Finite Group Databasebeta

← #11799759

Subgroups — #11799759

Order 1152.

216 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 37 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#10590389C211yesmaximal, characteristic
2#10590314C211yesmaximal, characteristic, complemented
3#10590150C211yesmaximal, characteristic, complemented
4#10590067C212yesmaximal, complemented
5#10590064C212yesmaximal
6C3×#870—21no—
7#63822C2211yescharacteristic
8#63815—21no—
9#63773C2212yes—
10C4×C3⋊(C3⋊C8)C2211yescharacteristic
11C3×#805—21no—
12#63578C2211yescharacteristic
13#63576—21no—
14#63574C2212yes—
15#5065—61no—
16#4824—61no—
17C3×#235—21no—
18C32×C42D411yescharacteristic
19C2×C3⋊(C3⋊C8)D411yescharacteristic
20C2×C3⋊(C3⋊C8)C2311yescharacteristic
21C3×C4⋊Dic3—22no—
22C3×Dic3⋊C4—42no—
23C3×#208—21no—
24#3718Q811yescharacteristic
25#3715—21no—
26#3713Q811yescharacteristic
27#3711—41no—
28D3×C3⋊C8—41no—
29#3708—22no—
30#2231—91nomaximal, Sylow
31C3×#125—61no—
32#950—61no—
33#948—61no—
34#907—61no—
35#870—21no—
36C3×#104—61no—
37#822—61no—
38#808—62no—
39#807—62no—
40#805—21no—
41C4×C3⋊C8—61no—
42C4×C3⋊C8—61no—
43C2×C32×C4—21no—
44C2×C32×C4C2×D411yescharacteristic
45C3×#67—41no—
46C2×C3×Dic3—42no—
47C3×D12—21no—
48C3×C4×D3—41no—
49C3×Dic6—21no—
50C3⋊(C3⋊C8)SD1611yescharacteristic
51C3⋊(C3⋊C8)SD1611yescharacteristic
52C3⋊(C3⋊C8)C2×Q811yescharacteristic
53C3⋊(C3⋊C8)#4111yescharacteristic
54C3×C3⋊C8—41no—
55#499—91no—
56#443—91no—
57#365—92no—
58#364—91no—
59#360—92no—
60C3×#41—61no—
61#235—21no—
62C3×M16—61no—
63C3×C4⋊C4—62no—
64C3×C4⋊C4—122no—
65C3×C42—21no—
66C3×C42—21no—
67#216—61no—
68#215—61no—
69#214—61no—
70#213—61no—
71C4⋊Dic3—22no—
72Dic3⋊C4—42no—
73#208—21no—
74#208—121no—
75C2×C3⋊C8—61no—
76C2×C3⋊C8—61no—
77C2×C3⋊C8—61no—
78C2×C3⋊C8—61no—
79C2×C3⋊C8—121no—
80ΓL(1,𝔽25)—121no—
81D3×C8—121no—
82C22×C32AGL(1,ℤ/8)11yescharacteristic
83C2×C3×D3—41no—
84C32×C4—41no—
85C32×C4C22⋊Q811yescharacteristic
86C32×C4C2×SD1611yescharacteristic
87C3×Dic3—41no—
88C3×Dic3—82no—
89#135—91no—
90#131—181no—
91#125—61no—
92M32—92no—
93#108—91no—
94#107—181no—
95#106—92no—
96#104—61no—
97C4×C8—91no—
98C3×Q8—61no—
99C3×D4—61no—
100C3×D4—121no—
101C2×C3×C4—22no—
102C2×C3×C4—21no—
103C2×C3×C4—21no—
104C2×C3×C4—41no—
105C2×C3×C4—121no—
106C2×C3×C4—122no—
107#67—41no—
108C2×Dic3—42no—
109D12—21no—
110C4×D3—41no—
111Dic6—21no—
112C3×C8—121no—
113C3⋊C8—41no—
114C3⋊C8—61no—
115C3⋊C8—61no—
116C3⋊C8—61no—
117C3⋊C8—61no—
118C3⋊C8—61no—
119C3⋊C8—61no—
120C3⋊C8—61no—
121C3⋊C8—61no—
122C2×C32—21no—
123C2×C32#47611yescharacteristic
124C3×D3—81no—
125#41—61no—
126Q16—91no—
127SD16—181no—
128D8—91no—
129M16—61no—
130M16—361no—
131C2×C8—91no—
132C2×C8—91no—
133C2×C8—361no—
134C4⋊C4—62no—
135C4⋊C4—122no—
136C42GO+(4,𝔽2)11yescharacteristic
137C16—182no—
138C22×C3—21no—
139C22×C3—21no—
140C22×C3—121no—
141C2×D3—41no—
142C3×C4—21no—
143C3×C4—21no—
144C3×C4—21no—
145C3×C4—21no—
146C3×C4—42no—
147C3×C4—42no—
148C3×C4—121no—
149C3×C4—242no—
150Dic3—41no—
151Dic3—82no—
152C32#223111yescharacteristic, complemented, Sylow
153Q8—61no—
154D4—61no—
155D4—121no—
156C2×C4—21no—
157C2×C4—121no—
158C2×C4—122no—
159C2×C4C2×GO+(4,𝔽2)11yescharacteristic
160C8—91no—
161C8—91no—
162C8—91no—
163C8—91no—
164C8—121no—
165C2×C3—22no—
166C2×C3—21no—
167C2×C3—21no—
168C2×C3—41no—
169C2×C3—241no—
170D3—81no—
171C22—121no—
172C22#6423611yescharacteristic
173C4—41no—
174C4—121no—
175C4—242no—
176C4D32⋊Q811yescharacteristic
177C4#6422711yescharacteristic
178C3—21no—
179C3—21no—
180C2—21no—
181C2—241no—
182C2#1059335711yescharacteristic
subgroupG/H
centerC2#10593357
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC2×C32#476
prime radical#63822C22
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2231
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10590314C2semidirect
3. #10590150C2semidirect
4. #10590067C2semidirect
152. C32#2231semidirect

Maximal subgroups

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

subgroupindex
#105903892
#105903142
#105901502
#105900672
#105900642
#22319