Finite Group Databasebeta

← #11782036

Subgroups — #11782036

Order 1152.

327 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 327 conjugacy classes of subgroups — too many to draw. Only its 88 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#10592723C211yesmaximal, characteristic
2C3×#5021C212yesmaximal
3#10590312C211yesmaximal, characteristic
4#10589098C211yesmaximal, characteristic
5#10589095C212yesmaximal
6#71153—32nomaximal
7C32×C4×Q8C2211yescharacteristic
8C3×#869C2212yes—
9C4⋊(C3⋊(C3⋊C8))—21no—
10C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
11#63630—21no—
12C4×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×#835—22no—
14C3×#807—22no—
15C3×C4⋊(C3⋊C8)C2212yes—
16#63576—21no—
17#63576—21no—
18C3×#477—32no—
19#5078—32no—
20#5024—32no—
21#5024—61no—
22#5021D312yes—
23#4546—32no—
24#4481—32no—
25#4480—32no—
26C2×C32×Q8D411yescharacteristic
27C2×C3×Dic6—22no—
28C32×C4⋊C4—21no—
29C32×C4⋊C4D411yescharacteristic
30C32×C42—21no—
31C32×C42C2311yescharacteristic
32C2×C3⋊(C3⋊C8)—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—
40C3×C4×Q8—21no—
41C3×C4×Q8C2×D312yes—
42#869C2×D312yes—
43C3×#107—62no—
44C3×C4⋊C8—32no—
45C3×#103—62no—
46#835—22no—
47#807—22no—
48#807—62no—
49#807—62no—
50C4⋊(C3⋊C8)—32no—
51C4⋊(C3⋊C8)—61no—
52C4⋊(C3⋊C8)—62no—
53C4⋊(C3⋊C8)—62no—
54C4⋊(C3⋊C8)C2×D312yes—
55#803—62no—
56#803—62no—
57C4×C3⋊C8—32no—
58C4×C3⋊C8—61no—
59C32×Q8—22no—
60C2×C32×C4—21no—
61C2×C32×C4—21no—
62C2×C32×C4C2×D411yescharacteristic
63C2×C32×C4C2×D411yescharacteristic
64C2×C32×C4#4111yescharacteristic
65C2×C3×Dic3—42no—
66C3×Dic6—82no—
67C3⋊(C3⋊C8)—21no—
68C3⋊(C3⋊C8)—41no—
69C3⋊(C3⋊C8)Q1612yes—
70C3×C3⋊C8—42no—
71#500—91no—
72#477—32no—
73#446—91no—
74#334—91no—
75#333—92no—
76C2×C3×Q8—21no—
77C2×C3×Q8—62no—
78C2×C3×Q8#6712yes—
79C2×Dic6—22no—
80C2×C3×C8—62no—
81C3×C4⋊C4—22no—
82C3×C4⋊C4—22no—
83C3×C4⋊C4—21no—
84C3×C4⋊C4—62no—
85C3×C4⋊C4—62no—
86C3×C4⋊C4#6712yes—
87C3×C42—22no—
88C3×C42—22no—
89C3×C42—21no—
90C3×C42C22×D312yes—
91C4⋊Dic3—22no—
92C4⋊Dic3—22no—
93C2×C3⋊C8—22no—
94C2×C3⋊C8—32no—
95C2×C3⋊C8—32no—
96C2×C3⋊C8—61no—
97C2×C3⋊C8—61no—
98C2×C3⋊C8—62no—
99C2×C3⋊C8—62no—
100C22×C32#12111yescharacteristic
101C32×C4—21no—
102C32×C4—41no—
103C32×C4—41no—
104C32×C4C2×Q1611yescharacteristic
105C32×C4#13711yescharacteristic
106C32×C4#13712yes—
107C3×Dic3—82no—
108C4⋊Q8—32no—
109C4×Q8D3211yescharacteristic
110#107—62no—
111#107—181no—
112#107—181no—
113C4⋊C8—32no—
114C4⋊C8—91no—
115C4⋊C8—181no—
116#103—62no—
117#97—181no—
118C4×C8—91no—
119C3×Q8—22no—
120C3×Q8—22no—
121C3×Q8—42no—
122C3×Q8—242no—
123C2×C3×C4—22no—
124C2×C3×C4—22no—
125C2×C3×C4—22no—
126C2×C3×C4—22no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—122no—
131C2×C3×C4D3×D412yes—
132C2×C3×C4#23712yes—
133C2×C3×C4C2×#6712yes—
134C2×Dic3—42no—
135Dic6—82no—
136C3×C8—122no—
137C3⋊C8—34no—
138C3⋊C8—42no—
139C3⋊C8—62no—
140C3⋊C8—62no—
141C3⋊C8—121no—
142C3⋊C8—122no—
143C3⋊C8—122no—
144C2×C32#46211yescharacteristic
145C2×C32#47011yescharacteristic
146C2×C32#47211yescharacteristic
147C2×Q8—62no—
148C2×Q8#62511yescharacteristic
149C2×C8—62no—
150C2×C8—91no—
151C2×C8—91no—
152C2×C8—181no—
153C4⋊C4—21no—
154C4⋊C4—62no—
155C4⋊C4—62no—
156C4⋊C4#62511yescharacteristic
157C42—21no—
158C42C2×D3211yescharacteristic
159C22×C3—21no—
160C22×C3#93912yes—
161C3×C4—22no—
162C3×C4—22no—
163C3×C4—21no—
164C3×C4—21no—
165C3×C4—41no—
166C3×C4—42no—
167C3×C4—42no—
168C3×C4—42no—
169C3×C4—42no—
170C3×C4—242no—
171C3×C4D3×Q1612yes—
172C3×C4#91812yes—
173C3×C4#94212yes—
174C3×C4#95112yes—
175Dic3—82no—
176C32#169611yescharacteristic, complemented, Sylow
177Q8—22no—
178Q8—242no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—122no—
182C2×C4#380511yescharacteristic
183C2×C4C2×#62511yescharacteristic
184C2×C4#381111yescharacteristic
185C8—92no—
186C8—122no—
187C8—181no—
188C8—361no—
189C2×C3—21no—
190C2×C3—21no—
191C2×C3—21no—
192C2×C3#505212yes—
193C2×C3#518212yes—
194C2×C3#519912yes—
195C22#6398011yescharacteristic
196C4—21no—
197C4—41no—
198C4—41no—
199C4—242no—
200C4#6382712yes—
201C4#6394411yescharacteristic
202C4#6394511yescharacteristic
203C3—21no—
204C3#7115312yescomplemented
205C2#1059118911yescharacteristic
206C2#1059163311yescharacteristic
207C2#1059167811yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socle, prime radicalC22×C32#121
hypercenterC4×Q8D32
hypocenterC32#1696
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
176. C32#1696semidirect
204. C3#71153semidirect

Maximal subgroups

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

subgroupindex
#105927232
C3×#50212
#105903122
#105890982
#105890952
#711533