Finite Group Databasebeta

← #11882216

Subgroups — #11882216

Order 1152.

746 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 746 conjugacy classes of subgroups — too many to draw. Only its 105 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
1#10594929C212yesmaximal, complemented
2C2×#63779C211yesmaximal, characteristic, complemented
3#10593520C214yesmaximal, complemented
4#10593426C214yesmaximal, complemented
5#10593367C214yesmaximal, complemented
6C2×#3805—22no—
7C22×#622C2212yes—
8C2×#3774C2214yes—
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C3×#930—22no—
11#63980C2214yes—
12#63919C2212yes—
13#63915—22no—
14#63914C2212yes—
15#63902C2214yes—
16#63898—22no—
17#63779C2214yes—
18#63743C2214yes—
19#63739C2218yes—
20#5596—62no—
21C22×C32×C4D411yescharacteristic
22C22×C3⋊Dic3D411yescharacteristic
23C22×C3⋊Dic3C2311yescharacteristic
24C2×C3×#67—24no—
25C2×C3×D12—22no—
26C2×#627—22no—
27C2×#625—22no—
28C2×#625C2314yes—
29#3805—48no—
30C2×D3×Dic3—24no—
31C2×#622—42no—
32C2×#622C2314yes—
33#3774—44no—
34C4×C3⋊Dic3D412yes—
35C4×C3⋊Dic3C2312yes—
36C3×(C2×D3)⋊C4—24no—
37C3×C4⋊Dic3—22no—
38#3724C2314yes—
39(C2×D3)⋊Dic3—24no—
40#3245—91nomaximal, Sylow
41C2×#237—64no—
42C3×#121—62no—
43#940—62no—
44#939—64no—
45D4×Dic3—62no—
46#930—22no—
47C2×C4×Dic3—62no—
48#893—62no—
49#888—62no—
50#885—64no—
51#67⋊C4—64no—
52C23×C32C2×D411yescharacteristic
53C22×C3×D3—24no—
54C2×C32×C4—41no—
55C2×C32×C4C2×D412yes—
56C2×C3⋊Dic3—21no—
57C2×C3⋊Dic3—21no—
58C2×C3⋊Dic3D814yescomplemented
59C2×C3⋊Dic3C2×D411yescharacteristic
60C2×C3⋊Dic3C2×D412yes—
61C2×C3⋊Dic3C2411yescharacteristic
62C3×#67—48no—
63C2×C3×Dic3—24no—
64C3×D12—44no—
65#627—44no—
66#625—24no—
67#625—24no—
68#625—44no—
69D3×Dic3—48no—
70#622—24no—
71#532—92no—
72#474—94no—
73#466—94no—
74#459—94no—
75C2×C4⋊C8—91no—
76C2×C3×D4—62no—
77C2×C3×D4—64no—
78C22×C3×C4—22no—
79C2×#67—24no—
80C2×#67—64no—
81C2×#67—64no—
82C22×Dic3—62no—
83C22×Dic3—62no—
84C22×Dic3—64no—
85#237—1216no—
86C2×D12—22no—
87C2×C4×D3—64no—
88C2×Dic6—64no—
89C3×C4⋊C4—62no—
90C3×C22⋊C4—64no—
91#217—64no—
92(C2×D3)⋊C4—24no—
93(C2×D3)⋊C4—64no—
94C4⋊Dic3—22no—
95Dic3⋊C4—64no—
96C4×Dic3—62no—
97C4×Dic3—62no—
98C4×Dic3—62no—
99C4×Dic3—62no—
100C22×C32—21no—
101C22×C32—21no—
102C22×C32C2×D812yes—
103C22×C32C22×D411yescharacteristic
104C2×C3×D3—44no—
105C2×C3×D3—44no—
106C2×C3×D3—44no—
107C32×C4—22no—
108C3⋊Dic3—21no—
109C3⋊Dic3C2×D814yes—
110C3⋊Dic3H(5,𝔽2)11yescharacteristic
111C3⋊Dic32−1+411yescharacteristic
112C3×Dic3—44no—
113C2×#41—182no—
114C2×D8—94no—
115C22×C8—92no—
116C4⋊Q8—92no—
117#127—92no—
118#124—182no—
119#121—62no—
120#121—94no—
121C4×D4—94no—
122C4×D4—182no—
123C2×C42—91no—
124#107—94no—
125C4⋊C8—94no—
126#102—98no—
127C23×C3—22no—
128C23×C3—64no—
129C22×D3—24no—
130C3×D4—124no—
131C3×D4—128no—
132C2×C3×C4—22no—
133C2×C3×C4—22no—
134C2×C3×C4—44no—
135C2×C3×C4—64no—
136#67—48no—
137#67—124no—
138#67—124no—
139#67—128no—
140C2×Dic3—24no—
141C2×Dic3—68no—
142C2×Dic3—62no—
143C2×Dic3—62no—
144C2×Dic3—62no—
145C2×Dic3—62no—
146C2×Dic3—122no—
147C2×Dic3—122no—
148C2×Dic3—128no—
149D12—44no—
150C4×D3—128no—
151Dic6—128no—
152C2×C32—22no—
153C2×C32#53711yescharacteristic
154C2×C32C22×D811yescharacteristic
155C2×C32#57511yescharacteristic
156C3×D3—84no—
157#41—368no—
158C2×Q8—182no—
159C2×D4—64no—
160C2×D4—62no—
161C2×D4—94no—
162C2×D4—182no—
163C22×C4—91no—
164C22×C4—91no—
165C22×C4—184no—
166C22×C4GO+(4,𝔽2)11yescharacteristic
167D8—364no—
168C2×C8—94no—
169C2×C8—362no—
170C4⋊C4—62no—
171C4⋊C4—94no—
172C22⋊C4—64no—
173C22⋊C4—184no—
174C42—92no—
175C42—92no—
176C22×C3—22no—
177C22×C3—24no—
178C22×C3—42no—
179C22×C3—42no—
180C22×C3—124no—
181C22×C3—124no—
182C22×C3—124no—
183C2×D3—44no—
184C2×D3—44no—
185C2×D3—44no—
186C3×C4—24no—
187C3×C4—42no—
188C3×C4—124no—
189Dic3—44no—
190Dic3—64no—
191Dic3—64no—
192Dic3—62no—
193Dic3—62no—
194Dic3—122no—
195C32#324511yescharacteristic, complemented, Sylow
196C23—64no—
197C23C2×GO+(4,𝔽2)11yescharacteristic
198Q8—364no—
199D4—124no—
200D4—128no—
201D4—184no—
202D4—184no—
203D4—364no—
204C2×C4—41no—
205C2×C4—64no—
206C2×C4—91no—
207C2×C4—92no—
208C2×C4—94no—
209C2×C4—91no—
210C2×C4—181no—
211C2×C4—181no—
212C2×C4—368no—
213C2×C4C2×GO+(4,𝔽2)12yes—
214C8—184no—
215C2×C3—22no—
216C2×C3—22no—
217C2×C3—22no—
218C2×C3—44no—
219C2×C3—244no—
220D3—84no—
221C22—21no—
222C22—21no—
223C22—124no—
224C22—124no—
225C22—124no—
226C22#6422512yes—
227C22C22×GO+(4,𝔽2)11yescharacteristic
228C4—22no—
229C4—94no—
230C4—91no—
231C4—91no—
232C4—124no—
233C4—181no—
234C3—22no—
235C2—22no—
236C2—244no—
237C2C2×#6422511yescharacteristic
238C2#1059651311yescharacteristic
239C2#1059653211yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC22×C32×C4D4
socleC22×C32C22×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#3245
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. #10594929C2semidirect
2. C2×#63779C2semidirect
3. #10593520C2semidirect
4. #10593426C2semidirect
5. #10593367C2semidirect
58. C2×C3⋊Dic3D8semidirect
195. C32#3245semidirect

Maximal subgroups

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

subgroupindex
#105949292
C2×#637792
#105935202
#105934262
#105933672
#32459