Finite Group Databasebeta

← #11771774

Subgroups — #11771774

Order 1152.

255 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 255 conjugacy classes of subgroups — too many to draw. Only its 56 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#10592836C211yesmaximal, characteristic
2C3×C3⋊#338C211yesmaximal, characteristic
3C3×#4553C211yesmaximal, characteristic
4#67537—31nomaximal
5#67484—31nomaximal
6C2×C32×M16C2211yescharacteristic
7#64133—21no—
8C2×#3746C411yescharacteristic
9C2×C3×#208—21no—
10#63644C411yescharacteristic
11#63643—21no—
12C3×#812—21no—
13#5137—31no—
14#5137—31no—
15#5137—61no—
16C3×#349—31no—
17C3×#338—31no—
18C3⋊#338D311yescharacteristic
19#4553D311yescharacteristic
20C22×C32×C4D411yescharacteristic
21C2×#634—21no—
22C32×M16—41no—
23C2×C32×C8C2×C411yescharacteristic
24C2×C32×C8D411yescharacteristic
25#3757—41no—
26C4⋊(C3⋊Dic3)—21no—
27#3750—41no—
28#3746—41no—
29C3×#208—41no—
30C3×#208—41no—
31C2×C3×C3⋊C8—22no—
32C3×C3⋊C16—41no—
33#1342—91noSylow
34C2×C3×M16—21no—
35C2×C3×M16—61no—
36C2×C3×M16C2×D311yescharacteristic
37C2×C3×M16C2×D311yescharacteristic
38#924—62no—
39#924—61no—
40#924—61no—
41C2×#208—21no—
42C2×Dic12—31no—
43C2×Dic12—31no—
44C2×Dic12—61no—
45C3×M32—61no—
46#817—31no—
47#817—31no—
48#817—61no—
49#816—62no—
50#816—61no—
51#816—61no—
52#812—21no—
53C23×C32SD1611yescharacteristic
54C2×C32×C4—21no—
55C2×C32×C4—21no—
56C2×C32×C4C22⋊C411yescharacteristic
57C2×C32×C4D811yescharacteristic
58C2×C3⋊Dic3—41no—
59C2×C3⋊Dic3—41no—
60#634—41no—
61#634—41no—
62C32×C8—21no—
63C32×C8—21no—
64C3×C3⋊C8—42no—
65#470—91no—
66#349—31no—
67#338—31no—
68C22×C3×C4—21no—
69C22×C3×C4D1211yescharacteristic
70C22×C3×C4#6711yescharacteristic
71C2×Dic6—62no—
72C2×Dic6—61no—
73C2×Dic6—61no—
74C3×M16—41no—
75C3×M16—41no—
76C3×M16—42no—
77C3×M16—121no—
78C3×M16—121no—
79C2×C3×C8—21no—
80C2×C3×C8—21no—
81C2×C3×C8—62no—
82C2×C3×C8C4×D311yescharacteristic
83C2×C3×C8C4×D311yescharacteristic
84C2×C3×C8D1211yescharacteristic
85C2×C3×C8#6711yescharacteristic
86#217—122no—
87#217—121no—
88#217—121no—
89C4⋊Dic3—62no—
90C4⋊Dic3—61no—
91C4⋊Dic3—61no—
92Dic3⋊C4—122no—
93Dic3⋊C4—121no—
94Dic3⋊C4—121no—
95#208—41no—
96#208—41no—
97C2×C3⋊C8—22no—
98Dic12—121no—
99Dic12—121no—
100Dic12—122no—
101C3×C16—121no—
102C3⋊C16—41no—
103C22×C32—21no—
104C22×C32—41no—
105C22×C32#10211yescharacteristic
106C32×C4—21no—
107C32×C4#9911yescharacteristic
108C32×C4#10411yescharacteristic
109C3⋊Dic3—81no—
110C3⋊Dic3—81no—
111C2×Q16—91no—
112C2×M16—61no—
113C2×M16D3211yescharacteristic
114C22⋊Q8—181no—
115M32—61no—
116#106—91no—
117#103—181no—
118C23×C3—21no—
119C23×C3#20411yescharacteristic
120C23×C3#21511yescharacteristic
121C2×C3×C4—21no—
122C2×C3×C4—21no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4—41no—
128C2×C3×C4—41no—
129C2×C3×C4D2411yescharacteristic
130C2×C3×C4(C2×D3)⋊C411yescharacteristic
131C2×C3×C4(C2×D3)⋊C411yescharacteristic
132C2×C3×C4#21311yescharacteristic
133C2×Dic3—122no—
134C2×Dic3—122no—
135C2×Dic3—121no—
136C2×Dic3—121no—
137C2×Dic3—121no—
138C2×Dic3—121no—
139Dic6—122no—
140Dic6—122no—
141Dic6—121no—
142Dic6—121no—
143Dic6—121no—
144Dic6—121no—
145C3×C8—22no—
146C3×C8—21no—
147C3×C8—21no—
148C3×C8—21no—
149C3×C8—21no—
150C3×C8—41no—
151C3×C8—122no—
152C3⋊C8—42no—
153C2×C32—21no—
154C2×C32—41no—
155C2×C32#32711yescharacteristic
156C2×Q8—181no—
157C22×C4#62611yescharacteristic
158Q16—361no—
159M16—41no—
160M16—121no—
161M16—121no—
162C2×C8—62no—
163C2×C8#62411yescharacteristic
164C2×C8#62611yescharacteristic
165C4⋊C4—181no—
166C4⋊C4—361no—
167C22⋊C4—361no—
168C16—121no—
169C22×C3—21no—
170C22×C3—21no—
171C22×C3—21no—
172C22×C3—41no—
173C22×C3—41no—
174C22×C3—41no—
175C22×C3—42no—
176C22×C3#80911yescharacteristic
177C22×C3#82111yescharacteristic
178C3×C4—21no—
179C3×C4—21no—
180C3×C4—21no—
181C3×C4—21no—
182C3×C4—41no—
183C3×C4#80511yescharacteristic
184C3×C4#80611yescharacteristic
185C3×C4#80611yescharacteristic
186C3×C4#82511yescharacteristic
187Dic3—242no—
188Dic3—242no—
189Dic3—241no—
190Dic3—241no—
191Dic3—241no—
192Dic3—241no—
193C32#134211yescharacteristic, complemented, Sylow
194C23#371711yescharacteristic
195Q8—361no—
196Q8—361no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—361no—
200C2×C4—361no—
201C2×C4#371411yescharacteristic
202C2×C4#372211yescharacteristic
203C8—21no—
204C8—21no—
205C8—122no—
206C2×C3—22no—
207C2×C3—21no—
208C2×C3—21no—
209C2×C3—21no—
210C2×C3—41no—
211C2×C3—41no—
212C2×C3—81no—
213C2×C3#445111yescharacteristic
214C2×C3#447011yescharacteristic
215C22—21no—
216C22—41no—
217C22#6356411yescharacteristic
218C4—21no—
219C4—721no—
220C4—721no—
221C4#6357011yescharacteristic
222C4#6358111yescharacteristic
223C3—21no—
224C3#6748411yescharacteristic, complemented
225C3#6753711yescharacteristic, complemented
226C2—21no—
227C2—41no—
228C2#1058915111yescharacteristic
subgroupG/H
centerC2#10589151
commutatorC2×C32×C8C2×C4
Frattini, hypercenterC2×M16D32
Fitting, cosocleC2×C32×M16C22
socleC2×C32#327
prime radicalC23×C32SD16
hypocenterC32#1342
LCSG ▷ C2×C32×C8 ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
193. C32#1342semidirect
224. C3#67484semidirect
225. C3#67537semidirect

Maximal subgroups

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

subgroupindex
#105928362
C3×C3⋊#3382
C3×#45532
#675373
#674843