Finite Group Databasebeta

← #11771961

Subgroups — #11771961

Order 1152.

299 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 299 conjugacy classes of subgroups — too many to draw. Only its 64 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#10592685C211yesmaximal, characteristic
2C3×#4530C211yesmaximal, characteristic
3C3×#4528C211yesmaximal, characteristic
4#67496—31nomaximal
5#67459—31nomaximal
6C2×C32×C4⋊C4C2211yescharacteristic
7C2×C4⋊(C3⋊Dic3)C411yescharacteristic
8C2×C3×#208—21no—
9#63658—21no—
10#63658—21no—
11#63658C411yescharacteristic
12C3×#830—21no—
13#4986—31no—
14#4986—31no—
15#4986—61no—
16C3×#343—31no—
17C3×#324—31no—
18#4530D311yescharacteristic
19#4528D311yescharacteristic
20C22×C32×C4C2×C411yescharacteristic
21C22×C32×C4D411yescharacteristic
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3—21no—
24C22×C3⋊Dic3—21no—
25C32×C4⋊C4—41no—
26C4⋊(C3⋊Dic3)—41no—
27C3×#208—22no—
28C3×#208—41no—
29C2×C3×C3⋊C8—41no—
30C2×C3×C3⋊C8—41no—
31#1353—91noSylow
32C2×C3×M16—61no—
33C2×C3×C4⋊C4—21no—
34C2×C3×C4⋊C4C2×D311yescharacteristic
35C2×C3×C4⋊C4C2×D311yescharacteristic
36C2×C4⋊Dic3—31no—
37C2×C4⋊Dic3—31no—
38C2×C4⋊Dic3—61no—
39C2×#208—21no—
40C3×C22⋊C8—61no—
41C3⋊#95—31no—
42C3⋊#95—31no—
43C3⋊#95—61no—
44C3⋊#95—62no—
45C3⋊#95—62no—
46C3⋊#95—61no—
47C3⋊#95—61no—
48C3⋊#95—61no—
49C3⋊#95—61no—
50#830—21no—
51C23×C32C22⋊C411yescharacteristic
52C2×C32×C4—21no—
53C2×C32×C4—21no—
54C2×C32×C4—21no—
55C2×C32×C4—21no—
56C2×C32×C4—41no—
57C2×C32×C4—41no—
58C2×C32×C4SD1611yescharacteristic
59C2×C32×C4Q1611yescharacteristic
60C2×C3⋊Dic3—41no—
61C2×C3⋊Dic3—41no—
62C2×C3⋊Dic3—42no—
63C2×C3⋊Dic3—41no—
64C2×C3⋊Dic3—41no—
65C3×C3⋊C8—42no—
66C3×C3⋊C8—81no—
67#400—91no—
68#343—31no—
69#324—31no—
70C22×C3×C4—21no—
71C22×C3×C4—21no—
72C22×C3×C4—21no—
73C22×C3×C4C4×D311yescharacteristic
74C22×C3×C4C4×D311yescharacteristic
75C22×C3×C4D1211yescharacteristic
76C22×C3×C4D1211yescharacteristic
77C22×C3×C4#6711yescharacteristic
78C22×C3×C4#6711yescharacteristic
79C22×Dic3—62no—
80C22×Dic3—62no—
81C22×Dic3—61no—
82C22×Dic3—61no—
83C22×Dic3—61no—
84C22×Dic3—61no—
85C3×M16—62no—
86C3×M16—121no—
87C2×C3×C8—121no—
88C2×C3×C8—121no—
89C3×C4⋊C4—41no—
90C3×C4⋊C4—41no—
91C3×C4⋊C4—42no—
92C4⋊Dic3—122no—
93C4⋊Dic3—121no—
94C4⋊Dic3—121no—
95#208—22no—
96#208—41no—
97C2×C3⋊C8—41no—
98C2×C3⋊C8—41no—
99C22×C32—21no—
100C22×C32—21no—
101C22×C32#9911yescharacteristic
102C22×C32#10311yescharacteristic
103C22×C32#10411yescharacteristic
104C32×C4—21no—
105C32×C4—21no—
106C32×C4—41no—
107C32×C4—41no—
108C3⋊Dic3—81no—
109C3⋊Dic3—81no—
110C2×M16—61no—
111C2×C4⋊C4—91no—
112C2×C4⋊C4D3211yescharacteristic
113C22⋊C8—61no—
114#95—91no—
115#95—181no—
116#95—181no—
117C23×C3—21no—
118C23×C3(C2×D3)⋊C411yescharacteristic
119C23×C3(C2×D3)⋊C411yescharacteristic
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4—21no—
123C2×C3×C4—21no—
124C2×C3×C4—22no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—41no—
132C2×C3×C4—41no—
133C2×C3×C4—41no—
134C2×C3×C4—42no—
135C2×C3×C4—41no—
136C2×C3×C4—41no—
137C2×C3×C4—41no—
138C2×C3×C4—41no—
139C2×C3×C4—42no—
140C2×C3×C4#20411yescharacteristic
141C2×C3×C4Dic1211yescharacteristic
142C2×C3×C4#21411yescharacteristic
143C2×C3×C4#21611yescharacteristic
144C2×Dic3—122no—
145C2×Dic3—122no—
146C2×Dic3—124no—
147C2×Dic3—122no—
148C2×Dic3—121no—
149C2×Dic3—121no—
150C2×Dic3—121no—
151C2×Dic3—121no—
152C2×Dic3—122no—
153C2×Dic3—122no—
154C2×Dic3—122no—
155C2×Dic3—121no—
156C2×Dic3—121no—
157C2×Dic3—121no—
158C2×Dic3—121no—
159C3×C8—122no—
160C3×C8—241no—
161C3⋊C8—42no—
162C3⋊C8—81no—
163C2×C32—21no—
164C2×C32—21no—
165C2×C32#32811yescharacteristic
166C2×C32#35211yescharacteristic
167C2×C32#35511yescharacteristic
168C22×C4—181no—
169C22×C4—181no—
170C22×C4#62411yescharacteristic
171C22×C4#62611yescharacteristic
172C22×C4#62611yescharacteristic
173M16—62no—
174M16—121no—
175C2×C8—121no—
176C2×C8—121no—
177C4⋊C4—41no—
178C4⋊C4—361no—
179C22×C3—22no—
180C22×C3—22no—
181C22×C3—21no—
182C22×C3—21no—
183C22×C3—21no—
184C22×C3—21no—
185C22×C3—21no—
186C22×C3—21no—
187C22×C3—21no—
188C22×C3#80511yescharacteristic
189C22×C3#80611yescharacteristic
190C22×C3#80611yescharacteristic
191C22×C3#81011yescharacteristic
192C22×C3#81611yescharacteristic
193C22×C3#82511yescharacteristic
194C3×C4—21no—
195C3×C4—21no—
196C3×C4—21no—
197C3×C4—21no—
198C3×C4—41no—
199C3×C4—41no—
200C3×C4—42no—
201C3×C4—41no—
202C3×C4—41no—
203C3×C4—41no—
204C3×C4—41no—
205C3×C4—81no—
206Dic3—242no—
207Dic3—241no—
208Dic3—241no—
209Dic3—242no—
210Dic3—241no—
211Dic3—241no—
212C32#135311yescharacteristic, complemented, Sylow
213C23#372211yescharacteristic
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—361no—
221C2×C4—361no—
222C2×C4—362no—
223C2×C4—361no—
224C2×C4—361no—
225C2×C4#371611yescharacteristic
226C2×C4#371911yescharacteristic
227C8—122no—
228C8—241no—
229C2×C3—22no—
230C2×C3—22no—
231C2×C3—21no—
232C2×C3—21no—
233C2×C3—21no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—21no—
238C2×C3#445211yescharacteristic
239C2×C3#446711yescharacteristic
240C2×C3#447211yescharacteristic
241C2×C3#447611yescharacteristic
242C2×C3#447711yescharacteristic
243C2×C3#447711yescharacteristic
244C22—21no—
245C22—21no—
246C22#6356711yescharacteristic
247C22#6357011yescharacteristic
248C22#6358111yescharacteristic
249C4—21no—
250C4—21no—
251C4—41no—
252C4—41no—
253C4—721no—
254C4—721no—
255C3—21no—
256C3#6745911yescharacteristic, complemented
257C3#6749611yescharacteristic, complemented
258C2—21no—
259C2—21no—
260C2#1058915411yescharacteristic
261C2#1058917711yescharacteristic
262C2#1058918311yescharacteristic
subgroupG/H
centerC22#63581
commutatorC22×C32×C4C2×C4
Frattini, hypercenterC2×C4⋊C4D32
Fitting, cosocleC2×C32×C4⋊C4C22
socleC22×C32#99
prime radicalC23×C32C22⋊C4
hypocenterC32#1353
LCSG ▷ C22×C32×C4 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
212. C32#1353semidirect
256. C3#67459semidirect
257. C3#67496semidirect

Maximal subgroups

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

subgroupindex
#105926852
C3×#45302
C3×#45282
#674963
#674593