Finite Group Databasebeta

← #11775764

Subgroups — #11775764

Order 1152.

482 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 112 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×#5688C211yesmaximal, characteristic
2#10590334C212yesmaximal
3#10589409C211yesmaximal, characteristic, complemented
4C3×#4543C211yesmaximal, characteristic, complemented
5#10589088C212yesmaximal, complemented
6#71821—31nomaximal
7#68362—31nomaximal
8C32×#125C2211yescharacteristic
9C3×#896—22no—
10C3×#892C412yes—
11C3×#888C412yes—
12C3×#887—22no—
13C3×C42×D3C2211yescharacteristic
14C3×#870C2211yescharacteristic
15C2×#3711—22no—
16#63630C2212yes—
17C3×#803C2212yes—
18Dic3×C3⋊C8—22no—
19C3×#533—31no—
20#5688D311yescharacteristic
21C4×#208—32no—
22#4707—32no—
23C3×#330—31no—
24#4543—31no—
25#4543—31no—
26#4543—32no—
27#4543—61no—
28#4543D311yescharacteristic, complemented
29#4465—32no—
30C2×C3×C4×D3C2×C411yescharacteristic
31C2×C3×C4×D3D412yes—
32C2×C3×Dic6—22no—
33C32×C4⋊C4—22no—
34C32×C4⋊C4C2×C412yes—
35C32×C42C2311yescharacteristic
36C2×C3⋊(C3⋊C8)—22no—
37C3×(C2×D3)⋊C4—22no—
38C3×C4⋊Dic3C2×C412yes—
39C3×Dic3⋊C4—22no—
40C3×Dic3⋊C4—22no—
41C3×C4×Dic3—22no—
42C3×C4×Dic3C2×C411yescharacteristic
43C3×C4×Dic3D412yes—
44C2×C3×C3⋊C8—22no—
45#3711—28no—
46#1526—91noSylow
47C3×C4⋊Q8—32no—
48C3×#125—21no—
49C3×#125—31no—
50C3×#125C2×D311yescharacteristic
51C3×#125C2×D311yescharacteristic
52C3×C22⋊Q8—62no—
53C3×C4×Q8—62no—
54C3×#117—32no—
55C2×C3×C42—31no—
56C2×#208—62no—
57C2×ΓL(1,𝔽25)—62no—
58#896—22no—
59#892Dic312yes—
60#888Dic312yes—
61#887—22no—
62C42×D3C2×D311yescharacteristic
63#870C2×D311yescharacteristic
64C3×#97—32no—
65C8×Dic3—62no—
66#803—32no—
67#803—32no—
68#803—62no—
69#803C2×D312yes—
70C4×C3⋊C8—62no—
71C22×C3×D3C22⋊C411yescharacteristic
72C2×C32×C4—22no—
73C2×C32×C4C22×C411yescharacteristic
74C2×C32×C4C2×D412yes—
75C2×C3×Dic3—22no—
76C2×C3×Dic3C22⋊C411yescharacteristic
77C2×C3×Dic3C22⋊C412yes—
78C3×C4×D3—22no—
79C3×C4×D3—24no—
80C3×Dic6—44no—
81C3⋊(C3⋊C8)—24no—
82C3×C3⋊C8—24no—
83#533—31no—
84C4×M16—92no—
85#330—31no—
86#330—92no—
87#330—91no—
88C2×C3×Q8—62no—
89C22×C3×C4—31no—
90C22×C3×C4—32no—
91C2×C4×D3C2×Dic311yescharacteristic
92C2×C4×D3#6712yes—
93C2×Dic6—22no—
94C2×C3×C8—62no—
95C3×C4⋊C4—22no—
96C3×C4⋊C4—22no—
97C3×C4⋊C4—22no—
98C3×C4⋊C4—32no—
99C3×C4⋊C4—42no—
100C3×C4⋊C4—62no—
101C3×C4⋊C4—62no—
102C3×C4⋊C4C4×D312yes—
103C3×C4⋊C4C2×Dic312yes—
104C3×C22⋊C4—62no—
105C3×C42—21no—
106C3×C42—31no—
107C3×C42—32no—
108C3×C42—62no—
109C3×C42C22×D311yescharacteristic
110C3×C42C22×D311yescharacteristic
111(C2×D3)⋊C4—22no—
112C4⋊Dic3C2×Dic312yes—
113Dic3⋊C4—22no—
114Dic3⋊C4—22no—
115C4×Dic3—22no—
116C4×Dic3C2×Dic311yescharacteristic
117C4×Dic3#6712yes—
118#208—68no—
119C2×C3⋊C8—22no—
120C2×C3⋊C8—62no—
121C2×C3⋊C8—62no—
122C2×C3⋊C8—122no—
123ΓL(1,𝔽25)—68no—
124C22×C32C2×C22⋊C411yescharacteristic
125C2×C3×D3—21no—
126C2×C3×D3—22no—
127C32×C4—21no—
128C32×C4—22no—
129C32×C4—42no—
130C3×Dic3—42no—
131C3×Dic3#10112yes—
132C3×Dic3#10414yes—
133C2×M16—182no—
134C4⋊Q8—32no—
135#125—31no—
136#125D3211yescharacteristic
137C22⋊Q8—62no—
138C4×Q8—62no—
139#117—32no—
140C2×C42—31no—
141#97—32no—
142#97—92no—
143C4×C8—182no—
144C23×C3—31no—
145C22×D3#21711yescharacteristic
146C3×Q8—124no—
147C2×C3×C4—22no—
148C2×C3×C4—22no—
149C2×C3×C4—21no—
150C2×C3×C4—22no—
151C2×C3×C4—31no—
152C2×C3×C4—32no—
153C2×C3×C4—42no—
154C2×C3×C4—64no—
155C2×C3×C4—62no—
156C2×C3×C4—62no—
157C2×C3×C4C2×C4×D311yescharacteristic
158C2×C3×C4D3×D412yes—
159C2×C3×C4C22×Dic311yescharacteristic
160C2×C3×C4C2×#6712yes—
161C2×Dic3—22no—
162C2×Dic3#21711yescharacteristic
163C2×Dic3#21712yes—
164C4×D3—22no—
165C4×D3—24no—
166Dic6—44no—
167C3×C8—64no—
168C3⋊C8—24no—
169C3⋊C8—64no—
170C3⋊C8—64no—
171C3⋊C8—124no—
172C2×C32C2×#10111yescharacteristic
173C2×C32C2×#10412yes—
174C3×D3—41no—
175C2×Q8—62no—
176C22×C4—31no—
177C22×C4—32no—
178M16—188no—
179C2×C8—62no—
180C2×C8—182no—
181C4⋊C4—22no—
182C4⋊C4—32no—
183C4⋊C4—62no—
184C4⋊C4—62no—
185C4⋊C4D3×Dic312yes—
186C22⋊C4—62no—
187C42—31no—
188C42—32no—
189C42—62no—
190C42C2×D3211yescharacteristic
191C22×C3—21no—
192C22×C3—61no—
193C22×C3—62no—
194C22×C3D3×C22⋊C411yescharacteristic
195C22×C3C2×#21711yescharacteristic
196C2×D3—21no—
197C2×D3—22no—
198C3×C4—21no—
199C3×C4—22no—
200C3×C4—21no—
201C3×C4—22no—
202C3×C4—32no—
203C3×C4—34no—
204C3×C4—42no—
205C3×C4—41no—
206C3×C4—42no—
207C3×C4—42no—
208C3×C4—82no—
209C3×C4—122no—
210Dic3—42no—
211Dic3#83612yes—
212Dic3#83714yes—
213C32#152611yescharacteristic, complemented, Sylow
214C23—31no—
215Q8—124no—
216C2×C4—22no—
217C2×C4—31no—
218C2×C4—32no—
219C2×C4—64no—
220C2×C4—62no—
221C2×C4—62no—
222C2×C4C2×D3×Dic311yescharacteristic
223C2×C4D3×#6712yes—
224C8—64no—
225C8—184no—
226C2×C3—21no—
227C2×C3—22no—
228C2×C3—121no—
229C2×C3D3×#10111yescharacteristic
230C2×C3D3×#10412yes—
231C2×C3C2×#83611yescharacteristic
232C2×C3C2×#83712yes—
233D3—41no—
234C22—61no—
235C22—62no—
236C22D3×#21711yescharacteristic
237C4—21no—
238C4—22no—
239C4—32no—
240C4—34no—
241C4—42no—
242C4—122no—
243C3—21no—
244C3#6836211yescharacteristic, complemented
245C3#7182111yescharacteristic, complemented
246C2—121no—
247C2D3×#83611yescharacteristic
248C2D3×#83712yes—
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×#125C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D3C22⋊C4
cosocleC32×C42C23
hypercenter#125D32
hypocenterC32#1526
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #10589409C2semidirect
4. C3×#4543C2semidirect
5. #10589088C2semidirect
28. #4543D3semidirect
213. C32#1526semidirect
244. C3#68362semidirect
245. C3#71821semidirect

Maximal subgroups

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

subgroupindex
C3×#56882
#105903342
#105894092
C3×#45432
#105890882
#718213
#683623