Finite Group Databasebeta

← #37583378

Subgroups — #37583378

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#27133243C211yesmaximal, characteristic, complemented
2#27133232C211yesmaximal, characteristic, complemented
3#27132987C211yesmaximal, characteristic, complemented
4#27132983C211yesmaximal, characteristic, complemented
5#27132978C211yesmaximal, characteristic, complemented
6#27132917C211yesmaximal, characteristic, complemented
7#27132912C211yesmaximal, characteristic, complemented
8#27132900C211yesmaximal, characteristic, complemented
9#27132895C211yesmaximal, characteristic, complemented
10#27132813C211yesmaximal, characteristic, complemented
11#27132811C211yesmaximal, characteristic, complemented
12#27132811C211yesmaximal, characteristic, complemented
13#27132799C211yesmaximal, characteristic, complemented
14#27132628C211yesmaximal, characteristic, complemented
15#485×C191C211yesmaximal, characteristic, complemented
16C2×#15690288C2211yescharacteristic, complemented
17C2×#15690287C2211yescharacteristic
18C22×D764C2211yescharacteristic
19C2×#15690274C2211yescharacteristic
20C2×#15690274C2211yescharacteristic
21C2×D1528C2211yescharacteristic
22C2×D1528C2211yescharacteristic
23C2×#15690270C2211yescharacteristic, complemented
24C2×C8×D191C2211yescharacteristic, complemented
25#20259319—21no—
26#20259310—21no—
27#20259300—21no—
28#20259298C2211yescharacteristic, complemented
29#20259297—21no—
30#20259297C2211yescharacteristic
31#20259297C2211yescharacteristic
32#20259297C2211yescharacteristic
33#20259297C2211yescharacteristic
34#20259297C2211yescharacteristic, complemented
35#20259296C2211yescharacteristic
36#20259295—21no—
37#20259295—21no—
38#20259292—21no—
39#20259292—21no—
40C4⋊C4×D191C2211yescharacteristic, complemented
41#20259255C2211yescharacteristic, complemented
42#20259253C2211yescharacteristic, complemented
43#20259244C2211yescharacteristic
44#20259244C2211yescharacteristic
45#20259242C2211yescharacteristic
46#20259242C2211yescharacteristic
47#20259242C2211yescharacteristic, complemented
48#20259242C2211yescharacteristic, complemented
49C22⋊(C191⋊C8)C2211yescharacteristic
50(C2×D191)⋊C8C2211yescharacteristic, complemented
51(C2×D191)⋊C8C2211yescharacteristic, complemented
52C22⋊Q8×C191C2211yescharacteristic
53#117×C191C2211yescharacteristic
54#107×C191C2211yescharacteristic, complemented
55#106×C191C2211yescharacteristic, complemented
56#103×C191C2211yescharacteristic, complemented
57#103×C191C2211yescharacteristic, complemented
58C22⋊C8×C191C2211yescharacteristic
59C23×D191—21no—
60#15690288—41no—
61#15690288—41no—
62#15690287—41no—
63#15690287—41no—
64C2×Dic382D411yescharacteristic
65C2×D764—21no—
66C2×D764—21no—
67C2×D764—21no—
68C2×D764—21no—
69C2×D764—21no—
70C2×D764—21no—
71C2×D764—21no—
72C2×D764—41no—
73C2×D764—41no—
74C2×D764D411yescharacteristic
75C2×D764C2311yescharacteristic
76C2×D764C2311yescharacteristic
77C2×D764C2311yescharacteristic
78C2×C22⋊D191—21no—
79C2×C22⋊D191D411yescharacteristic
80C2×C22⋊D191D411yescharacteristic
81C2×C4×D191—21no—
82C2×C4×D191—21no—
83C2×C4×D191C2311yescharacteristic
84C2×C4×D191C2311yescharacteristic
85#15690274—41no—
86#15690274—41no—
87D1528—41no—
88D1528—41no—
89#15690270—41no—
90C2×C191⋊C8C2311yescharacteristic
91C2×C191⋊C8C2311yescharacteristic
92C8×D191—41no—
93C4⋊Dic191C2311yescharacteristic
94Dic191⋊C4—21no—
95Dic191⋊C4—21no—
96(C2×D191)⋊C4—21no—
97(C2×D191)⋊C4—21no—
98(C2×D191)⋊C4—21no—
99(C2×D191)⋊C4—21no—
100(C2×D191)⋊C4—21no—
101(C2×D191)⋊C4—21no—
102(C2×D191)⋊C4—21no—
103C2×Q8×C191C2311yescharacteristic
104C22×C4×C191C2311yescharacteristic
105C2×C8×C191C2311yescharacteristic
106C2×C8×C191C2311yescharacteristic
107C4⋊C4×C191—21no—
108C4⋊C4×C191C2311yescharacteristic
109C4⋊C4×C191C2311yescharacteristic
110C4⋊C4×C191C2311yescharacteristic
111C22⋊C4×C191—21no—
112C22⋊C4×C191—21no—
113C42×C191—21no—
114C22×D191—21no—
115C22×D191—21no—
116C22×D191—21no—
117C22×D191—42no—
118C22×D191—81no—
119C22×D191—81no—
120C22×D191C2×D411yescharacteristic
121C22×D191C2×D411yescharacteristic
122Dic382—41no—
123D764—21no—
124D764—21no—
125D764—21no—
126D764—21no—
127D764—21no—
128D764—21no—
129D764—41no—
130D764—42no—
131D764—42no—
132D764—81no—
133D764—81no—
134D764—81no—
135D764—81no—
136D764—81no—
137C22⋊D191—41no—
138C22⋊D191—41no—
139C22⋊D191—81no—
140C2×Dic191—21no—
141C2×Dic191C2×D411yescharacteristic
142C2×Dic191C2×D411yescharacteristic
143C4×D191—21no—
144C4×D191—21no—
145C4×D191—21no—
146C4×D191—21no—
147C4×D191—42no—
148C4×D191—81no—
149C191⋊C8—21no—
150C191⋊C8—21no—
151C23×C191C2×D411yescharacteristic
152Q8×C191—21no—
153Q8×C191—21no—
154C2×C4×C191—21no—
155C2×C4×C191—21no—
156C2×C4×C191—21no—
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×C191C22×D411yescharacteristic
168C2×D191—21no—
169C2×D191—21no—
170C2×D191—21no—
171C2×D191—21no—
172C2×D191—21no—
173C2×D191—21no—
174C2×D191—41no—
175C2×D191—41no—
176C2×D191—41no—
177C2×D191—41no—
178C2×D191—41no—
179C2×D191—41no—
180C2×D191—41no—
181C2×D191—41no—
182C2×D191—41no—
183C2×D191—84no—
184C4×C191—21no—
185C4×C191—41no—
186C4×C191—41no—
187C4×C191—41no—
188C4×C191—41no—
189C4×C191H(5,𝔽2)11yescharacteristic
190C4×C191H(5,𝔽2)11yescharacteristic
191Dic191—21no—
192Dic191—21no—
193Dic191—41no—
194C2×C191—41no—
195C2×C191#53411yescharacteristic
196C2×C191#57611yescharacteristic
197C2×C191#57711yescharacteristic
198D191—41no—
199D191—41no—
200D191—81no—
201D191—81no—
202D191—81no—
203C191#319811yescharacteristic, complemented, Sylow
204#3198—1911nomaximal, Sylow
205#537—1911no—
206#535—1911no—
207#485D19111yescharacteristic, complemented
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#447—1911no—
219#408—1911no—
220C2×#41—1911no—
221C2×#41—1911no—
222C22×D4—1911no—
223C2×SD16—1911no—
224C2×SD16—1911no—
225C2×D8—1911no—
226C2×D8—1911no—
227C2×M16—1911no—
228C22×C8—1911no—
229#127—3821no—
230#124—3821no—
231C22⋊Q8—3821no—
232C22⋊Q8—1911no—
233C22⋊Q8C2×D19111yescharacteristic
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#121—1911no—
243#120—3821no—
244#120—3821no—
245#117C2×D19111yescharacteristic
246C2×C4⋊C4—1911no—
247#107—1911no—
248#107C2×D19111yescharacteristic, complemented
249#106—1911no—
250#106C2×D19111yescharacteristic, complemented
251#103C2×D19111yescharacteristic, complemented
252#103C2×D19111yescharacteristic, complemented
253#102—1911no—
254#102—1911no—
255#102—1911no—
256#102—1911no—
257#102—1911no—
258#102—1911no—
259C22⋊C8—1911no—
260C22⋊C8—1911no—
261C22⋊C8—1911no—
262C22⋊C8C2×D19111yescharacteristic
263C24—3821no—
264#41—7641no—
265#41—7641no—
266#41—7641no—
267#41—7641no—
268C2×Q8—1911no—
269C2×Q8C22×D19111yescharacteristic
270C2×D4—3821no—
271C2×D4—3821no—
272C2×D4—3821no—
273C2×D4—3821no—
274C2×D4—3821no—
275C2×D4—3821no—
276C2×D4—3821no—
277C2×D4—3821no—
278C2×D4—1911no—
279C2×D4—1911no—
280C2×D4—1911no—
281C2×D4—1911no—
282C2×D4—1911no—
283C2×D4—1911no—
284C2×D4—7641no—
285C2×D4—7641no—
286C22×C4—3821no—
287C22×C4—3821no—
288C22×C4—1911no—
289C22×C4—1911no—
290C22×C4C22×D19111yescharacteristic
291SD16—7641no—
292SD16—7641no—
293D8—7641no—
294D8—7641no—
295M16—7641no—
296C2×C8—1911no—
297C2×C8—1911no—
298C2×C8—7641no—
299C2×C8C22×D19111yescharacteristic
300C2×C8C22×D19111yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—3821no—
303C4⋊C4—3821no—
304C4⋊C4—1911no—
305C4⋊C4C22×D19111yescharacteristic
306C4⋊C4C22×D19111yescharacteristic
307C4⋊C4C22×D19111yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—3821no—
311C22⋊C4—3821no—
312C22⋊C4—3821no—
313C22⋊C4—3821no—
314C22⋊C4—3821no—
315C22⋊C4—3821no—
316C22⋊C4—3821no—
317C42—21no—
318C23—3821no—
319C23—3821no—
320C23—3821no—
321C23—1911no—
322C23—1911no—
323C23—15281no—
324C23—15281no—
325C23—7642no—
326C23D4×D19111yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—7641no—
330D4—3821no—
331D4—3821no—
332D4—3821no—
333D4—3821no—
334D4—3821no—
335D4—3821no—
336D4—15281no—
337D4—15281no—
338D4—15281no—
339D4—15281no—
340D4—15281no—
341D4—15281no—
342D4—7641no—
343D4—7642no—
344D4—7642no—
345D4—7641no—
346D4—7641no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
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—3821no—
372C22—3821no—
373C22—3821no—
374C22—3821no—
375C22—3821no—
376C22—3821no—
377C22—15284no—
378C22—7641no—
379C22—7641no—
380C22—7641no—
381C22—7641no—
382C22—7641no—
383C22—7641no—
384C22—7641no—
385C22—7641no—
386C22—7641no—
387C22C2×D4×D19111yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—3821no—
394C4—3821no—
395C4—7641no—
396C4#2025936811yescharacteristic
397C4#2025936811yescharacteristic
398C2—41no—
399C2—15281no—
400C2—15281no—
401C2—15281no—
402C2—7641no—
403C2—7641no—
404C2#2713322411yescharacteristic
405C2#2713346511yescharacteristic
406C2#2713347211yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#485×C191C2
socleC22×C191C22×D4
hypercenter#485D191
hypocenterC191#3198
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #27133243C2semidirect
2. #27133232C2semidirect
3. #27132987C2semidirect
4. #27132983C2semidirect
5. #27132978C2semidirect
6. #27132917C2semidirect
7. #27132912C2semidirect
8. #27132900C2semidirect
9. #27132895C2semidirect
10. #27132813C2semidirect
11. #27132811C2semidirect
12. #27132811C2semidirect
13. #27132799C2semidirect
14. #27132628C2semidirect
15. #485×C191C2semidirect
16. C2×#15690288C22semidirect
23. C2×#15690270C22semidirect
24. C2×C8×D191C22semidirect
28. #20259298C22semidirect
34. #20259297C22semidirect
40. C4⋊C4×D191C22semidirect
41. #20259255C22semidirect
42. #20259253C22semidirect
47. #20259242C22semidirect
48. #20259242C22semidirect
50. (C2×D191)⋊C8C22semidirect
51. (C2×D191)⋊C8C22semidirect
54. #107×C191C22semidirect
55. #106×C191C22semidirect
56. #103×C191C22semidirect
57. #103×C191C22semidirect
203. C191#3198semidirect
207. #485D191semidirect
248. #107C2×D191semidirect
250. #106C2×D191semidirect
251. #103C2×D191semidirect
252. #103C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271332432
#271332322
#271329872
#271329832
#271329782
#271329172
#271329122
#271329002
#271328952
#271328132
#271328112
#271327992
#271326282
#485×C1912
#3198191