Finite Group Databasebeta

← #11780683

Subgroups — #11780683

Order 1152.

437 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 437 conjugacy classes of subgroups — too many to draw. Only its 70 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#10593985C211yesmaximal, characteristic
2#10592781C211yesmaximal, characteristic, complemented
3C3×#5089C212yesmaximal, complemented
4#10589089C211yesmaximal, characteristic, complemented
5#10589086C212yesmaximal, complemented
6#71246—32nomaximal
7C32×C4⋊Q8C2211yescharacteristic
8#64079C2211yescharacteristic
9C3×#875C2212yes—
10#63891—22no—
11#63887—22no—
12#63885—22no—
13#63662—22no—
14#63630C2211yescharacteristic
15C3×#810—22no—
16C3×#809—22no—
17C3×#803C2212yes—
18#5684—32no—
19C3×#489—32no—
20#5089D312yescomplemented
21#5082—32no—
22#5082—61no—
23#4540—32no—
24#4465—32no—
25#4464—32no—
26C2×C32×Q8—21no—
27C2×C3×D12D412yes—
28C2×C3×Dic6D412yes—
29C2×#625—22no—
30C2×D3×Dic3—22no—
31C32×C4⋊C4—22no—
32C32×C42C2311yescharacteristic
33C4⋊(C3⋊Dic3)D412yes—
34#3750—22no—
35C2×C3⋊(C3⋊C8)—21no—
36C3×(C2×D3)⋊C4—22no—
37C3×(C2×D3)⋊C4—22no—
38C2×C3×C3⋊C8—22no—
39Dic3⋊Dic3—22no—
40(C2×D3)⋊Dic3—22no—
41#1662—91noSylow
42C3×C4⋊Q8—21no—
43C3×C4⋊Q8C2×D312yes—
44C3×#124—32no—
45#946—62no—
46#939—62no—
47#886—62no—
48#884—62no—
49#883—62no—
50#878—62no—
51#875C2×D312yes—
52#870—32no—
53#870—61no—
54C3×#103—62no—
55C3×#102—62no—
56C3×#97—32no—
57#835—62no—
58#835—62no—
59#835—64no—
60#810—22no—
61#809—22no—
62#803—32no—
63#803—61no—
64#803C2×D312yes—
65C22×C3×D3—22no—
66C32×Q8—42no—
67C2×C32×C4—41no—
68C2×C32×C4C2×D411yescharacteristic
69C2×C32×C4C2×D412yes—
70C2×C3⋊Dic3—22no—
71C2×C3×Dic3—22no—
72C3×D12—42no—
73C3×Dic6—42no—
74#625—82no—
75D3×Dic3—82no—
76C3⋊(C3⋊C8)—41no—
77C3×C3⋊C8—42no—
78#562—91no—
79#491—91no—
80#489—32no—
81#330—91no—
82#329—92no—
83C2×C3×Q8—22no—
84C2×C3×Q8—22no—
85C2×C3×Q8—32no—
86C2×C3×D4—32no—
87C2×#67—62no—
88C2×#67—62no—
89C22×Dic3—62no—
90C2×D12#6712yes—
91C2×C4×D3—62no—
92C2×Dic6#6712yes—
93C2×C3×C8—62no—
94C3×C4⋊C4—22no—
95C3×C4⋊C4—22no—
96C3×C4⋊C4—42no—
97C3×C22⋊C4—62no—
98C3×C22⋊C4—62no—
99C3×C42—21no—
100C3×C42C22×D312yes—
101#217—62no—
102(C2×D3)⋊C4—22no—
103(C2×D3)⋊C4—22no—
104(C2×D3)⋊C4—62no—
105C4⋊Dic3—32no—
106C4⋊Dic3—32no—
107C4⋊Dic3—62no—
108C4⋊Dic3—62no—
109Dic3⋊C4—62no—
110Dic3⋊C4—62no—
111Dic3⋊C4—62no—
112Dic3⋊C4—122no—
113C2×C3⋊C8—22no—
114C2×C3⋊C8—62no—
115C2×C3⋊C8—62no—
116C22×C32#12011yescharacteristic
117C2×C3×D3—42no—
118C2×C3×D3—42no—
119C2×C3×D3—42no—
120C32×C4—21no—
121C32×C4—22no—
122C32×C4—81no—
123C3⋊Dic3—42no—
124C3×Dic3—42no—
125C4⋊Q8D3211yescharacteristic
126#125—91no—
127#124—32no—
128#123—182no—
129C22⋊Q8—182no—
130#121—182no—
131#103—62no—
132#103—182no—
133#102—62no—
134#97—32no—
135#97—91no—
136C23×C3—62no—
137C22×D3—22no—
138C3×Q8—44no—
139C3×Q8—44no—
140C3×Q8—122no—
141C3×D4—122no—
142C2×C3×C4—22no—
143C2×C3×C4—21no—
144C2×C3×C4—42no—
145C2×C3×C4—42no—
146C2×C3×C4—62no—
147C2×C3×C4D3×D412yes—
148C2×C3×C4D3×D412yes—
149C2×C3×C4C2×#6712yes—
150#67—242no—
151#67—242no—
152C2×Dic3—22no—
153C2×Dic3—62no—
154C2×Dic3—62no—
155C2×Dic3—122no—
156C2×Dic3—242no—
157D12—42no—
158C4×D3—242no—
159Dic6—42no—
160C3×C8—122no—
161C3⋊C8—42no—
162C3⋊C8—122no—
163C3⋊C8—122no—
164C2×C32#45411yescharacteristic
165C2×C32#45512yes—
166C3×D3—82no—
167C2×Q8—21no—
168C2×Q8—32no—
169C2×D4—32no—
170C2×D4—182no—
171C22×C4—182no—
172C2×C8—62no—
173C2×C8—181no—
174C4⋊C4—22no—
175C4⋊C4—92no—
176C4⋊C4—182no—
177C4⋊C4—182no—
178C22⋊C4—62no—
179C22⋊C4—62no—
180C22⋊C4—182no—
181C42C2×D3211yescharacteristic
182C22×C3—21no—
183C22×C3—122no—
184C22×C3—122no—
185C22×C3—122no—
186C22×C3#93712yes—
187C2×D3—42no—
188C2×D3—42no—
189C2×D3—42no—
190C3×C4—22no—
191C3×C4—22no—
192C3×C4—22no—
193C3×C4—22no—
194C3×C4—42no—
195C3×C4—82no—
196C3×C4—82no—
197C3×C4—122no—
198Dic3—42no—
199Dic3—122no—
200Dic3—122no—
201Dic3—242no—
202C32#166211yescharacteristic, complemented, Sylow
203C23—62no—
204Q8—42no—
205Q8—122no—
206D4—122no—
207D4—722no—
208C2×C4—41no—
209C2×C4—62no—
210C2×C4—182no—
211C2×C4—722no—
212C2×C4D3×#6712yes—
213C2×C4#381111yescharacteristic
214C8—122no—
215C8—361no—
216C2×C3—21no—
217C2×C3—22no—
218C2×C3—242no—
219C2×C3#506112yes—
220C2×C3#520112yes—
221C2×C3#520212yes—
222D3—82no—
223C22—122no—
224C22—122no—
225C22—122no—
226C22#6398311yescharacteristic
227C4—21no—
228C4—22no—
229C4—81no—
230C4—122no—
231C4—362no—
232C3—21no—
233C3#7124612yescomplemented
234C2—242no—
235C2#1059152411yescharacteristic
236C2#1059165912yes—
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radical#10593985C2
hypercenterC4⋊Q8D32
hypocenterC32#1662
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
2. #10592781C2semidirect
3. C3×#5089C2semidirect
4. #10589089C2semidirect
5. #10589086C2semidirect
20. #5089D3semidirect
202. C32#1662semidirect
233. C3#71246semidirect

Maximal subgroups

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

subgroupindex
#105939852
#105927812
C3×#50892
#105890892
#105890862
#712463