Finite Group Databasebeta

← #11797692

Subgroups — #11797692

Order 1152.

284 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C2×#63735C211yesmaximal, characteristic
2#10590790C211yesmaximal, characteristic, complemented
3#10590740C211yesmaximal, characteristic
4#10590174C211yesmaximal, characteristic, complemented
5#10590069C211yesmaximal, characteristic, complemented
6#10590062C211yesmaximal, characteristic, complemented
7#10590061C211yesmaximal, characteristic
8#63898—21no—
9#63843—21no—
10C2×#3718C2211yescharacteristic
11C2×#3713C2211yescharacteristic
12C2×#3708C2211yescharacteristic
13C2×#3708C2211yescharacteristic
14#63735C414yescomplemented
15C8×C3⋊Dic3C2211yescharacteristic
16C3×#821—21no—
17C3×#816—21no—
18#63576C2211yescharacteristic
19#63576C2211yescharacteristic
20#4790—61no—
21#4756—61no—
22C2×C3×D12—21no—
23C2×C3×Dic6—21no—
24C2×D3×Dic3—41no—
25C2×C32×C8D411yescharacteristic
26C4×C3⋊Dic3D411yescharacteristic
27C2×C3⋊(C3⋊C8)C2311yescharacteristic
28C3×C4⋊Dic3—21no—
29C3×C4⋊Dic3—21no—
30Dic3⋊Dic3—41no—
31(C2×D3)⋊Dic3—41no—
32Dic32—41no—
33#3718—21no—
34#3718C2×C412yescomplemented
35#3713—21no—
36#3713C2×C412yes—
37#3708—21no—
38#3708C2×C412yescomplemented
39C4×SD32—91nomaximal, Sylow
40Q8×Dic3—61no—
41C2×#216—61no—
42D4×Dic3—61no—
43C2×#213—61no—
44#893—61no—
45#887—61no—
46C3×#103—61no—
47C3×#102—61no—
48#821—21no—
49#816—21no—
50C8×Dic3—61no—
51C8×Dic3—61no—
52#807—61no—
53#807—61no—
54C22×C3×D3—41no—
55C2×C32×C4C2×D411yescharacteristic
56C2×C3⋊Dic3D811yescharacteristic
57C2×C3⋊Dic3D811yescharacteristic
58C2×C3×Dic3—41no—
59C2×C3×Dic3—41no—
60C2×C3×Dic3—41no—
61C3×D12—22no—
62C3×D12—41no—
63C3×Dic6—22no—
64C3×Dic6—41no—
65D3×Dic3—82no—
66C32×C8—21no—
67C3⋊(C3⋊C8)C22×C411yescharacteristic
68C3⋊(C3⋊C8)#4111yescharacteristic
69C2×SD32—91no—
70C4×Q16—91no—
71C4×D8—91no—
72#367—91no—
73#358—91no—
74#357—91no—
75C4×C16—91no—
76C2×C3×Q8—61no—
77C2×C3×D4—61no—
78C22×Dic3—121no—
79C2×D12—21no—
80C2×C4×D3—121no—
81C2×Dic6—21no—
82C2×C3×C8—21no—
83C2×C3×C8—21no—
84C3×C4⋊C4—61no—
85C3×C4⋊C4—61no—
86#217—121no—
87#216—62no—
88#216—62no—
89#213—62no—
90#213—62no—
91(C2×D3)⋊C4—121no—
92C4⋊Dic3—21no—
93C4⋊Dic3—21no—
94C4⋊Dic3—121no—
95Dic3⋊C4—121no—
96C4×Dic3—61no—
97C4×Dic3—61no—
98C4×Dic3—121no—
99C4×Dic3—121no—
100C2×C3⋊C8—61no—
101C2×C3⋊C8—61no—
102C22×C32C2×D811yescharacteristic
103C2×C3×D3—42no—
104C2×C3×D3—81no—
105C2×C3×D3—81no—
106C32×C4C4×D411yescharacteristic
107C32×C4#13511yescharacteristic
108C3⋊Dic3—21no—
109C3⋊Dic3SD3212yescomplemented
110C3×Dic3—42no—
111C3×Dic3—81no—
112C3×Dic3—81no—
113C2×Q16—91no—
114C2×D8—91no—
115C4×Q8—181no—
116C4×D4—181no—
117SD32—94no—
118C2×C16—91no—
119C2×C16—91no—
120#107—91no—
121#107—91no—
122#103—61no—
123#102—61no—
124C4×C8—91no—
125C23×C3—121no—
126C22×D3—41no—
127C3×Q8—62no—
128C3×Q8—121no—
129C3×D4—62no—
130C3×D4—121no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—121no—
134C2×C3×C4—121no—
135C2×C3×C4—121no—
136C2×Dic3—41no—
137C2×Dic3—41no—
138C2×Dic3—41no—
139C2×Dic3—61no—
140C2×Dic3—61no—
141C2×Dic3—61no—
142C2×Dic3—61no—
143C2×Dic3—242no—
144D12—22no—
145D12—41no—
146C4×D3—242no—
147Dic6—22no—
148Dic6—41no—
149C3×C8—41no—
150C3×C8—41no—
151C3⋊C8—61no—
152C3⋊C8—61no—
153C3⋊C8—61no—
154C3⋊C8—61no—
155C2×C32C4×D811yescharacteristic
156C2×C32C2×SD3211yescharacteristic
157C2×C32#50811yescharacteristic
158C3×D3—82no—
159C2×Q8—61no—
160C2×D4—61no—
161C22×C4—361no—
162Q16—92no—
163Q16—181no—
164D8—92no—
165D8—181no—
166C2×C8—91no—
167C2×C8GO+(4,𝔽2)11yescharacteristic
168C4⋊C4—61no—
169C4⋊C4—61no—
170C4⋊C4—361no—
171C22⋊C4—361no—
172C42—91no—
173C42—361no—
174C16—92no—
175C16—181no—
176C22×C3—21no—
177C22×C3—21no—
178C22×C3—122no—
179C22×C3—241no—
180C22×C3—241no—
181C2×D3—42no—
182C2×D3—81no—
183C2×D3—81no—
184C3×C4—21no—
185C3×C4—21no—
186C3×C4—21no—
187C3×C4—21no—
188C3×C4—122no—
189C3×C4—241no—
190C3×C4—241no—
191Dic3—42no—
192Dic3—62no—
193Dic3—62no—
194Dic3—81no—
195Dic3—81no—
196Dic3—121no—
197Dic3—121no—
198C32C4×SD3211yescharacteristic, complemented, Sylow
199C23—121no—
200Q8—62no—
201Q8—121no—
202D4—62no—
203D4—121no—
204C2×C4—91no—
205C2×C4—91no—
206C2×C4—121no—
207C2×C4—121no—
208C2×C4—121no—
209C2×C4—722no—
210C2×C4C2×GO+(4,𝔽2)11yescharacteristic
211C8—21no—
212C8—91no—
213C8—91no—
214C2×C3—21no—
215C2×C3—21no—
216C2×C3—21no—
217C2×C3—21no—
218C2×C3—21no—
219C2×C3—21no—
220C2×C3—242no—
221D3—82no—
222C22—122no—
223C22—241no—
224C22—241no—
225C22#6422511yescharacteristic
226C4—92no—
227C4—122no—
228C4—181no—
229C4—241no—
230C4—241no—
231C4C4×GO+(4,𝔽2)11yescharacteristic
232C4#6423711yescharacteristic
233C3—21no—
234C3—21no—
235C2—242no—
236C2#1059327511yescharacteristic
237C2#1059327811yescharacteristic
238C2#1059342011yescharacteristic
subgroupG/H
centerC22#64225
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32C2×D8
prime radicalC2×#3713C22
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32C4×SD32
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10590790C2semidirect
4. #10590174C2semidirect
5. #10590069C2semidirect
6. #10590062C2semidirect
14. #63735C4semidirect
34. #3718C2×C4semidirect
38. #3708C2×C4semidirect
109. C3⋊Dic3SD32semidirect
198. C32C4×SD32semidirect

Maximal subgroups

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

subgroupindex
C2×#637352
#105907902
#105907402
#105901742
#105900692
#105900622
#105900612
C4×SD329