Finite Group Databasebeta

← #11771960

Subgroups — #11771960

Order 1152.

281 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 281 conjugacy classes of subgroups — too many to draw. Only its 66 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×#4986C211yesmaximal, characteristic
2#10589396C211yesmaximal, characteristic
3C3×#4528C211yesmaximal, characteristic
4#67652—31nomaximal
5#67459—31nomaximal
6C2×C32×C4⋊C4C2211yescharacteristic
7C2×#3748—21no—
8C2×C3×C4⋊Dic3C411yescharacteristic
9C3×C3⋊#95—21no—
10C3×C3⋊#95—21no—
11C3×C3⋊#95C411yescharacteristic
12C3×#830—21no—
13C3×#400—31no—
14#4986D311yescharacteristic
15C3×#324—31no—
16#4530—31no—
17#4530—31no—
18#4530—61no—
19#4528D311yescharacteristic
20C22×C32×C4C2×C411yescharacteristic
21C22×C32×C4D411yescharacteristic
22C22×C32×C4D411yescharacteristic
23C22×C3×Dic3—21no—
24C22×C3×Dic3—21no—
25C32×C4⋊C4—41no—
26#3748—22no—
27#3748—41no—
28C2×C3⋊(C3⋊C8)—41no—
29C3×C4⋊Dic3—41no—
30C2×C3×C3⋊C8—41no—
31#1353—91noSylow
32C2×C3×C4⋊C4—21no—
33C2×C3×C4⋊C4—31no—
34C2×C3×C4⋊C4C2×D311yescharacteristic
35C2×C3×C4⋊C4C2×D311yescharacteristic
36C2×C4⋊Dic3Dic311yescharacteristic
37C2×#208—62no—
38C2×#208—61no—
39C2×#208—61no—
40C3×C22⋊C8—61no—
41C3×#95—31no—
42C3×#95—61no—
43C3×#95—61no—
44C3⋊#95—21no—
45C3⋊#95—21no—
46C3⋊#95Dic311yescharacteristic
47#830—21no—
48C23×C32C22⋊C411yescharacteristic
49C2×C32×C4—21no—
50C2×C32×C4—21no—
51C2×C32×C4—21no—
52C2×C32×C4—21no—
53C2×C32×C4—41no—
54C2×C32×C4—41no—
55C2×C32×C4SD1611yescharacteristic
56C2×C32×C4Q1611yescharacteristic
57C2×C3×Dic3—41no—
58C2×C3×Dic3—41no—
59C2×C3×Dic3—42no—
60C2×C3×Dic3—41no—
61C2×C3×Dic3—41no—
62C3⋊(C3⋊C8)—42no—
63C3×C3⋊C8—81no—
64#400—31no—
65#343—91no—
66#324—31no—
67C22×C3×C4—21no—
68C22×C3×C4—21no—
69C22×C3×C4—21no—
70C22×C3×C4—61no—
71C22×C3×C4—61no—
72C22×C3×C4C4×D311yescharacteristic
73C22×C3×C4D1211yescharacteristic
74C22×C3×C4C2×Dic311yescharacteristic
75C22×C3×C4#6711yescharacteristic
76C22×C3×C4#6711yescharacteristic
77C22×C3×C4#6711yescharacteristic
78C22×Dic3—21no—
79C22×Dic3—21no—
80C2×C3×C8—121no—
81C3×C4⋊C4—41no—
82C3×C4⋊C4—41no—
83C3×C4⋊C4—42no—
84C3×C4⋊C4—121no—
85C4⋊Dic3—41no—
86#208—64no—
87#208—62no—
88#208—62no—
89#208—122no—
90#208—121no—
91#208—121no—
92C2×C3⋊C8—41no—
93C2×C3⋊C8—122no—
94C2×C3⋊C8—121no—
95C2×C3⋊C8—121no—
96C22×C32—21no—
97C22×C32—21no—
98C22×C32#9911yescharacteristic
99C22×C32#10311yescharacteristic
100C22×C32#10411yescharacteristic
101C32×C4—21no—
102C32×C4—21no—
103C32×C4—41no—
104C32×C4—41no—
105C3×Dic3—81no—
106C3×Dic3—81no—
107C2×M16—181no—
108C2×C4⋊C4—31no—
109C2×C4⋊C4D3211yescharacteristic
110C22⋊C8—61no—
111#95—31no—
112#95—61no—
113#95—61no—
114C23×C3—21no—
115C23×C3(C2×D3)⋊C411yescharacteristic
116C23×C3#21711yescharacteristic
117C2×C3×C4—22no—
118C2×C3×C4—22no—
119C2×C3×C4—21no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4—21no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—41no—
130C2×C3×C4—41no—
131C2×C3×C4—41no—
132C2×C3×C4—41no—
133C2×C3×C4—41no—
134C2×C3×C4—41no—
135C2×C3×C4—81no—
136C2×C3×C4—81no—
137C2×C3×C4—121no—
138C2×C3×C4—121no—
139C2×C3×C4—122no—
140C2×C3×C4—121no—
141C2×C3×C4—121no—
142C2×C3×C4#20411yescharacteristic
143C2×C3×C4Dic1211yescharacteristic
144C2×C3×C4#21511yescharacteristic
145C2×C3×C4#21611yescharacteristic
146C2×Dic3—41no—
147C2×Dic3—41no—
148C2×Dic3—42no—
149C2×Dic3—41no—
150C2×Dic3—41no—
151C3×C8—241no—
152C3⋊C8—81no—
153C3⋊C8—124no—
154C3⋊C8—122no—
155C3⋊C8—122no—
156C2×C32—21no—
157C2×C32—21no—
158C2×C32#32811yescharacteristic
159C2×C32#35211yescharacteristic
160C2×C32#35511yescharacteristic
161C22×C4—61no—
162C22×C4—61no—
163C22×C4D3×Dic311yescharacteristic
164C22×C4#62511yescharacteristic
165C22×C4#62611yescharacteristic
166M16—182no—
167M16—361no—
168C2×C8—121no—
169C2×C8—361no—
170C4⋊C4—41no—
171C4⋊C4—121no—
172C22×C3—21no—
173C22×C3—21no—
174C22×C3—21no—
175C22×C3—21no—
176C22×C3—21no—
177C22×C3—21no—
178C22×C3—21no—
179C22×C3—41no—
180C22×C3—41no—
181C22×C3#80611yescharacteristic
182C22×C3#81611yescharacteristic
183C22×C3#82511yescharacteristic
184C22×C3#83411yescharacteristic
185C22×C3#83511yescharacteristic
186C22×C3#83711yescharacteristic
187C3×C4—22no—
188C3×C4—22no—
189C3×C4—21no—
190C3×C4—21no—
191C3×C4—21no—
192C3×C4—21no—
193C3×C4—41no—
194C3×C4—41no—
195C3×C4—41no—
196C3×C4—41no—
197C3×C4—81no—
198C3×C4—81no—
199C3×C4—241no—
200C3×C4—241no—
201Dic3—81no—
202Dic3—81no—
203C32#135311yescharacteristic, complemented, Sylow
204C23(C2×D3)⋊Dic311yescharacteristic
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—121no—
212C2×C4—121no—
213C2×C4—122no—
214C2×C4—121no—
215C2×C4—121no—
216C2×C4#371711yescharacteristic
217C2×C4#371911yescharacteristic
218C8—241no—
219C8—362no—
220C2×C3—21no—
221C2×C3—21no—
222C2×C3—21no—
223C2×C3—21no—
224C2×C3—21no—
225C2×C3—21no—
226C2×C3—21no—
227C2×C3—41no—
228C2×C3—41no—
229C2×C3#446711yescharacteristic
230C2×C3#447211yescharacteristic
231C2×C3#447711yescharacteristic
232C2×C3#453811yescharacteristic
233C2×C3#453911yescharacteristic
234C2×C3#454211yescharacteristic
235C22—21no—
236C22—21no—
237C22#6356611yescharacteristic
238C22#6356811yescharacteristic
239C22#6358011yescharacteristic
240C4—21no—
241C4—21no—
242C4—41no—
243C4—41no—
244C4—241no—
245C4—241no—
246C3—21no—
247C3#6745911yescharacteristic, complemented
248C3#6765211yescharacteristic, complemented
249C2—21no—
250C2—21no—
251C2#1058915211yescharacteristic
252C2#1058917511yescharacteristic
253C2#1058918211yescharacteristic
subgroupG/H
centerC22#63580
commutatorC22×C32×C4C2×C4
Frattini, hypercenterC2×C4⋊C4D32
Fitting, cosocleC2×C32×C4⋊C4C22
socleC22×C32#99
prime radicalC23×C32C22⋊C4
hypocenterC32#1353
LCSG ▷ C22×C32×C4 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
203. C32#1353semidirect
247. C3#67459semidirect
248. C3#67652semidirect

Maximal subgroups

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

subgroupindex
C3×#49862
#105893962
C3×#45282
#676523
#674593