Finite Group Databasebeta

← #11782003

Subgroups — #11782003

Order 1152.

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

normal subgroups only

This group has 369 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#10592711C211yesmaximal, characteristic
2C3×#5008C212yesmaximal
3#10590312C211yesmaximal, characteristic, complemented
4#10589098C211yesmaximal, characteristic, complemented
5#10589095C212yesmaximal, complemented
6#71137—32nomaximal
7C32×C4×D4C2211yescharacteristic
8C2×#3748—21no—
9C3×#869C2212yes—
10#63657—21no—
11C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
12C4×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×#832—22no—
14C3×#808—22no—
15C3×C4⋊(C3⋊C8)C2212yes—
16#63576—21no—
17#63576—21no—
18C3×#476—32no—
19#5078—32no—
20#5012—32no—
21#5012—61no—
22#5008D312yes—
23#4546—32no—
24#4481—32no—
25#4480—32no—
26C2×C32×D4D411yescharacteristic
27C22×C32×C4—21no—
28C2×C3×Dic6—22no—
29C32×C4⋊C4D411yescharacteristic
30C32×C22⋊C4—21no—
31C32×C42C2311yescharacteristic
32#3748—42no—
33C2×C3⋊(C3⋊C8)—21no—
34C2×C3⋊(C3⋊C8)D411yescharacteristic
35C2×C3⋊(C3⋊C8)D411yescharacteristic
36C3×C4⋊Dic3—22no—
37C3×C4⋊Dic3—22no—
38C2×C3×C3⋊C8—22no—
39#1695—91noSylow
40C3×C4⋊Q8—32no—
41C3×C4×D4—21no—
42C3×C4×D4C2×D312yes—
43C2×#208—62no—
44C2×#208—62no—
45#869C2×D312yes—
46C3×#106—62no—
47C3×C4⋊C8—32no—
48C3×#102—62no—
49#832—22no—
50#830—62no—
51#830—62no—
52#808—22no—
53#807—62no—
54#807—62no—
55C4⋊(C3⋊C8)—32no—
56C4⋊(C3⋊C8)—61no—
57C4⋊(C3⋊C8)C2×D312yes—
58C4×C3⋊C8—32no—
59C4×C3⋊C8—61no—
60C23×C32—21no—
61C32×D4—22no—
62C2×C32×C4—21no—
63C2×C32×C4—41no—
64C2×C32×C4—41no—
65C2×C32×C4C2×D411yescharacteristic
66C2×C32×C4C2×D411yescharacteristic
67C2×C32×C4#4111yescharacteristic
68C2×C3×Dic3—42no—
69C3×Dic6—82no—
70C3⋊(C3⋊C8)—21no—
71C3⋊(C3⋊C8)—41no—
72C3⋊(C3⋊C8)SD1612yes—
73C3×C3⋊C8—42no—
74#500—91no—
75#476—32no—
76#436—91no—
77#334—91no—
78#333—92no—
79C2×C3×Q8—62no—
80C2×C3×D4—21no—
81C2×C3×D4#6712yes—
82C22×C3×C4—22no—
83C22×C3×C4—22no—
84C2×Dic6—22no—
85C2×C3×C8—62no—
86C3×C4⋊C4—21no—
87C3×C4⋊C4—62no—
88C3×C4⋊C4—62no—
89C3×C4⋊C4#6712yes—
90C3×C22⋊C4—22no—
91C3×C22⋊C4—22no—
92C3×C42—21no—
93C3×C42C22×D312yes—
94C4⋊Dic3—22no—
95C4⋊Dic3—22no—
96#208—124no—
97#208—124no—
98C2×C3⋊C8—22no—
99C2×C3⋊C8—32no—
100C2×C3⋊C8—32no—
101C2×C3⋊C8—61no—
102C2×C3⋊C8—61no—
103C2×C3⋊C8—62no—
104C2×C3⋊C8—62no—
105C22×C32—41no—
106C22×C32—41no—
107C22×C32—41no—
108C22×C32#12111yescharacteristic
109C32×C4—21no—
110C32×C4—41no—
111C32×C4C2×SD1611yescharacteristic
112C32×C4#13711yescharacteristic
113C32×C4#13712yes—
114C3×Dic3—82no—
115C2×M16—181no—
116C4⋊Q8—32no—
117C4×D4D3211yescharacteristic
118#107—181no—
119#107—181no—
120#106—62no—
121C4⋊C8—32no—
122C4⋊C8—91no—
123#102—62no—
124C22⋊C8—181no—
125C4×C8—91no—
126C23×C3—22no—
127C23×C3—22no—
128C3×Q8—242no—
129C3×D4—22no—
130C3×D4—22no—
131C3×D4—42no—
132C2×C3×C4—22no—
133C2×C3×C4—22no—
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—42no—
138C2×C3×C4—42no—
139C2×C3×C4—42no—
140C2×C3×C4—42no—
141C2×C3×C4—122no—
142C2×C3×C4D3×D412yes—
143C2×C3×C4#23712yes—
144C2×C3×C4C2×#6712yes—
145C2×Dic3—42no—
146Dic6—82no—
147C3×C8—122no—
148C3⋊C8—34no—
149C3⋊C8—42no—
150C3⋊C8—62no—
151C3⋊C8—62no—
152C3⋊C8—121no—
153C3⋊C8—122no—
154C3⋊C8—122no—
155C2×C32—81no—
156C2×C32#46111yescharacteristic
157C2×C32#47011yescharacteristic
158C2×C32#47211yescharacteristic
159C2×Q8—62no—
160C2×D4#62511yescharacteristic
161C22×C4—21no—
162M16—362no—
163C2×C8—62no—
164C2×C8—91no—
165C2×C8—91no—
166C2×C8—181no—
167C4⋊C4—62no—
168C4⋊C4—62no—
169C4⋊C4#62511yescharacteristic
170C22⋊C4—21no—
171C42C2×D3211yescharacteristic
172C22×C3—21no—
173C22×C3—42no—
174C22×C3—42no—
175C22×C3—42no—
176C22×C3—42no—
177C22×C3—42no—
178C22×C3—42no—
179C22×C3#93912yes—
180C3×C4—22no—
181C3×C4—22no—
182C3×C4—21no—
183C3×C4—21no—
184C3×C4—41no—
185C3×C4—42no—
186C3×C4—42no—
187C3×C4—242no—
188C3×C4D3×SD1612yes—
189C3×C4#91512yes—
190C3×C4#94212yes—
191C3×C4#95112yes—
192Dic3—82no—
193C32#169511yescharacteristic, complemented, Sylow
194C23—21no—
195Q8—242no—
196D4—22no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—122no—
201C2×C4#380511yescharacteristic
202C2×C4C2×#62511yescharacteristic
203C2×C4#381111yescharacteristic
204C8—92no—
205C8—122no—
206C8—181no—
207C8—361no—
208C2×C3—21no—
209C2×C3—21no—
210C2×C3—21no—
211C2×C3—82no—
212C2×C3—82no—
213C2×C3#505212yes—
214C2×C3#516212yes—
215C2×C3#519912yes—
216C22—41no—
217C22—41no—
218C22—41no—
219C22#6398011yescharacteristic
220C4—21no—
221C4—41no—
222C4—242no—
223C4#6382712yes—
224C4#6393011yescharacteristic
225C4#6393111yescharacteristic
226C3—21no—
227C3#7113712yescomplemented
228C2—81no—
229C2#1059118911yescharacteristic
230C2#1059149711yescharacteristic
231C2#1059167811yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1695
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10590312C2semidirect
4. #10589098C2semidirect
5. #10589095C2semidirect
193. C32#1695semidirect
227. C3#71137semidirect

Maximal subgroups

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

subgroupindex
#105927112
C3×#50082
#105903122
#105890982
#105890952
#711373