Finite Group Databasebeta

← #11800029

Subgroups — #11800029

Order 1152.

277 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 277 conjugacy classes of subgroups — too many to draw. Only its 64 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#10590914C211yesmaximal, characteristic
2#10590858C211yesmaximal, characteristic
3#10589380C211yesmaximal, characteristic
4C3×#4517C211yesmaximal, characteristic, complemented
5C3×#4513C211yesmaximal, characteristic, complemented
6#10589138C211yesmaximal, characteristic, complemented
7#10589129C211yesmaximal, characteristic, complemented
8#69314—31nomaximal
9#69267—31nomaximal
10C2×#3743C2211yescharacteristic
11C2×C3×Dic12C2211yescharacteristic
12#63871—21no—
13#63818—21no—
14C32×M32C2211yescharacteristic
15#63639C2211yescharacteristic
16C3×#819C2211yescharacteristic
17C3×#819C2211yescharacteristic
18C3×#817C2211yescharacteristic
19#63578—21no—
20#63565—21no—
21#5189—31no—
22#4893—31no—
23#4893—31no—
24#4867—31no—
25C3×#365—31no—
26C3×#362—31no—
27#4565—31no—
28#4517D311yescharacteristic, complemented
29#4514—31no—
30#4514—31no—
31#4514—61no—
32#4513D311yescharacteristic, complemented
33#4496—31no—
34#4494—31no—
35#4487—31no—
36C2×C4×C3⋊D3D411yescharacteristic
37C2×C3×Dic6—21no—
38C2×C32×C8C2311yescharacteristic
39C2×C3⋊(C3⋊C8)D411yescharacteristic
40#3743—21no—
41#3743—21no—
42C3×C4⋊Dic3—21no—
43C3×#208—21no—
44C3×#208—21no—
45C3×Dic12—21no—
46C3×Dic12—21no—
47Dic3⋊Dic3—41no—
48#3722—41no—
49#3712—41no—
50#3710—41no—
51C32×C16—21no—
52C3⋊(C3⋊C16)—21no—
53#2239—91noSylow
54C2×C3×Q16—31no—
55#946—61no—
56D3×M16—61no—
57D3×M16—61no—
58C2×Dic12C2×D311yescharacteristic
59C2×ΓL(1,𝔽25)—31no—
60C2×ΓL(1,𝔽25)—31no—
61C2×ΓL(1,𝔽25)—61no—
62#897—61no—
63C3×M32—21no—
64C3×M32C2×D311yescharacteristic
65C3×M32C2×D311yescharacteristic
66C3×#108—31no—
67C3×#108—31no—
68C3×#106—31no—
69#835—61no—
70#822—61no—
71#822—61no—
72#819C2×D311yescharacteristic
73#819C2×D311yescharacteristic
74#817C2×D311yescharacteristic
75#812—31no—
76#812—31no—
77#812—61no—
78#810—61no—
79C22×C3⋊D3SD1611yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C3⋊Dic3SD1611yescharacteristic
82C4×C3⋊D3—21no—
83C4×C3⋊D3—21no—
84C2×C3×Dic3—41no—
85C2×C3×Dic3—41no—
86C3×Dic6—41no—
87C3×Dic6—41no—
88C32×C8#4111yescharacteristic
89C32×C8#4111yescharacteristic
90C3⋊(C3⋊C8)—21no—
91C3×C3⋊C8—41no—
92C3×C3⋊C8—41no—
93#470—91no—
94#430—91no—
95#365—31no—
96#365—91no—
97#362—31no—
98#362—91no—
99#349—91no—
100C2×C3×Q8—61no—
101C2×C4×D3—31no—
102C2×C4×D3—31no—
103C2×C4×D3—61no—
104C2×Dic6—21no—
105C3×Q16—61no—
106C3×Q16—61no—
107C3×M16—61no—
108C3×M16—61no—
109C2×C3×C8—21no—
110C2×C3×C8C22×D311yescharacteristic
111C2×C3×C8C22×D311yescharacteristic
112C3×C4⋊C4—61no—
113(C2×D3)⋊C4—121no—
114(C2×D3)⋊C4—121no—
115C4⋊Dic3—21no—
116C4⋊Dic3—121no—
117Dic3⋊C4—121no—
118#208—21no—
119#208—21no—
120C2×C3⋊C8—31no—
121C2×C3⋊C8—31no—
122C2×C3⋊C8—61no—
123Dic12—21no—
124Dic12—21no—
125ΓL(1,𝔽25)—61no—
126ΓL(1,𝔽25)—61no—
127ΓL(1,𝔽25)—61no—
128ΓL(1,𝔽25)—61no—
129ΓL(1,𝔽25)—121no—
130ΓL(1,𝔽25)—121no—
131ΓL(1,𝔽25)—121no—
132ΓL(1,𝔽25)—121no—
133D3×C8—121no—
134D3×C8—121no—
135C3×C16—21no—
136C3×C16—21no—
137C3×C16—41no—
138C3⋊C16—61no—
139C3⋊C16—61no—
140C3⋊C16—121no—
141C22×C32C2×SD1611yescharacteristic
142C2×C3⋊D3—21no—
143C2×C3⋊D3—41no—
144C32×C4#12311yescharacteristic
145C32×C4AGL(1,ℤ/8)11yescharacteristic
146C3⋊Dic3—21no—
147C3×Dic3—81no—
148C3×Dic3—81no—
149C2×Q16—31no—
150C2×M16—91no—
151C2×M16—181no—
152C22⋊Q8—181no—
153M32—91no—
154M32D3211yescharacteristic
155#108—31no—
156#108—31no—
157#108—181no—
158#106—31no—
159#103—181no—
160C22×D3—31no—
161C22×D3—31no—
162C22×D3—61no—
163C3×Q8—121no—
164C3×Q8—121no—
165C2×C3×C4—21no—
166C2×C3×C4—121no—
167C2×C3×C4—121no—
168C2×C3×C4D3×D411yescharacteristic
169C2×C3×C4D3×D411yescharacteristic
170C2×Dic3—31no—
171C2×Dic3—31no—
172C2×Dic3—41no—
173C2×Dic3—41no—
174C2×Dic3—61no—
175C4×D3—61no—
176C4×D3—61no—
177C4×D3—61no—
178C4×D3—61no—
179C4×D3—121no—
180C4×D3—121no—
181Dic6—41no—
182Dic6—41no—
183C3×C8—21no—
184C3×C8—21no—
185C3×C8—121no—
186C3×C8—121no—
187C3×C8#23511yescharacteristic
188C3×C8#23511yescharacteristic
189C3×C8#23711yescharacteristic
190C3×C8#23911yescharacteristic
191C3⋊C8—41no—
192C3⋊C8—41no—
193C3⋊C8—61no—
194C3⋊C8—61no—
195C3⋊C8—121no—
196C2×C32—21no—
197C2×C32#48111yescharacteristic
198C3⋊D3—41no—
199C2×Q8—61no—
200C22×C4—91no—
201Q16—61no—
202Q16—61no—
203M16—61no—
204M16—61no—
205M16—181no—
206M16—181no—
207M16—361no—
208C2×C8—91no—
209C2×C8—361no—
210C2×C8C2×D3211yescharacteristic
211C4⋊C4—61no—
212C4⋊C4—361no—
213C22⋊C4—361no—
214C16—21no—
215C16—181no—
216C22×C3—21no—
217C22×C3D3×SD1611yescharacteristic
218C22×C3D3×SD1611yescharacteristic
219C2×D3—61no—
220C2×D3—61no—
221C2×D3—121no—
222C2×D3—121no—
223C2×D3—121no—
224C2×D3—241no—
225C3×C4—21no—
226C3×C4—21no—
227C3×C4—241no—
228C3×C4—241no—
229C3×C4#88311yescharacteristic
230C3×C4#89411yescharacteristic
231C3×C4#91111yescharacteristic
232C3×C4#91411yescharacteristic
233Dic3—61no—
234Dic3—61no—
235Dic3—81no—
236Dic3—81no—
237Dic3—121no—
238C32#223911yescharacteristic, complemented, Sylow
239C23—91no—
240Q8—121no—
241Q8—121no—
242C2×C4—91no—
243C2×C4—121no—
244C2×C4—121no—
245C2×C4—181no—
246C2×C4—181no—
247C2×C4#380211yescharacteristic
248C8—121no—
249C8—121no—
250C8—181no—
251C8#379911yescharacteristic
252C8#380411yescharacteristic
253C2×C3—21no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—41no—
257C2×C3#477711yescharacteristic
258C2×C3#486311yescharacteristic
259D3—121no—
260D3—121no—
261D3—241no—
262C22—181no—
263C22—361no—
264C22#6379611yescharacteristic
265C4—181no—
266C4—241no—
267C4—241no—
268C4#6379811yescharacteristic
269C4#6385411yescharacteristic
270C3—21no—
271C3#6926711yescharacteristic, complemented
272C3#6931411yescharacteristic, complemented
273C2—21no—
274C2—361no—
275C2#1059064911yescharacteristic
subgroupG/H
centerC2#10590649
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
4. C3×#4517C2semidirect
5. C3×#4513C2semidirect
6. #10589138C2semidirect
7. #10589129C2semidirect
28. #4517D3semidirect
32. #4513D3semidirect
238. C32#2239semidirect
271. C3#69267semidirect
272. C3#69314semidirect

Maximal subgroups

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

subgroupindex
#105909142
#105908582
#105893802
C3×#45172
C3×#45132
#105891382
#105891292
#693143
#692673