Finite Group Databasebeta

← #11775097

Subgroups — #11775097

Order 1152.

410 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 67 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#10593882C211yesmaximal, characteristic
2C4×C4⋊#157C211yesmaximal, characteristic
3#10590297C211yesmaximal, characteristic
4#10590034C214yesmaximal
5C2×C4⋊#157—21no—
6C2×C4×#157—21no—
7C42×C3⋊D3C2211yescharacteristic
8C3×C4×Dic6—21no—
9#63919C411yescharacteristic, complemented
10C4×#627C412yescomplemented
11#63874—21no—
12#63873C411yescharacteristic, complemented
13#63871—21no—
14#63870—21no—
15#63865C2212yes—
16#63781C2212yes—
17C3×C4×C3⋊C8—21no—
18#63572—21no—
19#63557C2212yes—
20#5578—61no—
21#4685—61no—
22C22×#157—22no—
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3C2311yescharacteristic
26C2×C3×Dic6—21no—
27C2×#627C2×C412yes—
28C4⋊#157—24no—
29C4×#157—42no—
30C32×C42D411yescharacteristic
31C4×C3⋊Dic3C2×C411yescharacteristic
32C4×C3⋊Dic3C2×C411yescharacteristic
33C4×C3⋊Dic3D411yescharacteristic
34C3×C4⋊Dic3—21no—
35C3×Dic3⋊C4—22no—
36C3×C4×Dic3—22no—
37C2×C3×C3⋊C8—22no—
38#3724—21no—
39#3724—21no—
40#3724C2×C412yes—
41Dic3⋊Dic3—22no—
42#3722—22no—
43#1503—91nomaximal, Sylow
44C3×C4×Q8—61no—
45#946—61no—
46#944—61no—
47#897—61no—
48#896—62no—
49#889—62no—
50#888—61no—
51#872—62no—
52C42×D3—61no—
53C42×D3—61no—
54C4×Dic6—21no—
55C4×Dic6—62no—
56C3×C4×C8—61no—
57(C2×D3)⋊C8—62no—
58Dic3⋊C8—62no—
59C4×C3⋊C8—21no—
60C22×C3⋊D3C2×D411yescharacteristic
61C2×#157—24no—
62C2×#157—42no—
63C2×#157—42no—
64C2×C32×C4C22⋊C411yescharacteristic
65C2×C32×C4C22⋊C411yescharacteristic
66C2×C32×C4C2×D411yescharacteristic
67C2×C3⋊Dic3C22⋊C411yescharacteristic
68C2×C3⋊Dic3C22⋊C411yescharacteristic
69C2×C3⋊Dic3C22×C411yescharacteristic
70C4×C3⋊D3—22no—
71C4×C3⋊D3—41no—
72C4×C3⋊D3SD1612yes—
73C4×C3⋊D3Q1612yes—
74C2×C3×Dic3—22no—
75C2×C3×Dic3—22no—
76C3×Dic6—42no—
77#627—42no—
78C3×C3⋊C8—42no—
79#533—91no—
80#431—91no—
81C4×C4⋊C4—91no—
82#328—94no—
83C2×C3×Q8—61no—
84C2×C4×D3—61no—
85C2×C4×D3—61no—
86C2×C4×D3—61no—
87C2×C4×D3—61no—
88C2×C4×D3—61no—
89C2×C4×D3—61no—
90C2×Dic6—21no—
91C2×Dic6—62no—
92C2×C3×C8—62no—
93C3×C4⋊C4—61no—
94C3×C4⋊C4—62no—
95C3×C42—21no—
96C3×C42—21no—
97C3×C42—62no—
98(C2×D3)⋊C4—62no—
99(C2×D3)⋊C4—62no—
100C4⋊Dic3—21no—
101C4⋊Dic3—62no—
102Dic3⋊C4—22no—
103Dic3⋊C4—62no—
104Dic3⋊C4—62no—
105Dic3⋊C4—62no—
106Dic3⋊C4—62no—
107C4×Dic3—22no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C4×Dic3—61no—
112C4×Dic3—61no—
113C4×Dic3—61no—
114C2×C3⋊C8—22no—
115C22×C32C2×C22⋊C411yescharacteristic
116C2×C3⋊D3—21no—
117C2×C3⋊D3—21no—
118C2×C3⋊D3C2×SD1611yescharacteristic
119C2×C3⋊D3C2×Q1611yescharacteristic
120#157—44no—
121C32×C4—21no—
122C32×C4#10312yes—
123C32×C4#10412yes—
124C3⋊Dic3—21no—
125C3⋊Dic3—21no—
126C3⋊Dic3#10312yes—
127C3×Dic3—42no—
128C3×Dic3—42no—
129C4⋊Q8—91no—
130C4⋊Q8—91no—
131#125—181no—
132C22⋊Q8—92no—
133C22⋊Q8—181no—
134C4×Q8—61no—
135C4×Q8—92no—
136#117—181no—
137C2×C4⋊C4—181no—
138C2×C42—91no—
139C2×C42—181no—
140C4⋊C8—181no—
141C22⋊C8—92no—
142C4×C8—61no—
143#95—92no—
144C22×D3—61no—
145C22×D3—61no—
146C3×Q8—122no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—62no—
154C2×C3×C4—62no—
155C2×Dic3—22no—
156C2×Dic3—22no—
157C2×Dic3—61no—
158C2×Dic3—61no—
159C2×Dic3—61no—
160C2×Dic3—61no—
161C2×Dic3—61no—
162C2×Dic3—61no—
163C4×D3—62no—
164C4×D3—62no—
165C4×D3—62no—
166C4×D3—62no—
167C4×D3—122no—
168C4×D3—122no—
169C4×D3—122no—
170C4×D3—122no—
171Dic6—42no—
172Dic6—124no—
173C3×C8—122no—
174C3⋊C8—42no—
175C2×C32#41011yescharacteristic
176C2×C32C2×#10311yescharacteristic
177C2×C32C2×#10411yescharacteristic
178C3⋊D3—21no—
179C3⋊D3—21no—
180C2×Q8—61no—
181C2×Q8—92no—
182C22×C4—91no—
183C22×C4—91no—
184C22×C4—91no—
185C22×C4—182no—
186C2×C8—62no—
187C4⋊C4—62no—
188C4⋊C4—61no—
189C4⋊C4—92no—
190C4⋊C4—181no—
191C4⋊C4—181no—
192C4⋊C4—182no—
193C4⋊C4—184no—
194C22⋊C4—182no—
195C42—62no—
196C42—91no—
197C42—91no—
198C42—91no—
199C42—362no—
200C42GO+(4,𝔽2)11yescharacteristic
201C22×C3—21no—
202C22×C3—21no—
203C2×D3—61no—
204C2×D3—61no—
205C2×D3—61no—
206C2×D3—61no—
207C2×D3—121no—
208C2×D3—121no—
209C2×D3—121no—
210C2×D3—121no—
211C3×C4—22no—
212C3×C4—22no—
213C3×C4—22no—
214C3×C4—22no—
215C3×C4—22no—
216C3×C4—41no—
217C3×C4—122no—
218C3×C4—122no—
219Dic3—42no—
220Dic3—42no—
221Dic3—62no—
222Dic3—62no—
223Dic3—62no—
224Dic3—121no—
225Dic3—121no—
226Dic3—121no—
227C32#150311yescharacteristic, complemented, Sylow
228C23—91no—
229Q8—122no—
230Q8—362no—
231C2×C4—62no—
232C2×C4—62no—
233C2×C4—91no—
234C2×C4—92no—
235C2×C4—92no—
236C2×C4—91no—
237C2×C4—91no—
238C2×C4—182no—
239C2×C4—184no—
240C2×C4—361no—
241C2×C4—362no—
242C2×C4—362no—
243C2×C4D32⋊C411yescharacteristic
244C2×C4D32⋊C411yescharacteristic
245C2×C4C2×GO+(4,𝔽2)11yescharacteristic
246C8—122no—
247C2×C3—21no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—21no—
253D3—121no—
254D3—121no—
255D3—121no—
256D3—121no—
257C22—91no—
258C22—91no—
259C22—181no—
260C22—181no—
261C22C2×D32⋊C411yescharacteristic
262C4—21no—
263C4—92no—
264C4—122no—
265C4—122no—
266C4—181no—
267C4—181no—
268C4—364no—
269C4#6373012yes—
270C4#6373112yes—
271C3—21no—
272C3—21no—
273C2—181no—
274C2—181no—
275C2C2×#6373011yescharacteristic
276C2C2×#6373111yescharacteristic
277C2#1059334511yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1503
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
9. #63919C4semidirect
10. C4×#627C4semidirect
12. #63873C4semidirect
227. C32#1503semidirect

Maximal subgroups

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

subgroupindex
#105938822
C4×C4⋊#1572
#105902972
#105900342
#15039