Finite Group Databasebeta

← #11781580

Subgroups — #11781580

Order 1152.

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

normal subgroups only

This group has 315 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#10590310C211yesmaximal, characteristic
4#10590285C211yesmaximal, characteristic
5#10589324C211yesmaximal, characteristic
6#10589095C211yesmaximal, characteristic
7#10589093C211yesmaximal, characteristic
8#71241—31nomaximal
9#70947—31nomaximal
10C3×#869C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C32×C4×C8C2211yescharacteristic
14C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C3×#816—21no—
17C3×#816—21no—
18C3×Dic3⋊C8—21no—
19C3×C8×Dic3—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21#63576—21no—
22#63574—21no—
23#63565—21no—
24#63565—21no—
25C3×#487—31no—
26C3×C8×Q8—31no—
27#5094—31no—
28#5091—31no—
29#5021—31no—
30#5020—31no—
31#4681D311yescharacteristic
32C8×Dic6D311yescharacteristic
33#4547—31no—
34#4546—31no—
35#4482—31no—
36#4481—31no—
37#4458—31no—
38#4458—31no—
39#4458—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#1684—91noSylow
57C3×C4⋊Q8—31no—
58C3×C4⋊Q8—31no—
59C3×C4×Q8—31no—
60#869C2×D311yescharacteristic
61#869C2×D311yescharacteristic
62C4×Dic6C2×D311yescharacteristic
63C3×C4⋊C8—31no—
64C3×C4⋊C8—61no—
65C3×#103—61no—
66C3×#103—61no—
67C3×C4×C8—21no—
68C3×C4×C8—61no—
69C3×C4×C8C2×D311yescharacteristic
70C3×C4×C8C2×D311yescharacteristic
71#835—61no—
72#835—61no—
73#816—21no—
74#816—21no—
75Dic3⋊C8—21no—
76C8×Dic3—21no—
77#810—61no—
78#810—61no—
79#808—61no—
80#808—61no—
81#807—61no—
82#807—61no—
83C4⋊(C3⋊C8)—31no—
84C4⋊(C3⋊C8)—31no—
85C4⋊(C3⋊C8)—31no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—61no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4#4111yescharacteristic
93C2×C3×Dic3—21no—
94C2×C3×Dic3—21no—
95C2×C3×Dic3—41no—
96C2×C3×Dic3—41no—
97C3×Dic6—21no—
98C3×Dic6—41no—
99C3×Dic6—41no—
100C3×Dic6—81no—
101C3×Dic6Q1612yes—
102C32×C8—21no—
103C32×C8—21no—
104C3⋊(C3⋊C8)—41no—
105C3⋊(C3⋊C8)—41no—
106C3×C3⋊C8—41no—
107#487—31no—
108#477—91no—
109#475—91no—
110C8×Q8—31no—
111#335—91no—
112#333—91no—
113#332—91no—
114C2×C3×Q8—31no—
115C2×C3×Q8—61no—
116C2×C3×Q8—61no—
117C2×Dic6—21no—
118C2×Dic6—21no—
119C2×Dic6D1211yescharacteristic
120C2×C3×C8—21no—
121C2×C3×C8—21no—
122C2×C3×C8—61no—
123C2×C3×C8#6711yescharacteristic
124C2×C3×C8#6711yescharacteristic
125C2×C3×C8#6711yescharacteristic
126C2×C3×C8#6711yescharacteristic
127C3×C4⋊C4—31no—
128C3×C4⋊C4—61no—
129C3×C4⋊C4—61no—
130C3×C4⋊C4—61no—
131C3×C4⋊C4—61no—
132C3×C4⋊C4—61no—
133C3×C42—21no—
134C3×C42—61no—
135C3×C42C22×D311yescharacteristic
136C3×C42C22×D311yescharacteristic
137C4⋊Dic3—21no—
138C4⋊Dic3—21no—
139C4⋊Dic3—21no—
140C4⋊Dic3—21no—
141C4⋊Dic3D1211yescharacteristic
142Dic3⋊C4—21no—
143C4×Dic3—21no—
144C2×C3⋊C8—21no—
145C2×C3⋊C8—61no—
146C2×C3⋊C8—61no—
147C2×C3⋊C8—61no—
148C2×C3⋊C8—61no—
149C2×C3⋊C8—121no—
150C2×C3⋊C8—121no—
151C22×C32#12111yescharacteristic
152C32×C4—21no—
153C32×C4C2×Q1611yescharacteristic
154C32×C4#13511yescharacteristic
155C32×C4#13511yescharacteristic
156C32×C4#13711yescharacteristic
157C3×Dic3—22no—
158C3×Dic3—41no—
159C3×Dic3—81no—
160C3×Dic3—81no—
161C4⋊Q8—31no—
162C4⋊Q8—31no—
163C4×Q8—31no—
164#107—181no—
165#106—181no—
166C4⋊C8—31no—
167C4⋊C8—61no—
168C4⋊C8—91no—
169C4⋊C8—91no—
170#103—61no—
171#103—61no—
172#103—181no—
173#103—181no—
174C4×C8—61no—
175C4×C8D3211yescharacteristic
176C3×Q8—32no—
177C3×Q8—61no—
178C3×Q8—121no—
179C3×Q8—121no—
180C3×Q8—241no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—61no—
185C2×C3×C4—61no—
186C2×C3×C4—121no—
187C2×C3×C4—121no—
188C2×C3×C4C2×D1211yescharacteristic
189C2×C3×C4#23511yescharacteristic
190C2×C3×C4D3×D411yescharacteristic
191C2×C3×C4#23711yescharacteristic
192C2×C3×C4C2×#6711yescharacteristic
193C2×C3×C4C2×#6711yescharacteristic
194C2×Dic3—21no—
195C2×Dic3—21no—
196C2×Dic3—41no—
197C2×Dic3—41no—
198Dic6—21no—
199Dic6—41no—
200Dic6—41no—
201Dic6—81no—
202Dic6Dic1212yes—
203C3×C8—22no—
204C3×C8—21no—
205C3×C8—21no—
206C3×C8—21no—
207C3×C8—21no—
208C3×C8—41no—
209C3×C8—121no—
210C3⋊C8—41no—
211C3⋊C8—121no—
212C3⋊C8—121no—
213C3⋊C8—121no—
214C3⋊C8—121no—
215C3⋊C8—241no—
216C3⋊C8—241no—
217C2×C32#46411yescharacteristic
218C2×C32#46711yescharacteristic
219C2×C32#47111yescharacteristic
220C2×Q8—31no—
221C2×Q8—61no—
222C2×Q8—61no—
223C2×C8—61no—
224C2×C8—181no—
225C2×C8—181no—
226C2×C8#62511yescharacteristic
227C2×C8#62511yescharacteristic
228C4⋊C4—31no—
229C4⋊C4—61no—
230C4⋊C4—61no—
231C4⋊C4—61no—
232C4⋊C4—61no—
233C4⋊C4—61no—
234C42—61no—
235C42C2×D3211yescharacteristic
236C22×C3—21no—
237C22×C3#93011yescharacteristic
238C22×C3#93811yescharacteristic
239C3×C4—21no—
240C3×C4—21no—
241C3×C4—21no—
242C3×C4—21no—
243C3×C4—21no—
244C3×C4—21no—
245C3×C4—41no—
246C3×C4—62no—
247C3×C4—121no—
248C3×C4—241no—
249C3×C4—241no—
250C3×C4#90411yescharacteristic
251C3×C4C2×Dic1211yescharacteristic
252C3×C4D3×Q1611yescharacteristic
253C3×C4#91911yescharacteristic
254C3×C4#94211yescharacteristic
255C3×C4#95011yescharacteristic
256C3×C4#95011yescharacteristic
257C3×C4#95111yescharacteristic
258Dic3—22no—
259Dic3—41no—
260Dic3—81no—
261Dic3—81no—
262C32#168411yescharacteristic, complemented, Sylow
263Q8—32no—
264Q8—61no—
265Q8—121no—
266Q8—121no—
267Q8—241no—
268C2×C4—61no—
269C2×C4—61no—
270C2×C4—121no—
271C2×C4—121no—
272C2×C4#379511yescharacteristic
273C2×C4D3×D1211yescharacteristic
274C2×C4C2×#62511yescharacteristic
275C8—21no—
276C8—21no—
277C8—121no—
278C8—361no—
279C8—361no—
280C2×C3—21no—
281C2×C3—21no—
282C2×C3—21no—
283C2×C3#502811yescharacteristic
284C2×C3#505411yescharacteristic
285C2×C3#511611yescharacteristic
286C2×C3#514111yescharacteristic
287C2×C3#517711yescharacteristic
288C2×C3#518811yescharacteristic
289C22#6390811yescharacteristic
290C4—21no—
291C4—62no—
292C4—121no—
293C4—241no—
294C4—241no—
295C4D3×Dic1211yescharacteristic
296C4#6380811yescharacteristic
297C4#6382211yescharacteristic
298C4#6382711yescharacteristic
299C3—21no—
300C3#7094711yescharacteristic, complemented
301C3#7124111yescharacteristic, complemented
302C2#1059026711yescharacteristic
303C2#1059085111yescharacteristic
304C2#1059092511yescharacteristic
subgroupG/H
centerC22#63908
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32#121
hypercenterC4×C8D32
hypocenterC32#1684
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
262. C32#1684semidirect
300. C3#70947semidirect
301. C3#71241semidirect

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
#105903102
#105902852
#105893242
#105890952
#105890932
#712413
#709473