Finite Group Databasebeta

← #11782640

Subgroups — #11782640

Order 1152.

445 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 445 conjugacy classes of subgroups — too many to draw. Only its 108 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
1#10592380C211yesmaximal, characteristic, complemented
2C3×#4693C211yesmaximal, characteristic
3#10590369C211yesmaximal, characteristic
4#10590311C211yesmaximal, characteristic, complemented
5#10590303C211yesmaximal, characteristic, complemented
6#10590273C211yesmaximal, characteristic
7C3×#4454C211yesmaximal, characteristic, complemented
8#71257—31nomaximal
9#68090—31nomaximal
10#64078C2211yescharacteristic
11#64078C2211yescharacteristic
12C2×C3×#204—22no—
13C3×#874C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C2×#3716—22no—
16C32×C4×C8C2211yescharacteristic
17#63643—22no—
18C3×C4×C3⋊C8C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63575—22no—
21#63573—22no—
22#63563—22no—
23C3×#492—31no—
24#5080—31no—
25#5078—31no—
26#5076—31no—
27#5070—31no—
28#4694—31no—
29#4693—31no—
30#4693D311yescharacteristic
31#4682—31no—
32#4681—31no—
33#4681—31no—
34#4681—61no—
35#4680—31no—
36C3×#322—31no—
37#4454D311yescharacteristic, complemented
38C2×#634—21no—
39C2×#634—21no—
40C2×C3×D12—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8D412yes—
45C32×C42C2311yescharacteristic
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C2×C3×C3⋊C8D412yes—
53C2×C3×C3⋊C8D412yes—
54C3×#204—44no—
55#3716—44no—
56#1714—91noSylow
57C2×C3×SD16—62no—
58C3×C4⋊Q8—31no—
59C3×#127—31no—
60C2×#214—62no—
61C2×#204—22no—
62C2×#204—62no—
63#874C2×D311yescharacteristic
64#869—31no—
65#869—31no—
66#869—31no—
67#869—31no—
68#869—61no—
69#869—61no—
70#869C2×D311yescharacteristic
71C3×C4×C8—21no—
72C3×C4×C8—31no—
73C3×C4×C8—31no—
74C3×C4×C8C2×D311yescharacteristic
75C3×C4×C8C2×D311yescharacteristic
76#832—62no—
77#821—62no—
78#818—62no—
79#817—62no—
80#816—64no—
81#816—62no—
82#816—62no—
83#808—62no—
84#807—62no—
85C4×C3⋊C8C2×D311yescharacteristic
86C4×C3⋊C8C2×D311yescharacteristic
87C22×C3×D3—41no—
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×D411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C3⋊Dic3—41no—
92C2×C3⋊Dic3—41no—
93#634—42no—
94#634—42no—
95C2×C3×Dic3—41no—
96C3×D12—42no—
97C3×D12—42no—
98C3×D12—42no—
99C3×Dic6—42no—
100C32×C8—22no—
101C3×C3⋊C8—22no—
102C3×C3⋊C8SD1614yescomplemented
103#500—91no—
104#498—91no—
105#492—31no—
106#492—91no—
107#487—91no—
108#486—91no—
109#322—31no—
110C2×C3×Q8—61no—
111C2×C3×D4—61no—
112C2×C3×D4—61no—
113C2×C3×D4—61no—
114C2×D12—21no—
115C2×D12—21no—
116C2×D12—21no—
117C2×Dic6—21no—
118C2×Dic6—62no—
119C2×Dic6—61no—
120C2×Dic6—61no—
121C2×Dic6—61no—
122C2×Dic6—61no—
123C2×Dic6—121no—
124C3×SD16—124no—
125C2×C3×C8—22no—
126C2×C3×C8—32no—
127C2×C3×C8—32no—
128C2×C3×C8D1212yes—
129C2×C3×C8#6712yes—
130C3×C4⋊C4—61no—
131C3×C4⋊C4—61no—
132C3×C42—21no—
133C3×C42C22×D311yescharacteristic
134C3×C42C22×D311yescharacteristic
135#214—124no—
136C4⋊Dic3—21no—
137C4⋊Dic3—21no—
138C4⋊Dic3—62no—
139C4⋊Dic3—61no—
140C4⋊Dic3—61no—
141C4⋊Dic3—61no—
142C4⋊Dic3—61no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4⋊Dic3—121no—
148C4⋊Dic3—121no—
149C4⋊Dic3—121no—
150C2×C3⋊C8D1212yes—
151C2×C3⋊C8D1212yes—
152#204—44no—
153#204—124no—
154C22×C32#12711yescharacteristic
155C2×C3×D3—81no—
156C2×C3×D3—81no—
157C2×C3×D3—81no—
158C32×C4C2×SD1612yes—
159C32×C4AGL(1,ℤ/8)12yes—
160C32×C4#13712yes—
161C3⋊Dic3—81no—
162C3⋊Dic3—81no—
163C3×Dic3—81no—
164C2×SD16—62no—
165C2×SD16—182no—
166C4⋊Q8—31no—
167C4⋊Q8—91no—
168C4⋊Q8—91no—
169#127—31no—
170#107—182no—
171#106—182no—
172#103—182no—
173#102—182no—
174C4×C8—31no—
175C4×C8—31no—
176C4×C8D3211yescharacteristic
177C23×C3—121no—
178C22×D3—41no—
179C3×Q8—122no—
180C3×D4—122no—
181C3×D4—122no—
182C3×D4—122no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—121no—
187C2×C3×C4C2×D1211yescharacteristic
188C2×C3×C4C2×D1211yescharacteristic
189C2×C3×C4C2×D1211yescharacteristic
190C2×C3×C4D3×D411yescharacteristic
191C2×C3×C4D3×D411yescharacteristic
192C2×C3×C4C2×#6711yescharacteristic
193C2×Dic3—41no—
194C2×Dic3—122no—
195C2×Dic3—122no—
196C2×Dic3—121no—
197C2×Dic3—121no—
198C2×Dic3—121no—
199C2×Dic3—121no—
200D12—42no—
201D12—42no—
202D12—42no—
203Dic6—42no—
204Dic6—124no—
205Dic6—122no—
206Dic6—122no—
207Dic6—122no—
208Dic6—122no—
209Dic6—242no—
210C3×C8—22no—
211C3×C8—22no—
212C3×C8—34no—
213C3×C8—42no—
214C3×C8—62no—
215C3⋊C8—22no—
216C3⋊C8#20414yescomplemented
217C2×C32#49211yescharacteristic
218C2×C32#49611yescharacteristic
219C2×C32#49711yescharacteristic
220C3×D3—161no—
221C2×Q8—61no—
222C2×Q8—181no—
223C2×Q8—181no—
224C2×D4—61no—
225C2×D4—61no—
226C2×D4—61no—
227SD16—124no—
228SD16—364no—
229C2×C8—32no—
230C2×C8—32no—
231C2×C8#62612yes—
232C4⋊C4—61no—
233C4⋊C4—61no—
234C4⋊C4—181no—
235C4⋊C4—181no—
236C4⋊C4—181no—
237C4⋊C4—181no—
238C42C2×D3211yescharacteristic
239C22×C3—21no—
240C22×C3—241no—
241C22×C3—241no—
242C22×C3—241no—
243C22×C3#87411yescharacteristic
244C22×C3#94011yescharacteristic
245C2×D3—81no—
246C2×D3—81no—
247C2×D3—81no—
248C3×C4—22no—
249C3×C4—22no—
250C3×C4—22no—
251C3×C4—241no—
252C3×C4C2×#20412yes—
253C3×C4#90812yes—
254C3×C4#90912yes—
255C3×C4D3×SD1612yes—
256C3×C4#91512yes—
257C3×C4#93212yes—
258Dic3—81no—
259Dic3—242no—
260Dic3—242no—
261Dic3—241no—
262Dic3—241no—
263Dic3—241no—
264Dic3—241no—
265C32#171411yescharacteristic, complemented, Sylow
266C23—121no—
267Q8—122no—
268Q8—362no—
269Q8—362no—
270D4—122no—
271D4—122no—
272D4—122no—
273C2×C4—121no—
274C2×C4—361no—
275C2×C4—361no—
276C2×C4D3×D1211yescharacteristic
277C2×C4D3×D1211yescharacteristic
278C2×C4C2×#62611yescharacteristic
279C8—22no—
280C8—34no—
281C8—62no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—481no—
286C2×C3#469311yescharacteristic
287C2×C3#471211yescharacteristic
288C2×C3#471511yescharacteristic
289C2×C3#507411yescharacteristic
290C2×C3#516711yescharacteristic
291C2×C3#517511yescharacteristic
292D3—161no—
293C22—241no—
294C22—241no—
295C22—241no—
296C22#6391111yescharacteristic
297C4—241no—
298C4—721no—
299C4—721no—
300C4D3×#20412yes—
301C4#6380012yes—
302C4#6383012yes—
303C3—21no—
304C3#6809011yescharacteristic, complemented
305C3#7125711yescharacteristic, complemented
306C2—481no—
307C2#1059037111yescharacteristic
308C2#1059087711yescharacteristic
309C2#1059089711yescharacteristic
subgroupG/H
centerC22#63911
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#127
prime radicalC3×#874C22
hypercenterC4×C8D32
hypocenterC32#1714
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10592380C2semidirect
4. #10590311C2semidirect
5. #10590303C2semidirect
7. C3×#4454C2semidirect
37. #4454D3semidirect
102. C3×C3⋊C8SD16semidirect
216. C3⋊C8#204semidirect
265. C32#1714semidirect
304. C3#68090semidirect
305. C3#71257semidirect

Maximal subgroups

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

subgroupindex
#105923802
C3×#46932
#105903692
#105903112
#105903032
#105902732
C3×#44542
#712573
#680903