Finite Group Databasebeta

← #11781534

Subgroups — #11781534

Order 1152.

347 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 347 conjugacy classes of subgroups — too many to draw. Only its 92 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×C8×D12C211yesmaximal, characteristic
2C3×#4681C211yesmaximal, characteristic, complemented
3#10590269C211yesmaximal, characteristic
4#10590266C211yesmaximal, characteristic
5#10589324C211yesmaximal, characteristic, complemented
6#10589095C211yesmaximal, characteristic, complemented
7#10589093C211yesmaximal, characteristic, complemented
8#71233—31nomaximal
9#70855—31nomaximal
10C2×C3×D3×C8—21no—
11C3×C4×D12C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C32×C4×C8C2211yescharacteristic
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×(C2×D3)⋊C8—21no—
18C3×#816—21no—
19C3×#816—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21#63576—21no—
22#63574—21no—
23#63562—21no—
24#63562—21no—
25C3×#487—31no—
26C3×C8×D4—31no—
27#5087—31no—
28#5084—31no—
29#5008—31no—
30#5007—31no—
31C8×D12D311yescharacteristic
32#4681D311yescharacteristic, complemented
33#4547—31no—
34#4546—31no—
35#4482—31no—
36#4481—31no—
37#4458—31no—
38#4458—31no—
39#4458—61no—
40C2×C3×D12D411yescharacteristic
41C2×C3×C4×D3—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8D411yescharacteristic
45C2×C32×C8D411yescharacteristic
46C32×C42C2311yescharacteristic
47C2×C3⋊(C3⋊C8)—21no—
48C2×C3⋊(C3⋊C8)—21no—
49C3×(C2×D3)⋊C4—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C2×C3×C3⋊C8—21no—
56C3×D3×C8—42no—
57#1683—91noSylow
58C22×C3×C8—61no—
59C3×C4⋊Q8—31no—
60C3×C4⋊Q8—31no—
61C3×C4×D4—31no—
62C2×D3×C8—21no—
63C4×D12C2×D311yescharacteristic
64#869C2×D311yescharacteristic
65#869C2×D311yescharacteristic
66C3×C4⋊C8—31no—
67C3×#103—61no—
68C3×#103—61no—
69C3×C22⋊C8—61no—
70C3×C4×C8—21no—
71C3×C4×C8C2×D311yescharacteristic
72C3×C4×C8C2×D311yescharacteristic
73#832—61no—
74#832—61no—
75(C2×D3)⋊C8—21no—
76#816—21no—
77#816—21no—
78#809—61no—
79#809—61no—
80#808—61no—
81#808—61no—
82#807—61no—
83#807—61no—
84C4⋊(C3⋊C8)—31no—
85C4⋊(C3⋊C8)—31no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C22×C3×D3—21no—
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4#4111yescharacteristic
95C2×C3×Dic3—21no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—41no—
98C3×D12—21no—
99C3×D12Q1612yes—
100C3×C4×D3—41no—
101C3×C4×D3—41no—
102C3×Dic6—41no—
103C3×Dic6—41no—
104C3×Dic6—81no—
105C32×C8—21no—
106C32×C8—21no—
107C3⋊(C3⋊C8)—41no—
108C3⋊(C3⋊C8)—41no—
109C3×C3⋊C8—41no—
110#487—31no—
111#476—91no—
112#474—91no—
113C8×D4—31no—
114#335—91no—
115#333—91no—
116#332—91no—
117C2×C3×Q8—61no—
118C2×C3×Q8—61no—
119C2×C3×D4—31no—
120C22×C3×C4—61no—
121C2×D12D1211yescharacteristic
122C2×C4×D3—21no—
123C2×Dic6—21no—
124C2×Dic6—21no—
125C2×C3×C8—21no—
126C2×C3×C8—21no—
127C2×C3×C8—61no—
128C2×C3×C8—122no—
129C2×C3×C8#6711yescharacteristic
130C2×C3×C8#6711yescharacteristic
131C2×C3×C8#6711yescharacteristic
132C2×C3×C8#6711yescharacteristic
133C3×C4⋊C4—31no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—61no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4—61no—
138C3×C22⋊C4—61no—
139C3×C42—21no—
140C3×C42C22×D311yescharacteristic
141C3×C42C22×D311yescharacteristic
142(C2×D3)⋊C4—21no—
143C4⋊Dic3—21no—
144C4⋊Dic3—21no—
145C4⋊Dic3—21no—
146C4⋊Dic3—21no—
147C4⋊Dic3D1211yescharacteristic
148C2×C3⋊C8—21no—
149C2×C3⋊C8—61no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—121no—
154C2×C3⋊C8—121no—
155D3×C8—42no—
156C22×C32#12111yescharacteristic
157C2×C3×D3—22no—
158C2×C3×D3—41no—
159C2×C3×D3—41no—
160C32×C4—21no—
161C32×C4C2×Q1611yescharacteristic
162C32×C4#13511yescharacteristic
163C32×C4#13511yescharacteristic
164C32×C4AGL(1,ℤ/8)11yescharacteristic
165C3×Dic3—41no—
166C3×Dic3—81no—
167C3×Dic3—81no—
168C22×C8—61no—
169C4⋊Q8—31no—
170C4⋊Q8—31no—
171C4×D4—31no—
172#107—181no—
173#106—181no—
174C4⋊C8—31no—
175C4⋊C8—91no—
176C4⋊C8—91no—
177#103—61no—
178#103—61no—
179#102—181no—
180#102—181no—
181C22⋊C8—61no—
182C4×C8D3211yescharacteristic
183C23×C3—61no—
184C22×D3—21no—
185C3×Q8—121no—
186C3×Q8—121no—
187C3×Q8—241no—
188C3×D4—32no—
189C3×D4—61no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—61no—
194C2×C3×C4—121no—
195C2×C3×C4—121no—
196C2×C3×C4—121no—
197C2×C3×C4—121no—
198C2×C3×C4C2×D1211yescharacteristic
199C2×C3×C4#23511yescharacteristic
200C2×C3×C4D3×D411yescharacteristic
201C2×C3×C4#23711yescharacteristic
202C2×C3×C4C2×#6711yescharacteristic
203C2×C3×C4C2×#6711yescharacteristic
204C2×Dic3—21no—
205C2×Dic3—41no—
206C2×Dic3—41no—
207D12—21no—
208D12Dic1212yes—
209C4×D3—41no—
210C4×D3—41no—
211Dic6—41no—
212Dic6—41no—
213Dic6—81no—
214C3×C8—22no—
215C3×C8—21no—
216C3×C8—21no—
217C3×C8—21no—
218C3×C8—21no—
219C3×C8—41no—
220C3×C8—121no—
221C3⋊C8—41no—
222C3⋊C8—121no—
223C3⋊C8—121no—
224C3⋊C8—121no—
225C3⋊C8—121no—
226C3⋊C8—241no—
227C3⋊C8—241no—
228C2×C32#46311yescharacteristic
229C2×C32#46711yescharacteristic
230C2×C32#47111yescharacteristic
231C3×D3—42no—
232C2×Q8—61no—
233C2×Q8—61no—
234C2×D4—31no—
235C22×C4—61no—
236C2×C8—61no—
237C2×C8—122no—
238C2×C8—181no—
239C2×C8—181no—
240C2×C8#62511yescharacteristic
241C2×C8#62511yescharacteristic
242C4⋊C4—31no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C22⋊C4—61no—
248C42C2×D3211yescharacteristic
249C22×C3—21no—
250C22×C3—62no—
251C22×C3—121no—
252C22×C3—121no—
253C22×C3#93011yescharacteristic
254C22×C3#93811yescharacteristic
255C2×D3—22no—
256C2×D3—41no—
257C2×D3—41no—
258C3×C4—21no—
259C3×C4—21no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—41no—
265C3×C4—121no—
266C3×C4—241no—
267C3×C4—241no—
268C3×C4#90411yescharacteristic
269C3×C4C2×Dic1211yescharacteristic
270C3×C4D3×Q1611yescharacteristic
271C3×C4#91911yescharacteristic
272C3×C4#93211yescharacteristic
273C3×C4#94911yescharacteristic
274C3×C4#95011yescharacteristic
275C3×C4#95011yescharacteristic
276Dic3—41no—
277Dic3—81no—
278Dic3—81no—
279C32#168311yescharacteristic, complemented, Sylow
280C23—61no—
281Q8—121no—
282Q8—121no—
283Q8—241no—
284D4—32no—
285D4—61no—
286C2×C4—61no—
287C2×C4—121no—
288C2×C4—121no—
289C2×C4—121no—
290C2×C4—121no—
291C2×C4#379511yescharacteristic
292C2×C4D3×D1211yescharacteristic
293C2×C4C2×#62511yescharacteristic
294C8—21no—
295C8—21no—
296C8—121no—
297C8—361no—
298C8—361no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—122no—
303C2×C3#501611yescharacteristic
304C2×C3#505711yescharacteristic
305C2×C3#511611yescharacteristic
306C2×C3#514111yescharacteristic
307C2×C3#517711yescharacteristic
308C2×C3#518811yescharacteristic
309D3—42no—
310C22—62no—
311C22—121no—
312C22—121no—
313C22#6390811yescharacteristic
314C4—21no—
315C4—121no—
316C4—241no—
317C4—241no—
318C4D3×Dic1211yescharacteristic
319C4#6380811yescharacteristic
320C4#6382211yescharacteristic
321C4#6382311yescharacteristic
322C3—21no—
323C3#7085511yescharacteristic, complemented
324C3#7123311yescharacteristic, complemented
325C2—122no—
326C2#1059034811yescharacteristic
327C2#1059085111yescharacteristic
328C2#1059092511yescharacteristic
subgroupG/H
centerC22#63908
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#121
prime radicalC2×C3×D12D4
hypercenterC4×C8D32
hypocenterC32#1683
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
5. #10589324C2semidirect
6. #10589095C2semidirect
7. #10589093C2semidirect
32. #4681D3semidirect
279. C32#1683semidirect
323. C3#70855semidirect
324. C3#71233semidirect

Maximal subgroups

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

subgroupindex
C3×C8×D122
C3×#46812
#105902692
#105902662
#105893242
#105890952
#105890932
#712333
#708553