Finite Group Databasebeta

← #11796392

Subgroups — #11796392

Order 1152.

620 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 54 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#10596301C211yesmaximal, characteristic
2C2×#63774C212yesmaximal, complemented
3#10590217C212yesmaximal, complemented
4#10590211C212yesmaximal, complemented
5C2×C32×#41C411yescharacteristic, complemented
6C22×C4⋊(C3⋊D3)C2211yescharacteristic
7C2×C22⋊#157—22no—
8#64156C411yescharacteristic, complemented
9#64156C2211yescharacteristic
10#64149C411yescharacteristic, complemented
11#64149C2211yescharacteristic
12#64146—22no—
13#64139—22no—
14#64135C411yescharacteristic, complemented
15#63774—22no—
16#63774C2214yes—
17#5830—62no—
18C23×C3⋊D3D412yes—
19C22×#157—42no—
20C32×#41—42no—
21C2×C32×Q8C2×C411yescharacteristic, complemented
22C2×C32×D4—21no—
23C2×C32×D4C2×C411yescharacteristic, complemented
24C22×C32×C4—21no—
25C22×C32×C4C2×C411yescharacteristic
26C2×#638—22no—
27C2×#638—22no—
28C2×C4⋊(C3⋊D3)—42no—
29C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
30C2×C4⋊(C3⋊D3)D412yes—
31C2×C4⋊(C3⋊D3)C2311yescharacteristic
32C22⋊#157—24no—
33C22⋊#157—42no—
34#3757—21no—
35#3752—22no—
36#3752—22no—
37C4⋊(C3⋊Dic3)—21no—
38C4×C3⋊Dic3C2×C411yescharacteristic, complemented
39C4×C3⋊Dic3C2×C411yescharacteristic, complemented
40#2127—91nomaximal, Sylow
41C2×C3×#41—22no—
42C22×D12—62no—
43#947—62no—
44#947—62no—
45#940—62no—
46#940—62no—
47#937—68no—
48#930—68no—
49#926—62no—
50C23×C32—21no—
51C23×C32C22⋊C411yescharacteristic
52C22×C3⋊D3—22no—
53C22×C3⋊D3—22no—
54C22×C3⋊D3—82no—
55C22×C3⋊D3C22⋊C412yes—
56C22×C3⋊D3C2×D412yes—
57C2×#157—44no—
58C2×#157—84no—
59C32×Q8—41no—
60C32×D4—41no—
61C32×D4—42no—
62C2×C32×C4—22no—
63C2×C32×C4—21no—
64C2×C32×C4—42no—
65C2×C32×C4C22⋊C411yescharacteristic
66C2×C32×C4C22×C411yescharacteristic
67#638—82no—
68#638—82no—
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3—21no—
71C4⋊(C3⋊D3)—41no—
72C4⋊(C3⋊D3)—42no—
73C4⋊(C3⋊D3)—41no—
74#535—91no—
75C2×#99—92no—
76#354—92no—
77#353—92no—
78C23×D3—64no—
79C3×#41—48no—
80C2×C3×Q8—22no—
81C2×C3×D4—24no—
82C2×C3×D4—22no—
83C22×C3×C4—24no—
84C22×C3×C4—22no—
85C2×#67—68no—
86C2×#67—68no—
87C2×D12—64no—
88C2×D12—62no—
89C2×D12—62no—
90C2×D12—128no—
91#217—64no—
92(C2×D3)⋊C4—68no—
93(C2×D3)⋊C4—68no—
94C4⋊Dic3—64no—
95C4×Dic3—62no—
96C4×Dic3—62no—
97C22×C32—41no—
98C22×C32—42no—
99C22×C32—41no—
100C22×C32#9912yes—
101C22×C32C2×C22⋊C411yescharacteristic
102C2×C3⋊D3—22no—
103C2×C3⋊D3—22no—
104C2×C3⋊D3—42no—
105C2×C3⋊D3—42no—
106C2×C3⋊D3—44no—
107C2×C3⋊D3—82no—
108#157—84no—
109C32×C4—21no—
110C32×C4—21no—
111C32×C4—41no—
112C3⋊Dic3—41no—
113C3⋊Dic3—41no—
114C2×#41#15711yescharacteristic, complemented
115C22×D4—91no—
116#127—91no—
117#127—91no—
118#124—91no—
119#124—91no—
120#121—182no—
121#120—182no—
122#117—91no—
123C2×C22⋊C4—182no—
124#99—94no—
125#99—182no—
126C23×C3—24no—
127C23×C3—22no—
128C22×D3—64no—
129C22×D3—64no—
130C22×D3—124no—
131C22×D3—124no—
132C22×D3—248no—
133C3×Q8—44no—
134C3×D4—44no—
135C3×D4—48no—
136C2×C3×C4—28no—
137C2×C3×C4—24no—
138C2×C3×C4—22no—
139C2×C3×C4—22no—
140C2×C3×C4—48no—
141#67—248no—
142#67—248no—
143C2×Dic3—64no—
144C2×Dic3—64no—
145D12—128no—
146D12—124no—
147D12—124no—
148C2×C32—21no—
149C2×C32—22no—
150C2×C32—81no—
151C2×C32C2×#9911yescharacteristic
152C3⋊D3—42no—
153C3⋊D3—42no—
154C24—92no—
155#41—42no—
156C2×Q8C2×#15711yescharacteristic, complemented
157C2×D4—21no—
158C2×D4—91no—
159C2×D4—91no—
160C2×D4—92no—
161C2×D4—182no—
162C2×D4—182no—
163C2×D4—362no—
164C2×D4C2×#15711yescharacteristic, complemented
165C22×C4—21no—
166C22×C4—362no—
167C22×C4C2×#15711yescharacteristic
168C4⋊C4—181no—
169C22⋊C4—182no—
170C22⋊C4—182no—
171C22⋊C4—181no—
172C22⋊C4—184no—
173C22⋊C4—362no—
174C42—91no—
175C42—91no—
176C22×C3—22no—
177C22×C3—24no—
178C22×C3—44no—
179C22×C3—48no—
180C22×C3—44no—
181C2×D3—124no—
182C2×D3—124no—
183C2×D3—128no—
184C2×D3—128no—
185C2×D3—248no—
186C2×D3—248no—
187C3×C4—24no—
188C3×C4—24no—
189C3×C4—44no—
190Dic3—124no—
191Dic3—124no—
192C32#212711yescharacteristic, complemented, Sylow
193C23—21no—
194C23—92no—
195C23—92no—
196C23—182no—
197C23—182no—
198C23—722no—
199C23C22⋊#15711yescharacteristic
200Q8—41no—
201D4—41no—
202D4—42no—
203D4—362no—
204D4—361no—
205D4—361no—
206D4—722no—
207D4—722no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—181no—
212C2×C4—181no—
213C2×C4—364no—
214C2×C4—724no—
215C2×C4C22⋊#15711yescharacteristic
216C2×C4C22×#15711yescharacteristic
217C2×C3—24no—
218C2×C3—22no—
219C2×C3—44no—
220C2×C3—84no—
221D3—244no—
222D3—244no—
223C22—41no—
224C22—42no—
225C22—41no—
226C22—182no—
227C22—182no—
228C22—362no—
229C22—362no—
230C22—364no—
231C22—722no—
232C22#6378612yes—
233C22C2×C22⋊#15711yescharacteristic
234C4—21no—
235C4—21no—
236C4—41no—
237C4—361no—
238C4—361no—
239C4—724no—
240C3—22no—
241C2—21no—
242C2—22no—
243C2—81no—
244C2—362no—
245C2—362no—
246C2C2×#6378611yescharacteristic
subgroupG/H
centerC2C2×#63786
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC2×C32×#41C4
socleC2×C32C2×#99
prime radical#10596301C2
cosocleC2×C4⋊(C3⋊D3)C23
hypercenterC2×#41#157
hypocenterC32#2127
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#63774C2semidirect
3. #10590217C2semidirect
4. #10590211C2semidirect
5. C2×C32×#41C4semidirect
8. #64156C4semidirect
10. #64149C4semidirect
14. #64135C4semidirect
21. C2×C32×Q8C2×C4semidirect
23. C2×C32×D4C2×C4semidirect
38. C4×C3⋊Dic3C2×C4semidirect
39. C4×C3⋊Dic3C2×C4semidirect
114. C2×#41#157semidirect
156. C2×Q8C2×#157semidirect
164. C2×D4C2×#157semidirect
192. C32#2127semidirect

Maximal subgroups

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

subgroupindex
#105963012
C2×#637742
#105902172
#105902112
#21279