Finite Group Databasebeta

← #11790475

Subgroups — #11790475

Order 1152.

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

normal subgroups only

This group has 326 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×#63771C211yesmaximal, characteristic
2#10593394C212yesmaximal
3#10590703C211yesmaximal, characteristic
4#10590685C211yesmaximal, characteristic
5#10590052C212yesmaximal
6C2×#3788C2212yes—
7C2×C8×C3⋊D3C2211yescharacteristic
8#63900C2212yes—
9#63874C2211yescharacteristic
10C2×#3712C2211yescharacteristic
11#63771C414yescomplemented
12#63743—22no—
13#63742—22no—
14C3×#817—21no—
15C3×#815—21no—
16#63574—21no—
17Dic3×C3⋊C8—21no—
18D3×#106—61no—
19#4708—61no—
20C2×C4×C3⋊D3C2311yescharacteristic
21C2×#624—22no—
22C2×#622—22no—
23#3788—22no—
24#3788C2×C414yes—
25C2×C32×C8D411yescharacteristic
26C2×C3⋊(C3⋊C8)D411yescharacteristic
27C8×C3⋊D3C2×C412yes—
28C8×C3⋊D3Q812yes—
29C3×C4⋊Dic3—22no—
30C3×C4×Dic3—21no—
31C2×C3×C3⋊C8—21no—
32#3724—22no—
33#3724D412yes—
34#3722—21no—
35#3712—21no—
36#3712Q812yes—
37#1951—91nomaximal, Sylow
38C2×ΓL(1,𝔽25)—61no—
39C2×D3×C8—61no—
40C2×D3×C8—61no—
41D3×C4⋊C4—62no—
42#872—61no—
43C3×#106—61no—
44C3×#97—61no—
45#817—21no—
46#815—21no—
47C8×Dic3—61no—
48#808—62no—
49C4×C3⋊C8—61no—
50C22×C3⋊D3#4111yescharacteristic
51C2×C32×C4C2×D411yescharacteristic
52C2×C3⋊Dic3C2×D411yescharacteristic
53C4×C3⋊D3C22×C411yescharacteristic
54C4×C3⋊D3C2×Q811yescharacteristic
55C4×C3⋊D3C2×Q811yescharacteristic
56C4×C3⋊D3#4111yescharacteristic
57C2×C3×Dic3—22no—
58C2×C3×Dic3—42no—
59#624—82no—
60#622—24no—
61C32×C8C4⋊C412yes—
62C3⋊(C3⋊C8)C4⋊C412yes—
63C3×C3⋊C8—22no—
64C2×#108—91no—
65#428—92no—
66C2×#106—91no—
67#405—91no—
68#343—92no—
69C2×C4×D3—61no—
70C2×C4×D3—61no—
71C2×C4×D3—122no—
72C2×C3×C8—21no—
73C2×C3×C8—21no—
74C2×C3×C8—61no—
75C3×C4⋊C4—62no—
76C3×C42—61no—
77(C2×D3)⋊C4—62no—
78C4⋊Dic3—22no—
79Dic3⋊C4—62no—
80Dic3⋊C4—122no—
81C4×Dic3—21no—
82C2×C3⋊C8—21no—
83C2×C3⋊C8—61no—
84C2×C3⋊C8—61no—
85ΓL(1,𝔽25)—62no—
86ΓL(1,𝔽25)—62no—
87D3×C8—62no—
88D3×C8—62no—
89D3×C8—62no—
90D3×C8—62no—
91C22×C32#12111yescharacteristic
92C2×C3⋊D3—22no—
93C2×C3⋊D3C4×Q811yescharacteristic
94C2×C3⋊D3#12511yescharacteristic
95C32×C4C2×C4⋊C411yescharacteristic
96C32×C4C22⋊Q811yescharacteristic
97C3⋊Dic3C4×D411yescharacteristic
98C3⋊Dic3C4⋊Q811yescharacteristic
99C3×Dic3—42no—
100C3×Dic3—82no—
101C2×M16—91no—
102C2×M16—92no—
103C22×C8—91no—
104#117—91no—
105C2×C4⋊C4—92no—
106#108—94no—
107#107—182no—
108#106—61no—
109#106—181no—
110#106—182no—
111#97—61no—
112C4×C8—181no—
113C22×D3—61no—
114C22×D3—61no—
115C2×C3×C4—21no—
116C2×C3×C4—21no—
117C2×C3×C4—62no—
118C2×C3×C4—122no—
119C2×Dic3—22no—
120C2×Dic3—42no—
121C2×Dic3—61no—
122C2×Dic3—61no—
123C4×D3—61no—
124C4×D3—61no—
125C4×D3—61no—
126C4×D3—61no—
127C4×D3—61no—
128C4×D3—61no—
129C4×D3—61no—
130C4×D3—61no—
131C4×D3—244no—
132C3×C8—22no—
133C3×C8—22no—
134C3×C8—62no—
135C3⋊C8—22no—
136C3⋊C8—62no—
137C3⋊C8—62no—
138C2×C32#38911yescharacteristic
139C2×C32#47112yes—
140C3⋊D3—21no—
141C3⋊D3—21no—
142C22×C4—91no—
143C22×C4—182no—
144M16—92no—
145M16—94no—
146M16—181no—
147M16—182no—
148C2×C8—61no—
149C2×C8—91no—
150C2×C8—92no—
151C2×C8—92no—
152C2×C8—182no—
153C2×C8GO+(4,𝔽2)11yescharacteristic
154C4⋊C4—62no—
155C4⋊C4—92no—
156C4⋊C4—182no—
157C22⋊C4—181no—
158C42—61no—
159C22×C3—21no—
160C22×C3—21no—
161C2×D3—61no—
162C2×D3—61no—
163C2×D3—61no—
164C2×D3—61no—
165C2×D3—64no—
166C2×D3—122no—
167C3×C4—21no—
168C3×C4—21no—
169C3×C4—21no—
170C3×C4—21no—
171C3×C4—122no—
172C3×C4—242no—
173Dic3—42no—
174Dic3—61no—
175Dic3—61no—
176Dic3—61no—
177Dic3—61no—
178Dic3—82no—
179C32#195111yescharacteristic, complemented, Sylow
180C23—91no—
181C2×C4—62no—
182C2×C4—91no—
183C2×C4—91no—
184C2×C4—91no—
185C2×C4—91no—
186C2×C4—91no—
187C2×C4—122no—
188C2×C4—722no—
189C2×C4C2×GO+(4,𝔽2)11yescharacteristic
190C8—62no—
191C8—92no—
192C8—184no—
193C8#377312yes—
194C2×C3—22no—
195C2×C3—22no—
196C2×C3—21no—
197C2×C3—21no—
198D3—62no—
199D3—62no—
200D3—121no—
201D3—121no—
202C22—91no—
203C22—91no—
204C22—182no—
205C22#6423011yescharacteristic
206C4—91no—
207C4—91no—
208C4—122no—
209C4—242no—
210C4D32⋊Q811yescharacteristic
211C4C2×#377311yescharacteristic
212C3—21no—
213C3—21no—
214C2—181no—
215C2—181no—
216C2#1059330212yes—
217C2#1059341211yescharacteristic
subgroupG/H
centerC22#64230
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
prime radicalC22×C3⋊D3#41
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1951
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
11. #63771C4semidirect
179. C32#1951semidirect

Maximal subgroups

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

subgroupindex
C2×#637712
#105933942
#105907032
#105906852
#105900522
#19519