Finite Group Databasebeta

← #11807972

Subgroups — #11807972

Order 1152.

917 conjugacy classes of subgroups.

The subgroup lattice has 301 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#869C211yesmaximal, characteristic
2#10592636C211yesmaximal, characteristic
3C3×#4937C211yesmaximal, characteristic
4#10591270C214yesmaximal
5#10591269C214yesmaximal
6#10591261C214yesmaximal
7#83231—31nomaximal
8#74265—31nomaximal
9C22×C3×Dic6C2212yes—
10C2×C32×C42C2211yescharacteristic
11C2×C3×C4⋊Dic3C2212yes—
12C2×C3×C4⋊Dic3C2212yes—
13C3×#869C418yescomplemented
14C2×Dic3⋊Dic3C2214yes—
15C2×Dic32C2214yes—
16#63658C2212yes—
17#63658C2212yes—
18#63658C2212yes—
19C3×C3⋊#95C2212yes—
20C3×C3⋊#95C2212yes—
21C3×C3⋊#95C2212yes—
22#63579C2218yes—
23C2×C3×C4⋊Q8—31no—
24C2×#869D311yescharacteristic
25C3×#383—31no—
26#5229—34no—
27#4980—34no—
28#4980—34no—
29#4937—31no—
30#4937—31no—
31#4937—61no—
32#4937D311yescharacteristic
33#4654—34no—
34#4653—34no—
35#4646—34no—
36C22×C32×C4C2311yescharacteristic
37C22×C32×C4C2311yescharacteristic
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3C2314yes—
40C22×C3×Dic3C2314yes—
41C22×C3×Dic3C2314yes—
42C2×C3×Dic6—42no—
43C2×C3×Dic6—42no—
44C2×C3×Dic6C2×C418yes—
45C32×C42C2×C414yes—
46C3×C4⋊Dic3C2×C418yes—
47C3×C4⋊Dic3C2×C418yes—
48Dic3⋊Dic3—44no—
49Dic32—44no—
50#2381—91noSylow
51C22×C3×Q8—32no—
52C22×Dic6C2×D312yes—
53C3×C4⋊Q8—38no—
54C2×C3×C4⋊C4—32no—
55C2×C3×C4⋊C4—32no—
56C2×C3×C42—21no—
57C2×C3×C42C2×D311yescharacteristic
58C2×C3×C42C2×D311yescharacteristic
59C2×C4⋊Dic3—34no—
60C2×C4⋊Dic3C2×D312yes—
61C2×C4⋊Dic3C2×D312yes—
62C2×Dic3⋊C4—34no—
63C2×C4×Dic3—34no—
64C2×C4×Dic3—34no—
65#869Dic318yescomplemented
66C3×#95—32no—
67C3×#95—32no—
68C3×#95—32no—
69C3⋊#95—32no—
70C3⋊#95—32no—
71C3⋊#95—32no—
72C3⋊#95—32no—
73C3⋊#95—32no—
74C3⋊#95—32no—
75C3⋊#95—38no—
76C3⋊#95—38no—
77C3⋊#95—62no—
78C3⋊#95—62no—
79C3⋊#95—62no—
80C3⋊#95C2×D312yes—
81C3⋊#95C2×D312yes—
82C3⋊#95C2×D312yes—
83C23×C32C2411yescharacteristic
84C2×C32×C4—22no—
85C2×C32×C4—22no—
86C2×C32×C4—22no—
87C2×C32×C4C22×C412yes—
88C2×C32×C4C22×C412yes—
89C2×C32×C4C22×C412yes—
90C2×C3⋊Dic3—24no—
91C2×C3⋊Dic3—24no—
92C2×C3⋊Dic3—24no—
93C2×C3×Dic3—24no—
94C2×C3×Dic3—24no—
95C2×C3×Dic3—24no—
96C2×C3×Dic3—24no—
97C2×C3×Dic3—24no—
98C2×C3×Dic3C22×C418yes—
99C3×Dic6—48no—
100C2×C4⋊Q8—31no—
101#391—94no—
102#387—94no—
103#387—94no—
104#383—31no—
105#383—91no—
106C2×C3×Q8—38no—
107C2×C3×Q8—122no—
108C2×C3×Q8—122no—
109C22×C3×C4—21no—
110C22×C3×C4—21no—
111C22×C3×C4—21no—
112C22×C3×C4—34no—
113C22×C3×C4—34no—
114C22×C3×C4C22×D311yescharacteristic
115C22×C3×C4C22×D311yescharacteristic
116C22×C3×C4C22×D311yescharacteristic
117C22×C3×C4C22×D311yescharacteristic
118C22×C3×C4C22×D311yescharacteristic
119C22×C3×C4C22×D311yescharacteristic
120C22×Dic3—34no—
121C22×Dic3—34no—
122C22×Dic3—64no—
123C22×Dic3C22×D314yes—
124C22×Dic3C22×D314yes—
125C2×Dic6—42no—
126C2×Dic6—42no—
127C2×Dic6C2×Dic318yes—
128C3×C4⋊C4—38no—
129C3×C4⋊C4—38no—
130C3×C42—24no—
131C3×C42C4×D314yes—
132C3×C42C2×Dic314yes—
133C4⋊Dic3—124no—
134C4⋊Dic3C2×Dic318yes—
135C4⋊Dic3C2×Dic318yes—
136Dic3⋊C4—124no—
137C4×Dic3—124no—
138C4×Dic3—124no—
139C22×C32C23×C411yescharacteristic
140C22×C32H(5,𝔽2)12yes—
141C22×C322−1+412yes—
142C22×C322−1+412yes—
143C32×C4—22no—
144C32×C4—22no—
145C32×C4—22no—
146C3⋊Dic3—44no—
147C3×Dic3—28no—
148C3×Dic3—44no—
149C22×Q8—32no—
150C4⋊Q8—38no—
151C2×C4⋊C4—32no—
152C2×C4⋊C4—32no—
153C2×C4⋊C4—94no—
154C2×C42—94no—
155C2×C42D3211yescharacteristic
156#95—32no—
157#95—32no—
158#95—32no—
159#95—98no—
160#95—92no—
161#95—92no—
162#95—92no—
163C23×C3—21no—
164C23×C3C23×D311yescharacteristic
165C23×C3C23×D311yescharacteristic
166C3×Q8—128no—
167C2×C3×C4—22no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—22no—
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4—22no—
175C2×C3×C4—22no—
176C2×C3×C4—38no—
177C2×C3×C4—42no—
178C2×C3×C4—42no—
179C2×C3×C4—42no—
180C2×C3×C4—64no—
181C2×C3×C4—64no—
182C2×C3×C4—64no—
183C2×C3×C4—64no—
184C2×C3×C4—64no—
185C2×C3×C4C2×C4×D312yes—
186C2×C3×C4C2×C4×D312yes—
187C2×C3×C4C2×C4×D312yes—
188C2×C3×C4C22×Dic312yes—
189C2×C3×C4C22×Dic312yes—
190C2×C3×C4C22×Dic312yes—
191C2×Dic3—24no—
192C2×Dic3—24no—
193C2×Dic3—24no—
194C2×Dic3—24no—
195C2×Dic3—24no—
196C2×Dic3—64no—
197C2×Dic3—64no—
198C2×Dic3—64no—
199C2×Dic3—64no—
200C2×Dic3—64no—
201C2×Dic3—64no—
202C2×Dic3—124no—
203C2×Dic3—124no—
204C2×Dic3—124no—
205C2×Dic3C22×Dic318yes—
206Dic6—48no—
207C2×C32#51811yescharacteristic
208C2×C32#51911yescharacteristic
209C2×C32#51911yescharacteristic
210C2×C32#56314yes—
211C2×Q8—38no—
212C2×Q8—122no—
213C2×Q8—122no—
214C22×C4—34no—
215C22×C4—34no—
216C22×C4—94no—
217C22×C4C2×D3211yescharacteristic
218C22×C4C2×D3211yescharacteristic
219C22×C4C2×D3211yescharacteristic
220C4⋊C4—38no—
221C4⋊C4—38no—
222C4⋊C4—364no—
223C42—364no—
224C42D3×Dic314yes—
225C22×C3—22no—
226C22×C3—22no—
227C22×C3—22no—
228C22×C3—21no—
229C22×C3C22×C4×D311yescharacteristic
230C22×C3#100412yes—
231C22×C3#100712yes—
232C22×C3#100712yes—
233C22×C3#100912yes—
234C22×C3#101012yes—
235C22×C3#101012yes—
236C22×C3C23×Dic311yescharacteristic
237C3×C4—22no—
238C3×C4—22no—
239C3×C4—22no—
240C3×C4—22no—
241C3×C4—22no—
242C3×C4—22no—
243C3×C4—42no—
244C3×C4—42no—
245C3×C4—42no—
246C3×C4—68no—
247C3×C4—124no—
248Dic3—28no—
249Dic3—44no—
250Dic3—124no—
251Dic3—124no—
252Dic3—244no—
253C32#238111yescharacteristic, complemented, Sylow
254C23C22×D3211yescharacteristic
255Q8—128no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—38no—
260C2×C4—64no—
261C2×C4—64no—
262C2×C4—64no—
263C2×C4—64no—
264C2×C4—64no—
265C2×C4—184no—
266C2×C4—184no—
267C2×C4—184no—
268C2×C4C2×D3×Dic312yes—
269C2×C4C2×D3×Dic312yes—
270C2×C4C2×D3×Dic312yes—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—24no—
274C2×C3—21no—
275C2×C3#551611yescharacteristic
276C2×C3#551611yescharacteristic
277C2×C3#552111yescharacteristic
278C2×C3#571214yes—
279C2×C3#573514yes—
280C2×C3#579811yescharacteristic
281C2×C3#581211yescharacteristic
282C2×C3#581211yescharacteristic
283C22#6429712yes—
284C22#6429712yes—
285C22#6430712yes—
286C22C22×D3×Dic311yescharacteristic
287C4—22no—
288C4—22no—
289C4—22no—
290C4—68no—
291C4—124no—
292C4—364no—
293C3—21no—
294C3#7426511yescharacteristic, complemented
295C3#8323111yescharacteristic, complemented
296C2#1059395714yes—
297C2#1059481811yescharacteristic
298C2#1059481811yescharacteristic
299C2#1059498211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2381
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
13. C3×#869C4semidirect
65. #869Dic3semidirect
253. C32#2381semidirect
294. C3#74265semidirect
295. C3#83231semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8692
#105926362
C3×#49372
#105912702
#105912692
#105912612
#832313
#742653