Finite Group Databasebeta

← #11781395

Subgroups — #11781395

Order 1152.

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

normal subgroups only

This group has 327 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×#4681C211yesmaximal, characteristic
2C3×C8×Dic6C211yesmaximal, characteristic
3#10590384C211yesmaximal, characteristic
4#10590285C211yesmaximal, characteristic
5#10589323C211yesmaximal, characteristic
6#10589093C211yesmaximal, characteristic
7#10589092C211yesmaximal, characteristic
8#71240—31nomaximal
9#70946—31nomaximal
10C3×#869C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C2×#3718—21no—
14C32×C4×C8C2211yescharacteristic
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×#816—21no—
18C3×#816—21no—
19C3×Dic3⋊C8—21no—
20C3×C8×Dic3—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22#63574—21no—
23#63565—21no—
24#63565—21no—
25C3×#487—31no—
26C3×C8×Q8—31no—
27#5094—31no—
28#5090—31no—
29#5031—31no—
30#5020—31no—
31#4681D311yescharacteristic
32C8×Dic6D311yescharacteristic
33#4547—31no—
34#4547—31no—
35#4486—31no—
36#4482—31no—
37#4457—31no—
38#4457—31no—
39#4457—61no—
40C2×C3×Dic6—21no—
41C2×C3×Dic6—21no—
42C2×C3×Dic6D411yescharacteristic
43C2×C32×C8D411yescharacteristic
44C2×C32×C8D411yescharacteristic
45C32×C42C2311yescharacteristic
46C2×C3⋊(C3⋊C8)—21no—
47C2×C3⋊(C3⋊C8)—21no—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C3×Dic3⋊C4—21no—
54C3×C4×Dic3—21no—
55C2×C3×C3⋊C8—21no—
56#3718—42no—
57#1680—91noSylow
58C3×C4⋊Q8—31no—
59C3×C4⋊Q8—31no—
60C3×C4×Q8—31no—
61C2×#216—61no—
62C2×#216—61no—
63#869C2×D311yescharacteristic
64#869C2×D311yescharacteristic
65C4×Dic6C2×D311yescharacteristic
66C3×C4⋊C8—31no—
67C3×C4⋊C8—61no—
68C3×#103—61no—
69C3×#103—61no—
70C3×C4×C8—21no—
71C3×C4×C8—61no—
72C3×C4×C8C2×D311yescharacteristic
73C3×C4×C8C2×D311yescharacteristic
74#835—61no—
75#835—61no—
76#816—21no—
77#816—21no—
78Dic3⋊C8—21no—
79C8×Dic3—21no—
80#810—61no—
81#810—61no—
82#808—61no—
83#808—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
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C3×Dic3—21no—
95C2×C3×Dic3—21no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—41no—
98C3×Dic6—21no—
99C3×Dic6—41no—
100C3×Dic6—41no—
101C3×Dic6—41no—
102C3×Dic6—41no—
103C3×Dic6SD1612yes—
104C32×C8—21no—
105C32×C8—21no—
106C3⋊(C3⋊C8)—41no—
107C3⋊(C3⋊C8)—41no—
108C3×C3⋊C8—41no—
109#487—31no—
110#475—91no—
111#462—91no—
112C8×Q8—31no—
113#334—91no—
114#332—91no—
115#332—91no—
116C2×C3×Q8—31no—
117C2×C3×Q8—61no—
118C2×C3×Q8—61no—
119C2×Dic6—21no—
120C2×Dic6—21no—
121C2×Dic6D1211yescharacteristic
122C2×C3×C8—21no—
123C2×C3×C8—21no—
124C2×C3×C8—61no—
125C2×C3×C8#6711yescharacteristic
126C2×C3×C8#6711yescharacteristic
127C2×C3×C8#6711yescharacteristic
128C2×C3×C8#6711yescharacteristic
129C3×C4⋊C4—31no—
130C3×C4⋊C4—61no—
131C3×C4⋊C4—61no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C42—21no—
136C3×C42—61no—
137C3×C42C22×D311yescharacteristic
138C3×C42C22×D311yescharacteristic
139#216—122no—
140#216—122no—
141C4⋊Dic3—21no—
142C4⋊Dic3—21no—
143C4⋊Dic3—21no—
144C4⋊Dic3—21no—
145C4⋊Dic3D1211yescharacteristic
146Dic3⋊C4—21no—
147C4×Dic3—21no—
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—
155C22×C32#12111yescharacteristic
156C32×C4—21no—
157C32×C4C2×SD1611yescharacteristic
158C32×C4#13511yescharacteristic
159C32×C4#13511yescharacteristic
160C32×C4#13711yescharacteristic
161C3×Dic3—22no—
162C3×Dic3—41no—
163C3×Dic3—81no—
164C3×Dic3—81no—
165C2×Q16—181no—
166C4⋊Q8—31no—
167C4⋊Q8—31no—
168C4×Q8—31no—
169#106—181no—
170C4⋊C8—31no—
171C4⋊C8—61no—
172C4⋊C8—91no—
173C4⋊C8—91no—
174#103—61no—
175#103—61no—
176#103—181no—
177#103—181no—
178C4×C8—61no—
179C4×C8D3211yescharacteristic
180C3×Q8—32no—
181C3×Q8—61no—
182C3×Q8—121no—
183C3×Q8—121no—
184C3×Q8—121no—
185C3×Q8—121no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—61no—
190C2×C3×C4—61no—
191C2×C3×C4—121no—
192C2×C3×C4—121no—
193C2×C3×C4C2×D1211yescharacteristic
194C2×C3×C4#23511yescharacteristic
195C2×C3×C4D3×D411yescharacteristic
196C2×C3×C4#23711yescharacteristic
197C2×C3×C4C2×#6711yescharacteristic
198C2×C3×C4C2×#6711yescharacteristic
199C2×Dic3—21no—
200C2×Dic3—21no—
201C2×Dic3—41no—
202C2×Dic3—41no—
203Dic6—21no—
204Dic6—41no—
205Dic6—41no—
206Dic6—41no—
207Dic6—41no—
208Dic6#20412yes—
209C3×C8—22no—
210C3×C8—21no—
211C3×C8—21no—
212C3×C8—21no—
213C3×C8—21no—
214C3×C8—41no—
215C3×C8—121no—
216C3⋊C8—41no—
217C3⋊C8—121no—
218C3⋊C8—121no—
219C3⋊C8—121no—
220C3⋊C8—121no—
221C3⋊C8—241no—
222C3⋊C8—241no—
223C2×C32#46411yescharacteristic
224C2×C32#46511yescharacteristic
225C2×C32#47311yescharacteristic
226C2×Q8—31no—
227C2×Q8—61no—
228C2×Q8—61no—
229Q16—362no—
230C2×C8—61no—
231C2×C8—181no—
232C2×C8—181no—
233C2×C8#62511yescharacteristic
234C2×C8#62511yescharacteristic
235C4⋊C4—31no—
236C4⋊C4—61no—
237C4⋊C4—61no—
238C4⋊C4—61no—
239C4⋊C4—61no—
240C4⋊C4—61no—
241C42—61no—
242C42C2×D3211yescharacteristic
243C22×C3—21no—
244C22×C3#93011yescharacteristic
245C22×C3#93811yescharacteristic
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—41no—
253C3×C4—62no—
254C3×C4—121no—
255C3×C4—241no—
256C3×C4—241no—
257C3×C4C2×#20411yescharacteristic
258C3×C4#90411yescharacteristic
259C3×C4D3×SD1611yescharacteristic
260C3×C4#91611yescharacteristic
261C3×C4#94211yescharacteristic
262C3×C4#95011yescharacteristic
263C3×C4#95011yescharacteristic
264C3×C4#95111yescharacteristic
265Dic3—22no—
266Dic3—41no—
267Dic3—81no—
268Dic3—81no—
269C32#168011yescharacteristic, complemented, Sylow
270Q8—32no—
271Q8—61no—
272Q8—121no—
273Q8—121no—
274Q8—121no—
275Q8—121no—
276C2×C4—61no—
277C2×C4—61no—
278C2×C4—121no—
279C2×C4—121no—
280C2×C4#379511yescharacteristic
281C2×C4D3×D1211yescharacteristic
282C2×C4C2×#62511yescharacteristic
283C8—21no—
284C8—21no—
285C8—121no—
286C8—361no—
287C8—361no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3#502811yescharacteristic
292C2×C3#505411yescharacteristic
293C2×C3#511411yescharacteristic
294C2×C3#514311yescharacteristic
295C2×C3#517111yescharacteristic
296C2×C3#519211yescharacteristic
297C22#6390811yescharacteristic
298C4—21no—
299C4—62no—
300C4—121no—
301C4—241no—
302C4—241no—
303C4D3×#20411yescharacteristic
304C4#6380611yescharacteristic
305C4#6382211yescharacteristic
306C4#6382711yescharacteristic
307C3—21no—
308C3#7094611yescharacteristic, complemented
309C3#7124011yescharacteristic, complemented
310C2#1059026711yescharacteristic
311C2#1059082911yescharacteristic
312C2#1059093011yescharacteristic
subgroupG/H
centerC22#63908
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32#121
hypercenterC4×C8D32
hypocenterC32#1680
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
269. C32#1680semidirect
308. C3#70946semidirect
309. C3#71240semidirect

Maximal subgroups

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

subgroupindex
C3×#46812
C3×C8×Dic62
#105903842
#105902852
#105893232
#105890932
#105890922
#712403
#709463