Finite Group Databasebeta

← #11799724

Subgroups — #11799724

Order 1152.

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

normal subgroups only

This group has 228 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#10590900C211yesmaximal, characteristic, complemented
3#10590178C211yesmaximal, characteristic, complemented
4#10590067C212yesmaximal, complemented
5#10590064C212yesmaximal
6C3×#901—21no—
7#63919—21no—
8#63822C2211yescharacteristic
9#63773C2212yes—
10C8×C3⋊Dic3C2211yescharacteristic
11C3×#817—21no—
12#63578C2211yescharacteristic
13#63574C2212yes—
14#63568—21no—
15#5144—61no—
16#4855—61no—
17C3×#235—21no—
18C2×#627—41no—
19C2×C32×C8D411yescharacteristic
20C4×C3⋊Dic3D411yescharacteristic
21C2×C3⋊(C3⋊C8)C2311yescharacteristic
22C3×C4⋊Dic3—22no—
23C3×#208—21no—
24C3×ΓL(1,𝔽25)—41no—
25C3×D3×C8—41no—
26#3724—41no—
27#3718Q811yescharacteristic, complemented
28#3715—21no—
29#3713Q811yescharacteristic, complemented
30#3708—22no—
31#2230—91nomaximal, Sylow
32C3×#131—61no—
33#950—61no—
34#901—21no—
35#888—62no—
36C3×#106—61no—
37#837—61no—
38#825—61no—
39#822—61no—
40#817—21no—
41C8×Dic3—61no—
42C8×Dic3—61no—
43#808—62no—
44C2×C32×C4C2×D411yescharacteristic
45C2×C3⋊Dic3—21no—
46C3×#67—41no—
47C2×C3×Dic3—42no—
48C3×D12—21no—
49C3×C4×D3—41no—
50C3×Dic6—21no—
51#627—82no—
52C32×C8SD1611yescharacteristic
53C32×C8SD1611yescharacteristic
54C3⋊(C3⋊C8)C2×Q811yescharacteristic
55C3⋊(C3⋊C8)#4111yescharacteristic
56C3×C3⋊C8—41no—
57#498—91no—
58#443—91no—
59#365—92no—
60#364—91no—
61#360—92no—
62C3×#41—61no—
63#235—21no—
64C2×Dic6—122no—
65C3×M16—61no—
66C3×M16—121no—
67C2×C3×C8—21no—
68C2×C3×C8—21no—
69C2×C3×C8—121no—
70C3×C4⋊C4—62no—
71#216—61no—
72#215—61no—
73#214—61no—
74#213—61no—
75C4⋊Dic3—22no—
76Dic3⋊C4—122no—
77C4×Dic3—61no—
78C4×Dic3—61no—
79#208—21no—
80C2×C3⋊C8—61no—
81C2×C3⋊C8—61no—
82ΓL(1,𝔽25)—41no—
83D3×C8—41no—
84C22×C32AGL(1,ℤ/8)11yescharacteristic
85C2×C3×D3—41no—
86C32×C4C22⋊Q811yescharacteristic
87C32×C4C2×SD1611yescharacteristic
88C3⋊Dic3—22no—
89C3×Dic3—41no—
90C3×Dic3—82no—
91#135—91no—
92#131—61no—
93C4⋊Q8—181no—
94M32—92no—
95#108—91no—
96#106—61no—
97#106—92no—
98#104—181no—
99C4×C8—91no—
100C3×Q8—61no—
101C3×D4—61no—
102C3×D4—121no—
103C2×C3×C4—21no—
104C2×C3×C4—21no—
105C2×C3×C4—121no—
106C2×C3×C4—122no—
107#67—41no—
108C2×Dic3—42no—
109C2×Dic3—62no—
110C2×Dic3—121no—
111D12—21no—
112C4×D3—41no—
113Dic6—21no—
114Dic6—244no—
115C3×C8—21no—
116C3×C8—21no—
117C3×C8—21no—
118C3×C8—21no—
119C3×C8—121no—
120C3⋊C8—41no—
121C3⋊C8—61no—
122C3⋊C8—61no—
123C3⋊C8—61no—
124C3⋊C8—61no—
125C2×C32—21no—
126C2×C32#47611yescharacteristic
127C3×D3—81no—
128#41—61no—
129C2×Q8—361no—
130Q16—91no—
131SD16—181no—
132D8—91no—
133M16—61no—
134M16—121no—
135C2×C8—91no—
136C2×C8—121no—
137C2×C8GO+(4,𝔽2)11yescharacteristic
138C4⋊C4—62no—
139C4⋊C4—361no—
140C42—91no—
141C16—182no—
142C22×C3—21no—
143C22×C3—21no—
144C22×C3—121no—
145C2×D3—41no—
146C3×C4—21no—
147C3×C4—21no—
148C3×C4—21no—
149C3×C4—21no—
150C3×C4—121no—
151C3×C4—242no—
152Dic3—41no—
153Dic3—64no—
154Dic3—82no—
155Dic3—122no—
156C32#223011yescharacteristic, complemented, Sylow
157Q8—61no—
158Q8—722no—
159D4—61no—
160D4—121no—
161C2×C4—121no—
162C2×C4—122no—
163C2×C4—181no—
164C2×C4C2×GO+(4,𝔽2)11yescharacteristic
165C8—91no—
166C8—91no—
167C8—121no—
168C8#377511yescharacteristic
169C8#377511yescharacteristic
170C2×C3—22no—
171C2×C3—21no—
172C2×C3—21no—
173C2×C3—41no—
174C2×C3—241no—
175D3—81no—
176C22—121no—
177C22#6422411yescharacteristic
178C4—121no—
179C4—182no—
180C4—242no—
181C4D32⋊Q811yescharacteristic
182C4C2×#377511yescharacteristic
183C3—21no—
184C3—21no—
185C2—21no—
186C2—241no—
187C2#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#2230
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. #10590900C2semidirect
3. #10590178C2semidirect
4. #10590067C2semidirect
27. #3718Q8semidirect
29. #3713Q8semidirect
156. C32#2230semidirect

Maximal subgroups

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

subgroupindex
#105909212
#105909002
#105901782
#105900672
#105900642
#22309