Finite Group Databasebeta

← #11782041

Subgroups — #11782041

Order 1152.

327 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 327 conjugacy classes of subgroups — too many to draw. Only its 82 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#10592530C211yesmaximal, characteristic
2#10590312C211yesmaximal, characteristic
3#10590284C212yesmaximal
4C3×#4481C212yesmaximal
5#10589098C211yesmaximal, characteristic
6#68513—32nomaximal
7C4×#634C2211yescharacteristic
8C3×#869C2212yes—
9C32×C4⋊C8C2211yescharacteristic
10#63642—21no—
11#63641—21no—
12C4×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×C4⋊(C3⋊C8)C2212yes—
14#63576—21no—
15#63576—21no—
16#63575—22no—
17#63567—22no—
18#5091—32no—
19#5078—32no—
20#4850—32no—
21#4831—32no—
22#4831—61no—
23C3×#333—32no—
24#4481D312yes—
25#4480—32no—
26C2×#634D411yescharacteristic
27C2×C3×Dic6—22no—
28C2×C32×C8—21no—
29C32×C42C2311yescharacteristic
30C4⋊(C3⋊Dic3)D411yescharacteristic
31#3750—21no—
32C4×C3⋊Dic3—21no—
33C2×C3⋊(C3⋊C8)D411yescharacteristic
34C2×C3⋊(C3⋊C8)D411yescharacteristic
35C3×C4⋊Dic3—22no—
36C3×C4⋊Dic3—22no—
37C2×C3×C3⋊C8—22no—
38#1696—91noSylow
39C3×C4⋊Q8—32no—
40#869C2×D312yes—
41C4×Dic6—32no—
42C4×Dic6—61no—
43C3×C4⋊C8—21no—
44C3×C4⋊C8—32no—
45C3×C4⋊C8C2×D312yes—
46#818—62no—
47#816—62no—
48#815—62no—
49#815—62no—
50Dic3⋊C8—62no—
51Dic3⋊C8—62no—
52#810—62no—
53#807—62no—
54#807—62no—
55#807—62no—
56C4⋊(C3⋊C8)C2×D312yes—
57C4×C3⋊C8—32no—
58C4×C3⋊C8—61no—
59C2×C32×C4C2×D411yescharacteristic
60C2×C32×C4C2×D411yescharacteristic
61C2×C32×C4#4111yescharacteristic
62C2×C3⋊Dic3—21no—
63C2×C3⋊Dic3—21no—
64#634—22no—
65C2×C3×Dic3—42no—
66C3×Dic6—82no—
67C32×C8—41no—
68C3⋊(C3⋊C8)—21no—
69C3⋊(C3⋊C8)Q1612yes—
70C3×C3⋊C8—42no—
71#500—91no—
72#477—92no—
73#446—91no—
74#334—91no—
75#333—32no—
76C2×C3×Q8—62no—
77C2×Dic6—22no—
78C2×Dic6—32no—
79C2×Dic6—61no—
80C2×C3×C8—22no—
81C2×C3×C8—22no—
82C2×C3×C8—62no—
83C3×C4⋊C4—62no—
84C3×C4⋊C4—62no—
85C3×C42—21no—
86C3×C42C22×D312yes—
87C4⋊Dic3—22no—
88C4⋊Dic3—22no—
89C4⋊Dic3—32no—
90C4⋊Dic3—61no—
91Dic3⋊C4—62no—
92Dic3⋊C4—62no—
93C4×Dic3—62no—
94C4×Dic3—62no—
95C2×C3⋊C8—22no—
96C2×C3⋊C8—32no—
97C2×C3⋊C8—32no—
98C2×C3⋊C8—61no—
99C2×C3⋊C8—61no—
100C22×C32#12111yescharacteristic
101C32×C4—21no—
102C32×C4C2×Q1611yescharacteristic
103C32×C4#13711yescharacteristic
104C32×C4#13712yes—
105C3⋊Dic3—41no—
106C3⋊Dic3—41no—
107C3×Dic3—82no—
108C4⋊Q8—32no—
109C4×Q8—91no—
110#107—181no—
111#107—181no—
112#107—182no—
113C4⋊C8—32no—
114C4⋊C8—181no—
115C4⋊C8D3211yescharacteristic
116#103—182no—
117#97—181no—
118C4×C8—91no—
119C3×Q8—242no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4—21no—
123C2×C3×C4—122no—
124C2×C3×C4#23512yes—
125C2×C3×C4D3×D412yes—
126C2×C3×C4D3×D412yes—
127C2×Dic3—42no—
128C2×Dic3—62no—
129C2×Dic3—62no—
130C2×Dic3—62no—
131C2×Dic3—62no—
132Dic6—62no—
133Dic6—62no—
134Dic6—82no—
135Dic6—122no—
136C3×C8—42no—
137C3×C8—42no—
138C3×C8—122no—
139C3⋊C8—34no—
140C3⋊C8—42no—
141C3⋊C8—62no—
142C3⋊C8—62no—
143C3⋊C8—121no—
144C2×C32#46211yescharacteristic
145C2×C32#47011yescharacteristic
146C2×C32#47211yescharacteristic
147C2×Q8—62no—
148C2×Q8—91no—
149C2×C8—21no—
150C2×C8—62no—
151C2×C8—91no—
152C2×C8—91no—
153C4⋊C4—62no—
154C4⋊C4—62no—
155C4⋊C4—91no—
156C4⋊C4—181no—
157C42—181no—
158C42C2×D3211yescharacteristic
159C22×C3—21no—
160C22×C3#88412yes—
161C3×C4—22no—
162C3×C4—22no—
163C3×C4—21no—
164C3×C4—21no—
165C3×C4—41no—
166C3×C4—242no—
167C3×C4#91512yes—
168C3×C4#91512yes—
169C3×C4D3×Q1612yes—
170C3×C4#91812yes—
171Dic3—82no—
172Dic3—122no—
173Dic3—122no—
174Dic3—122no—
175Dic3—122no—
176C32#169611yescharacteristic, complemented, Sylow
177Q8—182no—
178Q8—242no—
179C2×C4—122no—
180C2×C4—181no—
181C2×C4—181no—
182C2×C4#379811yescharacteristic
183C2×C4#380211yescharacteristic
184C2×C4#381111yescharacteristic
185C8—41no—
186C8—92no—
187C8—122no—
188C8—181no—
189C2×C3—21no—
190C2×C3—21no—
191C2×C3—21no—
192C2×C3#474912yes—
193C2×C3#479512yes—
194C2×C3#481612yes—
195C22#6391211yescharacteristic
196C4—21no—
197C4—242no—
198C4—361no—
199C4—361no—
200C4#6381112yes—
201C4#6393111yescharacteristic
202C4#6394411yescharacteristic
203C3—21no—
204C3#6851312yescomplemented
205C2#1059056611yescharacteristic
206C2#1059085611yescharacteristic
207C2#1059098811yescharacteristic
subgroupG/H
centerC22#63912
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
176. C32#1696semidirect
204. C3#68513semidirect

Maximal subgroups

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

subgroupindex
#105925302
#105903122
#105902842
C3×#44812
#105890982
#685133