Finite Group Databasebeta

← #11771930

Subgroups — #11771930

Order 1152.

312 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 29 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#10591205C211yesmaximal, characteristic
2#10590206C211yesmaximal, characteristic
3#10589146C211yesmaximal, characteristic
4C22×#627C411yescharacteristic, complemented
5C2×C22⋊#157—21no—
6C2×#3752C2211yescharacteristic
7C2×#3722—21no—
8C3×C3⋊#95—21no—
9C3×#830—21no—
10#63579C411yescharacteristic, complemented
11#4673—61no—
12#4468—61no—
13C23×C3⋊D3D411yescharacteristic
14C22×#157—41no—
15C22×C32×C4D411yescharacteristic
16C22×C3⋊Dic3C2×C411yescharacteristic
17C22×C3×Dic3—21no—
18C22×C3×Dic3—21no—
19C2×#627—41no—
20C2×#627—42no—
21C22⋊#157—22no—
22C22⋊#157—41no—
23#3752—41no—
24C2×C3×C3⋊C8—41no—
25#3722—42no—
26#1351—91nomaximal, Sylow
27C22×Dic6—61no—
28C2×(C2×D3)⋊C4—61no—
29C2×(C2×D3)⋊C4—61no—
30C2×(C2×D3)⋊C4—61no—
31C2×(C2×D3)⋊C4—61no—
32C3×C22⋊C8—61no—
33C3×#95—61no—
34C3⋊#95—21no—
35C3⋊#95—61no—
36#830—21no—
37C23×C32C22⋊C411yescharacteristic
38C22×C3⋊D3—21no—
39C22×C3⋊D3—21no—
40C22×C3⋊D3—41no—
41C22×C3⋊D3—41no—
42C22×C3⋊D3SD1611yescharacteristic
43C22×C3⋊D3Q1611yescharacteristic
44C2×#157—42no—
45C2×#157—81no—
46C2×#157—81no—
47C2×C32×C4—21no—
48C2×C32×C4—41no—
49C2×C3⋊Dic3—21no—
50C2×C3⋊Dic3—41no—
51C2×C3×Dic3—22no—
52C2×C3×Dic3—41no—
53C2×C3×Dic3—41no—
54C2×C3×Dic3—41no—
55C2×C3×Dic3—41no—
56C2×C3×Dic3—41no—
57#627—42no—
58#627—42no—
59C3×C3⋊C8—81no—
60#393—91no—
61#342—91no—
62#323—91no—
63C23×D3—61no—
64C23×D3—61no—
65C22×C3×C4—21no—
66C22×C3×C4—21no—
67C22×C3×C4—61no—
68C22×C3×C4—61no—
69C22×Dic3—21no—
70C22×Dic3—21no—
71C22×Dic3—61no—
72C22×Dic3—61no—
73C2×Dic6—122no—
74C2×Dic6—122no—
75C2×Dic6—122no—
76C2×C3×C8—121no—
77(C2×D3)⋊C4—122no—
78(C2×D3)⋊C4—122no—
79(C2×D3)⋊C4—122no—
80(C2×D3)⋊C4—121no—
81(C2×D3)⋊C4—121no—
82C2×C3⋊C8—41no—
83C22×C32—21no—
84C22×C32—21no—
85C22×C32#9911yescharacteristic
86C22×C32#10311yescharacteristic
87C22×C32#10411yescharacteristic
88C2×C3⋊D3—21no—
89C2×C3⋊D3—21no—
90C2×C3⋊D3—41no—
91C2×C3⋊D3—41no—
92C2×C3⋊D3—41no—
93C2×C3⋊D3—41no—
94C2×C3⋊D3—81no—
95#157—82no—
96C32×C4—41no—
97C3⋊Dic3—41no—
98C3×Dic3—42no—
99C3×Dic3—81no—
100C22×Q8—91no—
101C2×C22⋊C4—91no—
102C2×C22⋊C4—181no—
103C2×C22⋊C4—181no—
104C22⋊C8—61no—
105#95—61no—
106#95—91no—
107C23×C3—21no—
108C23×C3—21no—
109C22×D3—61no—
110C22×D3—61no—
111C22×D3—61no—
112C22×D3—61no—
113C22×D3—121no—
114C22×D3—121no—
115C22×D3—121no—
116C22×D3—121no—
117C22×D3—121no—
118C22×D3—121no—
119C22×D3—121no—
120C22×D3—121no—
121C22×D3—241no—
122C22×D3—241no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—41no—
126C2×C3×C4—41no—
127C2×C3×C4—41no—
128C2×C3×C4—62no—
129C2×C3×C4—81no—
130C2×C3×C4—121no—
131C2×C3×C4—121no—
132C2×C3×C4—121no—
133C2×C3×C4—121no—
134C2×C3×C4—121no—
135C2×Dic3—22no—
136C2×Dic3—41no—
137C2×Dic3—41no—
138C2×Dic3—41no—
139C2×Dic3—41no—
140C2×Dic3—41no—
141C2×Dic3—62no—
142C2×Dic3—121no—
143C2×Dic3—121no—
144C2×Dic3—121no—
145C2×Dic3—241no—
146Dic6—124no—
147Dic6—124no—
148C3×C8—241no—
149C3⋊C8—81no—
150C2×C32—21no—
151C2×C32—21no—
152C2×C32#32811yescharacteristic
153C2×C32AΣL(1,𝔽16)11yescharacteristic
154C2×C32#35411yescharacteristic
155C3⋊D3—41no—
156C3⋊D3—41no—
157C24—91no—
158C2×Q8—362no—
159C2×Q8—361no—
160C22×C4—61no—
161C22×C4—61no—
162C22×C4—91no—
163C22×C4—361no—
164C22×C4GO+(4,𝔽2)11yescharacteristic
165C2×C8—121no—
166C22⋊C4—182no—
167C22⋊C4—361no—
168C22⋊C4—362no—
169C22⋊C4—361no—
170C22×C3—21no—
171C22×C3—21no—
172C22×C3—21no—
173C22×C3—21no—
174C22×C3—21no—
175C22×C3—21no—
176C22×C3—21no—
177C22×C3—21no—
178C22×C3—21no—
179C22×C3—21no—
180C22×C3—41no—
181C22×C3—41no—
182C2×D3—121no—
183C2×D3—121no—
184C2×D3—121no—
185C2×D3—121no—
186C2×D3—121no—
187C2×D3—121no—
188C2×D3—121no—
189C2×D3—121no—
190C2×D3—241no—
191C2×D3—241no—
192C2×D3—241no—
193C2×D3—241no—
194C2×D3—241no—
195C2×D3—241no—
196C2×D3—241no—
197C2×D3—241no—
198C2×D3—242no—
199C3×C4—41no—
200C3×C4—41no—
201C3×C4—81no—
202C3×C4—122no—
203C3×C4—241no—
204Dic3—42no—
205Dic3—81no—
206Dic3—122no—
207Dic3—241no—
208C32#135111yescharacteristic, complemented, Sylow
209C23—91no—
210C23—91no—
211C23—181no—
212C23—181no—
213C23—361no—
214C23—361no—
215C23D32⋊C411yescharacteristic
216Q8—362no—
217Q8—362no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—62no—
221C2×C4—121no—
222C2×C4—121no—
223C2×C4—121no—
224C2×C4—121no—
225C2×C4—121no—
226C2×C4—181no—
227C2×C4—361no—
228C2×C4—362no—
229C2×C4—721no—
230C2×C4—721no—
231C8—241no—
232C2×C3—21no—
233C2×C3—21no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—21no—
238C2×C3—21no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—41no—
243C2×C3—41no—
244D3—241no—
245D3—241no—
246D3—241no—
247D3—241no—
248C22—21no—
249C22—21no—
250C22—181no—
251C22—181no—
252C22—361no—
253C22—361no—
254C22—361no—
255C22—361no—
256C22—721no—
257C22#6373011yescharacteristic
258C22#6373111yescharacteristic
259C22#6373811yescharacteristic
260C4—41no—
261C4—122no—
262C4—241no—
263C4—361no—
264C4—722no—
265C3—21no—
266C3—21no—
267C2—21no—
268C2—21no—
269C2—361no—
270C2—361no—
271C2#1059003411yescharacteristic
272C2#1059005711yescharacteristic
273C2#1059008111yescharacteristic
subgroupG/H
centerC22#63738
commutatorC22×C3⋊Dic3C2×C4
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#99
prime radicalC23×C3⋊D3D4
cosocleC2×#3752C22
hypocenterC32#1351
LCSG ▷ C22×C3⋊Dic3 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. C22×#627C4semidirect
10. #63579C4semidirect
208. C32#1351semidirect

Maximal subgroups

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

subgroupindex
#105912052
#105902062
#105891462
#13519