Finite Group Databasebeta

← #11771429

Subgroups — #11771429

Order 1152.

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

normal subgroups only

This group has 253 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×#5129C211yesmaximal, characteristic
2#10589419C211yesmaximal, characteristic, complemented
3C3×#4553C211yesmaximal, characteristic, complemented
4#67690—31nomaximal
5#67531—31nomaximal
6C2×C3×#235C411yescharacteristic
7C2×C32×M16C2211yescharacteristic
8C22×C3×C3⋊C8C411yescharacteristic
9#63639—21no—
10C3×(C2×D3)⋊C8—21no—
11C3×(C2×D3)⋊C8—21no—
12C3×#812—21no—
13C3×#408—31no—
14#5129D311yescharacteristic
15C3×#349—31no—
16#4553—31no—
17#4553—31no—
18#4553—61no—
19#4553D311yescharacteristic, 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
27C32×M16—41no—
28C2×C32×C8D411yescharacteristic
29C2×C32×C8D411yescharacteristic
30C2×C3×C3⋊C8—21no—
31C2×C3×C3⋊C8—41no—
32C3⋊(C3⋊C16)—41no—
33C3×C3⋊C16—41no—
34#1321—91noSylow
35C2×C3×#41—31no—
36C2×#235Dic311yescharacteristic
37C2×C3×M16—21no—
38C2×C3×M16C2×D311yescharacteristic
39C2×C3×M16C2×D311yescharacteristic
40C22×C3×C8—31no—
41C22×C3⋊C8Dic311yescharacteristic
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×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—
67#349—31no—
68#349—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—41no—
85C3×M16—41no—
86C3×M16—42no—
87C2×C3×C8—21no—
88C2×C3×C8—21no—
89C2×C3×C8—61no—
90C2×C3×C8—121no—
91C2×C3×C8D1211yescharacteristic
92C2×C3×C8#6711yescharacteristic
93C2×C3×C8#6711yescharacteristic
94C2×C3×C8#6711yescharacteristic
95C2×C3⋊C8—21no—
96C2×C3⋊C8—41no—
97C3×C16—121no—
98C3⋊C16—41no—
99C3⋊C16—122no—
100C3⋊C16—121no—
101C3⋊C16—121no—
102C22×C32—21no—
103C22×C32—41no—
104C22×C32C22⋊C811yescharacteristic
105C2×C3×D3—42no—
106C2×C3×D3—41no—
107C32×C4—21no—
108C32×C4#9911yescharacteristic
109C32×C4#10011yescharacteristic
110C3×Dic3—41no—
111C2×#41—31no—
112C2×M16D3211yescharacteristic
113C22×C8—31no—
114M32—61no—
115M32—181no—
116C22⋊C8—61no—
117C22⋊C8—61no—
118C23×C3—21no—
119C23×C3—61no—
120C23×C3ΓL(1,𝔽25)11yescharacteristic
121C23×C3#20811yescharacteristic
122C22×D3—21no—
123C3×Q8—121no—
124C3×D4—121no—
125C3×D4—122no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—21no—
132C2×C3×C4—41no—
133C2×C3×C4—41no—
134C2×C3×C4—61no—
135C2×C3×C4—121no—
136C2×C3×C4—121no—
137C2×C3×C4D3×C811yescharacteristic
138C2×C3×C4C2×C3⋊C811yescharacteristic
139C2×C3×C4(C2×D3)⋊C411yescharacteristic
140C2×C3×C4#21711yescharacteristic
141#67—42no—
142C2×Dic3—21no—
143D12—41no—
144C4×D3—41no—
145C4×D3—41no—
146Dic6—41no—
147C3×C8—22no—
148C3×C8—21no—
149C3×C8—21no—
150C3×C8—21no—
151C3×C8—21no—
152C3×C8—41no—
153C3×C8—121no—
154C3⋊C8—41no—
155C2×C32—21no—
156C2×C32—41no—
157C2×C32#32311yescharacteristic
158C3×D3—81no—
159#41—121no—
160#41—121no—
161C2×Q8—31no—
162C2×D4—31no—
163C2×D4—61no—
164C22×C4—61no—
165C22×C4D3×Dic311yescharacteristic
166M16—41no—
167C2×C8—61no—
168C2×C8—121no—
169C2×C8#62511yescharacteristic
170C2×C8#62611yescharacteristic
171C16—121no—
172C16—361no—
173C22×C3—21no—
174C22×C3—21no—
175C22×C3—21no—
176C22×C3—41no—
177C22×C3—41no—
178C22×C3—41no—
179C22×C3—81no—
180C22×C3—122no—
181C22×C3—121no—
182C22×C3(C2×D3)⋊C811yescharacteristic
183C22×C3#83011yescharacteristic
184C2×D3—42no—
185C2×D3—41no—
186C3×C4—21no—
187C3×C4—21no—
188C3×C4—21no—
189C3×C4—21no—
190C3×C4—41no—
191C3×C4—121no—
192C3×C4#80611yescharacteristic
193C3×C4#82311yescharacteristic
194C3×C4#83311yescharacteristic
195C3×C4#83411yescharacteristic
196Dic3—41no—
197C32#132111yescharacteristic, complemented, Sylow
198C23—61no—
199C23#371111yescharacteristic
200Q8—121no—
201D4—121no—
202D4—122no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—61no—
206C2×C4—121no—
207C2×C4—121no—
208C2×C4D3×C3⋊C811yescharacteristic
209C2×C4(C2×D3)⋊Dic311yescharacteristic
210C8—21no—
211C8—21no—
212C8—121no—
213C2×C3—21no—
214C2×C3—21no—
215C2×C3—21no—
216C2×C3—41no—
217C2×C3—41no—
218C2×C3—41no—
219C2×C3—81no—
220C2×C3—241no—
221C2×C3#446811yescharacteristic
222C2×C3#452511yescharacteristic
223D3—81no—
224C22—21no—
225C22—41no—
226C22—122no—
227C22—121no—
228C22(C2×D3)⋊(C3⋊C8)11yescharacteristic
229C4—21no—
230C4—121no—
231C4#6355811yescharacteristic
232C4#6358011yescharacteristic
233C3—21no—
234C3#6753111yescharacteristic, complemented
235C3#6769011yescharacteristic, complemented
236C2—21no—
237C2—41no—
238C2—241no—
239C2#1058914511yescharacteristic
subgroupG/H
centerC4#63580
commutatorC2×C32×C4C2×C8
Frattini, hypercenterC2×M16D32
Fitting, cosocleC2×C32×M16C22
socleC2×C32#323
prime radicalC2×C3×#235C4
hypocenterC32#1321
LCSG ▷ C2×C32×C4 ▷ 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
197. C32#1321semidirect
234. C3#67531semidirect
235. C3#67690semidirect

Maximal subgroups

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

subgroupindex
C3×#51292
#105894192
C3×#45532
#676903
#675313