Finite Group Databasebeta

← #11790116

Subgroups — #11790116

Order 1152.

394 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 79 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×#63768C211yesmaximal, characteristic
2#10593412C212yesmaximal
3#10590685C211yesmaximal, characteristic
4C8×#624C211yesmaximal, characteristic
5#10590049C212yesmaximal
6C2×C4⋊#157C2212yes—
7C2×#3773—22no—
8C2×C8×C3⋊D3C2211yescharacteristic
9#63900C2212yes—
10C4×#624C2211yescharacteristic
11C2×#3710C2211yescharacteristic
12#63768C414yescomplemented
13#63737—22no—
14C3×#817—21no—
15C3×C8×Dic3—21no—
16#63574—21no—
17Dic3×C3⋊C8—21no—
18D3×#106—61no—
19C4×D3×C8—61no—
20C22×#157—22no—
21C2×C4×C3⋊D3C2311yescharacteristic
22C2×#624—22no—
23C2×#624D412yes—
24C4⋊#157—22no—
25C4⋊#157C2×C414yes—
26#3773—44no—
27C2×C32×C8D411yescharacteristic
28C2×C3⋊(C3⋊C8)D411yescharacteristic
29C8×C3⋊D3C2×C412yes—
30C8×C3⋊D3Q812yes—
31C3×C4⋊Dic3—22no—
32C3×C4×Dic3—21no—
33C2×C3×C3⋊C8—21no—
34#3724—22no—
35Dic32—21no—
36#3710—21no—
37#3710Q812yes—
38#1941—91nomaximal, Sylow
39C2×D3×C8—61no—
40C2×D3×C8—61no—
41C2×D3×C8—61no—
42D3×C4⋊C4—62no—
43C42×D3—61no—
44C3×#106—61no—
45C3×C4×C8—61no—
46#817—21no—
47C8×Dic3—21no—
48C8×Dic3—61no—
49#808—62no—
50C4×C3⋊C8—61no—
51C22×C3⋊D3C2×D411yescharacteristic
52C2×#157—24no—
53C2×#157—42no—
54C2×#157—42no—
55C2×C32×C4C2×D411yescharacteristic
56C2×C3⋊Dic3#4111yescharacteristic
57C4×C3⋊D3C22×C411yescharacteristic
58C4×C3⋊D3C2×Q811yescharacteristic
59C4×C3⋊D3C2×Q811yescharacteristic
60C4×C3⋊D3#4111yescharacteristic
61C2×C3×Dic3—22no—
62C2×C3×Dic3—42no—
63#624—22no—
64#624—42no—
65#624—42no—
66#624SD1614yes—
67C32×C8C4⋊C412yescomplemented
68C3⋊(C3⋊C8)C4⋊C412yescomplemented
69C3×C3⋊C8—22no—
70C2×#106—91no—
71C2×#106—91no—
72C2×C4×C8—91no—
73#389—92no—
74#340—92no—
75C2×C4×D3—62no—
76C2×C4×D3—61no—
77C2×C4×D3—61no—
78C2×C4×D3—122no—
79C2×C3×C8—21no—
80C2×C3×C8—21no—
81C2×C3×C8—61no—
82C3×C4⋊C4—62no—
83C3×C42—61no—
84C4⋊Dic3—22no—
85Dic3⋊C4—122no—
86C4×Dic3—21no—
87C4×Dic3—62no—
88C2×C3⋊C8—21no—
89C2×C3⋊C8—61no—
90C2×C3⋊C8—61no—
91D3×C8—62no—
92D3×C8—62no—
93D3×C8—62no—
94D3×C8—62no—
95D3×C8—62no—
96D3×C8—62no—
97C22×C32#12111yescharacteristic
98C2×C3⋊D3C4×D411yescharacteristic
99C2×C3⋊D3C4⋊Q811yescharacteristic
100C2×C3⋊D3C2×SD1612yes—
101C2×C3⋊D3#13512yes—
102#157—44no—
103C32×C4C2×C4⋊C411yescharacteristic
104C32×C4C22⋊Q811yescharacteristic
105C3⋊Dic3C4×Q811yescharacteristic
106C3⋊Dic3#12511yescharacteristic
107C3×Dic3—24no—
108C3×Dic3—82no—
109C22×C8—91no—
110C22×C8—91no—
111C2×C4⋊C4—92no—
112C2×C4⋊C4—92no—
113C2×C4⋊C4—182no—
114C2×C42—91no—
115#106—61no—
116#106—94no—
117#106—181no—
118C4×C8—61no—
119C4×C8—181no—
120#95—182no—
121C22×D3—61no—
122C22×D3—61no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—62no—
126C2×C3×C4—122no—
127C2×Dic3—22no—
128C2×Dic3—42no—
129C2×Dic3—61no—
130C2×Dic3—61no—
131C4×D3—64no—
132C4×D3—61no—
133C4×D3—61no—
134C4×D3—61no—
135C4×D3—61no—
136C4×D3—61no—
137C4×D3—61no—
138C4×D3—61no—
139C4×D3—61no—
140C4×D3—64no—
141C4×D3—242no—
142C4×D3—242no—
143C3×C8—22no—
144C3×C8—22no—
145C3×C8—62no—
146C3⋊C8—22no—
147C3⋊C8—62no—
148C3⋊C8—62no—
149C2×C32#38911yescharacteristic
150C2×C32#46512yes—
151C3⋊D3C4×SD1612yes—
152C3⋊D3#49811yescharacteristic
153C3⋊D3#49911yescharacteristic
154C22×C4—92no—
155C22×C4—91no—
156C22×C4—182no—
157C22×C4—182no—
158C2×C8—61no—
159C2×C8—92no—
160C2×C8—91no—
161C2×C8—92no—
162C2×C8—92no—
163C2×C8—181no—
164C2×C8GO+(4,𝔽2)11yescharacteristic
165C4⋊C4—62no—
166C4⋊C4—94no—
167C4⋊C4—182no—
168C4⋊C4—182no—
169C4⋊C4—364no—
170C42—61no—
171C42—181no—
172C22×C3—21no—
173C22×C3—21no—
174C2×D3—61no—
175C2×D3—61no—
176C2×D3—61no—
177C2×D3—61no—
178C2×D3—62no—
179C2×D3—62no—
180C2×D3—62no—
181C2×D3—62no—
182C3×C4—21no—
183C3×C4—21no—
184C3×C4—21no—
185C3×C4—21no—
186C3×C4—64no—
187C3×C4—242no—
188Dic3—24no—
189Dic3—61no—
190Dic3—61no—
191Dic3—61no—
192Dic3—61no—
193Dic3—82no—
194C32#194111yescharacteristic, complemented, Sylow
195C23—91no—
196C2×C4—62no—
197C2×C4—94no—
198C2×C4—91no—
199C2×C4—91no—
200C2×C4—91no—
201C2×C4—91no—
202C2×C4—91no—
203C2×C4—122no—
204C2×C4—182no—
205C2×C4—184no—
206C2×C4—362no—
207C2×C4—362no—
208C2×C4—362no—
209C2×C4—362no—
210C2×C4C2×GO+(4,𝔽2)11yescharacteristic
211C8—62no—
212C8—92no—
213C8#377312yescomplemented
214C2×C3—22no—
215C2×C3—22no—
216C2×C3—21no—
217C2×C3—21no—
218D3—62no—
219D3—62no—
220D3—61no—
221D3—61no—
222D3—61no—
223D3—61no—
224C22—92no—
225C22—92no—
226C22—91no—
227C22—91no—
228C22#6423011yescharacteristic
229C4—64no—
230C4—91no—
231C4—91no—
232C4—242no—
233C4—364no—
234C4D32⋊Q811yescharacteristic
235C4C2×#377311yescharacteristic
236C3—21no—
237C3—21no—
238C2—92no—
239C2—91no—
240C2—91no—
241C2#1059328412yes—
242C2#1059341211yescharacteristic
subgroupG/H
centerC22#64230
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1941
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
12. #63768C4semidirect
67. C32×C8C4⋊C4semidirect
68. C3⋊(C3⋊C8)C4⋊C4semidirect
194. C32#1941semidirect
213. C8#3773semidirect

Maximal subgroups

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

subgroupindex
C2×#637682
#105934122
#105906852
C8×#6242
#105900492
#19419