Finite Group Databasebeta

← #11800030

Subgroups — #11800030

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#10590912C211yesmaximal, characteristic
2#10590853C211yesmaximal, characteristic
3#10589383C211yesmaximal, characteristic, complemented
4C3×#4514C211yesmaximal, characteristic
5C3×#4513C211yesmaximal, characteristic, complemented
6#10589136C211yesmaximal, characteristic, complemented
7#10589131C211yesmaximal, characteristic, complemented
8#69314—31nomaximal
9#69117—31nomaximal
10C2×#3746C2211yescharacteristic
11C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
12#63857—21no—
13D3×#208—21no—
14C32×M32C2211yescharacteristic
15#63646C2211yescharacteristic
16C3×#819C2211yescharacteristic
17C3×#817C2211yescharacteristic
18C3×#812C2211yescharacteristic
19#63577—21no—
20#63567—21no—
21#5137—31no—
22#5125—31no—
23#4893—31no—
24#4867—31no—
25C3×#365—31no—
26C3×#349—31no—
27#4517—31no—
28#4517—31no—
29#4517—31no—
30#4517—61no—
31#4514D311yescharacteristic
32#4513—31no—
33#4513D311yescharacteristic, complemented
34#4496—31no—
35#4487—31no—
36C2×#634—21no—
37C2×C3×C4×D3D411yescharacteristic
38C2×C32×C8C2311yescharacteristic
39#3748—21no—
40#3746—21no—
41#3746—21no—
42C3×C4⋊Dic3—21no—
43C3×#208—21no—
44C2×C3×C3⋊C8D411yescharacteristic
45C3×ΓL(1,𝔽25)—21no—
46C3×ΓL(1,𝔽25)—21no—
47Dic3⋊Dic3—41no—
48(C2×D3)⋊Dic3—41no—
49#3711—41no—
50D3×C3⋊C8—41no—
51C32×C16—21no—
52C3×C3⋊C16—21no—
53#2239—91noSylow
54C2×C3×M16—31no—
55#924—61no—
56C2×#208—61no—
57D3×M16—61no—
58C2×Dic12—31no—
59C2×Dic12—31no—
60C2×Dic12—61no—
61C2×ΓL(1,𝔽25)C2×D311yescharacteristic
62#897—61no—
63C3×M32—21no—
64C3×M32—31no—
65C3×M32C2×D311yescharacteristic
66C3×M32C2×D311yescharacteristic
67C3×#108—31no—
68C3×#106—31no—
69#822—61no—
70#819—31no—
71#819—31no—
72#819—61no—
73#819—61no—
74#819C2×D311yescharacteristic
75#817C2×D311yescharacteristic
76#816—61no—
77#812C2×D311yescharacteristic
78#810—61no—
79C22×C3×D3SD1611yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C3⋊Dic3—41no—
82#634—41no—
83#634—41no—
84C2×C3×Dic3—41no—
85C2×C3×Dic3SD1611yescharacteristic
86C3×C4×D3—21no—
87C3×C4×D3—21no—
88C32×C8#4111yescharacteristic
89C32×C8#4111yescharacteristic
90C3⋊(C3⋊C8)—41no—
91C3×C3⋊C8—21no—
92C3×C3⋊C8—41no—
93#470—91no—
94#430—91no—
95#365—31no—
96#365—91no—
97#362—91no—
98#362—91no—
99#349—31no—
100C22×C3×C4—31no—
101C2×C4×D3D1211yescharacteristic
102C2×Dic6—61no—
103C2×Dic6—61no—
104C2×Dic6—121no—
105C3×M16—61no—
106C3×M16—61no—
107C3×M16—61no—
108C2×C3×C8—21no—
109C2×C3×C8—31no—
110C2×C3×C8C22×D311yescharacteristic
111C2×C3×C8C22×D311yescharacteristic
112C3×C4⋊C4—61no—
113#217—121no—
114(C2×D3)⋊C4—121no—
115C4⋊Dic3—21no—
116C4⋊Dic3—121no—
117Dic3⋊C4—121no—
118#208—21no—
119#208—61no—
120#208—61no—
121#208—121no—
122#208—121no—
123C2×C3⋊C8—121no—
124C2×C3⋊C8D1211yescharacteristic
125Dic12—62no—
126Dic12—61no—
127Dic12—61no—
128Dic12—61no—
129Dic12—61no—
130Dic12—121no—
131ΓL(1,𝔽25)—21no—
132ΓL(1,𝔽25)—21no—
133ΓL(1,𝔽25)—121no—
134D3×C8—121no—
135C3×C16—21no—
136C3×C16—21no—
137C3×C16—41no—
138C3×C16—61no—
139C3⋊C16—21no—
140C22×C32C2×SD1611yescharacteristic
141C2×C3×D3—21no—
142C2×C3×D3—41no—
143C32×C4#12311yescharacteristic
144C32×C4AGL(1,ℤ/8)11yescharacteristic
145C3⋊Dic3—81no—
146C3×Dic3—21no—
147C3×Dic3—81no—
148C2×Q16—91no—
149C2×M16—31no—
150C2×M16—181no—
151C22⋊Q8—181no—
152M32—31no—
153M32D3211yescharacteristic
154#108—31no—
155#108—91no—
156#108—181no—
157#106—31no—
158#103—181no—
159C23×C3—31no—
160C22×D3#20411yescharacteristic
161C2×C3×C4—21no—
162C2×C3×C4—31no—
163C2×C3×C4—61no—
164C2×C3×C4—61no—
165C2×C3×C4—121no—
166C2×C3×C4C2×D1211yescharacteristic
167C2×C3×C4D3×D411yescharacteristic
168C2×Dic3—41no—
169C2×Dic3—121no—
170C2×Dic3—121no—
171C2×Dic3—241no—
172C2×Dic3#20411yescharacteristic
173C4×D3—21no—
174C4×D3—21no—
175Dic6—122no—
176Dic6—121no—
177Dic6—121no—
178Dic6—121no—
179Dic6—121no—
180Dic6—241no—
181C3×C8—21no—
182C3×C8—21no—
183C3×C8—61no—
184C3×C8—121no—
185C3×C8#23511yescharacteristic
186C3×C8#23711yescharacteristic
187C3×C8#23711yescharacteristic
188C3×C8#23911yescharacteristic
189C3⋊C8—21no—
190C3⋊C8—41no—
191C3⋊C8—121no—
192C3⋊C8—121no—
193C3⋊C8—241no—
194C2×C32—21no—
195C2×C32#48111yescharacteristic
196C3×D3—41no—
197C2×Q8—181no—
198C22×C4—31no—
199Q16—181no—
200Q16—181no—
201M16—61no—
202M16—61no—
203M16—61no—
204M16—181no—
205M16—361no—
206C2×C8—31no—
207C2×C8—361no—
208C2×C8C2×D3211yescharacteristic
209C4⋊C4—61no—
210C4⋊C4—361no—
211C22⋊C4—361no—
212C16—21no—
213C16—61no—
214C22×C3—21no—
215C22×C3—61no—
216C22×C3—121no—
217C22×C3C2×#20411yescharacteristic
218C22×C3D3×SD1611yescharacteristic
219C2×D3—21no—
220C2×D3—41no—
221C3×C4—21no—
222C3×C4—21no—
223C3×C4—61no—
224C3×C4—241no—
225C3×C4#88611yescharacteristic
226C3×C4#89411yescharacteristic
227C3×C4#90811yescharacteristic
228C3×C4#91411yescharacteristic
229Dic3—21no—
230Dic3—81no—
231Dic3—242no—
232Dic3—241no—
233Dic3—241no—
234C32#223911yescharacteristic, complemented, Sylow
235C23—31no—
236Q8—361no—
237Q8—361no—
238C2×C4—31no—
239C2×C4—61no—
240C2×C4—61no—
241C2×C4—121no—
242C2×C4—361no—
243C2×C4D3×D1211yescharacteristic
244C8—61no—
245C8—121no—
246C8—361no—
247C8#379611yescharacteristic
248C8#380411yescharacteristic
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—41no—
253C2×C3—121no—
254C2×C3#473511yescharacteristic
255C2×C3#486311yescharacteristic
256D3—41no—
257C22—61no—
258C22—121no—
259C22D3×#20411yescharacteristic
260C4—61no—
261C4—241no—
262C4—721no—
263C4#6379411yescharacteristic
264C4#6389011yescharacteristic
265C3—21no—
266C3#6911711yescharacteristic, complemented
267C3#6931411yescharacteristic, complemented
268C2—21no—
269C2—121no—
270C2#1059067711yescharacteristic
subgroupG/H
centerC2#10590677
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32#481
prime radicalC22×C3×D3SD16
hypercenterM32D32
hypocenterC32#2239
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
3. #10589383C2semidirect
5. C3×#4513C2semidirect
6. #10589136C2semidirect
7. #10589131C2semidirect
33. #4513D3semidirect
234. C32#2239semidirect
266. C3#69117semidirect
267. C3#69314semidirect

Maximal subgroups

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

subgroupindex
#105909122
#105908532
#105893832
C3×#45142
C3×#45132
#105891362
#105891312
#693143
#691173