Finite Group Databasebeta

← #11800112

Subgroups — #11800112

Order 1152.

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

normal subgroups only

This group has 246 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#10590353C211yesmaximal, characteristic
2#10590314C211yesmaximal, characteristic, complemented
3C4×#3708C211yesmaximal, characteristic, complemented
4#10590062C212yesmaximal, complemented
5#10590061C212yesmaximal
6C3×#875—21no—
7C3×#870—21no—
8C2×#3718C2211yescharacteristic
9C2×#3715—21no—
10C2×#3713C2211yescharacteristic
11C2×#3708C2212yes—
12C4×C3⋊(C3⋊C8)C2211yescharacteristic
13#63576C2212yes—
14#63574—21no—
15#5065—61no—
16#5059—61no—
17C2×C3×D12—21no—
18C2×C3×Dic6—21no—
19C32×C42D411yescharacteristic
20C2×C3⋊(C3⋊C8)D411yescharacteristic
21C2×C3⋊(C3⋊C8)C2311yescharacteristic
22C3×(C2×D3)⋊C4—42no—
23C3×C4⋊Dic3—22no—
24C3×Dic3⋊C4—42no—
25#3718—22no—
26#3715—42no—
27#3713—22no—
28#3708—22no—
29#2242—91nomaximal, Sylow
30C3×#125—61no—
31C3×#124—61no—
32C2×#216—61no—
33C2×#215—61no—
34C2×#214—61no—
35C2×#213—61no—
36#875—21no—
37#870—21no—
38#808—62no—
39#807—62no—
40C4×C3⋊C8—61no—
41C4×C3⋊C8—61no—
42C22×C3×D3—41no—
43C2×C32×C4D812yes—
44C2×C32×C4C2×D411yescharacteristic
45C2×C3×Dic3—42no—
46C2×C3×Dic3—41no—
47C3×D12—41no—
48C3×D12—41no—
49C3×Dic6—41no—
50C3×Dic6—41no—
51C3⋊(C3⋊C8)SD1612yes—
52C3⋊(C3⋊C8)#4112yes—
53#499—91no—
54#495—91no—
55#358—92no—
56#357—92no—
57C4×C16—91no—
58C2×C3×Q8—61no—
59C2×C3×D4—61no—
60C2×D12—21no—
61C2×Dic6—21no—
62C3×C4⋊C4—62no—
63C3×C4⋊C4—122no—
64C3×C22⋊C4—122no—
65C3×C42—21no—
66C3×C42—21no—
67#216—122no—
68#215—122no—
69#214—122no—
70#213—122no—
71(C2×D3)⋊C4—42no—
72C4⋊Dic3—22no—
73Dic3⋊C4—42no—
74C2×C3⋊C8—61no—
75C2×C3⋊C8—61no—
76C2×C3⋊C8—61no—
77C2×C3⋊C8—61no—
78C22×C32C2×D811yescharacteristic
79C2×C3×D3—81no—
80C2×C3×D3—82no—
81C32×C4—22no—
82C32×C4#12411yescharacteristic
83C32×C4C2×SD1611yescharacteristic
84C3×Dic3—81no—
85C3×Dic3—82no—
86C2×Q16—91no—
87C2×SD16—181no—
88C2×D8—91no—
89#125—61no—
90#124—61no—
91C2×C16—92no—
92#107—92no—
93#106—181no—
94C4×C8—91no—
95C23×C3—121no—
96C22×D3—41no—
97C3×Q8—121no—
98C3×Q8—121no—
99C3×D4—121no—
100C3×D4—121no—
101C2×C3×C4—21no—
102C2×C3×C4—21no—
103C2×C3×C4—22no—
104C2×C3×C4—22no—
105C2×C3×C4—121no—
106C2×C3×C4—122no—
107C2×Dic3—42no—
108C2×Dic3—41no—
109D12—41no—
110D12—41no—
111Dic6—41no—
112Dic6—41no—
113C3⋊C8—62no—
114C3⋊C8—62no—
115C3⋊C8—62no—
116C3⋊C8—62no—
117C2×C32#48611yescharacteristic
118C2×C32#50812yes—
119C3×D3—161no—
120C2×Q8—61no—
121C2×D4—61no—
122Q16—182no—
123SD16—362no—
124D8—182no—
125C2×C8—91no—
126C2×C8—91no—
127C4⋊C4—62no—
128C4⋊C4—122no—
129C22⋊C4—122no—
130C42GO+(4,𝔽2)11yescharacteristic
131C16—182no—
132C22×C3—21no—
133C22×C3—21no—
134C22×C3—241no—
135C22×C3—242no—
136C2×D3—81no—
137C2×D3—82no—
138C3×C4—21no—
139C3×C4—21no—
140C3×C4—21no—
141C3×C4—21no—
142C3×C4—42no—
143C3×C4—42no—
144C3×C4—241no—
145C3×C4—242no—
146Dic3—81no—
147Dic3—82no—
148C32#224211yescharacteristic, complemented, Sylow
149C23—121no—
150Q8—121no—
151Q8—121no—
152D4—121no—
153D4—121no—
154C2×C4—121no—
155C2×C4—122no—
156C2×C4#377412yes—
157C2×C4C2×GO+(4,𝔽2)11yescharacteristic
158C8—92no—
159C8—92no—
160C2×C3—22no—
161C2×C3—22no—
162C2×C3—21no—
163C2×C3—21no—
164C2×C3—481no—
165D3—161no—
166C22—242no—
167C22—241no—
168C22C2×#377411yescharacteristic
169C4—22no—
170C4—242no—
171C4—241no—
172C4#6422111yescharacteristic
173C4#6422711yescharacteristic
174C3—21no—
175C3—21no—
176C2—481no—
177C2#1059333312yes—
178C2#1059334811yescharacteristic
subgroupG/H
centerC22C2×#3774
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×D8
prime radicalC2×#3713C22
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2242
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. #10590314C2semidirect
3. C4×#3708C2semidirect
4. #10590062C2semidirect
148. C32#2242semidirect

Maximal subgroups

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

subgroupindex
#105903532
#105903142
C4×#37082
#105900622
#105900612
#22429