Finite Group Databasebeta

← #11873459

Subgroups — #11873459

Order 1152.

937 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 937 conjugacy classes of subgroups — too many to draw. Only its 164 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, complemented
2#10594009C211yesmaximal, characteristic
3C3×#5068C212yesmaximal, complemented
4#10590601C212yesmaximal, complemented
5#10590593C212yesmaximal
6#10590539C214yesmaximal, complemented
7C4×#3710C211yesmaximal, characteristic, complemented
8#10590274C212yesmaximal, complemented
9D3×#488—32nomaximal
10C2×#3802C2211yescharacteristic
11C2×#3797C2211yescharacteristic
12C32×#125C2211yescharacteristic, complemented
13C4⋊C4×C3⋊D3—22no—
14C4⋊C4×C3⋊D3C2212yes—
15#64099C2212yescomplemented
16#64098—22no—
17C42×C3⋊D3C2211yescharacteristic
18#64079C2211yescharacteristic, complemented
19C3×#875C2212yes—
20#63921—22no—
21#63915—22no—
22#63863C2212yes—
23C2×#3710C2212yes—
24C3×#810C2214yescomplemented
25C3×#809C2214yes—
26C3×C4×C3⋊C8C2212yescomplemented
27#63566C2214yescomplemented
28#63563C2214yes—
29#63553C2212yescomplemented
30D3×#125—32no—
31D3×#125—61no—
32D3×#124—32no—
33C3×#488—32no—
34#5068D312yescomplemented
35#5056—32no—
36D3×#103—34no—
37#4800—34no—
38D3×#102—34no—
39#4768—34no—
40#4697—32no—
41C4×D3×C8—32no—
42C22×D32—21no—
43C2×C4×C3⋊D3—22no—
44C2×C4×C3⋊D3D412yes—
45C2×C4×C3⋊D3C2311yescharacteristic
46C2×C3×D12C2312yes—
47C2×C3×Dic6C2312yes—
48C2×#627—21no—
49C2×#625—21no—
50C2×#624—21no—
51#3802—24no—
52#3797—24no—
53C32×C4⋊C4—22no—
54C32×C4⋊C4C2312yes—
55C32×C42C2311yescharacteristic
56C4⋊(C3⋊Dic3)—22no—
57C4⋊(C3⋊Dic3)C2312yes—
58#3750—22no—
59#3750—22no—
60#3750—22no—
61C4×C3⋊Dic3D412yes—
62C4×C3⋊Dic3C2311yescharacteristic
63C3×(C2×D3)⋊C4—24no—
64C2×C3×C3⋊C8C2314yes—
65(C2×D3)⋊Dic3—24no—
66#3710—24no—
67C2×#488—91noSylow
68C2×D3×Q8—32no—
69C2×D3×D4—32no—
70C3×#125—21no—
71C3×#125C2×D312yescomplemented
72C3×#124—32no—
73#947—32no—
74#936—32no—
75C2×D3×C8—34no—
76D3×C4⋊C4—34no—
77D3×C4⋊C4—62no—
78D3×C4⋊C4—64no—
79D3×C4⋊C4—64no—
80#890—34no—
81#890—62no—
82#889—64no—
83#889—64no—
84#885—64no—
85D3×C22⋊C4—64no—
86#875C2×D312yes—
87C42×D3—32no—
88C42×D3—61no—
89#870—32no—
90#870—61no—
91C3×#103—34no—
92C3×#102—34no—
93C3×C4×C8—32no—
94#835—34no—
95#832—34no—
96#821—34no—
97#816—34no—
98C8×Dic3—34no—
99#810C2×D314yescomplemented
100#809C2×D314yes—
101C4×C3⋊C8C2×D312yescomplemented
102C22×C3⋊D3C2×D411yescharacteristic
103C22×C3×D3—22no—
104C2×D32—42no—
105C2×D32—44no—
106C2×C32×C4—22no—
107C2×C32×C4C2×D412yes—
108C2×C32×C4C2411yescharacteristic
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3C2×D412yes—
111C2×C3⋊Dic3C2×D411yescharacteristic
112C4×C3⋊D3—24no—
113C4×C3⋊D3—44no—
114C4×C3⋊D3#4114yes—
115C2×C3×Dic3—22no—
116C3×D12—24no—
117C3×Dic6—24no—
118#627—42no—
119#625—42no—
120#624—42no—
121C3×C3⋊C8—24no—
122C2×#125—91no—
123C2×#124—91no—
124#488—32no—
125#488—92no—
126#488—94no—
127C2×#103—92no—
128C2×#102—92no—
129C2×C4×C8—91no—
130C23×D3—62no—
131C2×C3×Q8—32no—
132C2×C3×D4—32no—
133C2×#67—62no—
134D3×Q8—68no—
135D3×D4—68no—
136C2×D12C22×D312yes—
137C2×C4×D3—32no—
138C2×C4×D3—34no—
139C2×C4×D3—61no—
140C2×C4×D3—62no—
141C2×C4×D3—62no—
142C2×C4×D3—64no—
143C2×C4×D3—64no—
144C2×Dic6—62no—
145C2×Dic6C22×D312yes—
146C2×C3×C8—34no—
147C3×C4⋊C4—24no—
148C3×C4⋊C4—24no—
149C3×C4⋊C4—22no—
150C3×C4⋊C4C22×D314yes—
151C3×C22⋊C4—64no—
152C3×C42—21no—
153C3×C42C22×D312yes—
154#217—64no—
155(C2×D3)⋊C4—24no—
156(C2×D3)⋊C4—64no—
157C4⋊Dic3—34no—
158C4⋊Dic3—62no—
159C4⋊Dic3—64no—
160C4⋊Dic3—64no—
161Dic3⋊C4—64no—
162Dic3⋊C4—64no—
163Dic3⋊C4—64no—
164Dic3⋊C4—64no—
165Dic3⋊C4—64no—
166Dic3⋊C4—64no—
167C4×Dic3—34no—
168C4×Dic3—32no—
169C4×Dic3—62no—
170C4×Dic3—61no—
171C2×C3⋊C8C22×D314yes—
172D3×C8—68no—
173C22×C32C22×D411yescharacteristic
174C2×C3⋊D3#12412yes—
175C2×C3⋊D3#13514yes—
176C2×C3×D3—42no—
177C2×C3×D3—44no—
178D32—84no—
179C32×C4—22no—
180C32×C4—42no—
181C32×C4C2×#4112yes—
182C3⋊Dic3—22no—
183C3⋊Dic3—42no—
184C3⋊Dic3#12412yes—
185C3×Dic3—42no—
186C22×Q8—91no—
187C22×D4—91no—
188C22×C8—92no—
189#125—92no—
190#125—91no—
191#125—182no—
192#125D3211yescharacteristic, complemented
193#124—32no—
194#124—92no—
195#124—182no—
196C2×C4⋊C4—92no—
197C2×C4⋊C4—182no—
198C2×C22⋊C4—182no—
199C2×C42—91no—
200#103—34no—
201#103—94no—
202#102—34no—
203#102—94no—
204C4×C8—32no—
205C4×C8—92no—
206C23×C3—62no—
207C22×D3—22no—
208C22×D3—32no—
209C22×D3—61no—
210C22×D3—124no—
211C22×D3—128no—
212C3×Q8—64no—
213C3×D4—64no—
214C2×C3×C4—24no—
215C2×C3×C4—24no—
216C2×C3×C4—21no—
217C2×C3×C4—22no—
218C2×C3×C4—62no—
219C2×C3×C4D3×D414yes—
220C2×C3×C4C23×D312yes—
221#67—124no—
222C2×Dic3—22no—
223C2×Dic3—32no—
224C2×Dic3—34no—
225C2×Dic3—61no—
226C2×Dic3—62no—
227C2×Dic3—64no—
228C2×Dic3—64no—
229D12—24no—
230C4×D3—38no—
231C4×D3—64no—
232C4×D3—68no—
233C4×D3—124no—
234C4×D3—124no—
235C4×D3—128no—
236C4×D3—128no—
237Dic6—24no—
238Dic6—124no—
239C3×C8—64no—
240C3⋊C8—24no—
241C2×C32C2×#12411yescharacteristic
242C2×C32C2×#13512yes—
243C3⋊D3#48814yescomplemented
244C3×D3—82no—
245C24—181no—
246C2×Q8—32no—
247C2×Q8—181no—
248C2×Q8—184no—
249C2×D4—32no—
250C2×D4—184no—
251C2×D4—181no—
252C22×C4—91no—
253C22×C4—92no—
254C22×C4—182no—
255C22×C4—181no—
256C2×C8—34no—
257C2×C8—184no—
258C4⋊C4—22no—
259C4⋊C4—92no—
260C4⋊C4—182no—
261C4⋊C4—182no—
262C4⋊C4—182no—
263C4⋊C4—182no—
264C4⋊C4C2×D3212yes—
265C22⋊C4—64no—
266C22⋊C4—184no—
267C42—91no—
268C42—92no—
269C42C2×D3211yescharacteristic
270C22×C3—21no—
271C22×C3—122no—
272C22×C3—124no—
273C22×C3C2×D3×D412yes—
274C2×D3—34no—
275C2×D3—38no—
276C2×D3—42no—
277C2×D3—44no—
278C2×D3—62no—
279C2×D3—64no—
280C2×D3—248no—
281C3×C4—24no—
282C3×C4—22no—
283C3×C4—42no—
284C3×C4—44no—
285C3×C4—44no—
286C3×C4—122no—
287C3×C4D3×#4114yes—
288Dic3—34no—
289Dic3—42no—
290Dic3—62no—
291Dic3—64no—
292Dic3—122no—
293Dic3—124no—
294Dic3—124no—
295C32C2×#48811yescharacteristic, complemented, Sylow
296C23—62no—
297C23—91no—
298C23—362no—
299C23—364no—
300Q8—64no—
301Q8—362no—
302D4—64no—
303D4—362no—
304C2×C4—22no—
305C2×C4—62no—
306C2×C4—91no—
307C2×C4—94no—
308C2×C4—92no—
309C2×C4—184no—
310C2×C4—182no—
311C2×C4—364no—
312C2×C4—362no—
313C2×C4#381112yes—
314C2×C4C22×D3211yescharacteristic
315C8—64no—
316C2×C3—21no—
317C2×C3—22no—
318C2×C3—242no—
319C2×C3D3×#12412yes—
320C2×C3D3×#13514yes—
321D3—38no—
322D3—64no—
323D3—82no—
324C22—92no—
325C22—94no—
326C22—122no—
327C22—124no—
328C22—724no—
329C22C2×#381111yescharacteristic
330C4—22no—
331C4—42no—
332C4—92no—
333C4—122no—
334C4—182no—
335C4—362no—
336C4#6431912yes—
337C3—21no—
338C3D3×#48812yescomplemented
339C2—94no—
340C2—242no—
341C2#1059543211yescharacteristic
342C2#1059545912yes—
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenter#125D32
hypocenterC32C2×#488
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
1. C3⋊D3×#125C2semidirect
3. C3×#5068C2semidirect
4. #10590601C2semidirect
6. #10590539C2semidirect
7. C4×#3710C2semidirect
8. #10590274C2semidirect
12. C32×#125C22semidirect
15. #64099C22semidirect
18. #64079C22semidirect
24. C3×#810C22semidirect
26. C3×C4×C3⋊C8C22semidirect
27. #63566C22semidirect
29. #63553C22semidirect
34. #5068D3semidirect
71. C3×#125C2×D3semidirect
99. #810C2×D3semidirect
101. C4×C3⋊C8C2×D3semidirect
192. #125D32semidirect
243. C3⋊D3#488semidirect
295. C32C2×#488semidirect
338. C3D3×#488semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1252
#105940092
C3×#50682
#105906012
#105905932
#105905392
C4×#37102
#105902742
D3×#4883