Finite Group Databasebeta

← #11775056

Subgroups — #11775056

Order 1152.

594 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 70 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#10596196C211yesmaximal, characteristic
2C4×C4⋊#157C211yesmaximal, characteristic, complemented
3#10593727C211yesmaximal, characteristic, complemented
4#10590157C214yesmaximal, complemented
5C2×#3832—21no—
6C2×C4⋊#157—21no—
7C2×C4×#157—21no—
8C32×C4⋊Q8C411yescharacteristic, complemented
9#64156—21no—
10#64104—21no—
11#64104C2212yes—
12#64102—21no—
13#64102C412yescomplemented
14#64083C411yescharacteristic, complemented
15C42×C3⋊D3C2211yescharacteristic
16#63781C2212yes—
17#63778C2212yes—
18C4⋊#622—21no—
19C4×#622—21no—
20#5725—62no—
21C22×#157—22no—
22C2×C32×Q8—21no—
23#3832—42no—
24#3832—42no—
25C2×C4⋊(C3⋊D3)—22no—
26C2×C4⋊(C3⋊D3)—21no—
27C2×C4⋊(C3⋊D3)—21no—
28C2×C4⋊(C3⋊D3)C2×C412yes—
29C2×C4×C3⋊D3—22no—
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C4×C3⋊D3D411yescharacteristic
32C2×C4×C3⋊D3C2311yescharacteristic
33C2×#622—22no—
34C4⋊#157—24no—
35C4×#157—42no—
36C32×C4⋊C4—21no—
37C32×C4⋊C4C2×C412yes—
38C32×C42C2×C411yescharacteristic
39#3752—22no—
40#3752—22no—
41C4×C3⋊Dic3C2×C411yescharacteristic
42C4×C3⋊Dic3D411yescharacteristic
43C4×C3⋊Dic3D411yescharacteristic
44#1502—91nomaximal, Sylow
45C2×#239—64no—
46C3×C4⋊Q8—22no—
47#947—64no—
48#895—64no—
49#895—64no—
50#893—64no—
51#893—64no—
52#874—62no—
53C42×D3—62no—
54C22×C3⋊D3—22no—
55C22×C3⋊D3C2×D411yescharacteristic
56C2×#157—24no—
57C2×#157—42no—
58C2×#157—42no—
59C32×Q8—42no—
60C2×C32×C4—22no—
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4C22×C411yescharacteristic
64C2×C3⋊Dic3C22⋊C411yescharacteristic
65C2×C3⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3C2×D411yescharacteristic
67C4⋊(C3⋊D3)—42no—
68C4⋊(C3⋊D3)—42no—
69C4⋊(C3⋊D3)—42no—
70C4⋊(C3⋊D3)—42no—
71C4⋊(C3⋊D3)—42no—
72C4×C3⋊D3—22no—
73C4×C3⋊D3—41no—
74C4×C3⋊D3—44no—
75C4×C3⋊D3D812yes—
76C4×C3⋊D3SD1612yes—
77#622—42no—
78#532—91no—
79#431—91no—
80C4×C4⋊C4—91no—
81#327—94no—
82C2×C3×Q8—24no—
83#239—128no—
84#239—128no—
85C2×D12—64no—
86C2×D12—64no—
87C2×D12—64no—
88C2×D12—68no—
89C2×C4×D3—62no—
90C2×C4×D3—62no—
91C2×C4×D3—62no—
92C2×C4×D3—68no—
93C3×C4⋊C4—24no—
94C3×C4⋊C4—24no—
95C3×C42—22no—
96(C2×D3)⋊C4—68no—
97(C2×D3)⋊C4—68no—
98C4×Dic3—62no—
99C4×Dic3—62no—
100C4×Dic3—62no—
101C22×C32C2×C22⋊C411yescharacteristic
102C2×C3⋊D3—21no—
103C2×C3⋊D3—21no—
104C2×C3⋊D3—42no—
105C2×C3⋊D3—42no—
106C2×C3⋊D3—42no—
107C2×C3⋊D3C2×D811yescharacteristic
108C2×C3⋊D3C2×SD1611yescharacteristic
109#157—44no—
110C32×C4—21no—
111C32×C4—42no—
112C32×C4#10212yes—
113C32×C4#10412yes—
114C3⋊Dic3—21no—
115C3⋊Dic3—21no—
116C3⋊Dic3#10212yes—
117C2×#41—181no—
118C4⋊Q8#15711yescharacteristic, complemented
119#127—91no—
120#124—181no—
121#121—92no—
122#121—181no—
123C4×D4—92no—
124C4×D4—181no—
125C2×C4⋊C4—181no—
126C2×C42—91no—
127C2×C42—181no—
128C4⋊C8—181no—
129C22⋊C8—92no—
130C4×C8—181no—
131#95—92no—
132C22×D3—62no—
133C22×D3—68no—
134C3×Q8—48no—
135C2×C3×C4—28no—
136C2×C3×C4—22no—
137C2×C3×C4—22no—
138C2×C3×C4—22no—
139C2×Dic3—62no—
140C2×Dic3—62no—
141C2×Dic3—62no—
142D12—128no—
143D12—128no—
144D12—128no—
145D12—128no—
146D12—128no—
147C4×D3—64no—
148C4×D3—64no—
149C4×D3—124no—
150C4×D3—1216no—
151C4×D3—124no—
152C2×C32#41011yescharacteristic
153C2×C32C2×#10211yescharacteristic
154C2×C32C2×#10411yescharacteristic
155C3⋊D3—21no—
156C3⋊D3—21no—
157C3⋊D3—82no—
158#41—362no—
159#41—362no—
160C2×Q8—21no—
161C2×D4—92no—
162C2×D4—182no—
163C2×D4—181no—
164C2×D4—181no—
165C22×C4—91no—
166C22×C4—91no—
167C22×C4—91no—
168C22×C4—182no—
169C22×C4—182no—
170C2×C8—182no—
171C4⋊C4—21no—
172C4⋊C4—184no—
173C4⋊C4C2×#15712yes—
174C22⋊C4—182no—
175C22⋊C4—182no—
176C42—91no—
177C42—91no—
178C42—91no—
179C42—362no—
180C42C2×#15711yescharacteristic
181C22×C3—22no—
182C2×D3—62no—
183C2×D3—62no—
184C2×D3—122no—
185C2×D3—122no—
186C2×D3—128no—
187C2×D3—128no—
188C2×D3—128no—
189C3×C4—24no—
190C3×C4—24no—
191C3×C4—24no—
192C3×C4—48no—
193Dic3—64no—
194Dic3—122no—
195Dic3—122no—
196C32#150211yescharacteristic, complemented, Sylow
197C23—91no—
198C23—182no—
199Q8—42no—
200D4—362no—
201D4—362no—
202D4—362no—
203D4—362no—
204D4—362no—
205C2×C4—22no—
206C2×C4—91no—
207C2×C4—92no—
208C2×C4—92no—
209C2×C4—91no—
210C2×C4—91no—
211C2×C4—182no—
212C2×C4—184no—
213C2×C4—361no—
214C2×C4—364no—
215C2×C4—362no—
216C2×C4—362no—
217C2×C4C22⋊#15711yescharacteristic
218C2×C4C22⋊#15711yescharacteristic
219C2×C4C22×#15711yescharacteristic
220C8—362no—
221C2×C3—22no—
222C2×C3—22no—
223C2×C3—22no—
224D3—122no—
225D3—122no—
226D3—248no—
227C22—91no—
228C22—91no—
229C22—181no—
230C22—181no—
231C22—362no—
232C22—362no—
233C22—362no—
234C22C2×C22⋊#15711yescharacteristic
235C4—21no—
236C4—42no—
237C4—92no—
238C4—181no—
239C4—181no—
240C4—364no—
241C4#6378212yes—
242C4#6378512yes—
243C3—22no—
244C2—181no—
245C2—181no—
246C2—722no—
247C2C2×#6378211yescharacteristic
248C2C2×#6378511yescharacteristic
249C2#1059383211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4⋊Q8C4
socleC22×C32C2×C22⋊C4
prime radical#10596196C2
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊Q8#157
hypocenterC32#1502
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊#157C2semidirect
3. #10593727C2semidirect
4. #10590157C2semidirect
8. C32×C4⋊Q8C4semidirect
13. #64102C4semidirect
14. #64083C4semidirect
118. C4⋊Q8#157semidirect
196. C32#1502semidirect

Maximal subgroups

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

subgroupindex
#105961962
C4×C4⋊#1572
#105937272
#105901572
#15029