Finite Group Databasebeta

← #34080925

Subgroups — #34080925

Order 19328.

494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752867C211yesmaximal, characteristic, complemented
2D4×D604C211yesmaximal, characteristic, complemented
3#23752559C211yesmaximal, characteristic, complemented
4#23752527C212yesmaximal, complemented
5#23752492C211yesmaximal, characteristic, complemented
6#23752447C212yesmaximal, complemented
7#23752407C211yesmaximal, characteristic, complemented
8#23752344C212yesmaximal, complemented
9C8×D604C211yesmaximal, characteristic, complemented
10#102×D151C212yesmaximal, complemented
11C4×D8×C151C211yesmaximal, characteristic, complemented
12C2×#14559004—21no—
13C22×D604—21no—
14C2×D4×D151C2212yes—
15C2×#14558989C2212yescomplemented
16C2×C8×D151C2212yescomplemented
17#18012739C2211yescharacteristic, complemented
18#18012736C2211yescharacteristic
19#18012721—22no—
20#18012718—21no—
21#18012714C2212yes—
22#18012713—21no—
23#18012710C2212yescomplemented
24#18012709—22no—
25C4×D604C2211yescharacteristic
26C4⋊C4×D151C2212yescomplemented
27#18012672C2212yescomplemented
28C4⋊(C151⋊C8)C2211yescharacteristic, complemented
29#18012661C2212yescomplemented
30#18012661C2212yescomplemented
31#18012660C2212yes—
32#18012659C2212yescomplemented
33(C2×D151)⋊C8C2212yescomplemented
34C2×D8×C151C2211yescharacteristic
35C4×D4×C151C2211yescharacteristic
36C4×D4×C151C2211yescharacteristic, complemented
37#107×C151C2211yescharacteristic, complemented
38#102×C151C2211yescharacteristic
39#102×C151C2211yescharacteristic, complemented
40C4×C8×C151C2211yescharacteristic, complemented
41C23×D151—22no—
42#14559004—44no—
43C2×Dic302—21no—
44C2×D604—22no—
45C2×D604—21no—
46C2×D604—21no—
47C2×D604—44no—
48C2×D604D411yescharacteristic
49C2×D604C2312yes—
50C2×C22⋊D151—22no—
51C2×C22⋊D151—22no—
52D4×D151—24no—
53D4×D151—42no—
54C2×C4×D151—22no—
55C2×C4×D151C2312yes—
56#14558989—42no—
57C2×C151⋊C8C2312yes—
58C8×D151—42no—
59C4⋊Dic151—21no—
60C4⋊Dic151D411yescharacteristic
61C4⋊Dic151C2312yes—
62Dic151⋊C4—22no—
63C22⋊Dic151—22no—
64(C2×D151)⋊C4—22no—
65(C2×D151)⋊C4D412yes—
66C2×D4×C151C2311yescharacteristic
67C2×D4×C151C2311yescharacteristic
68C22×C4×C151—21no—
69C22×C4×C151—21no—
70D8×C151—22no—
71C2×C8×C151C2311yescharacteristic
72C2×C8×C151C2311yescharacteristic
73C4⋊C4×C151C2311yescharacteristic
74C4⋊C4×C151C2311yescharacteristic
75C22⋊C4×C151—21no—
76C22⋊C4×C151—21no—
77C42×C151C2311yescharacteristic
78C22×D151—22no—
79C22×D151—44no—
80C22×D151—44no—
81C22×D151—82no—
82C22×D151C2×D412yes—
83Dic302—42no—
84D604—22no—
85D604—22no—
86D604—44no—
87D604—42no—
88D604—81no—
89D604D814yescomplemented
90C22⋊D151—44no—
91C22⋊D151—44no—
92C2×Dic151—22no—
93C2×Dic151C2×D412yes—
94C4×D151—22no—
95C4×D151—22no—
96C4×D151—44no—
97C151⋊C8—22no—
98C23×C151—21no—
99C23×C151—21no—
100D4×C151—21no—
101D4×C151—21no—
102D4×C151—21no—
103D4×C151#4112yescomplemented
104C2×C4×C151—21no—
105C2×C4×C151—21no—
106C2×C4×C151—42no—
107C2×C4×C151—42no—
108C2×C4×C151C2×D411yescharacteristic
109C2×C4×C151C2×D411yescharacteristic
110C2×C4×C151C2411yescharacteristic
111C8×C151—21no—
112C8×C151—21no—
113C22×C151—22no—
114C22×C151—41no—
115C22×C151—41no—
116C22×C151—41no—
117C22×C151—41no—
118C22×C151—41no—
119C22×C151C22×D411yescharacteristic
120C2×D151—22no—
121C2×D151—22no—
122C2×D151—42no—
123C2×D151—42no—
124C2×D151—42no—
125C2×D151—88no—
126C2×D151C2×D814yes—
127C4×C151—21no—
128C4×C151—41no—
129C4×C151—41no—
130C4×C151C2×D812yes—
131C4×C151C2×#4111yescharacteristic
132C4×C151H(5,𝔽2)11yescharacteristic
133Dic151—22no—
134Dic151—42no—
135C2×C151—42no—
136C2×C151—81no—
137C2×C151#54611yescharacteristic
138C2×C151C22×D811yescharacteristic
139C2×C151#57711yescharacteristic
140D151—24no—
141D151—82no—
142C151#329411yescharacteristic, complemented, Sylow
143#3294—1511nomaximal, Sylow
144#547—1511no—
145D42—1511no—
146#486—1511no—
147#480—1512no—
148#474—1511no—
149#466—1512no—
150#459—1511no—
151#447—1512no—
152C4×D8D15111yescharacteristic, complemented
153C8×D4—1511no—
154C2×#102—1512no—
155C2×#41—3021no—
156C22×D4—3021no—
157C22×D4—1512no—
158C2×D8—1512no—
159C2×D8C2×D15111yescharacteristic
160C22×C8—1512no—
161C4⋊Q8—1511no—
162#127—1511no—
163#123—3022no—
164C22⋊Q8—3021no—
165#121—3021no—
166#121—1512no—
167#121—1512no—
168#120—3022no—
169C4×D4—1511no—
170C4×D4C2×D15111yescharacteristic
171C4×D4C2×D15111yescharacteristic, complemented
172C2×C4⋊C4—1512no—
173#107—1512no—
174#107C2×D15111yescharacteristic, complemented
175C4⋊C8—1511no—
176#102—1512no—
177#102—1512no—
178#102—1512no—
179#102—1512no—
180#102C2×D15111yescharacteristic
181#102C2×D15111yescharacteristic, complemented
182C22⋊C8—1512no—
183C4×C8C2×D15111yescharacteristic, complemented
184C24—3022no—
185#41—6044no—
186C2×Q8—3021no—
187C2×D4—3022no—
188C2×D4—3024no—
189C2×D4—3022no—
190C2×D4—3022no—
191C2×D4—3021no—
192C2×D4—3021no—
193C2×D4—6044no—
194C2×D4—6042no—
195C2×D4—1511no—
196C2×D4—1512no—
197C2×D4C22×D15111yescharacteristic
198C2×D4C22×D15111yescharacteristic
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—3022no—
202C22×C4—1512no—
203D8—22no—
204D8—6042no—
205C2×C8—6042no—
206C2×C8—1512no—
207C2×C8C22×D15111yescharacteristic
208C2×C8C22×D15111yescharacteristic
209C4⋊C4—3022no—
210C4⋊C4—3021no—
211C4⋊C4—1512no—
212C4⋊C4—1511no—
213C4⋊C4C22×D15111yescharacteristic
214C4⋊C4C22×D15111yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—3022no—
218C22⋊C4—3022no—
219C22⋊C4—1512no—
220C42C22×D15111yescharacteristic
221C23—21no—
222C23—21no—
223C23—3022no—
224C23—6044no—
225C23—6044no—
226C23—1512no—
227C23—12082no—
228Q8—6042no—
229D4—21no—
230D4—21no—
231D4—21no—
232D4—3022no—
233D4—3022no—
234D4—6044no—
235D4—6044no—
236D4—6044no—
237D4—6042no—
238D4—1514no—
239D4—12081no—
240D4#1455900412yescomplemented
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—3022no—
246C2×C4—3022no—
247C2×C4—3022no—
248C2×C4—6044no—
249C2×C4—1512no—
250C2×C4D4×D15111yescharacteristic
251C2×C4D4×D15111yescharacteristic
252C2×C4C23×D15111yescharacteristic
253C8—21no—
254C8—21no—
255C8—3022no—
256C22—22no—
257C22—41no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—3022no—
263C22—3022no—
264C22—6042no—
265C22—6042no—
266C22—6042no—
267C22—1514no—
268C22—12088no—
269C22C2×D4×D15111yescharacteristic
270C4—21no—
271C4—41no—
272C4—41no—
273C4—3022no—
274C4—6042no—
275C4D8×D15112yes—
276C4C2×#1455900411yescharacteristic
277C4#1801278511yescharacteristic
278C2—42no—
279C2—81no—
280C2—3024no—
281C2—12082no—
282C2#2375285811yescharacteristic
283C2C2×D8×D15111yescharacteristic
284C2#2375301911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC4×D8×C151C2
socleC22×C151C22×D4
hypercenterC4×D8D151
hypocenterC151#3294
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #23752867C2semidirect
2. D4×D604C2semidirect
3. #23752559C2semidirect
4. #23752527C2semidirect
5. #23752492C2semidirect
6. #23752447C2semidirect
7. #23752407C2semidirect
8. #23752344C2semidirect
9. C8×D604C2semidirect
10. #102×D151C2semidirect
11. C4×D8×C151C2semidirect
15. C2×#14558989C22semidirect
16. C2×C8×D151C22semidirect
17. #18012739C22semidirect
23. #18012710C22semidirect
26. C4⋊C4×D151C22semidirect
27. #18012672C22semidirect
28. C4⋊(C151⋊C8)C22semidirect
29. #18012661C22semidirect
30. #18012661C22semidirect
32. #18012659C22semidirect
33. (C2×D151)⋊C8C22semidirect
36. C4×D4×C151C22semidirect
37. #107×C151C22semidirect
39. #102×C151C22semidirect
40. C4×C8×C151C22semidirect
89. D604D8semidirect
103. D4×C151#41semidirect
142. C151#3294semidirect
152. C4×D8D151semidirect
171. C4×D4C2×D151semidirect
174. #107C2×D151semidirect
181. #102C2×D151semidirect
183. C4×C8C2×D151semidirect
240. D4#14559004semidirect

Maximal subgroups

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

subgroupindex
#237528672
D4×D6042
#237525592
#237525272
#237524922
#237524472
#237524072
#237523442
C8×D6042
#102×D1512
C4×D8×C1512
#3294151