Finite Group Databasebeta

← #11796749

Subgroups — #11796749

Order 1152.

394 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 61 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×#63802C211yesmaximal, characteristic
2#10593768C211yesmaximal, characteristic
3#10590625C211yesmaximal, characteristic
4#10590017C214yesmaximal, complemented
5C2×#3797—21no—
6#64286—21no—
7C2×C8×C3⋊D3C2211yescharacteristic
8C2×C3×Dic12—21no—
9C2×#3718C412yescomplemented
10#63802—21no—
11#63802—21no—
12#63802C412yescomplemented
13#63802C2212yes—
14#63769C2212yes—
15#63768—21no—
16C3×#812—21no—
17#63544—21no—
18#63542C2212yes—
19C2×D3×Q16—61no—
20D3×M32—61no—
21C2×C4×C3⋊D3D411yescharacteristic
22C2×C3×Dic6—22no—
23C2×#627—41no—
24C2×#624—41no—
25#3797—22no—
26#3797—22no—
27#3797—41no—
28#3797—41no—
29C22⋊#157—41no—
30C4⋊#157—22no—
31C4×#157—41no—
32C2×C32×C8D411yescharacteristic
33C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
34C8×C3⋊D3C2×C411yescharacteristic
35C8×C3⋊D3D411yescharacteristic
36C8×C3⋊D3D411yescharacteristic
37C8×C3⋊D3C2311yescharacteristic
38C3×Dic12—22no—
39C3×Dic12—22no—
40#3718—22no—
41#3718C2×C414yes—
42C3×C3⋊C16—22no—
43#2141—91nomaximal, Sylow
44C2×D3×Q8—62no—
45C2×C3×Q16—61no—
46C2×#216—62no—
47D3×Q16—62no—
48D3×Q16—62no—
49D3×Q16—62no—
50D3×Q16—62no—
51C2×Dic12—21no—
52C2×D3×C8—61no—
53C2×D3×C8—61no—
54C3×M32—61no—
55#812—21no—
56#798—62no—
57D3×C16—62no—
58C22×C3⋊D3D811yescharacteristic
59C2×#157—42no—
60C2×C32×C4C22⋊C411yescharacteristic
61C2×C3⋊Dic3SD1611yescharacteristic
62C4×C3⋊D3C22⋊C411yescharacteristic
63C4×C3⋊D3D811yescharacteristic
64C4×C3⋊D3SD1611yescharacteristic
65C4×C3⋊D3C2×D411yescharacteristic
66C2×C3×Dic3—42no—
67C3×Dic6—24no—
68C3×Dic6—42no—
69#627—42no—
70#627—42no—
71#624—42no—
72#624—42no—
73C32×C8C22⋊C411yescharacteristic
74C32×C8C2×D411yescharacteristic
75C3⋊(C3⋊C8)C22⋊C411yescharacteristic
76C3⋊(C3⋊C8)C22×C411yescharacteristic
77C22×Q16—91no—
78C2×M32—91no—
79#427—91no—
80#358—94no—
81C2×C3×Q8—62no—
82D3×Q8—64no—
83D3×Q8—64no—
84D3×Q8—122no—
85D3×Q8—122no—
86C2×C4×D3—61no—
87C2×C4×D3—61no—
88C2×C4×D3—122no—
89C2×Dic6—22no—
90C2×Dic6—122no—
91C3×Q16—62no—
92C3×Q16—62no—
93C2×C3×C8—21no—
94C2×C3×C8—21no—
95#216—64no—
96#216—64no—
97C2×C3⋊C8—61no—
98C2×C3⋊C8—61no—
99Dic12—22no—
100Dic12—22no—
101D3×C8—61no—
102D3×C8—61no—
103D3×C8—61no—
104D3×C8—61no—
105D3×C8—61no—
106D3×C8—61no—
107D3×C8—61no—
108D3×C8—61no—
109C3×C16—62no—
110C3⋊C16—22no—
111C22×C32#10211yescharacteristic
112C2×C3⋊D3—22no—
113C2×C3⋊D3#10211yescharacteristic
114C2×C3⋊D3C2×D811yescharacteristic
115#157—82no—
116C32×C4#10211yescharacteristic
117C32×C4C2×C22⋊C411yescharacteristic
118C3⋊Dic3#10211yescharacteristic
119C3⋊Dic3C2×SD1611yescharacteristic
120C3×Dic3—44no—
121C22×Q8—181no—
122C2×Q16—61no—
123C2×Q16—92no—
124C2×Q16—92no—
125C2×Q16—92no—
126C2×Q16—181no—
127C2×Q16—181no—
128C22×C8—91no—
129#117—181no—
130M32—61no—
131M32—181no—
132C2×C16—92no—
133#107—92no—
134#106—181no—
135C22×D3—61no—
136C22×D3—61no—
137C3×Q8—64no—
138C3×Q8—122no—
139C2×C3×C4—21no—
140C2×C3×C4—21no—
141C2×C3×C4—122no—
142C2×Dic3—42no—
143C2×Dic3—61no—
144C2×Dic3—61no—
145C4×D3—61no—
146C4×D3—61no—
147C4×D3—61no—
148C4×D3—61no—
149C4×D3—61no—
150C4×D3—61no—
151C4×D3—61no—
152C4×D3—61no—
153C4×D3—124no—
154C4×D3—124no—
155Dic6—24no—
156Dic6—42no—
157Dic6—124no—
158Dic6—124no—
159C3×C8—21no—
160C3×C8—21no—
161C3×C8—21no—
162C3×C8—21no—
163C3⋊C8—61no—
164C3⋊C8—61no—
165C3⋊C8—61no—
166C3⋊C8—61no—
167C2×C32—21no—
168C2×C32C2×#10211yescharacteristic
169C3⋊D3—21no—
170C3⋊D3#51012yes—
171C2×Q8—62no—
172C2×Q8—182no—
173C2×Q8—182no—
174C2×Q8—361no—
175C2×Q8—361no—
176C2×Q8—361no—
177C22×C4—91no—
178C22×C4—361no—
179Q16—62no—
180Q16—62no—
181Q16—94no—
182Q16—182no—
183C2×C8—91no—
184C2×C8—91no—
185C2×C8—91no—
186C2×C8—91no—
187C2×C8—91no—
188C2×C8GO+(4,𝔽2)11yescharacteristic
189C4⋊C4—182no—
190C22⋊C4—361no—
191C42—361no—
192C16—62no—
193C22×C3—21no—
194C22×C3—21no—
195C2×D3—61no—
196C2×D3—61no—
197C2×D3—61no—
198C2×D3—61no—
199C2×D3—64no—
200C2×D3—122no—
201C3×C4—21no—
202C3×C4—21no—
203C3×C4—21no—
204C3×C4—21no—
205C3×C4—124no—
206Dic3—44no—
207Dic3—61no—
208Dic3—61no—
209Dic3—61no—
210Dic3—61no—
211C32#214111yescharacteristic, complemented, Sylow
212C23—91no—
213Q8—64no—
214Q8—122no—
215Q8—362no—
216Q8—362no—
217C2×C4—91no—
218C2×C4—91no—
219C2×C4—91no—
220C2×C4—91no—
221C2×C4—91no—
222C2×C4—122no—
223C2×C4—362no—
224C2×C4—362no—
225C2×C4—362no—
226C2×C4D32⋊C411yescharacteristic
227C8—91no—
228C8—91no—
229C8D32⋊C411yescharacteristic
230C8C2×GO+(4,𝔽2)11yescharacteristic
231C2×C3—22no—
232C2×C3—21no—
233C2×C3—21no—
234C2×C3—41no—
235D3—62no—
236D3—62no—
237D3—62no—
238D3—121no—
239C22—91no—
240C22—91no—
241C22—182no—
242C22#6372911yescharacteristic
243C4—91no—
244C4—91no—
245C4—124no—
246C4—722no—
247C4#6372911yescharacteristic
248C4C2×D32⋊C411yescharacteristic
249C3—21no—
250C3—21no—
251C2—21no—
252C2—92no—
253C2—181no—
254C2C2×#6372911yescharacteristic
subgroupG/H
centerC2C2×#63729
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC8C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32C2×#102
prime radicalC22×C3⋊D3D8
cosocleC8×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2141
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
4. #10590017C2semidirect
9. C2×#3718C4semidirect
12. #63802C4semidirect
211. C32#2141semidirect

Maximal subgroups

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

subgroupindex
C2×#638022
#105937682
#105906252
#105900172
#21419