Finite Group Databasebeta

← #11775325

Subgroups — #11775325

Order 1152.

596 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 60 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×#64155C211yesmaximal, characteristic
2#10593811C211yesmaximal, characteristic
3#10593802C211yesmaximal, characteristic
4#10590215C214yesmaximal, complemented
5C22×C32×Q8C411yescharacteristic, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C22⋊#157—21no—
8C2×#3792—21no—
9#64155—21no—
10#64155—21no—
11#64155C412yescomplemented
12#64155C2212yes—
13C2×#3752—21no—
14C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
15C2×#3750—21no—
16#63781—21no—
17#63781C2212yes—
18#63778—21no—
19#63778C2212yes—
20C2×#946—62no—
21C23×C3⋊D3D411yescharacteristic
22C22×#157—22no—
23C2×C32×Q8—21no—
24C2×C32×Q8—42no—
25C2×C32×Q8C2×C412yes—
26C22×C32×C4—21no—
27C22×C32×C4C2×C411yescharacteristic
28C22×C3⋊Dic3—21no—
29C22×C3⋊Dic3D411yescharacteristic
30C2×C4×C3⋊D3—42no—
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3C2311yescharacteristic
35C22⋊#157—42no—
36#3792—42no—
37C2×#622—22no—
38#3752—22no—
39#3752—22no—
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)C2×C412yes—
42#3750—22no—
43#3750—22no—
44#1511—91nomaximal, Sylow
45C22×C3×Q8—22no—
46C22×C4×D3—62no—
47#946—64no—
48#946—64no—
49#946—64no—
50#946—64no—
51C2×(C2×D3)⋊C4—64no—
52C2×C4⋊Dic3—62no—
53C2×Dic3⋊C4—64no—
54C23×C32C22⋊C411yescharacteristic
55C22×C3⋊D3—22no—
56C22×C3⋊D3—22no—
57C22×C3⋊D3—41no—
58C22×C3⋊D3C22⋊C411yescharacteristic
59C22×C3⋊D3C2×D411yescharacteristic
60C2×#157—42no—
61C2×#157—42no—
62C2×#157—42no—
63C32×Q8—42no—
64C32×Q8—42no—
65C2×C32×C4—22no—
66C2×C32×C4—22no—
67C2×C32×C4—42no—
68C2×C32×C4C22⋊C411yescharacteristic
69C2×C32×C4C22×C411yescharacteristic
70C2×C3⋊Dic3—22no—
71C2×C3⋊Dic3—22no—
72C2×C3⋊Dic3—42no—
73C2×C3⋊Dic3C22⋊C411yescharacteristic
74C2×C3⋊Dic3C2×D411yescharacteristic
75C4×C3⋊D3—41no—
76C4×C3⋊D3—41no—
77C4×C3⋊D3—41no—
78C4×C3⋊D3—41no—
79#622—42no—
80C2×C22⋊Q8—91no—
81#407—91no—
82#381—91no—
83#328—94no—
84C23×D3—62no—
85C2×C3×Q8—24no—
86C2×C3×Q8—24no—
87C2×C3×Q8—48no—
88C22×C3×C4—24no—
89C22×C3×C4—22no—
90C22×Dic3—62no—
91C22×Dic3—64no—
92C2×C4×D3—62no—
93C2×C4×D3—62no—
94C2×C4×D3—62no—
95C2×C4×D3—62no—
96C2×C4×D3—128no—
97(C2×D3)⋊C4—68no—
98(C2×D3)⋊C4—68no—
99C4⋊Dic3—64no—
100C4⋊Dic3—64no—
101Dic3⋊C4—68no—
102Dic3⋊C4—68no—
103C22×C32—21no—
104C22×C32—21no—
105C22×C32#9912yes—
106C22×C32C2×C22⋊C411yescharacteristic
107C2×C3⋊D3—21no—
108C2×C3⋊D3—21no—
109C2×C3⋊D3—21no—
110C2×C3⋊D3—21no—
111C2×C3⋊D3—21no—
112C2×C3⋊D3—44no—
113C2×C3⋊D3#13712yes—
114#157—82no—
115C32×C4—21no—
116C32×C4—21no—
117C32×C4—42no—
118C3⋊Dic3—21no—
119C3⋊Dic3—21no—
120C3⋊Dic3—42no—
121C22×Q8#15711yescharacteristic, complemented
122C23×C4—91no—
123C2×M16—181no—
124C22⋊Q8—92no—
125C22⋊Q8—92no—
126C22⋊Q8—181no—
127C22⋊Q8—181no—
128C2×C4⋊C4—91no—
129C2×C4⋊C4—181no—
130C2×C22⋊C4—181no—
131C2×C22⋊C4—181no—
132C22⋊C8—92no—
133C22⋊C8—181no—
134#95—92no—
135#95—181no—
136C23×C3—22no—
137C22×D3—62no—
138C22×D3—62no—
139C22×D3—68no—
140C22×D3—124no—
141C22×D3—124no—
142C3×Q8—48no—
143C3×Q8—48no—
144C2×C3×C4—28no—
145C2×C3×C4—28no—
146C2×C3×C4—22no—
147C2×C3×C4—22no—
148C2×C3×C4—48no—
149C2×Dic3—62no—
150C2×Dic3—62no—
151C2×Dic3—68no—
152C2×Dic3—124no—
153C2×Dic3—128no—
154C4×D3—124no—
155C4×D3—124no—
156C4×D3—124no—
157C4×D3—124no—
158C2×C32—22no—
159C2×C32C2×#9911yescharacteristic
160C2×C32#41911yescharacteristic
161C2×C32#42111yescharacteristic
162C3⋊D3—22no—
163C3⋊D3—41no—
164C24—91no—
165C2×Q8—21no—
166C2×Q8—42no—
167C2×Q8C2×#15712yes—
168C22×C4—21no—
169C22×C4—91no—
170C22×C4—91no—
171C22×C4—91no—
172C22×C4—91no—
173C22×C4—91no—
174C22×C4—181no—
175C22×C4—182no—
176C22×C4—362no—
177C22×C4C2×#15711yescharacteristic
178M16—362no—
179C2×C8—182no—
180C4⋊C4—92no—
181C4⋊C4—182no—
182C4⋊C4—182no—
183C4⋊C4—181no—
184C22⋊C4—182no—
185C22⋊C4—182no—
186C22⋊C4—362no—
187C22×C3—24no—
188C22×C3—24no—
189C22×C3—22no—
190C22×C3—24no—
191C2×D3—64no—
192C2×D3—64no—
193C2×D3—122no—
194C2×D3—122no—
195C2×D3—122no—
196C2×D3—122no—
197C2×D3—1216no—
198C3×C4—24no—
199C3×C4—24no—
200C3×C4—48no—
201Dic3—122no—
202Dic3—122no—
203Dic3—128no—
204C32#151111yescharacteristic, complemented, Sylow
205C23—91no—
206C23—91no—
207C23—182no—
208C23—182no—
209C23—361no—
210C23C22⋊#15711yescharacteristic
211Q8—42no—
212Q8—42no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—42no—
216C2×C4—91no—
217C2×C4—91no—
218C2×C4—182no—
219C2×C4—182no—
220C2×C4—361no—
221C2×C4—361no—
222C2×C4—361no—
223C2×C4—361no—
224C2×C4—362no—
225C2×C4—362no—
226C2×C4—362no—
227C2×C4—362no—
228C2×C4C22⋊#15711yescharacteristic
229C2×C4C22×#15711yescharacteristic
230C8—362no—
231C2×C3—28no—
232C2×C3—22no—
233C2×C3—22no—
234C2×C3—22no—
235D3—124no—
236D3—124no—
237C22—21no—
238C22—21no—
239C22—92no—
240C22—181no—
241C22—181no—
242C22—181no—
243C22—181no—
244C22—181no—
245C22—364no—
246C22#6378612yes—
247C22C2×C22⋊#15711yescharacteristic
248C4—21no—
249C4—21no—
250C4—42no—
251C4—181no—
252C4—181no—
253C4—362no—
254C4—722no—
255C3—22no—
256C2—22no—
257C2—182no—
258C2—361no—
259C2#1059382911yescharacteristic
260C2#1059383111yescharacteristic
261C2C2×#6378611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC22×C32×Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×Q8#157
hypocenterC32#1511
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
4. #10590215C2semidirect
5. C22×C32×Q8C4semidirect
11. #64155C4semidirect
14. C2×C4⋊(C3⋊Dic3)C4semidirect
121. C22×Q8#157semidirect
204. C32#1511semidirect

Maximal subgroups

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

subgroupindex
C2×#641552
#105938112
#105938022
#105902152
#15119