Finite Group Databasebeta

← #37582663

Subgroups — #37582663

Order 24448.

450 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133198C211yesmaximal, characteristic, complemented
2C4×D4×D191C211yesmaximal, characteristic, complemented
3#27132995C211yesmaximal, characteristic, complemented
4#27132978C211yesmaximal, characteristic, complemented
5#27132960C211yesmaximal, characteristic, complemented
6#27132879C211yesmaximal, characteristic, complemented
7#27132878C211yesmaximal, characteristic, complemented
8#27132815C211yesmaximal, characteristic, complemented
9#27132798C211yesmaximal, characteristic
10#27132774C211yesmaximal, characteristic, complemented
11#27132772C211yesmaximal, characteristic, complemented
12#27132762C211yesmaximal, characteristic, complemented
13#27132760C211yesmaximal, characteristic, complemented
14#27132719C211yesmaximal, characteristic, complemented
15#478×C191C211yesmaximal, characteristic, complemented
16C2×D4×D191C2211yescharacteristic
17C22×C4×D191—21no—
18C2×#15690276C2211yescharacteristic
19C2×#15690275C2211yescharacteristic
20C2×D1528C2211yescharacteristic
21C2×#15690272C2211yescharacteristic
22#20259317—21no—
23#20259310C2211yescharacteristic, complemented
24#20259307—21no—
25#20259302C2211yescharacteristic
26#20259297C2211yescharacteristic
27#20259287C2211yescharacteristic, complemented
28C4×D764C2211yescharacteristic
29D4×Dic191C2211yescharacteristic
30#20259284—21no—
31#20259284C2211yescharacteristic
32#20259284C2211yescharacteristic, complemented
33C4×C22⋊D191—21no—
34(C22⋊D191)⋊C4—21no—
35#20259280—21no—
36C4⋊C4×D191C2211yescharacteristic
37C22⋊C4×D191—21no—
38C42×D191C2211yescharacteristic
39#20259255C2211yescharacteristic, complemented
40#20259253C2211yescharacteristic, complemented
41C4⋊(C191⋊C8)C2211yescharacteristic, complemented
42#20259247C2211yescharacteristic, complemented
43#20259245C2211yescharacteristic, complemented
44#20259244C2211yescharacteristic, complemented
45#20259242C2211yescharacteristic
46#20259242C2211yescharacteristic
47#20259242C2211yescharacteristic, complemented
48(C2×D191)⋊C8C2211yescharacteristic
49(C2×D191)⋊C8C2211yescharacteristic
50#20259232C2211yescharacteristic, complemented
51#20259232C2211yescharacteristic, complemented
52#125×C191C2211yescharacteristic, complemented
53C4×D4×C191C2211yescharacteristic
54#107×C191C2211yescharacteristic, complemented
55#106×C191C2211yescharacteristic, complemented
56C4⋊C8×C191C2211yescharacteristic, complemented
57#102×C191C2211yescharacteristic
58#102×C191C2211yescharacteristic
59C23×D191—21no—
60C2×Dic382C2311yescharacteristic
61C2×D764—21no—
62C2×D764C2311yescharacteristic
63C2×D764C2311yescharacteristic
64C2×C22⋊D191—21no—
65D4×D191—22no—
66D4×D191—22no—
67C22×Dic191—21no—
68C2×C4×D191—21no—
69C2×C4×D191—21no—
70C2×C4×D191—21no—
71C2×C4×D191—21no—
72C2×C4×D191—44no—
73C2×C4×D191D411yescharacteristic
74C2×C4×D191D411yescharacteristic
75C2×C4×D191C2311yescharacteristic
76#15690276—22no—
77#15690275—22no—
78D1528—22no—
79#15690272—22no—
80C2×C191⋊C8C2311yescharacteristic
81C2×C191⋊C8C2311yescharacteristic
82C4⋊Dic191—21no—
83C4⋊Dic191C2311yescharacteristic
84Dic191⋊C4—21no—
85Dic191⋊C4—21no—
86C22⋊Dic191—21no—
87(C2×D191)⋊C4—21no—
88(C2×D191)⋊C4—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×Dic191D411yescharacteristic
96C4×Dic191D411yescharacteristic
97C4×Dic191C2311yescharacteristic
98C2×D4×C191C2311yescharacteristic
99C22×C4×C191—21no—
100C2×C8×C191C2311yescharacteristic
101C2×C8×C191C2311yescharacteristic
102C4⋊C4×C191—21no—
103C4⋊C4×C191—21no—
104C4⋊C4×C191C2311yescharacteristic
105C4⋊C4×C191C2311yescharacteristic
106C4⋊C4×C191C2311yescharacteristic
107C22⋊C4×C191—21no—
108C42×C191C2311yescharacteristic
109C22×D191—24no—
110C22×D191—21no—
111C22×D191—21no—
112C22×D191—42no—
113C22×D191—42no—
114C22×D191C2×D411yescharacteristic
115Dic382—21no—
116Dic382—21no—
117D764—21no—
118D764—21no—
119D764—21no—
120D764—42no—
121D764#4112yes—
122C22⋊D191—24no—
123C2×Dic191—21no—
124C2×Dic191—21no—
125C2×Dic191—42no—
126C2×Dic191C2×D411yescharacteristic
127C2×Dic191C2×D411yescharacteristic
128C2×Dic191C2×D411yescharacteristic
129C4×D191—22no—
130C4×D191—21no—
131C4×D191—21no—
132C4×D191—41no—
133C4×D191—42no—
134C4×D191—42no—
135C4×D191—42no—
136C4×D191—42no—
137C191⋊C8—21no—
138C191⋊C8—21no—
139C23×C191—21no—
140D4×C191—21no—
141D4×C191#4112yes—
142C2×C4×C191—21no—
143C2×C4×C191—21no—
144C2×C4×C191—21no—
145C2×C4×C191—42no—
146C2×C4×C191C2×D411yescharacteristic
147C2×C4×C191C2×D411yescharacteristic
148C2×C4×C191C2411yescharacteristic
149C8×C191—21no—
150C8×C191—21no—
151C22×C191—22no—
152C22×C191—41no—
153C22×C191—41no—
154C22×C191C22×D411yescharacteristic
155C2×D191—21no—
156C2×D191—21no—
157C2×D191—22no—
158C2×D191—48no—
159C2×D191—41no—
160C2×D191—41no—
161C2×D191—41no—
162C2×D191—41no—
163C2×D191—41no—
164C2×D191AGL(1,ℤ/8)12yes—
165C4×C191—21no—
166C4×C191—21no—
167C4×C191—41no—
168C4×C191—41no—
169C4×C191—41no—
170C4×C191C2×#4111yescharacteristic
171C4×C191C2×#4111yescharacteristic
172Dic191—21no—
173Dic191—21no—
174Dic191—21no—
175Dic191—41no—
176Dic191—41no—
177C2×C191—42no—
178C2×C191#52511yescharacteristic
179C2×C191C2×AGL(1,ℤ/8)11yescharacteristic
180C2×C191#57511yescharacteristic
181D191—22no—
182D191—42no—
183D191—81no—
184C191#311411yescharacteristic, complemented, Sylow
185#3114—1911nomaximal, Sylow
186#529—1911no—
187C2×C4×D4—1911no—
188#483—1911no—
189#480—1911no—
190#478—1911no—
191#478D19111yescharacteristic, complemented
192#463—1911no—
193#463—1911no—
194#450—1911no—
195#447—1911no—
196#442—1911no—
197#442—1911no—
198#440—1911no—
199#440—1911no—
200#432—1911no—
201C22×D4—1911no—
202C23×C4—3821no—
203C2×SD16—1911no—
204C2×SD16—1911no—
205C2×D8—1911no—
206C2×D8—1911no—
207#126—3821no—
208#125C2×D19111yescharacteristic, complemented
209#124—1911no—
210#123—3821no—
211C22⋊Q8—1911no—
212#121—1911no—
213C4×Q8—1911no—
214C4×D4—3821no—
215C4×D4—3821no—
216C4×D4—3821no—
217C4×D4—1911no—
218C4×D4—1911no—
219C4×D4—1911no—
220C4×D4—1911no—
221C4×D4C2×D19111yescharacteristic
222#117—3821no—
223C2×C4⋊C4—1911no—
224C2×C22⋊C4—3821no—
225C2×C42—1911no—
226#107—1911no—
227#107C2×D19111yescharacteristic, complemented
228#106—1911no—
229#106C2×D19111yescharacteristic, complemented
230C4⋊C8—1911no—
231C4⋊C8C2×D19111yescharacteristic, complemented
232#103—1911no—
233#103—1911no—
234#102—1911no—
235#102—1911no—
236#102—1911no—
237#102—1911no—
238#102C2×D19111yescharacteristic
239#102C2×D19111yescharacteristic
240C22⋊C8—1911no—
241C22⋊C8—1911no—
242#97—1911no—
243#97—1911no—
244C24—3821no—
245C2×Q8—1911no—
246C2×D4—3821no—
247C2×D4—3822no—
248C2×D4—3822no—
249C2×D4—3821no—
250C2×D4—1911no—
251C2×D4—1911no—
252C2×D4C22×D19111yescharacteristic
253C22×C4—21no—
254C22×C4—3821no—
255C22×C4—3821no—
256C22×C4—3821no—
257C22×C4—3821no—
258C22×C4—3821no—
259C22×C4—1911no—
260C22×C4—1911no—
261C22×C4—1911no—
262C22×C4—7644no—
263SD16—3822no—
264SD16—3822no—
265D8—3822no—
266D8—3822no—
267C2×C8—1911no—
268C2×C8—1911no—
269C2×C8C22×D19111yescharacteristic
270C2×C8C22×D19111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—3821no—
274C4⋊C4—3821no—
275C4⋊C4—3821no—
276C4⋊C4—1911no—
277C4⋊C4C22×D19111yescharacteristic
278C4⋊C4C22×D19111yescharacteristic
279C4⋊C4C22×D19111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—3821no—
282C22⋊C4—3821no—
283C22⋊C4—3821no—
284C22⋊C4—3821no—
285C22⋊C4—3821no—
286C22⋊C4—3821no—
287C22⋊C4—3821no—
288C22⋊C4—3821no—
289C42—3821no—
290C42—1911no—
291C42—1911no—
292C42—1911no—
293C42C22×D19111yescharacteristic
294C23—21no—
295C23—3824no—
296C23—3821no—
297C23—3821no—
298C23—1911no—
299C23—7642no—
300C23—7642no—
301Q8—3821no—
302Q8—3821no—
303D4—21no—
304D4—3824no—
305D4—3821no—
306D4—3821no—
307D4—3821no—
308D4—1912no—
309D4—7642no—
310D4#1569028812yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—3822no—
316C2×C4—3821no—
317C2×C4—3821no—
318C2×C4—3821no—
319C2×C4—3821no—
320C2×C4—1911no—
321C2×C4—1911no—
322C2×C4—1911no—
323C2×C4—7641no—
324C2×C4—7642no—
325C2×C4—7642no—
326C2×C4—7642no—
327C2×C4—7642no—
328C2×C4—7642no—
329C2×C4D4×D19111yescharacteristic
330C2×C4D4×D19111yescharacteristic
331C2×C4C23×D19111yescharacteristic
332C8—21no—
333C8—21no—
334C8—3821no—
335C8—3821no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—3821no—
340C22—3821no—
341C22—3822no—
342C22—1912no—
343C22—7648no—
344C22—7641no—
345C22—7641no—
346C22—7641no—
347C22—7641no—
348C22—7641no—
349C22C2×D4×D19111yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—3821no—
356C4—3821no—
357C4—3821no—
358C4—7641no—
359C4—7641no—
360C4#41×D19111yescharacteristic
361C4C2×#1569028811yescharacteristic
362C2—42no—
363C2—3822no—
364C2—15281no—
365C2—7642no—
366C2#2713317611yescharacteristic
367C2AGL(1,ℤ/8)×D19111yescharacteristic
368C2#2713346011yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#478×C191C2
socleC22×C191C22×D4
prime radical#27132798C2
hypercenter#478D191
hypocenterC191#3114
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #27133198C2semidirect
2. C4×D4×D191C2semidirect
3. #27132995C2semidirect
4. #27132978C2semidirect
5. #27132960C2semidirect
6. #27132879C2semidirect
7. #27132878C2semidirect
8. #27132815C2semidirect
10. #27132774C2semidirect
11. #27132772C2semidirect
12. #27132762C2semidirect
13. #27132760C2semidirect
14. #27132719C2semidirect
15. #478×C191C2semidirect
23. #20259310C22semidirect
27. #20259287C22semidirect
32. #20259284C22semidirect
39. #20259255C22semidirect
40. #20259253C22semidirect
41. C4⋊(C191⋊C8)C22semidirect
42. #20259247C22semidirect
43. #20259245C22semidirect
44. #20259244C22semidirect
47. #20259242C22semidirect
50. #20259232C22semidirect
51. #20259232C22semidirect
52. #125×C191C22semidirect
54. #107×C191C22semidirect
55. #106×C191C22semidirect
56. C4⋊C8×C191C22semidirect
184. C191#3114semidirect
191. #478D191semidirect
208. #125C2×D191semidirect
227. #107C2×D191semidirect
229. #106C2×D191semidirect
231. C4⋊C8C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271331982
C4×D4×D1912
#271329952
#271329782
#271329602
#271328792
#271328782
#271328152
#271327982
#271327742
#271327722
#271327622
#271327602
#271327192
#478×C1912
#3114191