Finite Group Databasebeta

← #11799999

Subgroups — #11799999

Order 1152.

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

normal subgroups only

This group has 289 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, complemented
2#10590836C211yesmaximal, characteristic
3#10589379C211yesmaximal, characteristic, complemented
4C3×#4516C211yesmaximal, characteristic, complemented
5C3×#4514C211yesmaximal, characteristic, complemented
6#10589137C211yesmaximal, characteristic, complemented
7#10589127C211yesmaximal, characteristic, complemented
8#69257—31nomaximal
9#69116—31nomaximal
10C2×C3×D24C2211yescharacteristic
11C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
12#63908—21no—
13D3×#208—21no—
14C32×M32C2211yescharacteristic
15#63646C2211yescharacteristic
16#63644C2211yescharacteristic
17C3×#819C2211yescharacteristic
18C3×#812C2211yescharacteristic
19#63577—21no—
20#63563—21no—
21#5159—31no—
22#5135—31no—
23#5125—31no—
24#4893—31no—
25C3×#361—31no—
26C3×#349—31no—
27#4563—31no—
28#4516—31no—
29#4516D311yescharacteristic, complemented
30#4514D311yescharacteristic, complemented
31#4513—31no—
32#4513—31no—
33#4513—31no—
34#4513—61no—
35#4494—31no—
36C2×C3×D12—21no—
37C2×C3×C4×D3D411yescharacteristic
38C2×#625—41no—
39C2×C32×C8C2311yescharacteristic
40C4⋊(C3⋊Dic3)—21no—
41#3748—21no—
42C3×#208—21no—
43C2×C3×C3⋊C8D411yescharacteristic
44C3×D24—21no—
45C3×D24—21no—
46C3×ΓL(1,𝔽25)—21no—
47C3×ΓL(1,𝔽25)—21no—
48(C2×D3)⋊Dic3—41no—
49#3711—41no—
50D3×C3⋊C8—41no—
51C32×C16—21no—
52C3×C3⋊C16—21no—
53#2238—91noSylow
54C2×C3×D8—31no—
55C2×C3×M16—31no—
56#938—61no—
57#930—61no—
58C2×#208—61no—
59D3×M16—61no—
60C2×D24C2×D311yescharacteristic
61C2×ΓL(1,𝔽25)C2×D311yescharacteristic
62C3×M32—21no—
63C3×M32—31no—
64C3×M32C2×D311yescharacteristic
65C3×M32C2×D311yescharacteristic
66C3×#108—31no—
67#832—61no—
68#822—61no—
69#821—61no—
70#819—31no—
71#819—31no—
72#819—61no—
73#819—61no—
74#819C2×D311yescharacteristic
75#817—31no—
76#817—31no—
77#817—61no—
78#812C2×D311yescharacteristic
79C22×C3×D3—41no—
80C22×C3×D3SD1611yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3—41no—
83C2×C3×Dic3SD1611yescharacteristic
84C3×D12—41no—
85C3×D12—41no—
86C3×C4×D3—21no—
87C3×C4×D3—21no—
88#625—82no—
89C32×C8#4111yescharacteristic
90C32×C8#4111yescharacteristic
91C3⋊(C3⋊C8)—41no—
92C3×C3⋊C8—21no—
93C3×C3⋊C8—41no—
94#469—91no—
95#430—91no—
96#365—91no—
97#365—91no—
98#361—31no—
99#361—91no—
100#349—31no—
101C2×C3×D4—61no—
102C22×C3×C4—31no—
103C2×#67—121no—
104C2×#67—121no—
105C2×D12—21no—
106C2×C4×D3D1211yescharacteristic
107C3×D8—61no—
108C3×D8—61no—
109C3×M16—61no—
110C3×M16—61no—
111C3×M16—61no—
112C2×C3×C8—21no—
113C2×C3×C8—31no—
114C2×C3×C8C22×D311yescharacteristic
115C2×C3×C8C22×D311yescharacteristic
116#217—121no—
117(C2×D3)⋊C4—121no—
118C4⋊Dic3—61no—
119C4⋊Dic3—61no—
120C4⋊Dic3—121no—
121#208—21no—
122#208—61no—
123#208—61no—
124#208—121no—
125#208—121no—
126C2×C3⋊C8—121no—
127C2×C3⋊C8D1211yescharacteristic
128D24—21no—
129D24—21no—
130ΓL(1,𝔽25)—21no—
131ΓL(1,𝔽25)—21no—
132ΓL(1,𝔽25)—121no—
133D3×C8—121no—
134C3×C16—22no—
135C3×C16—21no—
136C3×C16—21no—
137C3×C16—61no—
138C3⋊C16—21no—
139C22×C32C2×SD1611yescharacteristic
140C2×C3×D3—21no—
141C2×C3×D3—41no—
142C2×C3×D3—81no—
143C2×C3×D3—81no—
144C2×C3×D3—81no—
145C32×C4#12311yescharacteristic
146C32×C4AGL(1,ℤ/8)11yescharacteristic
147C3⋊Dic3—81no—
148C3×Dic3—21no—
149C2×D8—31no—
150C2×M16—31no—
151C2×M16—181no—
152#121—181no—
153M32—31no—
154M32D3211yescharacteristic
155#108—31no—
156#108—91no—
157#108—181no—
158#106—91no—
159#102—181no—
160C23×C3—31no—
161C23×C3—121no—
162C22×D3—41no—
163C22×D3#20411yescharacteristic
164C3×D4—121no—
165C3×D4—121no—
166C2×C3×C4—21no—
167C2×C3×C4—31no—
168C2×C3×C4—61no—
169C2×C3×C4—61no—
170C2×C3×C4C2×D1211yescharacteristic
171C2×C3×C4D3×D411yescharacteristic
172#67—242no—
173#67—242no—
174C2×Dic3—121no—
175C2×Dic3—121no—
176C2×Dic3—241no—
177C2×Dic3#20411yescharacteristic
178D12—41no—
179D12—41no—
180C4×D3—21no—
181C4×D3—21no—
182C3×C8—21no—
183C3×C8—21no—
184C3×C8—61no—
185C3×C8—121no—
186C3×C8#23511yescharacteristic
187C3×C8#23711yescharacteristic
188C3×C8#23711yescharacteristic
189C3×C8#23711yescharacteristic
190C3⋊C8—21no—
191C3⋊C8—41no—
192C3⋊C8—121no—
193C3⋊C8—121no—
194C3⋊C8—241no—
195C2×C32—21no—
196C2×C32#48111yescharacteristic
197C3×D3—41no—
198C3×D3—161no—
199C2×D4—61no—
200C2×D4—361no—
201C22×C4—31no—
202D8—61no—
203D8—61no—
204M16—61no—
205M16—61no—
206M16—61no—
207M16—181no—
208M16—361no—
209C2×C8—31no—
210C2×C8—361no—
211C2×C8C2×D3211yescharacteristic
212C4⋊C4—181no—
213C22⋊C4—361no—
214C16—21no—
215C16—61no—
216C22×C3—21no—
217C22×C3—61no—
218C22×C3—121no—
219C22×C3—241no—
220C22×C3—241no—
221C22×C3—241no—
222C22×C3C2×#20411yescharacteristic
223C22×C3D3×SD1611yescharacteristic
224C2×D3—21no—
225C2×D3—41no—
226C2×D3—81no—
227C2×D3—81no—
228C2×D3—81no—
229C3×C4—21no—
230C3×C4—21no—
231C3×C4—61no—
232C3×C4#88311yescharacteristic
233C3×C4#88611yescharacteristic
234C3×C4#90811yescharacteristic
235C3×C4#91111yescharacteristic
236Dic3—21no—
237Dic3—241no—
238Dic3—241no—
239Dic3—481no—
240C32#223811yescharacteristic, complemented, Sylow
241C23—31no—
242C23—121no—
243D4—121no—
244D4—121no—
245D4—722no—
246C2×C4—31no—
247C2×C4—61no—
248C2×C4—61no—
249C2×C4—361no—
250C2×C4D3×D1211yescharacteristic
251C8—61no—
252C8—121no—
253C8—361no—
254C8#379511yescharacteristic
255C8#380511yescharacteristic
256C2×C3—21no—
257C2×C3—21no—
258C2×C3—21no—
259C2×C3—41no—
260C2×C3—121no—
261C2×C3—481no—
262C2×C3#473511yescharacteristic
263C2×C3#477711yescharacteristic
264D3—41no—
265D3—161no—
266C22—61no—
267C22—121no—
268C22—241no—
269C22—241no—
270C22—241no—
271C22D3×#20411yescharacteristic
272C4—61no—
273C4—721no—
274C4#6379511yescharacteristic
275C4#6389111yescharacteristic
276C3—21no—
277C3#6911611yescharacteristic, complemented
278C3#6925711yescharacteristic, complemented
279C2—21no—
280C2—121no—
281C2—481no—
282C2#1059067611yescharacteristic
subgroupG/H
centerC2#10590676
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32#481
prime radical#10590836C2
hypercenterM32D32
hypocenterC32#2238
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
1. #10590912C2semidirect
3. #10589379C2semidirect
4. C3×#4516C2semidirect
5. C3×#4514C2semidirect
6. #10589137C2semidirect
7. #10589127C2semidirect
29. #4516D3semidirect
30. #4514D3semidirect
240. C32#2238semidirect
277. C3#69116semidirect
278. C3#69257semidirect

Maximal subgroups

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

subgroupindex
#105909122
#105908362
#105893792
C3×#45162
C3×#45142
#105891372
#105891272
#692573
#691163