Finite Group Databasebeta

← #11779092

Subgroups — #11779092

Order 1152.

551 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 551 conjugacy classes of subgroups — too many to draw. Only its 86 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#10593988C211yesmaximal, characteristic, complemented
2#10592392C211yesmaximal, characteristic, complemented
3#10590349C212yesmaximal, complemented
4C3×#4459C212yesmaximal, complemented
5#10589096C211yesmaximal, characteristic, complemented
6#68199—32nomaximal
7C2×#3744—22no—
8#64083C2211yescharacteristic
9#64078C2211yescharacteristic
10C3×C4×D12C2212yes—
11#63913—22no—
12#63908—22no—
13#63841—22no—
14C2×#3714—22no—
15C32×C4×C8C2211yescharacteristic
16C3×C4⋊(C3⋊C8)C2212yes—
17#63564—22no—
18#5563—32no—
19#5015—32no—
20#4843—32no—
21#4693—32no—
22#4693—61no—
23C3×D4⋊C8—32no—
24#4481—32no—
25#4459D312yescomplemented
26C2×C4⋊(C3⋊D3)—21no—
27C2×C4⋊(C3⋊D3)—22no—
28C2×#634D412yes—
29C2×C3×D12D412yes—
30C2×C3×C4×D3—22no—
31C2×#625—22no—
32C2×C32×C8—21no—
33C32×C42C2311yescharacteristic
34C4⋊(C3⋊Dic3)—22no—
35#3744—44no—
36C3×(C2×D3)⋊C4—22no—
37C3×C4⋊Dic3D412yes—
38C2×C3×C3⋊C8—22no—
39(C2×D3)⋊Dic3—24no—
40Dic32—22no—
41#3714—44no—
42#1624—91noSylow
43C3×C4×D4—32no—
44#938—62no—
45C2×#213—62no—
46#930—62no—
47#926—62no—
48C2×D24—62no—
49C2×#204—64no—
50C2×#204—64no—
51#892—62no—
52#885—64no—
53#874—32no—
54#874—61no—
55C4×D12C2×D312yes—
56#869—32no—
57#869—61no—
58C3×C4⋊C8—32no—
59C3×C4×C8—21no—
60C3×C4×C8C2×D312yes—
61#821—62no—
62#809—62no—
63C4⋊(C3⋊C8)C2×D312yes—
64C22×C3⋊D3—41no—
65C22×C3×D3—22no—
66C2×C32×C4C2×D412yes—
67C2×C32×C4C2×D411yescharacteristic
68C2×C3⋊Dic3—22no—
69C4⋊(C3⋊D3)—42no—
70C4⋊(C3⋊D3)—42no—
71C4⋊(C3⋊D3)—42no—
72#634—42no—
73C2×C3×Dic3—22no—
74C3×D12—22no—
75C3×D12—22no—
76C3×C4×D3—42no—
77C3×C4×D3—42no—
78#625—82no—
79C32×C8—22no—
80C3×C3⋊C8—42no—
81#555—91no—
82#492—91no—
83#459—92no—
84#333—91no—
85D4⋊C8—32no—
86C2×C3×D4—32no—
87C22×C3×C4—62no—
88C2×#67—64no—
89C2×D12—62no—
90C2×D12—62no—
91C2×D12—62no—
92C2×D12—62no—
93C2×D12—122no—
94C2×D12D1212yes—
95C2×C4×D3—22no—
96C2×Dic6—34no—
97C2×Dic6—62no—
98C2×C3×C8—22no—
99C2×C3×C8—22no—
100C2×C3×C8—62no—
101C3×C4⋊C4—32no—
102C3×C22⋊C4—62no—
103C3×C42—21no—
104C3×C42C22×D312yes—
105#217—64no—
106#213—124no—
107(C2×D3)⋊C4—22no—
108(C2×D3)⋊C4—64no—
109C4⋊Dic3—62no—
110C4⋊Dic3—62no—
111C4⋊Dic3—122no—
112C4⋊Dic3D1212yes—
113C4×Dic3—64no—
114C2×C3⋊C8—22no—
115D24—124no—
116#204—128no—
117#204—128no—
118C22×C32#12011yescharacteristic
119C2×C3⋊D3—82no—
120C2×C3⋊D3—81no—
121C2×C3×D3—42no—
122C2×C3×D3—42no—
123C2×C3×D3—42no—
124C32×C4—21no—
125C32×C4#13512yes—
126C32×C4AGL(1,ℤ/8)12yes—
127C3⋊Dic3—42no—
128C3×Dic3—42no—
129C2×SD16—182no—
130C2×D8—182no—
131C4⋊Q8—91no—
132#127—91no—
133#124—182no—
134#121—182no—
135C4×D4—32no—
136#117—182no—
137C4⋊C8—32no—
138#102—182no—
139C4×C8D3211yescharacteristic
140C23×C3—62no—
141C22×D3—22no—
142C22×D3—122no—
143C22×D3—122no—
144C3×D4—62no—
145C3×D4—62no—
146C2×C3×C4—22no—
147C2×C3×C4—21no—
148C2×C3×C4—62no—
149C2×C3×C4—122no—
150C2×C3×C4—122no—
151C2×C3×C4C2×D1212yes—
152C2×C3×C4D3×D412yes—
153C2×C3×C4D3×D412yes—
154#67—244no—
155C2×Dic3—22no—
156C2×Dic3—64no—
157C2×Dic3—122no—
158D12—22no—
159D12—22no—
160D12—124no—
161D12—124no—
162D12—122no—
163D12—122no—
164D12—122no—
165D12—122no—
166D12—242no—
167D12—242no—
168C4×D3—42no—
169C4×D3—42no—
170Dic6—124no—
171Dic6—124no—
172C3×C8—24no—
173C3×C8—24no—
174C3×C8—122no—
175C3⋊C8—42no—
176C2×C32#44912yes—
177C2×C32#45311yescharacteristic
178C3⋊D3—161no—
179C3×D3—82no—
180C2×Q8—92no—
181C2×D4—32no—
182C2×D4—182no—
183C2×D4—182no—
184C2×D4—181no—
185C22×C4—62no—
186SD16—364no—
187D8—364no—
188C2×C8—21no—
189C2×C8—62no—
190C4⋊C4—32no—
191C4⋊C4—182no—
192C22⋊C4—62no—
193C22⋊C4—184no—
194C42—182no—
195C42C2×D3211yescharacteristic
196C22×C3—21no—
197C22×C3—122no—
198C22×C3—122no—
199C22×C3—122no—
200C22×C3#88212yes—
201C2×D3—42no—
202C2×D3—42no—
203C2×D3—42no—
204C2×D3—242no—
205C2×D3—244no—
206C2×D3—242no—
207C2×D3—242no—
208C2×D3—242no—
209C3×C4—22no—
210C3×C4—22no—
211C3×C4—22no—
212C3×C4—22no—
213C3×C4—122no—
214C3×C4#90412yes—
215C3×C4#90812yes—
216C3×C4#91112yes—
217C3×C4#91612yes—
218Dic3—42no—
219Dic3—124no—
220Dic3—242no—
221C32#162411yescharacteristic, complemented, Sylow
222C23—62no—
223C23—361no—
224Q8—362no—
225D4—62no—
226D4—62no—
227D4—362no—
228D4—362no—
229D4—362no—
230D4—722no—
231C2×C4—62no—
232C2×C4—122no—
233C2×C4—122no—
234C2×C4—182no—
235C2×C4D3×D1212yes—
236C2×C4#381111yescharacteristic
237C8—22no—
238C8—122no—
239C2×C3—21no—
240C2×C3—22no—
241C2×C3—242no—
242C2×C3#473412yes—
243C2×C3#478112yes—
244C2×C3#482212yes—
245D3—82no—
246D3—482no—
247D3—482no—
248C22—122no—
249C22—122no—
250C22—122no—
251C22—721no—
252C22—722no—
253C22#6392311yescharacteristic
254C4—21no—
255C4—122no—
256C4—362no—
257C4#6379512yes—
258C4#6380612yes—
259C3—21no—
260C3#6819912yescomplemented
261C2—242no—
262C2—1441no—
263C2#1059039711yescharacteristic
264C2#1059096812yes—
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
hypercenterC4×C8D32
hypocenterC32#1624
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10593988C2semidirect
2. #10592392C2semidirect
3. #10590349C2semidirect
4. C3×#4459C2semidirect
5. #10589096C2semidirect
25. #4459D3semidirect
221. C32#1624semidirect
260. C3#68199semidirect

Maximal subgroups

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

subgroupindex
#105939882
#105923922
#105903492
C3×#44592
#105890962
#681993