Finite Group Databasebeta

← #11797941

Subgroups — #11797941

Order 1152.

248 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 43 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#10593336C211yesmaximal, characteristic
2#10590922C211yesmaximal, characteristic
3#10590791C211yesmaximal, characteristic, complemented
4#10590179C211yesmaximal, characteristic, complemented
5#10590067C211yesmaximal, characteristic, complemented
6#10590066C211yesmaximal, characteristic, complemented
7#10590064C211yesmaximal, characteristic
8C3×#901—21no—
9#63843—21no—
10C2×#3718C2211yescharacteristic
11#63822C2211yescharacteristic
12#63773C2211yescharacteristic
13#63773C2211yescharacteristic
14#63736C412yescomplemented
15#63735C412yescomplemented
16#63642C2211yescharacteristic
17C3×#816—21no—
18#63578C2211yescharacteristic
19#63574C2211yescharacteristic
20#63568—21no—
21#5145—61no—
22#4789—61no—
23C3×#235—21no—
24C2×C3×Dic6—21no—
25C2×C32×C8D411yescharacteristic
26C4×C3⋊Dic3D411yescharacteristic
27C2×C3⋊(C3⋊C8)C2311yescharacteristic
28C3×C4⋊Dic3—21no—
29C3×#208—21no—
30C3×ΓL(1,𝔽25)—41no—
31C3×D3×C8—41no—
32Dic3⋊Dic3—41no—
33Dic32—41no—
34#3718—21no—
35#3718C2×C411yescharacteristic
36#3718C2×C412yes—
37#3715—21no—
38#3713C2×C411yescharacteristic
39#3708—21no—
40#3708C2×C412yes—
41#2180—91nomaximal, Sylow
42C3×#131—61no—
43#950—61no—
44Q8×Dic3—61no—
45C2×#216—61no—
46#901—21no—
47#887—61no—
48C3×#103—61no—
49#837—61no—
50#825—61no—
51#822—61no—
52#816—21no—
53#815—61no—
54#815—61no—
55#808—61no—
56C2×C32×C4C2×D411yescharacteristic
57C2×C3⋊Dic3—21no—
58C3×#67—41no—
59C2×C3×Dic3—41no—
60C2×C3×Dic3—41no—
61C3×D12—21no—
62C3×C4×D3—41no—
63C3×Dic6—21no—
64C3×Dic6—22no—
65C3×Dic6—41no—
66C32×C8—21no—
67C3⋊(C3⋊C8)C22×C411yescharacteristic
68C3⋊(C3⋊C8)#4111yescharacteristic
69C3×C3⋊C8—41no—
70#510—91no—
71#444—91no—
72#441—91no—
73#365—91no—
74#362—91no—
75#360—91no—
76#347—91no—
77C3×#41—61no—
78C2×C3×Q8—61no—
79#235—21no—
80C2×Dic6—21no—
81C3×M16—61no—
82C3×M16—121no—
83C2×C3×C8—21no—
84C2×C3×C8—21no—
85C2×C3×C8—121no—
86C3×C4⋊C4—61no—
87#216—62no—
88#216—61no—
89#216—62no—
90#215—61no—
91#214—61no—
92#213—61no—
93C4⋊Dic3—21no—
94C4⋊Dic3—121no—
95Dic3⋊C4—121no—
96C4×Dic3—61no—
97C4×Dic3—61no—
98C4×Dic3—121no—
99C4×Dic3—121no—
100#208—21no—
101C2×C3⋊C8—61no—
102C2×C3⋊C8—61no—
103ΓL(1,𝔽25)—41no—
104D3×C8—41no—
105C22×C32AGL(1,ℤ/8)11yescharacteristic
106C2×C3×D3—41no—
107C32×C4C4×D411yescharacteristic
108C32×C4AGL(1,ℤ/8)11yescharacteristic
109C3⋊Dic3—41no—
110C3×Dic3—42no—
111C3×Dic3—41no—
112C3×Dic3—81no—
113#135—91no—
114C2×Q16—91no—
115#131—61no—
116C4×Q8—181no—
117Q32—92no—
118SD32—92no—
119M32—91no—
120M32—91no—
121#108—91no—
122#106—91no—
123#104—181no—
124#103—61no—
125#97—91no—
126C3×Q8—61no—
127C3×Q8—62no—
128C3×Q8—121no—
129C3×D4—61no—
130C3×D4—121no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—121no—
134C2×C3×C4—121no—
135C2×C3×C4—121no—
136#67—41no—
137C2×Dic3—41no—
138C2×Dic3—41no—
139C2×Dic3—61no—
140C2×Dic3—61no—
141C2×Dic3—121no—
142D12—21no—
143C4×D3—41no—
144Dic6—21no—
145Dic6—22no—
146Dic6—41no—
147C3×C8—21no—
148C3×C8—21no—
149C3×C8—41no—
150C3×C8—121no—
151C3⋊C8—41no—
152C3⋊C8—61no—
153C3⋊C8—61no—
154C3⋊C8—61no—
155C3⋊C8—61no—
156C2×C32—21no—
157C2×C32#44211yescharacteristic
158C3×D3—81no—
159#41—61no—
160C2×Q8—61no—
161Q16—92no—
162Q16—91no—
163Q16—181no—
164SD16—181no—
165D8—91no—
166M16—61no—
167M16—121no—
168C2×C8—91no—
169C2×C8—121no—
170C2×C8GO+(4,𝔽2)11yescharacteristic
171C4⋊C4—61no—
172C4⋊C4—361no—
173C42—91no—
174C42—361no—
175C16—92no—
176C16—181no—
177C22×C3—21no—
178C22×C3—21no—
179C22×C3—121no—
180C2×D3—41no—
181C3×C4—21no—
182C3×C4—21no—
183C3×C4—21no—
184C3×C4—21no—
185C3×C4—121no—
186C3×C4—122no—
187C3×C4—241no—
188Dic3—42no—
189Dic3—41no—
190Dic3—81no—
191Dic3—121no—
192Dic3—121no—
193Dic3—241no—
194C32#218011yescharacteristic, complemented, Sylow
195Q8—61no—
196Q8—62no—
197Q8—121no—
198D4—61no—
199D4—121no—
200C2×C4—121no—
201C2×C4—121no—
202C2×C4—121no—
203C2×C4—181no—
204C2×C4C2×GO+(4,𝔽2)11yescharacteristic
205C8—21no—
206C8—91no—
207C8—91no—
208C8—121no—
209C2×C3—21no—
210C2×C3—21no—
211C2×C3—21no—
212C2×C3—21no—
213C2×C3—41no—
214C2×C3—241no—
215D3—81no—
216C22—121no—
217C22#6422411yescharacteristic
218C4—121no—
219C4—122no—
220C4—241no—
221C4—361no—
222C4C4×GO+(4,𝔽2)11yescharacteristic
223C4#6423611yescharacteristic
224C3—21no—
225C3—21no—
226C2—21no—
227C2—241no—
228C2#1059341911yescharacteristic
subgroupG/H
centerC2#10593419
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#442
prime radical#63822C22
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2180
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
3. #10590791C2semidirect
4. #10590179C2semidirect
5. #10590067C2semidirect
6. #10590066C2semidirect
14. #63736C4semidirect
15. #63735C4semidirect
194. C32#2180semidirect

Maximal subgroups

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

subgroupindex
#105933362
#105909222
#105907912
#105901792
#105900672
#105900662
#105900642
#21809