Finite Group Databasebeta

← #11801962

Subgroups — #11801962

Order 1152.

1177 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#872C211yesmaximal, characteristic
2C42×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C3×#4932C211yesmaximal, characteristic, complemented
4C4×Dic3⋊Dic3C212yesmaximal, complemented
5#10591286C214yesmaximal
6C4×(C2×D3)⋊Dic3C212yesmaximal
7#10591192C214yesmaximal, complemented
8#82229—31nomaximal
9#73385—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×C4×C3⋊Dic3C2212yes—
13C2×C4×C3⋊Dic3C2214yes—
14C2×C3×(C2×D3)⋊C4C2212yes—
15C2×C3×Dic3⋊C4C2212yes—
16C2×C3×C4×Dic3C2212yes—
17C2×C3×C4×Dic3C2211yescharacteristic
18C3×#872C418yescomplemented
19C2×Dic3⋊Dic3C2214yes—
20C2×(C2×D3)⋊Dic3C2214yes—
21C3×C3⋊#95C2214yes—
22#63579C2214yes—
23#63579C2214yes—
24C2×C3×#117—31no—
25C2×#872D311yescharacteristic
26C3×#376—31no—
27C4×#217—32no—
28#4980—34no—
29#4951—34no—
30C4×(C2×D3)⋊C4—32no—
31C4×C4⋊Dic3—32no—
32#4932D311yescharacteristic, complemented
33C4×Dic3⋊C4—32no—
34C42×Dic3—31no—
35C42×Dic3—31no—
36C42×Dic3—61no—
37#4669—34no—
38#4652—34no—
39C23×C3×D3C2311yescharacteristic
40C22×C32×C4C2312yes—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3C2314yes—
43C22×C3×Dic3C2314yes—
44C22×C3×Dic3C2312yes—
45C22×C3×Dic3C2311yescharacteristic
46C2×C3×C4×D3—24no—
47C2×C3×C4×D3C2×C414yes—
48C32×C42C2×C414yes—
49C4×C3⋊Dic3—24no—
50C4×C3⋊Dic3—28no—
51C3×(C2×D3)⋊C4C2×C418yes—
52C3×Dic3⋊C4C2×C418yes—
53C3×C4×Dic3—24no—
54C3×C4×Dic3C2×C414yes—
55Dic3⋊Dic3—28no—
56(C2×D3)⋊Dic3—28no—
57#2298—91noSylow
58C23×C3×C4—31no—
59C22×C4×D3C2×D311yescharacteristic
60C3×#117—38no—
61C2×C3×C4⋊C4—32no—
62C2×C3×C22⋊C4—32no—
63C2×C3×C42—21no—
64C2×C3×C42—31no—
65C2×C3×C42—32no—
66C2×C3×C42C2×D311yescharacteristic
67C2×C3×C42C2×D311yescharacteristic
68C2×#217—34no—
69C2×(C2×D3)⋊C4—34no—
70C2×(C2×D3)⋊C4C2×D312yes—
71C2×C4⋊Dic3—34no—
72C2×Dic3⋊C4—34no—
73C2×Dic3⋊C4C2×D312yes—
74C2×C4×Dic3—34no—
75C2×C4×Dic3—32no—
76C2×C4×Dic3—32no—
77C2×C4×Dic3—34no—
78C2×C4×Dic3—64no—
79C2×C4×Dic3—62no—
80C2×C4×Dic3C2×D312yes—
81C2×C4×Dic3C2×D311yescharacteristic
82#872Dic318yescomplemented
83C3×#95—34no—
84C3⋊#95—34no—
85C3⋊#95—34no—
86C3⋊#95—34no—
87C3⋊#95—34no—
88C3⋊#95C2×D314yes—
89C23×C32C2411yescharacteristic
90C22×C3×D3—24no—
91C22×C3×D3—22no—
92C22×C3×D3C22×C412yes—
93C2×C32×C4—24no—
94C2×C32×C4C22×C414yes—
95C2×C32×C4C22×C412yes—
96C2×C32×C4#4114yes—
97C2×C3⋊Dic3—24no—
98C2×C3⋊Dic3—24no—
99C2×C3⋊Dic3#4118yes—
100C2×C3×Dic3—24no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—24no—
103C2×C3×Dic3—24no—
104C2×C3×Dic3—24no—
105C2×C3×Dic3C22×C414yes—
106C2×C3×Dic3C22×C412yes—
107C3×C4×D3—28no—
108C2×#117—31no—
109#388—94no—
110#387—94no—
111C4×C4⋊C4—92no—
112C4×C22⋊C4—92no—
113#376—31no—
114C43—91no—
115C24×C3—31no—
116C23×D3C22×D311yescharacteristic
117C22×C3×C4—22no—
118C22×C3×C4—21no—
119C22×C3×C4—31no—
120C22×C3×C4—32no—
121C22×C3×C4—34no—
122C22×C3×C4—34no—
123C22×C3×C4—64no—
124C22×C3×C4C22×D312yes—
125C22×C3×C4C22×D312yes—
126C22×C3×C4C22×D311yescharacteristic
127C22×C3×C4C22×D311yescharacteristic
128C22×Dic3—34no—
129C22×Dic3—34no—
130C22×Dic3—64no—
131C22×Dic3C22×D314yes—
132C22×Dic3C22×D311yescharacteristic
133C22×Dic3C22×D312yes—
134C2×C4×D3—24no—
135C2×C4×D3C2×Dic314yes—
136C3×C4⋊C4—38no—
137C3×C22⋊C4—38no—
138C3×C42—24no—
139C3×C42—34no—
140C3×C42—64no—
141C3×C42C4×D314yes—
142C3×C42C2×Dic314yes—
143#217—68no—
144(C2×D3)⋊C4—68no—
145(C2×D3)⋊C4C2×Dic318yes—
146C4⋊Dic3—68no—
147Dic3⋊C4—68no—
148Dic3⋊C4C2×Dic318yes—
149C4×Dic3—24no—
150C4×Dic3—68no—
151C4×Dic3—68no—
152C4×Dic3—616no—
153C4×Dic3—68no—
154C4×Dic3—64no—
155C4×Dic3—64no—
156C4×Dic3C2×Dic314yes—
157C22×C32C23×C411yescharacteristic
158C22×C32C2×#4112yes—
159C22×C32C2×#4114yes—
160C2×C3×D3—22no—
161C2×C3×D3—24no—
162C2×C3×D3—44no—
163C32×C4—24no—
164C32×C4#11714yes—
165C3⋊Dic3—28no—
166C3×Dic3—22no—
167C3×Dic3—24no—
168C3×Dic3—44no—
169C23×C4—31no—
170#117—38no—
171C2×C4⋊C4—32no—
172C2×C4⋊C4—94no—
173C2×C22⋊C4—32no—
174C2×C22⋊C4—94no—
175C2×C42—31no—
176C2×C42—32no—
177C2×C42—94no—
178C2×C42—92no—
179C2×C42D3211yescharacteristic
180#95—34no—
181#95—94no—
182#95—94no—
183C23×C3—21no—
184C23×C3—32no—
185C23×C3—62no—
186C23×C3—64no—
187C23×C3C23×D311yescharacteristic
188C23×C3C23×D311yescharacteristic
189C22×D3—22no—
190C22×D3—24no—
191C22×D3C22×Dic312yes—
192C2×C3×C4—28no—
193C2×C3×C4—24no—
194C2×C3×C4—24no—
195C2×C3×C4—24no—
196C2×C3×C4—24no—
197C2×C3×C4—22no—
198C2×C3×C4—34no—
199C2×C3×C4—32no—
200C2×C3×C4—62no—
201C2×C3×C4—64no—
202C2×C3×C4—68no—
203C2×C3×C4—64no—
204C2×C3×C4—64no—
205C2×C3×C4—64no—
206C2×C3×C4C2×C4×D314yes—
207C2×C3×C4C2×C4×D312yes—
208C2×C3×C4#23514yes—
209C2×C3×C4#23514yes—
210C2×C3×C4C22×Dic314yes—
211C2×C3×C4C22×Dic312yes—
212C2×Dic3—22no—
213C2×Dic3—24no—
214C2×Dic3—24no—
215C2×Dic3—24no—
216C2×Dic3—24no—
217C2×Dic3—38no—
218C2×Dic3—38no—
219C2×Dic3—68no—
220C2×Dic3—68no—
221C2×Dic3—68no—
222C2×Dic3—64no—
223C2×Dic3—64no—
224C2×Dic3—64no—
225C2×Dic3—64no—
226C2×Dic3C22×Dic314yes—
227C2×Dic3C22×Dic312yes—
228C4×D3—28no—
229C2×C32C2×#11711yescharacteristic
230C2×C32C4×#4112yes—
231C2×C32#52914yes—
232C3×D3—42no—
233C24—31no—
234C22×C4—31no—
235C22×C4—32no—
236C22×C4—34no—
237C22×C4—34no—
238C22×C4—64no—
239C22×C4—94no—
240C22×C4C2×D3212yes—
241C22×C4C2×D3211yescharacteristic
242C4⋊C4—38no—
243C4⋊C4—188no—
244C22⋊C4—38no—
245C22⋊C4—188no—
246C42—34no—
247C42—64no—
248C42—188no—
249C42—184no—
250C42D3×Dic314yes—
251C22×C3—22no—
252C22×C3—24no—
253C22×C3—21no—
254C22×C3—62no—
255C22×C3—64no—
256C22×C3—124no—
257C22×C3C22×C4×D311yescharacteristic
258C22×C3C2×#23512yes—
259C22×C3C2×#23512yes—
260C22×C3D3×#4114yes—
261C22×C3D3×#4114yes—
262C22×C3C23×Dic311yescharacteristic
263C2×D3—22no—
264C2×D3—24no—
265C2×D3—44no—
266C3×C4—28no—
267C3×C4—24no—
268C3×C4—24no—
269C3×C4—24no—
270C3×C4—62no—
271C3×C4—64no—
272C3×C4—124no—
273C3×C4#87214yes—
274C3×C4#92614yes—
275Dic3—22no—
276Dic3—24no—
277Dic3—44no—
278Dic3—616no—
279Dic3—68no—
280Dic3—68no—
281C32#229811yescharacteristic, complemented, Sylow
282C23—32no—
283C23—62no—
284C23—64no—
285C23C22×D3211yescharacteristic
286C2×C4—24no—
287C2×C4—34no—
288C2×C4—32no—
289C2×C4—62no—
290C2×C4—64no—
291C2×C4—68no—
292C2×C4—64no—
293C2×C4—64no—
294C2×C4—64no—
295C2×C4—98no—
296C2×C4—184no—
297C2×C4—184no—
298C2×C4#379814yes—
299C2×C4C2×D3×Dic314yes—
300C2×C4C2×D3×Dic312yes—
301C2×C3—21no—
302C2×C3—22no—
303C2×C3—24no—
304C2×C3—122no—
305C2×C3C2×#87211yescharacteristic
306C2×C3#552212yes—
307C2×C3#552814yes—
308C2×C3#552814yes—
309C2×C3C2×#92611yescharacteristic
310C2×C3Dic3×#4112yes—
311D3—42no—
312C22—62no—
313C22—64no—
314C22—124no—
315C22C2×#379812yes—
316C22#6430614yes—
317C22C22×D3×Dic311yescharacteristic
318C4—24no—
319C4—62no—
320C4—64no—
321C4—124no—
322C4—188no—
323C4#6385514yes—
324C3—21no—
325C3#7338511yescharacteristic, complemented
326C3#8222911yescharacteristic, complemented
327C2—122no—
328C2#1059398014yes—
329C2C2×#6385511yescharacteristic
330C2#1059495812yes—
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2298
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C42×C3⋊Dic3C2semidirect
3. C3×#4932C2semidirect
4. C4×Dic3⋊Dic3C2semidirect
7. #10591192C2semidirect
18. C3×#872C4semidirect
32. #4932D3semidirect
82. #872Dic3semidirect
281. C32#2298semidirect
325. C3#73385semidirect
326. C3#82229semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8722
C42×C3⋊Dic32
C3×#49322
C4×Dic3⋊Dic32
#105912862
C4×(C2×D3)⋊Dic32
#105911922
#822293
#733853