Finite Group Databasebeta

← #11799753

Subgroups — #11799753

Order 1152.

263 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 263 conjugacy classes of subgroups — too many to draw. Only its 68 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#10590919C211yesmaximal, characteristic
2#10590874C211yesmaximal, characteristic, complemented
3#10589377C211yesmaximal, characteristic, complemented
4C3×#4518C211yesmaximal, characteristic
5C3×#4513C211yesmaximal, characteristic, complemented
6#10589138C211yesmaximal, characteristic, complemented
7#10589123C211yesmaximal, characteristic
8#69316—31nomaximal
9#69247—31nomaximal
10C3×#904C2211yescharacteristic
11#63872—21no—
12#63815—21no—
13C32×M32C2211yescharacteristic
14C8×C3⋊Dic3C2211yescharacteristic
15#63639C2211yescharacteristic
16C3×#819C2211yescharacteristic
17C3×#817C2211yescharacteristic
18C3×#817C2211yescharacteristic
19#63576—21no—
20#63568—21no—
21#5196—31no—
22#4895—31no—
23#4858—31no—
24#4858—31no—
25C3×#365—31no—
26C3×#360—31no—
27#4566—31no—
28#4518D311yescharacteristic
29#4513D311yescharacteristic, complemented
30#4511—31no—
31#4511—31no—
32#4511—61no—
33#4494—31no—
34#4488—31no—
35#4487—31no—
36C3×#235—21no—
37C2×C32×C8C2311yescharacteristic
38C4×C3⋊Dic3D411yescharacteristic
39C2×C3⋊(C3⋊C8)D411yescharacteristic
40C3×C4⋊Dic3—21no—
41C3×C4⋊Dic3—21no—
42C3×#208—21no—
43C3×Dic12Q811yescharacteristic
44C3×D24Q811yescharacteristic
45C3×#204—21no—
46Dic3⋊Dic3—41no—
47Dic3⋊Dic3—41no—
48#3711—41no—
49D3×C3⋊C8—41no—
50C32×C16—21no—
51C3⋊(C3⋊C16)—21no—
52#2231—91noSylow
53C3×#135—31no—
54#948—61no—
55#907—61no—
56#904C2×D311yescharacteristic
57#890—61no—
58#890—61no—
59C3×M32—21no—
60C3×M32C2×D311yescharacteristic
61C3×M32C2×D311yescharacteristic
62C3×#108—31no—
63C3×#106—31no—
64C3×#106—31no—
65#837—61no—
66#825—61no—
67#819C2×D311yescharacteristic
68#817C2×D311yescharacteristic
69#817C2×D311yescharacteristic
70C8×Dic3—31no—
71C8×Dic3—31no—
72C8×Dic3—61no—
73#812—31no—
74#812—31no—
75#812—61no—
76#807—61no—
77#807—61no—
78C2×C32×C4C2×D411yescharacteristic
79C2×C3⋊Dic3—21no—
80C3×#67—41no—
81C2×C3×Dic3—41no—
82C2×C3×Dic3—41no—
83C3×D12—21no—
84C3×C4×D3—41no—
85C3×Dic6—21no—
86C32×C8C2×Q811yescharacteristic
87C32×C8#4111yescharacteristic
88C3⋊(C3⋊C8)SD1611yescharacteristic
89C3⋊(C3⋊C8)SD1611yescharacteristic
90C3×C3⋊C8—41no—
91#499—91no—
92#443—91no—
93#365—31no—
94#365—91no—
95#364—91no—
96#360—31no—
97#360—91no—
98C3×#41—61no—
99#235—21no—
100C3×Q16—31no—
101C3×SD16—61no—
102C3×D8—31no—
103C3×M16—61no—
104C2×C3×C8—21no—
105C2×C3×C8C22×D311yescharacteristic
106C2×C3×C8C22×D311yescharacteristic
107C3×C4⋊C4—61no—
108C3×C4⋊C4—61no—
109C4⋊Dic3—21no—
110C4⋊Dic3—21no—
111C4⋊Dic3—121no—
112C4⋊Dic3—121no—
113Dic3⋊C4—121no—
114Dic3⋊C4—121no—
115C4×Dic3—31no—
116C4×Dic3—31no—
117C4×Dic3—61no—
118#208—21no—
119#208—121no—
120C2×C3⋊C8—31no—
121C2×C3⋊C8—31no—
122C2×C3⋊C8—61no—
123C2×C3⋊C8—121no—
124Dic12Dic611yescharacteristic
125D24Dic611yescharacteristic
126#204—21no—
127ΓL(1,𝔽25)—121no—
128D3×C8—121no—
129C3×C16—21no—
130C3×C16—21no—
131C3×C16—41no—
132C3⋊C16—61no—
133C3⋊C16—61no—
134C3⋊C16—121no—
135C22×C32AGL(1,ℤ/8)11yescharacteristic
136C2×C3×D3—41no—
137C32×C4C22⋊Q811yescharacteristic
138C32×C4C2×SD1611yescharacteristic
139C3⋊Dic3—41no—
140C3×Dic3—41no—
141C3×Dic3—81no—
142C3×Dic3—81no—
143#135—31no—
144#131—181no—
145#125—181no—
146M32—91no—
147M32D3211yescharacteristic
148#108—31no—
149#107—181no—
150#106—31no—
151#106—31no—
152#104—181no—
153C4×C8—91no—
154C3×Q8—61no—
155C3×D4—61no—
156C3×D4—121no—
157C2×C3×C4—21no—
158C2×C3×C4—121no—
159C2×C3×C4—121no—
160C2×C3×C4—121no—
161C2×C3×C4D3×D411yescharacteristic
162C2×C3×C4D3×D411yescharacteristic
163#67—41no—
164C2×Dic3—41no—
165C2×Dic3—41no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—121no—
169D12—21no—
170C4×D3—41no—
171Dic6—21no—
172C3×C8—21no—
173C3×C8—21no—
174C3×C8—121no—
175C3×C8C2×Dic611yescharacteristic
176C3×C8#23511yescharacteristic
177C3×C8#23711yescharacteristic
178C3×C8D3×Q811yescharacteristic
179C3⋊C8—31no—
180C3⋊C8—31no—
181C3⋊C8—31no—
182C3⋊C8—31no—
183C3⋊C8—41no—
184C3⋊C8—61no—
185C3⋊C8—61no—
186C2×C32—21no—
187C2×C32#47611yescharacteristic
188C3×D3—81no—
189#41—61no—
190Q16—31no—
191SD16—61no—
192D8—31no—
193M16—61no—
194M16—361no—
195C2×C8—91no—
196C2×C8—361no—
197C2×C8C2×D3211yescharacteristic
198C4⋊C4—61no—
199C4⋊C4—61no—
200C4⋊C4—361no—
201C4⋊C4—361no—
202C42—91no—
203C16—21no—
204C16—181no—
205C22×C3—21no—
206C22×C3—121no—
207C22×C3#91111yescharacteristic
208C22×C3#91411yescharacteristic
209C2×D3—41no—
210C3×C4—21no—
211C3×C4—21no—
212C3×C4—121no—
213C3×C4—241no—
214C3×C4—241no—
215C3×C4#87811yescharacteristic
216C3×C4#89611yescharacteristic
217C3×C4D3×SD1611yescharacteristic
218C3×C4D3×SD1611yescharacteristic
219Dic3—41no—
220Dic3—81no—
221Dic3—81no—
222Dic3—121no—
223Dic3—121no—
224Dic3—122no—
225C32#223111yescharacteristic, complemented, Sylow
226Q8—61no—
227D4—61no—
228D4—121no—
229C2×C4—121no—
230C2×C4—121no—
231C2×C4—121no—
232C2×C4—181no—
233C2×C4#380211yescharacteristic
234C8—91no—
235C8—91no—
236C8—121no—
237C8D3×Dic611yescharacteristic
238C8#380411yescharacteristic
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—41no—
243C2×C3—241no—
244C2×C3#476111yescharacteristic
245C2×C3#487011yescharacteristic
246D3—81no—
247C22—121no—
248C22#6379811yescharacteristic
249C4—121no—
250C4—241no—
251C4—241no—
252C4—361no—
253C4#6379611yescharacteristic
254C4#6389911yescharacteristic
255C3—21no—
256C3#6924711yescharacteristic, complemented
257C3#6931611yescharacteristic, complemented
258C2—21no—
259C2—241no—
260C2#1059077611yescharacteristic
subgroupG/H
centerC2#10590776
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32#476
prime radicalC3×#904C22
hypercenterM32D32
hypocenterC32#2231
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
2. #10590874C2semidirect
3. #10589377C2semidirect
5. C3×#4513C2semidirect
6. #10589138C2semidirect
29. #4513D3semidirect
225. C32#2231semidirect
256. C3#69247semidirect
257. C3#69316semidirect

Maximal subgroups

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

subgroupindex
#105909192
#105908742
#105893772
C3×#45182
C3×#45132
#105891382
#105891232
#693163
#692473