Finite Group Databasebeta

← #11803826

Subgroups — #11803826

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 297 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#869C211yesmaximal, characteristic
2C2×Dic3×Dic6C212yesmaximal
3#10592635C211yesmaximal, characteristic
4C3×#4932C211yesmaximal, characteristic
5#10591269C218yesmaximal
6#10591220C212yesmaximal
7#83227—31nomaximal
8#73388—31nomaximal
9C22×C3×Dic6C2212yes—
10C2×C32×C42C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2212yes—
12C2×C3×C4⋊Dic3C2214yes—
13C2×C3×C4×Dic3C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C3×#869C418yescomplemented
16C2×Dic3⋊Dic3C2214yes—
17C2×Dic32C2214yes—
18Dic3×Dic6—28no—
19#63658C2214yes—
20C3×C3⋊#95C2214yes—
21#63579C2218yes—
22C2×C3×C4⋊Q8—31no—
23C2×Q8×Dic3—32no—
24C2×#869D311yescharacteristic
25C2×C4×Dic6—32no—
26C3×#376—31no—
27#5229—32no—
28#4980—38no—
29#4936—31no—
30#4936—31no—
31#4936—61no—
32#4932D311yescharacteristic
33#4929—32no—
34#4653—38no—
35C22×C32×C4C2312yes—
36C22×C32×C4C2311yescharacteristic
37C22×C3⋊Dic3C2314yes—
38C22×C3×Dic3C2312yes—
39C22×C3×Dic3C2314yes—
40C22×C3×Dic3C2312yes—
41C2×C3×Dic6—24no—
42C2×C3×Dic6—24no—
43C2×C3×Dic6C2×C418yes—
44C32×C42C2×C414yes—
45C4⋊(C3⋊Dic3)—24no—
46C3×C4⋊Dic3C2×C4116yes—
47C3×C4×Dic3—22no—
48C3×C4×Dic3D414yes—
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×C42—21no—
57C2×C3×C42—31no—
58C2×C3×C42—31no—
59C2×C3×C42C2×D311yescharacteristic
60C2×C3×C42C2×D311yescharacteristic
61Q8×Dic3—68no—
62C2×C4⋊Dic3—32no—
63C2×C4⋊Dic3—32no—
64C2×C4⋊Dic3—34no—
65C2×C4⋊Dic3—62no—
66C2×C4⋊Dic3C2×D314yes—
67C2×Dic3⋊C4—34no—
68C2×C4×Dic3—34no—
69C2×C4×Dic3—34no—
70C2×C4×Dic3C2×D311yescharacteristic
71C2×C4×Dic3C2×D311yescharacteristic
72#869Dic318yescomplemented
73C4×Dic6—68no—
74C3×#95—34no—
75C3⋊#95—34no—
76C3⋊#95—34no—
77C3⋊#95—38no—
78C3⋊#95—38no—
79C3⋊#95—64no—
80C3⋊#95C2×D314yes—
81C23×C32C2411yescharacteristic
82C2×C32×C4—24no—
83C2×C32×C4C22×C414yes—
84C2×C32×C4C22×C412yes—
85C2×C32×C4C2×D412yes—
86C2×C32×C4#4112yes—
87C2×C3⋊Dic3—24no—
88C2×C3⋊Dic3—28no—
89C2×C3×Dic3—24no—
90C2×C3×Dic3—24no—
91C2×C3×Dic3—24no—
92C2×C3×Dic3—22no—
93C2×C3×Dic3—24no—
94C2×C3×Dic3C22×C418yes—
95C2×C3×Dic3C2×D414yes—
96C3×Dic6—216no—
97C2×C4⋊Q8—31no—
98C2×C4×Q8—92no—
99#391—92no—
100#387—98no—
101#382—91no—
102#376—31no—
103C2×C3×Q8—38no—
104C2×C3×Q8—64no—
105C2×C3×Q8—64no—
106C22×C3×C4—21no—
107C22×C3×C4—22no—
108C22×C3×C4—34no—
109C22×C3×C4—32no—
110C22×C3×C4—32no—
111C22×C3×C4C22×D312yes—
112C22×C3×C4C22×D312yes—
113C22×C3×C4C22×D311yescharacteristic
114C22×C3×C4C22×D311yescharacteristic
115C22×Dic3—34no—
116C22×Dic3—34no—
117C22×Dic3—64no—
118C22×Dic3C22×D312yes—
119C22×Dic3C22×D312yes—
120C22×Dic3C22×D314yes—
121C2×Dic6—24no—
122C2×Dic6—24no—
123C2×Dic6C2×Dic318yes—
124C3×C4⋊C4—316no—
125C3×C42—24no—
126C3×C42—34no—
127C3×C42—62no—
128C3×C42C4×D314yes—
129C3×C42C2×Dic314yes—
130C4⋊Dic3—64no—
131C4⋊Dic3—64no—
132C4⋊Dic3—68no—
133C4⋊Dic3—124no—
134C4⋊Dic3C2×Dic3116yes—
135Dic3⋊C4—68no—
136C4×Dic3—22no—
137C4×Dic3—68no—
138C4×Dic3—68no—
139C4×Dic3D1214yes—
140C22×C32C23×C411yescharacteristic
141C22×C32C22×D411yescharacteristic
142C22×C32C2×#4111yescharacteristic
143C22×C322−1+414yes—
144C32×C4—24no—
145C32×C4C4×D414yes—
146C3⋊Dic3—44no—
147C3×Dic3—28no—
148C3×Dic3—24no—
149C3×Dic3—42no—
150C22×Q8—32no—
151C4⋊Q8—38no—
152C4×Q8—188no—
153C2×C4⋊C4—34no—
154C2×C4⋊C4—94no—
155C2×C4⋊C4—92no—
156C2×C42—31no—
157C2×C42—31no—
158C2×C42—94no—
159C2×C42D3211yescharacteristic
160#95—34no—
161#95—98no—
162#95—94no—
163C23×C3—21no—
164C23×C3C23×D311yescharacteristic
165C23×C3C23×D311yescharacteristic
166C3×Q8—616no—
167C2×C3×C4—24no—
168C2×C3×C4—24no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—22no—
172C2×C3×C4—24no—
173C2×C3×C4—38no—
174C2×C3×C4—34no—
175C2×C3×C4—44no—
176C2×C3×C4—64no—
177C2×C3×C4—64no—
178C2×C3×C4—64no—
179C2×C3×C4—62no—
180C2×C3×C4—64no—
181C2×C3×C4C2×C4×D314yes—
182C2×C3×C4C2×C4×D312yes—
183C2×C3×C4C2×D1212yes—
184C2×C3×C4#23512yes—
185C2×C3×C4D3×D412yes—
186C2×C3×C4#23712yes—
187C2×C3×C4C22×Dic314yes—
188C2×C3×C4C22×Dic312yes—
189C2×Dic3—24no—
190C2×Dic3—24no—
191C2×Dic3—24no—
192C2×Dic3—22no—
193C2×Dic3—24no—
194C2×Dic3—64no—
195C2×Dic3—64no—
196C2×Dic3—68no—
197C2×Dic3—68no—
198C2×Dic3—124no—
199C2×Dic3—128no—
200C2×Dic3C2×D1214yes—
201C2×Dic3C22×Dic318yes—
202Dic6—216no—
203C2×C32C2×C4×D411yescharacteristic
204C2×C32#51912yes—
205C2×C32#53612yes—
206C2×C32#54112yes—
207C2×Q8—38no—
208C2×Q8—64no—
209C2×Q8—64no—
210C22×C4—32no—
211C22×C4—34no—
212C22×C4—32no—
213C22×C4—94no—
214C22×C4C2×D3212yes—
215C22×C4C2×D3211yescharacteristic
216C4⋊C4—316no—
217C4⋊C4—188no—
218C4⋊C4—184no—
219C42—34no—
220C42—62no—
221C42—188no—
222C42D3×Dic314yes—
223C22×C3—21no—
224C22×C3—24no—
225C22×C3—21no—
226C22×C3—21no—
227C22×C3C22×C4×D311yescharacteristic
228C22×C3C22×D1211yescharacteristic
229C22×C3C2×#23511yescharacteristic
230C22×C3C2×D3×D411yescharacteristic
231C22×C3C2×#23711yescharacteristic
232C22×C3#100714yes—
233C22×C3#101014yes—
234C22×C3C23×Dic311yescharacteristic
235C3×C4—24no—
236C3×C4—24no—
237C3×C4—24no—
238C3×C4—44no—
239C3×C4—64no—
240C3×C4—68no—
241C3×C4—122no—
242C3×C4C4×D1214yes—
243C3×C4D4×Dic314yes—
244Dic3—24no—
245Dic3—28no—
246Dic3—42no—
247Dic3—124no—
248Dic3—124no—
249Dic3—244no—
250C32#232711yescharacteristic, complemented, Sylow
251C23C22×D3211yescharacteristic
252Q8—616no—
253C2×C4—24no—
254C2×C4—34no—
255C2×C4—38no—
256C2×C4—64no—
257C2×C4—64no—
258C2×C4—64no—
259C2×C4—62no—
260C2×C4—64no—
261C2×C4—188no—
262C2×C4—184no—
263C2×C4#379512yes—
264C2×C4D3×D1212yes—
265C2×C4C2×D3×Dic314yes—
266C2×C4C2×D3×Dic312yes—
267C2×C3—22no—
268C2×C3—22no—
269C2×C3—21no—
270C2×C3—22no—
271C2×C3C2×C4×D1211yescharacteristic
272C2×C3#551612yes—
273C2×C3#551812yes—
274C2×C3#552612yes—
275C2×C3#572412yes—
276C2×C3#573112yes—
277C2×C3C2×D4×Dic311yescharacteristic
278C2×C3#581212yes—
279C22C2×#379511yescharacteristic
280C22#6429714yes—
281C22C2×D3×D1211yescharacteristic
282C22C22×D3×Dic311yescharacteristic
283C4—24no—
284C4—68no—
285C4—64no—
286C4—122no—
287C4—364no—
288C4Dic3×D1214yes—
289C3—21no—
290C3#7338811yescharacteristic, complemented
291C3#8322711yescharacteristic, complemented
292C2#1059386212yes—
293C2#1059389312yes—
294C2#1059481812yes—
295C2C2×Dic3×D1211yescharacteristic
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
72. #869Dic3semidirect
250. C32#2327semidirect
290. C3#73388semidirect
291. 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×Dic3×Dic62
#105926352
C3×#49322
#105912692
#105912202
#832273
#733883