Finite Group Databasebeta

← C2×#63783 #10593815

Subgroups — C2×#63783 #10593815

Order 576.

334 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 52 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×#3830C211yesmaximal, characteristic
2C2×C4×#157C211yesmaximal, characteristic, complemented
3C2×#3788C211yesmaximal, characteristic, complemented
4#63783C214yesmaximal, direct product factor
5C22×#157—21no—
6C2×C32×D4C411yescharacteristic, complemented
7C2×#638—21no—
8C22×C3⋊Dic3—21no—
9#3830—21no—
10#3830—21no—
11#3830C412yescomplemented
12#3830C2212yes—
13C2×C4×C3⋊D3C2211yescharacteristic
14C2×#634C411yescharacteristic, complemented
15C2×#622—21no—
16C4×#157—21no—
17C4×#157C2212yescomplemented
18#3788—21no—
19#3788C2212yescomplemented
20C2×#237—62no—
21C23×C32—21no—
22C22×C3⋊D3D411yescharacteristic
23C2×#157—24no—
24C2×#157—22no—
25C32×D4—21no—
26C32×D4C2×C412yescomplemented
27C2×C32×C4C2×C411yescharacteristic
28#638—22no—
29#638—22no—
30C2×C3⋊Dic3—21no—
31C2×C3⋊Dic3—22no—
32C2×C3⋊Dic3—22no—
33C2×C3⋊Dic3D411yescharacteristic
34C4×C3⋊D3C2×C411yescharacteristic
35C4×C3⋊D3D411yescharacteristic
36C4×C3⋊D3D411yescharacteristic
37C4×C3⋊D3C2311yescharacteristic
38#634—21no—
39#634C2×C412yescomplemented
40#622—22no—
41C2×#104—91nomaximal, Sylow
42C2×C3×D4—22no—
43C2×#67—64no—
44C22×Dic3—64no—
45#237—64no—
46#237—64no—
47#237—64no—
48#237—64no—
49C2×C4×D3—62no—
50C2×Dic6—62no—
51C22×C32—22no—
52C22×C32—42no—
53C22×C32C22⋊C411yescharacteristic
54C2×C3⋊D3—22no—
55C2×C3⋊D3C22⋊C411yescharacteristic
56C2×C3⋊D3C2×D411yescharacteristic
57#157—24no—
58C32×C4C22⋊C411yescharacteristic
59C32×C4C22×C411yescharacteristic
60C3⋊Dic3—22no—
61C3⋊Dic3C22⋊C411yescharacteristic
62C3⋊Dic3C2×D411yescharacteristic
63C2×#41—91no—
64C2×M16—91no—
65C2×C42—91no—
66#104—94no—
67C23×C3—24no—
68C22×D3—62no—
69C3×D4—24no—
70C3×D4—24no—
71C2×C3×C4—22no—
72#67—68no—
73#67—68no—
74C2×Dic3—62no—
75C2×Dic3—64no—
76C2×Dic3—68no—
77C2×Dic3—68no—
78C4×D3—62no—
79C4×D3—62no—
80C4×D3—62no—
81C4×D3—62no—
82Dic6—64no—
83Dic6—64no—
84C2×C32—42no—
85C2×C32#10412yescomplemented
86C2×C32C2×C22⋊C411yescharacteristic
87C3⋊D3—21no—
88C3⋊D3—21no—
89#41—92no—
90#41—92no—
91#41—181no—
92#41—181no—
93C2×Q8—91no—
94C2×D4—181no—
95C2×D4#15711yescharacteristic, complemented
96C22×C4—91no—
97C22×C4—181no—
98C22×C4—181no—
99M16—92no—
100M16—181no—
101C2×C8—181no—
102C42—92no—
103C42—181no—
104C22×C3—28no—
105C22×C3—22no—
106C22×C3—48no—
107C2×D3—62no—
108C2×D3—62no—
109C2×D3—124no—
110C3×C4—22no—
111C3×C4—22no—
112Dic3—62no—
113Dic3—62no—
114Dic3—68no—
115C32C2×#10411yescharacteristic, complemented, Sylow
116C23—21no—
117C23—91no—
118Q8—92no—
119Q8—181no—
120D4—21no—
121D4—182no—
122D4—182no—
123D4C2×#15712yescomplemented
124C2×C4—91no—
125C2×C4—91no—
126C2×C4—91no—
127C2×C4—91no—
128C2×C4—91no—
129C2×C4—182no—
130C2×C4—182no—
131C2×C4—182no—
132C2×C4—184no—
133C2×C4—181no—
134C2×C4C2×#15711yescharacteristic
135C8—182no—
136C2×C3—22no—
137C2×C3—24no—
138C2×C3—48no—
139D3—122no—
140D3—122no—
141C22—22no—
142C22—42no—
143C22—91no—
144C22—91no—
145C22—182no—
146C22C22⋊#15711yescharacteristic
147C4—91no—
148C4—91no—
149C4—184no—
150C4—182no—
151C4C22⋊#15711yescharacteristic
152C4C22×#15711yescharacteristic
153C3—22no—
154C2—42no—
155C2—181no—
156C2—181no—
157C2#6378312yesdirect product factor
158C2C2×C22⋊#15711yescharacteristic
subgroupG/H
centerC22C22⋊#157
commutatorC32×C4C22×C4
FrattiniC4C22×#157
FittingC2×C32×D4C4
socleC22×C32C22⋊C4
prime radicalC2×#3830C2
cosocleC4×C3⋊D3C23
hypercenterC2×D4#157
hypocenterC32C2×#104
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#157C2semidirect
3. C2×#3788C2semidirect
4. #63783C2direct (N × H)
6. C2×C32×D4C4semidirect
11. #3830C4semidirect
14. C2×#634C4semidirect
17. C4×#157C22semidirect
19. #3788C22semidirect
26. C32×D4C2×C4semidirect
39. #634C2×C4semidirect
85. C2×C32#104semidirect
95. C2×D4#157semidirect
115. C32C2×#104semidirect
123. D4C2×#157semidirect
157. C2#63783direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#38302
C2×C4×#1572
C2×#37882
#637832
C2×#1049