Finite Group Databasebeta

← #11795369

Subgroups — #11795369

Order 1152.

539 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 539 conjugacy classes of subgroups — too many to draw. Only its 110 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#10592906C211yesmaximal, characteristic
2C3×#5207C212yesmaximal
3#10591143C211yesmaximal, characteristic, complemented
4#10591141C212yesmaximal, complemented
5#10589159C211yesmaximal, characteristic, complemented
6#69987—32nomaximal
7C23×C32×C4C2211yescharacteristic
8C2×#3748C2211yescharacteristic
9C2×#3748C2211yescharacteristic
10C2×C3×#208C2212yes—
11C2×C3×#208C2212yes—
12#63657—22no—
13C3×#830—24no—
14#63578—22no—
15#63577—24no—
16C3×#407—32no—
17#5207—32no—
18#5207—61no—
19#5207D312yes—
20#5125—32no—
21#5124—32no—
22#5124—32no—
23C3⋊#338—32no—
24C24×C32Q811yescharacteristic
25C22×C32×C4—21no—
26C22×C32×C4—22no—
27C22×C32×C4—21no—
28C22×C32×C4—22no—
29C22×C32×C4Q811yescharacteristic
30C22×C32×C4C2311yescharacteristic
31#3748—22no—
32#3748—22no—
33C2×C3⋊(C3⋊C8)—21no—
34C2×C3⋊(C3⋊C8)D412yes—
35C3×#208—22no—
36C3×#208—22no—
37C3×#208—22no—
38C3×#208—22no—
39C2×C3×C3⋊C8—22no—
40C2×C3×C3⋊C8D414yes—
41#2091—91noSylow
42C23×C3×C4—21no—
43C23×C3×C4C2×D312yes—
44C2×C3×M16—32no—
45C2×C3×M16—32no—
46C2×#208—32no—
47C2×#208—32no—
48C2×#208—61no—
49C2×#208—61no—
50C2×#208C2×D312yes—
51C2×#208C2×D312yes—
52C3×C22⋊C8—64no—
53#830—24no—
54#830—64no—
55#830—64no—
56#822—64no—
57#822—64no—
58#819—64no—
59C23×C32—21no—
60C23×C32—22no—
61C23×C32—42no—
62C23×C32C2×Q811yescharacteristic
63C2×C32×C4—21no—
64C2×C32×C4—22no—
65C2×C32×C4—41no—
66C2×C32×C4—42no—
67C2×C32×C4—41no—
68C2×C32×C4C2×D411yescharacteristic
69C2×C32×C4C2×D412yes—
70C2×C32×C4#4112yes—
71C2×C32×C4#4111yescharacteristic
72C3⋊(C3⋊C8)—22no—
73C3⋊(C3⋊C8)—41no—
74C3×C3⋊C8—24no—
75C3×C3⋊C8—42no—
76#430—91no—
77#430—92no—
78#407—32no—
79#407—91no—
80#338—91no—
81C24×C3—21no—
82C24×C3Dic612yes—
83C22×C3×C4—22no—
84C22×C3×C4—22no—
85C22×C3×C4—22no—
86C22×C3×C4—22no—
87C22×C3×C4—22no—
88C22×C3×C4—22no—
89C22×C3×C4—22no—
90C22×C3×C4—22no—
91C22×C3×C4—21no—
92C22×C3×C4—21no—
93C22×C3×C4—42no—
94C22×C3×C4—42no—
95C22×C3×C4Dic612yes—
96C22×C3×C4C22×D312yes—
97C3×M16—62no—
98C3×M16—62no—
99C3×M16—62no—
100C3×M16—62no—
101C2×C3×C8—34no—
102C2×C3×C8—62no—
103#208—22no—
104#208—22no—
105#208—22no—
106#208—22no—
107#208—62no—
108#208—62no—
109#208—62no—
110#208—62no—
111#208—122no—
112#208—122no—
113C2×C3⋊C8—22no—
114C2×C3⋊C8—34no—
115C2×C3⋊C8—62no—
116C2×C3⋊C8—62no—
117C2×C3⋊C8—62no—
118C2×C3⋊C8#6714yes—
119C22×C32—22no—
120C22×C32—24no—
121C22×C32—41no—
122C22×C32—41no—
123C22×C32—42no—
124C22×C32—41no—
125C22×C32C22⋊Q811yescharacteristic
126C22×C32C22⋊Q812yes—
127C32×C4—41no—
128C32×C4#12311yescharacteristic
129C32×C4#12312yes—
130C32×C4#12711yescharacteristic
131C23×C4D3211yescharacteristic
132C2×M16—32no—
133C2×M16—32no—
134C2×M16—91no—
135C2×M16—91no—
136#108—184no—
137#108—182no—
138C22⋊C8—64no—
139C22⋊C8—182no—
140C23×C3—22no—
141C23×C3—22no—
142C23×C3—22no—
143C23×C3—22no—
144C23×C3—21no—
145C23×C3—42no—
146C23×C3—44no—
147C23×C3—44no—
148C23×C3C2×Dic612yes—
149C2×C3×C4—22no—
150C2×C3×C4—22no—
151C2×C3×C4—22no—
152C2×C3×C4—22no—
153C2×C3×C4—22no—
154C2×C3×C4—21no—
155C2×C3×C4—22no—
156C2×C3×C4—21no—
157C2×C3×C4—42no—
158C2×C3×C4—44no—
159C2×C3×C4—42no—
160C2×C3×C4—42no—
161C2×C3×C4—42no—
162C2×C3×C4—42no—
163C2×C3×C4—42no—
164C2×C3×C4—42no—
165C2×C3×C4#23512yes—
166C2×C3×C4D3×D412yes—
167C2×C3×C4D3×D412yes—
168C2×C3×C4#23712yes—
169C2×C3×C4#23712yes—
170C2×C3×C4C2×#6712yes—
171C3×C8—64no—
172C3×C8—122no—
173C3⋊C8—24no—
174C3⋊C8—42no—
175C3⋊C8—64no—
176C3⋊C8—122no—
177C3⋊C8—122no—
178C3⋊C8—122no—
179C2×C32—21no—
180C2×C32—22no—
181C2×C32—42no—
182C2×C32#39911yescharacteristic
183C24#62711yescharacteristic
184C22×C4—22no—
185C22×C4—21no—
186C22×C4—22no—
187C22×C4—21no—
188C22×C4#62711yescharacteristic
189C22×C4C2×D3211yescharacteristic
190M16—62no—
191M16—62no—
192M16—62no—
193M16—62no—
194M16—182no—
195M16—182no—
196C2×C8—34no—
197C2×C8—62no—
198C2×C8—92no—
199C2×C8—181no—
200C22×C3—24no—
201C22×C3—24no—
202C22×C3—24no—
203C22×C3—24no—
204C22×C3—22no—
205C22×C3—21no—
206C22×C3—44no—
207C22×C3—42no—
208C22×C3—42no—
209C22×C3—42no—
210C22×C3—42no—
211C22×C3—42no—
212C22×C3—42no—
213C22×C3—42no—
214C22×C3—44no—
215C22×C3—42no—
216C22×C3#87812yes—
217C22×C3#87812yes—
218C22×C3#92412yes—
219C3×C4—22no—
220C3×C4—21no—
221C3×C4—21no—
222C3×C4—42no—
223C3×C4—42no—
224C3×C4#88312yes—
225C3×C4#88312yes—
226C3×C4#93512yes—
227C3×C4#94012yes—
228C32#209111yescharacteristic, complemented, Sylow
229C23—22no—
230C23—21no—
231C23—42no—
232C23C2×#62711yescharacteristic
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4#380412yes—
239C2×C4#380511yescharacteristic
240C2×C4D3×#6712yes—
241C2×C4#381111yescharacteristic
242C8—64no—
243C8—122no—
244C8—182no—
245C8—361no—
246C2×C3—22no—
247C2×C3—22no—
248C2×C3—22no—
249C2×C3—22no—
250C2×C3—21no—
251C2×C3—42no—
252C2×C3—44no—
253C2×C3—44no—
254C2×C3#494912yes—
255C22—22no—
256C22—24no—
257C22—41no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22#6396412yes—
262C22#6398211yescharacteristic
263C4—41no—
264C4#6396912yes—
265C4#6397511yescharacteristic
266C4#6397911yescharacteristic
267C3—21no—
268C3#6998712yescomplemented
269C2—22no—
270C2—21no—
271C2—42no—
272C2#1059171511yescharacteristic
subgroupG/H
centerC4#63979
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC2×C32#399
prime radicalC24×C32Q8
hypercenterC23×C4D32
hypocenterC32#2091
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. #10591143C2semidirect
4. #10591141C2semidirect
5. #10589159C2semidirect
228. C32#2091semidirect
268. C3#69987semidirect

Maximal subgroups

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

subgroupindex
#105929062
C3×#52072
#105911432
#105911412
#105891592
#699873