Finite Group Databasebeta

← #11799719

Subgroups — #11799719

Order 1152.

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

normal subgroups only

This group has 275 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#10590900C211yesmaximal, characteristic, complemented
3#10589377C211yesmaximal, characteristic, complemented
4C3×#4518C211yesmaximal, characteristic
5C3×#4513C211yesmaximal, characteristic, complemented
6#10589138C211yesmaximal, characteristic, complemented
7#10589123C211yesmaximal, characteristic
8#69315—31nomaximal
9#69246—31nomaximal
10C3×#904C2211yescharacteristic
11#63919—21no—
12#63815—21no—
13C32×M32C2211yescharacteristic
14C8×C3⋊Dic3C2211yescharacteristic
15#63639C2211yescharacteristic
16C3×#819C2211yescharacteristic
17C3×#817C2211yescharacteristic
18C3×#817C2211yescharacteristic
19#63574—21no—
20#63568—21no—
21#5196—31no—
22#4895—31no—
23#4855—31no—
24#4855—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×#627—41no—
38C2×C32×C8C2311yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C2×C3⋊(C3⋊C8)D411yescharacteristic
41C3×C4⋊Dic3—21no—
42C3×C4⋊Dic3—21no—
43C3×#208—21no—
44C3×Dic12Q811yescharacteristic, complemented
45C3×D24Q811yescharacteristic, complemented
46C3×#204—21no—
47#3724—41no—
48#3711—41no—
49D3×C3⋊C8—41no—
50C32×C16—21no—
51C3⋊(C3⋊C16)—21no—
52#2230—91noSylow
53C3×#135—31no—
54#948—61no—
55#907—61no—
56#904C2×D311yescharacteristic
57#888—61no—
58#888—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#808—61no—
77#808—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—
86#627—82no—
87C32×C8C2×Q811yescharacteristic
88C32×C8#4111yescharacteristic
89C3⋊(C3⋊C8)SD1611yescharacteristic
90C3⋊(C3⋊C8)SD1611yescharacteristic
91C3×C3⋊C8—41no—
92#498—91no—
93#443—91no—
94#365—31no—
95#365—91no—
96#364—91no—
97#360—31no—
98#360—91no—
99C3×#41—61no—
100#235—21no—
101C2×Dic6—121no—
102C2×Dic6—121no—
103C3×Q16—31no—
104C3×SD16—61no—
105C3×D8—31no—
106C3×M16—61no—
107C2×C3×C8—21no—
108C2×C3×C8C22×D311yescharacteristic
109C2×C3×C8C22×D311yescharacteristic
110C3×C4⋊C4—61no—
111C3×C4⋊C4—61no—
112C4⋊Dic3—21no—
113C4⋊Dic3—21no—
114Dic3⋊C4—121no—
115Dic3⋊C4—121no—
116C4×Dic3—31no—
117C4×Dic3—31no—
118C4×Dic3—61no—
119#208—21no—
120#208—121no—
121C2×C3⋊C8—31no—
122C2×C3⋊C8—31no—
123C2×C3⋊C8—61no—
124C2×C3⋊C8—121no—
125Dic12Dic611yescharacteristic, complemented
126D24Dic611yescharacteristic, complemented
127#204—21no—
128ΓL(1,𝔽25)—121no—
129D3×C8—121no—
130C3×C16—21no—
131C3×C16—21no—
132C3×C16—41no—
133C3⋊C16—61no—
134C3⋊C16—61no—
135C3⋊C16—121no—
136C22×C32AGL(1,ℤ/8)11yescharacteristic
137C2×C3×D3—41no—
138C32×C4C22⋊Q811yescharacteristic
139C32×C4C2×SD1611yescharacteristic
140C3⋊Dic3—22no—
141C3×Dic3—41no—
142C3×Dic3—81no—
143C3×Dic3—81no—
144#135—31no—
145#131—181no—
146C4⋊Q8—181no—
147M32—91no—
148M32D3211yescharacteristic
149#108—31no—
150#106—31no—
151#106—31no—
152#106—181no—
153#104—181no—
154C4×C8—91no—
155C3×Q8—61no—
156C3×D4—61no—
157C3×D4—121no—
158C2×C3×C4—21no—
159C2×C3×C4—121no—
160C2×C3×C4—121no—
161C2×C3×C4—121no—
162C2×C3×C4D3×D411yescharacteristic
163C2×C3×C4D3×D411yescharacteristic
164#67—41no—
165C2×Dic3—41no—
166C2×Dic3—41no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—121no—
170D12—21no—
171C4×D3—41no—
172Dic6—21no—
173Dic6—242no—
174Dic6—242no—
175C3×C8—21no—
176C3×C8—21no—
177C3×C8—121no—
178C3×C8C2×Dic611yescharacteristic
179C3×C8#23511yescharacteristic
180C3×C8#23711yescharacteristic
181C3×C8D3×Q811yescharacteristic
182C3⋊C8—31no—
183C3⋊C8—31no—
184C3⋊C8—31no—
185C3⋊C8—31no—
186C3⋊C8—41no—
187C3⋊C8—61no—
188C3⋊C8—61no—
189C2×C32—21no—
190C2×C32#47611yescharacteristic
191C3×D3—81no—
192#41—61no—
193C2×Q8—361no—
194Q16—31no—
195SD16—61no—
196D8—31no—
197M16—61no—
198M16—361no—
199C2×C8—91no—
200C2×C8—361no—
201C2×C8C2×D3211yescharacteristic
202C4⋊C4—61no—
203C4⋊C4—61no—
204C4⋊C4—361no—
205C42—91no—
206C16—21no—
207C16—181no—
208C22×C3—21no—
209C22×C3—121no—
210C22×C3#91111yescharacteristic
211C22×C3#91411yescharacteristic
212C2×D3—41no—
213C3×C4—21no—
214C3×C4—21no—
215C3×C4—121no—
216C3×C4—241no—
217C3×C4—241no—
218C3×C4#87811yescharacteristic
219C3×C4#89611yescharacteristic
220C3×C4D3×SD1611yescharacteristic
221C3×C4D3×SD1611yescharacteristic
222Dic3—41no—
223Dic3—62no—
224Dic3—62no—
225Dic3—81no—
226Dic3—81no—
227Dic3—122no—
228C32#223011yescharacteristic, complemented, Sylow
229Q8—61no—
230Q8—722no—
231D4—61no—
232D4—121no—
233C2×C4—121no—
234C2×C4—121no—
235C2×C4—121no—
236C2×C4—181no—
237C2×C4#380211yescharacteristic
238C8—91no—
239C8—91no—
240C8—121no—
241C8D3×Dic611yescharacteristic
242C8#380411yescharacteristic
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—41no—
247C2×C3—241no—
248C2×C3#476111yescharacteristic
249C2×C3#487011yescharacteristic
250D3—81no—
251C22—121no—
252C22#6379811yescharacteristic
253C4—121no—
254C4—182no—
255C4—241no—
256C4—241no—
257C4#6379611yescharacteristic
258C4#6389911yescharacteristic
259C3—21no—
260C3#6924611yescharacteristic, complemented
261C3#6931511yescharacteristic, complemented
262C2—21no—
263C2—241no—
264C2#1059077611yescharacteristic
subgroupG/H
centerC2#10590776
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32#476
prime radicalC3×#904C22
hypercenterM32D32
hypocenterC32#2230
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. #10590900C2semidirect
3. #10589377C2semidirect
5. C3×#4513C2semidirect
6. #10589138C2semidirect
29. #4513D3semidirect
44. C3×Dic12Q8semidirect
45. C3×D24Q8semidirect
125. Dic12Dic6semidirect
126. D24Dic6semidirect
228. C32#2230semidirect
260. C3#69246semidirect
261. C3#69315semidirect

Maximal subgroups

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

subgroupindex
#105909192
#105909002
#105893772
C3×#45182
C3×#45132
#105891382
#105891232
#693153
#692463