Finite Group Databasebeta

← #37583368

Subgroups — #37583368

Order 24448.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133242C211yesmaximal, characteristic, complemented
2#27133230C211yesmaximal, characteristic, complemented
3#27133005C211yesmaximal, characteristic, complemented
4#27132984C211yesmaximal, characteristic, complemented
5#27132980C211yesmaximal, characteristic, complemented
6#27132975C211yesmaximal, characteristic, complemented
7#27132913C211yesmaximal, characteristic, complemented
8#27132908C211yesmaximal, characteristic, complemented
9#27132896C211yesmaximal, characteristic, complemented
10#27132891C211yesmaximal, characteristic, complemented
11#27132814C211yesmaximal, characteristic, complemented
12#27132805C211yesmaximal, characteristic, complemented
13#27132805C211yesmaximal, characteristic, complemented
14#27132628C211yesmaximal, characteristic, complemented
15#447×C191C211yesmaximal, characteristic, complemented
16C2×#15690287C2211yescharacteristic
17C2×#15690286C2211yescharacteristic, complemented
18C2×#15690275C2211yescharacteristic
19C2×#15690275C2211yescharacteristic
20C2×#15690270C2211yescharacteristic, complemented
21C2×C8×D191C2211yescharacteristic, complemented
22#20259318—21no—
23#20259309—21no—
24#20259302C2211yescharacteristic, complemented
25#20259301C2211yescharacteristic
26#20259299—21no—
27#20259295—21no—
28#20259294—21no—
29#20259293—21no—
30#20259293C2211yescharacteristic
31#20259293C2211yescharacteristic
32#20259293C2211yescharacteristic
33#20259293C2211yescharacteristic
34#20259293C2211yescharacteristic, complemented
35#20259291—21no—
36#20259291—21no—
37#20259281C2211yescharacteristic
38C4⋊C4×D191C2211yescharacteristic, complemented
39#20259256C2211yescharacteristic, complemented
40#20259255C2211yescharacteristic, complemented
41#20259254C2211yescharacteristic, complemented
42#20259253C2211yescharacteristic, complemented
43#20259247C2211yescharacteristic, complemented
44#20259247C2211yescharacteristic, complemented
45#20259243C2211yescharacteristic
46#20259243C2211yescharacteristic
47#20259243C2211yescharacteristic, complemented
48#20259243C2211yescharacteristic, complemented
49C22⋊(C191⋊C8)C2211yescharacteristic
50(C2×D191)⋊C8C2211yescharacteristic, complemented
51(C2×D191)⋊C8C2211yescharacteristic, complemented
52C22×D4×C191C2211yescharacteristic
53C2×D8×C191C2211yescharacteristic
54C2×D8×C191C2211yescharacteristic
55#121×C191C2211yescharacteristic
56#102×C191C2211yescharacteristic
57#102×C191C2211yescharacteristic
58C22⋊C8×C191C2211yescharacteristic
59#15690287—41no—
60#15690287—41no—
61#15690286—41no—
62#15690286—41no—
63C2×Dic382D411yescharacteristic
64C2×Dic382C2311yescharacteristic
65C2×D764D411yescharacteristic
66C2×C22⋊D191—21no—
67C2×C22⋊D191—21no—
68C2×C22⋊D191—21no—
69C2×C22⋊D191—21no—
70C2×C22⋊D191—21no—
71C2×C22⋊D191—21no—
72C2×C22⋊D191D411yescharacteristic
73C2×C22⋊D191D411yescharacteristic
74C22×Dic191—21no—
75C2×C4×D191—21no—
76C2×C4×D191C2311yescharacteristic
77C2×C4×D191C2311yescharacteristic
78#15690275—41no—
79#15690275—41no—
80#15690270—41no—
81C2×C191⋊C8C2311yescharacteristic
82C2×C191⋊C8C2311yescharacteristic
83C8×D191—41no—
84C4⋊Dic191—21no—
85C4⋊Dic191C2311yescharacteristic
86C4⋊Dic191C2311yescharacteristic
87C4⋊Dic191C2311yescharacteristic
88Dic191⋊C4—21no—
89Dic191⋊C4—21no—
90C22⋊Dic191—21no—
91C22⋊Dic191—21no—
92C22⋊Dic191—21no—
93C22⋊Dic191—21no—
94C22⋊Dic191—21no—
95C22⋊Dic191—21no—
96C22⋊Dic191—21no—
97(C2×D191)⋊C4—21no—
98C4×Dic191—21no—
99C24×C191—21no—
100C2×D4×C191—21no—
101C2×D4×C191—21no—
102C2×D4×C191—41no—
103C2×D4×C191—41no—
104C2×D4×C191C2311yescharacteristic
105C2×D4×C191C2311yescharacteristic
106C2×D4×C191C2311yescharacteristic
107C22×C4×C191C2311yescharacteristic
108D8×C191—41no—
109D8×C191—41no—
110C2×C8×C191C2311yescharacteristic
111C2×C8×C191C2311yescharacteristic
112C4⋊C4×C191C2311yescharacteristic
113C22⋊C4×C191—21no—
114C22×D191C2×D411yescharacteristic
115C22×D191C2×D411yescharacteristic
116Dic382—21no—
117Dic382—21no—
118Dic382—41no—
119D764—41no—
120C22⋊D191—41no—
121C22⋊D191—41no—
122C22⋊D191—42no—
123C22⋊D191—81no—
124C22⋊D191—81no—
125C22⋊D191—81no—
126C22⋊D191—81no—
127C22⋊D191—81no—
128C2×Dic191—21no—
129C2×Dic191—21no—
130C2×Dic191—21no—
131C2×Dic191—21no—
132C2×Dic191—42no—
133C2×Dic191C2×D411yescharacteristic
134C2×Dic191C2×D411yescharacteristic
135C4×D191—21no—
136C4×D191—21no—
137C4×D191—21no—
138C4×D191—21no—
139C4×D191—81no—
140C191⋊C8—21no—
141C191⋊C8—21no—
142C23×C191—21no—
143C23×C191—21no—
144C23×C191—21no—
145C23×C191—42no—
146C23×C191—81no—
147C23×C191—81no—
148C23×C191C2×D411yescharacteristic
149D4×C191—21no—
150D4×C191—21no—
151D4×C191—21no—
152D4×C191—21no—
153D4×C191—21no—
154D4×C191—21no—
155D4×C191—42no—
156D4×C191—81no—
157C2×C4×C191—21no—
158C2×C4×C191—21no—
159C2×C4×C191—21no—
160C2×C4×C191C2×D411yescharacteristic
161C2×C4×C191C2411yescharacteristic
162C8×C191—21no—
163C8×C191—21no—
164C22×C191—21no—
165C22×C191—21no—
166C22×C191—21no—
167C22×C191—41no—
168C22×C191—41no—
169C22×C191—41no—
170C22×C191—41no—
171C22×C191—41no—
172C22×C191—41no—
173C22×C191—41no—
174C22×C191—41no—
175C22×C191—41no—
176C22×C191—84no—
177C22×C191C22×D411yescharacteristic
178C2×D191—21no—
179C2×D191—21no—
180C2×D191—21no—
181C2×D191—21no—
182C2×D191—21no—
183C2×D191—21no—
184C4×C191—21no—
185C4×C191—41no—
186C4×C191H(5,𝔽2)11yescharacteristic
187C4×C191H(5,𝔽2)11yescharacteristic
188Dic191—21no—
189Dic191—21no—
190Dic191—41no—
191Dic191—41no—
192Dic191—41no—
193Dic191—41no—
194C2×C191—41no—
195C2×C191—81no—
196C2×C191—81no—
197C2×C191—81no—
198C2×C191#53411yescharacteristic
199C2×C191#57611yescharacteristic
200C2×C191#57711yescharacteristic
201D191—41no—
202D191—41no—
203C191#319811yescharacteristic, complemented, Sylow
204#3198—1911nomaximal, Sylow
205#537—1911no—
206#535—1911no—
207#485—1911no—
208#482—1911no—
209#481—1911no—
210#480—1911no—
211#469—1911no—
212#468—1911no—
213#466—1911no—
214#465—1911no—
215#450—1911no—
216#449—1911no—
217#449—1911no—
218#447D19111yescharacteristic, complemented
219#408—1911no—
220C2×#41—1911no—
221C2×#41—1911no—
222C22×D4C2×D19111yescharacteristic
223C2×SD16—1911no—
224C2×SD16—1911no—
225C2×D8C2×D19111yescharacteristic
226C2×D8C2×D19111yescharacteristic
227C2×M16—1911no—
228C22×C8—1911no—
229#127—3821no—
230#124—3821no—
231C22⋊Q8—3821no—
232C22⋊Q8—1911no—
233C22⋊Q8—1911no—
234#121—3821no—
235#121—3821no—
236#121—3821no—
237#121—1911no—
238#121—1911no—
239#121—1911no—
240#121—1911no—
241#121—1911no—
242#121C2×D19111yescharacteristic
243#120—3821no—
244#120—3821no—
245#117—1911no—
246C2×C4⋊C4—1911no—
247#107—1911no—
248#107—1911no—
249#106—1911no—
250#106—1911no—
251#103—1911no—
252#103—1911no—
253#102—1911no—
254#102—1911no—
255#102—1911no—
256#102—1911no—
257#102C2×D19111yescharacteristic
258#102C2×D19111yescharacteristic
259C22⋊C8—1911no—
260C22⋊C8—1911no—
261C22⋊C8—1911no—
262C22⋊C8C2×D19111yescharacteristic
263C24—21no—
264#41—7641no—
265#41—7641no—
266#41—7641no—
267#41—7641no—
268C2×Q8—1911no—
269C2×Q8—1911no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—3821no—
275C2×D4—3821no—
276C2×D4—3821no—
277C2×D4—3821no—
278C2×D4—3821no—
279C2×D4—3821no—
280C2×D4—1911no—
281C2×D4—1911no—
282C2×D4—1911no—
283C2×D4C22×D19111yescharacteristic
284C2×D4C22×D19111yescharacteristic
285C2×D4C22×D19111yescharacteristic
286C22×C4—3821no—
287C22×C4—3821no—
288C22×C4—1911no—
289C22×C4—1911no—
290C22×C4C22×D19111yescharacteristic
291SD16—7641no—
292SD16—7641no—
293D8—41no—
294D8—41no—
295M16—7641no—
296C2×C8—1911no—
297C2×C8—1911no—
298C2×C8—7641no—
299C2×C8C22×D19111yescharacteristic
300C2×C8C22×D19111yescharacteristic
301C4⋊C4—3821no—
302C4⋊C4—3821no—
303C4⋊C4—3821no—
304C4⋊C4—1911no—
305C4⋊C4—1911no—
306C4⋊C4—1911no—
307C4⋊C4C22×D19111yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—3821no—
310C22⋊C4—3821no—
311C22⋊C4—3821no—
312C22⋊C4—3821no—
313C22⋊C4—3821no—
314C22⋊C4—3821no—
315C22⋊C4—3821no—
316C22⋊C4—3821no—
317C42—3821no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—42no—
322C23—81no—
323C23—81no—
324C23—1911no—
325C23—1911no—
326C23D4×D19111yescharacteristic
327Q8—3821no—
328Q8—3821no—
329Q8—7641no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—42no—
337D4—81no—
338D4—15281no—
339D4—15281no—
340D4—15281no—
341D4—15281no—
342D4—15281no—
343D4—7641no—
344D4—7641no—
345D4—7641no—
346D4—7642no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—3821no—
351C2×C4—3821no—
352C2×C4—3821no—
353C2×C4—3821no—
354C2×C4—3821no—
355C2×C4—3821no—
356C2×C4—3821no—
357C2×C4—3821no—
358C2×C4—1911no—
359C2×C4—1911no—
360C2×C4—15281no—
361C2×C4—7642no—
362C2×C4D4×D19111yescharacteristic
363C2×C4C23×D19111yescharacteristic
364C8—21no—
365C8—21no—
366C8—3821no—
367C8—3821no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—84no—
381C22—3821no—
382C22—3821no—
383C22—3821no—
384C22—3821no—
385C22—3821no—
386C22—3821no—
387C22C2×D4×D19111yescharacteristic
388C4—21no—
389C4—41no—
390C4—3821no—
391C4—3821no—
392C4—7641no—
393C4—7641no—
394C4—7641no—
395C4—7641no—
396C4#2025936711yescharacteristic
397C4#2025936711yescharacteristic
398C2—41no—
399C2—81no—
400C2—81no—
401C2—81no—
402C2—7641no—
403C2—7641no—
404C2#2713322311yescharacteristic
405C2#2713346411yescharacteristic
406C2#2713347311yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#447×C191C2
socleC22×C191C22×D4
hypercenter#447D191
hypocenterC191#3198
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #27133242C2semidirect
2. #27133230C2semidirect
3. #27133005C2semidirect
4. #27132984C2semidirect
5. #27132980C2semidirect
6. #27132975C2semidirect
7. #27132913C2semidirect
8. #27132908C2semidirect
9. #27132896C2semidirect
10. #27132891C2semidirect
11. #27132814C2semidirect
12. #27132805C2semidirect
13. #27132805C2semidirect
14. #27132628C2semidirect
15. #447×C191C2semidirect
17. C2×#15690286C22semidirect
20. C2×#15690270C22semidirect
21. C2×C8×D191C22semidirect
24. #20259302C22semidirect
34. #20259293C22semidirect
38. C4⋊C4×D191C22semidirect
39. #20259256C22semidirect
40. #20259255C22semidirect
41. #20259254C22semidirect
42. #20259253C22semidirect
43. #20259247C22semidirect
44. #20259247C22semidirect
47. #20259243C22semidirect
48. #20259243C22semidirect
50. (C2×D191)⋊C8C22semidirect
51. (C2×D191)⋊C8C22semidirect
203. C191#3198semidirect
218. #447D191semidirect

Maximal subgroups

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

subgroupindex
#271332422
#271332302
#271330052
#271329842
#271329802
#271329752
#271329132
#271329082
#271328962
#271328912
#271328142
#271328052
#271326282
#447×C1912
#3198191