Finite Group Databasebeta

← #34079952

Subgroups — #34079952

Order 19328.

418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 117 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#23752723C212yesmaximal, complemented
2#23752554C212yesmaximal, complemented
3#23752537C212yesmaximal, complemented
4#23752470C211yesmaximal, characteristic, complemented
5#23752465C211yesmaximal, characteristic, complemented
6#23752458C212yesmaximal, complemented
7#23752376C212yesmaximal, complemented
8#23752359C212yesmaximal, complemented
9#407×C151C211yesmaximal, characteristic, complemented
10C2×#14559004C2212yes—
11C2×Dic604C2211yescharacteristic, complemented
12C2×#14558993C2212yescomplemented
13C2×D1208C2211yescharacteristic, complemented
14#18012722—22no—
15#18012718C2212yes—
16#18012718C2212yes—
17#18012713C2212yes—
18#18012713C2212yes—
19#18012708—22no—
20C4×C22⋊D151—22no—
21C4×C22⋊D151—22no—
22#18012698C2212yes—
23#18012673C2212yescomplemented
24#18012671C2211yescharacteristic, complemented
25#18012671C2211yescharacteristic, complemented
26#18012664C2212yescomplemented
27#18012664C2212yescomplemented
28#18012661C2212yescomplemented
29#18012661C2212yescomplemented
30C23×C4×C151C2211yescharacteristic
31C2×M16×C151C2211yescharacteristic
32C2×M16×C151C2211yescharacteristic
33C22⋊C8×C151C2212yes—
34C22⋊C8×C151C2212yes—
35#14559004—42no—
36#14559004—42no—
37C2×Dic302C2312yes—
38C2×D604C2312yes—
39C2×C22⋊D151—22no—
40C2×C22⋊D151—22no—
41C2×C22⋊D151—22no—
42C2×C4×D151—22no—
43Dic604—41no—
44#14558993—42no—
45D1208—41no—
46C4⋊Dic151C2312yes—
47C4⋊Dic151C2312yes—
48Dic151⋊C4—22no—
49Dic151⋊C4—22no—
50C22⋊Dic151—22no—
51C22⋊Dic151—22no—
52C22⋊Dic151—22no—
53(C2×D151)⋊C4—22no—
54(C2×D151)⋊C4—22no—
55C4×Dic151—22no—
56C24×C151D411yescharacteristic
57C22×C4×C151—41no—
58C22×C4×C151—41no—
59C22×C4×C151D411yescharacteristic
60C22×C4×C151D412yes—
61C22×C4×C151C2312yes—
62C22×C4×C151C2311yescharacteristic
63M16×C151—41no—
64M16×C151—41no—
65C2×C8×C151C2312yes—
66C2×C8×C151C2311yescharacteristic
67C2×C8×C151C2311yescharacteristic
68C22×D151—22no—
69Dic302—22no—
70Dic302—22no—
71D604—22no—
72D604—22no—
73C22⋊D151—44no—
74C22⋊D151—44no—
75C22⋊D151—44no—
76C2×Dic151—22no—
77C2×Dic151—22no—
78C2×Dic151—22no—
79C4×D151—44no—
80C23×C151—42no—
81C23×C151—41no—
82C23×C151C2×D411yescharacteristic
83C23×C151C2×D412yes—
84C2×C4×C151—22no—
85C2×C4×C151—22no—
86C2×C4×C151—21no—
87C2×C4×C151—21no—
88C2×C4×C151—42no—
89C2×C4×C151—41no—
90C2×C4×C151C2×D412yes—
91C2×C4×C151C2×D411yescharacteristic
92C2×C4×C151C2411yescharacteristic
93C8×C151—21no—
94C8×C151—22no—
95C8×C151—21no—
96C22×C151—21no—
97C22×C151—22no—
98C22×C151—22no—
99C22×C151—22no—
100C22×C151—22no—
101C22×C151—44no—
102C22×C151C22×D411yescharacteristic
103C2×D151—42no—
104C2×D151—42no—
105C2×D151—42no—
106C4×C151—21no—
107C4×C151—22no—
108C4×C151H(5,𝔽2)11yescharacteristic
109C4×C151H(5,𝔽2)11yescharacteristic
110Dic151—42no—
111Dic151—42no—
112Dic151—42no—
113C2×C151—41no—
114C2×C151—42no—
115C2×C151#53411yescharacteristic
116C2×C151#57512yes—
117D151—82no—
118C151#319711yescharacteristic, complemented, Sylow
119#3197—1511nomaximal, Sylow
120#525—1512no—
121#485—1512no—
122#482—1512no—
123#470—1511no—
124#469—1511no—
125#468—1512no—
126#452—1512no—
127#449—1512no—
128#407D15111yescharacteristic, complemented
129C2×#41—1512no—
130C23×C4C2×D15111yescharacteristic
131C2×Q16—1511no—
132C2×SD16—1512no—
133C2×D8—1511no—
134C2×M16C2×D15111yescharacteristic
135C2×M16C2×D15111yescharacteristic
136#123—3022no—
137C22⋊Q8—1512no—
138C22⋊Q8—1512no—
139#121—1512no—
140#121—1512no—
141#120—3022no—
142C4×D4—3022no—
143C4×D4—3022no—
144#117—1512no—
145#107—1512no—
146#106—1511no—
147#106—1511no—
148#103—1512no—
149#103—1512no—
150#102—1512no—
151#102—1512no—
152C22⋊C8C2×D15112yes—
153C22⋊C8C2×D15112yes—
154C24D60411yescharacteristic
155#41—6042no—
156#41—6042no—
157C2×Q8—1512no—
158C2×D4—3022no—
159C2×D4—3022no—
160C2×D4—3022no—
161C2×D4—1512no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—3022no—
165C22×C4D60411yescharacteristic
166C22×C4D60412yes—
167C22×C4C22×D15112yes—
168C22×C4C22×D15111yescharacteristic
169Q16—6041no—
170SD16—6042no—
171D8—6041no—
172M16—41no—
173M16—41no—
174C2×C8C22×D15111yescharacteristic
175C2×C8C22×D15112yes—
176C2×C8C22×D15111yescharacteristic
177C4⋊C4—3022no—
178C4⋊C4—3022no—
179C4⋊C4—1512no—
180C4⋊C4—1512no—
181C22⋊C4—3022no—
182C22⋊C4—3022no—
183C22⋊C4—3022no—
184C22⋊C4—3022no—
185C22⋊C4—3022no—
186C42—3022no—
187C23—41no—
188C23—42no—
189C23—3022no—
190C23C2×D60411yescharacteristic
191C23C2×D60412yes—
192Q8—3022no—
193Q8—3022no—
194D4—3022no—
195D4—3022no—
196D4—6044no—
197D4—6044no—
198D4—6044no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—3022no—
206C2×C4—3022no—
207C2×C4—3022no—
208C2×C4—6044no—
209C2×C4C2×D60412yes—
210C2×C4C2×D60411yescharacteristic
211C2×C4C23×D15111yescharacteristic
212C8—21no—
213C8—22no—
214C8—21no—
215C22—22no—
216C22—22no—
217C22—22no—
218C22—22no—
219C22—21no—
220C22—44no—
221C22—6042no—
222C22—6042no—
223C22—6042no—
224C22C22×D60411yescharacteristic
225C4—22no—
226C4—21no—
227C4—6042no—
228C4—6042no—
229C4—6042no—
230C4#1801278411yescharacteristic
231C4#1801278411yescharacteristic
232C2—41no—
233C2—42no—
234C2—12082no—
235C2#2375277411yescharacteristic
236C2#2375301212yes—
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#407×C151C2
socleC22×C151C22×D4
hypercenter#407D151
hypocenterC151#3197
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #23752723C2semidirect
2. #23752554C2semidirect
3. #23752537C2semidirect
4. #23752470C2semidirect
5. #23752465C2semidirect
6. #23752458C2semidirect
7. #23752376C2semidirect
8. #23752359C2semidirect
9. #407×C151C2semidirect
11. C2×Dic604C22semidirect
12. C2×#14558993C22semidirect
13. C2×D1208C22semidirect
23. #18012673C22semidirect
24. #18012671C22semidirect
25. #18012671C22semidirect
26. #18012664C22semidirect
27. #18012664C22semidirect
28. #18012661C22semidirect
29. #18012661C22semidirect
118. C151#3197semidirect
128. #407D151semidirect

Maximal subgroups

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

subgroupindex
#237527232
#237525542
#237525372
#237524702
#237524652
#237524582
#237523762
#237523592
#407×C1512
#3197151