Finite Group Databasebeta

← #11802692

Subgroups — #11802692

Order 1152.

1993 conjugacy classes of subgroups; only the 316 normal subgroups are shown.

normal subgroups only

This group has 1993 conjugacy classes of subgroups — too many to draw. Only its 316 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×#63957C212yesmaximal
3C3×#5211C212yesmaximal
4#10591697C212yesmaximal
5#10591273C218yesmaximal, complemented
6#74053—32nomaximal
7C23×C32×C4C2211yescharacteristic
8C23×C3⋊Dic3C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C22×#634—28no—
11C22×#634C418yescomplemented
12C22×#634C2214yes—
13C2×C3×#217C2214yes—
14C2×#3724C2214yes—
15#63957—28no—
16C2×Dic32C2214yes—
17C3×C3⋊#95C2218yes—
18#63579C2218yes—
19C23×Dic6—32no—
20C23×Dic6—61no—
21C2×#877—34no—
22C3×#381—32no—
23#5211D312yes—
24#4943—34no—
25#4646—316no—
26C24×C32C2311yescharacteristic
27C22×C32×C4—24no—
28C22×C32×C4C2×C414yes—
29C22×C32×C4C2312yes—
30C22×C3⋊Dic3—24no—
31C22×C3⋊Dic3C2×C414yes—
32C22×C3⋊Dic3C2×C414yes—
33C22×C3⋊Dic3D418yes—
34C22×C3⋊Dic3C2312yes—
35C22×C3⋊Dic3C2312yes—
36C2×#634—232no—
37C2×#634—28no—
38C2×#634—28no—
39C2×#634C2×C4116yes—
40C22×C3×Dic3C2318yes—
41C3×#217—28no—
42#3724—28no—
43Dic32—28no—
44#2310—91noSylow
45C23×C3×C4—21no—
46C23×C3×C4C2×D312yes—
47C23×Dic3—32no—
48C23×Dic3—32no—
49C23×Dic3—61no—
50C23×Dic3—61no—
51C22×Dic6—316no—
52C22×Dic6—38no—
53C22×Dic6—68no—
54C22×Dic6—64no—
55C22×Dic6—616no—
56C22×Dic6—616no—
57C2×C3×C22⋊C4—34no—
58C2×#217C2×D314yes—
59C2×Dic3⋊C4—38no—
60C2×C4×Dic3—38no—
61#877—616no—
62C3×#95—38no—
63C3⋊#95—316no—
64C3⋊#95C2×D318yes—
65C23×C32—24no—
66C23×C32C22×C412yes—
67C23×C32C2×D414yes—
68C23×C32C2411yescharacteristic
69C2×C32×C4—28no—
70C2×C32×C4—24no—
71C2×C32×C4C22×C414yes—
72C2×C3⋊Dic3—28no—
73C2×C3⋊Dic3—24no—
74C2×C3⋊Dic3C22⋊C4116yes—
75C2×C3⋊Dic3C22×C414yes—
76C2×C3⋊Dic3C22×C414yes—
77C2×C3⋊Dic3C2×D414yes—
78C2×C3⋊Dic3C2×D414yes—
79#634—232no—
80C2×C3×Dic3—28no—
81C2×C3×Dic3—216no—
82C23×Q8—91no—
83C2×#117—92no—
84#391—98no—
85#381—32no—
86#381—92no—
87C24×C3—21no—
88C24×C3C22×D312yes—
89C22×C3×C4—28no—
90C22×C3×C4—28no—
91C22×C3×C4—24no—
92C22×C3×C4—22no—
93C22×C3×C4—38no—
94C22×C3×C4C4×D318yes—
95C22×C3×C4C22×D314yes—
96C22×Dic3—38no—
97C22×Dic3—316no—
98C22×Dic3—34no—
99C22×Dic3—38no—
100C22×Dic3—34no—
101C22×Dic3—64no—
102C22×Dic3—64no—
103C22×Dic3—68no—
104C22×Dic3—62no—
105C22×Dic3—62no—
106C22×Dic3—68no—
107C22×Dic3—68no—
108C22×Dic3C22×D318yes—
109C2×Dic6—332no—
110C2×Dic6—616no—
111C2×Dic6—664no—
112C2×Dic6—616no—
113C2×Dic6—616no—
114C2×Dic6—664no—
115C2×Dic6—616no—
116C2×Dic6—616no—
117C3×C22⋊C4—68no—
118#217—28no—
119Dic3⋊C4—616no—
120C4×Dic3—616no—
121C22×C32—24no—
122C22×C32—28no—
123C22×C32C2×C22⋊C414yes—
124C22×C32C23×C411yescharacteristic
125C22×C32C22×D412yes—
126C22×C322−1+414yes—
127C32×C4—24no—
128C3⋊Dic3—24no—
129C3⋊Dic3C2×C22⋊C418yes—
130C3×Dic3—48no—
131C22×Q8—98no—
132C22×Q8—94no—
133C22×Q8—188no—
134C23×C4—91no—
135C23×C4—91no—
136C23×C4D3211yescharacteristic
137#117—188no—
138C2×C4⋊C4—94no—
139C2×C22⋊C4—34no—
140C2×C42—94no—
141#95—38no—
142#95—98no—
143C23×C3—28no—
144C23×C3—28no—
145C23×C3—21no—
146C23×C3—22no—
147C23×C3—24no—
148C23×C3C2×C4×D314yes—
149C23×C3D3×D418yes—
150C23×C3C23×D312yes—
151C2×C3×C4—28no—
152C2×C3×C4—216no—
153C2×C3×C4—216no—
154C2×C3×C4—28no—
155C2×C3×C4—24no—
156C2×C3×C4—68no—
157C2×C3×C4—616no—
158C2×C3×C4C2×C4×D318yes—
159C2×Dic3—28no—
160C2×Dic3—216no—
161C2×Dic3—332no—
162C2×Dic3—38no—
163C2×Dic3—38no—
164C2×Dic3—38no—
165C2×Dic3—38no—
166C2×Dic3—616no—
167C2×Dic3—64no—
168C2×Dic3—64no—
169C2×Dic3—64no—
170C2×Dic3—64no—
171C2×Dic3—68no—
172C2×Dic3—616no—
173C2×Dic3—616no—
174C2×Dic3—68no—
175Dic6—664no—
176Dic6—664no—
177C2×C32—24no—
178C2×C32C22×C22⋊C411yescharacteristic
179C2×C32#51912yes—
180C2×C32#53614yes—
181C24C2×D3211yescharacteristic
182C2×Q8—916no—
183C2×Q8—188no—
184C2×Q8—188no—
185C2×Q8—1832no—
186C22×C4—24no—
187C22×C4—38no—
188C22×C4—92no—
189C22×C4—94no—
190C22×C4—98no—
191C22×C4—92no—
192C22×C4—94no—
193C22×C4—184no—
194C22×C4#62414yes—
195C22×C4C2×D3212yes—
196C4⋊C4—188no—
197C22⋊C4—68no—
198C42—188no—
199C22×C3—28no—
200C22×C3—216no—
201C22×C3—216no—
202C22×C3—28no—
203C22×C3—24no—
204C22×C3—21no—
205C22×C3—22no—
206C22×C3—24no—
207C22×C3D3×C22⋊C418yes—
208C22×C3C22×C4×D312yes—
209C22×C3C2×D3×D414yes—
210C22×C3#101018yes—
211C3×C4—28no—
212C3×C4—28no—
213C3×C4—128no—
214Dic3—316no—
215Dic3—48no—
216Dic3—68no—
217Dic3—68no—
218Dic3—68no—
219C32#231011yescharacteristic, complemented, Sylow
220C23—24no—
221C23C2×#62412yes—
222C23#381114yes—
223C23C22×D3211yescharacteristic
224Q8—1832no—
225C2×C4—24no—
226C2×C4—28no—
227C2×C4—616no—
228C2×C4—68no—
229C2×C4—94no—
230C2×C4—94no—
231C2×C4—94no—
232C2×C4—916no—
233C2×C4—94no—
234C2×C4—184no—
235C2×C4—188no—
236C2×C4C2×#62414yes—
237C2×C3—28no—
238C2×C3—28no—
239C2×C3—22no—
240C2×C3—24no—
241C2×C3—21no—
242C2×C3C2×D3×C22⋊C412yes—
243C2×C3#551614yes—
244C2×C3#564818yes—
245C22—24no—
246C22—28no—
247C22#6397414yes—
248C22#6429814yes—
249C22C22×#62411yescharacteristic
250C22C2×#381112yes—
251C4—24no—
252C4—98no—
253C4—128no—
254C4—184no—
255C3—21no—
256C3#7405312yescomplemented
257C2—24no—
258C2#1059482812yes—
259C2#1059492114yes—
260C2C2×#6397411yescharacteristic
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
5. #10591273C2semidirect
11. C22×#634C4semidirect
219. C32#2310semidirect
256. C3#74053semidirect

Maximal subgroups

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

subgroupindex
C23×#6342
C2×#639572
C3×#52112
#105916972
#105912732
#740533