Finite Group Databasebeta

← #11782638

Subgroups — #11782638

Order 1152.

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

normal subgroups only

This group has 467 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#10592392C211yesmaximal, characteristic
2C3×#4681C211yesmaximal, characteristic, complemented
3#10590373C211yesmaximal, characteristic
4#10590311C211yesmaximal, characteristic, complemented
5#10590303C211yesmaximal, characteristic, complemented
6#10590281C211yesmaximal, characteristic
7C3×#4454C211yesmaximal, characteristic, complemented
8#71216—31nomaximal
9#68090—31nomaximal
10C2×#3744—22no—
11#64083C2211yescharacteristic
12#64078C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C2×#3717—22no—
16C32×C4×C8C2211yescharacteristic
17C3×#816—22no—
18C3×C4×C3⋊C8C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63575—22no—
21#63573—22no—
22#63564—22no—
23C3×#487—31no—
24#5088—31no—
25#5085—31no—
26#5080—31no—
27#5078—31no—
28#4694—31no—
29#4693—31no—
30#4693—31no—
31#4693—31no—
32#4693—61no—
33#4682—31no—
34#4681D311yescharacteristic, complemented
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—
48#3744—44no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8D412yes—
54C2×C3×C3⋊C8D412yes—
55#3717—44no—
56#1714—91noSylow
57C3×C4⋊Q8—31no—
58C3×C4⋊Q8—31no—
59C2×#215—62no—
60C2×#204—64no—
61C2×#204—62no—
62C2×#204—62no—
63C2×#204—62no—
64#874—31no—
65#874—31no—
66#874—61no—
67#869—31no—
68#869—31no—
69#869—61no—
70#869C2×D311yescharacteristic
71#869C2×D311yescharacteristic
72C3×#103—62no—
73C3×C4×C8—21no—
74C3×C4×C8—31no—
75C3×C4×C8—31no—
76C3×C4×C8C2×D311yescharacteristic
77C3×C4×C8C2×D311yescharacteristic
78#821—62no—
79#818—62no—
80#817—62no—
81#816—22no—
82#809—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—
92C4⋊(C3⋊D3)—42no—
93C4⋊(C3⋊D3)—42no—
94C4⋊(C3⋊D3)—42no—
95#634—42no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—41no—
98C3×Dic6—42no—
99C3×Dic6—42no—
100C32×C8—22no—
101C3×C3⋊C8—22no—
102C3×C3⋊C8SD1614yescomplemented
103#500—91no—
104#498—91no—
105#492—91no—
106#492—91no—
107#487—31no—
108#486—91no—
109#322—31no—
110C2×C3×Q8—61no—
111C2×C3×Q8—61no—
112C2×D12—62no—
113C2×D12—61no—
114C2×D12—61no—
115C2×D12—61no—
116C2×D12—61no—
117C2×D12—61no—
118C2×D12—61no—
119C2×D12—121no—
120C2×D12—121no—
121C2×Dic6—21no—
122C2×Dic6—21no—
123C2×Dic6—62no—
124C2×Dic6—61no—
125C2×Dic6—61no—
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
138#215—124no—
139C4⋊Dic3—21no—
140C4⋊Dic3—21no—
141C4⋊Dic3—21no—
142C4⋊Dic3—21no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4⋊Dic3—121no—
148C4⋊Dic3—121no—
149C2×C3⋊C8D1212yes—
150C2×C3⋊C8D1212yes—
151#204—128no—
152#204—124no—
153#204—124no—
154#204—124no—
155C22×C32#12711yescharacteristic
156C2×C3⋊D3—81no—
157C2×C3⋊D3—81no—
158C2×C3⋊D3—81no—
159C32×C4C2×SD1612yes—
160C32×C4AGL(1,ℤ/8)12yes—
161C32×C4#13712yes—
162C3⋊Dic3—81no—
163C3×Dic3—81no—
164C3×Dic3—81no—
165C2×SD16—182no—
166C2×SD16—182no—
167C4⋊Q8—31no—
168C4⋊Q8—31no—
169C4⋊Q8—91no—
170#127—91no—
171#107—182no—
172#106—182no—
173#103—62no—
174#102—182no—
175C4×C8—31no—
176C4×C8—31no—
177C4×C8D3211yescharacteristic
178C22×D3—122no—
179C22×D3—121no—
180C22×D3—121no—
181C3×Q8—122no—
182C3×Q8—122no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—121no—
187C2×C3×C4—121no—
188C2×C3×C4C2×D1211yescharacteristic
189C2×C3×C4C2×D1211yescharacteristic
190C2×C3×C4C2×D1211yescharacteristic
191C2×C3×C4D3×D411yescharacteristic
192C2×C3×C4D3×D411yescharacteristic
193C2×C3×C4C2×#6711yescharacteristic
194C2×Dic3—41no—
195C2×Dic3—41no—
196C2×Dic3—122no—
197C2×Dic3—121no—
198C2×Dic3—121no—
199D12—124no—
200D12—122no—
201D12—122no—
202D12—122no—
203D12—122no—
204D12—122no—
205D12—122no—
206D12—242no—
207D12—242no—
208Dic6—42no—
209Dic6—42no—
210Dic6—124no—
211Dic6—122no—
212Dic6—122no—
213C3×C8—24no—
214C3×C8—22no—
215C3×C8—22no—
216C3×C8—34no—
217C3×C8—62no—
218C3⋊C8—22no—
219C3⋊C8#20414yescomplemented
220C2×C32#49211yescharacteristic
221C2×C32#49611yescharacteristic
222C2×C32#49711yescharacteristic
223C3⋊D3—161no—
224C2×Q8—61no—
225C2×Q8—61no—
226C2×Q8—181no—
227C2×D4—181no—
228C2×D4—181no—
229C2×D4—181no—
230SD16—364no—
231SD16—364no—
232C2×C8—32no—
233C2×C8—32no—
234C2×C8#62612yes—
235C4⋊C4—61no—
236C4⋊C4—61no—
237C4⋊C4—61no—
238C4⋊C4—61no—
239C4⋊C4—181no—
240C4⋊C4—181no—
241C42C2×D3211yescharacteristic
242C22×C3—21no—
243C22×C3#87411yescharacteristic
244C22×C3#94011yescharacteristic
245C2×D3—242no—
246C2×D3—242no—
247C2×D3—242no—
248C2×D3—241no—
249C2×D3—241no—
250C2×D3—241no—
251C2×D3—241no—
252C2×D3—241no—
253C2×D3—241no—
254C3×C4—22no—
255C3×C4—22no—
256C3×C4—22no—
257C3×C4—241no—
258C3×C4—241no—
259C3×C4C2×#20412yes—
260C3×C4#90812yes—
261C3×C4#90912yes—
262C3×C4D3×SD1612yes—
263C3×C4#91812yes—
264C3×C4#94912yes—
265Dic3—81no—
266Dic3—81no—
267Dic3—242no—
268Dic3—241no—
269Dic3—241no—
270C32#171411yescharacteristic, complemented, Sylow
271C23—361no—
272Q8—122no—
273Q8—122no—
274Q8—362no—
275D4—362no—
276D4—362no—
277D4—362no—
278C2×C4—121no—
279C2×C4—121no—
280C2×C4—361no—
281C2×C4D3×D1211yescharacteristic
282C2×C4D3×D1211yescharacteristic
283C2×C4C2×#62611yescharacteristic
284C8—22no—
285C8—34no—
286C8—62no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3#469311yescharacteristic
291C2×C3#471211yescharacteristic
292C2×C3#471511yescharacteristic
293C2×C3#505811yescharacteristic
294C2×C3#517511yescharacteristic
295C2×C3#519011yescharacteristic
296D3—482no—
297D3—481no—
298D3—481no—
299C22—721no—
300C22—721no—
301C22—721no—
302C22#6391111yescharacteristic
303C4—241no—
304C4—241no—
305C4—721no—
306C4D3×#20412yes—
307C4#6380112yes—
308C4#6382512yes—
309C3—21no—
310C3#6809011yescharacteristic, complemented
311C3#7121611yescharacteristic, complemented
312C2—1441no—
313C2#1059035111yescharacteristic
314C2#1059087711yescharacteristic
315C2#1059089911yescharacteristic
subgroupG/H
centerC22#63911
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#127
prime radical#64083C22
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
2. C3×#4681C2semidirect
4. #10590311C2semidirect
5. #10590303C2semidirect
7. C3×#4454C2semidirect
34. #4681D3semidirect
37. #4454D3semidirect
102. C3×C3⋊C8SD16semidirect
219. C3⋊C8#204semidirect
270. C32#1714semidirect
310. C3#68090semidirect
311. C3#71216semidirect

Maximal subgroups

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

subgroupindex
#105923922
C3×#46812
#105903732
#105903112
#105903032
#105902812
C3×#44542
#712163
#680903