Finite Group Databasebeta

← #11803827

Subgroups — #11803827

Order 1152.

1121 conjugacy classes of subgroups.

The subgroup lattice has 303 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#869C211yesmaximal, characteristic
2C2×#63843C212yesmaximal
3#10592631C211yesmaximal, characteristic
4C3×#4936C211yesmaximal, characteristic
5#10591270C218yesmaximal
6#10591221C212yesmaximal
7#83227—31nomaximal
8#74152—31nomaximal
9C22×C3×Dic6C2212yes—
10C2×C32×C42C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C3×C4⋊Dic3C2212yes—
14C2×C3×C4⋊Dic3C2214yes—
15C3×#869C418yescomplemented
16C2×Dic3⋊Dic3C2214yes—
17C2×Dic32C2214yes—
18#63843—28no—
19#63658C2214yes—
20C3×C3⋊#95C2214yes—
21#63579C2218yes—
22C2×C3×C4⋊Q8—31no—
23C2×Q8×Dic3—32no—
24C2×#887—32no—
25C2×#869D311yescharacteristic
26C3×#382—31no—
27#5229—32no—
28#4980—38no—
29#4973—32no—
30#4936D311yescharacteristic
31#4932—31no—
32#4932—31no—
33#4932—61no—
34#4654—38no—
35C22×C32×C4C2312yes—
36C22×C32×C4C2311yescharacteristic
37C22×C3⋊Dic3C2312yes—
38C22×C3⋊Dic3C2312yes—
39C22×C3×Dic3C2314yes—
40C22×C3×Dic3C2314yes—
41C2×C3×Dic6—24no—
42C2×C3×Dic6—24no—
43C2×C3×Dic6C2×C418yes—
44C32×C42C2×C414yes—
45C4×C3⋊Dic3—22no—
46C4×C3⋊Dic3D414yes—
47C3×C4⋊Dic3—24no—
48C3×C4⋊Dic3C2×C4116yes—
49Dic3⋊Dic3—28no—
50Dic32—28no—
51#2327—91noSylow
52C22×C3×Q8—32no—
53C22×Dic6C2×D312yes—
54C3×C4⋊Q8—38no—
55C2×C3×C4⋊C4—34no—
56C2×C3×C4⋊C4—32no—
57C2×C3×C42—21no—
58C2×C3×C42C2×D311yescharacteristic
59C2×C3×C42C2×D311yescharacteristic
60Q8×Dic3—68no—
61C2×C4⋊Dic3—34no—
62C2×C4⋊Dic3C2×D312yes—
63C2×C4⋊Dic3C2×D314yes—
64C2×Dic3⋊C4—34no—
65C2×C4×Dic3—31no—
66C2×C4×Dic3—31no—
67C2×C4×Dic3—31no—
68C2×C4×Dic3—31no—
69C2×C4×Dic3—34no—
70C2×C4×Dic3—34no—
71C2×C4×Dic3—61no—
72C2×C4×Dic3—61no—
73#887—68no—
74#869Dic318yescomplemented
75C3×#95—34no—
76C3⋊#95—34no—
77C3⋊#95—34no—
78C3⋊#95—38no—
79C3⋊#95—38no—
80C3⋊#95—64no—
81C3⋊#95C2×D314yes—
82C23×C32C2411yescharacteristic
83C2×C32×C4—24no—
84C2×C32×C4C22×C414yes—
85C2×C32×C4C22×C412yes—
86C2×C32×C4C2×D412yes—
87C2×C32×C4#4112yes—
88C2×C3⋊Dic3—22no—
89C2×C3⋊Dic3—24no—
90C2×C3⋊Dic3—24no—
91C2×C3⋊Dic3C2×D414yes—
92C2×C3×Dic3—24no—
93C2×C3×Dic3—24no—
94C2×C3×Dic3—24no—
95C2×C3×Dic3—28no—
96C2×C3×Dic3C22×C418yes—
97C3×Dic6—216no—
98C2×C4⋊Q8—31no—
99C2×C4×Q8—92no—
100#391—92no—
101#387—98no—
102#382—31no—
103#376—91no—
104C2×C3×Q8—38no—
105C2×C3×Q8—64no—
106C2×C3×Q8—64no—
107C22×C3×C4—21no—
108C22×C3×C4—22no—
109C22×C3×C4—34no—
110C22×C3×C4—34no—
111C22×C3×C4C22×D312yes—
112C22×C3×C4C22×D312yes—
113C22×C3×C4C22×D311yescharacteristic
114C22×C3×C4C22×D311yescharacteristic
115C22×Dic3—32no—
116C22×Dic3—32no—
117C22×Dic3—32no—
118C22×Dic3—32no—
119C22×Dic3—62no—
120C22×Dic3—62no—
121C22×Dic3C22×D314yes—
122C22×Dic3C22×D314yes—
123C2×Dic6—24no—
124C2×Dic6—24no—
125C2×Dic6C2×Dic318yes—
126C3×C4⋊C4—316no—
127C3×C4⋊C4—64no—
128C3×C42—24no—
129C3×C42C4×D314yes—
130C3×C42C2×Dic314yes—
131C4⋊Dic3—24no—
132C4⋊Dic3—68no—
133C4⋊Dic3C2×Dic3116yes—
134Dic3⋊C4—68no—
135C4×Dic3—34no—
136C4×Dic3—34no—
137C4×Dic3—64no—
138C4×Dic3—68no—
139C4×Dic3—68no—
140C4×Dic3—64no—
141C4×Dic3—62no—
142C4×Dic3—62no—
143C22×C32C23×C411yescharacteristic
144C22×C32C22×D411yescharacteristic
145C22×C32C2×#4111yescharacteristic
146C22×C322−1+414yes—
147C32×C4—24no—
148C32×C4C4×D414yes—
149C3⋊Dic3—24no—
150C3⋊Dic3—42no—
151C3×Dic3—28no—
152C3×Dic3—44no—
153C22×Q8—32no—
154C4⋊Q8—38no—
155C4×Q8—188no—
156C2×C4⋊C4—34no—
157C2×C4⋊C4—32no—
158C2×C4⋊C4—94no—
159C2×C42—91no—
160C2×C42—94no—
161C2×C42—91no—
162C2×C42D3211yescharacteristic
163#95—34no—
164#95—98no—
165#95—94no—
166C23×C3—21no—
167C23×C3C23×D311yescharacteristic
168C23×C3C23×D311yescharacteristic
169C3×Q8—616no—
170C2×C3×C4—24no—
171C2×C3×C4—24no—
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4—22no—
175C2×C3×C4—24no—
176C2×C3×C4—38no—
177C2×C3×C4—44no—
178C2×C3×C4—64no—
179C2×C3×C4—64no—
180C2×C3×C4—64no—
181C2×C3×C4—68no—
182C2×C3×C4C2×C4×D314yes—
183C2×C3×C4C2×C4×D312yes—
184C2×C3×C4D3×D412yes—
185C2×C3×C4D3×D412yes—
186C2×C3×C4#23712yes—
187C2×C3×C4#23912yes—
188C2×C3×C4C22×Dic314yes—
189C2×C3×C4C22×Dic312yes—
190C2×Dic3—24no—
191C2×Dic3—24no—
192C2×Dic3—24no—
193C2×Dic3—28no—
194C2×Dic3—34no—
195C2×Dic3—34no—
196C2×Dic3—64no—
197C2×Dic3—64no—
198C2×Dic3—64no—
199C2×Dic3—64no—
200C2×Dic3—62no—
201C2×Dic3—62no—
202C2×Dic3—64no—
203C2×Dic3—64no—
204C2×Dic3—124no—
205C2×Dic3—124no—
206C2×Dic3C22×Dic318yes—
207Dic6—216no—
208C2×C32C2×C4×D411yescharacteristic
209C2×C32#51912yes—
210C2×C32#53612yes—
211C2×C32#54112yes—
212C2×Q8—38no—
213C2×Q8—64no—
214C2×Q8—64no—
215C22×C4—34no—
216C22×C4—34no—
217C22×C4—92no—
218C22×C4—92no—
219C22×C4C2×D3212yes—
220C22×C4C2×D3211yescharacteristic
221C4⋊C4—316no—
222C4⋊C4—64no—
223C4⋊C4—188no—
224C42—94no—
225C42—188no—
226C42—182no—
227C42D3×Dic314yes—
228C22×C3—21no—
229C22×C3—24no—
230C22×C3—21no—
231C22×C3—21no—
232C22×C3C22×C4×D311yescharacteristic
233C22×C3C2×D3×D411yescharacteristic
234C22×C3C2×D3×D411yescharacteristic
235C22×C3C2×#23711yescharacteristic
236C22×C3C2×#23911yescharacteristic
237C22×C3#100714yes—
238C22×C3#101014yes—
239C22×C3C23×Dic311yescharacteristic
240C3×C4—24no—
241C3×C4—24no—
242C3×C4—24no—
243C3×C4—44no—
244C3×C4—68no—
245C3×C4—124no—
246C3×C4#89314yes—
247C3×C4D4×Dic314yes—
248Dic3—28no—
249Dic3—44no—
250Dic3—64no—
251Dic3—64no—
252Dic3—124no—
253Dic3—124no—
254Dic3—122no—
255Dic3—122no—
256C32#232711yescharacteristic, complemented, Sylow
257C23C22×D3211yescharacteristic
258Q8—616no—
259C2×C4—24no—
260C2×C4—38no—
261C2×C4—64no—
262C2×C4—64no—
263C2×C4—68no—
264C2×C4—64no—
265C2×C4—94no—
266C2×C4—184no—
267C2×C4—182no—
268C2×C4—184no—
269C2×C4#379612yes—
270C2×C4#380212yes—
271C2×C4C2×D3×Dic314yes—
272C2×C4C2×D3×Dic312yes—
273C2×C3—22no—
274C2×C3—22no—
275C2×C3—21no—
276C2×C3—22no—
277C2×C3C2×#89311yescharacteristic
278C2×C3#551612yes—
279C2×C3#567512yes—
280C2×C3#569812yes—
281C2×C3#572412yes—
282C2×C3#573112yes—
283C2×C3C2×D4×Dic311yescharacteristic
284C2×C3#581212yes—
285C22C2×#379611yescharacteristic
286C22#6429714yes—
287C22C2×#380211yescharacteristic
288C22C22×D3×Dic311yescharacteristic
289C4—24no—
290C4—68no—
291C4—124no—
292C4—184no—
293C4—362no—
294C4#6389814yes—
295C3—21no—
296C3#7415211yescharacteristic, complemented
297C3#8322711yescharacteristic, complemented
298C2#1059386712yes—
299C2#1059390812yes—
300C2#1059481812yes—
301C2C2×#6389811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2327
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
15. C3×#869C4semidirect
74. #869Dic3semidirect
256. C32#2327semidirect
296. C3#74152semidirect
297. C3#83227semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8692
C2×#638432
#105926312
C3×#49362
#105912702
#105912212
#832273
#741523