Finite Group Databasebeta

← #11780717

Subgroups — #11780717

Order 1152.

430 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 72 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#10596157C211yesmaximal, characteristic
2C3×#5069C211yesmaximal, characteristic
3#10590305C212yesmaximal
4C3×#4543C211yesmaximal, characteristic
5#10589089C212yesmaximal
6#71252—31nomaximal
7#68377—31nomaximal
8C32×#125C2211yescharacteristic
9#64099—22no—
10#64098—22no—
11#64098—22no—
12#64079C2212yes—
13C3×#869C2211yescharacteristic
14C3×#810—22no—
15C3×#803C2212yes—
16C3×#803C2211yescharacteristic
17#63575—22no—
18#63573—22no—
19C3⋊#564—31no—
20C3⋊#564—31no—
21C3⋊#564—61no—
22C3×#491—31no—
23#5081—32no—
24#5069D311yescharacteristic
25#4702—32no—
26C3×#330—31no—
27#4543D311yescharacteristic
28#4465—32no—
29#4465—32no—
30C2×C3×Dic6—21no—
31C32×C4⋊C4—22no—
32C32×C4⋊C4D412yes—
33C32×C42C2311yescharacteristic
34C4⋊(C3⋊Dic3)—22no—
35C4⋊(C3⋊Dic3)D412yes—
36C4⋊(C3⋊Dic3)D412yes—
37#3750—22no—
38#3750—22no—
39#3750—22no—
40#3750—22no—
41C4×C3⋊Dic3—22no—
42C3×C4⋊Dic3—22no—
43C2×C3×C3⋊C8—22no—
44C2×C3×C3⋊C8—21no—
45#1663—91noSylow
46C3×C4⋊Q8—31no—
47C3×#125—21no—
48C3×#125C2×D311yescharacteristic
49C3×#125C2×D311yescharacteristic
50#890—62no—
51#890—62no—
52#890—64no—
53#889—62no—
54#889—62no—
55#889—64no—
56#889—64no—
57#889—62no—
58#889—62no—
59#870—32no—
60#870—32no—
61#870—62no—
62#869C2×D311yescharacteristic
63C3×#103—62no—
64C3×#97—32no—
65C3×#97—31no—
66#818—62no—
67#817—62no—
68#810—22no—
69#808—62no—
70#807—62no—
71#803C2×D311yescharacteristic
72#803C2×D312yes—
73C2×C32×C4—22no—
74C2×C32×C4C2×D411yescharacteristic
75C2×C32×C4C2×D412yes—
76C2×C3⋊Dic3—22no—
77C2×C3⋊Dic3—22no—
78C2×C3×Dic3—41no—
79C3×Dic6—42no—
80C3×C3⋊C8—24no—
81C3×C3⋊C8—41no—
82#564—91no—
83#501—92no—
84#491—31no—
85#330—31no—
86#330—92no—
87C2×C3×Q8—61no—
88C2×Dic6—21no—
89C2×C3×C8—62no—
90C2×C3×C8—61no—
91C3×C4⋊C4—24no—
92C3×C4⋊C4—22no—
93C3×C4⋊C4—22no—
94C3×C4⋊C4—22no—
95C3×C4⋊C4—62no—
96C3×C4⋊C4D1212yes—
97C3×C4⋊C4#6712yes—
98C3×C42—21no—
99C3×C42C22×D311yescharacteristic
100C3×C42C22×D311yescharacteristic
101C4⋊Dic3—22no—
102C4⋊Dic3—32no—
103C4⋊Dic3—32no—
104C4⋊Dic3—32no—
105C4⋊Dic3—32no—
106C4⋊Dic3—62no—
107C4⋊Dic3—62no—
108C4⋊Dic3—64no—
109C4⋊Dic3—62no—
110C4⋊Dic3—62no—
111Dic3⋊C4—64no—
112Dic3⋊C4—64no—
113Dic3⋊C4—64no—
114Dic3⋊C4—62no—
115Dic3⋊C4—62no—
116Dic3⋊C4—64no—
117Dic3⋊C4—62no—
118Dic3⋊C4—62no—
119Dic3⋊C4—62no—
120Dic3⋊C4—62no—
121Dic3⋊C4—62no—
122Dic3⋊C4—62no—
123C4×Dic3—64no—
124C4×Dic3—62no—
125C4×Dic3—62no—
126C2×C3⋊C8—22no—
127C2×C3⋊C8—21no—
128C22×C32#12011yescharacteristic
129C32×C4—21no—
130C32×C4—22no—
131C32×C4—42no—
132C3⋊Dic3—42no—
133C3⋊Dic3—42no—
134C3×Dic3—81no—
135C4⋊Q8—31no—
136#125—92no—
137#125—182no—
138#125—182no—
139#125—182no—
140#125D3211yescharacteristic
141#107—182no—
142#106—182no—
143#103—62no—
144#97—32no—
145#97—31no—
146C3×Q8—122no—
147C2×C3×C4—24no—
148C2×C3×C4—22no—
149C2×C3×C4—22no—
150C2×C3×C4—21no—
151C2×C3×C4—22no—
152C2×C3×C4—121no—
153C2×C3×C4C2×D1211yescharacteristic
154C2×C3×C4D3×D412yes—
155C2×C3×C4D3×D412yes—
156C2×C3×C4C2×#6711yescharacteristic
157C2×Dic3—41no—
158C2×Dic3—64no—
159C2×Dic3—64no—
160C2×Dic3—62no—
161C2×Dic3—62no—
162C2×Dic3—62no—
163C2×Dic3—62no—
164Dic6—42no—
165C3×C8—64no—
166C3×C8—121no—
167C3⋊C8—24no—
168C3⋊C8—41no—
169C2×C32#45411yescharacteristic
170C2×C32#45612yes—
171C2×Q8—61no—
172C2×C8—62no—
173C2×C8—61no—
174C4⋊C4—22no—
175C4⋊C4—62no—
176C4⋊C4—92no—
177C4⋊C4—92no—
178C4⋊C4—182no—
179C4⋊C4—182no—
180C4⋊C4—182no—
181C4⋊C4—182no—
182C4⋊C4—182no—
183C4⋊C4#62612yes—
184C42—182no—
185C42C2×D3211yescharacteristic
186C22×C3—21no—
187C22×C3#88211yescharacteristic
188C22×C3#93711yescharacteristic
189C3×C4—22no—
190C3×C4—21no—
191C3×C4—21no—
192C3×C4—22no—
193C3×C4—41no—
194C3×C4—42no—
195C3×C4—44no—
196C3×C4—42no—
197C3×C4—42no—
198C3×C4—241no—
199Dic3—81no—
200Dic3—124no—
201Dic3—124no—
202Dic3—122no—
203Dic3—122no—
204Dic3—122no—
205Dic3—122no—
206C32#166311yescharacteristic, complemented, Sylow
207Q8—122no—
208C2×C4—22no—
209C2×C4—121no—
210C2×C4—182no—
211C2×C4—182no—
212C2×C4C2×#62611yescharacteristic
213C2×C4#381112yes—
214C8—64no—
215C8—121no—
216C2×C3—21no—
217C2×C3—22no—
218C2×C3#475311yescharacteristic
219C2×C3#482612yes—
220C2×C3#506211yescharacteristic
221C2×C3#520512yes—
222C22#6398111yescharacteristic
223C4—21no—
224C4—22no—
225C4—42no—
226C4—241no—
227C4—362no—
228C4—362no—
229C3—21no—
230C3#6837711yescharacteristic, complemented
231C3#7125211yescharacteristic, complemented
232C2#1059164711yescharacteristic
233C2#1059166812yes—
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#125C22
socle, prime radicalC22×C32#120
hypercenter#125D32
hypocenterC32#1663
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
206. C32#1663semidirect
230. C3#68377semidirect
231. C3#71252semidirect

Maximal subgroups

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

subgroupindex
#105961572
C3×#50692
#105903052
C3×#45432
#105890892
#712523
#683773