Finite Group Databasebeta

← #11771355

Subgroups — #11771355

Order 1152.

265 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 265 conjugacy classes of subgroups — too many to draw. Only its 70 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×#5110C211yesmaximal, characteristic
2#10589415C211yesmaximal, characteristic, complemented
3C3×#4549C211yesmaximal, characteristic, complemented
4#67689—31nomaximal
5#67523—31nomaximal
6C2×C3×#235C411yescharacteristic
7C22×C32×C8C2211yescharacteristic
8C2×C3×#208C411yescharacteristic
9C2×C3⋊(C3⋊C16)—21no—
10C3×(C2×D3)⋊C8—21no—
11C3×(C2×D3)⋊C8—21no—
12C2×C3×C3⋊C16—21no—
13C3×#408—31no—
14#5110D311yescharacteristic
15C3×C22⋊C16—31no—
16#4549—31no—
17#4549—31no—
18#4549—61no—
19#4549D311yescharacteristic, complemented
20C22×C32×C4C2×C411yescharacteristic
21C2×C3×#67—21no—
22C3×#235—41no—
23C3×#235—41no—
24C2×C3×D12C811yescharacteristic
25C2×C3×C4×D3—21no—
26C2×C3×Dic6C811yescharacteristic
27C2×C32×C8—41no—
28C2×C32×C8D411yescharacteristic
29C2×C32×C8D411yescharacteristic
30C3×#208—41no—
31C2×C3×C3⋊C8—21no—
32C3⋊(C3⋊C16)—41no—
33C3×C3⋊C16—41no—
34#1315—91noSylow
35C2×C3×#41—31no—
36C2×#235Dic311yescharacteristic
37C2×C3×M16—31no—
38C22×C3×C8—21no—
39C22×C3×C8C2×D311yescharacteristic
40C22×C3×C8C2×D311yescharacteristic
41C2×#208Dic311yescharacteristic
42C2×C3×C16—61no—
43C3×C22⋊C8—61no—
44C3×C22⋊C8—61no—
45(C2×D3)⋊C8—21no—
46(C2×D3)⋊C8—21no—
47C2×C3⋊C16—21no—
48C2×C3⋊C16—62no—
49C2×C3⋊C16—61no—
50C2×C3⋊C16—61no—
51C23×C32M1611yescharacteristic
52C22×C3×D3—21no—
53C2×C32×C4—21no—
54C2×C32×C4—21no—
55C2×C32×C4C22⋊C411yescharacteristic
56C2×C32×C4C2×C811yescharacteristic
57C3×#67—42no—
58C2×C3×Dic3—21no—
59C3×D12—41no—
60C3×C4×D3—41no—
61C3×C4×D3—41no—
62C3×Dic6—41no—
63C32×C8—21no—
64C32×C8—21no—
65C3×C3⋊C8—41no—
66#408—31no—
67C22⋊C16—31no—
68C22⋊C16—91no—
69C3×#41—121no—
70C3×#41—121no—
71C2×C3×Q8—31no—
72C2×C3×D4—31no—
73C2×C3×D4—61no—
74C22×C3×C4—21no—
75C22×C3×C4—61no—
76C22×C3×C4C4×D311yescharacteristic
77C22×C3×C4C2×Dic311yescharacteristic
78C2×#67—21no—
79#235—41no—
80#235—41no—
81C2×D12C3⋊C811yescharacteristic
82C2×C4×D3—21no—
83C2×Dic6C3⋊C811yescharacteristic
84C3×M16—121no—
85C2×C3×C8—21no—
86C2×C3×C8—21no—
87C2×C3×C8—41no—
88C2×C3×C8—41no—
89C2×C3×C8—42no—
90C2×C3×C8—61no—
91C2×C3×C8D1211yescharacteristic
92C2×C3×C8#6711yescharacteristic
93C2×C3×C8#6711yescharacteristic
94C2×C3×C8#6711yescharacteristic
95#208—41no—
96C2×C3⋊C8—21no—
97C3×C16—121no—
98C3⋊C16—41no—
99C3⋊C16—122no—
100C3⋊C16—121no—
101C3⋊C16—121no—
102C22×C32—21no—
103C22×C32—21no—
104C22×C32—21no—
105C22×C32C22⋊C811yescharacteristic
106C2×C3×D3—41no—
107C2×C3×D3—41no—
108C2×C3×D3—41no—
109C32×C4—21no—
110C32×C4#9911yescharacteristic
111C32×C4#10011yescharacteristic
112C3×Dic3—41no—
113C2×#41—31no—
114C2×M16—31no—
115C22×C8D3211yescharacteristic
116C2×C16—61no—
117C2×C16—181no—
118C22⋊C8—61no—
119C22⋊C8—61no—
120C23×C3—21no—
121C23×C3—61no—
122C23×C3ΓL(1,𝔽25)11yescharacteristic
123C23×C3#20811yescharacteristic
124C22×D3—21no—
125C3×Q8—121no—
126C3×D4—121no—
127C3×D4—122no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—41no—
135C2×C3×C4—41no—
136C2×C3×C4—61no—
137C2×C3×C4—121no—
138C2×C3×C4—121no—
139C2×C3×C4D3×C811yescharacteristic
140C2×C3×C4C2×C3⋊C811yescharacteristic
141C2×C3×C4(C2×D3)⋊C411yescharacteristic
142C2×C3×C4#21711yescharacteristic
143#67—42no—
144C2×Dic3—21no—
145D12—41no—
146C4×D3—41no—
147C4×D3—41no—
148Dic6—41no—
149C3×C8—22no—
150C3×C8—21no—
151C3×C8—21no—
152C3×C8—21no—
153C3×C8—21no—
154C3×C8—41no—
155C3×C8—121no—
156C3⋊C8—41no—
157C2×C32—41no—
158C2×C32#32311yescharacteristic
159C2×C32#35011yescharacteristic
160C2×C32#35011yescharacteristic
161C3×D3—81no—
162#41—121no—
163#41—121no—
164C2×Q8—31no—
165C2×D4—31no—
166C2×D4—61no—
167C22×C4—61no—
168C22×C4D3×Dic311yescharacteristic
169M16—121no—
170C2×C8—41no—
171C2×C8—61no—
172C2×C8#62511yescharacteristic
173C2×C8#62611yescharacteristic
174C16—121no—
175C16—361no—
176C22×C3—22no—
177C22×C3—21no—
178C22×C3—21no—
179C22×C3—21no—
180C22×C3—21no—
181C22×C3—21no—
182C22×C3—21no—
183C22×C3—21no—
184C22×C3—41no—
185C22×C3—41no—
186C22×C3—121no—
187C22×C3—121no—
188C22×C3—121no—
189C22×C3(C2×D3)⋊C811yescharacteristic
190C22×C3#83011yescharacteristic
191C2×D3—41no—
192C2×D3—41no—
193C2×D3—41no—
194C3×C4—21no—
195C3×C4—21no—
196C3×C4—21no—
197C3×C4—21no—
198C3×C4—41no—
199C3×C4—121no—
200C3×C4#80611yescharacteristic
201C3×C4#82311yescharacteristic
202C3×C4#83311yescharacteristic
203C3×C4#83411yescharacteristic
204Dic3—41no—
205C32#131511yescharacteristic, complemented, Sylow
206C23—61no—
207C23#371111yescharacteristic
208Q8—121no—
209D4—121no—
210D4—122no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—61no—
214C2×C4—121no—
215C2×C4—121no—
216C2×C4D3×C3⋊C811yescharacteristic
217C2×C4(C2×D3)⋊Dic311yescharacteristic
218C8—21no—
219C8—21no—
220C8—121no—
221C2×C3—21no—
222C2×C3—21no—
223C2×C3—21no—
224C2×C3—42no—
225C2×C3—41no—
226C2×C3—41no—
227C2×C3—241no—
228C2×C3#446811yescharacteristic
229C2×C3#450811yescharacteristic
230C2×C3#451511yescharacteristic
231C2×C3#452511yescharacteristic
232C2×C3#456111yescharacteristic
233C2×C3#456111yescharacteristic
234D3—81no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—121no—
239C22—121no—
240C22—121no—
241C22(C2×D3)⋊(C3⋊C8)11yescharacteristic
242C4—21no—
243C4—121no—
244C4#6355811yescharacteristic
245C4#6358011yescharacteristic
246C3—21no—
247C3#6752311yescharacteristic, complemented
248C3#6768911yescharacteristic, complemented
249C2—41no—
250C2—241no—
251C2#1058911111yescharacteristic
252C2#1058911211yescharacteristic
253C2#1058914511yescharacteristic
subgroupG/H
centerC2×C4(C2×D3)⋊Dic3
commutatorC2×C32×C4C2×C8
Frattini, hypercenterC22×C8D32
Fitting, cosocleC22×C32×C8C22
socleC22×C32C22⋊C8
prime radicalC2×C3×#235C4
hypocenterC32#1315
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10589415C2semidirect
3. C3×#4549C2semidirect
19. #4549D3semidirect
205. C32#1315semidirect
247. C3#67523semidirect
248. C3#67689semidirect

Maximal subgroups

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

subgroupindex
C3×#51102
#105894152
C3×#45492
#676893
#675233