Finite Group Databasebeta

← #11797929

Subgroups — #11797929

Order 1152.

313 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 313 conjugacy classes of subgroups — too many to draw. Only its 78 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#10590918C211yesmaximal, characteristic
2#10590812C211yesmaximal, characteristic, complemented
3#10590642C211yesmaximal, characteristic
4#10589384C211yesmaximal, characteristic
5C3×#4517C211yesmaximal, characteristic, complemented
6C3×#4512C211yesmaximal, characteristic, complemented
7#10589137C211yesmaximal, characteristic, complemented
8#69264—31nomaximal
9#69090—31nomaximal
10#64113C2211yescharacteristic
11C2×C3×Dic12C2211yescharacteristic
12Dic3×Dic6—21no—
13#63817—21no—
14C32×M32C2211yescharacteristic
15#63644C2211yescharacteristic
16C3×#819C2211yescharacteristic
17C3×#815C2211yescharacteristic
18C3×#812C2211yescharacteristic
19#63570—21no—
20#63566—21no—
21#63551C412yescomplemented
22#63549C412yescomplemented
23#5184—31no—
24#5179—31no—
25#4909—31no—
26#4894—31no—
27#4717—31no—
28#4716—31no—
29C3×#362—31no—
30C3×#347—31no—
31#4518—31no—
32#4518—31no—
33#4518—61no—
34#4517D311yescharacteristic, complemented
35#4513—31no—
36#4512D311yescharacteristic, complemented
37#4494—31no—
38#3828—21no—
39C2×C3×Dic6—21no—
40C2×C32×C8C2311yescharacteristic
41C4⋊(C3⋊Dic3)—21no—
42#3746C2×C411yescharacteristic
43#3745C2×C411yescharacteristic
44#3744—21no—
45C3×C4×Dic3D411yescharacteristic
46C3×#208—21no—
47C2×C3×C3⋊C8D411yescharacteristic
48C3×Dic12—21no—
49C3×Dic12C2×C412yes—
50Dic3⋊Dic3—41no—
51Dic32—41no—
52#3712—41no—
53#3710—41no—
54C32×C16—21no—
55C3×C3⋊C16C2×C412yes—
56#2180—91noSylow
57C2×C3×Q16—31no—
58Q8×Dic3—61no—
59#907—61no—
60C2×Dic12C2×D311yescharacteristic
61#904—31no—
62#904—31no—
63#904—61no—
64#901—61no—
65C4×Dic6—61no—
66C3×M32—21no—
67C3×M32—31no—
68C3×M32C2×D311yescharacteristic
69C3×M32C2×D311yescharacteristic
70C3×#108—31no—
71C3×#97—31no—
72#835—61no—
73#829—32no—
74#828—32no—
75#825—61no—
76#819C2×D311yescharacteristic
77#817—31no—
78#817—31no—
79#817—61no—
80#816—61no—
81#815C2×D311yescharacteristic
82#812C2×D311yescharacteristic
83#805—61no—
84Dic24—32no—
85#800—32no—
86C2×C32×C4C2×D411yescharacteristic
87#638—41no—
88C2×C3⋊Dic3—41no—
89C4⋊(C3⋊D3)—21no—
90C4×C3⋊D3—41no—
91#634—21no—
92C2×C3×Dic3—21no—
93C2×C3×Dic3—41no—
94C3×Dic6—22no—
95C3×Dic6—41no—
96C32×C8C22×C411yescharacteristic
97C32×C8#4111yescharacteristic
98C3×C3⋊C8—21no—
99C3×C3⋊C8—41no—
100#510—91no—
101#444—91no—
102#441—91no—
103#365—91no—
104#362—31no—
105#360—91no—
106#347—31no—
107C2×C3×Q8—61no—
108#235—61no—
109#235—61no—
110#235—121no—
111C2×Dic6—21no—
112C3×Q16—32no—
113C3×Q16—61no—
114C3×M16—61no—
115C2×C3×C8—21no—
116C2×C3×C8—31no—
117C2×C3×C8C22×D311yescharacteristic
118C2×C3×C8C22×D311yescharacteristic
119C3×C42—31no—
120C4⋊Dic3—61no—
121C4⋊Dic3—61no—
122C4⋊Dic3—121no—
123C4⋊Dic3—121no—
124Dic3⋊C4—121no—
125C4×Dic3—121no—
126C4×Dic3—121no—
127C4×Dic3D1211yescharacteristic
128#208—21no—
129C2×C3⋊C8D1211yescharacteristic
130Dic12—21no—
131Dic12—31no—
132Dic12—31no—
133Dic12—61no—
134Dic12C4×D312yes—
135D24—31no—
136D24—31no—
137D24—61no—
138#204—61no—
139#204—61no—
140#204—121no—
141ΓL(1,𝔽25)—121no—
142ΓL(1,𝔽25)—121no—
143D3×C8—121no—
144D3×C8—121no—
145C3×C16—21no—
146C3×C16—21no—
147C3×C16—32no—
148C3×C16—41no—
149C3⋊C16C4×D312yes—
150C22×C32AGL(1,ℤ/8)11yescharacteristic
151C2×C3⋊D3—41no—
152C32×C4C4×D411yescharacteristic
153C32×C4AGL(1,ℤ/8)11yescharacteristic
154C3⋊Dic3—41no—
155C3⋊Dic3—81no—
156C3×Dic3—41no—
157C3×Dic3—42no—
158#135—91no—
159C2×Q16—31no—
160#131—181no—
161C4×Q8—181no—
162Q32—92no—
163SD32—92no—
164M32—31no—
165M32D3211yescharacteristic
166#108—31no—
167#106—91no—
168#104—181no—
169#103—181no—
170#97—31no—
171C3×Q8—62no—
172C3×Q8—121no—
173C2×C3×C4—21no—
174C2×C3×C4—61no—
175C2×C3×C4—121no—
176C2×C3×C4C2×D1211yescharacteristic
177C2×C3×C4D3×D411yescharacteristic
178#67—121no—
179#67—121no—
180#67—241no—
181C2×Dic3—21no—
182C2×Dic3—41no—
183C2×Dic3—121no—
184C2×Dic3—121no—
185C2×Dic3—241no—
186D12—61no—
187D12—61no—
188D12—121no—
189C4×D3—121no—
190C4×D3—121no—
191C4×D3—241no—
192Dic6—22no—
193Dic6—41no—
194Dic6—61no—
195Dic6—61no—
196Dic6—121no—
197C3×C8—21no—
198C3×C8—21no—
199C3×C8—61no—
200C3×C8—121no—
201C3×C8C2×C4×D311yescharacteristic
202C3×C8C2×C4×D311yescharacteristic
203C3×C8#23511yescharacteristic
204C3×C8#23711yescharacteristic
205C3⋊C8—21no—
206C3⋊C8—41no—
207C2×C32—21no—
208C2×C32#44211yescharacteristic
209C3⋊D3—81no—
210#41—181no—
211C2×Q8—61no—
212Q16—32no—
213Q16—61no—
214Q16—91no—
215SD16—181no—
216D8—91no—
217M16—61no—
218M16—361no—
219C2×C8—31no—
220C2×C8—361no—
221C2×C8C2×D3211yescharacteristic
222C4⋊C4—181no—
223C4⋊C4—361no—
224C42—31no—
225C42—361no—
226C16—21no—
227C16—32no—
228C22×C3—21no—
229C22×C3#90811yescharacteristic
230C22×C3#91411yescharacteristic
231C2×D3—121no—
232C2×D3—121no—
233C2×D3—241no—
234C3×C4—21no—
235C3×C4—21no—
236C3×C4—121no—
237C3×C4—122no—
238C3×C4C4×D1211yescharacteristic
239C3×C4#67⋊C411yescharacteristic
240C3×C4#90811yescharacteristic
241C3×C4#91111yescharacteristic
242Dic3—41no—
243Dic3—42no—
244Dic3—121no—
245Dic3—121no—
246Dic3—241no—
247Dic3—241no—
248Dic3—241no—
249Dic3—481no—
250C32#218011yescharacteristic, complemented, Sylow
251Q8—62no—
252Q8—121no—
253Q8—181no—
254D4—181no—
255D4—361no—
256C2×C4—61no—
257C2×C4—121no—
258C2×C4—361no—
259C2×C4—361no—
260C2×C4D3×D1211yescharacteristic
261C8—61no—
262C8—121no—
263C8C4×D3211yescharacteristic
264C8#380411yescharacteristic
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—41no—
269C2×C3#471111yescharacteristic
270C2×C3#478511yescharacteristic
271D3—241no—
272D3—241no—
273D3—481no—
274C22—361no—
275C22#6379411yescharacteristic
276C4—121no—
277C4—122no—
278C4—361no—
279C4—721no—
280C4#6379511yescharacteristic
281C4#6388011yescharacteristic
282C3—21no—
283C3#6909011yescharacteristic, complemented
284C3#6926411yescharacteristic, complemented
285C2—21no—
286C2—721no—
287C2#1059074611yescharacteristic
subgroupG/H
centerC2#10590746
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32#442
prime radical#64113C22
cosocleC2×C32×C8C23
hypercenterM32D32
hypocenterC32#2180
LCSG ▷ 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. #10590812C2semidirect
5. C3×#4517C2semidirect
6. C3×#4512C2semidirect
7. #10589137C2semidirect
21. #63551C4semidirect
22. #63549C4semidirect
34. #4517D3semidirect
36. #4512D3semidirect
250. C32#2180semidirect
283. C3#69090semidirect
284. C3#69264semidirect

Maximal subgroups

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

subgroupindex
#105909182
#105908122
#105906422
#105893842
C3×#45172
C3×#45122
#105891372
#692643
#690903