Finite Group Databasebeta

← #11780687

Subgroups — #11780687

Order 1152.

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

normal subgroups only

This group has 422 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
2C3×#5069C211yesmaximal, characteristic, complemented
3#10590280C212yesmaximal, complemented
4#10589409C211yesmaximal, characteristic, complemented
5#10589086C212yesmaximal, complemented
6#71954—31nomaximal
7#71251—31nomaximal
8C32×#125C2211yescharacteristic
9C3×#896—22no—
10C3×#895—22no—
11C3×#894—22no—
12C3×#875C2212yes—
13C3×#869C2211yescharacteristic
14#63630C2212yes—
15C3×#810—22no—
16C3×#803C2211yescharacteristic
17#63565—22no—
18#63562—22no—
19C3×#562—31no—
20#5700D311yescharacteristic
21C3×#491—31no—
22#5089—32no—
23#5069D311yescharacteristic, complemented
24#5055—32no—
25#4543—31no—
26#4543—31no—
27#4543—61no—
28#4540—32no—
29#4464—32no—
30C2×C3×D12—22no—
31C2×C3×D12D412yes—
32C2×C3×C4×D3—22no—
33C2×C3×Dic6—21no—
34C2×C3×Dic6D412yes—
35C32×C4⋊C4—22no—
36C32×C4⋊C4D412yes—
37C32×C42C2311yescharacteristic
38C2×C3⋊(C3⋊C8)—22no—
39C3×(C2×D3)⋊C4—22no—
40C3×(C2×D3)⋊C4—22no—
41C3×(C2×D3)⋊C4—22no—
42C3×C4⋊Dic3—22no—
43C3×Dic3⋊C4—22no—
44C2×C3×C3⋊C8—21no—
45#1662—91noSylow
46C3×C4⋊Q8—31no—
47C3×#125—21no—
48C3×#125C2×D311yescharacteristic
49C3×#125C2×D311yescharacteristic
50C3×#124—32no—
51C3×#123—62no—
52C3×C22⋊Q8—62no—
53C3×#121—62no—
54#896—22no—
55#895—22no—
56#894—22no—
57#875C2×D312yes—
58#869C2×D311yescharacteristic
59C3×#103—62no—
60C3×#97—31no—
61#835—62no—
62#832—62no—
63#810—22no—
64#810—62no—
65#809—62no—
66#803—32no—
67#803—32no—
68#803—62no—
69#803C2×D311yescharacteristic
70C22×C3×D3—22no—
71C2×C32×C4—22no—
72C2×C32×C4C2×D412yes—
73C2×C32×C4C2×D411yescharacteristic
74C2×C3×Dic3—22no—
75C2×C3×Dic3—41no—
76C3×D12—42no—
77C3×D12—82no—
78C3×C4×D3—82no—
79C3×Dic6—42no—
80C3×Dic6—42no—
81C3⋊(C3⋊C8)—42no—
82C3×C3⋊C8—41no—
83#562—31no—
84#491—31no—
85#489—92no—
86#330—91no—
87#329—92no—
88C2×C3×Q8—32no—
89C2×C3×Q8—61no—
90C2×C3×D4—32no—
91C2×C3×D4—62no—
92C22×C3×C4—62no—
93C2×D12—22no—
94C2×D12#6712yes—
95C2×C4×D3—22no—
96C2×Dic6—21no—
97C2×Dic6#6712yes—
98C2×C3×C8—61no—
99C3×C4⋊C4—22no—
100C3×C4⋊C4—22no—
101C3×C4⋊C4—22no—
102C3×C4⋊C4—42no—
103C3×C4⋊C4—62no—
104C3×C4⋊C4—62no—
105C3×C4⋊C4#6712yes—
106C3×C4⋊C4#6712yes—
107C3×C22⋊C4—62no—
108C3×C22⋊C4—62no—
109C3×C22⋊C4—62no—
110C3×C42—21no—
111C3×C42C22×D311yescharacteristic
112C3×C42C22×D311yescharacteristic
113(C2×D3)⋊C4—22no—
114(C2×D3)⋊C4—22no—
115(C2×D3)⋊C4—22no—
116C4⋊Dic3—22no—
117Dic3⋊C4—22no—
118C2×C3⋊C8—21no—
119C2×C3⋊C8—62no—
120C2×C3⋊C8—62no—
121C2×C3⋊C8—122no—
122C22×C32#12011yescharacteristic
123C2×C3×D3—42no—
124C2×C3×D3—42no—
125C2×C3×D3—42no—
126C32×C4—21no—
127C32×C4—22no—
128C32×C4—42no—
129C3×Dic3—42no—
130C3×Dic3—81no—
131C4⋊Q8—31no—
132#125D3211yescharacteristic
133#124—32no—
134#123—62no—
135C22⋊Q8—62no—
136#121—62no—
137#103—62no—
138#103—182no—
139#102—182no—
140#97—31no—
141#97—92no—
142C23×C3—62no—
143C22×D3—22no—
144C3×Q8—122no—
145C3×Q8—122no—
146C3×D4—122no—
147C3×D4—242no—
148C2×C3×C4—22no—
149C2×C3×C4—22no—
150C2×C3×C4—21no—
151C2×C3×C4—22no—
152C2×C3×C4—42no—
153C2×C3×C4—62no—
154C2×C3×C4—121no—
155C2×C3×C4—242no—
156C2×C3×C4D3×D412yes—
157C2×C3×C4C2×#6711yescharacteristic
158C2×C3×C4C2×#6711yescharacteristic
159C2×C3×C4C2×#6712yes—
160C2×Dic3—22no—
161C2×Dic3—41no—
162D12—42no—
163D12—82no—
164C4×D3—82no—
165Dic6—42no—
166Dic6—42no—
167C3×C8—121no—
168C3⋊C8—41no—
169C3⋊C8—122no—
170C3⋊C8—122no—
171C3⋊C8—124no—
172C2×C32#45411yescharacteristic
173C2×C32#45512yes—
174C3×D3—82no—
175C2×Q8—32no—
176C2×Q8—61no—
177C2×D4—32no—
178C2×D4—62no—
179C22×C4—62no—
180C2×C8—61no—
181C2×C8—182no—
182C4⋊C4—22no—
183C4⋊C4—62no—
184C4⋊C4—62no—
185C4⋊C4#62512yes—
186C22⋊C4—62no—
187C22⋊C4—62no—
188C22⋊C4—62no—
189C42C2×D3211yescharacteristic
190C22×C3—21no—
191C22×C3—122no—
192C22×C3—122no—
193C22×C3—122no—
194C22×C3#93711yescharacteristic
195C22×C3#95311yescharacteristic
196C2×D3—42no—
197C2×D3—42no—
198C2×D3—42no—
199C3×C4—22no—
200C3×C4—22no—
201C3×C4—21no—
202C3×C4—21no—
203C3×C4—42no—
204C3×C4—41no—
205C3×C4—42no—
206C3×C4—42no—
207C3×C4—82no—
208C3×C4—122no—
209C3×C4—241no—
210Dic3—42no—
211Dic3—81no—
212C32#166211yescharacteristic, complemented, Sylow
213C23—62no—
214Q8—122no—
215Q8—122no—
216D4—122no—
217D4—242no—
218C2×C4—22no—
219C2×C4—62no—
220C2×C4—121no—
221C2×C4—242no—
222C2×C4C2×#62511yescharacteristic
223C2×C4D3×#6712yes—
224C8—121no—
225C8—362no—
226C2×C3—21no—
227C2×C3—22no—
228C2×C3—242no—
229C2×C3#506211yescharacteristic
230C2×C3#520212yes—
231C2×C3#524212yes—
232C2×C3#524511yescharacteristic
233D3—82no—
234C22—122no—
235C22—122no—
236C22—122no—
237C22#6397611yescharacteristic
238C4—21no—
239C4—22no—
240C4—42no—
241C4—122no—
242C4—241no—
243C3—21no—
244C3#7125111yescharacteristic, complemented
245C3#7195411yescharacteristic, complemented
246C2—242no—
247C2#1059164511yescharacteristic
248C2#1059166412yes—
subgroupG/H
centerC22#63976
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. C3×#5069C2semidirect
3. #10590280C2semidirect
4. #10589409C2semidirect
5. #10589086C2semidirect
23. #5069D3semidirect
212. C32#1662semidirect
244. C3#71251semidirect
245. C3#71954semidirect

Maximal subgroups

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

subgroupindex
C3×#57002
C3×#50692
#105902802
#105894092
#105890862
#719543
#712513