Finite Group Databasebeta

← #11781938

Subgroups — #11781938

Order 1152.

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

normal subgroups only

This group has 393 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×#5019C212yesmaximal
3#10590312C211yesmaximal, characteristic, complemented
4#10589098C211yesmaximal, characteristic, complemented
5#10589093C212yesmaximal, complemented
6#71041—32nomaximal
7C32×C4×D4C2211yescharacteristic
8C2×#3748—21no—
9C2×C3×#214—22no—
10C3×#869C2212yes—
11#63657—21no—
12C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
13C4×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#810—22no—
15C3×C4⋊(C3⋊C8)C2212yes—
16#63576—21no—
17#63576—21no—
18C3×#461—32no—
19#5078—32no—
20#5019D312yes—
21#5012—32no—
22#5012—61no—
23#4547—32no—
24#4482—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×#214—44no—
37C3×C4⋊Dic3—22no—
38C3×C4⋊Dic3—22no—
39C2×C3×C3⋊C8—22no—
40#1693—91noSylow
41C2×C3×SD16—62no—
42C3×C4⋊Q8—32no—
43C3×C4×D4—21no—
44C3×C4×D4C2×D312yes—
45C2×#214—22no—
46C2×#208—62no—
47C2×#208—62no—
48#869C2×D312yes—
49C3×C4⋊C8—32no—
50C3×#103—62no—
51#830—62no—
52#830—62no—
53#810—22no—
54#807—62no—
55#807—62no—
56C4⋊(C3⋊C8)—32no—
57C4⋊(C3⋊C8)—61no—
58C4⋊(C3⋊C8)C2×D312yes—
59C4×C3⋊C8—32no—
60C4×C3⋊C8—61no—
61C23×C32—21no—
62C32×D4—22no—
63C2×C32×C4—21no—
64C2×C32×C4—41no—
65C2×C32×C4—41no—
66C2×C32×C4C2×D411yescharacteristic
67C2×C32×C4C2×D411yescharacteristic
68C2×C32×C4#4111yescharacteristic
69C2×C3×Dic3—42no—
70C3×Dic6—42no—
71C3×Dic6—42no—
72C3⋊(C3⋊C8)—21no—
73C3⋊(C3⋊C8)—41no—
74C3⋊(C3⋊C8)SD1612yescomplemented
75C3×C3⋊C8—42no—
76#500—91no—
77#461—32no—
78#436—91no—
79#334—91no—
80#332—92no—
81C2×C3×Q8—62no—
82C2×C3×D4—21no—
83C2×C3×D4#6712yes—
84C22×C3×C4—22no—
85C22×C3×C4—22no—
86C2×Dic6—22no—
87C3×SD16—124no—
88C2×C3×C8—62no—
89C3×C4⋊C4—21no—
90C3×C4⋊C4—62no—
91C3×C4⋊C4—62no—
92C3×C4⋊C4#6712yes—
93C3×C22⋊C4—22no—
94C3×C22⋊C4—22no—
95C3×C42—21no—
96C3×C42C22×D312yes—
97#214—44no—
98C4⋊Dic3—22no—
99C4⋊Dic3—22no—
100#208—124no—
101#208—124no—
102C2×C3⋊C8—22no—
103C2×C3⋊C8—32no—
104C2×C3⋊C8—32no—
105C2×C3⋊C8—61no—
106C2×C3⋊C8—61no—
107C2×C3⋊C8—62no—
108C2×C3⋊C8—62no—
109C22×C32—41no—
110C22×C32—41no—
111C22×C32—41no—
112C22×C32#12111yescharacteristic
113C32×C4—21no—
114C32×C4—41no—
115C32×C4C2×SD1611yescharacteristic
116C32×C4AGL(1,ℤ/8)12yes—
117C32×C4#13711yescharacteristic
118C3×Dic3—82no—
119C2×SD16—62no—
120C2×M16—181no—
121C4⋊Q8—32no—
122C4×D4D3211yescharacteristic
123#107—181no—
124#107—181no—
125C4⋊C8—32no—
126C4⋊C8—91no—
127#103—62no—
128C22⋊C8—181no—
129C4×C8—91no—
130C23×C3—22no—
131C23×C3—22no—
132C3×Q8—122no—
133C3×Q8—122no—
134C3×D4—22no—
135C3×D4—22no—
136C3×D4—42no—
137C2×C3×C4—22no—
138C2×C3×C4—22no—
139C2×C3×C4—21no—
140C2×C3×C4—21no—
141C2×C3×C4—21no—
142C2×C3×C4—42no—
143C2×C3×C4—42no—
144C2×C3×C4—42no—
145C2×C3×C4—42no—
146C2×C3×C4—122no—
147C2×C3×C4D3×D412yes—
148C2×C3×C4#23712yes—
149C2×C3×C4C2×#6712yes—
150C2×Dic3—42no—
151Dic6—42no—
152Dic6—42no—
153C3×C8—122no—
154C3⋊C8—34no—
155C3⋊C8—42no—
156C3⋊C8—62no—
157C3⋊C8—62no—
158C3⋊C8—121no—
159C3⋊C8—122no—
160C3⋊C8—122no—
161C2×C32—81no—
162C2×C32#46111yescharacteristic
163C2×C32#46911yescharacteristic
164C2×C32#47311yescharacteristic
165C2×Q8—62no—
166C2×D4#62511yescharacteristic
167C22×C4—21no—
168SD16—124no—
169M16—362no—
170C2×C8—62no—
171C2×C8—91no—
172C2×C8—91no—
173C2×C8—181no—
174C4⋊C4—62no—
175C4⋊C4—62no—
176C4⋊C4#62511yescharacteristic
177C22⋊C4—21no—
178C42C2×D3211yescharacteristic
179C22×C3—21no—
180C22×C3—42no—
181C22×C3—42no—
182C22×C3—42no—
183C22×C3—42no—
184C22×C3—42no—
185C22×C3—42no—
186C22×C3#93912yes—
187C3×C4—22no—
188C3×C4—22no—
189C3×C4—21no—
190C3×C4—21no—
191C3×C4—41no—
192C3×C4—42no—
193C3×C4—42no—
194C3×C4—242no—
195C3×C4D3×SD1612yes—
196C3×C4#91512yes—
197C3×C4#93212yes—
198C3×C4#94912yes—
199Dic3—82no—
200C32#169311yescharacteristic, complemented, Sylow
201C23—21no—
202Q8—122no—
203Q8—122no—
204D4—22no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—122no—
209C2×C4#380511yescharacteristic
210C2×C4C2×#62511yescharacteristic
211C2×C4#381111yescharacteristic
212C8—92no—
213C8—122no—
214C8—181no—
215C8—361no—
216C2×C3—21no—
217C2×C3—21no—
218C2×C3—21no—
219C2×C3—82no—
220C2×C3—82no—
221C2×C3#503912yes—
222C2×C3#516212yes—
223C2×C3#520412yes—
224C22—41no—
225C22—41no—
226C22—41no—
227C22#6398011yescharacteristic
228C4—21no—
229C4—41no—
230C4—242no—
231C4#6382312yes—
232C4#6393011yescharacteristic
233C4#6393111yescharacteristic
234C3—21no—
235C3#7104112yescomplemented
236C2—81no—
237C2#1059116711yescharacteristic
238C2#1059149711yescharacteristic
239C2#1059168311yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1693
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. #10589093C2semidirect
74. C3⋊(C3⋊C8)SD16semidirect
200. C32#1693semidirect
235. C3#71041semidirect

Maximal subgroups

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

subgroupindex
#105927112
C3×#50192
#105903122
#105890982
#105890932
#710413