Finite Group Databasebeta

← #26183328

Subgroups — #26183328

Order 12032.

936 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257003C211yesmaximal, characteristic
2#20252513C211yesmaximal, characteristic, complemented
3#20241862C211yesmaximal, characteristic, complemented
4#20241854C211yesmaximal, characteristic, complemented
5#20241849C211yesmaximal, characteristic, complemented
6#20241836C211yesmaximal, characteristic, complemented
7#20241823C211yesmaximal, characteristic, complemented
8#20241818C211yesmaximal, characteristic, complemented
9#20241802C211yesmaximal, characteristic, complemented
10#20241797C211yesmaximal, characteristic, complemented
11#20241792C211yesmaximal, characteristic, complemented
12#20241784C211yesmaximal, characteristic, complemented
13#20241776C211yesmaximal, characteristic, complemented
14C2×#15688855C211yesmaximal, characteristic, complemented
15C47×#2922C211yesmaximal, characteristic, complemented
16#15689851C411yescharacteristic
17#15689846C411yescharacteristic
18#15689841—21no—
19#15689813C411yescharacteristic
20#15689813C411yescharacteristic
21#15689806—21no—
22#15689806—21no—
23D4×Dic94C411yescharacteristic
24#15689782C411yescharacteristic
25#15689782C411yescharacteristic
26#15689777C411yescharacteristic
27#15689772—21no—
28#15689680C2211yescharacteristic
29#15689677—21no—
30#15689657C2211yescharacteristic
31#15689657C2211yescharacteristic
32#15689653—21no—
33#15689653—21no—
34C4×#10625350C2211yescharacteristic
35C4×#10625352—21no—
36C2×C4×Dic94C2211yescharacteristic
37C2×C4×Dic94C2211yescharacteristic
38#15689254—21no—
39#15689195—21no—
40#15689195—21no—
41D4×C47⋊C8—21no—
42#15689180C2211yescharacteristic
43#15689180C2211yescharacteristic
44#15689176C2211yescharacteristic
45#15689147C2211yescharacteristic
46C2×C4⋊(C47⋊C8)C2211yescharacteristic
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×#433—21no—
66C47×#433—21no—
67C47×#431C2211yescharacteristic
68C47×#431C2211yescharacteristic
69C47×#431C2211yescharacteristic
70C47×#431C2211yescharacteristic
71C47×#424—21no—
72C47×#408—21no—
73C4×M16×C47C2211yescharacteristic
74C2×C4×C8×C47C2211yescharacteristic
75C2×#10625350C2×C411yescharacteristic
76C2×#10625352—21no—
77C22×Dic94C2×C411yescharacteristic
78C22×Dic94C2×C411yescharacteristic
79C2×#10625329—21no—
80C22×C47⋊C8—21no—
81C22×C47⋊C8—21no—
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#13094016—21no—
93#13094016C2×C411yescharacteristic
94#13094016C2×C411yescharacteristic
95#13094014—21no—
96#13094014—21no—
97#13094014—21no—
98#13094014—21no—
99#13094012C2×C411yescharacteristic
100#13094012C2×C411yescharacteristic
101#13094010—21no—
102#13094010—21no—
103#13094008—21no—
104#13094008—21no—
105#13094007—21no—
106#13094007—21no—
107#13094005—21no—
108#13094005—21no—
109#13094004—21no—
110#13094003—21no—
111#13094003C2×C411yescharacteristic
112#13094003C2×C411yescharacteristic
113#13094003C2×C411yescharacteristic
114#13094003C2×C411yescharacteristic
115#13094002—21no—
116#13094002—21no—
117#13094001—21no—
118#13094001—21no—
119#13094000—21no—
120#13093998C2×C411yescharacteristic
121#13093998C2×C411yescharacteristic
122#13093996—21no—
123#13093996—21no—
124C4×Dic94—21no—
125C4×Dic94—21no—
126C4×Dic94—21no—
127C4×Dic94—21no—
128C4×Dic94—21no—
129C4×Dic94C2×C411yescharacteristic
130C4×Dic94C2×C411yescharacteristic
131C4×Dic94C2×C411yescharacteristic
132C4×Dic94C2×C411yescharacteristic
133C4×Dic94C2×C411yescharacteristic
134C4×Dic94C2311yescharacteristic
135C4×Dic94C2311yescharacteristic
136C4×Dic94C2311yescharacteristic
137#13093989—21no—
138C4×D188C2×C411yescharacteristic
139C4×D188C2311yescharacteristic
140D4×Dic47—21no—
141C4×C22⋊D47—21no—
142C4×C22⋊D47—21no—
143C4×C22⋊D47—21no—
144C4×C22⋊D47—21no—
145(C22⋊D47)⋊C4—21no—
146(C22⋊D47)⋊C4—21no—
147#13093983—21no—
148#13093983C2×C411yescharacteristic
149#13093982—21no—
150#13093981—21no—
151#13093981—21no—
152#13093981—21no—
153#13093980—21no—
154#13093980—21no—
155C2×C4⋊Dic47C2×C411yescharacteristic
156C2×C4⋊Dic47C2×C411yescharacteristic
157C2×Dic47⋊C4—21no—
158C2×Dic47⋊C4—21no—
159C2×C4×Dic47—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×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×C47—21no—
195C4⋊C8×C47—21no—
196C22⋊C8×C47—21no—
197C22⋊C8×C47—21no—
198C22⋊C8×C47—21no—
199C22⋊C8×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—
225C22×Dic47—21no—
226C22×Dic47—21no—
227#10625352—44no—
228#10625350—22no—
229#10625350—41no—
230C2×D188C22×C411yescharacteristic
231C2×C4×D47—21no—
232C2×C4×D47—21no—
233C2×C4×D47—21no—
234C2×Dic94—22no—
235C2×Dic94—22no—
236C2×Dic94—21no—
237C2×Dic94—21no—
238C2×Dic94—21no—
239C2×Dic94—41no—
240C2×Dic94—41no—
241C2×Dic94C22×C411yescharacteristic
242C2×Dic94C22×C411yescharacteristic
243C2×Dic94C22×C411yescharacteristic
244M16×C47—42no—
245C2×C8×C47—21no—
246C2×C8×C47—21no—
247C2×C8×C47—21no—
248C2×C8×C47—21no—
249C2×C8×C47—42no—
250C4⋊C4×C47C22⋊C411yescharacteristic
251C4⋊C4×C47C22⋊C411yescharacteristic
252C4⋊C4×C47C22⋊C411yescharacteristic
253C4⋊C4×C47C22⋊C411yescharacteristic
254C4⋊C4×C47C22⋊C411yescharacteristic
255C4⋊C4×C47C22⋊C411yescharacteristic
256C22⋊C4×C47C22⋊C411yescharacteristic
257C22⋊C4×C47C22⋊C411yescharacteristic
258C22⋊C4×C47C22⋊C411yescharacteristic
259C22⋊C4×C47C22⋊C411yescharacteristic
260C22⋊C4×C47C22⋊C411yescharacteristic
261C22⋊C4×C47C22⋊C411yescharacteristic
262C42×C47C22×C411yescharacteristic
263C42×C47C22×C411yescharacteristic
264C42×C47C22×C411yescharacteristic
265C42×C47C2×D411yescharacteristic
266C42×C47C2×D411yescharacteristic
267C42×C47C2×D411yescharacteristic
268C42×C47C2×D411yescharacteristic
269C42×C47C2×D411yescharacteristic
270C42×C47C2×D411yescharacteristic
271C42×C47C2411yescharacteristic
272C22⋊Dic47—21no—
273C22⋊Dic47—21no—
274C22⋊Dic47—21no—
275C22⋊Dic47—21no—
276C22⋊Dic47—21no—
277(C2×D47)⋊C4—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—
285C4⋊Dic47—21no—
286C4⋊Dic47—21no—
287C4⋊Dic47—21no—
288C4⋊Dic47—21no—
289C4⋊Dic47—21no—
290C4⋊Dic47C22×C411yescharacteristic
291C4⋊Dic47C22×C411yescharacteristic
292C4⋊Dic47C22×C411yescharacteristic
293C4⋊Dic47C22×C411yescharacteristic
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—
308Dic47⋊C4—21no—
309Dic47⋊C4—21no—
310C4×Dic47—21no—
311C4×Dic47—21no—
312C4×Dic47—21no—
313C4×Dic47—21no—
314C4×Dic47—21no—
315C4×Dic47—21no—
316C4×Dic47—21no—
317C4×Dic47—21no—
318C4×Dic47—21no—
319#10625329—81no—
320C2×C47⋊C8—21no—
321C2×C47⋊C8—21no—
322C2×C47⋊C8—21no—
323C2×C47⋊C8—21no—
324C2×C47⋊C8—81no—
325C2×C47⋊C8—81no—
326C23×C47C2×C22⋊C411yescharacteristic
327C23×C47C2×C22⋊C411yescharacteristic
328C23×C47C2×C22⋊C411yescharacteristic
329C22×D47—21no—
330Q8×C47—41no—
331D4×C47—22no—
332D4×C47—22no—
333D4×C47—41no—
334C2×C4×C47—22no—
335C2×C4×C47—21no—
336C2×C4×C47—21no—
337C2×C4×C47—21no—
338C2×C4×C47—21no—
339C2×C4×C47—21no—
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—41no—
348C2×C4×C47—41no—
349C2×C4×C47C2×C22⋊C411yescharacteristic
350C2×C4×C47C2×C22⋊C411yescharacteristic
351C2×C4×C47C2×C22⋊C411yescharacteristic
352C2×C4×C47C2×C22⋊C411yescharacteristic
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×C47C23×C411yescharacteristic
359C2×C4×C47C22×D411yescharacteristic
360C2×C4×C47C22×D411yescharacteristic
361C22⋊D47—42no—
362C22⋊D47—42no—
363C22⋊D47—42no—
364C2×Dic47—21no—
365C2×Dic47—21no—
366C2×Dic47—21no—
367C2×Dic47—21no—
368C2×Dic47—21no—
369C2×Dic47—21no—
370C2×Dic47—21no—
371C2×Dic47—42no—
372C2×Dic47—42no—
373C2×Dic47—42no—
374C2×Dic47—42no—
375D188—21no—
376D188—21no—
377C4×D47—42no—
378C4×D47—42no—
379C4×D47—41no—
380C4×D47—41no—
381Dic94—21no—
382Dic94—21no—
383Dic94—21no—
384Dic94—21no—
385Dic94—21no—
386Dic94—42no—
387Dic94—42no—
388Dic94—42no—
389Dic94#13112yes—
390C8×C47—41no—
391C8×C47—41no—
392C8×C47—41no—
393C8×C47—41no—
394C47⋊C8—41no—
395C47⋊C8—41no—
396C47⋊C8—41no—
397C47⋊C8—41no—
398#17524—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—21no—
407C22×C47#42112yes—
408C22×C47C22×C22⋊C411yescharacteristic
409C2×D47—41no—
410C2×D47—41no—
411C2×D47—41no—
412C4×C47—21no—
413C4×C47—21no—
414C4×C47—21no—
415C4×C47—21no—
416C4×C47—21no—
417C4×C47—21no—
418C4×C47—21no—
419C4×C47—21no—
420C4×C47—21no—
421C4×C47—21no—
422C4×C47C2×#13111yescharacteristic
423C4×C47#56811yescharacteristic
424C4×C47#57711yescharacteristic
425C4×C47#57811yescharacteristic
426Dic47—22no—
427Dic47—41no—
428Dic47—41no—
429Dic47—41no—
430Dic47—41no—
431Dic47—41no—
432Dic47—41no—
433#3482—471no—
434#2990—471no—
435#2922D4711yescharacteristic, complemented
436#1497—471no—
437#1495—471no—
438#1494—471no—
439#1491—471no—
440#1488—471no—
441#1487—471no—
442#1483—471no—
443#1482—471no—
444#1481—471no—
445#1479—471no—
446#1477—471no—
447C2×Q8⋊C8—471no—
448C2×C47—22no—
449C2×C47—41no—
450C2×C47—41no—
451C2×C47#288011yescharacteristic
452C2×C47#289811yescharacteristic
453C2×C47C2×#42111yescharacteristic
454D47—81no—
455#557—471no—
456#556—471no—
457#556—941no—
458#552—471no—
459#552—471no—
460#552—941no—
461#552—941no—
462D4×Q8—471no—
463#548—471no—
464#548—471no—
465#547—471no—
466#547—941no—
467#533—471no—
468#533—941no—
469#529—471no—
470#529—471no—
471#529—941no—
472#529—941no—
473C4×#41—471no—
474C4×#41—941no—
475C4×#41C2×D4711yescharacteristic
476C2×C4×Q8—471no—
477C2×C4×Q8—471no—
478#446—941no—
479#435—941no—
480#435—941no—
481C8×D4—941no—
482#433—21no—
483#433—21no—
484#432—471no—
485#432—471no—
486#431—471no—
487#431C2×D4711yescharacteristic
488#431C2×D4711yescharacteristic
489#431C2×D4711yescharacteristic
490#431C2×D4711yescharacteristic
491#424—21no—
492#423—471no—
493C2×C4⋊C8—471no—
494C2×C4⋊C8—471no—
495#408—21no—
496C4×M16C2×D4711yescharacteristic
497C2×C4×C8C2×D4711yescharacteristic
498Q8⋊C8—471no—
499Q8⋊C8—471no—
500Q8⋊C8—471no—
501Q8⋊C8—471no—
502Q8⋊C8—471no—
503Q8⋊C8—471no—
504Q8⋊C8—471no—
505Q8⋊C8—471no—
506Q8⋊C8—471no—
507Q8⋊C8—471no—
508Q8⋊C8—471no—
509Q8⋊C8—471no—
510D4⋊C8—471no—
511D4⋊C8—471no—
512D4⋊C8—471no—
513D4⋊C8—471no—
514C47#1752411yescharacteristic, complemented, Sylow
515C2×#41—471no—
516C2×#41—941no—
517C2×#41C22⋊D4711yescharacteristic
518C22×Q8—471no—
519C22×Q8—471no—
520C2×M16—21no—
521C2×M16—941no—
522C22×C8—21no—
523C22×C8—941no—
524C22×C8—941no—
525C4⋊Q8—471no—
526C4⋊Q8—471no—
527C4⋊Q8—941no—
528C4⋊Q8—941no—
529#126—941no—
530#126—941no—
531#126—941no—
532#126—941no—
533#126—941no—
534#126—941no—
535#125—471no—
536#125—471no—
537#125—941no—
538#125—941no—
539#125—941no—
540#125—941no—
541#125—941no—
542#124—471no—
543#124—471no—
544#124—941no—
545#124—941no—
546#123—941no—
547#123—941no—
548#123—941no—
549#123—941no—
550#123—941no—
551#123—941no—
552C22⋊Q8—471no—
553C22⋊Q8—471no—
554C22⋊Q8—471no—
555C22⋊Q8—471no—
556C22⋊Q8—941no—
557C22⋊Q8—941no—
558C22⋊Q8—941no—
559C22⋊Q8—941no—
560C22⋊Q8—941no—
561C22⋊Q8—941no—
562C22⋊Q8—941no—
563#121—471no—
564#121—471no—
565#121—941no—
566#121—941no—
567C4×Q8—471no—
568C4×Q8—471no—
569C4×Q8—471no—
570C4×Q8—471no—
571C4×Q8—471no—
572C4×Q8—471no—
573C4×Q8—471no—
574C4×Q8—471no—
575C4×Q8—941no—
576C4×Q8—941no—
577C4×Q8—941no—
578C4×Q8—941no—
579C4×Q8—941no—
580C4×Q8—941no—
581C4×Q8C4×D4711yescharacteristic
582C4×Q8D18811yescharacteristic
583C4×D4—471no—
584C4×D4—471no—
585C4×D4—941no—
586C4×D4—941no—
587C4×D4—941no—
588C4×D4—941no—
589C4×D4—941no—
590C4×D4—941no—
591C4×D4—941no—
592C4×D4C4×D4711yescharacteristic
593C4×D4C4×D4711yescharacteristic
594C4×D4C4×D4711yescharacteristic
595C4×D4D18811yescharacteristic
596C4×D4D18811yescharacteristic
597C4×D4D18811yescharacteristic
598#117—471no—
599#117—941no—
600#117—941no—
601#117—941no—
602#117—941no—
603#117—941no—
604#117—941no—
605#117—941no—
606#117C22⋊D4711yescharacteristic
607#117C22⋊D4711yescharacteristic
608#117C22⋊D4711yescharacteristic
609C2×C4⋊C4—471no—
610C2×C4⋊C4—471no—
611C2×C4⋊C4—941no—
612C2×C4⋊C4—941no—
613C2×C42—941no—
614C2×C42—941no—
615C2×C42—941no—
616C2×C42C22×D4711yescharacteristic
617C2×C42C22×D4711yescharacteristic
618C2×C42C22×D4711yescharacteristic
619C4⋊C8—21no—
620C4⋊C8—21no—
621C4⋊C8—21no—
622C4⋊C8—21no—
623C4⋊C8—471no—
624C4⋊C8—471no—
625C4⋊C8—471no—
626C4⋊C8—471no—
627C4⋊C8—941no—
628C4⋊C8—941no—
629C4⋊C8—941no—
630C22⋊C8—21no—
631C22⋊C8—21no—
632C22⋊C8—21no—
633C22⋊C8—21no—
634C22⋊C8—941no—
635C22⋊C8—941no—
636C22⋊C8—941no—
637#97—21no—
638#97—941no—
639#97—941no—
640C4×C8—21no—
641C4×C8—941no—
642C4×C8C22×D4711yescharacteristic
643C4×C8C22×D4711yescharacteristic
644C4×C8C22×D4711yescharacteristic
645C4×C8C22×D4711yescharacteristic
646#41—42no—
647#41—942no—
648#41—1881no—
649#41—1884no—
650C2×Q8—471no—
651C2×Q8—471no—
652C2×Q8—471no—
653C2×Q8—942no—
654C2×Q8—942no—
655C2×Q8—941no—
656C2×Q8—941no—
657C2×Q8—941no—
658C2×Q8—1881no—
659C2×Q8—1881no—
660C2×Q8(C2×D47)⋊C411yescharacteristic
661C2×D4—471no—
662C2×D4—941no—
663C2×D4—941no—
664C2×D4—941no—
665C2×D4(C2×D47)⋊C411yescharacteristic
666C2×D4(C2×D47)⋊C411yescharacteristic
667C2×D4(C2×D47)⋊C411yescharacteristic
668C22×C4—941no—
669C22×C4—941no—
670C22×C4—941no—
671C22×C4—941no—
672C22×C4—941no—
673C22×C4—941no—
674C22×C4—941no—
675C22×C4C2×C4×D4711yescharacteristic
676C22×C4C2×C4×D4711yescharacteristic
677C22×C4C2×C4×D4711yescharacteristic
678C22×C4C2×D18811yescharacteristic
679C22×C4C2×D18811yescharacteristic
680C22×C4C2×D18811yescharacteristic
681C22×C4C2×C22⋊D4711yescharacteristic
682C22×C4C2×C22⋊D4711yescharacteristic
683C22×C4C2×C22⋊D4711yescharacteristic
684M16—42no—
685M16—3761no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—42no—
691C2×C8—941no—
692C2×C8—941no—
693C2×C8—941no—
694C2×C8—941no—
695C2×C8—3761no—
696C2×C8—3761no—
697C4⋊C4—471no—
698C4⋊C4—471no—
699C4⋊C4—471no—
700C4⋊C4—471no—
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(C2×D47)⋊C411yescharacteristic
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
728C22⋊C4—941no—
729C22⋊C4—941no—
730C22⋊C4—941no—
731C22⋊C4—941no—
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(C2×D47)⋊C411yescharacteristic
742C22⋊C4(C2×D47)⋊C411yescharacteristic
743C22⋊C4(C2×D47)⋊C411yescharacteristic
744C22⋊C4(C2×D47)⋊C411yescharacteristic
745C22⋊C4(C2×D47)⋊C411yescharacteristic
746C22⋊C4(C2×D47)⋊C411yescharacteristic
747C42—941no—
748C42—941no—
749C42—941no—
750C42—941no—
751C42—941no—
752C42—941no—
753C42—941no—
754C42—941no—
755C42—941no—
756C42C2×C4×D4711yescharacteristic
757C42C2×C4×D4711yescharacteristic
758C42C2×C4×D4711yescharacteristic
759C42C2×D18811yescharacteristic
760C42C2×D18811yescharacteristic
761C42C2×D18811yescharacteristic
762C42C2×C22⋊D4711yescharacteristic
763C42C2×C22⋊D4711yescharacteristic
764C42C2×C22⋊D4711yescharacteristic
765C42C23×D4711yescharacteristic
766C23—941no—
767C23C2×(C2×D47)⋊C411yescharacteristic
768C23C2×(C2×D47)⋊C411yescharacteristic
769C23C2×(C2×D47)⋊C411yescharacteristic
770Q8—41no—
771Q8—472no—
772Q8—941no—
773Q8—941no—
774Q8—941no—
775Q8—941no—
776Q8—941no—
777Q8—1882no—
778Q8—1882no—
779Q8—1882no—
780D4—22no—
781D4—22no—
782D4—41no—
783D4—941no—
784D4—941no—
785D4—1882no—
786D4—1882no—
787D4—1882no—
788C2×C4—22no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—941no—
804C2×C4—941no—
805C2×C4—941no—
806C2×C4—941no—
807C2×C4—941no—
808C2×C4—941no—
809C2×C4—941no—
810C2×C4—1882no—
811C2×C4—1882no—
812C2×C4—1882no—
813C2×C4—1882no—
814C2×C4—1882no—
815C2×C4—1882no—
816C2×C4—1881no—
817C2×C4—1881no—
818C2×C4C2×(C2×D47)⋊C411yescharacteristic
819C2×C4C2×(C2×D47)⋊C411yescharacteristic
820C2×C4C2×(C2×D47)⋊C411yescharacteristic
821C2×C4C2×(C2×D47)⋊C411yescharacteristic
822C2×C4C2×(C2×D47)⋊C411yescharacteristic
823C2×C4C2×(C2×D47)⋊C411yescharacteristic
824C2×C4C2×(C2×D47)⋊C411yescharacteristic
825C2×C4C2×(C2×D47)⋊C411yescharacteristic
826C2×C4C2×(C2×D47)⋊C411yescharacteristic
827C2×C4C22×C4×D4711yescharacteristic
828C2×C4C22×C22⋊D4711yescharacteristic
829C2×C4C22×D18811yescharacteristic
830C8—41no—
831C8—41no—
832C8—41no—
833C8—41no—
834C8—1881no—
835C8—1881no—
836C8—1881no—
837C8—1881no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—1881no—
847C22—1881no—
848C22—1881no—
849C22#1568914112yes—
850C22C22×(C2×D47)⋊C411yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—942no—
862C4—1881no—
863C4—1881no—
864C4—1881no—
865C4—1881no—
866C4—1881no—
867C4—1881no—
868C4#131×D4711yescharacteristic
869C4#1568988811yescharacteristic
870C4#1568993511yescharacteristic
871C4#1568994011yescharacteristic
872C2—22no—
873C2—41no—
874C2—41no—
875C2—3761no—
876C2#2025183511yescharacteristic
877C2#2025192211yescharacteristic
878C2C2×#1568914111yescharacteristic
subgroupG/H
centerC2×C4C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2922C2
socleC22×C47C22×C22⋊C4
prime radical#20257003C2
cosocleC42×C47C24
hypercenter#2922D47
hypocenterC47#17524
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2922

Complements

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

NH ≅ G/Ntype
2. #20252513C2semidirect
3. #20241862C2semidirect
4. #20241854C2semidirect
5. #20241849C2semidirect
6. #20241836C2semidirect
7. #20241823C2semidirect
8. #20241818C2semidirect
9. #20241802C2semidirect
10. #20241797C2semidirect
11. #20241792C2semidirect
12. #20241784C2semidirect
13. #20241776C2semidirect
14. C2×#15688855C2semidirect
15. C47×#2922C2semidirect
435. #2922D47semidirect
514. C47#17524semidirect

Maximal subgroups

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

subgroupindex
#202570032
#202525132
#202418622
#202418542
#202418492
#202418362
#202418232
#202418182
#202418022
#202417972
#202417922
#202417842
#202417762
C2×#156888552
C47×#29222
#1752447