Finite Group Databasebeta

← #11779502

Subgroups — #11779502

Order 1152.

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

normal subgroups only

This group has 497 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
2#10592398C211yesmaximal, characteristic, complemented
3#10590268C212yesmaximal, complemented
4C3×#4459C212yesmaximal, complemented
5#10589096C211yesmaximal, characteristic, complemented
6#68203—32nomaximal
7C2×#3746—22no—
8#64078C2211yescharacteristic
9#64078C2211yescharacteristic
10C3×C4×D12C2212yes—
11#63913—22no—
12#63908—22no—
13#63841—22no—
14C32×C4×C8C2211yescharacteristic
15C3×C4⋊(C3⋊C8)C2212yes—
16#63573—22no—
17#63563—22no—
18#5563—32no—
19#5008—32no—
20#4842—32no—
21#4699—32no—
22#4699—61no—
23C3×D4⋊C8—32no—
24#4481—32no—
25#4459D312yescomplemented
26C2×#634—21no—
27C2×#634D412yes—
28C2×C3×D12D412yes—
29C2×C3×C4×D3—22no—
30C2×#625—22no—
31C2×C32×C8—21no—
32C32×C42C2311yescharacteristic
33C4⋊(C3⋊Dic3)—22no—
34C4⋊(C3⋊Dic3)—22no—
35#3746—44no—
36C3×(C2×D3)⋊C4—22no—
37C3×C4⋊Dic3D412yes—
38C2×C3×C3⋊C8—22no—
39(C2×D3)⋊Dic3—24no—
40Dic32—22no—
41#1634—91noSylow
42C3×C4×D4—32no—
43#938—62no—
44#930—62no—
45#926—62no—
46C2×Dic12—64no—
47C2×Dic12—64no—
48#892—62no—
49#885—64no—
50C4×D12C2×D312yes—
51#869—32no—
52#869—32no—
53#869—61no—
54#869—61no—
55C3×C4⋊C8—32no—
56C3×C4×C8—21no—
57C3×C4×C8C2×D312yes—
58#832—62no—
59#821—62no—
60#817—62no—
61#808—62no—
62C4⋊(C3⋊C8)C2×D312yes—
63C22×C3×D3—22no—
64C2×C32×C4C2×D412yes—
65C2×C32×C4C2×D411yescharacteristic
66C2×C3⋊Dic3—22no—
67C2×C3⋊Dic3—41no—
68#634—42no—
69#634—42no—
70C2×C3×Dic3—22no—
71C3×D12—22no—
72C3×D12—22no—
73C3×C4×D3—42no—
74C3×C4×D3—42no—
75#625—82no—
76C32×C8—22no—
77C3×C3⋊C8—42no—
78#555—91no—
79#494—91no—
80#476—92no—
81#333—91no—
82D4⋊C8—32no—
83C2×C3×D4—32no—
84C22×C3×C4—62no—
85C2×#67—64no—
86C2×D12D1212yes—
87C2×C4×D3—22no—
88C2×Dic6—34no—
89C2×Dic6—62no—
90C2×Dic6—62no—
91C2×Dic6—62no—
92C2×C3×C8—22no—
93C2×C3×C8—22no—
94C2×C3×C8—62no—
95C3×C4⋊C4—32no—
96C3×C22⋊C4—62no—
97C3×C42—21no—
98C3×C42C22×D312yes—
99#217—64no—
100(C2×D3)⋊C4—22no—
101(C2×D3)⋊C4—64no—
102C4⋊Dic3—62no—
103C4⋊Dic3—62no—
104C4⋊Dic3—62no—
105C4⋊Dic3—62no—
106C4⋊Dic3—122no—
107C4⋊Dic3—122no—
108C4⋊Dic3D1212yes—
109C4×Dic3—64no—
110C2×C3⋊C8—22no—
111Dic12—128no—
112Dic12—128no—
113C22×C32#12011yescharacteristic
114C2×C3×D3—42no—
115C2×C3×D3—42no—
116C2×C3×D3—42no—
117C32×C4—21no—
118C32×C4#13512yes—
119C32×C4#13712yes—
120C3⋊Dic3—42no—
121C3⋊Dic3—81no—
122C3×Dic3—42no—
123C2×Q16—182no—
124C4⋊Q8—91no—
125C4⋊Q8—91no—
126#124—182no—
127#121—182no—
128C4×D4—32no—
129#117—182no—
130#106—182no—
131C4⋊C8—32no—
132#102—182no—
133C4×C8D3211yescharacteristic
134C23×C3—62no—
135C22×D3—22no—
136C3×D4—62no—
137C3×D4—62no—
138C2×C3×C4—22no—
139C2×C3×C4—21no—
140C2×C3×C4—62no—
141C2×C3×C4—122no—
142C2×C3×C4—122no—
143C2×C3×C4C2×D1212yes—
144C2×C3×C4D3×D412yes—
145C2×C3×C4D3×D412yes—
146#67—244no—
147C2×Dic3—22no—
148C2×Dic3—64no—
149C2×Dic3—122no—
150C2×Dic3—122no—
151C2×Dic3—122no—
152D12—22no—
153D12—22no—
154C4×D3—42no—
155C4×D3—42no—
156Dic6—124no—
157Dic6—124no—
158Dic6—124no—
159Dic6—124no—
160C3×C8—24no—
161C3×C8—24no—
162C3×C8—122no—
163C3⋊C8—42no—
164C2×C32#45212yes—
165C2×C32#45311yescharacteristic
166C3×D3—82no—
167C2×Q8—92no—
168C2×Q8—181no—
169C2×D4—32no—
170C2×D4—182no—
171C22×C4—62no—
172Q16—364no—
173C2×C8—21no—
174C2×C8—62no—
175C4⋊C4—32no—
176C4⋊C4—182no—
177C4⋊C4—182no—
178C22⋊C4—62no—
179C22⋊C4—184no—
180C42—182no—
181C42C2×D3211yescharacteristic
182C22×C3—21no—
183C22×C3—122no—
184C22×C3—122no—
185C22×C3—122no—
186C22×C3#88212yes—
187C2×D3—42no—
188C2×D3—42no—
189C2×D3—42no—
190C3×C4—22no—
191C3×C4—22no—
192C3×C4—22no—
193C3×C4—22no—
194C3×C4—122no—
195C3×C4#90412yes—
196C3×C4#90912yes—
197C3×C4#91212yes—
198C3×C4#91512yes—
199Dic3—42no—
200Dic3—124no—
201Dic3—242no—
202Dic3—242no—
203Dic3—242no—
204C32#163411yescharacteristic, complemented, Sylow
205C23—62no—
206Q8—362no—
207Q8—362no—
208D4—62no—
209D4—62no—
210D4—722no—
211C2×C4—62no—
212C2×C4—122no—
213C2×C4—122no—
214C2×C4—182no—
215C2×C4—361no—
216C2×C4D3×D1212yes—
217C2×C4#381111yescharacteristic
218C8—22no—
219C8—122no—
220C2×C3—21no—
221C2×C3—22no—
222C2×C3—242no—
223C2×C3#473312yes—
224C2×C3#478312yes—
225C2×C3#482212yes—
226D3—82no—
227C22—122no—
228C22—122no—
229C22—122no—
230C22#6392311yescharacteristic
231C4—21no—
232C4—122no—
233C4—362no—
234C4—721no—
235C4#6380012yes—
236C4#6380712yes—
237C3—21no—
238C3#6820312yescomplemented
239C2—242no—
240C2#1059039711yescharacteristic
241C2#1059096912yes—
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
prime radical#10593988C2
hypercenterC4×C8D32
hypocenterC32#1634
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
2. #10592398C2semidirect
3. #10590268C2semidirect
4. C3×#4459C2semidirect
5. #10589096C2semidirect
25. #4459D3semidirect
204. C32#1634semidirect
238. C3#68203semidirect

Maximal subgroups

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

subgroupindex
#105939882
#105923982
#105902682
C3×#44592
#105890962
#682033