Finite Group Databasebeta

← #11772363

Subgroups — #11772363

Order 1152.

246 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 55 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×#63764C211yesmaximal, characteristic
2#10590700C211yesmaximal, characteristic
3C2×#63544C211yesmaximal, characteristic
4C2×C8×C3⋊D3C2211yescharacteristic
5#63874C411yescharacteristic
6C2×#3712C411yescharacteristic
7C2×#3708—21no—
8#63764—21no—
9#63764C412yescomplemented
10C3×C8×Dic3—21no—
11C2×C3×C3⋊C16—21no—
12#63554—21no—
13#63544—21no—
14#63544C412yescomplemented
15C2×#798—61no—
16#4689—61no—
17C2×C4×C3⋊D3C2×C411yescharacteristic
18C2×C32×C8D411yescharacteristic
19C2×C3⋊(C3⋊C8)D411yescharacteristic
20C8×C3⋊D3C2×C411yescharacteristic
21C8×C3⋊D3C2×C411yescharacteristic
22C8×C3⋊D3D411yescharacteristic
23C8×C3⋊D3Q811yescharacteristic
24C3×C4×Dic3—21no—
25C2×C3×C3⋊C8—21no—
26#3724C812yes—
27#3722—21no—
28#3712—21no—
29#3712C812yes—
30#3708—22no—
31C3×C3⋊C16—22no—
32#1379—91nomaximal, Sylow
33C2×ΓL(1,𝔽25)—61no—
34C2×D3×C8—61no—
35C2×D3×C8—61no—
36#872—61no—
37C2×C3×C16—61no—
38C3×C4×C8—61no—
39#815—61no—
40C8×Dic3—21no—
41C2×C3⋊C16—21no—
42#803—61no—
43#798—62no—
44#798—62no—
45C22×C3⋊D3M1611yescharacteristic
46C2×C32×C4C22⋊C411yescharacteristic
47C2×C3⋊Dic3C2×C811yescharacteristic
48C4×C3⋊D3C4211yescharacteristic
49C4×C3⋊D3C4⋊C411yescharacteristic
50C4×C3⋊D3C2×C811yescharacteristic
51C4×C3⋊D3M1611yescharacteristic
52C2×C3×Dic3—22no—
53C32×C8C22⋊C411yescharacteristic
54C32×C8C4⋊C411yescharacteristic
55C3⋊(C3⋊C8)C22⋊C411yescharacteristic
56C3⋊(C3⋊C8)C4⋊C411yescharacteristic
57C3×C3⋊C8—22no—
58C2×M32—91no—
59C22×C16—91no—
60#405—91no—
61C2×C4×D3—61no—
62C2×C4×D3—61no—
63C2×C3×C8—21no—
64C2×C3×C8—21no—
65C2×C3×C8—61no—
66C3×C42—61no—
67(C2×D3)⋊C4—62no—
68Dic3⋊C4—62no—
69C4×Dic3—21no—
70C2×C3⋊C8—21no—
71C2×C3⋊C8—61no—
72C2×C3⋊C8—61no—
73ΓL(1,𝔽25)—62no—
74ΓL(1,𝔽25)—62no—
75D3×C8—61no—
76D3×C8—61no—
77D3×C8—61no—
78D3×C8—61no—
79D3×C8—61no—
80D3×C8—61no—
81D3×C8—61no—
82D3×C8—61no—
83C3×C16—62no—
84C3⋊C16—22no—
85C22×C32C22⋊C811yescharacteristic
86C2×C3⋊D3—22no—
87C2×C3⋊D3#9711yescharacteristic
88C2×C3⋊D3C4⋊C811yescharacteristic
89C32×C4#9511yescharacteristic
90C32×C4C22⋊C811yescharacteristic
91C3⋊Dic3C4×C811yescharacteristic
92C3⋊Dic3C4⋊C811yescharacteristic
93C3×Dic3—42no—
94C2×M16—91no—
95C22×C8—91no—
96#117—91no—
97M32—92no—
98M32—181no—
99C2×C16—61no—
100C2×C16—92no—
101C2×C16—181no—
102C2×C16—181no—
103#97—181no—
104C4×C8—61no—
105C22×D3—61no—
106C22×D3—61no—
107C2×C3×C4—21no—
108C2×C3×C4—21no—
109C2×C3×C4—62no—
110C2×Dic3—22no—
111C2×Dic3—61no—
112C2×Dic3—61no—
113C4×D3—61no—
114C4×D3—61no—
115C4×D3—61no—
116C4×D3—61no—
117C4×D3—61no—
118C4×D3—61no—
119C4×D3—61no—
120C4×D3—61no—
121C3×C8—21no—
122C3×C8—21no—
123C3×C8—21no—
124C3×C8—21no—
125C3×C8—62no—
126C3⋊C8—22no—
127C3⋊C8—61no—
128C3⋊C8—61no—
129C3⋊C8—61no—
130C3⋊C8—61no—
131C2×C32#33611yescharacteristic
132C2×C32#35012yes—
133C3⋊D3—21no—
134C3⋊D3—21no—
135C22×C4—91no—
136M16—92no—
137M16—181no—
138C2×C8—61no—
139C2×C8—91no—
140C2×C8—91no—
141C2×C8—91no—
142C2×C8—91no—
143C2×C8—91no—
144C2×C8GO+(4,𝔽2)11yescharacteristic
145C4⋊C4—92no—
146C22⋊C4—181no—
147C42—61no—
148C16—62no—
149C16—182no—
150C22×C3—21no—
151C22×C3—21no—
152C2×D3—61no—
153C2×D3—61no—
154C2×D3—61no—
155C2×D3—61no—
156C2×D3—122no—
157C2×D3—122no—
158C3×C4—21no—
159C3×C4—21no—
160C3×C4—21no—
161C3×C4—21no—
162C3×C4—122no—
163Dic3—42no—
164Dic3—61no—
165Dic3—61no—
166Dic3—61no—
167Dic3—61no—
168C32#137911yescharacteristic, complemented, Sylow
169C23—91no—
170C2×C4—62no—
171C2×C4—91no—
172C2×C4—91no—
173C2×C4—91no—
174C2×C4—91no—
175C2×C4—91no—
176C2×C4D32⋊C411yescharacteristic
177C8—62no—
178C8—91no—
179C8—91no—
180C8D32⋊C411yescharacteristic
181C8#377311yescharacteristic
182C2×C3—22no—
183C2×C3—22no—
184C2×C3—21no—
185C2×C3—21no—
186D3—121no—
187D3—121no—
188D3—121no—
189D3—121no—
190C22—91no—
191C22—91no—
192C22—182no—
193C22D32⋊C811yescharacteristic
194C4—91no—
195C4—91no—
196C4—122no—
197C4D32⋊C811yescharacteristic
198C4#6373711yescharacteristic
199C3—21no—
200C3—21no—
201C2—181no—
202C2—181no—
203C2#1059001512yes—
204C2#1059004311yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2×C8GO+(4,𝔽2)
commutatorC3⋊Dic3C4×C8
FittingC2×C32×C8D4
socleC22×C32C22⋊C8
prime radicalC22×C3⋊D3M16
cosocleC2×C8×C3⋊D3C22
hypocenterC32#1379
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
9. #63764C4semidirect
14. #63544C4semidirect
168. C32#1379semidirect

Maximal subgroups

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

subgroupindex
C2×#637642
#105907002
C2×#635442
#13799