Finite Group Databasebeta

← #11771947

Subgroups — #11771947

Order 1152.

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

normal subgroups only

This group has 296 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#10591203C211yesmaximal, characteristic
2#10590206C211yesmaximal, characteristic
3#10589146C211yesmaximal, characteristic
4C2×C22⋊#157—21no—
5C2×#3752C2211yescharacteristic
6C2×C3×Dic3⋊C4—21no—
7C2×#3724C411yescharacteristic, complemented
8C2×#3722—21no—
9C3×#830—21no—
10#63579C411yescharacteristic, complemented
11#4993—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—
19C22⋊#157—22no—
20C22⋊#157—41no—
21#3752—41no—
22C3×Dic3⋊C4—42no—
23C2×C3×C3⋊C8—41no—
24#3724—41no—
25#3722—42no—
26#1352—91nomaximal, Sylow
27C2×C3×C4⋊C4—61no—
28C2×(C2×D3)⋊C4—61no—
29C2×(C2×D3)⋊C4—61no—
30C2×(C2×D3)⋊C4—61no—
31C2×(C2×D3)⋊C4—61no—
32C2×Dic3⋊C4—21no—
33C2×Dic3⋊C4—61no—
34C3×C22⋊C8—61no—
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—
57C3×C3⋊C8—81no—
58#399—91no—
59#342—91no—
60#323—91no—
61C23×D3—61no—
62C23×D3—61no—
63C22×C3×C4—21no—
64C22×C3×C4—21no—
65C22×C3×C4—61no—
66C22×C3×C4—61no—
67C22×Dic3—21no—
68C22×Dic3—21no—
69C22×Dic3—61no—
70C22×Dic3—61no—
71C2×C3×C8—121no—
72C3×C4⋊C4—122no—
73(C2×D3)⋊C4—122no—
74(C2×D3)⋊C4—122no—
75(C2×D3)⋊C4—122no—
76(C2×D3)⋊C4—121no—
77(C2×D3)⋊C4—121no—
78Dic3⋊C4—42no—
79Dic3⋊C4—122no—
80C2×C3⋊C8—41no—
81C22×C32—21no—
82C22×C32—21no—
83C22×C32#9911yescharacteristic
84C22×C32#10311yescharacteristic
85C22×C32#10411yescharacteristic
86C2×C3⋊D3—21no—
87C2×C3⋊D3—21no—
88C2×C3⋊D3—41no—
89C2×C3⋊D3—41no—
90C2×C3⋊D3—41no—
91C2×C3⋊D3—41no—
92C2×C3⋊D3—81no—
93#157—82no—
94C32×C4—41no—
95C3⋊Dic3—41no—
96C3×Dic3—42no—
97C3×Dic3—81no—
98C2×C4⋊C4—61no—
99C2×C4⋊C4—91no—
100C2×C22⋊C4—91no—
101C2×C22⋊C4—181no—
102C2×C22⋊C4—181no—
103C22⋊C8—61no—
104#95—91no—
105C23×C3—21no—
106C23×C3—21no—
107C22×D3—61no—
108C22×D3—61no—
109C22×D3—61no—
110C22×D3—61no—
111C22×D3—121no—
112C22×D3—121no—
113C22×D3—121no—
114C22×D3—121no—
115C22×D3—121no—
116C22×D3—121no—
117C22×D3—121no—
118C22×D3—121no—
119C22×D3—241no—
120C22×D3—241no—
121C2×C3×C4—21no—
122C2×C3×C4—21no—
123C2×C3×C4—41no—
124C2×C3×C4—41no—
125C2×C3×C4—41no—
126C2×C3×C4—62no—
127C2×C3×C4—81no—
128C2×C3×C4—121no—
129C2×C3×C4—121no—
130C2×C3×C4—121no—
131C2×C3×C4—121no—
132C2×C3×C4—121no—
133C2×Dic3—22no—
134C2×Dic3—41no—
135C2×Dic3—41no—
136C2×Dic3—41no—
137C2×Dic3—41no—
138C2×Dic3—41no—
139C2×Dic3—62no—
140C2×Dic3—121no—
141C2×Dic3—121no—
142C2×Dic3—121no—
143C2×Dic3—241no—
144C3×C8—241no—
145C3⋊C8—81no—
146C2×C32—21no—
147C2×C32—21no—
148C2×C32#32811yescharacteristic
149C2×C32#35211yescharacteristic
150C2×C32#35311yescharacteristic
151C3⋊D3—41no—
152C3⋊D3—41no—
153C24—91no—
154C22×C4—61no—
155C22×C4—61no—
156C22×C4—91no—
157C22×C4—361no—
158C22×C4GO+(4,𝔽2)11yescharacteristic
159C2×C8—121no—
160C4⋊C4—122no—
161C4⋊C4—361no—
162C22⋊C4—182no—
163C22⋊C4—361no—
164C22⋊C4—362no—
165C22⋊C4—361no—
166C22×C3—21no—
167C22×C3—21no—
168C22×C3—21no—
169C22×C3—21no—
170C22×C3—21no—
171C22×C3—21no—
172C22×C3—21no—
173C22×C3—21no—
174C22×C3—21no—
175C22×C3—21no—
176C22×C3—41no—
177C22×C3—41no—
178C2×D3—121no—
179C2×D3—121no—
180C2×D3—121no—
181C2×D3—121no—
182C2×D3—121no—
183C2×D3—121no—
184C2×D3—121no—
185C2×D3—121no—
186C2×D3—241no—
187C2×D3—241no—
188C2×D3—241no—
189C2×D3—241no—
190C2×D3—241no—
191C2×D3—241no—
192C2×D3—241no—
193C2×D3—241no—
194C2×D3—242no—
195C3×C4—41no—
196C3×C4—41no—
197C3×C4—81no—
198C3×C4—122no—
199C3×C4—241no—
200Dic3—42no—
201Dic3—81no—
202Dic3—122no—
203Dic3—241no—
204C32#135211yescharacteristic, complemented, Sylow
205C23—91no—
206C23—91no—
207C23—181no—
208C23—181no—
209C23—361no—
210C23—361no—
211C23D32⋊C411yescharacteristic
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—62no—
215C2×C4—121no—
216C2×C4—121no—
217C2×C4—121no—
218C2×C4—121no—
219C2×C4—121no—
220C2×C4—181no—
221C2×C4—361no—
222C2×C4—362no—
223C2×C4—721no—
224C2×C4—721no—
225C8—241no—
226C2×C3—21no—
227C2×C3—21no—
228C2×C3—21no—
229C2×C3—21no—
230C2×C3—21no—
231C2×C3—21no—
232C2×C3—21no—
233C2×C3—21no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—41no—
237C2×C3—41no—
238D3—241no—
239D3—241no—
240D3—241no—
241D3—241no—
242C22—21no—
243C22—21no—
244C22—181no—
245C22—181no—
246C22—361no—
247C22—361no—
248C22—361no—
249C22—361no—
250C22—721no—
251C22#6373011yescharacteristic
252C22#6373111yescharacteristic
253C22#6373811yescharacteristic
254C4—41no—
255C4—122no—
256C4—241no—
257C4—361no—
258C4—722no—
259C3—21no—
260C3—21no—
261C2—21no—
262C2—21no—
263C2—361no—
264C2—361no—
265C2#1059003411yescharacteristic
266C2#1059005811yescharacteristic
267C2#1059008011yescharacteristic
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#1352
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
7. C2×#3724C4semidirect
10. #63579C4semidirect
204. C32#1352semidirect

Maximal subgroups

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

subgroupindex
#105912032
#105902062
#105891462
#13529