Finite Group Databasebeta

← #11808018

Subgroups — #11808018

Order 1152.

929 conjugacy classes of subgroups; only the 244 normal subgroups are shown.

normal subgroups only

This group has 929 conjugacy classes of subgroups — too many to draw. Only its 244 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
1C2×#64079C211yesmaximal, characteristic
2C3×#4936C212yesmaximal
3#10591271C214yesmaximal
4#10591264C214yesmaximal
5#10591263C214yesmaximal
6#74161—32nomaximal
7C2×C32×C42C2211yescharacteristic
8C2×C4⋊(C3⋊Dic3)C2212yes—
9C2×#3750C2214yes—
10#64079C418yescomplemented
11C2×C3×C4⋊Dic3C2212yes—
12C2×C3×C4⋊Dic3C2212yes—
13C2×#3724C2214yes—
14C2×Dic32C2214yes—
15C3×C3⋊#95C2214yes—
16C3×C3⋊#95C2214yes—
17#63579C2214yes—
18#63579C2214yes—
19C2×#870—32no—
20C2×#870—61no—
21C3×#382—32no—
22#4978—34no—
23#4976—34no—
24#4936D312yes—
25#4655—34no—
26#4654—34no—
27#4653—34no—
28#4647—34no—
29C22×C32×C4C2312yes—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3C2314yes—
32C22×C3×Dic3C2314yes—
33C22×C3×Dic3C2314yes—
34C32×C42C2×C414yes—
35C4⋊(C3⋊Dic3)C2×C418yes—
36#3750C2×C4116yes—
37C3×C4⋊Dic3—42no—
38C3×C4⋊Dic3—42no—
39#3724—44no—
40Dic32—44no—
41#2382—91noSylow
42C2×C3×C4⋊C4—32no—
43C2×C3×C4⋊C4—32no—
44C2×C3×C42—21no—
45C2×C3×C42C2×D312yes—
46C2×C4⋊Dic3—32no—
47C2×C4⋊Dic3—32no—
48C2×C4⋊Dic3—62no—
49C2×C4⋊Dic3C2×D312yes—
50C2×C4⋊Dic3C2×D312yes—
51C2×Dic3⋊C4—34no—
52C2×Dic3⋊C4—34no—
53C2×Dic3⋊C4—34no—
54C2×Dic3⋊C4—34no—
55C2×Dic3⋊C4—64no—
56C2×C4×Dic3—34no—
57C2×C4×Dic3—34no—
58#870—316no—
59#870—68no—
60C3×#95—34no—
61C3×#95—34no—
62C3⋊#95—34no—
63C3⋊#95—34no—
64C3⋊#95—34no—
65C3⋊#95—34no—
66C3⋊#95C2×D314yes—
67C3⋊#95C2×D314yes—
68C23×C32C2411yescharacteristic
69C2×C32×C4—21no—
70C2×C32×C4—21no—
71C2×C32×C4—22no—
72C2×C32×C4—22no—
73C2×C32×C4C22×C414yes—
74C2×C32×C4C22×C412yes—
75C2×C3⋊Dic3—24no—
76C2×C3⋊Dic3—24no—
77C2×C3⋊Dic3C22×C418yes—
78C2×C3×Dic3—24no—
79C2×C3×Dic3—24no—
80C2×C3×Dic3—24no—
81C2×C3×Dic3—24no—
82C2×C3×Dic3—24no—
83C2×C3×Dic3—24no—
84C2×#125—91no—
85#389—94no—
86#387—94no—
87#387—94no—
88#382—32no—
89C22×C3×C4—21no—
90C22×C3×C4—22no—
91C22×C3×C4—34no—
92C22×C3×C4—34no—
93C22×C3×C4C22×D312yes—
94C22×C3×C4C22×D312yes—
95C22×C3×C4C22×D312yes—
96C22×Dic3—34no—
97C22×Dic3—34no—
98C22×Dic3—64no—
99C22×Dic3C22×D314yes—
100C22×Dic3C22×D314yes—
101C3×C4⋊C4—122no—
102C3×C4⋊C4—122no—
103C3×C42—24no—
104C3×C42C4×D318yes—
105C4⋊Dic3—38no—
106C4⋊Dic3—38no—
107C4⋊Dic3—42no—
108C4⋊Dic3—42no—
109C4⋊Dic3—68no—
110Dic3⋊C4—316no—
111Dic3⋊C4—316no—
112Dic3⋊C4—616no—
113Dic3⋊C4—124no—
114Dic3⋊C4—124no—
115C4×Dic3—124no—
116C4×Dic3—124no—
117C22×C32C23×C411yescharacteristic
118C22×C32H(5,𝔽2)12yes—
119C22×C322−1+412yes—
120C22×C322−1+411yescharacteristic
121C22×C322−1+411yescharacteristic
122C32×C4—22no—
123C32×C4—24no—
124C3⋊Dic3—28no—
125C3×Dic3—44no—
126C3×Dic3—44no—
127#125—98no—
128C2×C4⋊C4—32no—
129C2×C4⋊C4—32no—
130C2×C4⋊C4—92no—
131C2×C4⋊C4—94no—
132C2×C4⋊C4—94no—
133C2×C42—94no—
134C2×C42D3211yescharacteristic
135#95—34no—
136#95—34no—
137#95—94no—
138#95—94no—
139C23×C3—21no—
140C23×C3C23×D312yes—
141C2×C3×C4—22no—
142C2×C3×C4—22no—
143C2×C3×C4—22no—
144C2×C3×C4—22no—
145C2×C3×C4—22no—
146C2×C3×C4—22no—
147C2×C3×C4—22no—
148C2×C3×C4—22no—
149C2×C3×C4—22no—
150C2×C3×C4—24no—
151C2×C3×C4—42no—
152C2×C3×C4—42no—
153C2×C3×C4—64no—
154C2×C3×C4—64no—
155C2×C3×C4—64no—
156C2×C3×C4—64no—
157C2×C3×C4—64no—
158C2×C3×C4—64no—
159C2×C3×C4C2×C4×D314yes—
160C2×C3×C4C2×C4×D314yes—
161C2×C3×C4C2×C4×D314yes—
162C2×Dic3—24no—
163C2×Dic3—24no—
164C2×Dic3—24no—
165C2×Dic3—24no—
166C2×Dic3—24no—
167C2×Dic3—24no—
168C2×Dic3—38no—
169C2×Dic3—38no—
170C2×Dic3—68no—
171C2×Dic3—64no—
172C2×Dic3—64no—
173C2×Dic3—64no—
174C2×Dic3—64no—
175C2×Dic3—124no—
176C2×Dic3—124no—
177C2×C32#51911yescharacteristic
178C2×C32#52012yes—
179C2×C32#56211yescharacteristic
180C2×C32#56312yes—
181C2×C32#56411yescharacteristic
182C22×C4—34no—
183C22×C4—34no—
184C22×C4—94no—
185C22×C4C2×D3211yescharacteristic
186C22×C4C2×D3212yes—
187C4⋊C4—916no—
188C4⋊C4—98no—
189C4⋊C4—122no—
190C4⋊C4—122no—
191C4⋊C4—364no—
192C42—364no—
193C42#62414yes—
194C22×C3—22no—
195C22×C3—21no—
196C22×C3—21no—
197C22×C3—22no—
198C22×C3—21no—
199C22×C3C22×C4×D312yes—
200C22×C3#100412yes—
201C22×C3#100712yes—
202C22×C3#100912yes—
203C22×C3#101012yes—
204C22×C3#101012yes—
205C22×C3#101012yes—
206C3×C4—24no—
207C3×C4—24no—
208C3×C4—24no—
209C3×C4—24no—
210C3×C4—44no—
211C3×C4—124no—
212C3×C4—124no—
213Dic3—44no—
214Dic3—44no—
215Dic3—68no—
216Dic3—68no—
217Dic3—128no—
218C32#238211yescharacteristic, complemented, Sylow
219C23C22×D3211yescharacteristic
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—64no—
225C2×C4—64no—
226C2×C4—64no—
227C2×C4—64no—
228C2×C4—64no—
229C2×C4—64no—
230C2×C4—98no—
231C2×C4—184no—
232C2×C4—184no—
233C2×C4C2×#62412yes—
234C2×C4C2×#62414yes—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—22no—
238C2×C3—22no—
239C2×C3—21no—
240C2×C3#550412yes—
241C2×C3#551612yes—
242C2×C3#552312yes—
243C2×C3#567212yes—
244C2×C3#568412yes—
245C2×C3C3⋊#56412yes—
246C2×C3#569912yes—
247C22#6429712yes—
248C22#6429811yescharacteristic
249C22#6429811yescharacteristic
250C22#6430712yes—
251C22C22×#62411yescharacteristic
252C4—22no—
253C4—24no—
254C4—124no—
255C4—124no—
256C4—188no—
257C3—21no—
258C3#7416112yescomplemented
259C2#1059386811yescharacteristic
260C2#1059395212yes—
261C2#1059398511yescharacteristic
262C2#1059482811yescharacteristic
263C2#1059499012yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2382
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
10. #64079C4semidirect
218. C32#2382semidirect
258. C3#74161semidirect

Maximal subgroups

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

subgroupindex
C2×#640792
C3×#49362
#105912712
#105912642
#105912632
#741613