Finite Group Databasebeta

← C2×#23752496 #34078874

Subgroups — C2×#23752496 #34078874

Order 19328.

416 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C2×#18012738C211yesmaximal, characteristic
2C2×#18012704C211yesmaximal, characteristic
3#23752496C218yesmaximal, direct product factor
4C2×#18012670C211yesmaximal, characteristic
5C2×Dic151⋊C8C211yesmaximal, characteristic
6C2×#18012664C211yesmaximal, characteristic
7C2×#18012662C211yesmaximal, characteristic
8C2×#106×C151C211yesmaximal, characteristic
9C22×Dic302—21no—
10C22×Dic302C2211yescharacteristic
11C22×C151⋊C8C2211yescharacteristic
12#18012738—22no—
13#18012738C2214yes—
14#18012704—22no—
15#18012704C2214yes—
16C2×C4⋊Dic151C2211yescharacteristic
17C2×Dic151⋊C4—21no—
18C2×Dic151⋊C4—21no—
19C2×C4×Dic151—21no—
20C2×C4×Dic151C2211yescharacteristic
21#18012670C2214yes—
22Dic151⋊C8C2214yes—
23#18012664C2214yes—
24#18012662C2214yes—
25C22×C8×C151C2211yescharacteristic
26C2×C4⋊C4×C151C2211yescharacteristic
27C2×C4⋊C4×C151C2211yescharacteristic
28#106×C151C2214yes—
29C2×Dic302—24no—
30C2×Dic302—21no—
31C2×Dic302—22no—
32C2×Dic302—44no—
33C2×Dic302Q814yescomplemented
34C2×Dic302C2312yes—
35C22×Dic151—21no—
36C22×Dic151—21no—
37C22×Dic151D411yescharacteristic
38C22×Dic151D411yescharacteristic
39C2×C151⋊C8—22no—
40C2×C151⋊C8C2312yes—
41C4⋊Dic151—21no—
42C4⋊Dic151C2312yes—
43Dic151⋊C4—24no—
44Dic151⋊C4—24no—
45C4×Dic151—24no—
46C4×Dic151D412yes—
47C4×Dic151C2312yes—
48C22×C4×C151—21no—
49C22×C4×C151—21no—
50C22×C4×C151C2311yescharacteristic
51C2×C8×C151—22no—
52C2×C8×C151C2312yes—
53C4⋊C4×C151—21no—
54C4⋊C4×C151—21no—
55C4⋊C4×C151C2312yes—
56C4⋊C4×C151C2312yes—
57Dic302—24no—
58Dic302—22no—
59Dic302—48no—
60Dic302C2×Q814yescomplemented
61C2×Dic151—24no—
62C2×Dic151—22no—
63C2×Dic151—22no—
64C2×Dic151—22no—
65C2×Dic151—42no—
66C2×Dic151SD1614yes—
67C2×Dic151C2×D412yes—
68C2×Dic151C2×D412yes—
69C151⋊C8—22no—
70C23×C151C2×D411yescharacteristic
71C2×C4×C151—22no—
72C2×C4×C151—22no—
73C2×C4×C151—42no—
74C2×C4×C151—42no—
75C2×C4×C151C2×D411yescharacteristic
76C2×C4×C151C2×Q812yes—
77C2×C4×C151#4112yes—
78C2×C4×C151C2411yescharacteristic
79C8×C151—22no—
80C22×C151C22⋊Q812yes—
81C22×C151C2×SD1612yes—
82C22×C151#13712yes—
83C22×C151C22×D411yescharacteristic
84C4×C151—42no—
85C4×C151—42no—
86C4×C151C22⋊Q812yes—
87C4×C151C22×Q811yescharacteristic
88C4×C151C2×#4111yescharacteristic
89Dic151—24no—
90Dic151—22no—
91Dic151—42no—
92Dic151C2×SD1614yes—
93C2×C151#47514yescomplemented
94C2×C151C2×C22⋊Q811yescharacteristic
95C2×C151C22×SD1611yescharacteristic
96C2×C151C2×#13711yescharacteristic
97C151C2×#47511yescharacteristic, complemented, Sylow
98C2×#475—1511nomaximal, Sylow
99C2×C4⋊Q8—1511no—
100C2×C4×Q8—1511no—
101#475—1518no—
102C2×#106—1511no—
103C2×#106D15111yescharacteristic
104C2×C4⋊C8—1511no—
105C2×#103—1511no—
106C2×#103—1511no—
107C22×Q8—3021no—
108C22×Q8—1511no—
109C22×C8—1511no—
110C22×C8C2×D15111yescharacteristic
111C4⋊Q8—3022no—
112C4⋊Q8—1514no—
113C4×Q8—3022no—
114C4×Q8—1514no—
115C2×C4⋊C4—3021no—
116C2×C4⋊C4—3021no—
117C2×C4⋊C4—1511no—
118C2×C4⋊C4C2×D15111yescharacteristic
119C2×C4⋊C4C2×D15111yescharacteristic
120C2×C42—3021no—
121C2×C42—1511no—
122#106—1514no—
123#106C2×D15114yes—
124C4⋊C8—1514no—
125#103—1514no—
126#103—1514no—
127C2×Q8—3024no—
128C2×Q8—3021no—
129C2×Q8—3022no—
130C2×Q8—6044no—
131C2×Q8—1514no—
132C2×Q8—1512no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—3021no—
136C22×C4—3021no—
137C22×C4—1511no—
138C22×C4—1511no—
139C22×C4C22×D15111yescharacteristic
140C2×C8—22no—
141C2×C8—3022no—
142C2×C8—1512no—
143C2×C8C22×D15112yes—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—3024no—
147C4⋊C4—3024no—
148C4⋊C4—3021no—
149C4⋊C4—1512no—
150C4⋊C4C22×D15112yes—
151C4⋊C4C22×D15112yes—
152C42—3024no—
153C42—1512no—
154C42—1512no—
155C23D4×D15111yescharacteristic
156Q8—3024no—
157Q8—3022no—
158Q8—6048no—
159Q8—1514no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—3024no—
165C2×C4—3022no—
166C2×C4—3022no—
167C2×C4—3022no—
168C2×C4—6042no—
169C2×C4—1512no—
170C2×C4—1514no—
171C2×C4—1512no—
172C2×C4D4×D15111yescharacteristic
173C2×C4Q8×D15112yes—
174C2×C4#1455900412yes—
175C2×C4C23×D15111yescharacteristic
176C8—22no—
177C8—3022no—
178C22#1801271712yes—
179C22SD16×D15112yes—
180C22#1801276812yes—
181C22C2×D4×D15111yescharacteristic
182C4—42no—
183C4—42no—
184C4—3024no—
185C4—3022no—
186C4—6042no—
187C4—1514no—
188C4#1801271712yes—
189C4C2×Q8×D15111yescharacteristic
190C4C2×#1455900411yescharacteristic
191C2#2375249614yesdirect product factor
192C2C2×#1801271711yescharacteristic
193C2C2×SD16×D15111yescharacteristic
194C2C2×#1801276811yescharacteristic
subgroupG/H
centerC23D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#106×C151C2
socle, prime radicalC23×C151C2×D4
hypercenterC2×#106D151
hypocenterC151C2×#475
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
3. #23752496C2direct (N × H)
33. C2×Dic302Q8semidirect
60. Dic302C2×Q8semidirect
93. C2×C151#475semidirect
97. C151C2×#475semidirect
191. C2#23752496direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#180127382
C2×#180127042
#237524962
C2×#180126702
C2×Dic151⋊C82
C2×#180126642
C2×#180126622
C2×#106×C1512
C2×#475151