Finite Group Databasebeta

← #11799745

Subgroups — #11799745

Order 1152.

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

normal subgroups only

This group has 283 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#10592557C211yesmaximal, characteristic, complemented
2#10590919C211yesmaximal, characteristic
3C3×#4488C211yesmaximal, characteristic
4C3×#4487C211yesmaximal, characteristic, complemented
5#10589137C211yesmaximal, characteristic, complemented
6#10589135C211yesmaximal, characteristic, complemented
7#10589124C211yesmaximal, characteristic
8#69316—31nomaximal
9#69247—31nomaximal
10#64099—21no—
11C3×#904C2211yescharacteristic
12#63815—21no—
13C32×#106C2211yescharacteristic
14#63644C2211yescharacteristic
15C8×C3⋊Dic3C2211yescharacteristic
16#63634—21no—
17C3×#819C2211yescharacteristic
18C3×#812C2211yescharacteristic
19C3×#812C2211yescharacteristic
20#63568—21no—
21#5196—31no—
22#4895—31no—
23#4858—31no—
24#4858—31no—
25#4858—61no—
26C3×#365—31no—
27C3×#360—31no—
28#4566—31no—
29#4518—31no—
30#4513—31no—
31#4511—31no—
32#4511—31no—
33#4494—31no—
34#4488D311yescharacteristic
35#4487D311yescharacteristic, complemented
36C3×#235—21no—
37C2×C32×C8C2311yescharacteristic
38C32×C4⋊C4—21no—
39C4⋊(C3⋊Dic3)—21no—
40C4⋊(C3⋊Dic3)—41no—
41#3750—41no—
42C4×C3⋊Dic3D411yescharacteristic
43C2×C3⋊(C3⋊C8)D411yescharacteristic
44C3×#208—21no—
45C3×Dic12Q811yescharacteristic
46C3×D24Q811yescharacteristic
47C3×#204—21no—
48#3711—41no—
49D3×C3⋊C8—41no—
50C3×C3⋊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—
59#890—62no—
60C3×M32—31no—
61C3×M32—31no—
62C3×#108—31no—
63C3×#106—21no—
64C3×#106C2×D311yescharacteristic
65C3×#106C2×D311yescharacteristic
66#837—61no—
67#825—61no—
68#819C2×D311yescharacteristic
69#817—31no—
70#817—31no—
71#817—61no—
72C8×Dic3—31no—
73C8×Dic3—31no—
74C8×Dic3—61no—
75#812C2×D311yescharacteristic
76#812C2×D311yescharacteristic
77#807—61no—
78#807—61no—
79#807—62no—
80C2×C32×C4—41no—
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—41no—
84C3×#67—41no—
85C3×D12—21no—
86C3×C4×D3—41no—
87C3×Dic6—21no—
88C32×C8C2×Q811yescharacteristic
89C32×C8#4111yescharacteristic
90C3⋊(C3⋊C8)SD1611yescharacteristic
91C3⋊(C3⋊C8)SD1611yescharacteristic
92C3×C3⋊C8—41no—
93#499—91no—
94#443—91no—
95#365—31no—
96#365—91no—
97#364—91no—
98#360—31no—
99#360—91no—
100C3×#41—61no—
101#235—21no—
102C3×Q16—31no—
103C3×SD16—61no—
104C3×D8—31no—
105C3×M16—61no—
106C2×C3×C8—21no—
107C2×C3×C8C22×D311yescharacteristic
108C2×C3×C8C22×D311yescharacteristic
109C3×C4⋊C4—22no—
110C3×C4⋊C4—21no—
111C3×C4⋊C4—21no—
112C4⋊Dic3—62no—
113C4⋊Dic3—61no—
114C4⋊Dic3—61no—
115C4⋊Dic3—122no—
116C4⋊Dic3—121no—
117C4⋊Dic3—121no—
118Dic3⋊C4—122no—
119Dic3⋊C4—121no—
120Dic3⋊C4—121no—
121C4×Dic3—31no—
122C4×Dic3—31no—
123C4×Dic3—61no—
124#208—21no—
125#208—121no—
126C2×C3⋊C8—31no—
127C2×C3⋊C8—31no—
128C2×C3⋊C8—61no—
129C2×C3⋊C8—121no—
130Dic12Dic611yescharacteristic
131D24Dic611yescharacteristic
132#204—21no—
133ΓL(1,𝔽25)—121no—
134D3×C8—121no—
135C3×C16—61no—
136C3×C16—61no—
137C3⋊C16—21no—
138C3⋊C16—21no—
139C22×C32AGL(1,ℤ/8)11yescharacteristic
140C2×C3×D3—41no—
141C32×C4—81no—
142C32×C4C22⋊Q811yescharacteristic
143C32×C4C2×SD1611yescharacteristic
144C3⋊Dic3—41no—
145C3⋊Dic3—81no—
146C3×Dic3—41no—
147#135—31no—
148#131—181no—
149#125—181no—
150M32—31no—
151M32—31no—
152#108—31no—
153#107—181no—
154#106—91no—
155#106D3211yescharacteristic
156#104—181no—
157C4×C8—91no—
158C3×Q8—61no—
159C3×D4—61no—
160C3×D4—121no—
161C2×C3×C4—21no—
162C2×C3×C4—42no—
163C2×C3×C4—41no—
164C2×C3×C4—41no—
165C2×C3×C4—121no—
166C2×C3×C4D3×D411yescharacteristic
167C2×C3×C4D3×D411yescharacteristic
168#67—41no—
169C2×Dic3—62no—
170C2×Dic3—61no—
171C2×Dic3—61no—
172C2×Dic3—122no—
173C2×Dic3—121no—
174C2×Dic3—121no—
175D12—21no—
176C4×D3—41no—
177Dic6—21no—
178C3×C8—21no—
179C3×C8—21no—
180C3×C8—121no—
181C3×C8C2×Dic611yescharacteristic
182C3×C8#23511yescharacteristic
183C3×C8#23711yescharacteristic
184C3×C8D3×Q811yescharacteristic
185C3⋊C8—31no—
186C3⋊C8—31no—
187C3⋊C8—31no—
188C3⋊C8—31no—
189C3⋊C8—41no—
190C3⋊C8—61no—
191C3⋊C8—61no—
192C2×C32—21no—
193C2×C32#47611yescharacteristic
194C3×D3—81no—
195#41—61no—
196Q16—31no—
197SD16—61no—
198D8—31no—
199M16—61no—
200M16—361no—
201C2×C8—91no—
202C2×C8—361no—
203C2×C8C2×D3211yescharacteristic
204C4⋊C4—21no—
205C4⋊C4—181no—
206C4⋊C4—361no—
207C4⋊C4—361no—
208C42—91no—
209C16—61no—
210C16—61no—
211C22×C3—21no—
212C22×C3—121no—
213C22×C3#91111yescharacteristic
214C22×C3#91411yescharacteristic
215C2×D3—41no—
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—82no—
219C3×C4—81no—
220C3×C4—81no—
221C3×C4—121no—
222C3×C4#87811yescharacteristic
223C3×C4#89611yescharacteristic
224C3×C4D3×SD1611yescharacteristic
225C3×C4D3×SD1611yescharacteristic
226Dic3—41no—
227Dic3—122no—
228Dic3—121no—
229Dic3—121no—
230Dic3—242no—
231Dic3—241no—
232Dic3—241no—
233C32#223111yescharacteristic, complemented, Sylow
234Q8—61no—
235D4—61no—
236D4—121no—
237C2×C4—41no—
238C2×C4—121no—
239C2×C4—181no—
240C2×C4—361no—
241C2×C4#381111yescharacteristic
242C8—91no—
243C8—91no—
244C8—121no—
245C8D3×Dic611yescharacteristic
246C8#379511yescharacteristic
247C2×C3—22no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—241no—
252C2×C3#476111yescharacteristic
253C2×C3#487011yescharacteristic
254D3—81no—
255C22—121no—
256C22#6393711yescharacteristic
257C4—81no—
258C4—121no—
259C4—361no—
260C4—721no—
261C4#6389611yescharacteristic
262C4#6394011yescharacteristic
263C3—21no—
264C3#6924711yescharacteristic, complemented
265C3#6931611yescharacteristic, complemented
266C2—21no—
267C2—241no—
268C2#1059047211yescharacteristic
subgroupG/H
centerC2#10590472
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#106C22
socleC2×C32#476
prime radicalC3×#904C22
hypercenter#106D32
hypocenterC32#2231
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
1. #10592557C2semidirect
4. C3×#4487C2semidirect
5. #10589137C2semidirect
6. #10589135C2semidirect
35. #4487D3semidirect
233. C32#2231semidirect
264. C3#69247semidirect
265. C3#69316semidirect

Maximal subgroups

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

subgroupindex
#105925572
#105909192
C3×#44882
C3×#44872
#105891372
#105891352
#105891242
#693163
#692473