Finite Group Databasebeta

← #11882214

Subgroups — #11882214

Order 1152.

746 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 746 conjugacy classes of subgroups — too many to draw. Only its 113 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#10595032C212yesmaximal, complemented
2C2×C4⋊#622C211yesmaximal, characteristic, complemented
3#10593520C214yesmaximal, complemented
4#10593417C214yesmaximal, complemented
5#10593347C214yesmaximal, complemented
6C2×C3×#235—22no—
7C22×#622C2212yes—
8C2×#3774C2214yes—
9C2×C4×C3⋊Dic3C2211yescharacteristic
10#63980—22no—
11#63980C2214yes—
12#63914C2212yes—
13C4×#625—22no—
14C4×#625C2214yes—
15#63873C2212yes—
16#63863—22no—
17C4⋊#622C2214yes—
18#63743C2214yes—
19#63739C2218yes—
20#5832—62no—
21C22×C32×C4D411yescharacteristic
22C22×C3⋊Dic3D411yescharacteristic
23C22×C3⋊Dic3C2311yescharacteristic
24C2×C3×#67—24no—
25C3×#235—48no—
26C2×C3×D12—22no—
27C2×C3×C4×D3—24no—
28C2×C3×Dic6—22no—
29C2×#625—22no—
30C2×#625C2314yes—
31C2×#622—42no—
32C2×#622C2314yes—
33#3774—44no—
34C4×C3⋊Dic3D412yes—
35C4×C3⋊Dic3C2312yes—
36#3724—22no—
37#3724C2314yes—
38(C2×D3)⋊Dic3—24no—
39(C2×D3)⋊Dic3—24no—
40#3245—91nomaximal, Sylow
41C2×C3×#41—62no—
42C2×#235—22no—
43#947—62no—
44#944—62no—
45#940—62no—
46#939—64no—
47#939—64no—
48#936—62no—
49C4×#67—64no—
50C4×#67—64no—
51C2×C4×Dic3—62no—
52C23×C32C2×D411yescharacteristic
53C22×C3×D3—24no—
54C2×C32×C4D814yescomplemented
55C2×C32×C4C2×D412yes—
56C2×C3⋊Dic3—21no—
57C2×C3⋊Dic3—21no—
58C2×C3⋊Dic3—41no—
59C2×C3⋊Dic3C2×D411yescharacteristic
60C2×C3⋊Dic3C2×D412yes—
61C2×C3⋊Dic3C2411yescharacteristic
62C3×#67—48no—
63C2×C3×Dic3—24no—
64C3×D12—44no—
65C3×C4×D3—48no—
66C3×Dic6—44no—
67#625—24no—
68#625—24no—
69#625—44no—
70#622—24no—
71#532—92no—
72#474—94no—
73#466—94no—
74#459—94no—
75C2×C4⋊C8—91no—
76C3×#41—128no—
77C2×C3×Q8—62no—
78C2×C3×D4—62no—
79C2×C3×D4—64no—
80C22×C3×C4—22no—
81C22×C3×C4—64no—
82C2×#67—24no—
83C2×#67—64no—
84C2×#67—64no—
85C22×Dic3—62no—
86C22×Dic3—62no—
87#235—48no—
88C2×D12—22no—
89C2×C4×D3—24no—
90C2×Dic6—22no—
91#217—64no—
92#217—64no—
93(C2×D3)⋊C4—64no—
94(C2×D3)⋊C4—64no—
95Dic3⋊C4—64no—
96Dic3⋊C4—64no—
97C4×Dic3—62no—
98C4×Dic3—62no—
99C4×Dic3—62no—
100C4×Dic3—62no—
101C22×C32—21no—
102C22×C32—21no—
103C22×C32C2×D812yes—
104C22×C32C22×D411yescharacteristic
105C2×C3×D3—44no—
106C2×C3×D3—44no—
107C2×C3×D3—44no—
108C32×C4C2×D814yes—
109C3⋊Dic3—22no—
110C3⋊Dic3—21no—
111C3⋊Dic3H(5,𝔽2)11yescharacteristic
112C3⋊Dic32−1+411yescharacteristic
113C3×Dic3—44no—
114C2×#41—62no—
115C2×D8—94no—
116C22×C8—92no—
117C4⋊Q8—92no—
118#127—92no—
119#124—182no—
120#121—94no—
121#121—182no—
122C4×D4—94no—
123C4×D4—182no—
124C2×C42—91no—
125#107—94no—
126C4⋊C8—94no—
127#102—98no—
128C23×C3—22no—
129C23×C3—64no—
130C22×D3—24no—
131C3×Q8—124no—
132C3×D4—124no—
133C3×D4—128no—
134C2×C3×C4—22no—
135C2×C3×C4—22no—
136C2×C3×C4—28no—
137C2×C3×C4—64no—
138C2×C3×C4—128no—
139#67—48no—
140#67—124no—
141#67—124no—
142#67—128no—
143C2×Dic3—24no—
144C2×Dic3—62no—
145C2×Dic3—62no—
146C2×Dic3—62no—
147C2×Dic3—62no—
148C2×Dic3—122no—
149C2×Dic3—122no—
150C2×Dic3—124no—
151D12—44no—
152C4×D3—48no—
153Dic6—44no—
154C2×C32—22no—
155C2×C32#53711yescharacteristic
156C2×C32C22×D811yescharacteristic
157C2×C32#57511yescharacteristic
158C3×D3—84no—
159#41—128no—
160C2×Q8—62no—
161C2×D4—64no—
162C2×D4—62no—
163C2×D4—94no—
164C2×D4—182no—
165C22×C4—64no—
166C22×C4—91no—
167C22×C4—91no—
168C22×C4GO+(4,𝔽2)11yescharacteristic
169D8—364no—
170C2×C8—94no—
171C2×C8—362no—
172C4⋊C4—94no—
173C4⋊C4—182no—
174C22⋊C4—184no—
175C22⋊C4—184no—
176C42—92no—
177C42—92no—
178C22×C3—22no—
179C22×C3—24no—
180C22×C3—42no—
181C22×C3—42no—
182C22×C3—124no—
183C22×C3—124no—
184C22×C3—124no—
185C2×D3—44no—
186C2×D3—44no—
187C2×D3—44no—
188C3×C4—24no—
189C3×C4—24no—
190C3×C4—124no—
191Dic3—44no—
192Dic3—62no—
193Dic3—62no—
194Dic3—64no—
195Dic3—122no—
196Dic3—122no—
197C32#324511yescharacteristic, complemented, Sylow
198C23—64no—
199C23C2×GO+(4,𝔽2)11yescharacteristic
200Q8—124no—
201D4—128no—
202D4—124no—
203D4—184no—
204D4—184no—
205D4—364no—
206C2×C4—64no—
207C2×C4—91no—
208C2×C4—91no—
209C2×C4—92no—
210C2×C4—128no—
211C2×C4—181no—
212C2×C4—181no—
213C2×C4—361no—
214C2×C4#377414yescomplemented
215C2×C4C2×GO+(4,𝔽2)12yes—
216C8—184no—
217C2×C3—22no—
218C2×C3—22no—
219C2×C3—22no—
220C2×C3—44no—
221C2×C3—244no—
222D3—84no—
223C22—21no—
224C22—21no—
225C22—124no—
226C22—124no—
227C22—124no—
228C22C2×#377412yes—
229C22C22×GO+(4,𝔽2)11yescharacteristic
230C4—91no—
231C4—91no—
232C4—124no—
233C4—182no—
234C4—181no—
235C4C2×#377414yes—
236C3—22no—
237C2—22no—
238C2—244no—
239C2#1059650211yescharacteristic
240C2#1059651311yescharacteristic
241C2C22×#377411yescharacteristic
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. #10595032C2semidirect
2. C2×C4⋊#622C2semidirect
3. #10593520C2semidirect
4. #10593417C2semidirect
5. #10593347C2semidirect
54. C2×C32×C4D8semidirect
197. C32#3245semidirect
214. C2×C4#3774semidirect

Maximal subgroups

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

subgroupindex
#105950322
C2×C4⋊#6222
#105935202
#105934172
#105933472
#32459