Finite Group Databasebeta

← #37582473

Subgroups — #37582473

Order 24448.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133229C211yesmaximal, characteristic
2#27133143C211yesmaximal, characteristic, complemented
3#27132989C211yesmaximal, characteristic, complemented
4#27132987C211yesmaximal, characteristic, complemented
5#27132986C211yesmaximal, characteristic, complemented
6#27132982C211yesmaximal, characteristic, complemented
7#27132980C211yesmaximal, characteristic, complemented
8#27132978C211yesmaximal, characteristic, complemented
9#27132974C211yesmaximal, characteristic, complemented
10#27132704C211yesmaximal, characteristic, complemented
11#27132698C211yesmaximal, characteristic, complemented
12#27132666C211yesmaximal, characteristic, complemented
13#102×D191C211yesmaximal, characteristic, complemented
14#27132628C211yesmaximal, characteristic, complemented
15#482×C191C211yesmaximal, characteristic, complemented
16C2×#15690287C2211yescharacteristic
17C2×D4×D191C2211yescharacteristic
18C2×#15690270C2211yescharacteristic
19C2×C8×D191C2211yescharacteristic
20#20259318—21no—
21#20259308—21no—
22#20259297C2211yescharacteristic
23#20259296C2211yescharacteristic
24#20259293C2211yescharacteristic
25#20259292—21no—
26#20259290—21no—
27C4×Dic382—21no—
28C4×D764—21no—
29(C22⋊D191)⋊C4—21no—
30(C22⋊D191)⋊C4—21no—
31#20259280C2211yescharacteristic
32#20259280C2211yescharacteristic
33#20259280C2211yescharacteristic, complemented
34C2×C4⋊Dic191C2211yescharacteristic, complemented
35C4⋊C4×D191C2211yescharacteristic
36C4⋊C4×D191C2211yescharacteristic, complemented
37#20259255C2211yescharacteristic, complemented
38#20259255C2211yescharacteristic, complemented
39#20259255C2211yescharacteristic, complemented
40#20259254C2211yescharacteristic, complemented
41#20259254C2211yescharacteristic, complemented
42#20259253C2211yescharacteristic, complemented
43#20259244C2211yescharacteristic
44#20259244C2211yescharacteristic
45#20259243C2211yescharacteristic
46#20259243C2211yescharacteristic
47#20259242C2211yescharacteristic
48#20259242C2211yescharacteristic
49C22⋊(C191⋊C8)C2211yescharacteristic, complemented
50(C2×D191)⋊C8C2211yescharacteristic, complemented
51(C2×D191)⋊C8C2211yescharacteristic, complemented
52#121×C191C2211yescharacteristic
53#117×C191C2211yescharacteristic, complemented
54#107×C191C2211yescharacteristic, complemented
55#106×C191C2211yescharacteristic, complemented
56#102×C191C2211yescharacteristic
57#102×C191C2211yescharacteristic
58C22⋊C8×C191C2211yescharacteristic, complemented
59C23×D191—21no—
60#15690287—22no—
61#15690287—22no—
62C2×Dic382D411yescharacteristic
63C2×D764—21no—
64C2×D764D411yescharacteristic
65C2×D764C2311yescharacteristic
66C2×C22⋊D191—21no—
67C2×C22⋊D191—21no—
68C2×C22⋊D191—21no—
69C2×C22⋊D191D411yescharacteristic
70C2×C22⋊D191D411yescharacteristic
71D4×D191—22no—
72D4×D191—22no—
73C22×Dic191—21no—
74C2×C4×D191—21no—
75C2×C4×D191—21no—
76C2×C4×D191C2311yescharacteristic
77C2×C4×D191C2311yescharacteristic
78#15690270—22no—
79C2×C191⋊C8C2311yescharacteristic
80C2×C191⋊C8C2311yescharacteristic
81C8×D191—22no—
82C4⋊Dic191—21no—
83C4⋊Dic191C2311yescharacteristic
84C4⋊Dic191C2311yescharacteristic
85C4⋊Dic191C2311yescharacteristic
86Dic191⋊C4—21no—
87Dic191⋊C4—21no—
88C22⋊Dic191—21no—
89(C2×D191)⋊C4—21no—
90(C2×D191)⋊C4—21no—
91(C2×D191)⋊C4—21no—
92(C2×D191)⋊C4—21no—
93(C2×D191)⋊C4—21no—
94C4×Dic191—21no—
95C4×Dic191—21no—
96C4×Dic191—21no—
97C2×D4×C191—21no—
98C2×D4×C191C2311yescharacteristic
99C22×C4×C191C2311yescharacteristic
100C2×C8×C191C2311yescharacteristic
101C2×C8×C191C2311yescharacteristic
102C4⋊C4×C191C2311yescharacteristic
103C4⋊C4×C191C2311yescharacteristic
104C4⋊C4×C191C2311yescharacteristic
105C22⋊C4×C191—21no—
106C22⋊C4×C191—21no—
107C42×C191—21no—
108C22×D191—21no—
109C22×D191—42no—
110C22×D191—81no—
111C22×D191—81no—
112C22×D191C2×D411yescharacteristic
113C22×D191C2×D411yescharacteristic
114Dic382—22no—
115D764—22no—
116D764—21no—
117D764—21no—
118D764—81no—
119C22⋊D191—22no—
120C22⋊D191—22no—
121C22⋊D191—42no—
122C22⋊D191—81no—
123C22⋊D191—81no—
124C2×Dic191—21no—
125C2×Dic191—21no—
126C2×Dic191—21no—
127C2×Dic191—81no—
128C2×Dic191C2×D411yescharacteristic
129C2×Dic191C2×D411yescharacteristic
130C4×D191—21no—
131C4×D191—21no—
132C4×D191—81no—
133C4×D191—81no—
134C4×D191#4112yes—
135C4×D191#4112yes—
136C191⋊C8—21no—
137C191⋊C8—21no—
138C23×C191—21no—
139C23×C191C2×D411yescharacteristic
140D4×C191—21no—
141D4×C191—21no—
142D4×C191—81no—
143C2×C4×C191—21no—
144C2×C4×C191—21no—
145C2×C4×C191—21no—
146C2×C4×C191—21no—
147C2×C4×C191—21no—
148C2×C4×C191C2×D411yescharacteristic
149C2×C4×C191C2411yescharacteristic
150C8×C191—21no—
151C8×C191—21no—
152C22×C191—21no—
153C22×C191—21no—
154C22×C191—21no—
155C22×C191—41no—
156C22×C191—41no—
157C22×C191—41no—
158C22×C191C22×D411yescharacteristic
159C2×D191—21no—
160C2×D191—21no—
161C2×D191—21no—
162C2×D191—21no—
163C2×D191—21no—
164C2×D191—41no—
165C2×D191—41no—
166C2×D191—41no—
167C2×D191—84no—
168C2×D191#12312yes—
169C4×C191—21no—
170C4×C191—41no—
171C4×C191—41no—
172C4×C191—41no—
173C4×C191C2×#4111yescharacteristic
174C4×C191C2×#4111yescharacteristic
175Dic191—21no—
176Dic191—41no—
177Dic191—41no—
178Dic191—41no—
179Dic191#12312yes—
180C2×C191—41no—
181C2×C191—81no—
182C2×C191C2×#12311yescharacteristic
183C2×C191#57611yescharacteristic
184C2×C191#57711yescharacteristic
185D191—22no—
186D191—41no—
187D191—81no—
188C191#309611yescharacteristic, complemented, Sylow
189#3096—1911nomaximal, Sylow
190#535—1911no—
191#520—1911no—
192#482—1911no—
193#482—1911no—
194#482—1911no—
195#482D19111yescharacteristic, complemented
196#481—1911no—
197#481—1911no—
198#480—1911no—
199#480—1911no—
200#428—1911no—
201#427—1911no—
202#418—1911no—
203C2×#102—1911no—
204#408—1911no—
205C2×#41—1911no—
206C22×D4—1911no—
207C2×M16—1911no—
208C22×C8—1911no—
209#127—3821no—
210#124—3821no—
211#121—1911no—
212#121—1911no—
213#121—1911no—
214#121C2×D19111yescharacteristic
215#120—3821no—
216#120—3821no—
217C4×Q8—3821no—
218C4×D4—3821no—
219C4×D4—3821no—
220C4×D4—3821no—
221#117—1911no—
222#117—1911no—
223#117—1911no—
224#117C2×D19111yescharacteristic, complemented
225C2×C4⋊C4—1911no—
226C2×C4⋊C4—1911no—
227C2×C4⋊C4—1911no—
228#107—1911no—
229#107—1911no—
230#107—1911no—
231#107C2×D19111yescharacteristic, complemented
232#106—1911no—
233#106—1911no—
234#106—1911no—
235#106C2×D19111yescharacteristic, complemented
236#102—1911no—
237#102—1911no—
238#102—1911no—
239#102—1911no—
240#102—1911no—
241#102—1911no—
242#102C2×D19111yescharacteristic
243#102C2×D19111yescharacteristic
244C22⋊C8—1911no—
245C22⋊C8—1911no—
246C22⋊C8—1911no—
247C22⋊C8C2×D19111yescharacteristic, complemented
248C24—3821no—
249#41—3822no—
250#41—3822no—
251C2×Q8—1911no—
252C2×D4—21no—
253C2×D4—3821no—
254C2×D4—3821no—
255C2×D4—3821no—
256C2×D4—3822no—
257C2×D4—3822no—
258C2×D4—3821no—
259C2×D4—1911no—
260C2×D4—1911no—
261C2×D4—1911no—
262C2×D4—1911no—
263C2×D4C22×D19111yescharacteristic
264C22×C4—3821no—
265C22×C4—3821no—
266C22×C4—3821no—
267C22×C4—1911no—
268C22×C4—1911no—
269C22×C4C22×D19111yescharacteristic
270M16—3822no—
271C2×C8—3822no—
272C2×C8—1911no—
273C2×C8—1911no—
274C2×C8C22×D19111yescharacteristic
275C2×C8C22×D19111yescharacteristic
276C4⋊C4—3821no—
277C4⋊C4—3821no—
278C4⋊C4—3821no—
279C4⋊C4—1911no—
280C4⋊C4—1911no—
281C4⋊C4—1911no—
282C4⋊C4C22×D19111yescharacteristic
283C4⋊C4C22×D19111yescharacteristic
284C4⋊C4C22×D19111yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—3821no—
288C22⋊C4—3821no—
289C22⋊C4—3821no—
290C22⋊C4—3821no—
291C22⋊C4—3821no—
292C22⋊C4—3821no—
293C42—21no—
294C42—3821no—
295C42—3821no—
296C42—3821no—
297C23—21no—
298C23—3821no—
299C23—1911no—
300C23—1911no—
301C23—15281no—
302C23—15281no—
303C23—7642no—
304C23D4×D19111yescharacteristic
305Q8—3822no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—3822no—
310D4—3822no—
311D4—3822no—
312D4—3821no—
313D4—3821no—
314D4—15281no—
315D4—15281no—
316D4—15281no—
317D4—7642no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—3821no—
324C2×C4—3821no—
325C2×C4—3821no—
326C2×C4—3821no—
327C2×C4—3821no—
328C2×C4—1911no—
329C2×C4—1911no—
330C2×C4—1912no—
331C2×C4—1912no—
332C2×C4—15281no—
333C2×C4—15281no—
334C2×C4—15281no—
335C2×C4D4×D19111yescharacteristic
336C2×C4C23×D19111yescharacteristic
337C8—21no—
338C8—21no—
339C8—3821no—
340C8—3821no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—3821no—
348C22—3821no—
349C22—3821no—
350C22—3821no—
351C22—3821no—
352C22—1912no—
353C22—15284no—
354C22—7641no—
355C22—7641no—
356C22—7641no—
357C22C2×D4×D19111yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—3821no—
363C4—1912no—
364C4—7641no—
365C4—7641no—
366C4—7641no—
367C4#41×D19111yescharacteristic
368C4#41×D19111yescharacteristic
369C2—41no—
370C2—81no—
371C2—3822no—
372C2—15281no—
373C2—7641no—
374C2#123×D19111yescharacteristic
375C2#2713346711yescharacteristic
376C2#2713347011yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#482×C191C2
socleC22×C191C22×D4
prime radical#27133229C2
hypercenter#482D191
hypocenterC191#3096
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #27133143C2semidirect
3. #27132989C2semidirect
4. #27132987C2semidirect
5. #27132986C2semidirect
6. #27132982C2semidirect
7. #27132980C2semidirect
8. #27132978C2semidirect
9. #27132974C2semidirect
10. #27132704C2semidirect
11. #27132698C2semidirect
12. #27132666C2semidirect
13. #102×D191C2semidirect
14. #27132628C2semidirect
15. #482×C191C2semidirect
33. #20259280C22semidirect
34. C2×C4⋊Dic191C22semidirect
36. C4⋊C4×D191C22semidirect
37. #20259255C22semidirect
38. #20259255C22semidirect
39. #20259255C22semidirect
40. #20259254C22semidirect
41. #20259254C22semidirect
42. #20259253C22semidirect
49. C22⋊(C191⋊C8)C22semidirect
50. (C2×D191)⋊C8C22semidirect
51. (C2×D191)⋊C8C22semidirect
53. #117×C191C22semidirect
54. #107×C191C22semidirect
55. #106×C191C22semidirect
58. C22⋊C8×C191C22semidirect
188. C191#3096semidirect
195. #482D191semidirect
224. #117C2×D191semidirect
231. #107C2×D191semidirect
235. #106C2×D191semidirect
247. C22⋊C8C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271332292
#271331432
#271329892
#271329872
#271329862
#271329822
#271329802
#271329782
#271329742
#271327042
#271326982
#271326662
#102×D1912
#271326282
#482×C1912
#3096191