Finite Group Databasebeta

← C2×#23752593 #34079528

Subgroups — C2×#23752593 #34079528

Order 19328.

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

normal subgroups only

This group has 592 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×#14558994C211yesmaximal, characteristic, complemented
2C22×#14558993C211yesmaximal, characteristic, complemented
3C22×#14558989C211yesmaximal, characteristic
4C2×#18012728C211yesmaximal, characteristic, complemented
5C2×#18012726C211yesmaximal, characteristic, complemented
6#23752593C218yesmaximal, direct product factor
7C2×C8×Dic151C211yesmaximal, characteristic, complemented
8C22×SD16×C151C211yesmaximal, characteristic, complemented
9C22×Dic302C2211yescharacteristic
10C22×D604C2211yescharacteristic
11C2×#14558994—24no—
12C2×#14558994C2214yescomplemented
13C2×#14558993—24no—
14C2×#14558993C2214yescomplemented
15C2×#14558989—24no—
16C2×#14558989C2214yes—
17C22×C151⋊C8C2211yescharacteristic
18#18012728—22no—
19#18012728C2214yescomplemented
20#18012726—22no—
21#18012726C2214yescomplemented
22C2×C22⋊Dic151—22no—
23C2×(C2×D151)⋊C4—22no—
24C2×C4×Dic151C2211yescharacteristic
25C8×Dic151C2214yescomplemented
26C22×Q8×C151C2211yescharacteristic
27C22×D4×C151C2211yescharacteristic
28C2×SD16×C151—24no—
29C2×SD16×C151C2214yescomplemented
30C22×C8×C151C2211yescharacteristic
31C23×D151—21no—
32C2×Dic302—21no—
33C2×Dic302—22no—
34C2×Dic302—22no—
35C2×Dic302C2312yes—
36C2×D604—22no—
37C2×D604—22no—
38C2×D604—21no—
39C2×D604C2312yes—
40C22×Dic151—21no—
41C22×Dic151D412yes—
42#14558994—28no—
43#14558993—28no—
44#14558989—28no—
45C2×C151⋊C8D414yes—
46C2×C151⋊C8C2312yes—
47C22⋊Dic151—28no—
48(C2×D151)⋊C4—28no—
49C4×Dic151D412yes—
50C4×Dic151C2312yes—
51C24×C151—21no—
52C2×Q8×C151—21no—
53C2×Q8×C151—22no—
54C2×Q8×C151—22no—
55C2×Q8×C151C2312yes—
56C2×D4×C151—22no—
57C2×D4×C151—22no—
58C2×D4×C151—21no—
59C2×D4×C151C2312yes—
60C22×C4×C151—21no—
61C22×C4×C151C2311yescharacteristic
62SD16×C151—28no—
63C2×C8×C151D414yes—
64C2×C8×C151C2312yes—
65C22×D151—22no—
66C22×D151—42no—
67C22×D151—44no—
68Dic302—22no—
69Dic302—22no—
70Dic302—42no—
71D604—22no—
72D604—22no—
73D604—42no—
74C2×Dic151—24no—
75C2×Dic151—22no—
76C2×Dic151—42no—
77C2×Dic151C2×D414yes—
78C151⋊C8C2×D414yes—
79C23×C151—22no—
80C23×C151—42no—
81C23×C151—44no—
82C23×C151C2×D411yescharacteristic
83Q8×C151—22no—
84Q8×C151—22no—
85Q8×C151—42no—
86D4×C151—22no—
87D4×C151—22no—
88D4×C151—42no—
89C2×C4×C151—22no—
90C2×C4×C151—42no—
91C2×C4×C151C2×D411yescharacteristic
92C2×C4×C151C2×D412yes—
93C2×C4×C151C2×D412yes—
94C2×C4×C151C2411yescharacteristic
95C8×C151C2×D414yes—
96C22×C151—42no—
97C22×C151—44no—
98C22×C151—84no—
99C22×C151#12712yes—
100C22×C151#13514yes—
101C22×C151C22×D411yescharacteristic
102C2×D151—42no—
103C2×D151—44no—
104C2×D151—84no—
105C4×C151—42no—
106C4×C151#12712yes—
107C4×C151C22×D411yescharacteristic
108C4×C151C22×D411yescharacteristic
109Dic151—24no—
110Dic151—42no—
111C2×C151—82no—
112C2×C151#49514yescomplemented
113C2×C151C2×#12711yescharacteristic
114C2×C151C2×#13512yes—
115D151—82no—
116C151C2×#49511yescharacteristic, complemented, Sylow
117C2×#495—1511nomaximal, Sylow
118C22×Q16—1511no—
119C22×SD16—1511no—
120C22×SD16D15111yescharacteristic, complemented
121C22×D8—1511no—
122C2×#124—1511no—
123C2×#124—1511no—
124#495—1518no—
125C2×C4×C8—1511no—
126C22×Q8—1511no—
127C22×Q8C2×D15111yescharacteristic
128C22×D4—1511no—
129C22×D4C2×D15111yescharacteristic
130C2×Q16—3024no—
131C2×Q16—1514no—
132C2×SD16—24no—
133C2×SD16—3024no—
134C2×SD16—1514no—
135C2×SD16C2×D15114yescomplemented
136C2×D8—3024no—
137C2×D8—1514no—
138C22×C8—1511no—
139C22×C8C2×D15111yescharacteristic
140#124—3022no—
141#124—3022no—
142#124—1514no—
143#124—1514no—
144C2×C22⋊C4—3022no—
145C2×C22⋊C4—3022no—
146C2×C42—1511no—
147C4×C8—1514no—
148C24—21no—
149C24—3021no—
150C2×Q8—21no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—3021no—
154C2×Q8—3022no—
155C2×Q8—3022no—
156C2×Q8—1512no—
157C2×Q8C22×D15112yes—
158C2×D4—22no—
159C2×D4—21no—
160C2×D4—22no—
161C2×D4—3022no—
162C2×D4—3021no—
163C2×D4—3022no—
164C2×D4—1512no—
165C2×D4C22×D15112yes—
166C22×C4—21no—
167C22×C4—3021no—
168C22×C4—1512no—
169C22×C4C22×D15111yescharacteristic
170Q16—3028no—
171SD16—28no—
172SD16—3028no—
173D8—3028no—
174C2×C8—1514no—
175C2×C8—1512no—
176C2×C8C22⋊D15114yes—
177C2×C8C22×D15112yes—
178C22⋊C4—3028no—
179C22⋊C4—3028no—
180C42—1512no—
181C42—1512no—
182C23—22no—
183C23—42no—
184C23—44no—
185C23—3022no—
186C23—6042no—
187C23—6044no—
188C23D4×D15111yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—3022no—
193Q8—3022no—
194Q8—6042no—
195D4—22no—
196D4—22no—
197D4—42no—
198D4—3022no—
199D4—3022no—
200D4—6042no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—3024no—
204C2×C4—3022no—
205C2×C4—6042no—
206C2×C4—1514no—
207C2×C4D4×D15111yescharacteristic
208C2×C4D4×D15112yes—
209C2×C4C2×C22⋊D15112yes—
210C2×C4C23×D15111yescharacteristic
211C8—1514no—
212C8C2×C22⋊D15114yes—
213C22—44no—
214C22—42no—
215C22—84no—
216C22—6044no—
217C22—6042no—
218C22—12084no—
219C22#1801273512yes—
220C22#1801276014yes—
221C22C2×D4×D15111yescharacteristic
222C4—42no—
223C4—3024no—
224C4—6042no—
225C4#1801273512yes—
226C4C2×D4×D15111yescharacteristic
227C4C22×C22⋊D15111yescharacteristic
228C2—82no—
229C2—12082no—
230C2#2375259314yesdirect product factor
231C2C2×#1801273511yescharacteristic
232C2C2×#1801276012yes—
subgroupG/H
centerC23D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC22×SD16×C151C2
socleC23×C151C2×D4
prime radicalC22×#14558989C2
hypercenterC22×SD16D151
hypocenterC151C2×#495
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×#14558994C2semidirect
2. C22×#14558993C2semidirect
4. C2×#18012728C2semidirect
5. C2×#18012726C2semidirect
6. #23752593C2direct (N × H)
7. C2×C8×Dic151C2semidirect
8. C22×SD16×C151C2semidirect
12. C2×#14558994C22semidirect
14. C2×#14558993C22semidirect
19. #18012728C22semidirect
21. #18012726C22semidirect
25. C8×Dic151C22semidirect
29. C2×SD16×C151C22semidirect
112. C2×C151#495semidirect
116. C151C2×#495semidirect
120. C22×SD16D151semidirect
135. C2×SD16C2×D151semidirect
230. C2#23752593direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145589942
C22×#145589932
C22×#145589892
C2×#180127282
C2×#180127262
#237525932
C2×C8×Dic1512
C22×SD16×C1512
C2×#495151