Finite Group Databasebeta

← #11799758

Subgroups — #11799758

Order 1152.

216 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 39 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#10590921C211yesmaximal, characteristic
2#10590875C211yesmaximal, characteristic, complemented
3#10590178C211yesmaximal, characteristic, complemented
4#10590067C212yesmaximal, complemented
5#10590064C212yesmaximal
6C3×#901—21no—
7#63872—21no—
8#63822C2211yescharacteristic
9#63773C2212yes—
10C8×C3⋊Dic3C2211yescharacteristic
11C3×#818—21no—
12#63578C2211yescharacteristic
13#63574C2212yes—
14#63568—21no—
15#5144—61no—
16#4878—61no—
17C3×#235—21no—
18C2×C32×C8D411yescharacteristic
19C4×C3⋊Dic3D411yescharacteristic
20C2×C3⋊(C3⋊C8)C2311yescharacteristic
21C3×C4⋊Dic3—22no—
22C3×#208—21no—
23C3×ΓL(1,𝔽25)—41no—
24C3×D3×C8—41no—
25Dic3⋊Dic3—42no—
26#3718Q811yescharacteristic
27#3715—21no—
28#3713Q811yescharacteristic
29#3708—22no—
30#2231—91nomaximal, Sylow
31C3×#131—61no—
32#950—61no—
33#901—21no—
34#890—62no—
35C3×#107—61no—
36#837—61no—
37#825—61no—
38#822—61no—
39#818—21no—
40C8×Dic3—61no—
41C8×Dic3—61no—
42#808—62no—
43C2×C32×C4C2×D411yescharacteristic
44C2×C3⋊Dic3—21no—
45C3×#67—41no—
46C2×C3×Dic3—42no—
47C3×D12—21no—
48C3×C4×D3—41no—
49C3×Dic6—21no—
50C32×C8SD1611yescharacteristic
51C32×C8SD1611yescharacteristic
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×M16—121no—
64C2×C3×C8—21no—
65C2×C3×C8—21no—
66C2×C3×C8—121no—
67C3×C4⋊C4—62no—
68#216—61no—
69#215—61no—
70#214—61no—
71#213—61no—
72C4⋊Dic3—22no—
73C4⋊Dic3—122no—
74Dic3⋊C4—122no—
75C4×Dic3—61no—
76C4×Dic3—61no—
77#208—21no—
78C2×C3⋊C8—61no—
79C2×C3⋊C8—61no—
80ΓL(1,𝔽25)—41no—
81D3×C8—41no—
82C22×C32AGL(1,ℤ/8)11yescharacteristic
83C2×C3×D3—41no—
84C32×C4C22⋊Q811yescharacteristic
85C32×C4C2×SD1611yescharacteristic
86C3⋊Dic3—41no—
87C3×Dic3—41no—
88C3×Dic3—82no—
89#135—91no—
90#131—61no—
91#125—181no—
92M32—92no—
93#108—91no—
94#107—61no—
95#106—92no—
96#104—181no—
97C4×C8—91no—
98C3×Q8—61no—
99C3×D4—61no—
100C3×D4—121no—
101C2×C3×C4—21no—
102C2×C3×C4—21no—
103C2×C3×C4—121no—
104C2×C3×C4—122no—
105#67—41no—
106C2×Dic3—42no—
107C2×Dic3—61no—
108C2×Dic3—61no—
109C2×Dic3—121no—
110D12—21no—
111C4×D3—41no—
112Dic6—21no—
113C3×C8—21no—
114C3×C8—21no—
115C3×C8—21no—
116C3×C8—21no—
117C3×C8—121no—
118C3⋊C8—41no—
119C3⋊C8—61no—
120C3⋊C8—61no—
121C3⋊C8—61no—
122C3⋊C8—61no—
123C2×C32—21no—
124C2×C32#47611yescharacteristic
125C3×D3—81no—
126#41—61no—
127Q16—91no—
128SD16—181no—
129D8—91no—
130M16—61no—
131M16—121no—
132C2×C8—91no—
133C2×C8—121no—
134C2×C8GO+(4,𝔽2)11yescharacteristic
135C4⋊C4—62no—
136C4⋊C4—362no—
137C42—91no—
138C16—182no—
139C22×C3—21no—
140C22×C3—21no—
141C22×C3—121no—
142C2×D3—41no—
143C3×C4—21no—
144C3×C4—21no—
145C3×C4—21no—
146C3×C4—21no—
147C3×C4—121no—
148C3×C4—242no—
149Dic3—41no—
150Dic3—82no—
151Dic3—121no—
152Dic3—121no—
153Dic3—122no—
154C32#223111yescharacteristic, complemented, Sylow
155Q8—61no—
156D4—61no—
157D4—121no—
158C2×C4—121no—
159C2×C4—122no—
160C2×C4—181no—
161C2×C4C2×GO+(4,𝔽2)11yescharacteristic
162C8—91no—
163C8—91no—
164C8—121no—
165C8#377511yescharacteristic
166C8#377511yescharacteristic
167C2×C3—21no—
168C2×C3—21no—
169C2×C3—21no—
170C2×C3—21no—
171C2×C3—41no—
172C2×C3—241no—
173D3—81no—
174C22—121no—
175C22#6422411yescharacteristic
176C4—121no—
177C4—242no—
178C4—361no—
179C4D32⋊Q811yescharacteristic
180C4C2×#377511yescharacteristic
181C3—21no—
182C3—21no—
183C2—21no—
184C2—241no—
185C2#1059335911yescharacteristic
subgroupG/H
centerC2#10593359
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#476
prime radical#63822C22
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2231
LCSG ▷ C2×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
2. #10590875C2semidirect
3. #10590178C2semidirect
4. #10590067C2semidirect
154. C32#2231semidirect

Maximal subgroups

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

subgroupindex
#105909212
#105908752
#105901782
#105900672
#105900642
#22319