Finite Group Databasebeta

← #37581349

Subgroups — #37581349

Order 24448.

506 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
1C2×#20259346C211yesmaximal, characteristic
2#27133142C211yesmaximal, characteristic, complemented
3#27133135C211yesmaximal, characteristic, complemented
4#27132772C211yesmaximal, characteristic, complemented
5#27132765C211yesmaximal, characteristic, complemented
6#27132760C211yesmaximal, characteristic, complemented
7#27132750C211yesmaximal, characteristic, complemented
8C4×#15690275C211yesmaximal, characteristic, complemented
9D8×Dic191C211yesmaximal, characteristic, complemented
10C4×#15690272C211yesmaximal, characteristic, complemented
11#27132702C211yesmaximal, characteristic, complemented
12#27132656C211yesmaximal, characteristic, complemented
13#102×D191C211yesmaximal, characteristic, complemented
14#27132620C211yesmaximal, characteristic, complemented
15#442×C191C211yesmaximal, characteristic, complemented
16C2×#15690286C2211yescharacteristic
17C2×D4×D191C2211yescharacteristic
18#20259346C418yescomplemented
19C2×#15690276C2211yescharacteristic
20C2×#15690275C2211yescharacteristic
21C2×#15690272C2211yescharacteristic
22C2×#15690270C2211yescharacteristic
23C2×C8×D191C2211yescharacteristic
24C4×Dic382C2211yescharacteristic, complemented
25#20259287C2211yescharacteristic, complemented
26C4×D764C2211yescharacteristic
27D4×Dic191C2211yescharacteristic
28D4×Dic191C2211yescharacteristic, complemented
29#20259284C2211yescharacteristic
30C4×C22⋊D191—21no—
31C4×C22⋊D191—21no—
32(C22⋊D191)⋊C4—21no—
33(C22⋊D191)⋊C4—21no—
34#20259280C2211yescharacteristic
35#20259279C2211yescharacteristic
36#20259278—21no—
37C2×Dic191⋊C4—21no—
38C4⋊C4×D191C2211yescharacteristic
39C2×(C2×D191)⋊C4—21no—
40C22⋊C4×D191—21no—
41#20259256C2211yescharacteristic, complemented
42#20259255C2211yescharacteristic, complemented
43#20259253C2211yescharacteristic, complemented
44#20259247C2211yescharacteristic, complemented
45#20259245C2211yescharacteristic, complemented
46#20259244C2211yescharacteristic
47#20259243C2211yescharacteristic
48#20259243C2211yescharacteristic, complemented
49#20259242C2211yescharacteristic
50#20259232C2211yescharacteristic, complemented
51C4×C191⋊C8C2211yescharacteristic, complemented
52C8×Dic191C2211yescharacteristic, complemented
53C2×D8×C191C2211yescharacteristic
54C4×D4×C191C2211yescharacteristic
55C4×D4×C191C2211yescharacteristic, complemented
56#106×C191C2211yescharacteristic, complemented
57#102×C191C2211yescharacteristic
58#102×C191C2211yescharacteristic, complemented
59#97×C191C2211yescharacteristic, complemented
60C23×D191—21no—
61#15690286—22no—
62#15690286C2×C414yescomplemented
63C2×Dic382C2311yescharacteristic
64C2×D764C2311yescharacteristic
65C2×C22⋊D191—21no—
66C2×C22⋊D191—21no—
67D4×D191—22no—
68D4×D191C2×C414yescomplemented
69C22×Dic191—21no—
70C22×Dic191—21no—
71C22×Dic191—21no—
72C2×C4×D191—21no—
73C2×C4×D191—21no—
74C2×C4×D191—21no—
75C2×C4×D191C2311yescharacteristic
76#15690276C2×C414yescomplemented
77#15690275C2×C414yescomplemented
78#15690272C2×C414yescomplemented
79#15690270C2×C414yescomplemented
80C2×C191⋊C8C2311yescharacteristic
81C2×C191⋊C8C2311yescharacteristic
82C8×D191—22no—
83C4⋊Dic191C2311yescharacteristic
84C4⋊Dic191C2311yescharacteristic
85Dic191⋊C4—21no—
86Dic191⋊C4—21no—
87Dic191⋊C4—21no—
88Dic191⋊C4D411yescharacteristic
89Dic191⋊C4D411yescharacteristic
90C22⋊Dic191—21no—
91C22⋊Dic191—21no—
92(C2×D191)⋊C4—21no—
93(C2×D191)⋊C4—21no—
94(C2×D191)⋊C4—21no—
95(C2×D191)⋊C4D411yescharacteristic
96(C2×D191)⋊C4D411yescharacteristic
97C4×Dic191—21no—
98C4×Dic191—21no—
99C4×Dic191—21no—
100C4×Dic191C2311yescharacteristic
101C2×D4×C191C2311yescharacteristic
102C2×D4×C191C2311yescharacteristic
103C22×C4×C191—21no—
104C22×C4×C191—21no—
105D8×C191C2×C414yescomplemented
106C2×C8×C191C2311yescharacteristic
107C2×C8×C191C2311yescharacteristic
108C4⋊C4×C191C2311yescharacteristic
109C4⋊C4×C191C2311yescharacteristic
110C22⋊C4×C191—21no—
111C22⋊C4×C191—21no—
112C42×C191C2311yescharacteristic
113C22×D191—21no—
114C22×D191—24no—
115C22×D191—81no—
116C22×D191—81no—
117C22×D191C2×D411yescharacteristic
118Dic382—21no—
119Dic382C22×C412yes—
120D764—21no—
121D764C22×C412yes—
122C22⋊D191—24no—
123C22⋊D191—24no—
124C2×Dic191—21no—
125C2×Dic191—24no—
126C2×Dic191—21no—
127C2×Dic191—21no—
128C2×Dic191—81no—
129C2×Dic191—81no—
130C2×Dic191C2×D411yescharacteristic
131C2×Dic191C2×D411yescharacteristic
132C2×Dic191C2×D411yescharacteristic
133C4×D191—81no—
134C4×D191—81no—
135C4×D191—81no—
136C4×D191C22×C412yes—
137C4×D191#4112yes—
138C191⋊C8—21no—
139C191⋊C8C22×C412yes—
140C23×C191—21no—
141C23×C191—21no—
142D4×C191—21no—
143D4×C191—21no—
144D4×C191C22×C412yes—
145D4×C191C22×C412yes—
146C2×C4×C191—21no—
147C2×C4×C191—21no—
148C2×C4×C191—81no—
149C2×C4×C191—81no—
150C2×C4×C191C2×D411yescharacteristic
151C2×C4×C191C2×D411yescharacteristic
152C2×C4×C191C2411yescharacteristic
153C8×C191—21no—
154C8×C191C22×C412yes—
155C22×C191—22no—
156C22×C191—22no—
157C22×C191—41no—
158C22×C191—41no—
159C22×C191—41no—
160C22×C191—41no—
161C22×C191C22×D411yescharacteristic
162C2×D191—21no—
163C2×D191—21no—
164C2×D191—22no—
165C2×D191—41no—
166C2×D191—41no—
167C2×D191—84no—
168C2×D191C4×D412yes—
169C4×C191—21no—
170C4×C191—21no—
171C4×C191—41no—
172C4×C191—41no—
173C4×C191C23×C411yescharacteristic
174C4×C191C2×#4111yescharacteristic
175Dic191—22no—
176Dic191—21no—
177Dic191—21no—
178Dic191—41no—
179Dic191—41no—
180Dic191C4×D412yes—
181C2×C191—42no—
182C2×C191—42no—
183C2×C191C2×C4×D411yescharacteristic
184C2×C191#57611yescharacteristic
185C2×C191#57711yescharacteristic
186D191—22no—
187D191—42no—
188C191#294611yescharacteristic, complemented, Sylow
189#2946—1911nomaximal, Sylow
190C2×AGL(1,ℤ/8)—1911no—
191#520—1911no—
192#518—1911no—
193#442—1911no—
194#442D19111yescharacteristic, complemented
195#440—1911no—
196#440—1911no—
197C4×SD16—1911no—
198C4×SD16—1911no—
199C4×D8—1911no—
200C4×D8—1911no—
201#428—1911no—
202#416—1911no—
203C2×#102—1911no—
204#405—1911no—
205C2×#41—1911no—
206C22×D4—1911no—
207AGL(1,ℤ/8)—1918no—
208C2×SD16—1911no—
209C2×SD16—1911no—
210C2×D8—1911no—
211C2×D8C2×D19111yescharacteristic
212C2×M16—1911no—
213C22×C8—1911no—
214C4×Q8—1911no—
215C4×Q8—1911no—
216C4×D4—3821no—
217C4×D4—3821no—
218C4×D4—3821no—
219C4×D4—3821no—
220C4×D4—1911no—
221C4×D4—1911no—
222C4×D4—1911no—
223C4×D4—1911no—
224C4×D4C2×D19111yescharacteristic
225C4×D4C2×D19111yescharacteristic, complemented
226#117—3821no—
227#117—1911no—
228#117—1911no—
229C2×C4⋊C4—3821no—
230C2×C4⋊C4—1911no—
231C2×C22⋊C4—3821no—
232C2×C22⋊C4—3821no—
233#107—1911no—
234#107—1911no—
235#106—1911no—
236#106C2×D19111yescharacteristic, complemented
237#103—1911no—
238#103—1911no—
239#102—1911no—
240#102—1911no—
241#102—1911no—
242#102—1911no—
243#102C2×D19111yescharacteristic
244#102C2×D19111yescharacteristic, complemented
245#97—1911no—
246#97C2×D19111yescharacteristic, complemented
247C4×C8—1911no—
248C4×C8—1911no—
249C24—3821no—
250#41—3822no—
251#41—1914no—
252C2×Q8—1911no—
253C2×D4—3821no—
254C2×D4—3822no—
255C2×D4—3821no—
256C2×D4—1914no—
257C2×D4—1911no—
258C2×D4C22×D19111yescharacteristic
259C2×D4C22×D19111yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—3821no—
263C22×C4—3821no—
264C22×C4—3821no—
265C22×C4—3821no—
266C22×C4—3821no—
267C22×C4—3821no—
268C22×C4—1911no—
269SD16—1914no—
270SD16—1914no—
271D8—1914no—
272D8C4×D19114yescomplemented
273M16—1914no—
274C2×C8—3822no—
275C2×C8—1911no—
276C2×C8—1911no—
277C2×C8C22×D19111yescharacteristic
278C2×C8C22×D19111yescharacteristic
279C4⋊C4—3821no—
280C4⋊C4—3821no—
281C4⋊C4—3821no—
282C4⋊C4—1911no—
283C4⋊C4—1911no—
284C4⋊C4—1911no—
285C4⋊C4—1911no—
286C4⋊C4C22×D19111yescharacteristic
287C4⋊C4C22×D19111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—3821no—
291C22⋊C4—3821no—
292C22⋊C4—3821no—
293C22⋊C4—3821no—
294C22⋊C4—3821no—
295C22⋊C4—1911no—
296C22⋊C4—1911no—
297C42—3821no—
298C42—3821no—
299C42—3821no—
300C42—1911no—
301C42C22×D19111yescharacteristic
302C23—21no—
303C23—21no—
304C23—3824no—
305C23—3821no—
306C23—1911no—
307C23—15281no—
308C23—15281no—
309Q8—3821no—
310Q8—1912no—
311D4—21no—
312D4—21no—
313D4—3824no—
314D4—3824no—
315D4—3821no—
316D4—1912no—
317D4C2×C4×D19112yes—
318D4C2×C4×D19112yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—3821no—
324C2×C4—3824no—
325C2×C4—3821no—
326C2×C4—3821no—
327C2×C4—1911no—
328C2×C4—1911no—
329C2×C4—1911no—
330C2×C4—1912no—
331C2×C4—1912no—
332C2×C4—15281no—
333C2×C4—15281no—
334C2×C4—15281no—
335C2×C4—15281no—
336C2×C4—15281no—
337C2×C4D4×D19111yescharacteristic
338C2×C4D4×D19111yescharacteristic
339C2×C4C23×D19111yescharacteristic
340C8—21no—
341C8—3821no—
342C8—1912no—
343C8C2×C4×D19112yes—
344C22—22no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—3821no—
351C22—3821no—
352C22—3822no—
353C22—1912no—
354C22—15284no—
355C22—7641no—
356C22—7641no—
357C22C2×D4×D19111yescharacteristic
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—3821no—
363C4—3821no—
364C4—3822no—
365C4—1912no—
366C4—7641no—
367C4—7641no—
368C4C22×C4×D19111yescharacteristic
369C4#41×D19111yescharacteristic
370C2—42no—
371C2—42no—
372C2—3822no—
373C2—7642no—
374C2C4×D4×D19111yescharacteristic
375C2#2713346711yescharacteristic
376C2#2713347311yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutatorC4×C191C23×C4
FrattiniC2×C4C23×D191
Fitting#442×C191C2
socleC22×C191C22×D4
prime radicalC2×#20259346C2
cosocleC2×C4×C191C24
hypercenter#442D191
hypocenterC191#2946
LCSG ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #27133142C2semidirect
3. #27133135C2semidirect
4. #27132772C2semidirect
5. #27132765C2semidirect
6. #27132760C2semidirect
7. #27132750C2semidirect
8. C4×#15690275C2semidirect
9. D8×Dic191C2semidirect
10. C4×#15690272C2semidirect
11. #27132702C2semidirect
12. #27132656C2semidirect
13. #102×D191C2semidirect
14. #27132620C2semidirect
15. #442×C191C2semidirect
18. #20259346C4semidirect
24. C4×Dic382C22semidirect
25. #20259287C22semidirect
28. D4×Dic191C22semidirect
41. #20259256C22semidirect
42. #20259255C22semidirect
43. #20259253C22semidirect
44. #20259247C22semidirect
45. #20259245C22semidirect
48. #20259243C22semidirect
50. #20259232C22semidirect
51. C4×C191⋊C8C22semidirect
52. C8×Dic191C22semidirect
55. C4×D4×C191C22semidirect
56. #106×C191C22semidirect
58. #102×C191C22semidirect
59. #97×C191C22semidirect
62. #15690286C2×C4semidirect
68. D4×D191C2×C4semidirect
76. #15690276C2×C4semidirect
77. #15690275C2×C4semidirect
78. #15690272C2×C4semidirect
79. #15690270C2×C4semidirect
105. D8×C191C2×C4semidirect
188. C191#2946semidirect
194. #442D191semidirect
225. C4×D4C2×D191semidirect
236. #106C2×D191semidirect
244. #102C2×D191semidirect
246. #97C2×D191semidirect
272. D8C4×D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593462
#271331422
#271331352
#271327722
#271327652
#271327602
#271327502
C4×#156902752
D8×Dic1912
C4×#156902722
#271327022
#271326562
#102×D1912
#271326202
#442×C1912
#2946191