Finite Group Databasebeta

← #26183884

Subgroups — #26183884

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#20252046C211yesmaximal, characteristic, complemented
3#20241963C211yesmaximal, characteristic, complemented
4#20241947C211yesmaximal, characteristic, complemented
5#20241942C211yesmaximal, characteristic, complemented
6#20241934C211yesmaximal, characteristic, complemented
7#20241924C211yesmaximal, characteristic, complemented
8#20241916C211yesmaximal, characteristic, complemented
9#20241911C211yesmaximal, characteristic, complemented
10#20241895C211yesmaximal, characteristic, complemented
11#20241890C211yesmaximal, characteristic, complemented
12#20241882C211yesmaximal, characteristic, complemented
13#20241872C211yesmaximal, characteristic, complemented
14C2×#15688856C211yesmaximal, characteristic, complemented
15C47×#2343C211yesmaximal, 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#15689184—21no—
39#15689184—21no—
40#15689180C2211yescharacteristic, complemented
41#15689180C2211yescharacteristic, complemented
42#15689176C2211yescharacteristic, complemented
43#15689176C2211yescharacteristic, complemented
44#15689150—21no—
45#15689087C2211yescharacteristic
46C2×C22⋊(C47⋊C8)C2211yescharacteristic
47#15689079—21no—
48#15688859C2211yescharacteristic, complemented
49#15688859C2211yescharacteristic, complemented
50#15688859C2211yescharacteristic, complemented
51#15688859C2211yescharacteristic, complemented
52#15688856C2211yescharacteristic
53#15688856C2211yescharacteristic
54#15688856C2211yescharacteristic
55#15688856C2211yescharacteristic
56#15688856C2211yescharacteristic
57#15688856C2211yescharacteristic
58#15688856C2211yescharacteristic
59#15688856C2211yescharacteristic
60#15688856C2211yescharacteristic, complemented
61#15688856C2211yescharacteristic, complemented
62#15688856C2211yescharacteristic, complemented
63#15688856C2211yescharacteristic, complemented
64C2×#117×C47C2211yescharacteristic
65C47×#387—21no—
66C47×#387—21no—
67C47×#385—21no—
68C47×#383C2211yescharacteristic, complemented
69C47×#382C2211yescharacteristic, complemented
70C47×#381C2211yescharacteristic
71C4×C4⋊C4×C47C2211yescharacteristic, complemented
72C4×C22⋊C4×C47—21no—
73C47×#376C2211yescharacteristic, complemented
74C2×#95×C47C2211yescharacteristic
75C2×#10625350—21no—
76C2×#10625350—21no—
77C2×#10625350C2×C411yescharacteristic
78C22×D188C2×C411yescharacteristic
79C22×C22⋊D47—21no—
80C2×#10625329—21no—
81C22×C47⋊C8—21no—
82#13094024C2×C411yescharacteristic, complemented
83#13094024C2×C411yescharacteristic, complemented
84#13094023—21no—
85#13094021C2×C411yescharacteristic, complemented
86#13094021C2×C411yescharacteristic, complemented
87#13094019—21no—
88#13094019—21no—
89#13094018—21no—
90#13094018—21no—
91#13094016C2×C411yescharacteristic, complemented
92#13094016C2×C411yescharacteristic, complemented
93#13094015—21no—
94#13094012—21no—
95#13094012—21no—
96#13094012C2×C411yescharacteristic, complemented
97#13094012C2×C411yescharacteristic, complemented
98#13094010—21no—
99#13094010—21no—
100#13094009—21no—
101#13094009—21no—
102#13094009—21no—
103#13094009—21no—
104#13094007—21no—
105#13094007—21no—
106#13094007—21no—
107#13094006—21no—
108#13094006—21no—
109#13094003C2×C411yescharacteristic
110#13094003C2311yescharacteristic
111#13094002—21no—
112#13094002—21no—
113#13094001—21no—
114#13094001—21no—
115#13093999—21no—
116#13093999—21no—
117#13093998—21no—
118#13093998—21no—
119#13093998—21no—
120#13093998—21no—
121#13093998C2×C411yescharacteristic
122#13093998C2×C411yescharacteristic
123#13093998C2×C411yescharacteristic
124#13093998C2311yescharacteristic
125#13093998C2311yescharacteristic
126#13093998C2311yescharacteristic
127#13093997—21no—
128#13093997—21no—
129#13093997—21no—
130#13093997—21no—
131#13093994—21no—
132#13093994—21no—
133#13093993—21no—
134C4×Dic94C2×C411yescharacteristic, complemented
135C4×Dic94C2×C411yescharacteristic, complemented
136C4×D188—21no—
137C4×D188—21no—
138C4×D188C2×C411yescharacteristic, complemented
139C4×D188C2×C411yescharacteristic, complemented
140C4×D188C2×C411yescharacteristic, complemented
141C4×D188C2×C411yescharacteristic, complemented
142C4×D188C2×C411yescharacteristic, complemented
143C4×D188C2×C411yescharacteristic, complemented
144#13093986—21no—
145#13093986—21no—
146C4×C22⋊D47—21no—
147C4×C22⋊D47—21no—
148C4×C22⋊D47—21no—
149C4×C22⋊D47—21no—
150(C22⋊D47)⋊C4—21no—
151(C22⋊D47)⋊C4—21no—
152#13093983C2×C411yescharacteristic
153#13093982—21no—
154#13093981—21no—
155#13093981—21no—
156C2×C4⋊Dic47C2×C411yescharacteristic
157C4⋊C4×D47—21no—
158C2×(C2×D47)⋊C4—21no—
159C22⋊C4×D47—21no—
160C22⋊C4×D47—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
207C23×D47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—42no—
213C22×C4×C47—42no—
214C22×C4×C47—42no—
215C22×C4×C47—81no—
216C22×C4×C47C22×C411yescharacteristic
217C22×C4×C47C22×C411yescharacteristic
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×C47C2×D411yescharacteristic
225C22×C4×C47C2411yescharacteristic
226C2×C22⋊D47—21no—
227C2×C22⋊D47—21no—
228C2×C22⋊D47—21no—
229C2×C22⋊D47—21no—
230C2×C22⋊D47—21no—
231C2×C22⋊D47—21no—
232C2×C22⋊D47—21no—
233C2×C22⋊D47—81no—
234C2×C22⋊D47—81no—
235C22×Dic47—21no—
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
260C4⋊C4×C47—42no—
261C4⋊C4×C47—81no—
262C4⋊C4×C47C22⋊C411yescharacteristic
263C4⋊C4×C47C22⋊C411yescharacteristic
264C4⋊C4×C47C22⋊C411yescharacteristic
265C4⋊C4×C47C22⋊C411yescharacteristic
266C4⋊C4×C47C22⋊C411yescharacteristic
267C4⋊C4×C47C22⋊C411yescharacteristic
268C4⋊C4×C47C22⋊C411yescharacteristic
269C4⋊C4×C47C22⋊C411yescharacteristic
270C22⋊C4×C47—42no—
271C22⋊C4×C47C22⋊C411yescharacteristic
272C22⋊C4×C47C22⋊C411yescharacteristic
273C22⋊C4×C47C22⋊C411yescharacteristic
274C22⋊C4×C47C22⋊C411yescharacteristic
275C22⋊C4×C47C22⋊C411yescharacteristic
276C22⋊C4×C47C22⋊C411yescharacteristic
277C22⋊C4×C47C22⋊C411yescharacteristic
278C22⋊C4×C47C22⋊C411yescharacteristic
279C42×C47—42no—
280C42×C47—81no—
281C42×C47C22×C411yescharacteristic
282C42×C47C22×C411yescharacteristic
283C42×C47C22×C411yescharacteristic
284C42×C47C22×C411yescharacteristic
285C42×C47C2×D411yescharacteristic
286C42×C47C2×D411yescharacteristic
287C42×C47C2×D411yescharacteristic
288C42×C47C2×D411yescharacteristic
289C22⋊Dic47—21no—
290C22⋊Dic47—21no—
291C22⋊Dic47—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—
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—
308C4⋊Dic47—21no—
309C4⋊Dic47—21no—
310C4⋊Dic47—21no—
311C4⋊Dic47C22×C411yescharacteristic
312C4⋊Dic47C22×C411yescharacteristic
313C4⋊Dic47C22×C411yescharacteristic
314C4⋊Dic47C22×C411yescharacteristic
315Dic47⋊C4—21no—
316Dic47⋊C4—21no—
317Dic47⋊C4—21no—
318Dic47⋊C4—21no—
319Dic47⋊C4—21no—
320Dic47⋊C4—21no—
321Dic47⋊C4—21no—
322Dic47⋊C4—21no—
323C4×Dic47—21no—
324C4×Dic47—21no—
325C4×Dic47—21no—
326#10625329—42no—
327C2×C47⋊C8—21no—
328C2×C47⋊C8—21no—
329C2×C47⋊C8—21no—
330C2×C47⋊C8—21no—
331C2×C47⋊C8—42no—
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—22no—
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—41no—
359C2×C4×C47—41no—
360C2×C4×C47—41no—
361C2×C4×C47—41no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
364C2×C4×C47—41no—
365C2×C4×C47—41no—
366C2×C4×C47—41no—
367C2×C4×C47—41no—
368C2×C4×C47—41no—
369C2×C4×C47—84no—
370C2×C4×C47C2×C22⋊C411yescharacteristic
371C2×C4×C47C2×C22⋊C411yescharacteristic
372C2×C4×C47C2×C22⋊C411yescharacteristic
373C2×C4×C47C2×C22⋊C411yescharacteristic
374C2×C4×C47C2×C22⋊C411yescharacteristic
375C2×C4×C47C2×C22⋊C411yescharacteristic
376C2×C4×C47C2×C22⋊C411yescharacteristic
377C2×C4×C47C2×C22⋊C411yescharacteristic
378C2×C4×C47C2×C22⋊C411yescharacteristic
379C2×C4×C47C2×C22⋊C411yescharacteristic
380C2×C4×C47C23×C411yescharacteristic
381C2×C4×C47C22×D411yescharacteristic
382C22⋊D47—41no—
383C22⋊D47—41no—
384C22⋊D47—41no—
385C22⋊D47—41no—
386C22⋊D47—41no—
387C22⋊D47—41no—
388C22⋊D47—42no—
389C22⋊D47—81no—
390C22⋊D47—81no—
391C22⋊D47—81no—
392C2×Dic47—21no—
393C2×Dic47—21no—
394C2×Dic47—21no—
395C2×Dic47—21no—
396C2×Dic47—21no—
397C2×Dic47—81no—
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—
416C47⋊C8—41no—
417C47⋊C8—41no—
418C47⋊C8—41no—
419C47⋊C8—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—
456C4×C47—42no—
457C4×C47—81no—
458C4×C47—81no—
459C4×C47—81no—
460Dic47—41no—
461Dic47—41no—
462Dic47—41no—
463Dic47—41no—
464Dic47—41no—
465#3494—471no—
466#2924—471no—
467#2343D4711yescharacteristic, complemented
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—941no—
514#433—941no—
515#432—471no—
516#432—471no—
517#431—471no—
518#431—471no—
519#424—941no—
520#407—471no—
521C2×C22⋊C8—471no—
522#405—941no—
523#387—21no—
524#387—21no—
525#385—21no—
526#383C2×D4711yescharacteristic, complemented
527#382C2×D4711yescharacteristic, complemented
528#381C2×D4711yescharacteristic
529C4×C4⋊C4C2×D4711yescharacteristic, complemented
530C4×C22⋊C4—21no—
531#376C2×D4711yescharacteristic, complemented
532C2×#95C2×D4711yescharacteristic
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—21no—
556C23×C4C22×D4711yescharacteristic
557C2×M16—941no—
558C22×C8—941no—
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#117D18811yescharacteristic
638#117D18811yescharacteristic
639#117D18811yescharacteristic
640#117D18811yescharacteristic
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—471no—
644C2×C4⋊C4—941no—
645C2×C4⋊C4C22⋊D4711yescharacteristic
646C2×C4⋊C4C22⋊D4711yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—941no—
649C2×C22⋊C4—941no—
650C2×C22⋊C4—941no—
651C2×C22⋊C4C22⋊D4711yescharacteristic
652C2×C22⋊C4C22⋊D4711yescharacteristic
653C2×C42—21no—
654C2×C42—21no—
655C2×C42C22×D4711yescharacteristic
656C2×C42C22×D4711yescharacteristic
657C4⋊C8—941no—
658C4⋊C8—941no—
659C4⋊C8—941no—
660C4⋊C8—941no—
661C22⋊C8—471no—
662C22⋊C8—471no—
663C22⋊C8—471no—
664C22⋊C8—471no—
665C22⋊C8—941no—
666C22⋊C8—941no—
667#97—941no—
668#97—941no—
669C4×C8—941no—
670C4×C8—941no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95C22×D4711yescharacteristic
678#95C22×D4711yescharacteristic
679#95C22×D4711yescharacteristic
680#95C22×D4711yescharacteristic
681C24—941no—
682C24C2×C22⋊D4711yescharacteristic
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—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—42no—
714C22×C4—42no—
715C22×C4—42no—
716C22×C4—81no—
717C22×C4—941no—
718C22×C4—941no—
719C22×C4—941no—
720C22×C4—941no—
721C22×C4—941no—
722C22×C4—941no—
723C22×C4—941no—
724C22×C4—941no—
725C22×C4C2×C4×D4711yescharacteristic
726C22×C4C2×C4×D4711yescharacteristic
727C22×C4C2×D18811yescharacteristic
728C22×C4C2×D18811yescharacteristic
729C22×C4C2×C22⋊D4711yescharacteristic
730C22×C4C2×C22⋊D4711yescharacteristic
731C22×C4C2×C22⋊D4711yescharacteristic
732C22×C4C2×C22⋊D4711yescharacteristic
733C22×C4C2×C22⋊D4711yescharacteristic
734C22×C4C23×D4711yescharacteristic
735M16—1882no—
736C2×C8—941no—
737C2×C8—941no—
738C2×C8—941no—
739C2×C8—941no—
740C2×C8—1882no—
741C4⋊C4—42no—
742C4⋊C4—81no—
743C4⋊C4—471no—
744C4⋊C4—471no—
745C4⋊C4—471no—
746C4⋊C4—471no—
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—941no—
757C4⋊C4—941no—
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—42no—
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—941no—
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—42no—
795C42—81no—
796C42—941no—
797C42—941no—
798C42—941no—
799C42C2×C4×D4711yescharacteristic
800C42C2×C4×D4711yescharacteristic
801C42C2×C4×D4711yescharacteristic
802C42C2×C4×D4711yescharacteristic
803C42C2×D18811yescharacteristic
804C42C2×D18811yescharacteristic
805C42C2×D18811yescharacteristic
806C42C2×D18811yescharacteristic
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×C22⋊D4711yescharacteristic
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—22no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—84no—
866C2×C4—941no—
867C2×C4—941no—
868C2×C4—941no—
869C2×C4—941no—
870C2×C4—941no—
871C2×C4—3761no—
872C2×C4—3761no—
873C2×C4—3761no—
874C2×C4—3761no—
875C2×C4—3761no—
876C2×C4—3761no—
877C2×C4—3761no—
878C2×C4—1882no—
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×D18811yescharacteristic
891C8—1881no—
892C8—1881no—
893C8—1881no—
894C8—1881no—
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#1568992611yescharacteristic
917C22#1568993111yescharacteristic
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—42no—
931C4—81no—
932C4—81no—
933C4—81no—
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#2025191111yescharacteristic
948C2#2025193611yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2343C2
socleC22×C47C22×C22⋊C4
prime radical#20257123C2
cosocleC22×C4×C47C24
hypercenter#2343D47
hypocenterC47#17604
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. #20241947C2semidirect
5. #20241942C2semidirect
6. #20241934C2semidirect
7. #20241924C2semidirect
8. #20241916C2semidirect
9. #20241911C2semidirect
10. #20241895C2semidirect
11. #20241890C2semidirect
12. #20241882C2semidirect
13. #20241872C2semidirect
14. C2×#15688856C2semidirect
15. C47×#2343C2semidirect
24. #15689751C4semidirect
25. #15689744C4semidirect
26. #15689744C4semidirect
27. #15689728C4semidirect
28. #15689728C4semidirect
29. #15689692C4semidirect
36. #15689603C4semidirect
37. #15689597C4semidirect
40. #15689180C22semidirect
41. #15689180C22semidirect
42. #15689176C22semidirect
43. #15689176C22semidirect
48. #15688859C22semidirect
49. #15688859C22semidirect
50. #15688859C22semidirect
51. #15688859C22semidirect
60. #15688856C22semidirect
61. #15688856C22semidirect
62. #15688856C22semidirect
63. #15688856C22semidirect
68. C47×#383C22semidirect
69. C47×#382C22semidirect
71. C4×C4⋊C4×C47C22semidirect
73. C47×#376C22semidirect
82. #13094024C2×C4semidirect
83. #13094024C2×C4semidirect
85. #13094021C2×C4semidirect
86. #13094021C2×C4semidirect
91. #13094016C2×C4semidirect
92. #13094016C2×C4semidirect
96. #13094012C2×C4semidirect
97. #13094012C2×C4semidirect
134. C4×Dic94C2×C4semidirect
135. C4×Dic94C2×C4semidirect
138. C4×D188C2×C4semidirect
139. C4×D188C2×C4semidirect
140. C4×D188C2×C4semidirect
141. C4×D188C2×C4semidirect
142. C4×D188C2×C4semidirect
143. C4×D188C2×C4semidirect
467. #2343D47semidirect
526. #383C2×D47semidirect
527. #382C2×D47semidirect
529. C4×C4⋊C4C2×D47semidirect
531. #376C2×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
#202520462
#202419632
#202419472
#202419422
#202419342
#202419242
#202419162
#202419112
#202418952
#202418902
#202418822
#202418722
C2×#156888562
C47×#23432
#1760447