Finite Group Databasebeta

← C2×#10590217 #11796342

Subgroups — C2×#10590217 #11796342

Order 1152.

614 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 58 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×#64156C211yesmaximal, characteristic
2C2×#63774C212yesmaximal
3#10590217C214yesmaximal, direct product factor
4C22×C32×Q8C411yescharacteristic, complemented
5C22×C4⋊(C3⋊D3)C2211yescharacteristic
6C2×C22⋊#157—22no—
7#64156—22no—
8#64156C412yescomplemented
9#64156C2212yes—
10C2×#3752—22no—
11C2×C4×C3⋊Dic3C411yescharacteristic, complemented
12#63774—22no—
13#63774C2214yes—
14C2×#947—62no—
15C23×C3⋊D3D412yes—
16C22×#157—42no—
17C2×C32×Q8—21no—
18C2×C32×Q8—41no—
19C2×C32×Q8—41no—
20C2×C32×Q8C2×C412yescomplemented
21C22×C32×C4—21no—
22C22×C32×C4C2×C411yescharacteristic
23C22×C3⋊Dic3—21no—
24C2×C4⋊(C3⋊D3)—41no—
25C2×C4⋊(C3⋊D3)—41no—
26C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
27C2×C4⋊(C3⋊D3)D412yes—
28C2×C4⋊(C3⋊D3)C2311yescharacteristic
29C22⋊#157—24no—
30C22⋊#157—42no—
31#3752—24no—
32#3752—24no—
33C4×C3⋊Dic3—21no—
34C4×C3⋊Dic3C2×C412yescomplemented
35C2×#354—91nomaximal, Sylow
36C22×C3×Q8—22no—
37C22×D12—62no—
38#947—64no—
39#947—64no—
40#947—68no—
41C2×(C2×D3)⋊C4—68no—
42C2×C4×Dic3—62no—
43C23×C32C22⋊C411yescharacteristic
44C22×C3⋊D3—22no—
45C22×C3⋊D3—22no—
46C22×C3⋊D3—44no—
47C22×C3⋊D3C22⋊C412yes—
48C22×C3⋊D3C2×D412yes—
49C2×#157—44no—
50C2×#157—84no—
51C32×Q8—42no—
52C32×Q8—42no—
53C2×C32×C4—21no—
54C2×C32×C4—21no—
55C2×C32×C4—22no—
56C2×C32×C4—41no—
57C2×C32×C4—41no—
58C2×C32×C4C22⋊C411yescharacteristic
59C2×C32×C4C22×C411yescharacteristic
60C2×C3⋊Dic3—22no—
61C2×C3⋊Dic3—42no—
62C4⋊(C3⋊D3)—41no—
63C4⋊(C3⋊D3)—42no—
64C4⋊(C3⋊D3)—41no—
65C2×#124—91no—
66C2×#99—92no—
67#354—94no—
68C23×D3—64no—
69C2×C3×Q8—24no—
70C2×C3×Q8—24no—
71C2×C3×Q8—44no—
72C2×C3×Q8—44no—
73C22×C3×C4—24no—
74C22×C3×C4—22no—
75C22×Dic3—64no—
76C2×D12—62no—
77C2×D12—64no—
78C2×D12—62no—
79C2×D12—124no—
80C2×D12—124no—
81(C2×D3)⋊C4—616no—
82(C2×D3)⋊C4—616no—
83C4×Dic3—64no—
84C4×Dic3—64no—
85C22×C32—22no—
86C22×C32#9911yescharacteristic
87C22×C32#9911yescharacteristic
88C22×C32C2×C22⋊C411yescharacteristic
89C2×C3⋊D3—22no—
90C2×C3⋊D3—22no—
91C2×C3⋊D3—42no—
92C2×C3⋊D3—42no—
93C2×C3⋊D3—44no—
94C2×C3⋊D3—82no—
95#157—84no—
96C32×C4—21no—
97C32×C4—21no—
98C32×C4—42no—
99C3⋊Dic3—42no—
100C22×Q8#15711yescharacteristic, complemented
101C22×D4—91no—
102#124—92no—
103#124—92no—
104#124—182no—
105C2×C22⋊C4—182no—
106C2×C22⋊C4—182no—
107C2×C42—91no—
108#99—94no—
109#99—182no—
110C23×C3—22no—
111C22×D3—64no—
112C22×D3—64no—
113C22×D3—124no—
114C22×D3—124no—
115C22×D3—1216no—
116C3×Q8—48no—
117C3×Q8—48no—
118C2×C3×C4—24no—
119C2×C3×C4—24no—
120C2×C3×C4—28no—
121C2×C3×C4—22no—
122C2×C3×C4—22no—
123C2×C3×C4—44no—
124C2×C3×C4—44no—
125C2×Dic3—68no—
126C2×Dic3—128no—
127D12—124no—
128D12—128no—
129D12—124no—
130C2×C32—21no—
131C2×C32—21no—
132C2×C32#35412yescomplemented
133C2×C32C2×#9911yescharacteristic
134C3⋊D3—42no—
135C3⋊D3—42no—
136C24—92no—
137C2×Q8—21no—
138C2×Q8—41no—
139C2×Q8—41no—
140C2×Q8C2×#15712yescomplemented
141C2×D4—91no—
142C2×D4—91no—
143C2×D4—92no—
144C2×D4—361no—
145C2×D4—361no—
146C22×C4—21no—
147C22×C4—181no—
148C22×C4—362no—
149C22×C4C2×#15711yescharacteristic
150C22⋊C4—184no—
151C22⋊C4—184no—
152C22⋊C4—184no—
153C22⋊C4—362no—
154C42—92no—
155C42—181no—
156C22×C3—28no—
157C22×C3—22no—
158C22×C3—22no—
159C22×C3—22no—
160C2×D3—124no—
161C2×D3—124no—
162C2×D3—128no—
163C2×D3—128no—
164C2×D3—248no—
165C2×D3—248no—
166C3×C4—24no—
167C3×C4—24no—
168C3×C4—48no—
169Dic3—128no—
170C32C2×#35411yescharacteristic, complemented, Sylow
171C23—92no—
172C23—92no—
173C23—182no—
174C23—182no—
175C23—364no—
176C23C22⋊#15711yescharacteristic
177Q8—42no—
178Q8—42no—
179D4—361no—
180D4—361no—
181D4—362no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—182no—
188C2×C4—362no—
189C2×C4—364no—
190C2×C4—724no—
191C2×C4C22⋊#15711yescharacteristic
192C2×C4C22×#15711yescharacteristic
193C2×C3—24no—
194C2×C3—24no—
195C2×C3—24no—
196C2×C3—22no—
197D3—244no—
198D3—244no—
199C22—22no—
200C22—182no—
201C22—182no—
202C22—362no—
203C22—362no—
204C22—364no—
205C22—722no—
206C22#6378611yescharacteristic
207C22#6378611yescharacteristic
208C22C2×C22⋊#15711yescharacteristic
209C4—21no—
210C4—21no—
211C4—42no—
212C4—362no—
213C4—724no—
214C3—22no—
215C2—21no—
216C2—21no—
217C2—362no—
218C2—362no—
219C2#1059021712yesdirect product factor
220C2C2×#6378611yescharacteristic
subgroupG/H
centerC22#63786
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC22×C32×Q8C4
socleC22×C32#99
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC2×C4⋊(C3⋊D3)C23
hypercenterC22×Q8#157
hypocenterC32C2×#354
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #10590217C2direct (N × H)
4. C22×C32×Q8C4semidirect
8. #64156C4semidirect
11. C2×C4×C3⋊Dic3C4semidirect
20. C2×C32×Q8C2×C4semidirect
34. C4×C3⋊Dic3C2×C4semidirect
100. C22×Q8#157semidirect
132. C2×C32#354semidirect
140. C2×Q8C2×#157semidirect
170. C32C2×#354semidirect
219. C2#10590217direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641562
C2×#637742
#105902172
C2×#3549