Finite Group Databasebeta

← #11802690

Subgroups — #11802690

Order 1152.

1993 conjugacy classes of subgroups; only the 436 normal subgroups are shown.

normal subgroups only

This group has 1993 conjugacy classes of subgroups — too many to draw. Only its 436 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
1C23×#634C211yesmaximal, characteristic
2C2×C3×#926C212yesmaximal
3#10591697C214yesmaximal
4#10591213C218yesmaximal, complemented
5#82230—32nomaximal
6C23×C32×C4C2211yescharacteristic
7C23×C3⋊Dic3C2212yes—
8C22×#634—28no—
9C22×#634C418yescomplemented
10C22×#634C2214yes—
11C2×C3×#217C2214yes—
12C3×#926—28no—
13C2×C3×C4⋊Dic3C2214yes—
14C2×C3×C4×Dic3C2214yes—
15#63579C22116yes—
16C23×Dic6—32no—
17C23×Dic6—61no—
18C2×C3×#117—32no—
19C2×#926D312yes—
20#4973—38no—
21#4943—38no—
22#4929—38no—
23C24×C32C2311yescharacteristic
24C22×C32×C4C2×C414yes—
25C22×C32×C4D418yes—
26C22×C32×C4C2312yes—
27C22×C3⋊Dic3—28no—
28C22×C3⋊Dic3C2×C418yes—
29C22×C3⋊Dic3C2314yes—
30C2×#634—232no—
31C2×#634—28no—
32C2×#634—28no—
33C2×#634C2×C4116yes—
34C22×C3×Dic3C2318yes—
35C3×#217—28no—
36C3×C4⋊Dic3—28no—
37C3×C4×Dic3—28no—
38#2310—91noSylow
39C23×C3×C4—21no—
40C23×C3×C4C2×D312yes—
41C23×Dic3—34no—
42C23×Dic3—62no—
43C22×Dic6—316no—
44C22×Dic6—34no—
45C22×Dic6—34no—
46C22×Dic6—68no—
47C22×Dic6—64no—
48C22×Dic6—616no—
49C22×Dic6—68no—
50C22×Dic6—68no—
51C3×#117—68no—
52C2×C3×C4⋊C4—34no—
53C2×C3×C22⋊C4—34no—
54C2×C3×C42—34no—
55C2×#217C2×D314yes—
56#926—28no—
57C2×C4⋊Dic3C2×D314yes—
58C2×C4×Dic3C2×D314yes—
59C3⋊#95—332no—
60C23×C32—24no—
61C23×C32C22×C412yes—
62C23×C32C2×D414yes—
63C23×C32C2411yescharacteristic
64C2×C32×C4C22⋊C4116yes—
65C2×C32×C4C22×C414yes—
66C2×C32×C4C2×D414yes—
67C2×C32×C4C2×D414yes—
68C2×C3⋊Dic3—216no—
69C2×C3⋊Dic3—28no—
70C2×C3⋊Dic3C22×C418yes—
71#634—232no—
72C2×C3×Dic3—28no—
73C2×C3×Dic3—216no—
74C23×Q8—91no—
75C2×#117—32no—
76#391—98no—
77#381—94no—
78C24×C3—21no—
79C24×C3C22×D312yes—
80C22×C3×C4—24no—
81C22×C3×C4—28no—
82C22×C3×C4—22no—
83C22×C3×C4—38no—
84C22×C3×C4C4×D318yes—
85C22×C3×C4D1218yes—
86C22×C3×C4#6718yes—
87C22×C3×C4C22×D312yes—
88C22×C3×C4C22×D312yes—
89C22×Dic3—316no—
90C22×Dic3—38no—
91C22×Dic3—68no—
92C22×Dic3—64no—
93C22×Dic3—616no—
94C22×Dic3—68no—
95C22×Dic3—68no—
96C22×Dic3C22×D318yes—
97C2×Dic6—316no—
98C2×Dic6—316no—
99C2×Dic6—616no—
100C2×Dic6—664no—
101C2×Dic6—616no—
102C2×Dic6—616no—
103C2×Dic6—664no—
104C2×Dic6—68no—
105C2×Dic6—68no—
106C2×Dic6—68no—
107C2×Dic6—68no—
108C3×C4⋊C4—68no—
109C3×C22⋊C4—68no—
110C3×C42—68no—
111#217—28no—
112C4⋊Dic3—28no—
113C4×Dic3—28no—
114C22×C32—24no—
115C22×C32—28no—
116C22×C32C2×C22⋊C414yes—
117C22×C32C23×C411yescharacteristic
118C22×C32C22×D412yes—
119C22×C322−1+414yes—
120C32×C4C2×C22⋊C418yes—
121C3⋊Dic3—28no—
122C3×Dic3—48no—
123C22×Q8—98no—
124C22×Q8—94no—
125C22×Q8—188no—
126C23×C4—92no—
127C23×C4D3211yescharacteristic
128#117—68no—
129C2×C4⋊C4—34no—
130C2×C22⋊C4—34no—
131C2×C42—34no—
132#95—916no—
133C23×C3—28no—
134C23×C3—28no—
135C23×C3—21no—
136C23×C3—22no—
137C23×C3—24no—
138C23×C3C2×C4×D314yes—
139C23×C3C2×D1214yes—
140C23×C3C2×#6714yes—
141C23×C3C23×D312yes—
142C2×C3×C4—216no—
143C2×C3×C4—24no—
144C2×C3×C4—24no—
145C2×C3×C4—24no—
146C2×C3×C4—68no—
147C2×C3×C4—616no—
148C2×C3×C4(C2×D3)⋊C4132yes—
149C2×C3×C4C2×C4×D314yes—
150C2×C3×C4C2×C4×D314yes—
151C2×C3×C4C2×D1214yes—
152C2×C3×C4C2×D1214yes—
153C2×C3×C4C2×#6714yes—
154C2×C3×C4C2×#6714yes—
155C2×Dic3—216no—
156C2×Dic3—28no—
157C2×Dic3—316no—
158C2×Dic3—68no—
159C2×Dic3—616no—
160C2×Dic3—632no—
161C2×Dic3—632no—
162C2×Dic3—68no—
163C2×Dic3—68no—
164Dic6—664no—
165Dic6—632no—
166Dic6—632no—
167C2×C32—24no—
168C2×C32C22×C22⋊C411yescharacteristic
169C2×C32#51912yes—
170C2×C32#53614yes—
171C24C2×D3211yescharacteristic
172C2×Q8—916no—
173C2×Q8—1832no—
174C2×Q8—188no—
175C2×Q8—188no—
176C22×C4—38no—
177C22×C4—94no—
178C22×C4—98no—
179C22×C4—188no—
180C22×C4#62414yes—
181C22×C4#62618yes—
182C22×C4C2×D3212yes—
183C4⋊C4—68no—
184C22⋊C4—68no—
185C42—68no—
186C22×C3—28no—
187C22×C3—216no—
188C22×C3—28no—
189C22×C3—28no—
190C22×C3—28no—
191C22×C3—24no—
192C22×C3—21no—
193C22×C3—22no—
194C22×C3—24no—
195C22×C3C2×(C2×D3)⋊C418yes—
196C22×C3C22×C4×D312yes—
197C22×C3C22×D1212yes—
198C22×C3#101018yes—
199C22×C3C22×#6712yes—
200C3×C4—28no—
201C3×C4—128no—
202C3×C4C2×(C2×D3)⋊C418yes—
203C3×C4C2×(C2×D3)⋊C418yes—
204Dic3—48no—
205Dic3—616no—
206Dic3—616no—
207C32#231011yescharacteristic, complemented, Sylow
208C23—24no—
209C23C2×#62412yes—
210C23C2×#62614yes—
211C23C22×D3211yescharacteristic
212Q8—1832no—
213C2×C4—616no—
214C2×C4—68no—
215C2×C4—98no—
216C2×C4—188no—
217C2×C4—1816no—
218C2×C4#3722116yes—
219C2×C4C2×#62414yes—
220C2×C4C2×#62614yes—
221C2×C4C2×#62614yes—
222C2×C3—28no—
223C2×C3—28no—
224C2×C3—22no—
225C2×C3—24no—
226C2×C3—21no—
227C2×C3#551614yes—
228C2×C3#552614yes—
229C2×C3C22×(C2×D3)⋊C412yes—
230C2×C3#582514yes—
231C22—24no—
232C22—28no—
233C22C2×#372214yes—
234C22#6429814yes—
235C22C22×#62411yescharacteristic
236C22C22×#62612yes—
237C4—128no—
238C4—188no—
239C4C2×#372218yes—
240C3—21no—
241C3#8223012yescomplemented
242C2—24no—
243C2#1059482812yes—
244C2#1059485614yes—
245C2C22×#372211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2310
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. #10591213C2semidirect
9. C22×#634C4semidirect
207. C32#2310semidirect
241. C3#82230semidirect

Maximal subgroups

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

subgroupindex
C23×#6342
C2×C3×#9262
#105916972
#105912132
#822303