Finite Group Databasebeta

← #11799721

Subgroups — #11799721

Order 1152.

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

normal subgroups only

This group has 273 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
1#10590915C211yesmaximal, characteristic
2#10590889C211yesmaximal, characteristic, complemented
3#10589379C211yesmaximal, characteristic, complemented
4C3×#4518C211yesmaximal, characteristic
5C3×#4511C211yesmaximal, characteristic, complemented
6#10589136C211yesmaximal, characteristic, complemented
7#10589124C211yesmaximal, characteristic
8#69307—31nomaximal
9#69246—31nomaximal
10C3×#904C2211yescharacteristic
11#63918—21no—
12#63814—21no—
13C32×M32C2211yescharacteristic
14#63646C2211yescharacteristic
15#63644C2211yescharacteristic
16C3×#817C2211yescharacteristic
17C3×C8×Dic3C2211yescharacteristic
18C3×#812C2211yescharacteristic
19#63573—21no—
20#63569—21no—
21#5196—31no—
22#4855—31no—
23#4700—31no—
24#4680—31no—
25C3×#364—31no—
26C3×#360—31no—
27#4566—31no—
28#4518—31no—
29#4518D311yescharacteristic
30#4513—31no—
31#4513—31no—
32#4513—31no—
33#4513—61no—
34#4511D311yescharacteristic, complemented
35#4487—31no—
36C3×#235—21no—
37C2×#627—41no—
38C2×C32×C8C2311yescharacteristic
39C4⋊(C3⋊Dic3)—21no—
40#3748—21no—
41C3×C4⋊Dic3—21no—
42C3×C4×Dic3D411yescharacteristic
43C2×C3×C3⋊C8D411yescharacteristic
44C3×Dic12Q811yescharacteristic, complemented
45C3×D24Q811yescharacteristic, complemented
46C3×#204—21no—
47Dic3⋊Dic3—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#904C2×D311yescharacteristic
56#901—61no—
57#888—61no—
58#869—61no—
59C3×M32—21no—
60C3×M32—31no—
61C3×M32C2×D311yescharacteristic
62C3×M32C2×D311yescharacteristic
63C3×#106—31no—
64C3×C4×C8—31no—
65#837—61no—
66#819—31no—
67#819—31no—
68#819—61no—
69#817—31no—
70#817—31no—
71#817—61no—
72#817—61no—
73#817C2×D311yescharacteristic
74C8×Dic3C2×D311yescharacteristic
75#812C2×D311yescharacteristic
76#808—61no—
77#805—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—
86#627—82no—
87C32×C8C2×Q811yescharacteristic
88C32×C8#4111yescharacteristic
89C3⋊(C3⋊C8)—41no—
90C3×C3⋊C8SD1611yescharacteristic
91C3×C3⋊C8SD1611yescharacteristic
92#498—91no—
93#443—91no—
94#365—91no—
95#365—91no—
96#364—31no—
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—
106C2×C3×C8—21no—
107C2×C3×C8—31no—
108C2×C3×C8C22×D311yescharacteristic
109C2×C3×C8C22×D311yescharacteristic
110C3×C4⋊C4—61no—
111C3×C42—31no—
112C4⋊Dic3—21no—
113C4⋊Dic3—61no—
114C4⋊Dic3—61no—
115C4⋊Dic3—121no—
116C4⋊Dic3—121no—
117Dic3⋊C4—121no—
118C4×Dic3D1211yescharacteristic
119#208—61no—
120#208—61no—
121#208—121no—
122#208—121no—
123C2×C3⋊C8—121no—
124C2×C3⋊C8D1211yescharacteristic
125Dic12Dic611yescharacteristic, complemented
126D24Dic611yescharacteristic, complemented
127#204—21no—
128ΓL(1,𝔽25)—121no—
129D3×C8—121no—
130C3×C16—22no—
131C3×C16—21no—
132C3×C16—21no—
133C3×C16—61no—
134C3⋊C16—21no—
135C22×C32AGL(1,ℤ/8)11yescharacteristic
136C2×C3×D3—41no—
137C32×C4C22⋊Q811yescharacteristic
138C32×C4C2×SD1611yescharacteristic
139C3⋊Dic3—81no—
140C3×Dic3—22no—
141C3×Dic3—41no—
142C3×Dic3—81no—
143#135—31no—
144#131—181no—
145C4⋊Q8—181no—
146M32—31no—
147M32D3211yescharacteristic
148#108—91no—
149#106—31no—
150#106—91no—
151#106—181no—
152#104—181no—
153C4×C8—31no—
154C3×Q8—61no—
155C3×D4—61no—
156C3×D4—121no—
157C2×C3×C4—21no—
158C2×C3×C4—61no—
159C2×C3×C4—121no—
160C2×C3×C4—121no—
161C2×C3×C4C2×D1211yescharacteristic
162C2×C3×C4D3×D411yescharacteristic
163#67—41no—
164C2×Dic3—21no—
165C2×Dic3—41no—
166C2×Dic3—121no—
167C2×Dic3—121no—
168C2×Dic3—241no—
169D12—21no—
170C4×D3—41no—
171Dic6—21no—
172Dic6—242no—
173Dic6—242no—
174C3×C8—21no—
175C3×C8—21no—
176C3×C8—31no—
177C3×C8—31no—
178C3×C8C2×Dic611yescharacteristic
179C3×C8#23711yescharacteristic
180C3×C8#23711yescharacteristic
181C3×C8D3×Q811yescharacteristic
182C3⋊C8—121no—
183C3⋊C8—121no—
184C3⋊C8—241no—
185C3⋊C8#20411yescharacteristic
186C3⋊C8#20411yescharacteristic
187C2×C32—21no—
188C2×C32#47611yescharacteristic
189C3×D3—81no—
190#41—61no—
191C2×Q8—361no—
192Q16—31no—
193SD16—61no—
194D8—31no—
195M16—181no—
196M16—361no—
197C2×C8—31no—
198C2×C8—361no—
199C2×C8C2×D3211yescharacteristic
200C4⋊C4—61no—
201C4⋊C4—181no—
202C4⋊C4—361no—
203C42—31no—
204C16—21no—
205C16—61no—
206C22×C3—21no—
207C22×C3—121no—
208C22×C3#90811yescharacteristic
209C22×C3#91111yescharacteristic
210C2×D3—41no—
211C3×C4—21no—
212C3×C4—21no—
213C3×C4—62no—
214C3×C4—121no—
215C3×C4—241no—
216C3×C4#87811yescharacteristic
217C3×C4#89711yescharacteristic
218C3×C4C2×#20411yescharacteristic
219C3×C4D3×SD1611yescharacteristic
220Dic3—22no—
221Dic3—41no—
222Dic3—81no—
223Dic3—241no—
224Dic3—241no—
225Dic3—481no—
226C32#223011yescharacteristic, complemented, Sylow
227Q8—61no—
228Q8—722no—
229D4—61no—
230D4—121no—
231C2×C4—61no—
232C2×C4—121no—
233C2×C4—121no—
234C2×C4—361no—
235C2×C4D3×D1211yescharacteristic
236C8—31no—
237C8—31no—
238C8—361no—
239C8D3×Dic611yescharacteristic
240C8#380511yescharacteristic
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—41no—
245C2×C3—241no—
246C2×C3#476111yescharacteristic
247C2×C3#484211yescharacteristic
248D3—81no—
249C22—121no—
250C22#6379511yescharacteristic
251C4—62no—
252C4—121no—
253C4—241no—
254C4—721no—
255C4D3×#20411yescharacteristic
256C4#6389311yescharacteristic
257C3—21no—
258C3#6924611yescharacteristic, complemented
259C3#6930711yescharacteristic, complemented
260C2—21no—
261C2—241no—
262C2#1059075711yescharacteristic
subgroupG/H
centerC2#10590757
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. #10590889C2semidirect
3. #10589379C2semidirect
5. C3×#4511C2semidirect
6. #10589136C2semidirect
34. #4511D3semidirect
44. C3×Dic12Q8semidirect
45. C3×D24Q8semidirect
125. Dic12Dic6semidirect
126. D24Dic6semidirect
226. C32#2230semidirect
258. C3#69246semidirect
259. C3#69307semidirect

Maximal subgroups

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

subgroupindex
#105909152
#105908892
#105893792
C3×#45182
C3×#45112
#105891362
#105891242
#693073
#692463