Finite Group Databasebeta

← #11771416

Subgroups — #11771416

Order 1152.

285 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 285 conjugacy classes of subgroups — too many to draw. Only its 62 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×#5126C211yesmaximal, characteristic
2#10589419C211yesmaximal, characteristic, complemented
3C3×#4553C211yesmaximal, characteristic, complemented
4#67681—31nomaximal
5#67530—31nomaximal
6C22×C3×C4×D3C411yescharacteristic
7C2×C32×M16C2211yescharacteristic
8C2×C3×#208C411yescharacteristic
9#63639—21no—
10C3×(C2×D3)⋊C8—21no—
11C3×(C2×D3)⋊C8—21no—
12C3×#812—21no—
13C3×#407—31no—
14#5126D311yescharacteristic
15C3×#349—31no—
16#4553—31no—
17#4553—31no—
18#4553—61no—
19#4553D311yescharacteristic, complemented
20C23×C3×D3C811yescharacteristic
21C22×C32×C4C2×C411yescharacteristic
22C22×C3×Dic3C811yescharacteristic
23C2×C3×C4×D3—21no—
24C2×C3×C4×D3—21no—
25C2×C3×C4×D3—41no—
26C2×C3×C4×D3—41no—
27C32×M16—41no—
28C2×C32×C8D411yescharacteristic
29C2×C32×C8D411yescharacteristic
30C3×#208—41no—
31C2×C3×C3⋊C8—21no—
32C3⋊(C3⋊C16)—41no—
33C3×C3⋊C16—41no—
34#1320—91noSylow
35C23×C3×C4—31no—
36C22×C4×D3Dic311yescharacteristic
37C2×C3×M16—21no—
38C2×C3×M16—31no—
39C2×C3×M16C2×D311yescharacteristic
40C2×C3×M16C2×D311yescharacteristic
41C2×#208Dic311yescharacteristic
42C3×M32—61no—
43C3×C22⋊C8—61no—
44C3×C22⋊C8—61no—
45(C2×D3)⋊C8—21no—
46(C2×D3)⋊C8—21no—
47#812—21no—
48#812—62no—
49#812—61no—
50#812—61no—
51C23×C32C2×C811yescharacteristic
52C22×C3×D3—21no—
53C22×C3×D3—42no—
54C22×C3×D3—41no—
55C2×C32×C4—21no—
56C2×C32×C4—21no—
57C2×C32×C4C22⋊C411yescharacteristic
58C2×C32×C4M1611yescharacteristic
59C2×C3×Dic3—21no—
60C2×C3×Dic3—41no—
61C3×C4×D3—42no—
62C3×C4×D3—41no—
63C3×C4×D3—41no—
64C32×C8—21no—
65C32×C8—21no—
66C3×C3⋊C8—41no—
67#407—31no—
68#349—31no—
69#349—91no—
70C24×C3—31no—
71C23×D3C3⋊C811yescharacteristic
72C22×C3×C4—21no—
73C22×C3×C4—31no—
74C22×C3×C4—61no—
75C22×C3×C4—61no—
76C22×C3×C4—121no—
77C22×C3×C4—121no—
78C22×C3×C4C4×D311yescharacteristic
79C22×C3×C4C2×Dic311yescharacteristic
80C22×Dic3C3⋊C811yescharacteristic
81C2×C4×D3—21no—
82C2×C4×D3—21no—
83C2×C4×D3—41no—
84C2×C4×D3—41no—
85C3×M16—41no—
86C3×M16—41no—
87C3×M16—42no—
88C3×M16—121no—
89C2×C3×C8—21no—
90C2×C3×C8—21no—
91C2×C3×C8—61no—
92C2×C3×C8D1211yescharacteristic
93C2×C3×C8#6711yescharacteristic
94C2×C3×C8#6711yescharacteristic
95C2×C3×C8#6711yescharacteristic
96#208—41no—
97C2×C3⋊C8—21no—
98C3×C16—121no—
99C3⋊C16—41no—
100C3⋊C16—122no—
101C3⋊C16—121no—
102C3⋊C16—121no—
103C22×C32—21no—
104C22×C32—41no—
105C22×C32C22⋊C811yescharacteristic
106C2×C3×D3—22no—
107C2×C3×D3—41no—
108C2×C3×D3—42no—
109C2×C3×D3—41no—
110C2×C3×D3—42no—
111C32×C4—21no—
112C32×C4#9911yescharacteristic
113C32×C4#10011yescharacteristic
114C3×Dic3—41no—
115C23×C4—31no—
116C2×M16—31no—
117C2×M16D3211yescharacteristic
118M32—61no—
119M32—181no—
120C22⋊C8—61no—
121C22⋊C8—61no—
122C23×C3—21no—
123C23×C3—61no—
124C23×C3—121no—
125C23×C3—122no—
126C23×C3D3×C811yescharacteristic
127C23×C3C2×C3⋊C811yescharacteristic
128C22×D3—21no—
129C22×D3—42no—
130C22×D3—41no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—41no—
138C2×C3×C4—41no—
139C2×C3×C4—61no—
140C2×C3×C4—122no—
141C2×C3×C4—121no—
142C2×C3×C4—121no—
143C2×C3×C4—121no—
144C2×C3×C4ΓL(1,𝔽25)11yescharacteristic
145C2×C3×C4#20811yescharacteristic
146C2×C3×C4(C2×D3)⋊C411yescharacteristic
147C2×C3×C4#21711yescharacteristic
148C2×Dic3—21no—
149C2×Dic3—41no—
150C4×D3—42no—
151C4×D3—41no—
152C4×D3—41no—
153C3×C8—22no—
154C3×C8—21no—
155C3×C8—21no—
156C3×C8—21no—
157C3×C8—21no—
158C3×C8—41no—
159C3×C8—121no—
160C3⋊C8—41no—
161C2×C32—21no—
162C2×C32—41no—
163C2×C32#32311yescharacteristic
164C3×D3—42no—
165C24—31no—
166C22×C4—31no—
167C22×C4—61no—
168C22×C4—61no—
169C22×C4—121no—
170C22×C4—121no—
171C22×C4D3×Dic311yescharacteristic
172M16—41no—
173M16—121no—
174C2×C8—61no—
175C2×C8#62511yescharacteristic
176C2×C8#62611yescharacteristic
177C16—121no—
178C16—361no—
179C22×C3—21no—
180C22×C3—21no—
181C22×C3—21no—
182C22×C3—41no—
183C22×C3—41no—
184C22×C3—41no—
185C22×C3—62no—
186C22×C3—81no—
187C22×C3—121no—
188C22×C3—122no—
189C22×C3—122no—
190C22×C3—121no—
191C22×C3(C2×D3)⋊C811yescharacteristic
192C22×C3#83011yescharacteristic
193C2×D3—22no—
194C2×D3—41no—
195C2×D3—42no—
196C2×D3—41no—
197C2×D3—42no—
198C3×C4—21no—
199C3×C4—21no—
200C3×C4—21no—
201C3×C4—21no—
202C3×C4—41no—
203C3×C4—121no—
204C3×C4#80611yescharacteristic
205C3×C4#82311yescharacteristic
206C3×C4#83311yescharacteristic
207C3×C4#83411yescharacteristic
208Dic3—41no—
209C32#132011yescharacteristic, complemented, Sylow
210C23—61no—
211C23—121no—
212C23—122no—
213C23D3×C3⋊C811yescharacteristic
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—61no—
217C2×C4—122no—
218C2×C4—121no—
219C2×C4—121no—
220C2×C4—121no—
221C2×C4#371111yescharacteristic
222C2×C4(C2×D3)⋊Dic311yescharacteristic
223C8—21no—
224C8—21no—
225C8—121no—
226C2×C3—21no—
227C2×C3—21no—
228C2×C3—21no—
229C2×C3—41no—
230C2×C3—41no—
231C2×C3—41no—
232C2×C3—81no—
233C2×C3—122no—
234C2×C3#446811yescharacteristic
235C2×C3#452511yescharacteristic
236D3—42no—
237C22—21no—
238C22—41no—
239C22—62no—
240C22—121no—
241C22—122no—
242C22—122no—
243C22—121no—
244C22(C2×D3)⋊(C3⋊C8)11yescharacteristic
245C4—21no—
246C4—121no—
247C4#6355811yescharacteristic
248C4#6358011yescharacteristic
249C3—21no—
250C3#6753011yescharacteristic, complemented
251C3#6768111yescharacteristic, complemented
252C2—21no—
253C2—41no—
254C2—122no—
255C2#1058914511yescharacteristic
subgroupG/H
centerC4#63580
commutatorC23×C32C2×C8
Frattini, hypercenterC2×M16D32
Fitting, cosocleC2×C32×M16C22
socleC2×C32#323
prime radicalC23×C3×D3C8
hypocenterC32#1320
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10589419C2semidirect
3. C3×#4553C2semidirect
19. #4553D3semidirect
209. C32#1320semidirect
250. C3#67530semidirect
251. C3#67681semidirect

Maximal subgroups

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

subgroupindex
C3×#51262
#105894192
C3×#45532
#676813
#675303