Finite Group Databasebeta

← #26183892

Subgroups — #26183892

Order 12032.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257123C211yesmaximal, characteristic
2#20246248C211yesmaximal, characteristic, complemented
3#20241966C211yesmaximal, characteristic, complemented
4#20241949C211yesmaximal, characteristic, complemented
5#20241945C211yesmaximal, characteristic, complemented
6#20241936C211yesmaximal, characteristic, complemented
7#20241927C211yesmaximal, characteristic, complemented
8#20241918C211yesmaximal, characteristic, complemented
9#20241914C211yesmaximal, characteristic, complemented
10#20241897C211yesmaximal, characteristic, complemented
11#20241893C211yesmaximal, characteristic, complemented
12#20241884C211yesmaximal, characteristic, complemented
13#20241875C211yesmaximal, characteristic, complemented
14C2×#15688858C211yesmaximal, characteristic, complemented
15C47×#2924C211yesmaximal, characteristic, complemented
16#15689836—21no—
17#15689821—21no—
18#15689817—21no—
19#15689797—21no—
20#15689797—21no—
21#15689774—21no—
22#15689763—21no—
23#15689763—21no—
24#15689751C411yescharacteristic, complemented
25#15689744C411yescharacteristic, complemented
26#15689744C411yescharacteristic, complemented
27#15689728C411yescharacteristic, complemented
28#15689728C411yescharacteristic, complemented
29#15689692C411yescharacteristic, complemented
30#15689673C2211yescharacteristic
31#15689673C2211yescharacteristic
32#15689657C2211yescharacteristic
33#15689657C2211yescharacteristic
34#15689634C2211yescharacteristic
35C2×#13093998C2211yescharacteristic
36#15689603C411yescharacteristic, complemented
37#15689597C411yescharacteristic, complemented
38#15689009—21no—
39#15689009—21no—
40#15688998—21no—
41#15688991C2211yescharacteristic, complemented
42#15688989C2211yescharacteristic, complemented
43#15688986C2211yescharacteristic
44C4×C4⋊Dic47C2211yescharacteristic, complemented
45C22⋊C4×Dic47—21no—
46#15688969C2211yescharacteristic, complemented
47C2×C47⋊#95C2211yescharacteristic
48#15688861C2211yescharacteristic, complemented
49#15688861C2211yescharacteristic, complemented
50#15688861C2211yescharacteristic, complemented
51#15688861C2211yescharacteristic, complemented
52#15688858C2211yescharacteristic
53#15688858C2211yescharacteristic
54#15688858C2211yescharacteristic
55#15688858C2211yescharacteristic
56#15688858C2211yescharacteristic
57#15688858C2211yescharacteristic
58#15688858C2211yescharacteristic
59#15688858C2211yescharacteristic
60#15688858C2211yescharacteristic, complemented
61#15688858C2211yescharacteristic, complemented
62#15688858C2211yescharacteristic, complemented
63#15688858C2211yescharacteristic, complemented
64C2×#117×C47C2211yescharacteristic
65C47×#433—21no—
66C47×#433—21no—
67C47×#432C2211yescharacteristic, complemented
68C47×#432C2211yescharacteristic, complemented
69C47×#431C2211yescharacteristic, complemented
70C47×#431C2211yescharacteristic, complemented
71C47×#424—21no—
72C47×#407C2211yescharacteristic
73C2×C22⋊C8×C47C2211yescharacteristic
74C47×#405—21no—
75C2×#10625350—21no—
76C2×#10625350—21no—
77C2×#10625350C2×C411yescharacteristic
78C22×D188C2×C411yescharacteristic
79C22×C22⋊D47—21no—
80C23×Dic47—21no—
81#13094024C2×C411yescharacteristic, complemented
82#13094024C2×C411yescharacteristic, complemented
83#13094023—21no—
84#13094021C2×C411yescharacteristic, complemented
85#13094021C2×C411yescharacteristic, complemented
86#13094019—21no—
87#13094019—21no—
88#13094018—21no—
89#13094018—21no—
90#13094016C2×C411yescharacteristic, complemented
91#13094016C2×C411yescharacteristic, complemented
92#13094015—21no—
93#13094012—21no—
94#13094012—21no—
95#13094012C2×C411yescharacteristic, complemented
96#13094012C2×C411yescharacteristic, complemented
97#13094010—21no—
98#13094010—21no—
99#13094009—21no—
100#13094009—21no—
101#13094009—21no—
102#13094009—21no—
103#13094007—21no—
104#13094007—21no—
105#13094007—21no—
106#13094006—21no—
107#13094006—21no—
108#13094003C2×C411yescharacteristic
109#13094003C2311yescharacteristic
110#13094002—21no—
111#13094002—21no—
112#13094001—21no—
113#13094001—21no—
114#13093999—21no—
115#13093999—21no—
116#13093998—21no—
117#13093998—21no—
118#13093998—21no—
119#13093998—21no—
120#13093998C2×C411yescharacteristic
121#13093998C2×C411yescharacteristic
122#13093998C2×C411yescharacteristic
123#13093998C2311yescharacteristic
124#13093998C2311yescharacteristic
125#13093998C2311yescharacteristic
126#13093997—21no—
127#13093997—21no—
128#13093997—21no—
129#13093997—21no—
130#13093994—21no—
131#13093994—21no—
132#13093993—21no—
133C4×Dic94C2×C411yescharacteristic, complemented
134C4×Dic94C2×C411yescharacteristic, complemented
135C4×D188—21no—
136C4×D188—21no—
137C4×D188C2×C411yescharacteristic, complemented
138C4×D188C2×C411yescharacteristic, complemented
139C4×D188C2×C411yescharacteristic, complemented
140C4×D188C2×C411yescharacteristic, complemented
141C4×D188C2×C411yescharacteristic, complemented
142C4×D188C2×C411yescharacteristic, complemented
143#13093986—21no—
144#13093986—21no—
145C4×C22⋊D47—21no—
146C4×C22⋊D47—21no—
147C4×C22⋊D47—21no—
148C4×C22⋊D47—21no—
149(C22⋊D47)⋊C4—21no—
150(C22⋊D47)⋊C4—21no—
151#13093983C2×C411yescharacteristic
152#13093982—21no—
153#13093981—21no—
154#13093981—21no—
155C2×C4⋊Dic47—21no—
156C2×C4⋊Dic47—21no—
157C2×C4⋊Dic47C2×C411yescharacteristic
158C4⋊C4×D47—21no—
159C2×C22⋊Dic47—21no—
160C2×(C2×D47)⋊C4—21no—
161C22⋊C4×D47—21no—
162C22⋊C4×D47—21no—
163C2×C4×Dic47—21no—
164C2×C4×Dic47—21no—
165C47⋊#95—21no—
166C47⋊#95—21no—
167C47⋊#95—21no—
168C47⋊#95—21no—
169C47⋊#95—21no—
170C47⋊#95—21no—
171C47⋊#95C2311yescharacteristic
172C47⋊#95C2311yescharacteristic
173C47⋊#95C2311yescharacteristic
174C47⋊#95C2311yescharacteristic
175C23×C4×C47C2311yescharacteristic
176C2×M16×C47—21no—
177C22×C8×C47—21no—
178#117×C47C2×C411yescharacteristic
179#117×C47C2×C411yescharacteristic
180#117×C47C2×C411yescharacteristic
181#117×C47C2×C411yescharacteristic
182#117×C47D411yescharacteristic
183#117×C47D411yescharacteristic
184#117×C47D411yescharacteristic
185#117×C47D411yescharacteristic
186C2×C4⋊C4×C47D411yescharacteristic
187C2×C4⋊C4×C47D411yescharacteristic
188C2×C22⋊C4×C47D411yescharacteristic
189C2×C22⋊C4×C47D411yescharacteristic
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×C47C2311yescharacteristic
199C22⋊C8×C47C2311yescharacteristic
200C22⋊C8×C47C2311yescharacteristic
201C22⋊C8×C47C2311yescharacteristic
202#97×C47—21no—
203#97×C47—21no—
204C4×C8×C47—21no—
205C4×C8×C47—21no—
206C24×C47C2×D411yescharacteristic
207C23×D47—21no—
208C22×C4×C47—42no—
209C22×C4×C47C22×C411yescharacteristic
210C22×C4×C47C22×C411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2411yescharacteristic
219C2×C22⋊D47—21no—
220C2×C22⋊D47—21no—
221C2×C22⋊D47—21no—
222C2×C22⋊D47—21no—
223C2×C22⋊D47—21no—
224C2×C22⋊D47—21no—
225C2×C22⋊D47—21no—
226C2×C22⋊D47—81no—
227C2×C22⋊D47—81no—
228C22×Dic47—21no—
229C22×Dic47—21no—
230C22×Dic47—21no—
231C22×Dic47—21no—
232C22×Dic47—21no—
233C22×Dic47—42no—
234C22×Dic47—42no—
235C22×Dic47—81no—
236#10625350—42no—
237#10625350—81no—
238#10625350—81no—
239#10625350—81no—
240#10625350—81no—
241C2×D188—21no—
242C2×D188—21no—
243C2×D188—21no—
244C2×D188—21no—
245C2×D188—21no—
246C2×D188—42no—
247C2×D188C22×C411yescharacteristic
248C2×D188C22×C411yescharacteristic
249C2×D188C22×C411yescharacteristic
250C2×C4×D47—21no—
251C2×C4×D47—21no—
252C2×C4×D47—21no—
253C2×C4×D47—21no—
254C2×C4×D47—21no—
255C2×C4×D47—21no—
256C2×C4×D47—21no—
257C2×Dic94—21no—
258C2×Dic94—21no—
259C2×Dic94C22×C411yescharacteristic
260M16×C47—42no—
261C2×C8×C47—21no—
262C2×C8×C47—21no—
263C2×C8×C47—21no—
264C2×C8×C47—21no—
265C2×C8×C47—42no—
266C4⋊C4×C47C22⋊C411yescharacteristic
267C4⋊C4×C47C22⋊C411yescharacteristic
268C4⋊C4×C47C22⋊C411yescharacteristic
269C4⋊C4×C47C22⋊C411yescharacteristic
270C4⋊C4×C47C22⋊C411yescharacteristic
271C4⋊C4×C47C22⋊C411yescharacteristic
272C4⋊C4×C47C22⋊C411yescharacteristic
273C4⋊C4×C47C22⋊C411yescharacteristic
274C22⋊C4×C47C22⋊C411yescharacteristic
275C22⋊C4×C47C22⋊C411yescharacteristic
276C22⋊C4×C47C22⋊C411yescharacteristic
277C22⋊C4×C47C22⋊C411yescharacteristic
278C22⋊C4×C47C22⋊C411yescharacteristic
279C22⋊C4×C47C22⋊C411yescharacteristic
280C22⋊C4×C47C22⋊C411yescharacteristic
281C22⋊C4×C47C22⋊C411yescharacteristic
282C42×C47C22×C411yescharacteristic
283C42×C47C22×C411yescharacteristic
284C42×C47C22×C411yescharacteristic
285C42×C47C22×C411yescharacteristic
286C42×C47C2×D411yescharacteristic
287C42×C47C2×D411yescharacteristic
288C42×C47C2×D411yescharacteristic
289C42×C47C2×D411yescharacteristic
290C22⋊Dic47—21no—
291C22⋊Dic47—21no—
292C22⋊Dic47—21no—
293C22⋊Dic47—42no—
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—
303(C2×D47)⋊C4—21no—
304(C2×D47)⋊C4—21no—
305(C2×D47)⋊C4—21no—
306(C2×D47)⋊C4—21no—
307(C2×D47)⋊C4—21no—
308(C2×D47)⋊C4—21no—
309(C2×D47)⋊C4—21no—
310C4⋊Dic47—21no—
311C4⋊Dic47—21no—
312C4⋊Dic47—21no—
313C4⋊Dic47—42no—
314C4⋊Dic47—81no—
315C4⋊Dic47C22×C411yescharacteristic
316C4⋊Dic47C22×C411yescharacteristic
317C4⋊Dic47C22×C411yescharacteristic
318C4⋊Dic47C22×C411yescharacteristic
319Dic47⋊C4—21no—
320Dic47⋊C4—21no—
321Dic47⋊C4—21no—
322Dic47⋊C4—21no—
323Dic47⋊C4—21no—
324Dic47⋊C4—21no—
325Dic47⋊C4—21no—
326Dic47⋊C4—21no—
327C4×Dic47—21no—
328C4×Dic47—21no—
329C4×Dic47—21no—
330C4×Dic47—42no—
331C4×Dic47—81no—
332C23×C47—21no—
333C23×C47—21no—
334C23×C47—22no—
335C23×C47—41no—
336C23×C47C2×C22⋊C411yescharacteristic
337C23×C47C2×C22⋊C411yescharacteristic
338C23×C47C22×D411yescharacteristic
339C22×D47—21no—
340C22×D47—21no—
341C22×D47—21no—
342C22×D47—42no—
343C22×D47—81no—
344C22×D47—81no—
345C2×C4×C47—21no—
346C2×C4×C47—21no—
347C2×C4×C47—21no—
348C2×C4×C47—21no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
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×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×C47C2×C22⋊C411yescharacteristic
365C2×C4×C47C2×C22⋊C411yescharacteristic
366C2×C4×C47C2×C22⋊C411yescharacteristic
367C2×C4×C47C23×C411yescharacteristic
368C2×C4×C47C22×D411yescharacteristic
369C22⋊D47—41no—
370C22⋊D47—41no—
371C22⋊D47—41no—
372C22⋊D47—41no—
373C22⋊D47—41no—
374C22⋊D47—41no—
375C22⋊D47—42no—
376C22⋊D47—81no—
377C22⋊D47—81no—
378C22⋊D47—81no—
379C2×Dic47—22no—
380C2×Dic47—21no—
381C2×Dic47—21no—
382C2×Dic47—21no—
383C2×Dic47—21no—
384C2×Dic47—21no—
385C2×Dic47—41no—
386C2×Dic47—41no—
387C2×Dic47—41no—
388C2×Dic47—41no—
389C2×Dic47—41no—
390C2×Dic47—41no—
391C2×Dic47—41no—
392C2×Dic47—41no—
393C2×Dic47—41no—
394C2×Dic47—41no—
395C2×Dic47—41no—
396C2×Dic47—81no—
397C2×Dic47—84no—
398D188—41no—
399D188—41no—
400D188—41no—
401D188—42no—
402D188—81no—
403D188—81no—
404D188—81no—
405D188—81no—
406C4×D47—42no—
407C4×D47—81no—
408C4×D47—81no—
409C4×D47—81no—
410C4×D47—81no—
411C4×D47—81no—
412C4×D47—81no—
413Dic94—41no—
414Dic94—81no—
415Dic94—81no—
416C8×C47—41no—
417C8×C47—41no—
418C8×C47—41no—
419C8×C47—41no—
420#17604—471nomaximal, Sylow
421C22×C47—21no—
422C22×C47—21no—
423C22×C47—21no—
424C22×C47—21no—
425C22×C47—21no—
426C22×C47—21no—
427C22×C47—21no—
428C22×C47—42no—
429C22×C47—42no—
430C22×C47#41012yes—
431C22×C47C22×C22⋊C411yescharacteristic
432C22×C47#57611yescharacteristic
433C22×C47#57711yescharacteristic
434C2×D47—41no—
435C2×D47—41no—
436C2×D47—41no—
437C2×D47—41no—
438C2×D47—41no—
439C2×D47—41no—
440C2×D47—41no—
441C2×D47—41no—
442C2×D47—41no—
443C2×D47—162no—
444C4×C47—21no—
445C4×C47—21no—
446C4×C47—21no—
447C4×C47—21no—
448C4×C47—21no—
449C4×C47—21no—
450C4×C47—21no—
451C4×C47—21no—
452C4×C47—21no—
453C4×C47—21no—
454C4×C47—21no—
455C4×C47—21no—
456Dic47—42no—
457Dic47—41no—
458Dic47—41no—
459Dic47—41no—
460Dic47—41no—
461Dic47—41no—
462Dic47—81no—
463Dic47—81no—
464Dic47—81no—
465#3494—471no—
466#2924D4711yescharacteristic, complemented
467#2343—471no—
468#1521—471no—
469#1517—471no—
470#1516—471no—
471#1514—471no—
472#1512—471no—
473#1510—471no—
474#1509—471no—
475#1505—471no—
476#1504—471no—
477#1502—471no—
478#1500—471no—
479C2×#327—471no—
480C2×C47—21no—
481C2×C47—21no—
482C2×C47—22no—
483C2×C47—41no—
484C2×C47C2×#41011yescharacteristic
485C2×C47#289711yescharacteristic
486C2×C47#290111yescharacteristic
487D47—81no—
488D47—81no—
489D47—81no—
490#555—941no—
491#553—941no—
492#553—941no—
493#551—941no—
494#551—941no—
495#547—941no—
496#546—941no—
497#546—941no—
498#544—471no—
499#542—471no—
500#542—471no—
501#540—471no—
502#540—471no—
503#535—471no—
504#532—471no—
505#532—471no—
506#529—471no—
507#529—471no—
508#525—471no—
509C2×#121—471no—
510#520—471no—
511#518—471no—
512C2×#117C2×D4711yescharacteristic
513#433—21no—
514#433—21no—
515#432C2×D4711yescharacteristic, complemented
516#432C2×D4711yescharacteristic, complemented
517#431C2×D4711yescharacteristic, complemented
518#431C2×D4711yescharacteristic, complemented
519#424—21no—
520#407C2×D4711yescharacteristic
521C2×C22⋊C8C2×D4711yescharacteristic
522#405—21no—
523#387—941no—
524#387—941no—
525#385—941no—
526#383—471no—
527#382—471no—
528#381—471no—
529C4×C4⋊C4—471no—
530C4×C22⋊C4—941no—
531#376—471no—
532C2×#95—471no—
533#328—471no—
534#328—471no—
535#328—471no—
536#328—471no—
537#327—471no—
538#327—471no—
539#327—471no—
540#327—471no—
541#327—471no—
542#327—471no—
543#327—471no—
544#327—471no—
545#327—471no—
546#327—471no—
547#327—471no—
548#327—471no—
549C47#1760411yescharacteristic, complemented, Sylow
550C2×#41—471no—
551C2×#41—941no—
552C2×#41—941no—
553C22×D4—471no—
554C22×D4—941no—
555C23×C4—941no—
556C23×C4C22×D4711yescharacteristic
557C2×M16—21no—
558C22×C8—21no—
559C4⋊Q8—471no—
560C4⋊Q8—471no—
561C4⋊Q8—941no—
562#127—471no—
563#127—471no—
564#126—941no—
565#126—941no—
566#126—941no—
567#126—941no—
568#125—471no—
569#125—471no—
570#125—941no—
571#124—471no—
572#124—471no—
573#124—941no—
574#124—941no—
575#124—941no—
576#124—941no—
577#123—941no—
578#123—941no—
579#123—941no—
580#123—941no—
581#123—941no—
582#123—941no—
583#123—941no—
584#123—941no—
585#123—941no—
586C22⋊Q8—471no—
587C22⋊Q8—471no—
588C22⋊Q8—941no—
589C22⋊Q8—941no—
590C22⋊Q8—941no—
591C22⋊Q8—941no—
592#121—471no—
593#121—471no—
594#121—471no—
595#121—471no—
596#121—471no—
597#121—471no—
598#121—941no—
599#121—941no—
600#121—941no—
601#121—941no—
602#121—941no—
603#121—941no—
604#121—941no—
605#121—941no—
606#121—941no—
607#121—941no—
608#120—941no—
609#120—941no—
610#120—941no—
611C4×Q8—471no—
612C4×Q8—471no—
613C4×D4—471no—
614C4×D4—471no—
615C4×D4—471no—
616C4×D4—471no—
617C4×D4—471no—
618C4×D4—471no—
619C4×D4—941no—
620C4×D4—941no—
621C4×D4—941no—
622C4×D4—941no—
623C4×D4—941no—
624C4×D4—941no—
625C4×D4—941no—
626C4×D4—941no—
627C4×D4—941no—
628C4×D4—941no—
629#117—471no—
630#117—941no—
631#117—941no—
632#117—941no—
633#117C4×D4711yescharacteristic
634#117C4×D4711yescharacteristic
635#117C4×D4711yescharacteristic
636#117C4×D4711yescharacteristic
637#117C22⋊D4711yescharacteristic
638#117C22⋊D4711yescharacteristic
639#117C22⋊D4711yescharacteristic
640#117C22⋊D4711yescharacteristic
641C2×C4⋊C4—471no—
642C2×C4⋊C4—941no—
643C2×C4⋊C4—941no—
644C2×C4⋊C4—941no—
645C2×C4⋊C4D18811yescharacteristic
646C2×C4⋊C4D18811yescharacteristic
647C2×C22⋊C4—941no—
648C2×C22⋊C4—941no—
649C2×C22⋊C4—941no—
650C2×C22⋊C4—941no—
651C2×C22⋊C4D18811yescharacteristic
652C2×C22⋊C4D18811yescharacteristic
653C2×C42—941no—
654C2×C42—941no—
655C2×C42C22×D4711yescharacteristic
656C2×C42C22×D4711yescharacteristic
657C4⋊C8—21no—
658C4⋊C8—21no—
659C4⋊C8—21no—
660C4⋊C8—21no—
661C22⋊C8—21no—
662C22⋊C8—21no—
663C22⋊C8C22×D4711yescharacteristic
664C22⋊C8C22×D4711yescharacteristic
665C22⋊C8C22×D4711yescharacteristic
666C22⋊C8C22×D4711yescharacteristic
667#97—21no—
668#97—21no—
669C4×C8—21no—
670C4×C8—21no—
671#95—471no—
672#95—471no—
673#95—471no—
674#95—471no—
675#95—941no—
676#95—941no—
677#95—941no—
678#95—941no—
679#95—941no—
680#95—941no—
681C24—941no—
682C24C2×D18811yescharacteristic
683#41—3761no—
684#41—3761no—
685#41—3761no—
686#41—3761no—
687#41—1882no—
688C2×Q8—471no—
689C2×Q8—941no—
690C2×Q8—941no—
691C2×D4—471no—
692C2×D4—471no—
693C2×D4—471no—
694C2×D4—941no—
695C2×D4—941no—
696C2×D4—941no—
697C2×D4—941no—
698C2×D4—941no—
699C2×D4—941no—
700C2×D4—941no—
701C2×D4—941no—
702C2×D4—941no—
703C2×D4—941no—
704C2×D4—941no—
705C2×D4—941no—
706C2×D4—3761no—
707C2×D4—3761no—
708C2×D4—1882no—
709C22×C4—42no—
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—3761no—
723C22×C4—1882no—
724C22×C4—1882no—
725C22×C4C2×C4×D4711yescharacteristic
726C22×C4C2×C4×D4711yescharacteristic
727C22×C4C2×D18811yescharacteristic
728C22×C4C2×D18811yescharacteristic
729C22×C4C2×D18811yescharacteristic
730C22×C4C2×D18811yescharacteristic
731C22×C4C2×D18811yescharacteristic
732C22×C4C2×C22⋊D4711yescharacteristic
733C22×C4C2×C22⋊D4711yescharacteristic
734C22×C4C23×D4711yescharacteristic
735M16—42no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—42no—
741C4⋊C4—471no—
742C4⋊C4—471no—
743C4⋊C4—471no—
744C4⋊C4—471no—
745C4⋊C4—941no—
746C4⋊C4—941no—
747C4⋊C4—941no—
748C4⋊C4—941no—
749C4⋊C4—941no—
750C4⋊C4—941no—
751C4⋊C4—941no—
752C4⋊C4—941no—
753C4⋊C4—941no—
754C4⋊C4—941no—
755C4⋊C4—941no—
756C4⋊C4—3761no—
757C4⋊C4—1882no—
758C4⋊C4(C2×D47)⋊C411yescharacteristic
759C4⋊C4(C2×D47)⋊C411yescharacteristic
760C4⋊C4(C2×D47)⋊C411yescharacteristic
761C4⋊C4(C2×D47)⋊C411yescharacteristic
762C4⋊C4(C2×D47)⋊C411yescharacteristic
763C4⋊C4(C2×D47)⋊C411yescharacteristic
764C4⋊C4(C2×D47)⋊C411yescharacteristic
765C4⋊C4(C2×D47)⋊C411yescharacteristic
766C22⋊C4—941no—
767C22⋊C4—941no—
768C22⋊C4—941no—
769C22⋊C4—941no—
770C22⋊C4—941no—
771C22⋊C4—941no—
772C22⋊C4—941no—
773C22⋊C4—941no—
774C22⋊C4—941no—
775C22⋊C4—941no—
776C22⋊C4—941no—
777C22⋊C4—941no—
778C22⋊C4—941no—
779C22⋊C4—941no—
780C22⋊C4—941no—
781C22⋊C4—941no—
782C22⋊C4—941no—
783C22⋊C4—941no—
784C22⋊C4—941no—
785C22⋊C4—1882no—
786C22⋊C4(C2×D47)⋊C411yescharacteristic
787C22⋊C4(C2×D47)⋊C411yescharacteristic
788C22⋊C4(C2×D47)⋊C411yescharacteristic
789C22⋊C4(C2×D47)⋊C411yescharacteristic
790C22⋊C4(C2×D47)⋊C411yescharacteristic
791C22⋊C4(C2×D47)⋊C411yescharacteristic
792C22⋊C4(C2×D47)⋊C411yescharacteristic
793C22⋊C4(C2×D47)⋊C411yescharacteristic
794C42—941no—
795C42—941no—
796C42—941no—
797C42—3761no—
798C42—1882no—
799C42C2×C4×D4711yescharacteristic
800C42C2×C4×D4711yescharacteristic
801C42C2×C4×D4711yescharacteristic
802C42C2×C4×D4711yescharacteristic
803C42C2×C22⋊D4711yescharacteristic
804C42C2×C22⋊D4711yescharacteristic
805C42C2×C22⋊D4711yescharacteristic
806C42C2×C22⋊D4711yescharacteristic
807C23—22no—
808C23—21no—
809C23—21no—
810C23—41no—
811C23—941no—
812C23—941no—
813C23—941no—
814C23—3761no—
815C23—3761no—
816C23—1882no—
817C23C2×(C2×D47)⋊C411yescharacteristic
818C23C2×(C2×D47)⋊C411yescharacteristic
819C23C22×D18811yescharacteristic
820Q8—3761no—
821Q8—3761no—
822Q8—1881no—
823D4—3761no—
824D4—3761no—
825D4—3761no—
826D4—3761no—
827D4—3761no—
828D4—3761no—
829D4—3761no—
830D4—1881no—
831D4—1881no—
832D4—1881no—
833D4—1882no—
834D4—1882no—
835D4—1881no—
836D4—1881no—
837D4—1881no—
838D4—1881no—
839D4—1881no—
840D4—1881no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—942no—
854C2×C4—941no—
855C2×C4—941no—
856C2×C4—941no—
857C2×C4—941no—
858C2×C4—941no—
859C2×C4—3761no—
860C2×C4—3761no—
861C2×C4—3761no—
862C2×C4—3761no—
863C2×C4—3761no—
864C2×C4—3761no—
865C2×C4—3764no—
866C2×C4—3761no—
867C2×C4—1882no—
868C2×C4—1881no—
869C2×C4—1881no—
870C2×C4—1881no—
871C2×C4—1881no—
872C2×C4—1881no—
873C2×C4—1881no—
874C2×C4—1881no—
875C2×C4—1881no—
876C2×C4—1881no—
877C2×C4—1881no—
878C2×C4—1881no—
879C2×C4C2×(C2×D47)⋊C411yescharacteristic
880C2×C4C2×(C2×D47)⋊C411yescharacteristic
881C2×C4C2×(C2×D47)⋊C411yescharacteristic
882C2×C4C2×(C2×D47)⋊C411yescharacteristic
883C2×C4C2×(C2×D47)⋊C411yescharacteristic
884C2×C4C2×(C2×D47)⋊C411yescharacteristic
885C2×C4C2×(C2×D47)⋊C411yescharacteristic
886C2×C4C2×(C2×D47)⋊C411yescharacteristic
887C2×C4C2×(C2×D47)⋊C411yescharacteristic
888C2×C4C2×(C2×D47)⋊C411yescharacteristic
889C2×C4C22×C4×D4711yescharacteristic
890C2×C4C22×C22⋊D4711yescharacteristic
891C8—41no—
892C8—41no—
893C8—41no—
894C8—41no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—42no—
903C22—42no—
904C22—1881no—
905C22—1881no—
906C22—1881no—
907C22—1881no—
908C22—1881no—
909C22—1881no—
910C22—1881no—
911C22—1881no—
912C22—1881no—
913C22—7522no—
914C22#1568909612yes—
915C22C22×(C2×D47)⋊C411yescharacteristic
916C22#1568992811yescharacteristic
917C22#1568993511yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—3761no—
931C4—3761no—
932C4—3761no—
933C4—1882no—
934C4—1881no—
935C4—1881no—
936C4—1881no—
937C4—1881no—
938C4—1881no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—3761no—
944C2—3761no—
945C2—3761no—
946C2C2×#1568909611yescharacteristic
947C2#2025191511yescharacteristic
948C2#2025193311yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2924C2
socleC22×C47C22×C22⋊C4
prime radical#20257123C2
cosocleC22×C4×C47C24
hypercenter#2924D47
hypocenterC47#17604
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #20246248C2semidirect
3. #20241966C2semidirect
4. #20241949C2semidirect
5. #20241945C2semidirect
6. #20241936C2semidirect
7. #20241927C2semidirect
8. #20241918C2semidirect
9. #20241914C2semidirect
10. #20241897C2semidirect
11. #20241893C2semidirect
12. #20241884C2semidirect
13. #20241875C2semidirect
14. C2×#15688858C2semidirect
15. C47×#2924C2semidirect
24. #15689751C4semidirect
25. #15689744C4semidirect
26. #15689744C4semidirect
27. #15689728C4semidirect
28. #15689728C4semidirect
29. #15689692C4semidirect
36. #15689603C4semidirect
37. #15689597C4semidirect
41. #15688991C22semidirect
42. #15688989C22semidirect
44. C4×C4⋊Dic47C22semidirect
46. #15688969C22semidirect
48. #15688861C22semidirect
49. #15688861C22semidirect
50. #15688861C22semidirect
51. #15688861C22semidirect
60. #15688858C22semidirect
61. #15688858C22semidirect
62. #15688858C22semidirect
63. #15688858C22semidirect
67. C47×#432C22semidirect
68. C47×#432C22semidirect
69. C47×#431C22semidirect
70. C47×#431C22semidirect
81. #13094024C2×C4semidirect
82. #13094024C2×C4semidirect
84. #13094021C2×C4semidirect
85. #13094021C2×C4semidirect
90. #13094016C2×C4semidirect
91. #13094016C2×C4semidirect
95. #13094012C2×C4semidirect
96. #13094012C2×C4semidirect
133. C4×Dic94C2×C4semidirect
134. C4×Dic94C2×C4semidirect
137. C4×D188C2×C4semidirect
138. C4×D188C2×C4semidirect
139. C4×D188C2×C4semidirect
140. C4×D188C2×C4semidirect
141. C4×D188C2×C4semidirect
142. C4×D188C2×C4semidirect
466. #2924D47semidirect
515. #432C2×D47semidirect
516. #432C2×D47semidirect
517. #431C2×D47semidirect
518. #431C2×D47semidirect
549. C47#17604semidirect

Maximal subgroups

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

subgroupindex
#202571232
#202462482
#202419662
#202419492
#202419452
#202419362
#202419272
#202419182
#202419142
#202418972
#202418932
#202418842
#202418752
C2×#156888582
C47×#29242
#1760447