Finite Group Databasebeta

← C2×#23752598 #34079541

Subgroups — C2×#23752598 #34079541

Order 19328.

668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×#14558991C211yesmaximal, characteristic, complemented
2C22×D1208C211yesmaximal, characteristic, complemented
3C22×#14558989C211yesmaximal, characteristic, complemented
4C2×#18012735C211yesmaximal, characteristic, complemented
5C2×#18012728C211yesmaximal, characteristic, complemented
6#23752598C218yesmaximal, direct product factor
7C2×#18012649C211yesmaximal, characteristic, complemented
8C22×SD16×C151C211yesmaximal, characteristic, complemented
9C22×D604C2211yescharacteristic
10C22×D604C2211yescharacteristic
11C22×C22⋊D151—22no—
12C2×#14558991—24no—
13C2×#14558991C2214yescomplemented
14C2×D1208—24no—
15C2×D1208C2214yescomplemented
16C2×#14558989—24no—
17C2×#14558989C2214yescomplemented
18C22×C151⋊C8C2211yescharacteristic
19#18012735—22no—
20#18012735C2214yescomplemented
21#18012728—22no—
22#18012728C2214yescomplemented
23C2×(C2×D151)⋊C4—22no—
24C2×C4×Dic151C2211yescharacteristic
25#18012649C2214yescomplemented
26C22×Q8×C151C2211yescharacteristic
27C22×D4×C151C2211yescharacteristic
28C2×SD16×C151—24no—
29C2×SD16×C151C2214yescomplemented
30C22×C8×C151C2211yescharacteristic
31C23×D151—21no—
32C23×D151—21no—
33C2×D604—22no—
34C2×D604—22no—
35C2×D604—22no—
36C2×D604—22no—
37C2×D604—21no—
38C2×D604—21no—
39C2×D604C2312yes—
40C2×D604C2312yes—
41C2×C22⋊D151—28no—
42C2×C22⋊D151—48no—
43C22×Dic151D412yes—
44#14558991—28no—
45D1208—28no—
46#14558989—28no—
47C2×C151⋊C8D414yescomplemented
48C2×C151⋊C8C2312yes—
49(C2×D151)⋊C4—28no—
50C4×Dic151D412yes—
51C4×Dic151C2312yes—
52C24×C151—21no—
53C2×Q8×C151—21no—
54C2×Q8×C151—22no—
55C2×Q8×C151—22no—
56C2×Q8×C151C2312yes—
57C2×D4×C151—22no—
58C2×D4×C151—22no—
59C2×D4×C151—21no—
60C2×D4×C151C2312yes—
61C22×C4×C151—21no—
62C22×C4×C151C2311yescharacteristic
63SD16×C151—28no—
64C2×C8×C151D414yescomplemented
65C2×C8×C151C2312yes—
66C22×D151—22no—
67C22×D151—22no—
68C22×D151—42no—
69C22×D151—42no—
70C22×D151—44no—
71C22×D151—44no—
72D604—22no—
73D604—22no—
74D604—22no—
75D604—22no—
76D604—42no—
77D604—42no—
78C22⋊D151—416no—
79C2×Dic151—24no—
80C2×Dic151C2×D414yes—
81C151⋊C8C2×D414yescomplemented
82C23×C151—22no—
83C23×C151—42no—
84C23×C151—44no—
85C23×C151C2×D411yescharacteristic
86Q8×C151—22no—
87Q8×C151—22no—
88Q8×C151—42no—
89D4×C151—22no—
90D4×C151—22no—
91D4×C151—42no—
92C2×C4×C151—22no—
93C2×C4×C151—42no—
94C2×C4×C151C2×D411yescharacteristic
95C2×C4×C151C2×D412yes—
96C2×C4×C151C2×D412yes—
97C2×C4×C151C2411yescharacteristic
98C8×C151C2×D414yescomplemented
99C22×C151—42no—
100C22×C151—44no—
101C22×C151—84no—
102C22×C151#12712yes—
103C22×C151AGL(1,ℤ/8)14yes—
104C22×C151C22×D411yescharacteristic
105C2×D151—42no—
106C2×D151—42no—
107C2×D151—44no—
108C2×D151—44no—
109C2×D151—84no—
110C2×D151—84no—
111C4×C151—42no—
112C4×C151#12712yes—
113C4×C151C22×D411yescharacteristic
114C4×C151C22×D411yescharacteristic
115Dic151—24no—
116C2×C151—82no—
117C2×C151#49614yescomplemented
118C2×C151C2×#12711yescharacteristic
119C2×C151C2×AGL(1,ℤ/8)12yes—
120D151—82no—
121D151—82no—
122C151C2×#49611yescharacteristic, complemented, Sylow
123C2×#496—1511nomaximal, Sylow
124C22×SD16—1511no—
125C22×SD16D15111yescharacteristic, complemented
126C22×D8—1511no—
127C22×D8—1511no—
128C2×#127—1511no—
129C2×#124—1511no—
130#496—1518no—
131C2×#97—1511no—
132C22×Q8C2×D15111yescharacteristic
133C22×D4—3022no—
134C22×D4—1511no—
135C22×D4—1511no—
136C22×D4C2×D15111yescharacteristic
137C2×SD16—24no—
138C2×SD16—3024no—
139C2×SD16—1514no—
140C2×SD16C2×D15114yescomplemented
141C2×D8—3024no—
142C2×D8—3024no—
143C2×D8—1514no—
144C2×D8—1514no—
145C22×C8—1511no—
146C22×C8C2×D15111yescharacteristic
147#127—3022no—
148#127—1514no—
149#124—3022no—
150#124—1514no—
151C2×C22⋊C4—3022no—
152C2×C42—1511no—
153#97—1514no—
154C24—21no—
155C24—3021no—
156C24—3021no—
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D15112yes—
161C2×D4—22no—
162C2×D4—21no—
163C2×D4—22no—
164C2×D4—3028no—
165C2×D4—3022no—
166C2×D4—3022no—
167C2×D4—3021no—
168C2×D4—3021no—
169C2×D4—3022no—
170C2×D4—3022no—
171C2×D4—6048no—
172C2×D4—1512no—
173C2×D4—1512no—
174C2×D4C22×D15112yes—
175C22×C4—21no—
176C22×C4—1512no—
177C22×C4C22×D15111yescharacteristic
178SD16—28no—
179SD16—3028no—
180D8—3028no—
181D8—3028no—
182C2×C8—1514no—
183C2×C8—1512no—
184C2×C8C22⋊D15114yescomplemented
185C2×C8C22×D15112yes—
186C22⋊C4—3028no—
187C42—1512no—
188C42—1512no—
189C23—22no—
190C23—42no—
191C23—44no—
192C23—3022no—
193C23—3022no—
194C23—6042no—
195C23—6042no—
196C23—6044no—
197C23—6044no—
198C23D4×D15111yescharacteristic
199Q8—22no—
200Q8—22no—
201Q8—42no—
202D4—22no—
203D4—22no—
204D4—42no—
205D4—3022no—
206D4—3022no—
207D4—3022no—
208D4—3022no—
209D4—60416no—
210D4—6042no—
211D4—6042no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—3024no—
215C2×C4—1514no—
216C2×C4D4×D15111yescharacteristic
217C2×C4D4×D15112yes—
218C2×C4C2×C22⋊D15112yes—
219C2×C4C23×D15111yescharacteristic
220C8—1514no—
221C8C2×C22⋊D15114yescomplemented
222C22—44no—
223C22—42no—
224C22—84no—
225C22—6044no—
226C22—6044no—
227C22—6042no—
228C22—6042no—
229C22—12084no—
230C22—12084no—
231C22#1801273512yes—
232C22#1801276614yes—
233C22C2×D4×D15111yescharacteristic
234C4—42no—
235C4—3024no—
236C4#1801273512yes—
237C4C2×D4×D15111yescharacteristic
238C4C22×C22⋊D15111yescharacteristic
239C2—82no—
240C2—12082no—
241C2—12082no—
242C2#2375259814yesdirect product factor
243C2C2×#1801273511yescharacteristic
244C2C2×#1801276612yes—
subgroupG/H
centerC23D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC22×SD16×C151C2
socleC23×C151C2×D4
hypercenterC22×SD16D151
hypocenterC151C2×#496
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#14558991C2semidirect
2. C22×D1208C2semidirect
3. C22×#14558989C2semidirect
4. C2×#18012735C2semidirect
5. C2×#18012728C2semidirect
6. #23752598C2direct (N × H)
7. C2×#18012649C2semidirect
8. C22×SD16×C151C2semidirect
13. C2×#14558991C22semidirect
15. C2×D1208C22semidirect
17. C2×#14558989C22semidirect
20. #18012735C22semidirect
22. #18012728C22semidirect
25. #18012649C22semidirect
29. C2×SD16×C151C22semidirect
47. C2×C151⋊C8D4semidirect
64. C2×C8×C151D4semidirect
81. C151⋊C8C2×D4semidirect
98. C8×C151C2×D4semidirect
117. C2×C151#496semidirect
122. C151C2×#496semidirect
125. C22×SD16D151semidirect
140. C2×SD16C2×D151semidirect
184. C2×C8C22⋊D151semidirect
221. C8C2×C22⋊D151semidirect
242. C2#23752598direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145589912
C22×D12082
C22×#145589892
C2×#180127352
C2×#180127282
#237525982
C2×#180126492
C22×SD16×C1512
C2×#496151