Finite Group Databasebeta

← #11797139

Subgroups — #11797139

Order 1152.

254 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C2×#63773C211yesmaximal, characteristic
2C2×#63578C211yesmaximal, characteristic
3#10591138C211yesmaximal, characteristic
4#10590067C214yesmaximal, complemented
5C22×C3⋊(C3⋊C8)C2211yescharacteristic
6C3×#926—21no—
7C2×C3×#208—21no—
8#63773C412yescomplemented
9#63773C2212yes—
10C2×#3708C412yescomplemented
11#63578—21no—
12#63578C2212yes—
13#63576—21no—
14#63574C2212yes—
15C2×#822—61no—
16#4998—61no—
17C22×C32×C4D411yescharacteristic
18C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
19C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
20C2×C3⋊(C3⋊C8)D411yescharacteristic
21C2×C3⋊(C3⋊C8)Q811yescharacteristic
22C2×C3⋊(C3⋊C8)Q811yescharacteristic
23C2×C3⋊(C3⋊C8)C2311yescharacteristic
24C3×#217—41no—
25C3×C4⋊Dic3—22no—
26C3×C4×Dic3—41no—
27C3×#208—22no—
28C3×#208—41no—
29C2×C3×C3⋊C8—41no—
30#3708C2×C414yes—
31#2155—91nomaximal, Sylow
32C2×C3×M16—61no—
33C3×#117—61no—
34#926—21no—
35C2×#208—21no—
36C22×C3⋊C8—61no—
37C22×C3⋊C8—61no—
38#822—62no—
39#822—62no—
40#808—62no—
41#807—62no—
42C23×C32SD1611yescharacteristic
43C2×C32×C4C4⋊C411yescharacteristic
44C2×C32×C4C4⋊C411yescharacteristic
45C2×C32×C4SD1611yescharacteristic
46C2×C32×C4SD1611yescharacteristic
47C2×C32×C4SD1611yescharacteristic
48C2×C32×C4C2×D411yescharacteristic
49C2×C3×Dic3—42no—
50C3⋊(C3⋊C8)C4⋊C411yescharacteristic
51C3⋊(C3⋊C8)C4⋊C411yescharacteristic
52C3⋊(C3⋊C8)C22×C411yescharacteristic
53C3⋊(C3⋊C8)C2×Q811yescharacteristic
54C3×C3⋊C8—42no—
55C2×M32—91no—
56C2×#108—91no—
57#427—91no—
58#365—94no—
59C22×C3×C4—21no—
60C22×C3×C4—21no—
61C3×M16—62no—
62C3×M16—121no—
63C2×C3×C8—121no—
64C3×C4⋊C4—62no—
65C3×C22⋊C4—121no—
66C3×C42—121no—
67#217—41no—
68C4⋊Dic3—22no—
69C4×Dic3—41no—
70#208—22no—
71#208—41no—
72C2×C3⋊C8—41no—
73C2×C3⋊C8—61no—
74C2×C3⋊C8—61no—
75C2×C3⋊C8—61no—
76C2×C3⋊C8—61no—
77C2×C3⋊C8—61no—
78C2×C3⋊C8—61no—
79C2×C3⋊C8—61no—
80C2×C3⋊C8—61no—
81C2×C3⋊C8—61no—
82C2×C3⋊C8—61no—
83C2×C3⋊C8—61no—
84C2×C3⋊C8—61no—
85C22×C32—41no—
86C22×C32#10611yescharacteristic
87C22×C32#10611yescharacteristic
88C22×C32C2×SD1611yescharacteristic
89C32×C4#10611yescharacteristic
90C32×C4#10611yescharacteristic
91C32×C4C2×C4⋊C411yescharacteristic
92C32×C4C2×SD1611yescharacteristic
93C3×Dic3—82no—
94C2×M16—61no—
95C22×C8—91no—
96#117—61no—
97M32—92no—
98M32—92no—
99C2×C16—92no—
100#108—92no—
101#108—181no—
102#107—181no—
103#106—92no—
104C23×C3—21no—
105C23×C3—21no—
106C2×C3×C4—21no—
107C2×C3×C4—21no—
108C2×C3×C4—21no—
109C2×C3×C4—21no—
110C2×C3×C4—21no—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×C3×C4—21no—
116C2×C3×C4—21no—
117C2×C3×C4—21no—
118C2×C3×C4—122no—
119C2×Dic3—42no—
120C3×C8—122no—
121C3⋊C8—42no—
122C3⋊C8—61no—
123C3⋊C8—61no—
124C3⋊C8—61no—
125C3⋊C8—61no—
126C3⋊C8—61no—
127C3⋊C8—61no—
128C3⋊C8—61no—
129C3⋊C8—61no—
130C2×C32—21no—
131C2×C32—21no—
132C2×C32—21no—
133C2×C32C2×#10611yescharacteristic
134C22×C4GO+(4,𝔽2)11yescharacteristic
135M16—62no—
136M16—121no—
137C2×C8—91no—
138C2×C8—91no—
139C2×C8—91no—
140C2×C8—91no—
141C2×C8—91no—
142C2×C8—91no—
143C2×C8—121no—
144C4⋊C4—62no—
145C22⋊C4—121no—
146C42—121no—
147C16—94no—
148C22×C3—21no—
149C22×C3—21no—
150C22×C3—21no—
151C22×C3—21no—
152C22×C3—21no—
153C22×C3—21no—
154C22×C3—42no—
155C22×C3—42no—
156C3×C4—21no—
157C3×C4—21no—
158C3×C4—21no—
159C3×C4—21no—
160C3×C4—21no—
161C3×C4—21no—
162C3×C4—21no—
163C3×C4—21no—
164C3×C4—242no—
165Dic3—82no—
166C32#215511yescharacteristic, complemented, Sylow
167C23#377511yescharacteristic
168C2×C4—122no—
169C2×C4#377311yescharacteristic
170C2×C4#377311yescharacteristic
171C2×C4#377511yescharacteristic
172C2×C4#377511yescharacteristic
173C2×C4#377511yescharacteristic
174C2×C4C2×GO+(4,𝔽2)11yescharacteristic
175C8—91no—
176C8—91no—
177C8—91no—
178C8—91no—
179C8—122no—
180C2×C3—22no—
181C2×C3—22no—
182C2×C3—21no—
183C2×C3—21no—
184C2×C3—41no—
185C2×C3—41no—
186C2×C3—41no—
187C2×C3—41no—
188C22—41no—
189C22#6374211yescharacteristic
190C22#6374211yescharacteristic
191C22C2×#377511yescharacteristic
192C4—242no—
193C4#6374211yescharacteristic
194C4#6374211yescharacteristic
195C4C2×#377311yescharacteristic
196C4C2×#377511yescharacteristic
197C3—21no—
198C3—21no—
199C2—21no—
200C2—21no—
201C2—21no—
202C2C2×#6374211yescharacteristic
subgroupG/H
centerC4#63742
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC2×C32C2×#106
prime radicalC23×C32SD16
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2155
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590067C2semidirect
8. #63773C4semidirect
10. C2×#3708C4semidirect
166. C32#2155semidirect

Maximal subgroups

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

subgroupindex
C2×#637732
C2×#635782
#105911382
#105900672
#21559