Finite Group Databasebeta

← #11780502

Subgroups — #11780502

Order 1152.

490 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C3×#5700C211yesmaximal, characteristic, complemented
2C3×#5067C211yesmaximal, characteristic, complemented
3#10590354C212yesmaximal, complemented
4#10589409C211yesmaximal, characteristic, complemented
5#10589086C212yesmaximal, complemented
6#71952—31nomaximal
7#71248—31nomaximal
8C32×#125C2211yescharacteristic
9C3×#896—22no—
10C3×#895—22no—
11C3×#894—22no—
12C3×#875C2212yes—
13C3×#874C2211yescharacteristic
14C2×#3715—22no—
15C2×#3713—22no—
16#63630C2212yes—
17C3×#809—22no—
18C3×#803C2211yescharacteristic
19C3×#562—31no—
20#5700D311yescharacteristic, complemented
21C3×#490—31no—
22#5074—32no—
23#5067D311yescharacteristic, complemented
24#5058—32no—
25#4543—31no—
26#4543—31no—
27#4543—61no—
28#4540—32no—
29#4464—32no—
30C2×C3×D12—22no—
31C2×C3×D12—21no—
32C2×C3×D12—22no—
33C2×C3×D12D412yes—
34C2×C3×C4×D3—22no—
35C2×C3×Dic6D412yes—
36C32×C4⋊C4—22no—
37C32×C4⋊C4D412yes—
38C32×C42C2311yescharacteristic
39C2×C3⋊(C3⋊C8)—22no—
40C3×(C2×D3)⋊C4—22no—
41C3×(C2×D3)⋊C4—22no—
42C3×(C2×D3)⋊C4—22no—
43C3×Dic3⋊C4—22no—
44C2×C3×C3⋊C8—21no—
45#3715—44no—
46#3713—44no—
47#1656—91noSylow
48C3×#127—31no—
49C3×#125—21no—
50C3×#125C2×D311yescharacteristic
51C3×#125C2×D311yescharacteristic
52C3×#124—32no—
53C3×#123—62no—
54C3×C22⋊Q8—62no—
55C3×#121—62no—
56C2×#215—62no—
57C2×#214—62no—
58C2×#213—62no—
59C2×#213—62no—
60#896—22no—
61#895—22no—
62#894—22no—
63#875C2×D312yes—
64#874C2×D311yescharacteristic
65C3×#102—62no—
66C3×#97—31no—
67#809—22no—
68#803—32no—
69#803—32no—
70#803—62no—
71#803C2×D311yescharacteristic
72C22×C3×D3—22no—
73C22×C3×D3—41no—
74C2×C32×C4—22no—
75C2×C32×C4C2×D412yes—
76C2×C32×C4C2×D411yescharacteristic
77C2×C3×Dic3—22no—
78C3×D12—42no—
79C3×D12—42no—
80C3×D12—42no—
81C3×D12—42no—
82C3×D12—82no—
83C3×C4×D3—82no—
84C3×Dic6—42no—
85C3⋊(C3⋊C8)—24no—
86C3×C3⋊C8—41no—
87#562—31no—
88#496—92no—
89#490—31no—
90#330—91no—
91#329—92no—
92C2×C3×Q8—32no—
93C2×C3×D4—32no—
94C2×C3×D4—62no—
95C2×C3×D4—61no—
96C2×C3×D4—62no—
97C22×C3×C4—62no—
98C2×D12—22no—
99C2×D12—21no—
100C2×D12—22no—
101C2×D12#6712yes—
102C2×C4×D3—22no—
103C2×Dic6#6712yes—
104C2×C3×C8—61no—
105C3×C4⋊C4—22no—
106C3×C4⋊C4—22no—
107C3×C4⋊C4—22no—
108C3×C4⋊C4—42no—
109C3×C4⋊C4—62no—
110C3×C4⋊C4#6712yes—
111C3×C4⋊C4#6712yes—
112C3×C22⋊C4—62no—
113C3×C22⋊C4—62no—
114C3×C22⋊C4—62no—
115C3×C42—21no—
116C3×C42C22×D311yescharacteristic
117C3×C42C22×D311yescharacteristic
118#215—124no—
119#214—124no—
120#213—124no—
121#213—124no—
122(C2×D3)⋊C4—22no—
123(C2×D3)⋊C4—22no—
124(C2×D3)⋊C4—22no—
125Dic3⋊C4—22no—
126C2×C3⋊C8—21no—
127C2×C3⋊C8—62no—
128C2×C3⋊C8—62no—
129C2×C3⋊C8—122no—
130C22×C32#12011yescharacteristic
131C2×C3×D3—42no—
132C2×C3×D3—42no—
133C2×C3×D3—42no—
134C2×C3×D3—82no—
135C2×C3×D3—81no—
136C32×C4—22no—
137C32×C4—21no—
138C32×C4—42no—
139C3×Dic3—42no—
140C2×SD16—182no—
141C2×D8—182no—
142#127—31no—
143#125D3211yescharacteristic
144#124—32no—
145#123—62no—
146C22⋊Q8—62no—
147#121—62no—
148#102—62no—
149#97—31no—
150#97—92no—
151C23×C3—62no—
152C23×C3—121no—
153C22×D3—22no—
154C22×D3—41no—
155C3×Q8—122no—
156C3×D4—122no—
157C3×D4—122no—
158C3×D4—122no—
159C3×D4—122no—
160C3×D4—242no—
161C2×C3×C4—22no—
162C2×C3×C4—22no—
163C2×C3×C4—21no—
164C2×C3×C4—22no—
165C2×C3×C4—42no—
166C2×C3×C4—62no—
167C2×C3×C4—242no—
168C2×C3×C4D3×D412yes—
169C2×C3×C4C2×#6711yescharacteristic
170C2×C3×C4C2×#6711yescharacteristic
171C2×C3×C4C2×#6712yes—
172C2×Dic3—22no—
173D12—42no—
174D12—42no—
175D12—42no—
176D12—42no—
177D12—82no—
178C4×D3—82no—
179Dic6—42no—
180C3×C8—121no—
181C3⋊C8—41no—
182C3⋊C8—64no—
183C3⋊C8—64no—
184C3⋊C8—124no—
185C2×C32#45312yes—
186C2×C32#45411yescharacteristic
187C3×D3—82no—
188C3×D3—161no—
189C2×Q8—32no—
190C2×D4—32no—
191C2×D4—62no—
192C2×D4—61no—
193C2×D4—62no—
194C22×C4—62no—
195SD16—364no—
196D8—364no—
197C2×C8—61no—
198C2×C8—182no—
199C4⋊C4—22no—
200C4⋊C4—62no—
201C4⋊C4#62512yes—
202C22⋊C4—62no—
203C22⋊C4—62no—
204C22⋊C4—62no—
205C42C2×D3211yescharacteristic
206C22×C3—21no—
207C22×C3—122no—
208C22×C3—122no—
209C22×C3—122no—
210C22×C3—242no—
211C22×C3—241no—
212C22×C3#93711yescharacteristic
213C22×C3#95311yescharacteristic
214C2×D3—42no—
215C2×D3—42no—
216C2×D3—42no—
217C2×D3—82no—
218C2×D3—81no—
219C3×C4—22no—
220C3×C4—22no—
221C3×C4—21no—
222C3×C4—21no—
223C3×C4—42no—
224C3×C4—41no—
225C3×C4—42no—
226C3×C4—42no—
227C3×C4—82no—
228C3×C4—122no—
229Dic3—42no—
230C32#165611yescharacteristic, complemented, Sylow
231C23—62no—
232C23—121no—
233Q8—122no—
234D4—122no—
235D4—122no—
236D4—122no—
237D4—122no—
238D4—242no—
239C2×C4—22no—
240C2×C4—62no—
241C2×C4—242no—
242C2×C4C2×#62511yescharacteristic
243C2×C4D3×#6712yes—
244C8—121no—
245C8—184no—
246C2×C3—21no—
247C2×C3—22no—
248C2×C3—242no—
249C2×C3—481no—
250C2×C3#506211yescharacteristic
251C2×C3#519812yes—
252C2×C3#524112yes—
253C2×C3#524511yescharacteristic
254D3—82no—
255D3—161no—
256C22—122no—
257C22—122no—
258C22—122no—
259C22—241no—
260C22—242no—
261C22#6397611yescharacteristic
262C4—21no—
263C4—22no—
264C4—42no—
265C4—122no—
266C3—21no—
267C3#7124811yescharacteristic, complemented
268C3#7195211yescharacteristic, complemented
269C2—242no—
270C2—481no—
271C2#1059164511yescharacteristic
272C2#1059166512yes—
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#125C22
socleC22×C32#120
hypercenter#125D32
hypocenterC32#1656
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C3×#5700C2semidirect
2. C3×#5067C2semidirect
3. #10590354C2semidirect
4. #10589409C2semidirect
5. #10589086C2semidirect
20. #5700D3semidirect
23. #5067D3semidirect
230. C32#1656semidirect
267. C3#71248semidirect
268. C3#71952semidirect

Maximal subgroups

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

subgroupindex
C3×#57002
C3×#50672
#105903542
#105894092
#105890862
#719523
#712483