Finite Group Databasebeta

← #34078905

Subgroups — #34078905

Order 19328.

440 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752768C211yesmaximal, characteristic, complemented
2C4×D4×D151C211yesmaximal, characteristic
3#23752513C211yesmaximal, characteristic, complemented
4#23752512C211yesmaximal, characteristic, complemented
5#23752509C211yesmaximal, characteristic, complemented
6#23752501C211yesmaximal, characteristic, complemented
7#23752500C211yesmaximal, characteristic, complemented
8#23752491C211yesmaximal, characteristic, complemented
9#23752490C211yesmaximal, characteristic, complemented
10#23752253C211yesmaximal, characteristic, complemented
11#23752251C211yesmaximal, characteristic, complemented
12#23752234C211yesmaximal, characteristic, complemented
13#23752215C211yesmaximal, characteristic
14#23752215C211yesmaximal, characteristic
15#478×C151C211yesmaximal, characteristic, complemented
16C2×D4×D151C2211yescharacteristic
17C22×C4×D151—21no—
18C2×#14558987C2211yescharacteristic
19C2×#14558987C2211yescharacteristic
20#18012738C2211yescharacteristic, complemented
21#18012738C2211yescharacteristic, complemented
22#18012731C2211yescharacteristic, complemented
23#18012717—21no—
24#18012717—21no—
25#18012704—21no—
26#18012704—21no—
27C4×D604C2211yescharacteristic
28D4×Dic151C2211yescharacteristic
29#18012701C2211yescharacteristic
30C4×C22⋊D151—21no—
31(C22⋊D151)⋊C4—21no—
32#18012697C2211yescharacteristic
33#18012697C2211yescharacteristic
34C4⋊C4×D151C2211yescharacteristic
35C22⋊C4×D151—21no—
36C42×D151C2211yescharacteristic
37#18012673C2211yescharacteristic, complemented
38#18012672C2211yescharacteristic, complemented
39#18012672C2211yescharacteristic, complemented
40#18012671C2211yescharacteristic, complemented
41#18012670C2211yescharacteristic, complemented
42#18012670C2211yescharacteristic, complemented
43C4⋊(C151⋊C8)C2211yescharacteristic, complemented
44Dic151⋊C8C2211yescharacteristic, complemented
45Dic151⋊C8C2211yescharacteristic, complemented
46#18012661C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012660C2211yescharacteristic
49#18012660C2211yescharacteristic
50#18012659C2211yescharacteristic
51#18012659C2211yescharacteristic
52#125×C151C2211yescharacteristic, complemented
53C4×D4×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic, complemented
55#106×C151C2211yescharacteristic, complemented
56C4⋊C8×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59C23×D151—21no—
60C2×Dic302—21no—
61C2×Dic302—21no—
62C2×D604C2311yescharacteristic
63C2×C22⋊D151—21no—
64D4×D151—22no—
65D4×D151Q814yescomplemented
66C22×Dic151—21no—
67C2×C4×D151—21no—
68C2×C4×D151—21no—
69C2×C4×D151—21no—
70C2×C4×D151—44no—
71C2×C4×D151D411yescharacteristic
72C2×C4×D151D411yescharacteristic
73C2×C4×D151C2311yescharacteristic
74#14558987—22no—
75#14558987—22no—
76C2×C151⋊C8C2311yescharacteristic
77C2×C151⋊C8C2311yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79C4⋊Dic151C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86C22⋊Dic151—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91C4×Dic151—21no—
92C4×Dic151—21no—
93C4×Dic151D411yescharacteristic
94C4×Dic151D411yescharacteristic
95C4×Dic151C2311yescharacteristic
96C2×D4×C151C2311yescharacteristic
97C22×C4×C151—21no—
98C2×C8×C151C2311yescharacteristic
99C2×C8×C151C2311yescharacteristic
100C4⋊C4×C151—21no—
101C4⋊C4×C151—21no—
102C4⋊C4×C151C2311yescharacteristic
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C22⋊C4×C151—21no—
106C42×C151C2311yescharacteristic
107C22×D151—21no—
108C22×D151—24no—
109C22×D151—42no—
110C22×D151—42no—
111C22×D151C2×D411yescharacteristic
112Dic302—42no—
113Dic302—42no—
114D604—21no—
115D604C2×Q812yes—
116C22⋊D151—24no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—42no—
121C2×Dic151C2×D411yescharacteristic
122C2×Dic151C2×D411yescharacteristic
123C2×Dic151C2×D411yescharacteristic
124C4×D151—22no—
125C4×D151—41no—
126C4×D151—42no—
127C4×D151—42no—
128C4×D151—42no—
129C4×D151C2×Q812yes—
130C4×D151#4112yes—
131C151⋊C8—21no—
132C151⋊C8—21no—
133C23×C151—21no—
134D4×C151—21no—
135D4×C151C2×Q812yes—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—42no—
140C2×C4×C151C2×D411yescharacteristic
141C2×C4×C151C2×D411yescharacteristic
142C2×C4×C151C2411yescharacteristic
143C8×C151—21no—
144C8×C151—21no—
145C22×C151—22no—
146C22×C151—41no—
147C22×C151—41no—
148C22×C151C22×D411yescharacteristic
149C2×D151—21no—
150C2×D151—21no—
151C2×D151—22no—
152C2×D151—48no—
153C2×D151—41no—
154C2×D151—41no—
155C2×D151C22⋊Q812yes—
156C4×C151—21no—
157C4×C151—21no—
158C4×C151—41no—
159C4×C151—41no—
160C4×C151—41no—
161C4×C151C22×Q811yescharacteristic
162C4×C151C2×#4111yescharacteristic
163Dic151—21no—
164Dic151—41no—
165Dic151—41no—
166Dic151—41no—
167Dic151C22⋊Q812yes—
168Dic151AGL(1,ℤ/8)12yes—
169C2×C151—42no—
170C2×C151C2×C22⋊Q811yescharacteristic
171C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
172C2×C151#57511yescharacteristic
173D151—22no—
174D151—42no—
175C151#307711yescharacteristic, complemented, Sylow
176#3077—1511nomaximal, Sylow
177#533—1511no—
178C2×C4×D4—1511no—
179#478—1511no—
180#478—1511no—
181#478—1511no—
182#478D15111yescharacteristic, complemented
183#476—1511no—
184#476—1511no—
185#474—1511no—
186#474—1511no—
187#428—1511no—
188#428—1511no—
189#423—1511no—
190#418—1511no—
191#418—1511no—
192C22×D4—1511no—
193C23×C4—3021no—
194C2×M16—1511no—
195C2×M16—1511no—
196C4⋊Q8—1511no—
197C4⋊Q8—1511no—
198#125—1511no—
199#125C2×D15111yescharacteristic, complemented
200C22⋊Q8—3021no—
201C22⋊Q8—3021no—
202C4×Q8—3021no—
203C4×Q8—3021no—
204C4×D4—3021no—
205C4×D4—3021no—
206C4×D4—1511no—
207C4×D4—1511no—
208C4×D4—1511no—
209C4×D4C2×D15111yescharacteristic
210#117—1511no—
211#117—1511no—
212C2×C4⋊C4—1511no—
213C2×C22⋊C4—3021no—
214C2×C42—1511no—
215#107—1511no—
216#107—1511no—
217#107—1511no—
218#107C2×D15111yescharacteristic, complemented
219#106—1511no—
220#106—1511no—
221#106—1511no—
222#106C2×D15111yescharacteristic, complemented
223C4⋊C8—1511no—
224C4⋊C8—1511no—
225C4⋊C8—1511no—
226C4⋊C8C2×D15111yescharacteristic, complemented
227#102—1511no—
228#102—1511no—
229#102—1511no—
230#102—1511no—
231#102—1511no—
232#102—1511no—
233#102C2×D15111yescharacteristic
234#102C2×D15111yescharacteristic
235C24—3021no—
236C2×Q8—3021no—
237C2×Q8—3021no—
238C2×D4—3022no—
239C2×D4—3021no—
240C2×D4—1514no—
241C2×D4—1511no—
242C2×D4C22×D15111yescharacteristic
243C22×C4—21no—
244C22×C4—3021no—
245C22×C4—3021no—
246C22×C4—3021no—
247C22×C4—3021no—
248C22×C4—6044no—
249C22×C4—1511no—
250C22×C4—1511no—
251C22×C4—1511no—
252M16—3022no—
253M16—3022no—
254C2×C8—1511no—
255C2×C8—1511no—
256C2×C8C22×D15111yescharacteristic
257C2×C8C22×D15111yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—3021no—
261C4⋊C4—3021no—
262C4⋊C4—3021no—
263C4⋊C4—3021no—
264C4⋊C4—3021no—
265C4⋊C4—1511no—
266C4⋊C4—1511no—
267C4⋊C4—1511no—
268C4⋊C4C22×D15111yescharacteristic
269C4⋊C4C22×D15111yescharacteristic
270C4⋊C4C22×D15111yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—3021no—
273C22⋊C4—3021no—
274C22⋊C4—3021no—
275C22⋊C4—3021no—
276C22⋊C4—3021no—
277C42—3021no—
278C42—3021no—
279C42—1511no—
280C42—1511no—
281C42—1511no—
282C42C22×D15111yescharacteristic
283C23—21no—
284C23—3024no—
285C23—3021no—
286C23—6042no—
287C23—6042no—
288C23—1511no—
289Q8—6042no—
290Q8—6042no—
291D4—21no—
292D4—3024no—
293D4—3021no—
294D4—1512no—
295D4Q8×D15112yes—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—3022no—
301C2×C4—3021no—
302C2×C4—3021no—
303C2×C4—3021no—
304C2×C4—6041no—
305C2×C4—6042no—
306C2×C4—6042no—
307C2×C4—6042no—
308C2×C4—6042no—
309C2×C4—1511no—
310C2×C4—1511no—
311C2×C4—1511no—
312C2×C4—1512no—
313C2×C4—1512no—
314C2×C4D4×D15111yescharacteristic
315C2×C4D4×D15111yescharacteristic
316C2×C4C23×D15111yescharacteristic
317C8—21no—
318C8—21no—
319C8—3021no—
320C8—3021no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—3021no—
325C22—3021no—
326C22—3022no—
327C22—6048no—
328C22—6041no—
329C22—6041no—
330C22—1512no—
331C22C2×D4×D15111yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—3021no—
338C4—6041no—
339C4—6041no—
340C4—6041no—
341C4—1512no—
342C4—1512no—
343C4C2×Q8×D15111yescharacteristic
344C4#41×D15111yescharacteristic
345C2—42no—
346C2—3022no—
347C2—6042no—
348C2C22⋊Q8×D15111yescharacteristic
349C2AGL(1,ℤ/8)×D15111yescharacteristic
350C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#478×C151C2
socleC22×C151C22×D4
prime radicalC2×D4×D151C22
hypercenter#478D151
hypocenterC151#3077
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #23752768C2semidirect
3. #23752513C2semidirect
4. #23752512C2semidirect
5. #23752509C2semidirect
6. #23752501C2semidirect
7. #23752500C2semidirect
8. #23752491C2semidirect
9. #23752490C2semidirect
10. #23752253C2semidirect
11. #23752251C2semidirect
12. #23752234C2semidirect
15. #478×C151C2semidirect
20. #18012738C22semidirect
21. #18012738C22semidirect
22. #18012731C22semidirect
37. #18012673C22semidirect
38. #18012672C22semidirect
39. #18012672C22semidirect
40. #18012671C22semidirect
41. #18012670C22semidirect
42. #18012670C22semidirect
43. C4⋊(C151⋊C8)C22semidirect
44. Dic151⋊C8C22semidirect
45. Dic151⋊C8C22semidirect
52. #125×C151C22semidirect
54. #107×C151C22semidirect
55. #106×C151C22semidirect
56. C4⋊C8×C151C22semidirect
65. D4×D151Q8semidirect
175. C151#3077semidirect
182. #478D151semidirect
199. #125C2×D151semidirect
218. #107C2×D151semidirect
222. #106C2×D151semidirect
226. C4⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527682
C4×D4×D1512
#237525132
#237525122
#237525092
#237525012
#237525002
#237524912
#237524902
#237522532
#237522512
#237522342
#237522152
#478×C1512
#3077151