Finite Group Databasebeta

← #11800057

Subgroups — #11800057

Order 1152.

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

normal subgroups only

This group has 290 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
1#10590352C211yesmaximal, characteristic
2#10590312C211yesmaximal, characteristic, complemented
3C4×#3708C211yesmaximal, characteristic, complemented
4#10590061C214yesmaximal, complemented
5C3×#874—21no—
6C3×#869—21no—
7C2×#3713—21no—
8C2×#3713C2212yes—
9C2×#3708C2212yes—
10C4×C3⋊(C3⋊C8)C2211yescharacteristic
11#63576—21no—
12#63576C2212yes—
13#5078—61no—
14#5073—61no—
15C2×C3×D12—22no—
16C2×C3×D12—41no—
17C2×C3×D12—41no—
18C2×C3×Dic6—41no—
19C32×C42D411yescharacteristic
20C2×C3⋊(C3⋊C8)D411yescharacteristic
21C2×C3⋊(C3⋊C8)C2311yescharacteristic
22C3×C4⋊Dic3—22no—
23C3×C4⋊Dic3—41no—
24#3713—24no—
25#3713—42no—
26#3708—22no—
27#2240—91nomaximal, Sylow
28C3×C4⋊Q8—61no—
29C3×#127—61no—
30C2×#213—62no—
31C2×#213—62no—
32#874—21no—
33#869—21no—
34#807—62no—
35#807—62no—
36C4×C3⋊C8—61no—
37C4×C3⋊C8—61no—
38C22×C3×D3—42no—
39C2×C32×C4D811yescharacteristic
40C2×C32×C4D811yescharacteristic
41C2×C32×C4C2×D411yescharacteristic
42C2×C3×Dic3—42no—
43C3×D12—42no—
44C3×D12—42no—
45C3×D12—82no—
46C3×D12—82no—
47C3×Dic6—82no—
48C3⋊(C3⋊C8)SD1612yes—
49C3⋊(C3⋊C8)#4112yes—
50#500—91no—
51#493—91no—
52#357—94no—
53C4×C16—91no—
54C2×C3×Q8—121no—
55C2×C3×D4—62no—
56C2×C3×D4—121no—
57C2×C3×D4—121no—
58C2×D12—22no—
59C2×D12—41no—
60C2×D12—41no—
61C2×Dic6—41no—
62C3×C4⋊C4—62no—
63C3×C4⋊C4—121no—
64C3×C42—21no—
65C3×C42—21no—
66#213—124no—
67#213—124no—
68C4⋊Dic3—22no—
69C4⋊Dic3—41no—
70C2×C3⋊C8—61no—
71C2×C3⋊C8—61no—
72C2×C3⋊C8—61no—
73C2×C3⋊C8—61no—
74C22×C32C2×D811yescharacteristic
75C2×C3×D3—82no—
76C2×C3×D3—82no—
77C2×C3×D3—82no—
78C32×C4D1612yes—
79C32×C4SD3212yes—
80C32×C4#12411yescharacteristic
81C32×C4C2×SD1611yescharacteristic
82C3×Dic3—82no—
83C2×D8—92no—
84C2×D8—181no—
85C4⋊Q8—61no—
86#127—61no—
87C2×C16—92no—
88#107—92no—
89#107—181no—
90C4×C8—91no—
91C23×C3—122no—
92C22×D3—42no—
93C3×Q8—242no—
94C3×D4—122no—
95C3×D4—122no—
96C3×D4—242no—
97C3×D4—242no—
98C2×C3×C4—21no—
99C2×C3×C4—21no—
100C2×C3×C4—21no—
101C2×C3×C4—21no—
102C2×C3×C4—21no—
103C2×C3×C4—21no—
104C2×C3×C4—122no—
105C2×Dic3—42no—
106D12—42no—
107D12—42no—
108D12—82no—
109D12—82no—
110Dic6—82no—
111C3⋊C8—62no—
112C3⋊C8—62no—
113C3⋊C8—62no—
114C3⋊C8—62no—
115C2×C32#48611yescharacteristic
116C2×C32C2×D1611yescharacteristic
117C2×C32C2×SD3211yescharacteristic
118C3×D3—162no—
119C2×Q8—121no—
120C2×D4—62no—
121C2×D4—121no—
122C2×D4—121no—
123D8—184no—
124D8—362no—
125C2×C8—91no—
126C2×C8—91no—
127C4⋊C4—62no—
128C4⋊C4—121no—
129C42GO+(4,𝔽2)11yescharacteristic
130C16—182no—
131C22×C3—21no—
132C22×C3—21no—
133C22×C3—242no—
134C22×C3—242no—
135C22×C3—242no—
136C2×D3—82no—
137C2×D3—82no—
138C2×D3—82no—
139C3×C4—21no—
140C3×C4—21no—
141C3×C4—21no—
142C3×C4—21no—
143C3×C4—22no—
144C3×C4—22no—
145C3×C4—22no—
146C3×C4—22no—
147C3×C4—242no—
148Dic3—82no—
149C32#224011yescharacteristic, complemented, Sylow
150C23—122no—
151Q8—242no—
152D4—122no—
153D4—122no—
154D4—242no—
155D4—242no—
156C2×C4—122no—
157C2×C4#377411yescharacteristic
158C2×C4#377411yescharacteristic
159C2×C4C2×GO+(4,𝔽2)11yescharacteristic
160C8—92no—
161C8—92no—
162C2×C3—21no—
163C2×C3—21no—
164C2×C3—21no—
165C2×C3—21no—
166C2×C3—21no—
167C2×C3—21no—
168C2×C3—482no—
169D3—162no—
170C22—242no—
171C22—242no—
172C22—242no—
173C22C2×#377411yescharacteristic
174C4—242no—
175C4#6373412yes—
176C4#6373512yes—
177C4#6422111yescharacteristic
178C4#6422711yescharacteristic
179C3—21no—
180C3—21no—
181C2—482no—
182C2C2×#6373411yescharacteristic
183C2C2×#6373511yescharacteristic
184C2#1059334811yescharacteristic
subgroupG/H
centerC22C2×#3774
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×D8
prime radical#10590352C2
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2240
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10590312C2semidirect
3. C4×#3708C2semidirect
4. #10590061C2semidirect
149. C32#2240semidirect

Maximal subgroups

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

subgroupindex
#105903522
#105903122
C4×#37082
#105900612
#22409