Finite Group Databasebeta

← #11874916

Subgroups — #11874916

Order 1152.

833 conjugacy classes of subgroups; only the 188 normal subgroups are shown.

normal subgroups only

This group has 833 conjugacy classes of subgroups — too many to draw. Only its 188 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
1C3⋊D3×#125C211yesmaximal, characteristic
2#10593948C211yesmaximal, characteristic
3C3×#5065C212yesmaximal, complemented
4#10590575C212yesmaximal
5#10590573C212yesmaximal
6#10590417C214yesmaximal, complemented
7C4×#3710C211yesmaximal, characteristic
8#10590304C212yesmaximal, complemented
9D3×#499—32nomaximal
10C32×#125C2211yescharacteristic
11C4⋊C4×C3⋊D3—22no—
12C4⋊C4×C3⋊D3C2212yes—
13#64099C2212yes—
14#64098—22no—
15C42×C3⋊D3C2211yescharacteristic
16#64079C2211yescharacteristic
17C3×#870C2212yes—
18#63900C2212yes—
19#63883—22no—
20#63872C2212yes—
21#63870—22no—
22C2×#3710C2211yescharacteristic
23C2×#3710C2211yescharacteristic
24C3×#808C2214yes—
25C3×#807C2214yes—
26C3×C4×C3⋊C8C2212yes—
27#63575C2214yes—
28#63573C2214yes—
29#63553C2212yes—
30D3×#125—32no—
31D3×#125—32no—
32D3×#125—61no—
33C3×#499—32no—
34#5065—32no—
35#5065D312yescomplemented
36D3×#107—34no—
37#4878—34no—
38D3×#106—34no—
39#4858—34no—
40C4×D3×C8—32no—
41#4683—32no—
42C2×C4×C3⋊D3—22no—
43C2×C4×C3⋊D3D412yes—
44C2×C4×C3⋊D3C2311yescharacteristic
45C2×#624—22no—
46C32×C4⋊C4—22no—
47C32×C4⋊C4C2312yes—
48C32×C42C2311yescharacteristic
49C4⋊(C3⋊Dic3)—22no—
50C4⋊(C3⋊Dic3)C2312yes—
51#3750—22no—
52#3750—22no—
53#3750—22no—
54C4×C3⋊Dic3D412yes—
55C4×C3⋊Dic3C2311yescharacteristic
56C3×C4⋊Dic3C2314yes—
57C3×Dic3⋊C4—24no—
58C2×C3×C3⋊C8C2312yes—
59C2×C3×C3⋊C8C2312yes—
60#3724—22no—
61Dic3⋊Dic3—24no—
62#3710Q814yes—
63#3710Q814yes—
64C2×#499—91noSylow
65C3×#125—21no—
66C3×#125—32no—
67C3×#125C2×D312yes—
68C2×D3×C8—32no—
69C2×D3×C8—32no—
70D3×C4⋊C4—34no—
71D3×C4⋊C4—34no—
72D3×C4⋊C4—62no—
73D3×C4⋊C4—64no—
74D3×C4⋊C4—64no—
75D3×C4⋊C4—64no—
76#890—34no—
77#890—34no—
78#890—62no—
79#889—64no—
80#889—64no—
81#889—64no—
82C42×D3—32no—
83C42×D3—61no—
84#870—32no—
85#870—61no—
86#870C2×D312yes—
87C3×#107—34no—
88C3×#106—34no—
89C3×C4×C8—32no—
90#818—34no—
91#817—34no—
92C8×Dic3—32no—
93C8×Dic3—32no—
94#808—34no—
95#808C2×D314yes—
96#807—34no—
97#807C2×D314yes—
98C4×C3⋊C8C2×D312yes—
99C22×C3⋊D3C2×D411yescharacteristic
100C2×C32×C4—22no—
101C2×C32×C4C2×D412yes—
102C2×C32×C4C2411yescharacteristic
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3C2×D412yes—
105C2×C3⋊Dic3C2×D411yescharacteristic
106C4×C3⋊D3—24no—
107C4×C3⋊D3—44no—
108C4×C3⋊D3C2×Q812yes—
109C4×C3⋊D3C2×Q812yes—
110C2×C3×Dic3—24no—
111#624—44no—
112C3×C3⋊C8C2×Q814yes—
113C3×C3⋊C8C2×Q814yes—
114C2×#125—91no—
115C2×#125—91no—
116#499—32no—
117#499—92no—
118#499—94no—
119C2×#107—92no—
120C2×#106—92no—
121C2×C4×C8—91no—
122C2×C4×D3—32no—
123C2×C4×D3—34no—
124C2×C4×D3—61no—
125C2×C4×D3—62no—
126C2×C4×D3—64no—
127C2×C4×D3—64no—
128C2×C4×D3—64no—
129C2×C3×C8—32no—
130C2×C3×C8—32no—
131C3×C4⋊C4—24no—
132C3×C4⋊C4—24no—
133C3×C4⋊C4—22no—
134C3×C4⋊C4—34no—
135C3×C4⋊C4—64no—
136C3×C4⋊C4C22×D314yes—
137C3×C42—21no—
138C3×C42C22×D312yes—
139C4⋊Dic3—34no—
140C4⋊Dic3—62no—
141C4⋊Dic3—64no—
142C4⋊Dic3—64no—
143C4⋊Dic3—64no—
144C4⋊Dic3C22×D314yes—
145Dic3⋊C4—24no—
146Dic3⋊C4—64no—
147Dic3⋊C4—64no—
148Dic3⋊C4—64no—
149Dic3⋊C4—64no—
150Dic3⋊C4—64no—
151Dic3⋊C4—64no—
152Dic3⋊C4—64no—
153Dic3⋊C4—64no—
154C4×Dic3—34no—
155C4×Dic3—32no—
156C4×Dic3—62no—
157C4×Dic3—61no—
158C2×C3⋊C8C22×D312yes—
159C2×C3⋊C8C22×D312yes—
160D3×C8—38no—
161D3×C8—38no—
162C22×C32C22×D411yescharacteristic
163C2×C3⋊D3C4⋊Q812yes—
164C2×C3⋊D3#13514yes—
165C32×C4—22no—
166C32×C4—42no—
167C32×C4C22×Q811yescharacteristic
168C32×C4C22×Q811yescharacteristic
169C3⋊Dic3—22no—
170C3⋊Dic3—42no—
171C3⋊Dic3C4⋊Q812yes—
172C3×Dic3—44no—
173C22×C8—91no—
174C22×C8—91no—
175#125—32no—
176#125—92no—
177#125—92no—
178#125—91no—
179#125—182no—
180#125—182no—
181#125D3211yescharacteristic
182C2×C4⋊C4—92no—
183C2×C4⋊C4—92no—
184C2×C4⋊C4—182no—
185C2×C4⋊C4—182no—
186C2×C42—91no—
187#107—34no—
188#107—94no—
189#106—34no—
190#106—94no—
191C4×C8—32no—
192C4×C8—92no—
193C22×D3—32no—
194C22×D3—61no—
195C2×C3×C4—24no—
196C2×C3×C4—24no—
197C2×C3×C4—21no—
198C2×C3×C4—22no—
199C2×C3×C4—64no—
200C2×C3×C4D3×D414yes—
201C2×C3×C4C23×D312yes—
202C2×Dic3—24no—
203C2×Dic3—32no—
204C2×Dic3—34no—
205C2×Dic3—61no—
206C2×Dic3—62no—
207C2×Dic3—64no—
208C2×Dic3—64no—
209C4×D3—34no—
210C4×D3—34no—
211C4×D3—62no—
212C4×D3—62no—
213C4×D3—68no—
214C4×D3—124no—
215C4×D3—128no—
216C4×D3—128no—
217C4×D3—128no—
218C3×C8—34no—
219C3×C8—34no—
220C3⋊C8D3×Q814yes—
221C3⋊C8D3×Q814yes—
222C2×C32C2×C4⋊Q811yescharacteristic
223C2×C32C2×#13512yes—
224C3⋊D3#49914yescomplemented
225C22×C4—91no—
226C22×C4—92no—
227C22×C4—182no—
228C22×C4—182no—
229C2×C8—32no—
230C2×C8—32no—
231C2×C8—94no—
232C2×C8—94no—
233C4⋊C4—22no—
234C4⋊C4—34no—
235C4⋊C4—64no—
236C4⋊C4—92no—
237C4⋊C4—182no—
238C4⋊C4—182no—
239C4⋊C4—182no—
240C4⋊C4—182no—
241C4⋊C4—184no—
242C4⋊C4—182no—
243C4⋊C4C2×D3212yes—
244C42—91no—
245C42—92no—
246C42C2×D3211yescharacteristic
247C22×C3—21no—
248C22×C3C2×D3×D412yes—
249C2×D3—34no—
250C2×D3—38no—
251C2×D3—62no—
252C2×D3—64no—
253C3×C4—24no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—42no—
257C3×C4—44no—
258C3×C4—44no—
259C3×C4—124no—
260C3×C4C2×D3×Q812yes—
261C3×C4C2×D3×Q812yes—
262Dic3—34no—
263Dic3—44no—
264Dic3—62no—
265Dic3—64no—
266Dic3—122no—
267Dic3—124no—
268Dic3—124no—
269C32C2×#49911yescharacteristic, complemented, Sylow
270C23—91no—
271C2×C4—22no—
272C2×C4—64no—
273C2×C4—91no—
274C2×C4—92no—
275C2×C4—92no—
276C2×C4—92no—
277C2×C4—184no—
278C2×C4—182no—
279C2×C4—364no—
280C2×C4—364no—
281C2×C4#381112yes—
282C2×C4C22×D3211yescharacteristic
283C8—34no—
284C8—34no—
285C2×C3—21no—
286C2×C3—22no—
287C2×C3D3×C4⋊Q812yes—
288C2×C3D3×#13514yes—
289D3—38no—
290D3—64no—
291C22—92no—
292C22—94no—
293C22C2×#381111yescharacteristic
294C4—22no—
295C4—42no—
296C4—92no—
297C4—124no—
298C4—182no—
299C4—362no—
300C4D32×Q811yescharacteristic
301C4D32×Q811yescharacteristic
302C3—21no—
303C3D3×#49912yescomplemented
304C2—94no—
305C2#1059536511yescharacteristic
306C2#1059545912yes—
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#125D32
hypocenterC32C2×#499
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. C3×#5065C2semidirect
6. #10590417C2semidirect
8. #10590304C2semidirect
35. #5065D3semidirect
224. C3⋊D3#499semidirect
269. C32C2×#499semidirect
303. C3D3×#499semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1252
#105939482
C3×#50652
#105905752
#105905732
#105904172
C4×#37102
#105903042
D3×#4993