Finite Group Databasebeta

← #11782032

Subgroups — #11782032

Order 1152.

329 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 329 conjugacy classes of subgroups — too many to draw. Only its 96 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
1#10592381C211yesmaximal, characteristic
2C3×#4679C211yesmaximal, characteristic
3#10590283C212yesmaximal
4C3×#4457C211yesmaximal, characteristic
5#10589096C212yesmaximal
6#70965—31nomaximal
7#68553—31nomaximal
8#64078C2212yes—
9C3×C4×Dic6C2211yescharacteristic
10C32×C4×C8C2211yescharacteristic
11#63645—21no—
12#63645—21no—
13C3×#815—21no—
14C3×Dic3⋊C8—21no—
15C3×C4⋊(C3⋊C8)C2212yes—
16C3×C4⋊(C3⋊C8)C2211yescharacteristic
17#63575—22no—
18#63566—22no—
19C3×#446—31no—
20#5021—32no—
21#4850—32no—
22#4682—31no—
23#4682—31no—
24#4682—61no—
25#4679D311yescharacteristic
26C3×#334—31no—
27#4481—32no—
28#4481—32no—
29#4457D311yescharacteristic
30C2×#634—22no—
31C2×C3×Dic6D411yescharacteristic
32C2×C32×C8D411yescharacteristic
33C2×C32×C8D411yescharacteristic
34C32×C42C2311yescharacteristic
35C4⋊(C3⋊Dic3)—22no—
36C4⋊(C3⋊Dic3)—22no—
37C3×C4⋊Dic3D411yescharacteristic
38C3×Dic3⋊C4—21no—
39C3×C4×Dic3—21no—
40C2×C3×C3⋊C8—22no—
41C2×C3×C3⋊C8—21no—
42#1696—91noSylow
43C3×C4×Q8—31no—
44#869—32no—
45#869—32no—
46#869—62no—
47C4×Dic6C2×D311yescharacteristic
48C3×C4⋊C8—31no—
49C3×C4⋊C8—32no—
50C3×C4⋊C8—61no—
51C3×#97—61no—
52C3×C4×C8—21no—
53C3×C4×C8C2×D311yescharacteristic
54C3×C4×C8C2×D311yescharacteristic
55#835—62no—
56#818—62no—
57#818—62no—
58#818—61no—
59#818—61no—
60#818—61no—
61#818—61no—
62#818—62no—
63#816—62no—
64#815—21no—
65Dic3⋊C8—21no—
66#807—62no—
67C4⋊(C3⋊C8)C2×D311yescharacteristic
68C4⋊(C3⋊C8)C2×D312yes—
69C2×C32×C4C2×D411yescharacteristic
70C2×C32×C4C2×D411yescharacteristic
71C2×C32×C4#4111yescharacteristic
72C2×C3⋊Dic3—42no—
73#634—82no—
74C2×C3×Dic3—21no—
75C2×C3×Dic3—21no—
76C3×Dic6—22no—
77C32×C8—21no—
78C32×C8Q1612yes—
79C3×C3⋊C8—42no—
80C3×C3⋊C8—41no—
81#500—91no—
82#477—92no—
83#446—31no—
84#334—31no—
85#333—92no—
86C2×C3×Q8—31no—
87C2×Dic6—62no—
88C2×Dic6—62no—
89C2×Dic6—122no—
90C2×Dic6D1211yescharacteristic
91C2×C3×C8—21no—
92C2×C3×C8—21no—
93C2×C3×C8—62no—
94C2×C3×C8—61no—
95C2×C3×C8D1211yescharacteristic
96C2×C3×C8D1211yescharacteristic
97C2×C3×C8#6711yescharacteristic
98C2×C3×C8#6711yescharacteristic
99C3×C4⋊C4—31no—
100C3×C4⋊C4—61no—
101C3×C42—21no—
102C3×C42—61no—
103C3×C42C22×D311yescharacteristic
104C3×C42C22×D311yescharacteristic
105C4⋊Dic3—64no—
106C4⋊Dic3—62no—
107C4⋊Dic3—62no—
108C4⋊Dic3—62no—
109C4⋊Dic3—62no—
110C4⋊Dic3—122no—
111C4⋊Dic3D1211yescharacteristic
112Dic3⋊C4—21no—
113C4×Dic3—21no—
114C2×C3⋊C8—22no—
115C2×C3⋊C8—21no—
116C22×C32#12111yescharacteristic
117C32×C4—21no—
118C32×C4C2×Q1611yescharacteristic
119C32×C4#13712yes—
120C32×C4#13711yescharacteristic
121C3⋊Dic3—82no—
122C3×Dic3—41no—
123C3×Dic3—41no—
124C4⋊Q8—92no—
125C4×Q8—31no—
126#107—182no—
127#107—181no—
128#107—181no—
129C4⋊C8—31no—
130C4⋊C8—32no—
131C4⋊C8—61no—
132#103—182no—
133#97—61no—
134C4×C8D3211yescharacteristic
135C3×Q8—62no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—61no—
140C2×C3×C4—61no—
141C2×C3×C4C2×D1211yescharacteristic
142C2×C3×C4C2×D1211yescharacteristic
143C2×C3×C4#23511yescharacteristic
144C2×C3×C4D3×D411yescharacteristic
145C2×C3×C4#23911yescharacteristic
146C2×C3×C4C2×#6711yescharacteristic
147C2×Dic3—21no—
148C2×Dic3—21no—
149C2×Dic3—124no—
150C2×Dic3—122no—
151C2×Dic3—122no—
152Dic6—22no—
153Dic6—244no—
154Dic6—242no—
155Dic6—242no—
156C3×C8—22no—
157C3×C8—21no—
158C3×C8—21no—
159C3×C8—22no—
160C3×C8—122no—
161C3×C8—121no—
162C3×C8Dic1212yes—
163C3×C8#21612yes—
164C3⋊C8—42no—
165C3⋊C8—41no—
166C2×C32#46211yescharacteristic
167C2×C32#47011yescharacteristic
168C2×C32#47211yescharacteristic
169C2×Q8—31no—
170C2×Q8—182no—
171C2×C8—62no—
172C2×C8—61no—
173C2×C8#62611yescharacteristic
174C2×C8#62611yescharacteristic
175C4⋊C4—31no—
176C4⋊C4—61no—
177C4⋊C4—182no—
178C4⋊C4—182no—
179C42—61no—
180C42C2×D3211yescharacteristic
181C22×C3—21no—
182C22×C3#89511yescharacteristic
183C22×C3#93011yescharacteristic
184C3×C4—22no—
185C3×C4—21no—
186C3×C4—21no—
187C3×C4—22no—
188C3×C4—21no—
189C3×C4—21no—
190C3×C4—121no—
191C3×C4—121no—
192C3×C4C2×Dic1211yescharacteristic
193C3×C4#90912yes—
194C3×C4#90911yescharacteristic
195C3×C4#91512yes—
196C3×C4C2×#21611yescharacteristic
197C3×C4#95111yescharacteristic
198Dic3—41no—
199Dic3—41no—
200Dic3—244no—
201Dic3—242no—
202Dic3—242no—
203C32#169611yescharacteristic, complemented, Sylow
204Q8—62no—
205Q8—722no—
206C2×C4—61no—
207C2×C4—61no—
208C2×C4—362no—
209C2×C4#379911yescharacteristic
210C2×C4D3×D1211yescharacteristic
211C2×C4C2×#62611yescharacteristic
212C8—21no—
213C8—122no—
214C8—121no—
215C8#371912yes—
216C2×C3—21no—
217C2×C3—21no—
218C2×C3—21no—
219C2×C3#484911yescharacteristic
220C2×C3#486711yescharacteristic
221C2×C3#489711yescharacteristic
222C2×C3#503111yescharacteristic
223C2×C3#513711yescharacteristic
224C2×C3#514211yescharacteristic
225C22#6390911yescharacteristic
226C4—21no—
227C4—121no—
228C4—121no—
229C4—722no—
230C4#6380012yes—
231C4#6383111yescharacteristic
232C4C2×#371911yescharacteristic
233C3—21no—
234C3#6855311yescharacteristic, complemented
235C3#7096511yescharacteristic, complemented
236C2#1059038511yescharacteristic
237C2#1059085311yescharacteristic
238C2#1059092711yescharacteristic
subgroupG/H
centerC22#63909
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32#121
hypercenterC4×C8D32
hypocenterC32#1696
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
203. C32#1696semidirect
234. C3#68553semidirect
235. C3#70965semidirect

Maximal subgroups

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

subgroupindex
#105923812
C3×#46792
#105902832
C3×#44572
#105890962
#709653
#685533