Finite Group Databasebeta

← #11781780

Subgroups — #11781780

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×#5007C212yesmaximal
3#10590387C211yesmaximal, characteristic, complemented
4#10589098C211yesmaximal, characteristic, complemented
5#10589092C212yesmaximal, complemented
6#71105—32nomaximal
7C32×C4×D4C2211yescharacteristic
8C2×#3748—21no—
9C3×#869C2212yes—
10C2×#3718—21no—
11C2×#3718—21no—
12#63657—21no—
13C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
14C4×C3⋊(C3⋊C8)C2211yescharacteristic
15C3×#832—22no—
16C3×#807—22no—
17C3×C4⋊(C3⋊C8)C2212yes—
18C3×#474—32no—
19#5092—32no—
20#5012—32no—
21#5012—61no—
22#5007D312yes—
23#4547—32no—
24#4486—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#3718—42no—
40#3718—42no—
41#1689—91noSylow
42C3×C4⋊Q8—32no—
43C3×C4×D4—21no—
44C3×C4×D4C2×D312yes—
45C2×#216—62no—
46C2×#216—62no—
47C2×#208—62no—
48C2×#208—62no—
49#869C2×D312yes—
50C3×#107—62no—
51C3×C4⋊C8—32no—
52C3×#102—62no—
53#832—22no—
54#830—62no—
55#830—62no—
56#807—22no—
57C4⋊(C3⋊C8)—32no—
58C4⋊(C3⋊C8)—61no—
59C4⋊(C3⋊C8)C2×D312yes—
60C4×C3⋊C8—32no—
61C4×C3⋊C8—61no—
62C23×C32—21no—
63C32×D4—22no—
64C2×C32×C4—21no—
65C2×C32×C4—41no—
66C2×C32×C4—41no—
67C2×C32×C4C2×D411yescharacteristic
68C2×C32×C4C2×D411yescharacteristic
69C2×C32×C4#4111yescharacteristic
70C2×C3×Dic3—42no—
71C3×Dic6—42no—
72C3×Dic6—42no—
73C3⋊(C3⋊C8)—21no—
74C3⋊(C3⋊C8)—41no—
75C3⋊(C3⋊C8)D812yes—
76C3×C3⋊C8—42no—
77#494—91no—
78#474—32no—
79#436—91no—
80#334—91no—
81#332—92no—
82C2×C3×Q8—62no—
83C2×C3×D4—21no—
84C2×C3×D4#6712yes—
85C22×C3×C4—22no—
86C22×C3×C4—22no—
87C2×Dic6—22no—
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#216—124no—
98#216—124no—
99C4⋊Dic3—22no—
100C4⋊Dic3—22no—
101#208—124no—
102#208—124no—
103C2×C3⋊C8—22no—
104C2×C3⋊C8—32no—
105C2×C3⋊C8—32no—
106C2×C3⋊C8—61no—
107C2×C3⋊C8—61no—
108C2×C3⋊C8—62no—
109C2×C3⋊C8—62no—
110C22×C32—41no—
111C22×C32—41no—
112C22×C32—41no—
113C22×C32#12111yescharacteristic
114C32×C4—21no—
115C32×C4—41no—
116C32×C4C2×D811yescharacteristic
117C32×C4AGL(1,ℤ/8)11yescharacteristic
118C32×C4#13712yes—
119C3×Dic3—82no—
120C2×Q16—181no—
121C2×Q16—181no—
122C2×M16—181no—
123C4⋊Q8—32no—
124C4×D4D3211yescharacteristic
125#107—62no—
126C4⋊C8—32no—
127C4⋊C8—91no—
128#102—62no—
129C22⋊C8—181no—
130C4×C8—91no—
131C23×C3—22no—
132C23×C3—22no—
133C3×Q8—122no—
134C3×Q8—122no—
135C3×D4—22no—
136C3×D4—22no—
137C3×D4—42no—
138C2×C3×C4—22no—
139C2×C3×C4—22no—
140C2×C3×C4—21no—
141C2×C3×C4—21no—
142C2×C3×C4—21no—
143C2×C3×C4—42no—
144C2×C3×C4—42no—
145C2×C3×C4—42no—
146C2×C3×C4—42no—
147C2×C3×C4—122no—
148C2×C3×C4D3×D412yes—
149C2×C3×C4#23712yes—
150C2×C3×C4C2×#6712yes—
151C2×Dic3—42no—
152Dic6—42no—
153Dic6—42no—
154C3×C8—122no—
155C3⋊C8—34no—
156C3⋊C8—42no—
157C3⋊C8—62no—
158C3⋊C8—62no—
159C3⋊C8—121no—
160C3⋊C8—122no—
161C3⋊C8—122no—
162C2×C32—81no—
163C2×C32#45911yescharacteristic
164C2×C32#47011yescharacteristic
165C2×C32#47311yescharacteristic
166C2×Q8—62no—
167C2×D4#62511yescharacteristic
168C22×C4—21no—
169Q16—362no—
170Q16—362no—
171M16—362no—
172C2×C8—62no—
173C2×C8—91no—
174C2×C8—91no—
175C2×C8—181no—
176C4⋊C4—62no—
177C4⋊C4—62no—
178C4⋊C4#62511yescharacteristic
179C22⋊C4—21no—
180C42C2×D3211yescharacteristic
181C22×C3—21no—
182C22×C3—42no—
183C22×C3—42no—
184C22×C3—42no—
185C22×C3—42no—
186C22×C3—42no—
187C22×C3—42no—
188C22×C3#93912yes—
189C3×C4—22no—
190C3×C4—22no—
191C3×C4—21no—
192C3×C4—21no—
193C3×C4—41no—
194C3×C4—42no—
195C3×C4—42no—
196C3×C4—242no—
197C3×C4D3×D812yes—
198C3×C4#91112yes—
199C3×C4#94212yes—
200C3×C4#95112yes—
201Dic3—82no—
202C32#168911yescharacteristic, complemented, Sylow
203C23—21no—
204Q8—122no—
205Q8—122no—
206D4—22no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—122no—
211C2×C4#380511yescharacteristic
212C2×C4C2×#62511yescharacteristic
213C2×C4#381111yescharacteristic
214C8—92no—
215C8—122no—
216C8—181no—
217C8—361no—
218C2×C3—21no—
219C2×C3—21no—
220C2×C3—21no—
221C2×C3—82no—
222C2×C3—82no—
223C2×C3#505212yes—
224C2×C3#515012yes—
225C2×C3#520412yes—
226C22—41no—
227C22—41no—
228C22—41no—
229C22#6398011yescharacteristic
230C4—21no—
231C4—41no—
232C4—242no—
233C4#6382712yes—
234C4#6392611yescharacteristic
235C4#6392711yescharacteristic
236C3—21no—
237C3#7110512yescomplemented
238C2—81no—
239C2#1059118911yescharacteristic
240C2#1059148611yescharacteristic
241C2#1059168311yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1689
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. #10590387C2semidirect
4. #10589098C2semidirect
5. #10589092C2semidirect
202. C32#1689semidirect
237. C3#71105semidirect

Maximal subgroups

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

subgroupindex
#105927112
C3×#50072
#105903872
#105890982
#105890922
#711053