Finite Group Databasebeta

← #11780685

Subgroups — #11780685

Order 1152.

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

normal subgroups only

This group has 437 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
2#10592768C211yesmaximal, characteristic, complemented
3#10590276C212yesmaximal, complemented
4C3×#4543C211yesmaximal, characteristic, complemented
5#10589086C212yesmaximal, complemented
6#71954—31nomaximal
7#68374—31nomaximal
8C32×#125C2211yescharacteristic
9#64078C2211yescharacteristic
10C3×#896—22no—
11C3×#895—22no—
12C3×#894—22no—
13C3×#875C2212yes—
14#63637—22no—
15#63630C2211yescharacteristic
16C3×#803C2212yes—
17#63566—22no—
18#63563—22no—
19C3×#562—31no—
20#5700D311yescharacteristic
21#5069—31no—
22#5069—31no—
23#5069—61no—
24#5055—32no—
25#4714—32no—
26C3×#330—31no—
27#4543D311yescharacteristic, complemented
28#4540—32no—
29#4464—32no—
30C2×#634—21no—
31C2×C3×D12—22no—
32C2×C3×D12D412yes—
33C2×C3×C4×D3—22no—
34C2×C3×Dic6D412yes—
35C32×C4⋊C4—22no—
36C32×C4⋊C4D412yes—
37C32×C42C2311yescharacteristic
38C4⋊(C3⋊Dic3)—22no—
39C2×C3⋊(C3⋊C8)—21no—
40C3×(C2×D3)⋊C4—22no—
41C3×(C2×D3)⋊C4—22no—
42C3×(C2×D3)⋊C4—22no—
43C3×Dic3⋊C4—22no—
44C2×C3×C3⋊C8—22no—
45#1662—91noSylow
46C3×#125—21no—
47C3×#125C2×D311yescharacteristic
48C3×#125C2×D311yescharacteristic
49C3×#124—32no—
50C3×#123—62no—
51C3×C22⋊Q8—62no—
52C3×#121—62no—
53#896—22no—
54#895—22no—
55#894—22no—
56#875C2×D312yes—
57#869—31no—
58#869—31no—
59#869—61no—
60C3×#97—32no—
61#835—62no—
62#832—62no—
63#821—62no—
64#816—62no—
65#810—64no—
66#810—62no—
67#810—62no—
68#803—31no—
69#803—31no—
70#803—61no—
71#803C2×D312yes—
72C22×C3×D3—22no—
73C2×C32×C4—22no—
74C2×C32×C4C2×D411yescharacteristic
75C2×C32×C4C2×D412yes—
76C2×C3⋊Dic3—41no—
77#634—42no—
78C2×C3×Dic3—22no—
79C3×D12—42no—
80C3×D12—82no—
81C3×C4×D3—82no—
82C3×Dic6—42no—
83C3⋊(C3⋊C8)—41no—
84C3×C3⋊C8—42no—
85#562—31no—
86#491—91no—
87#489—92no—
88#330—31no—
89#329—92no—
90C2×C3×Q8—32no—
91C2×C3×D4—32no—
92C2×C3×D4—62no—
93C22×C3×C4—62no—
94C2×D12—22no—
95C2×D12#6712yes—
96C2×C4×D3—22no—
97C2×Dic6—62no—
98C2×Dic6—61no—
99C2×Dic6—61no—
100C2×Dic6#6712yes—
101C2×C3×C8—62no—
102C3×C4⋊C4—22no—
103C3×C4⋊C4—22no—
104C3×C4⋊C4—22no—
105C3×C4⋊C4—42no—
106C3×C4⋊C4—62no—
107C3×C4⋊C4D1212yes—
108C3×C4⋊C4#6712yes—
109C3×C22⋊C4—62no—
110C3×C22⋊C4—62no—
111C3×C22⋊C4—62no—
112C3×C42—21no—
113C3×C42C22×D311yescharacteristic
114C3×C42C22×D311yescharacteristic
115(C2×D3)⋊C4—22no—
116(C2×D3)⋊C4—22no—
117(C2×D3)⋊C4—22no—
118C4⋊Dic3—62no—
119C4⋊Dic3—62no—
120C4⋊Dic3—122no—
121Dic3⋊C4—22no—
122C2×C3⋊C8—22no—
123C2×C3⋊C8—62no—
124C2×C3⋊C8—61no—
125C2×C3⋊C8—61no—
126C22×C32#12011yescharacteristic
127C2×C3×D3—42no—
128C2×C3×D3—42no—
129C2×C3×D3—42no—
130C32×C4—21no—
131C32×C4—22no—
132C32×C4—42no—
133C3⋊Dic3—81no—
134C3×Dic3—42no—
135C4⋊Q8—91no—
136#125D3211yescharacteristic
137#124—32no—
138#123—62no—
139C22⋊Q8—62no—
140#121—62no—
141#103—182no—
142#103—182no—
143#102—182no—
144#97—32no—
145#97—91no—
146C23×C3—62no—
147C22×D3—22no—
148C3×Q8—122no—
149C3×D4—122no—
150C3×D4—242no—
151C2×C3×C4—22no—
152C2×C3×C4—22no—
153C2×C3×C4—21no—
154C2×C3×C4—22no—
155C2×C3×C4—42no—
156C2×C3×C4—62no—
157C2×C3×C4—242no—
158C2×C3×C4C2×D1211yescharacteristic
159C2×C3×C4D3×D412yes—
160C2×C3×C4C2×#6711yescharacteristic
161C2×C3×C4C2×#6712yes—
162C2×Dic3—22no—
163C2×Dic3—122no—
164C2×Dic3—121no—
165C2×Dic3—121no—
166D12—42no—
167D12—82no—
168C4×D3—82no—
169Dic6—42no—
170Dic6—124no—
171Dic6—122no—
172Dic6—122no—
173C3×C8—122no—
174C3⋊C8—42no—
175C3⋊C8—122no—
176C3⋊C8—121no—
177C3⋊C8—121no—
178C2×C32#45411yescharacteristic
179C2×C32#45512yes—
180C3×D3—82no—
181C2×Q8—32no—
182C2×Q8—181no—
183C2×D4—32no—
184C2×D4—62no—
185C22×C4—62no—
186C2×C8—62no—
187C2×C8—181no—
188C4⋊C4—22no—
189C4⋊C4—62no—
190C4⋊C4—182no—
191C4⋊C4#62612yes—
192C22⋊C4—62no—
193C22⋊C4—62no—
194C22⋊C4—62no—
195C42C2×D3211yescharacteristic
196C22×C3—21no—
197C22×C3—122no—
198C22×C3—122no—
199C22×C3—122no—
200C22×C3#88211yescharacteristic
201C22×C3#95311yescharacteristic
202C2×D3—42no—
203C2×D3—42no—
204C2×D3—42no—
205C3×C4—22no—
206C3×C4—22no—
207C3×C4—21no—
208C3×C4—21no—
209C3×C4—22no—
210C3×C4—42no—
211C3×C4—42no—
212C3×C4—42no—
213C3×C4—82no—
214C3×C4—122no—
215Dic3—42no—
216Dic3—242no—
217Dic3—241no—
218Dic3—241no—
219C32#166211yescharacteristic, complemented, Sylow
220C23—62no—
221Q8—122no—
222Q8—362no—
223D4—122no—
224D4—242no—
225C2×C4—22no—
226C2×C4—62no—
227C2×C4—242no—
228C2×C4—361no—
229C2×C4C2×#62611yescharacteristic
230C2×C4D3×#6712yes—
231C8—122no—
232C8—361no—
233C2×C3—21no—
234C2×C3—22no—
235C2×C3—242no—
236C2×C3#475311yescharacteristic
237C2×C3#482512yes—
238C2×C3#524212yes—
239C2×C3#524511yescharacteristic
240D3—82no—
241C22—122no—
242C22—122no—
243C22—122no—
244C22#6397711yescharacteristic
245C4—21no—
246C4—22no—
247C4—42no—
248C4—122no—
249C4—721no—
250C3—21no—
251C3#6837411yescharacteristic, complemented
252C3#7195411yescharacteristic, complemented
253C2—242no—
254C2#1059164611yescharacteristic
255C2#1059168812yes—
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#125C22
socleC22×C32#120
prime radicalC3×#5700C2
hypercenter#125D32
hypocenterC32#1662
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
2. #10592768C2semidirect
3. #10590276C2semidirect
4. C3×#4543C2semidirect
5. #10589086C2semidirect
27. #4543D3semidirect
219. C32#1662semidirect
251. C3#68374semidirect
252. C3#71954semidirect

Maximal subgroups

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

subgroupindex
C3×#57002
#105927682
#105902762
C3×#45432
#105890862
#719543
#683743