Finite Group Databasebeta

← #11771910

Subgroups — #11771910

Order 1152.

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

normal subgroups only

This group has 265 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#10592815C211yesmaximal, characteristic
2C3×#4552C211yesmaximal, characteristic
3C3×#4549C211yesmaximal, characteristic
4#67529—31nomaximal
5#67488—31nomaximal
6C22×C32×C8C2211yescharacteristic
7#64133—21no—
8C2×#3746C411yescharacteristic
9C2×C3×#208—21no—
10#63645C411yescharacteristic
11#63643—21no—
12C2×C3×C3⋊C16—21no—
13#5116—31no—
14#5116—31no—
15#5116—61no—
16C3×C22⋊C16—31no—
17C3×#341—31no—
18#4552D311yescharacteristic
19#4549D311yescharacteristic
20C22×C32×C4D411yescharacteristic
21C2×#634—21no—
22C2×C32×C8—41no—
23C2×C32×C8C2×C411yescharacteristic
24C2×C32×C8D411yescharacteristic
25#3757—41no—
26C4⋊(C3⋊Dic3)—21no—
27#3750—41no—
28#3746—41no—
29C3×#208—22no—
30C3×#208—41no—
31C2×C3×C3⋊C8—41no—
32C3×C3⋊C16—41no—
33#1350—91noSylow
34C2×C3×M16—61no—
35C22×C3×C8—21no—
36C22×C3×C8C2×D311yescharacteristic
37C22×C3×C8C2×D311yescharacteristic
38#924—62no—
39#924—61no—
40#924—61no—
41C2×#208—21no—
42C2×Dic12—31no—
43C2×Dic12—31no—
44C2×Dic12—61no—
45C2×C3×C16—61no—
46#818—31no—
47#818—31no—
48#818—61no—
49#816—62no—
50#816—61no—
51#816—61no—
52C2×C3⋊C16—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#467—91no—
66C22⋊C16—31no—
67#341—31no—
68C22×C3×C4—21no—
69C22×C3×C4D1211yescharacteristic
70C22×C3×C4#6711yescharacteristic
71C2×Dic6—62no—
72C2×Dic6—61no—
73C2×Dic6—61no—
74C3×M16—62no—
75C3×M16—121no—
76C2×C3×C8—21no—
77C2×C3×C8—21no—
78C2×C3×C8—41no—
79C2×C3×C8—41no—
80C2×C3×C8—42no—
81C2×C3×C8—121no—
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—22no—
96#208—41no—
97C2×C3⋊C8—41no—
98Dic12—121no—
99Dic12—121no—
100Dic12—122no—
101C3×C16—121no—
102C3⋊C16—41no—
103C22×C32—21no—
104C22×C32—21no—
105C22×C32—21no—
106C22×C32#10211yescharacteristic
107C32×C4—21no—
108C32×C4#9911yescharacteristic
109C32×C4#10411yescharacteristic
110C3⋊Dic3—81no—
111C3⋊Dic3—81no—
112C2×Q16—91no—
113C2×M16—61no—
114C22×C8D3211yescharacteristic
115C22⋊Q8—181no—
116C2×C16—61no—
117#107—91no—
118#103—181no—
119C23×C3—21no—
120C23×C3#20411yescharacteristic
121C23×C3#21511yescharacteristic
122C2×C3×C4—21no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—41no—
129C2×C3×C4—41no—
130C2×C3×C4D2411yescharacteristic
131C2×C3×C4(C2×D3)⋊C411yescharacteristic
132C2×C3×C4(C2×D3)⋊C411yescharacteristic
133C2×C3×C4#21311yescharacteristic
134C2×Dic3—122no—
135C2×Dic3—122no—
136C2×Dic3—121no—
137C2×Dic3—121no—
138C2×Dic3—121no—
139C2×Dic3—121no—
140Dic6—122no—
141Dic6—122no—
142Dic6—121no—
143Dic6—121no—
144Dic6—121no—
145Dic6—121no—
146C3×C8—22no—
147C3×C8—21no—
148C3×C8—21no—
149C3×C8—21no—
150C3×C8—21no—
151C3×C8—41no—
152C3×C8—122no—
153C3⋊C8—42no—
154C2×C32—41no—
155C2×C32#32711yescharacteristic
156C2×C32#35911yescharacteristic
157C2×C32#36211yescharacteristic
158C2×Q8—181no—
159C22×C4#62611yescharacteristic
160Q16—361no—
161M16—62no—
162M16—121no—
163C2×C8—41no—
164C2×C8—121no—
165C2×C8#62411yescharacteristic
166C2×C8#62611yescharacteristic
167C4⋊C4—181no—
168C4⋊C4—361no—
169C22⋊C4—361no—
170C16—121no—
171C22×C3—22no—
172C22×C3—21no—
173C22×C3—21no—
174C22×C3—21no—
175C22×C3—21no—
176C22×C3—21no—
177C22×C3—21no—
178C22×C3—21no—
179C22×C3—41no—
180C22×C3—41no—
181C22×C3#80911yescharacteristic
182C22×C3#82111yescharacteristic
183C3×C4—21no—
184C3×C4—21no—
185C3×C4—21no—
186C3×C4—21no—
187C3×C4—41no—
188C3×C4#80511yescharacteristic
189C3×C4#80611yescharacteristic
190C3×C4#80611yescharacteristic
191C3×C4#82511yescharacteristic
192Dic3—242no—
193Dic3—242no—
194Dic3—241no—
195Dic3—241no—
196Dic3—241no—
197Dic3—241no—
198C32#135011yescharacteristic, complemented, Sylow
199C23#371711yescharacteristic
200Q8—361no—
201Q8—361no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—361no—
205C2×C4—361no—
206C2×C4#371411yescharacteristic
207C2×C4#372211yescharacteristic
208C8—21no—
209C8—21no—
210C8—122no—
211C2×C3—21no—
212C2×C3—21no—
213C2×C3—21no—
214C2×C3—42no—
215C2×C3—41no—
216C2×C3—41no—
217C2×C3#445111yescharacteristic
218C2×C3#447011yescharacteristic
219C2×C3#449611yescharacteristic
220C2×C3#449711yescharacteristic
221C2×C3#451011yescharacteristic
222C2×C3#451711yescharacteristic
223C22—21no—
224C22—21no—
225C22—21no—
226C22#6356411yescharacteristic
227C4—21no—
228C4—721no—
229C4—721no—
230C4#6357011yescharacteristic
231C4#6358111yescharacteristic
232C3—21no—
233C3#6748811yescharacteristic, complemented
234C3#6752911yescharacteristic, complemented
235C2—41no—
236C2#1058912211yescharacteristic
237C2#1058913111yescharacteristic
238C2#1058915111yescharacteristic
subgroupG/H
centerC22#63564
commutatorC2×C32×C8C2×C4
Frattini, hypercenterC22×C8D32
Fitting, cosocleC22×C32×C8C22
socleC22×C32#102
prime radicalC23×C32SD16
hypocenterC32#1350
LCSG ▷ C2×C32×C8 ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
198. C32#1350semidirect
233. C3#67488semidirect
234. C3#67529semidirect

Maximal subgroups

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

subgroupindex
#105928152
C3×#45522
C3×#45492
#675293
#674883