Finite Group Databasebeta

← #11782890

Subgroups — #11782890

Order 1152.

431 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 431 conjugacy classes of subgroups — too many to draw. Only its 100 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#10592393C211yesmaximal, characteristic
2C3×#4699C211yesmaximal, characteristic, complemented
3#10590303C211yesmaximal, characteristic, complemented
4#10590288C211yesmaximal, characteristic, complemented
5#10590281C211yesmaximal, characteristic
6#10590281C211yesmaximal, characteristic
7C3×#4454C211yesmaximal, characteristic, complemented
8#71300—31nomaximal
9#68097—31nomaximal
10#64083C2211yescharacteristic
11#64078C2211yescharacteristic
12C2×C3×Dic12—22no—
13C3×#869C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C32×C4×C8C2211yescharacteristic
16#63648—22no—
17C3×C4×C3⋊C8C2211yescharacteristic
18C3×C4×C3⋊C8C2211yescharacteristic
19#63573—22no—
20#63567—22no—
21#63564—22no—
22#63564—22no—
23C3×#494—31no—
24#5093—31no—
25#5088—31no—
26#5088—31no—
27#5080—31no—
28#4699D311yescharacteristic, complemented
29#4694—31no—
30#4694—31no—
31#4694—31no—
32#4694—31no—
33#4694—61no—
34#4681—31no—
35#4680—31no—
36C3×#322—31no—
37#4454D311yescharacteristic, complemented
38C2×C4⋊(C3⋊D3)—21no—
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×#634—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8D412yes—
45C32×C42C2311yescharacteristic
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C2×C3×C3⋊C8D412yes—
53C2×C3×C3⋊C8D412yes—
54C3×Dic12—44no—
55#1720—91noSylow
56C2×C3×Q16—62no—
57C3×C4⋊Q8—31no—
58C3×C4⋊Q8—31no—
59C2×Dic12—22no—
60#874—31no—
61#874—31no—
62#874—61no—
63#869—31no—
64#869—31no—
65#869—61no—
66#869C2×D311yescharacteristic
67#869C2×D311yescharacteristic
68C3×C4×C8—21no—
69C3×C4×C8—31no—
70C3×C4×C8—31no—
71C3×C4×C8C2×D311yescharacteristic
72C3×C4×C8C2×D311yescharacteristic
73#821—62no—
74#821—62no—
75#821—64no—
76#821—62no—
77#821—62no—
78#817—62no—
79#816—62no—
80#810—62no—
81#809—62no—
82#809—62no—
83#808—62no—
84C4×C3⋊C8C2×D311yescharacteristic
85C4×C3⋊C8C2×D311yescharacteristic
86C22×C3⋊D3—41no—
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×D411yescharacteristic
90C2×C3⋊Dic3—41no—
91C4⋊(C3⋊D3)—42no—
92C4⋊(C3⋊D3)—42no—
93C4⋊(C3⋊D3)—42no—
94#634—42no—
95C2×C3×Dic3—41no—
96C2×C3×Dic3—41no—
97C3×Dic6—42no—
98C3×Dic6—42no—
99C32×C8—22no—
100C3×C3⋊C8—22no—
101C3×C3⋊C8—22no—
102#498—91no—
103#494—31no—
104#487—91no—
105#486—91no—
106#486—91no—
107#486—91no—
108#322—31no—
109C2×C3×Q8—61no—
110C2×C3×Q8—61no—
111C2×D12—62no—
112C2×D12—61no—
113C2×D12—61no—
114C2×D12—61no—
115C2×D12—61no—
116C2×D12—61no—
117C2×D12—61no—
118C2×D12—121no—
119C2×D12—121no—
120C2×Dic6—21no—
121C2×Dic6—21no—
122C2×Dic6—61no—
123C2×Dic6—61no—
124C2×Dic6—121no—
125C3×Q16—124no—
126C2×C3×C8—22no—
127C2×C3×C8—32no—
128C2×C3×C8—32no—
129C2×C3×C8D1212yes—
130C2×C3×C8#6712yes—
131C3×C4⋊C4—61no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C42—21no—
136C3×C42C22×D311yescharacteristic
137C3×C42C22×D311yescharacteristic
138C4⋊Dic3—21no—
139C4⋊Dic3—21no—
140C4⋊Dic3—21no—
141C4⋊Dic3—21no—
142C4⋊Dic3—62no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4⋊Dic3—121no—
148C2×C3⋊C8D1212yes—
149C2×C3⋊C8D1212yes—
150Dic12—44no—
151C22×C32#12711yescharacteristic
152C2×C3⋊D3—81no—
153C2×C3⋊D3—81no—
154C2×C3⋊D3—81no—
155C32×C4#13512yes—
156C32×C4AGL(1,ℤ/8)12yes—
157C32×C4#13712yes—
158C3⋊Dic3—81no—
159C3×Dic3—81no—
160C3×Dic3—81no—
161C2×Q16—62no—
162C4⋊Q8—31no—
163C4⋊Q8—31no—
164C4⋊Q8—91no—
165#127—91no—
166#106—182no—
167#103—182no—
168#102—182no—
169#102—182no—
170#102—182no—
171C4×C8—31no—
172C4×C8—31no—
173C4×C8D3211yescharacteristic
174C22×D3—122no—
175C22×D3—121no—
176C22×D3—121no—
177C3×Q8—122no—
178C3×Q8—122no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—121no—
183C2×C3×C4—121no—
184C2×C3×C4C2×D1211yescharacteristic
185C2×C3×C4C2×D1211yescharacteristic
186C2×C3×C4C2×D1211yescharacteristic
187C2×C3×C4D3×D411yescharacteristic
188C2×C3×C4D3×D411yescharacteristic
189C2×C3×C4C2×#6711yescharacteristic
190C2×Dic3—41no—
191C2×Dic3—41no—
192C2×Dic3—122no—
193C2×Dic3—121no—
194C2×Dic3—121no—
195D12—124no—
196D12—122no—
197D12—122no—
198D12—122no—
199D12—122no—
200D12—122no—
201D12—122no—
202D12—242no—
203D12—242no—
204Dic6—42no—
205Dic6—42no—
206Dic6—122no—
207Dic6—122no—
208Dic6—242no—
209C3×C8—22no—
210C3×C8—22no—
211C3×C8—42no—
212C3×C8—62no—
213C3×C8—62no—
214C3⋊C8—22no—
215C3⋊C8—22no—
216C2×C32#49511yescharacteristic
217C2×C32#49611yescharacteristic
218C2×C32#49711yescharacteristic
219C3⋊D3—161no—
220C2×Q8—61no—
221C2×Q8—61no—
222C2×Q8—181no—
223C2×D4—181no—
224C2×D4—181no—
225C2×D4—181no—
226Q16—124no—
227C2×C8—32no—
228C2×C8—32no—
229C2×C8#62612yes—
230C4⋊C4—61no—
231C4⋊C4—61no—
232C4⋊C4—61no—
233C4⋊C4—61no—
234C4⋊C4—181no—
235C4⋊C4—181no—
236C42C2×D3211yescharacteristic
237C22×C3—21no—
238C22×C3#87411yescharacteristic
239C22×C3#94011yescharacteristic
240C2×D3—242no—
241C2×D3—242no—
242C2×D3—242no—
243C2×D3—241no—
244C2×D3—241no—
245C2×D3—241no—
246C2×D3—241no—
247C2×D3—241no—
248C2×D3—241no—
249C3×C4—22no—
250C3×C4—22no—
251C3×C4—22no—
252C3×C4—241no—
253C3×C4—241no—
254C3×C4#90412yes—
255C3×C4#90812yes—
256C3×C4#90912yes—
257C3×C4#91812yes—
258C3×C4#91912yes—
259C3×C4#93212yes—
260Dic3—81no—
261Dic3—81no—
262Dic3—242no—
263Dic3—241no—
264Dic3—241no—
265C32#172011yescharacteristic, complemented, Sylow
266C23—361no—
267Q8—122no—
268Q8—122no—
269Q8—362no—
270D4—362no—
271D4—362no—
272D4—362no—
273C2×C4—121no—
274C2×C4—121no—
275C2×C4—361no—
276C2×C4D3×D1211yescharacteristic
277C2×C4D3×D1211yescharacteristic
278C2×C4C2×#62611yescharacteristic
279C8—22no—
280C8—62no—
281C8—62no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3#469611yescharacteristic
286C2×C3#471211yescharacteristic
287C2×C3#471511yescharacteristic
288C2×C3#507411yescharacteristic
289C2×C3#519011yescharacteristic
290C2×C3#519111yescharacteristic
291D3—482no—
292D3—481no—
293D3—481no—
294C22—721no—
295C22—721no—
296C22—721no—
297C22#6391111yescharacteristic
298C4—241no—
299C4—241no—
300C4—721no—
301C4#6380112yes—
302C4#6380812yes—
303C4#6383012yes—
304C3—21no—
305C3#6809711yescharacteristic, complemented
306C3#7130011yescharacteristic, complemented
307C2—1441no—
308C2#1059037111yescharacteristic
309C2#1059086511yescharacteristic
310C2#1059089911yescharacteristic
subgroupG/H
centerC22#63911
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#127
prime radical#64083C22
hypercenterC4×C8D32
hypocenterC32#1720
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
2. C3×#4699C2semidirect
3. #10590303C2semidirect
4. #10590288C2semidirect
7. C3×#4454C2semidirect
28. #4699D3semidirect
37. #4454D3semidirect
265. C32#1720semidirect
305. C3#68097semidirect
306. C3#71300semidirect

Maximal subgroups

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

subgroupindex
#105923932
C3×#46992
#105903032
#105902882
#105902812
C3×#44542
#713003
#680973