Finite Group Databasebeta

← #11799756

Subgroups — #11799756

Order 1152.

261 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 261 conjugacy classes of subgroups — too many to draw. Only its 72 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×#4895C211yesmaximal, characteristic
2#10590871C211yesmaximal, characteristic, complemented
3#10589360C211yesmaximal, characteristic, complemented
4C3×#4494C211yesmaximal, characteristic, complemented
5#10589134C211yesmaximal, characteristic, complemented
6#10589124C211yesmaximal, characteristic
7#10589123C211yesmaximal, characteristic
8#70920—31nomaximal
9#69316—31nomaximal
10C3×#907—21no—
11C3×#904C2211yescharacteristic
12#63869—21no—
13C32×#108C2211yescharacteristic
14#63644C2211yescharacteristic
15#63639C2211yescharacteristic
16C3×#825—21no—
17C3×#817C2211yescharacteristic
18C3×C8×Dic3C2211yescharacteristic
19C3×#812C2211yescharacteristic
20#63575—21no—
21C3×#443—31no—
22#4895D311yescharacteristic
23#4858—31no—
24#4683—31no—
25C3×#365—31no—
26#4566—31no—
27#4566—31no—
28#4518—31no—
29#4511—31no—
30#4494—31no—
31#4494—31no—
32#4494—61no—
33#4494D311yescharacteristic, complemented
34#4488—31no—
35#4463—31no—
36C3×#235—21no—
37C32×M16—21no—
38C2×C32×C8C2311yescharacteristic
39C4⋊(C3⋊Dic3)—21no—
40C3×C4⋊Dic3—21no—
41C3×C4×Dic3D411yescharacteristic
42C2×C3×C3⋊C8D411yescharacteristic
43C3×Dic12Q811yescharacteristic
44C3×D24Q811yescharacteristic
45C3×#204—21no—
46C3×ΓL(1,𝔽25)—41no—
47C3×D3×C8—41no—
48#3724—41no—
49Dic3⋊Dic3—41no—
50C3⋊(C3⋊C16)—21no—
51C3×C3⋊C16—21no—
52#2231—91noSylow
53C3×#135—31no—
54C3×#131—61no—
55#907—21no—
56#904C2×D311yescharacteristic
57#890—61no—
58#870—61no—
59C3×M32—31no—
60C3×#108—21no—
61C3×#108C2×D311yescharacteristic
62C3×#108C2×D311yescharacteristic
63C3×#106—31no—
64C3×#104—61no—
65C3×C4×C8—31no—
66#825—21no—
67#818—61no—
68#817—31no—
69#817—31no—
70#817—61no—
71#817C2×D311yescharacteristic
72C8×Dic3C2×D311yescharacteristic
73#812—31no—
74#812—31no—
75#812—61no—
76#812C2×D311yescharacteristic
77#807—61no—
78C2×C32×C4C2×D411yescharacteristic
79C2×C3⋊Dic3—41no—
80C3×#67—41no—
81C2×C3×Dic3—21no—
82C2×C3×Dic3—41no—
83C3×D12—21no—
84C3×C4×D3—41no—
85C3×Dic6—21no—
86C32×C8—41no—
87C32×C8C2×Q811yescharacteristic
88C32×C8#4111yescharacteristic
89C3×C3⋊C8SD1611yescharacteristic
90C3×C3⋊C8SD1611yescharacteristic
91#499—91no—
92#443—31no—
93#365—31no—
94#365—91no—
95#364—91no—
96#360—91no—
97#360—91no—
98C3×#41—61no—
99#235—21no—
100C3×Q16—31no—
101C3×SD16—61no—
102C3×D8—31no—
103C3×M16—21no—
104C3×M16—21no—
105C3×M16—41no—
106C3×M16—121no—
107C2×C3×C8—21no—
108C2×C3×C8—31no—
109C2×C3×C8—121no—
110C2×C3×C8C22×D311yescharacteristic
111C2×C3×C8C22×D311yescharacteristic
112C3×C4⋊C4—61no—
113C3×C42—31no—
114C4⋊Dic3—21no—
115C4⋊Dic3—61no—
116C4⋊Dic3—61no—
117C4⋊Dic3—121no—
118C4⋊Dic3—121no—
119Dic3⋊C4—121no—
120Dic3⋊C4—121no—
121Dic3⋊C4—121no—
122C4×Dic3#6711yescharacteristic
123C2×C3⋊C8#6711yescharacteristic
124Dic12Dic611yescharacteristic
125D24Dic611yescharacteristic
126#204—21no—
127ΓL(1,𝔽25)—41no—
128D3×C8—41no—
129C3×C16—61no—
130C3⋊C16—21no—
131C3⋊C16—62no—
132C3⋊C16—61no—
133C3⋊C16—61no—
134C22×C32AGL(1,ℤ/8)11yescharacteristic
135C2×C3×D3—41no—
136C32×C4C22⋊Q811yescharacteristic
137C32×C4C2×SD1611yescharacteristic
138C3⋊Dic3—81no—
139C3×Dic3—41no—
140C3×Dic3—41no—
141C3×Dic3—81no—
142#135—31no—
143#131—61no—
144#125—181no—
145M32—31no—
146M32—91no—
147#108D3211yescharacteristic
148#107—181no—
149#106—31no—
150#106—91no—
151#104—61no—
152C4×C8—31no—
153C3×Q8—61no—
154C3×D4—61no—
155C3×D4—121no—
156C2×C3×C4—21no—
157C2×C3×C4—61no—
158C2×C3×C4—121no—
159C2×C3×C4—121no—
160C2×C3×C4D3×D411yescharacteristic
161C2×C3×C4C2×#6711yescharacteristic
162#67—41no—
163C2×Dic3—21no—
164C2×Dic3—41no—
165C2×Dic3—121no—
166C2×Dic3—121no—
167C2×Dic3—241no—
168D12—21no—
169C4×D3—41no—
170Dic6—21no—
171C3×C8—21no—
172C3×C8—21no—
173C3×C8—31no—
174C3×C8—31no—
175C3×C8—41no—
176C3×C8—41no—
177C3×C8—81no—
178C3×C8C2×Dic611yescharacteristic
179C3×C8#23511yescharacteristic
180C3×C8#23511yescharacteristic
181C3×C8D3×Q811yescharacteristic
182C3⋊C8#21411yescharacteristic
183C3⋊C8#21411yescharacteristic
184C2×C32—21no—
185C2×C32#47611yescharacteristic
186C3×D3—81no—
187#41—61no—
188Q16—31no—
189SD16—61no—
190D8—31no—
191M16—21no—
192M16—121no—
193C2×C8—31no—
194C2×C8—121no—
195C2×C8C2×D3211yescharacteristic
196C4⋊C4—61no—
197C4⋊C4—181no—
198C4⋊C4—361no—
199C4⋊C4—361no—
200C42—31no—
201C16—61no—
202C16—181no—
203C22×C3—21no—
204C22×C3—121no—
205C22×C3#91411yescharacteristic
206C22×C3#94911yescharacteristic
207C2×D3—41no—
208C3×C4—21no—
209C3×C4—21no—
210C3×C4—121no—
211C3×C4—121no—
212C3×C4—241no—
213C3×C4#89611yescharacteristic
214C3×C4D3×SD1611yescharacteristic
215C3×C4#92411yescharacteristic
216C3×C4C2×#21411yescharacteristic
217Dic3—41no—
218Dic3—41no—
219Dic3—81no—
220Dic3—241no—
221Dic3—241no—
222Dic3—481no—
223C32#223111yescharacteristic, complemented, Sylow
224Q8—61no—
225D4—61no—
226D4—121no—
227C2×C4—61no—
228C2×C4—121no—
229C2×C4—121no—
230C2×C4—361no—
231C2×C4D3×#6711yescharacteristic
232C8—31no—
233C8—31no—
234C8—41no—
235C8D3×Dic611yescharacteristic
236C8#379811yescharacteristic
237C2×C3—21no—
238C2×C3—21no—
239C2×C3—21no—
240C2×C3—41no—
241C2×C3—241no—
242C2×C3#487011yescharacteristic
243C2×C3#500811yescharacteristic
244D3—81no—
245C22—121no—
246C22#6393911yescharacteristic
247C4—121no—
248C4—121no—
249C4—241no—
250C4—721no—
251C4#6385111yescharacteristic
252C4D3×#21411yescharacteristic
253C3—21no—
254C3#6931611yescharacteristic, complemented
255C3#7092011yescharacteristic, complemented
256C2—21no—
257C2—241no—
258C2#1059055811yescharacteristic
subgroupG/H
centerC2#10590558
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#108C22
socleC2×C32#476
prime radicalC3×#904C22
hypercenter#108D32
hypocenterC32#2231
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #108

Complements

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

NH ≅ G/Ntype
2. #10590871C2semidirect
3. #10589360C2semidirect
4. C3×#4494C2semidirect
5. #10589134C2semidirect
33. #4494D3semidirect
223. C32#2231semidirect
254. C3#69316semidirect
255. C3#70920semidirect

Maximal subgroups

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

subgroupindex
C3×#48952
#105908712
#105893602
C3×#44942
#105891342
#105891242
#105891232
#709203
#693163