Finite Group Databasebeta

← C2×#10590159 #11775685

Subgroups — C2×#10590159 #11775685

Order 1152.

458 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 74 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×#64099C211yesmaximal, characteristic
2C2×#63777C211yesmaximal, characteristic
3C2×#63777C211yesmaximal, characteristic
4#10590159C214yesmaximal, direct product factor
5C22×#622—21no—
6C22×#622—21no—
7C2×C32×C4⋊C4C411yescharacteristic
8C2×C4⋊(C3⋊Dic3)—21no—
9C2×C4⋊(C3⋊Dic3)C411yescharacteristic
10C2×#3750—21no—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12#64099—21no—
13#64099—21no—
14#64099C412yes—
15#64099C2212yes—
16#63777—21no—
17#63777—21no—
18#63777C2212yes—
19#63777C2212yes—
20C2×#890—62no—
21C22×C32×C4—21no—
22C22×C32×C4C2×C411yescharacteristic
23C22×C3⋊Dic3—21no—
24C22×C3⋊Dic3D411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C2×#622—24no—
27C2×#622—24no—
28C2×#622—22no—
29C2×#622—22no—
30C32×C4⋊C4—21no—
31C32×C4⋊C4C2×C412yes—
32C4⋊(C3⋊Dic3)—21no—
33C4⋊(C3⋊Dic3)—22no—
34C4⋊(C3⋊Dic3)—22no—
35C4⋊(C3⋊Dic3)C2×C412yes—
36#3750—22no—
37#3750—22no—
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3C2311yescharacteristic
42C2×#330—91nomaximal, Sylow
43C2×C3×C4⋊C4—22no—
44C2×C4⋊Dic3—62no—
45C2×C4⋊Dic3—64no—
46C2×Dic3⋊C4—64no—
47C2×C4×Dic3—62no—
48#890—64no—
49#890—64no—
50#890—64no—
51#890—64no—
52C23×C32C22⋊C411yescharacteristic
53C2×C32×C4—22no—
54C2×C32×C4—22no—
55C2×C32×C4—42no—
56C2×C32×C4C22⋊C411yescharacteristic
57C2×C32×C4C22×C411yescharacteristic
58C2×C3⋊Dic3—22no—
59C2×C3⋊Dic3—22no—
60C2×C3⋊Dic3—22no—
61C2×C3⋊Dic3—42no—
62C2×C3⋊Dic3C22⋊C411yescharacteristic
63C2×C3⋊Dic3C22⋊C411yescharacteristic
64C2×C3⋊Dic3C2×D411yescharacteristic
65C2×C3⋊Dic3C2×D411yescharacteristic
66#622—24no—
67#622—24no—
68C2×#125—91no—
69C2×#97—91no—
70C2×#97—91no—
71#330—94no—
72C22×C3×C4—24no—
73C22×C3×C4—22no—
74C22×Dic3—62no—
75C22×Dic3—62no—
76C22×Dic3—64no—
77C3×C4⋊C4—24no—
78C3×C4⋊C4—24no—
79C4⋊Dic3—64no—
80C4⋊Dic3—68no—
81C4⋊Dic3—68no—
82C4⋊Dic3—64no—
83Dic3⋊C4—68no—
84Dic3⋊C4—68no—
85C4×Dic3—62no—
86C4×Dic3—62no—
87C4×Dic3—62no—
88C4×Dic3—62no—
89C22×C32#10112yes—
90C22×C32#10412yes—
91C22×C32#10412yes—
92C22×C32C2×C22⋊C411yescharacteristic
93C32×C4—21no—
94C32×C4—21no—
95C32×C4—42no—
96C3⋊Dic3—21no—
97C3⋊Dic3—21no—
98C3⋊Dic3—21no—
99C3⋊Dic3—21no—
100C3⋊Dic3—42no—
101C22×C8—181no—
102C22×C8—181no—
103#125—92no—
104#125—92no—
105#125—181no—
106#125—181no—
107C2×C4⋊C4—91no—
108C2×C4⋊C4—181no—
109C2×C4⋊C4—181no—
110C2×C4⋊C4#15711yescharacteristic
111C2×C42—91no—
112#97—92no—
113#97—92no—
114#97—181no—
115#97—181no—
116C23×C3—22no—
117C2×C3×C4—28no—
118C2×C3×C4—28no—
119C2×C3×C4—22no—
120C2×C3×C4—22no—
121C2×C3×C4—48no—
122C2×Dic3—62no—
123C2×Dic3—62no—
124C2×Dic3—62no—
125C2×Dic3—62no—
126C2×Dic3—68no—
127C2×Dic3—124no—
128C2×Dic3—124no—
129C2×Dic3—128no—
130C2×C32#33014yescomplemented
131C2×C32C2×#10111yescharacteristic
132C2×C32C2×#10411yescharacteristic
133C2×C32C2×#10411yescharacteristic
134C22×C4—21no—
135C22×C4—91no—
136C22×C4—91no—
137C22×C4—181no—
138C22×C4C2×#15711yescharacteristic
139C2×C8—182no—
140C2×C8—182no—
141C2×C8—184no—
142C2×C8—184no—
143C4⋊C4—21no—
144C4⋊C4—92no—
145C4⋊C4—182no—
146C4⋊C4—182no—
147C4⋊C4—182no—
148C4⋊C4—182no—
149C4⋊C4—181no—
150C4⋊C4C2×#15712yes—
151C42—91no—
152C42—91no—
153C42—91no—
154C42—91no—
155C22×C3—24no—
156C22×C3—22no—
157C22×C3—24no—
158C22×C3—24no—
159C3×C4—24no—
160C3×C4—24no—
161C3×C4—48no—
162Dic3—122no—
163Dic3—122no—
164Dic3—122no—
165Dic3—122no—
166Dic3—128no—
167C32C2×#33011yescharacteristic, complemented, Sylow
168C23C22⋊#15711yescharacteristic
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—42no—
172C2×C4—91no—
173C2×C4—91no—
174C2×C4—91no—
175C2×C4—91no—
176C2×C4—182no—
177C2×C4—182no—
178C2×C4—182no—
179C2×C4—362no—
180C2×C4C22⋊#15711yescharacteristic
181C2×C4C22×#15711yescharacteristic
182C8—184no—
183C8—184no—
184C2×C3—22no—
185C2×C3—22no—
186C2×C3—22no—
187C2×C3—28no—
188C22#6378012yes—
189C22#6378312yes—
190C22#6378512yes—
191C22C2×C22⋊#15711yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—181no—
196C4—181no—
197C4—181no—
198C4—181no—
199C4—362no—
200C3—22no—
201C2#1059015914yesdirect product factor
202C2C2×#6378011yescharacteristic
203C2C2×#6378311yescharacteristic
204C2C2×#6378511yescharacteristic
subgroupG/H
centerC23C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC2×C32×C4⋊C4C4
socle, prime radicalC23×C32C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32C2×#330
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10590159C2direct (N × H)
130. C2×C32#330semidirect
167. C32C2×#330semidirect
201. C2#10590159direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640992
C2×#637772
#105901592
C2×#3309