711yescharacteristic
640C22⋊C8—21no—
641C22⋊C8—21no—
642C22⋊C8—21no—
643C22⋊C8—21no—
644C22⋊C8—941no—
645C22⋊C8—941no—
646C22⋊C8—941no—
647#97—21no—
648#97—21no—
649#97—941no—
650#97—941no—
651C4×C8—21no—
652C4×C8—21no—
653C4×C8—471no—
654C4×C8—471no—
655C4×C8—471no—
656C4×C8—471no—
657C4×C8—941no—
658C24—941no—
659#41—41no—
660#41—41no—
661#41—942no—
662#41—942no—
663#41—1881no—
664#41—1881no—
665C2×Q8—471no—
666C2×Q8—471no—
667C2×Q8—941no—
668C2×Q8(C2×D47)⋊C411yescharacteristic
669C2×D4—471no—
670C2×D4—471no—
671C2×D4—942no—
672C2×D4—941no—
673C2×D4—941no—
674C2×D4—941no—
675C2×D4—941no—
676C2×D4—941no—
677C2×D4—1881no—
678C2×D4(C2×D47)⋊C411yescharacteristic
679C2×D4(C2×D47)⋊C411yescharacteristic
680C2×D4(C2×D47)⋊C411yescharacteristic
681C22×C4—941no—
682C22×C4—941no—
683C22×C4—941no—
684C22×C4—941no—
685C22×C4—941no—
686C22×C4—941no—
687C22×C4—941no—
688C22×C4—941no—
689C22×C4—941no—
690C22×C4—1882no—
691C22×C4—1882no—
692C22×C4C2×C4×D4711yescharacteristic
693C22×C4C2×C4×D4711yescharacteristic
694C22×C4C2×C4×D4711yescharacteristic
695C22×C4C2×D18811yescharacteristic
696C22×C4C2×D18811yescharacteristic
697C22×C4C2×D18811yescharacteristic
698C22×C4C2×C22⋊D4711yescharacteristic
699C22×C4C2×C22⋊D4711yescharacteristic
700C22×C4C2×C22⋊D4711yescharacteristic
701M16—42no—
702M16—1882no—
703M16—1882no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—42no—
709C2×C8—941no—
710C2×C8—941no—
711C2×C8—941no—
712C2×C8—941no—
713C2×C8—1882no—
714C4⋊C4—471no—
715C4⋊C4—471no—
716C4⋊C4—471no—
717C4⋊C4—471no—
718C4⋊C4—941no—
719C4⋊C4—941no—
720C4⋊C4—941no—
721C4⋊C4—941no—
722C4⋊C4—941no—
723C4⋊C4—941no—
724C4⋊C4—941no—
725C4⋊C4—941no—
726C4⋊C4—941no—
727C4⋊C4—941no—
728C4⋊C4—941no—
729C4⋊C4—941no—
730C4⋊C4—941no—
731C4⋊C4—941no—
732C4⋊C4—941no—
733C4⋊C4—941no—
734C4⋊C4(C2×D47)⋊C411yescharacteristic
735C4⋊C4(C2×D47)⋊C411yescharacteristic
736C4⋊C4(C2×D47)⋊C411yescharacteristic
737C4⋊C4(C2×D47)⋊C411yescharacteristic
738C4⋊C4(C2×D47)⋊C411yescharacteristic
739C4⋊C4(C2×D47)⋊C411yescharacteristic
740C22⋊C4—941no—
741C22⋊C4—941no—
742C22⋊C4—941no—
743C22⋊C4—941no—
744C22⋊C4—941no—
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(C2×D47)⋊C411yescharacteristic
759C22⋊C4(C2×D47)⋊C411yescharacteristic
760C22⋊C4(C2×D47)⋊C411yescharacteristic
761C22⋊C4(C2×D47)⋊C411yescharacteristic
762C22⋊C4(C2×D47)⋊C411yescharacteristic
763C22⋊C4(C2×D47)⋊C411yescharacteristic
764C42—941no—
765C42—941no—
766C42—941no—
767C42—941no—
768C42—941no—
769C42—941no—
770C42C2×C4×D4711yescharacteristic
771C42C2×C4×D4711yescharacteristic
772C42C2×C4×D4711yescharacteristic
773C42C2×D18811yescharacteristic
774C42C2×D18811yescharacteristic
775C42C2×D18811yescharacteristic
776C42C2×C22⋊D4711yescharacteristic
777C42C2×C22⋊D4711yescharacteristic
778C42C2×C22⋊D4711yescharacteristic
779C42C23×D4711yescharacteristic
780C23—941no—
781C23—941no—
782C23—3761no—
783C23—1882no—
784C23—1882no—
785C23C2×(C2×D47)⋊C411yescharacteristic
786C23C2×(C2×D47)⋊C411yescharacteristic
787C23C2×(C2×D47)⋊C411yescharacteristic
788Q8—41no—
789Q8—941no—
790Q8—941no—
791Q8—941no—
792Q8—941no—
793Q8—3761no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—472no—
798D4—941no—
799D4—941no—
800D4—941no—
801D4—3761no—
802D4—3761no—
803D4—1882no—
804D4—1882no—
805D4—1882no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—941no—
822C2×C4—941no—
823C2×C4—941no—
824C2×C4—941no—
825C2×C4—941no—
826C2×C4—941no—
827C2×C4—3761no—
828C2×C4—3761no—
829C2×C4—1882no—
830C2×C4—1882no—
831C2×C4—1882no—
832C2×C4—1882no—
833C2×C4—1882no—
834C2×C4—1881no—
835C2×C4—1881no—
836C2×C4—1881no—
837C2×C4—1881no—
838C2×C4C2×(C2×D47)⋊C411yescharacteristic
839C2×C4C2×(C2×D47)⋊C411yescharacteristic
840C2×C4C2×(C2×D47)⋊C411yescharacteristic
841C2×C4C2×(C2×D47)⋊C411yescharacteristic
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×C4C22×C4×D4711yescharacteristic
848C2×C4C22×C22⋊D4711yescharacteristic
849C2×C4C22×D18811yescharacteristic
850C8—41no—
851C8—41no—
852C8—41no—
853C8—41no—
854C8—942no—
855C8—1881no—
856C8—1881no—
857C8—1881no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—942no—
868C22—3764no—
869C22—1881no—
870C22—1881no—
871C22—1881no—
872C22—1881no—
873C22—1881no—
874C22C22×(C2×D47)⋊C411yescharacteristic
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—1881no—
886C4—1881no—
887C4—1881no—
888C4—1881no—
889C4—1881no—
890C4—1881no—
891C4#131×D4711yescharacteristic
892C4#1568988811yescharacteristic
893C4#1568992111yescharacteristic
894C4#1568992111yescharacteristic
895C2—41no—
896C2—41no—
897C2—41no—
898C2—3761no—
899C2—1882no—
900C2#2025183511yescharacteristic
901C2#2025190511yescharacteristic
902C2#2025193311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2925C2
socleC22×C47C22×C22⋊C4
prime radical#20256952C2
cosocleC42×C47C24
hypercenter#2925D47
hypocenterC47#17513
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2925

Complements

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

NH ≅ G/Ntype
2. #20252355C2semidirect
3. #20241860C2semidirect
4. #20241851C2semidirect
5. #20241846C2semidirect
6. #20241830C2semidirect
7. #20241825C2semidirect
8. #20241820C2semidirect
9. #20241808C2semidirect
10. #20241799C2semidirect
11. #20241794C2semidirect
12. #20241778C2semidirect
13. #20241773C2semidirect
14. #20241768C2semidirect
15. C47×#2925C2semidirect
43. #15689176C22semidirect
44. #15689176C22semidirect
46. C4×#10625329C22semidirect
47. C2×C4×C47⋊C8C22semidirect
48. #15688853C22semidirect
49. #15688853C22semidirect
50. #15688853C22semidirect
51. #15688853C22semidirect
52. #15688853C22semidirect
53. #15688853C22semidirect
54. #15688853C22semidirect
55. #15688853C22semidirect
68. C47×#432C22semidirect
70. C47×#431C22semidirect
71. C47×#423C22semidirect
72. C2×C4⋊C8×C47C22semidirect
446. #2925D47semidirect
497. #432C2×D47semidirect
502. #431C2×D47semidirect
503. #423C2×D47semidirect
504. C2×C4⋊C8C2×D47semidirect
526. C47#17513semidirect

Maximal subgroups

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

subgroupindex
#202569522
#202523552
#202418602
#202418512
#202418462
#202418302
#202418252
#202418202
#202418082
#202417992
#202417942
#202417782
#202417732
#202417682
C47×#29252
#1751347