Finite Group Databasebeta

← #11801965

Subgroups — #11801965

Order 1152.

1213 conjugacy classes of subgroups; only the 292 normal subgroups are shown.

normal subgroups only

This group has 1213 conjugacy classes of subgroups — too many to draw. Only its 292 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×#64081C211yesmaximal, characteristic
2C3×C4×C4⋊Dic3C212yesmaximal, complemented
3C4×#3722C212yesmaximal
4#10591266C214yesmaximal
5#10591263C214yesmaximal, complemented
6C4×Dic32C211yesmaximal, characteristic, complemented
7#10591222C211yesmaximal, characteristic, complemented
8#73620—32nomaximal
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×C32×C42C2211yescharacteristic
11C2×#3752C2212yes—
12C2×#3750C2212yes—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64081C418yescomplemented
15C2×C3×C4⋊Dic3C2214yes—
16C2×C3×C4×Dic3C2212yes—
17C2×C3×C4×Dic3C2212yes—
18C2×#3722C2214yes—
19C2×Dic32C2214yes—
20C3×C3⋊#95C2214yes—
21#63579C2214yes—
22#63579C2214yes—
23C2×#872—32no—
24C2×#872—61no—
25C3×C4×C4⋊C4—32no—
26#4990—34no—
27#4978—34no—
28C4×(C2×D3)⋊C4—32no—
29C4×(C2×D3)⋊C4—32no—
30C4×C4⋊Dic3D312yescomplemented
31#4932—32no—
32C42×Dic3—32no—
33#4670—34no—
34#4655—34no—
35C23×C3⋊D3C2311yescharacteristic
36C22×C32×C4C2312yes—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3C2311yescharacteristic
39C22×C3⋊Dic3C2312yes—
40C2×C4×C3⋊D3—24no—
41C2×C4×C3⋊D3C2×C414yes—
42C22×C3×Dic3C2314yes—
43C22×C3×Dic3C2314yes—
44C32×C42C2×C414yes—
45#3752C2×C418yes—
46#3750C2×C418yes—
47C4×C3⋊Dic3C2×C414yes—
48C3×C4⋊Dic3—28no—
49C3×C4×Dic3—24no—
50C3×C4×Dic3—24no—
51#3722—28no—
52Dic32—28no—
53#2298—91noSylow
54C22×C4×D3—32no—
55C22×C4×D3—61no—
56C2×C3×C4⋊C4—34no—
57C2×C3×C42—21no—
58C2×C3×C42—32no—
59C2×C3×C42—32no—
60C2×C3×C42C2×D312yes—
61C2×(C2×D3)⋊C4—32no—
62C2×(C2×D3)⋊C4—32no—
63C2×(C2×D3)⋊C4—34no—
64C2×(C2×D3)⋊C4—34no—
65C2×(C2×D3)⋊C4—62no—
66C2×C4⋊Dic3C2×D314yes—
67C2×Dic3⋊C4—32no—
68C2×Dic3⋊C4—32no—
69C2×Dic3⋊C4—62no—
70C2×C4×Dic3—32no—
71C2×C4×Dic3—34no—
72C2×C4×Dic3—34no—
73C2×C4×Dic3—61no—
74C2×C4×Dic3C2×D312yes—
75C2×C4×Dic3C2×D312yes—
76#872—316no—
77#872—68no—
78C3×#95—34no—
79C3⋊#95—34no—
80C3⋊#95—34no—
81C3⋊#95—34no—
82C3⋊#95—34no—
83C3⋊#95C2×D314yes—
84C23×C32C2411yescharacteristic
85C22×C3⋊D3—22no—
86C22×C3⋊D3—24no—
87C22×C3⋊D3C22×C412yes—
88C2×C32×C4—24no—
89C2×C32×C4C22×C414yes—
90C2×C32×C4C22×C412yes—
91C2×C32×C4#4114yes—
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3—24no—
94C2×C3⋊Dic3C22×C414yes—
95C2×C3⋊Dic3C22×C412yes—
96C4×C3⋊D3—28no—
97C2×C3×Dic3—24no—
98C2×C3×Dic3—24no—
99C2×C3×Dic3—24no—
100C2×C3×Dic3—24no—
101C2×C3×Dic3—24no—
102C2×C3×Dic3#4118yes—
103C2×#117—91no—
104#388—94no—
105#387—94no—
106C4×C4⋊C4—32no—
107C4×C22⋊C4—92no—
108#376—91no—
109C43—91no—
110C23×D3—32no—
111C23×D3—61no—
112C22×C3×C4—22no—
113C22×C3×C4—21no—
114C22×C3×C4—34no—
115C22×C3×C4—34no—
116C22×C3×C4C22×D312yes—
117C22×C3×C4C22×D312yes—
118C22×C3×C4C22×D312yes—
119C22×Dic3—32no—
120C22×Dic3—32no—
121C22×Dic3—32no—
122C22×Dic3—61no—
123C22×Dic3—62no—
124C22×Dic3C22×D314yes—
125C22×Dic3C22×D314yes—
126C2×C4×D3—38no—
127C2×C4×D3—64no—
128C2×C4×D3—68no—
129C2×C4×D3—64no—
130C2×C4×D3—64no—
131C3×C4⋊C4—68no—
132C3×C42—24no—
133C3×C42—64no—
134C3×C42—64no—
135C3×C42C4×D318yes—
136(C2×D3)⋊C4—38no—
137(C2×D3)⋊C4—38no—
138(C2×D3)⋊C4—68no—
139(C2×D3)⋊C4—68no—
140(C2×D3)⋊C4—68no—
141C4⋊Dic3—28no—
142Dic3⋊C4—38no—
143Dic3⋊C4—38no—
144Dic3⋊C4—68no—
145C4×Dic3—24no—
146C4×Dic3—24no—
147C4×Dic3—38no—
148C4×Dic3—64no—
149C4×Dic3—68no—
150C4×Dic3—68no—
151C22×C32C23×C411yescharacteristic
152C22×C32C2×#4114yes—
153C22×C32C2×#4112yes—
154C2×C3⋊D3—22no—
155C2×C3⋊D3—24no—
156C2×C3⋊D3—44no—
157C32×C4—24no—
158C32×C4#11714yes—
159C3⋊Dic3—22no—
160C3⋊Dic3—24no—
161C3×Dic3—28no—
162C3×Dic3—44no—
163C23×C4—91no—
164#117—98no—
165C2×C4⋊C4—34no—
166C2×C4⋊C4—92no—
167C2×C22⋊C4—92no—
168C2×C22⋊C4—94no—
169C2×C42—32no—
170C2×C42—32no—
171C2×C42—91no—
172C2×C42—94no—
173C2×C42D3211yescharacteristic
174#95—34no—
175#95—94no—
176#95—94no—
177C23×C3—21no—
178C23×C3C23×D312yes—
179C22×D3—34no—
180C22×D3—62no—
181C22×D3—64no—
182C22×D3—64no—
183C22×D3—62no—
184C22×D3—62no—
185C22×D3—64no—
186C22×D3—124no—
187C2×C3×C4—24no—
188C2×C3×C4—24no—
189C2×C3×C4—24no—
190C2×C3×C4—22no—
191C2×C3×C4—24no—
192C2×C3×C4—38no—
193C2×C3×C4—44no—
194C2×C3×C4—64no—
195C2×C3×C4—64no—
196C2×C3×C4—64no—
197C2×C3×C4—64no—
198C2×C3×C4—64no—
199C2×C3×C4C2×C4×D314yes—
200C2×C3×C4C2×C4×D314yes—
201C2×C3×C4C2×C4×D314yes—
202C2×C3×C4#23714yes—
203C2×C3×C4#23914yes—
204C2×Dic3—24no—
205C2×Dic3—24no—
206C2×Dic3—24no—
207C2×Dic3—24no—
208C2×Dic3—24no—
209C2×Dic3—34no—
210C2×Dic3—34no—
211C2×Dic3—34no—
212C2×Dic3—62no—
213C2×Dic3—64no—
214C2×Dic3—64no—
215C2×Dic3—64no—
216C2×Dic3—62no—
217C2×Dic3—62no—
218C2×Dic3—64no—
219C2×Dic3—124no—
220C2×Dic3#23518yes—
221C4×D3—616no—
222C4×D3—616no—
223C2×C32C2×#11711yescharacteristic
224C2×C32C4×#4112yes—
225C2×C32#52914yes—
226C3⋊D3—42no—
227C24—91no—
228C22×C4—34no—
229C22×C4—34no—
230C22×C4—91no—
231C22×C4—92no—
232C22×C4—94no—
233C22×C4—184no—
234C22×C4C2×D3212yes—
235C22×C4C2×D3211yescharacteristic
236C4⋊C4—68no—
237C4⋊C4—98no—
238C22⋊C4—98no—
239C22⋊C4—188no—
240C42—64no—
241C42—64no—
242C42—94no—
243C42—188no—
244C42#62414yes—
245C22×C3—22no—
246C22×C3—24no—
247C22×C3—21no—
248C22×C3C22×C4×D312yes—
249C22×C3C2×#23514yes—
250C22×C3C2×#23712yes—
251C22×C3C2×#23912yes—
252C22×C3D3×#4114yes—
253C2×D3—64no—
254C2×D3—64no—
255C2×D3—64no—
256C2×D3—64no—
257C2×D3—124no—
258C2×D3—128no—
259C2×D3—124no—
260C2×D3—124no—
261C3×C4—24no—
262C3×C4—24no—
263C3×C4—24no—
264C3×C4—44no—
265C3×C4—68no—
266C3×C4—124no—
267C3×C4#89218yes—
268Dic3—28no—
269Dic3—44no—
270Dic3—64no—
271Dic3—64no—
272Dic3—64no—
273Dic3—64no—
274Dic3—124no—
275C32#229811yescharacteristic, complemented, Sylow
276C23—92no—
277C23—182no—
278C23—184no—
279C23C22×D3211yescharacteristic
280C2×C4—24no—
281C2×C4—38no—
282C2×C4—64no—
283C2×C4—64no—
284C2×C4—64no—
285C2×C4—64no—
286C2×C4—64no—
287C2×C4—94no—
288C2×C4—92no—
289C2×C4—182no—
290C2×C4—184no—
291C2×C4—188no—
292C2×C4#379614yes—
293C2×C4C2×#62414yes—
294C2×C4C2×#62412yes—
295C2×C3—21no—
296C2×C3—24no—
297C2×C3—22no—
298C2×C3C4×#23512yes—
299C2×C3C2×#89212yes—
300C2×C3#552212yes—
301C2×C3#553814yes—
302C2×C3#558014yes—
303D3—124no—
304D3—124no—
305C22—182no—
306C22—184no—
307C22—364no—
308C22C2×#379612yes—
309C22D3×#23514yes—
310C22C22×#62411yescharacteristic
311C4—24no—
312C4—68no—
313C4—124no—
314C4—182no—
315C4—184no—
316C4#6384914yes—
317C3—21no—
318C3#7362012yescomplemented
319C2—362no—
320C2#1059391114yes—
321C2C2×#6384911yescharacteristic
322C2#1059495412yes—
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. C3×C4×C4⋊Dic3C2semidirect
5. #10591263C2semidirect
6. C4×Dic32C2semidirect
7. #10591222C2semidirect
14. #64081C4semidirect
30. C4×C4⋊Dic3D3semidirect
275. C32#2298semidirect
318. C3#73620semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C3×C4×C4⋊Dic32
C4×#37222
#105912662
#105912632
C4×Dic322
#105912222
#736203