Finite Group Databasebeta

← #11771962

Subgroups — #11771962

Order 1152.

271 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 271 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C3×#4986C211yesmaximal, characteristic
2#10589394C211yesmaximal, characteristic
3C3×#4530C211yesmaximal, characteristic
4#67652—31nomaximal
5#67496—31nomaximal
6C2×C32×C4⋊C4C2211yescharacteristic
7C2×C3×C4⋊Dic3C411yescharacteristic
8C2×C3×#208—21no—
9#63657—21no—
10C3×C3⋊#95—21no—
11C3×C3⋊#95—21no—
12C3×C3⋊#95C411yescharacteristic
13C3×#400—31no—
14#4986D311yescharacteristic
15C3×#343—31no—
16#4530D311yescharacteristic
17#4528—31no—
18#4528—31no—
19#4528—61no—
20C22×C32×C4C2×C411yescharacteristic
21C22×C32×C4D411yescharacteristic
22C22×C32×C4D411yescharacteristic
23C22×C3×Dic3—21no—
24C22×C3×Dic3—21no—
25C32×C4⋊C4—41no—
26C2×C3⋊(C3⋊C8)—41no—
27C3×C4⋊Dic3—41no—
28C3×#208—22no—
29C3×#208—41no—
30C2×C3×C3⋊C8—41no—
31#1353—91noSylow
32C2×C3×M16—61no—
33C2×C3×C4⋊C4—21no—
34C2×C3×C4⋊C4—31no—
35C2×C3×C4⋊C4C2×D311yescharacteristic
36C2×C3×C4⋊C4C2×D311yescharacteristic
37C2×C4⋊Dic3Dic311yescharacteristic
38C2×#208—21no—
39C3×#95—31no—
40C3×#95—61no—
41C3×#95—61no—
42C3⋊#95—21no—
43C3⋊#95—21no—
44C3⋊#95Dic311yescharacteristic
45#830—62no—
46#830—61no—
47#830—61no—
48C23×C32C22⋊C411yescharacteristic
49C2×C32×C4—21no—
50C2×C32×C4—21no—
51C2×C32×C4—21no—
52C2×C32×C4—21no—
53C2×C32×C4—41no—
54C2×C32×C4—41no—
55C2×C32×C4SD1611yescharacteristic
56C2×C32×C4Q1611yescharacteristic
57C2×C3×Dic3—41no—
58C2×C3×Dic3—41no—
59C2×C3×Dic3—42no—
60C2×C3×Dic3—41no—
61C2×C3×Dic3—41no—
62C3⋊(C3⋊C8)—81no—
63C3×C3⋊C8—42no—
64#400—31no—
65#343—31no—
66#324—91no—
67C22×C3×C4—21no—
68C22×C3×C4—21no—
69C22×C3×C4—21no—
70C22×C3×C4—61no—
71C22×C3×C4—61no—
72C22×C3×C4C4×D311yescharacteristic
73C22×C3×C4D1211yescharacteristic
74C22×C3×C4C2×Dic311yescharacteristic
75C22×C3×C4#6711yescharacteristic
76C22×C3×C4#6711yescharacteristic
77C22×C3×C4#6711yescharacteristic
78C22×Dic3—21no—
79C22×Dic3—21no—
80C3×M16—62no—
81C3×M16—121no—
82C2×C3×C8—121no—
83C3×C4⋊C4—41no—
84C3×C4⋊C4—41no—
85C3×C4⋊C4—42no—
86C3×C4⋊C4—121no—
87C4⋊Dic3—41no—
88#208—22no—
89#208—41no—
90C2×C3⋊C8—41no—
91C2×C3⋊C8—122no—
92C2×C3⋊C8—121no—
93C2×C3⋊C8—121no—
94C22×C32—21no—
95C22×C32—21no—
96C22×C32#9911yescharacteristic
97C22×C32#10311yescharacteristic
98C22×C32#10411yescharacteristic
99C32×C4—21no—
100C32×C4—21no—
101C32×C4—41no—
102C32×C4—41no—
103C3×Dic3—81no—
104C3×Dic3—81no—
105C2×M16—61no—
106C2×C4⋊C4—31no—
107C2×C4⋊C4D3211yescharacteristic
108C22⋊C8—181no—
109#95—31no—
110#95—61no—
111#95—61no—
112C23×C3—21no—
113C23×C3(C2×D3)⋊C411yescharacteristic
114C23×C3#21711yescharacteristic
115C2×C3×C4—21no—
116C2×C3×C4—21no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—22no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4—21no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—21no—
126C2×C3×C4—41no—
127C2×C3×C4—41no—
128C2×C3×C4—41no—
129C2×C3×C4—41no—
130C2×C3×C4—41no—
131C2×C3×C4—41no—
132C2×C3×C4—41no—
133C2×C3×C4—81no—
134C2×C3×C4—81no—
135C2×C3×C4—121no—
136C2×C3×C4—121no—
137C2×C3×C4—122no—
138C2×C3×C4—121no—
139C2×C3×C4—121no—
140C2×C3×C4#21411yescharacteristic
141C2×C3×C4#21511yescharacteristic
142C2×C3×C4#21611yescharacteristic
143C2×C3×C4#21611yescharacteristic
144C2×Dic3—41no—
145C2×Dic3—41no—
146C2×Dic3—42no—
147C2×Dic3—41no—
148C2×Dic3—41no—
149C3×C8—122no—
150C3⋊C8—42no—
151C3⋊C8—242no—
152C3⋊C8—241no—
153C3⋊C8—241no—
154C2×C32—21no—
155C2×C32—21no—
156C2×C32#32811yescharacteristic
157C2×C32#35211yescharacteristic
158C2×C32#35511yescharacteristic
159C22×C4—61no—
160C22×C4—61no—
161C22×C4D3×Dic311yescharacteristic
162C22×C4#62511yescharacteristic
163C22×C4#62611yescharacteristic
164M16—62no—
165M16—121no—
166C2×C8—121no—
167C2×C8—361no—
168C4⋊C4—41no—
169C4⋊C4—121no—
170C22×C3—21no—
171C22×C3—21no—
172C22×C3—21no—
173C22×C3—21no—
174C22×C3—21no—
175C22×C3—21no—
176C22×C3—21no—
177C22×C3—41no—
178C22×C3—41no—
179C22×C3#80511yescharacteristic
180C22×C3#80611yescharacteristic
181C22×C3#81011yescharacteristic
182C22×C3#83411yescharacteristic
183C22×C3#83511yescharacteristic
184C22×C3#83711yescharacteristic
185C3×C4—21no—
186C3×C4—21no—
187C3×C4—21no—
188C3×C4—21no—
189C3×C4—41no—
190C3×C4—41no—
191C3×C4—42no—
192C3×C4—41no—
193C3×C4—41no—
194C3×C4—41no—
195C3×C4—41no—
196C3×C4—81no—
197C3×C4—241no—
198C3×C4—241no—
199Dic3—81no—
200Dic3—81no—
201C32#135311yescharacteristic, complemented, Sylow
202C23(C2×D3)⋊Dic311yescharacteristic
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—121no—
210C2×C4—121no—
211C2×C4—122no—
212C2×C4—121no—
213C2×C4—121no—
214C2×C4#371511yescharacteristic
215C2×C4#371811yescharacteristic
216C8—122no—
217C8—721no—
218C2×C3—21no—
219C2×C3—21no—
220C2×C3—21no—
221C2×C3—21no—
222C2×C3—21no—
223C2×C3—21no—
224C2×C3—21no—
225C2×C3—41no—
226C2×C3—41no—
227C2×C3#445211yescharacteristic
228C2×C3#447611yescharacteristic
229C2×C3#447711yescharacteristic
230C2×C3#453811yescharacteristic
231C2×C3#453911yescharacteristic
232C2×C3#454211yescharacteristic
233C22—21no—
234C22—21no—
235C22#6356511yescharacteristic
236C22#6356911yescharacteristic
237C22#6358011yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—41no—
242C4—241no—
243C4—241no—
244C3—21no—
245C3#6749611yescharacteristic, complemented
246C3#6765211yescharacteristic, complemented
247C2—21no—
248C2—21no—
249C2#1058915311yescharacteristic
250C2#1058917611yescharacteristic
251C2#1058918211yescharacteristic
subgroupG/H
centerC22#63580
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
201. C32#1353semidirect
245. C3#67496semidirect
246. C3#67652semidirect

Maximal subgroups

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

subgroupindex
C3×#49862
#105893942
C3×#45302
#676523
#674963