Finite Group Databasebeta

← C2×#10590161 #11774205

Subgroups — C2×#10590161 #11774205

Order 1152.

578 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 106 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×#64096C211yesmaximal, characteristic
2C2×C4⋊#622C211yesmaximal, characteristic
3C2×C4×#622C211yesmaximal, characteristic
4#10590161C214yesmaximal, direct product factor
5C22×#634C411yescharacteristic
6C22×#622—21no—
7C22×#622—21no—
8C2×C32×C4⋊C4C411yescharacteristic
9C2×#3750—21no—
10C2×C4×C3⋊Dic3—21no—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12#64096—21no—
13#64096—21no—
14#64096C412yes—
15#64096C2212yes—
16C4⋊#622—21no—
17C4⋊#622C2212yes—
18C4×#622—21no—
19C4×#622C2212yes—
20C2×#887—62no—
21C22×C32×C4—21no—
22C22×C32×C4C2×C411yescharacteristic
23C22×C3⋊Dic3—21no—
24C22×C3⋊Dic3D411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C2×#634—21no—
27C2×#634—22no—
28C2×#634C814yescomplemented
29C2×#634C2×C412yes—
30C2×#622—24no—
31C2×#622—22no—
32C2×#622—22no—
33C2×#622—42no—
34C32×C4⋊C4—21no—
35C32×C4⋊C4C2×C412yes—
36#3750—22no—
37#3750—22no—
38C4×C3⋊Dic3—22no—
39C4×C3⋊Dic3—22no—
40C4×C3⋊Dic3C2×C411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C4×C3⋊Dic3D411yescharacteristic
43C4×C3⋊Dic3C2311yescharacteristic
44C2×Q8⋊C8—91nomaximal, Sylow
45C22×Dic6—62no—
46C2×C3×C4⋊C4—22no—
47C2×Dic3⋊C4—64no—
48C2×C4×Dic3—62no—
49C2×C4×Dic3—64no—
50#887—64no—
51#887—64no—
52#887—64no—
53#887—64no—
54C23×C32C22⋊C411yescharacteristic
55C2×C32×C4—22no—
56C2×C32×C4—42no—
57C2×C32×C4C22⋊C411yescharacteristic
58C2×C32×C4C2×C812yes—
59C2×C32×C4M1612yes—
60C2×C32×C4C22×C411yescharacteristic
61C2×C3⋊Dic3—24no—
62C2×C3⋊Dic3—22no—
63C2×C3⋊Dic3—22no—
64C2×C3⋊Dic3C22⋊C411yescharacteristic
65C2×C3⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3SD1612yes—
67C2×C3⋊Dic3Q1612yes—
68C2×C3⋊Dic3C2×D411yescharacteristic
69C2×C3⋊Dic3C2×D411yescharacteristic
70#634—24no—
71#634—22no—
72#634C2×C814yescomplemented
73#622—24no—
74#622—42no—
75C2×C4×Q8—91no—
76C2×C4⋊C8—91no—
77C2×C4×C8—91no—
78Q8⋊C8—94no—
79C22×C3×C4—24no—
80C22×C3×C4—22no—
81C22×Dic3—62no—
82C22×Dic3—62no—
83C22×Dic3—64no—
84C2×Dic6—64no—
85C2×Dic6—68no—
86C2×Dic6—64no—
87C2×Dic6—68no—
88C3×C4⋊C4—24no—
89C3×C4⋊C4—24no—
90Dic3⋊C4—68no—
91Dic3⋊C4—68no—
92C4×Dic3—62no—
93C4×Dic3—62no—
94C4×Dic3—62no—
95C4×Dic3—62no—
96C4×Dic3—68no—
97C4×Dic3—68no—
98C22×C32C22⋊C812yes—
99C22×C32#10312yes—
100C22×C32#10412yes—
101C22×C32C2×C22⋊C411yescharacteristic
102C32×C4—42no—
103C32×C4C22⋊C812yes—
104C32×C4C22×C811yescharacteristic
105C32×C4C2×M1611yescharacteristic
106C3⋊Dic3—24no—
107C3⋊Dic3—21no—
108C3⋊Dic3—21no—
109C3⋊Dic3#10312yes—
110C3⋊Dic3C2×SD1611yescharacteristic
111C3⋊Dic3C2×Q1611yescharacteristic
112C22×Q8—91no—
113C22×C8—181no—
114C22×C8—181no—
115C4×Q8—92no—
116C4×Q8—92no—
117C4×Q8—181no—
118C4×Q8—181no—
119C2×C4⋊C4—181no—
120C2×C4⋊C4#15711yescharacteristic
121C2×C42—91no—
122C2×C42—181no—
123C4⋊C8—92no—
124C4⋊C8—181no—
125C4×C8—92no—
126C4×C8—181no—
127C23×C3—22no—
128C2×C3×C4—28no—
129C2×C3×C4—22no—
130C2×C3×C4—24no—
131C2×C3×C4—24no—
132C2×C3×C4—22no—
133C2×C3×C4—48no—
134C2×Dic3—62no—
135C2×Dic3—64no—
136C2×Dic3—64no—
137C2×Dic3—62no—
138C2×Dic3—62no—
139C2×Dic3—62no—
140C2×Dic3—68no—
141C2×Dic3—616no—
142C2×Dic3—124no—
143Dic6—68no—
144Dic6—68no—
145Dic6—616no—
146C2×C32Q8⋊C814yescomplemented
147C2×C32C2×C22⋊C811yescharacteristic
148C2×C32C2×#10311yescharacteristic
149C2×C32C2×#10411yescharacteristic
150C2×Q8—92no—
151C2×Q8—94no—
152C2×Q8—182no—
153C2×Q8—181no—
154C22×C4—21no—
155C22×C4—91no—
156C22×C4—91no—
157C22×C4—181no—
158C22×C4C2×#15711yescharacteristic
159C2×C8—182no—
160C2×C8—184no—
161C2×C8—182no—
162C2×C8—362no—
163C4⋊C4—21no—
164C4⋊C4—182no—
165C4⋊C4—182no—
166C4⋊C4C2×#15712yes—
167C42—91no—
168C42—91no—
169C42—91no—
170C42—91no—
171C42—182no—
172C42—182no—
173C22×C3—24no—
174C22×C3—22no—
175C22×C3—24no—
176C22×C3—24no—
177C3×C4—22no—
178C3×C4—22no—
179C3×C4—24no—
180C3×C4—48no—
181Dic3—64no—
182Dic3—62no—
183Dic3—62no—
184Dic3—616no—
185Dic3—122no—
186Dic3—122no—
187C32C2×Q8⋊C811yescharacteristic, complemented, Sylow
188C23C22⋊#15711yescharacteristic
189Q8—94no—
190Q8—182no—
191Q8—184no—
192C2×C4—22no—
193C2×C4—42no—
194C2×C4—91no—
195C2×C4—91no—
196C2×C4—92no—
197C2×C4—92no—
198C2×C4—91no—
199C2×C4—91no—
200C2×C4—184no—
201C2×C4—182no—
202C2×C4—182no—
203C2×C4#378712yes—
204C2×C4#378812yes—
205C2×C4C22⋊#15711yescharacteristic
206C2×C4C22×#15711yescharacteristic
207C8—184no—
208C8—362no—
209C2×C3—22no—
210C2×C3—22no—
211C2×C3—22no—
212C2×C3—28no—
213C22#6377812yes—
214C22#6378312yes—
215C22#6378412yes—
216C22C2×C22⋊#15711yescharacteristic
217C4—42no—
218C4—91no—
219C4—91no—
220C4—92no—
221C4—184no—
222C4—181no—
223C4—181no—
224C4#6377812yes—
225C4C2×#378711yescharacteristic
226C4C2×#378811yescharacteristic
227C3—22no—
228C2#1059016114yesdirect product factor
229C2C2×#6377811yescharacteristic
230C2C2×#6378311yescharacteristic
231C2C2×#6378411yescharacteristic
subgroupG/H
centerC23C22⋊#157
commutatorC32×C4C22×C8
FrattiniC2×C4C22×#157
FittingC2×C32×C4⋊C4C4
socle, prime radicalC23×C32C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32C2×Q8⋊C8
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10590161C2direct (N × H)
28. C2×#634C8semidirect
72. #634C2×C8semidirect
146. C2×C32Q8⋊C8semidirect
187. C32C2×Q8⋊C8semidirect
228. C2#10590161direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640962
C2×C4⋊#6222
C2×C4×#6222
#105901612
C2×Q8⋊C89