Finite Group Databasebeta

← #11796550

Subgroups — #11796550

Order 1152.

596 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 54 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#10596276C211yesmaximal, characteristic
2#10593808C212yesmaximal, complemented
3#10590212C214yesmaximal, complemented
4C22×C32×D4C411yescharacteristic
5C2×#3828C2211yescharacteristic
6#64283—22no—
7#64162—22no—
8#64149C412yes—
9#64147—22no—
10#64145C2212yes—
11#64135C411yescharacteristic
12#63788—22no—
13#63780C2214yescomplemented
14#5805—62no—
15C24×C32—21no—
16C2×C32×D4—21no—
17C2×C32×D4—42no—
18C2×C32×D4C2×C412yes—
19C22×C32×C4C2×C411yescharacteristic
20C2×#638—24no—
21C2×#638D412yes—
22#3828—42no—
23C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
24C2×C4×C3⋊D3D412yes—
25C2×#634C2311yescharacteristic
26#3792—24no—
27#3788—42no—
28#3787—42no—
29#3757—21no—
30#3757—24no—
31C4⋊(C3⋊Dic3)—21no—
32C4×C3⋊Dic3C2×C412yes—
33#2134—91nomaximal, Sylow
34C22×C3×D4—22no—
35C2×#235—62no—
36#953—68no—
37#940—64no—
38#938—68no—
39#936—64no—
40#926—62no—
41C23×C32—22no—
42C23×C32—42no—
43C23×C32—82no—
44C23×C32C22⋊C411yescharacteristic
45C22×C3⋊D3C22⋊C412yes—
46C32×D4—42no—
47C32×D4—42no—
48C2×C32×C4—22no—
49C2×C32×C4C22⋊C411yescharacteristic
50C2×C32×C4C22×C411yescharacteristic
51#638—42no—
52#638—84no—
53C2×C3⋊Dic3—22no—
54C2×C3⋊Dic3C2×D412yes—
55C4⋊(C3⋊D3)—41no—
56C4×C3⋊D3—22no—
57C4×C3⋊D3—22no—
58#634—41no—
59#622—44no—
60#535—91no—
61#413—92no—
62#355—94no—
63C24×C3—24no—
64C2×C3×D4—24no—
65C2×C3×D4—24no—
66C2×C3×D4—48no—
67C22×C3×C4—22no—
68C2×#67—64no—
69C2×#67—616no—
70#235—128no—
71C2×D12—62no—
72C2×C4×D3—64no—
73C2×Dic6—62no—
74#217—64no—
75#217—616no—
76C4⋊Dic3—64no—
77C4×Dic3—64no—
78C22×C32—21no—
79C22×C32—41no—
80C22×C32—44no—
81C22×C32—42no—
82C22×C32—84no—
83C22×C32C2×C22⋊C411yescharacteristic
84C2×C3⋊D3—22no—
85C2×C3⋊D3—42no—
86C32×C4—21no—
87C32×C4#9912yes—
88C3⋊Dic3—22no—
89C3⋊Dic3—42no—
90C2×#41—91no—
91C22×D4#15711yescharacteristic
92C2×M16—182no—
93#127—92no—
94#124—92no—
95#121—182no—
96#120—182no—
97#117—91no—
98#101—94no—
99#100—182no—
100C23×C3—28no—
101C23×C3—22no—
102C23×C3—48no—
103C23×C3—88no—
104C22×D3—64no—
105C3×D4—48no—
106C3×D4—48no—
107C2×C3×C4—28no—
108C2×C3×C4—22no—
109C2×C3×C4—22no—
110#67—128no—
111#67—2416no—
112C2×Dic3—64no—
113C2×Dic3—68no—
114D12—124no—
115C4×D3—124no—
116C4×D3—124no—
117Dic6—124no—
118C2×C32—21no—
119C2×C32—41no—
120C2×C32—82no—
121C2×C32C2×#9911yescharacteristic
122C3⋊D3—42no—
123C24—21no—
124#41—362no—
125C2×Q8—91no—
126C2×D4—21no—
127C2×D4—42no—
128C2×D4—92no—
129C2×D4—91no—
130C2×D4—184no—
131C2×D4C2×#15712yes—
132C22×C4—92no—
133C22×C4C2×#15711yescharacteristic
134M16—184no—
135M16—362no—
136C2×C8—362no—
137C4⋊C4—181no—
138C22⋊C4—184no—
139C22⋊C4—181no—
140C42—92no—
141C22×C3—24no—
142C22×C3—22no—
143C22×C3—44no—
144C22×C3—416no—
145C22×C3—48no—
146C22×C3—816no—
147C2×D3—124no—
148C2×D3—128no—
149C3×C4—24no—
150C3×C4—24no—
151Dic3—124no—
152Dic3—128no—
153C32#213411yescharacteristic, complemented, Sylow
154C23—22no—
155C23—42no—
156C23—82no—
157C23—92no—
158C23C22⋊#15711yescharacteristic
159Q8—361no—
160D4—42no—
161D4—42no—
162D4—361no—
163D4—362no—
164D4—724no—
165C2×C4—22no—
166C2×C4—92no—
167C2×C4—182no—
168C2×C4—182no—
169C2×C4—182no—
170C2×C4C22⋊#15711yescharacteristic
171C2×C4C22×#15711yescharacteristic
172C8—364no—
173C2×C3—24no—
174C2×C3—22no—
175C2×C3—44no—
176C2×C3—88no—
177D3—244no—
178C22—21no—
179C22—41no—
180C22—44no—
181C22—42no—
182C22—84no—
183C22—182no—
184C22—362no—
185C22C2×C22⋊#15711yescharacteristic
186C4—21no—
187C4—182no—
188C4—362no—
189C4#6378612yes—
190C3—22no—
191C2—21no—
192C2—41no—
193C2—82no—
194C2—362no—
195C2C2×#6378611yescharacteristic
subgroupG/H
centerC2C2×#63786
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC22×C32×D4C4
socleC2×C32C2×#99
prime radical#10596276C2
cosocleC2×#634C23
hypercenterC22×D4#157
hypocenterC32#2134
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10593808C2semidirect
3. #10590212C2semidirect
13. #63780C22semidirect
153. C32#2134semidirect

Maximal subgroups

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

subgroupindex
#105962762
#105938082
#105902122
#21349