Finite Group Databasebeta

← C2×#10593333 #11899529

Subgroups — C2×#10593333 #11899529

Order 1152.

634 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 111 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×#63822C212yesmaximal, complemented
2C22×#3708C211yesmaximal, characteristic, complemented
3C2×#63736C211yesmaximal, characteristic, complemented
4C2×#63735C212yesmaximal, complemented
5#10593333C218yesmaximal, direct product factor
6C2×#63734C211yesmaximal, characteristic, complemented
7C2×C3×#235—22no—
8C22×C3⋊(C3⋊C8)C2211yescharacteristic
9C2×#3718C2212yes—
10C2×#3715—22no—
11#63822—24no—
12#63822C2218yescomplemented
13C2×#3713C2212yes—
14C2×#3708C2211yescharacteristic
15C2×#3708C2211yescharacteristic
16C2×#3708C2214yescomplemented
17#63736C2214yescomplemented
18#63735C2218yescomplemented
19#63734C2214yescomplemented
20C2×#950—62no—
21C22×C32×C4D411yescharacteristic
22C2×C3×#67—42no—
23C3×#235—28no—
24C3×#235—44no—
25C2×C3×D12—22no—
26C2×C3×C4×D3—42no—
27C2×C3×Dic6—22no—
28C2×C3⋊(C3⋊C8)D412yes—
29C2×C3⋊(C3⋊C8)D411yescharacteristic
30C2×C3⋊(C3⋊C8)C2311yescharacteristic
31C2×C3⋊(C3⋊C8)C2312yes—
32#3718—22no—
33#3718C2314yes—
34#3715—28no—
35#3713—22no—
36#3713C2314yes—
37#3708C2312yes—
38#3708C2312yes—
39C2×#508—91nomaximal, Sylow
40C2×C3×#41—62no—
41C2×#235—22no—
42#950—68no—
43#950—68no—
44C2×#216—62no—
45C2×#215—62no—
46C2×#214—62no—
47C2×#213—62no—
48C22×C3⋊C8—62no—
49C23×C32D811yescharacteristic
50C22×C3×D3—42no—
51C2×C32×C4D811yescharacteristic
52C2×C32×C4D812yes—
53C2×C32×C4C2×D411yescharacteristic
54C2×C32×C4C2×D412yes—
55C3×#67—48no—
56C2×C3×Dic3—42no—
57C3×D12—24no—
58C3×D12—42no—
59C3×C4×D3—48no—
60C3×Dic6—24no—
61C3×Dic6—42no—
62C3⋊(C3⋊C8)C2×D411yescharacteristic
63C3⋊(C3⋊C8)C2×D412yes—
64C3⋊(C3⋊C8)C2411yescharacteristic
65C2×#135—92no—
66#508—98no—
67C2×Q32—91no—
68C2×SD32—92no—
69C2×D16—91no—
70C22×C16—91no—
71C3×#41—68no—
72C3×#41—124no—
73C2×C3×Q8—62no—
74C2×C3×D4—62no—
75C2×C3×D4—122no—
76C22×C3×C4—22no—
77C22×C3×C4—122no—
78C2×#67—42no—
79#235—28no—
80#235—44no—
81C2×D12—22no—
82C2×C4×D3—42no—
83C2×Dic6—22no—
84#216—64no—
85#216—64no—
86#215—68no—
87#214—68no—
88#213—64no—
89#213—64no—
90C2×C3⋊C8—62no—
91C2×C3⋊C8—62no—
92C2×C3⋊C8—64no—
93C2×C3⋊C8—64no—
94C22×C32—22no—
95C22×C32C2×D812yes—
96C22×C32C2×D811yescharacteristic
97C2×C3×D3—44no—
98C2×C3×D3—84no—
99C32×C4C2×D811yescharacteristic
100C32×C4C2×D812yes—
101C32×C4C22×D411yescharacteristic
102C3×Dic3—44no—
103C2×#41—62no—
104#135—98no—
105#135—184no—
106C2×Q16—92no—
107C2×SD16—182no—
108C2×D8—92no—
109C22×C8—91no—
110Q32—94no—
111SD32—98no—
112D16—94no—
113C2×C16—91no—
114C2×C16—91no—
115C2×C16—94no—
116C23×C3—22no—
117C23×C3—122no—
118C22×D3—42no—
119C3×Q8—64no—
120C3×Q8—122no—
121C3×D4—64no—
122C3×D4—122no—
123C3×D4—128no—
124C2×C3×C4—22no—
125C2×C3×C4—24no—
126C2×C3×C4—24no—
127C2×C3×C4—22no—
128C2×C3×C4—128no—
129C2×C3×C4—122no—
130#67—48no—
131C2×Dic3—42no—
132D12—24no—
133D12—42no—
134C4×D3—48no—
135Dic6—24no—
136Dic6—42no—
137C3⋊C8—62no—
138C3⋊C8—64no—
139C3⋊C8—62no—
140C2×C32—22no—
141C2×C32#50812yescomplemented
142C2×C32C22×D811yescharacteristic
143C3×D3—84no—
144#41—68no—
145#41—124no—
146C2×Q8—62no—
147C2×D4—62no—
148C2×D4—122no—
149C22×C4—122no—
150C22×C4GO+(4,𝔽2)11yescharacteristic
151Q16—94no—
152Q16—182no—
153SD16—188no—
154D8—94no—
155D8—182no—
156C2×C8—91no—
157C2×C8—92no—
158C2×C8—91no—
159C2×C8—92no—
160C16—92no—
161C16—92no—
162C22×C3—22no—
163C22×C3—24no—
164C22×C3—44no—
165C22×C3—124no—
166C22×C3—244no—
167C2×D3—44no—
168C2×D3—84no—
169C3×C4—22no—
170C3×C4—22no—
171C3×C4—24no—
172C3×C4—124no—
173Dic3—44no—
174C32C2×#50811yescharacteristic, complemented, Sylow
175C23—122no—
176C23#377411yescharacteristic
177Q8—64no—
178Q8—122no—
179D4—64no—
180D4—128no—
181D4—122no—
182C2×C4—122no—
183C2×C4—128no—
184C2×C4#377412yes—
185C2×C4#377411yescharacteristic
186C2×C4C2×GO+(4,𝔽2)11yescharacteristic
187C2×C4C2×GO+(4,𝔽2)12yes—
188C8—91no—
189C8—91no—
190C8—92no—
191C2×C3—24no—
192C2×C3—22no—
193C2×C3—44no—
194C2×C3—244no—
195D3—84no—
196C22—22no—
197C22—124no—
198C22—244no—
199C22C2×#377412yes—
200C22C2×#377411yescharacteristic
201C4—124no—
202C4C2×#377412yes—
203C4C2×#377411yescharacteristic
204C4C22×GO+(4,𝔽2)11yescharacteristic
205C3—22no—
206C2—22no—
207C2—244no—
208C2#1059333312yesdirect product factor
209C2C22×#377411yescharacteristic
subgroupG/H
centerC2×C4#3774
commutator, cosocleC3⋊(C3⋊C8)C24
FrattiniC4C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×D8
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#508
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#63822C2semidirect
2. C22×#3708C2semidirect
3. C2×#63736C2semidirect
4. C2×#63735C2semidirect
5. #10593333C2direct (N × H)
6. C2×#63734C2semidirect
12. #63822C22semidirect
16. C2×#3708C22semidirect
17. #63736C22semidirect
18. #63735C22semidirect
19. #63734C22semidirect
141. C2×C32#508semidirect
174. C32C2×#508semidirect
208. C2#10593333direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638222
C22×#37082
C2×#637362
C2×#637352
#105933332
C2×#637342
C2×#5089