Finite Group Databasebeta

← #11781582

Subgroups — #11781582

Order 1152.

339 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 339 conjugacy classes of subgroups — too many to draw. Only its 94 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
1Q8×C3⋊(C3⋊C8)C211yesmaximal, characteristic
2C3×#5021C211yesmaximal, characteristic
3C3×#5020C211yesmaximal, characteristic
4#10590290C211yesmaximal, characteristic
5#10589100C211yesmaximal, characteristic
6#10589095C211yesmaximal, characteristic
7#10589092C211yesmaximal, characteristic
8#71151—31nomaximal
9#71119—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C4⋊(C3⋊(C3⋊C8))—21no—
14C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
15C4×C3⋊(C3⋊C8)—21no—
16C4×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#835—21no—
18C3×#835—21no—
19C3×#808—21no—
20C3×#807—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63565—21no—
24#63565—21no—
25C3×#477—31no—
26C3×#475—31no—
27#5093—31no—
28#5079—31no—
29Q8×C3⋊C8—31no—
30Q8×C3⋊C8—31no—
31Q8×C3⋊C8—61no—
32#5021D311yescharacteristic
33#5020D311yescharacteristic
34#4547—31no—
35#4546—31no—
36#4486—31no—
37#4481—31no—
38#4479—31no—
39#4479—31no—
40C2×C32×Q8D411yescharacteristic
41C2×C3×Dic6—21no—
42C2×C3×Dic6—21no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4D411yescharacteristic
45C32×C42—21no—
46C32×C42C2311yescharacteristic
47C2×C3⋊(C3⋊C8)—21no—
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56#1684—91noSylow
57C3×C4⋊Q8—31no—
58C3×C4⋊Q8—31no—
59C3×C4×Q8—21no—
60C3×C4×Q8C2×D311yescharacteristic
61C3×C4×Q8C2×D311yescharacteristic
62#869C2×D311yescharacteristic
63#869C2×D311yescharacteristic
64C3×#107—61no—
65C3×#106—61no—
66C3×C4⋊C8—31no—
67C3×C4⋊C8—31no—
68C3×#103—61no—
69C3×#103—61no—
70#835—21no—
71#835—21no—
72#835—61no—
73#835—61no—
74#810—61no—
75#810—61no—
76#808—21no—
77#807—21no—
78C4⋊(C3⋊C8)—31no—
79C4⋊(C3⋊C8)—31no—
80C4⋊(C3⋊C8)—61no—
81C4⋊(C3⋊C8)—61no—
82C4⋊(C3⋊C8)—61no—
83C4⋊(C3⋊C8)—62no—
84C4⋊(C3⋊C8)C2×D311yescharacteristic
85C4⋊(C3⋊C8)C2×D311yescharacteristic
86C4×C3⋊C8—31no—
87C4×C3⋊C8—31no—
88C4×C3⋊C8—61no—
89C4×C3⋊C8—61no—
90C4×C3⋊C8—61no—
91C4×C3⋊C8—62no—
92C32×Q8—21no—
93C32×Q8Q1612yes—
94C2×C32×C4—21no—
95C2×C32×C4—21no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C3×Dic3—41no—
100C2×C3×Dic3—41no—
101C3×Dic6—41no—
102C3×Dic6—41no—
103C3×Dic6—81no—
104C3⋊(C3⋊C8)—21no—
105C3⋊(C3⋊C8)—21no—
106C3⋊(C3⋊C8)—41no—
107C3×C3⋊C8—41no—
108C3×C3⋊C8—41no—
109#487—91no—
110#477—31no—
111#475—31no—
112C8×Q8—91no—
113#335—91no—
114#333—91no—
115#332—91no—
116C2×C3×Q8—21no—
117C2×C3×Q8—61no—
118C2×C3×Q8—61no—
119C2×C3×Q8#6711yescharacteristic
120C2×C3×Q8#6711yescharacteristic
121C2×Dic6—21no—
122C2×Dic6—21no—
123C2×C3×C8—61no—
124C2×C3×C8—61no—
125C3×C4⋊C4—22no—
126C3×C4⋊C4—21no—
127C3×C4⋊C4—21no—
128C3×C4⋊C4—21no—
129C3×C4⋊C4—61no—
130C3×C4⋊C4—61no—
131C3×C4⋊C4—61no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4#6711yescharacteristic
134C3×C4⋊C4#6711yescharacteristic
135C3×C42—22no—
136C3×C42—21no—
137C3×C42—21no—
138C3×C42—21no—
139C3×C42C22×D311yescharacteristic
140C3×C42C22×D311yescharacteristic
141C4⋊Dic3—21no—
142C4⋊Dic3—21no—
143C4⋊Dic3—21no—
144C4⋊Dic3—21no—
145C2×C3⋊C8—21no—
146C2×C3⋊C8—21no—
147C2×C3⋊C8—31no—
148C2×C3⋊C8—31no—
149C2×C3⋊C8—31no—
150C2×C3⋊C8—31no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—62no—
154C2×C3⋊C8—61no—
155C2×C3⋊C8—61no—
156C22×C32#12111yescharacteristic
157C32×C4—22no—
158C32×C4—21no—
159C32×C4—41no—
160C32×C4C2×Q1611yescharacteristic
161C32×C4#13511yescharacteristic
162C32×C4#13511yescharacteristic
163C32×C4#13711yescharacteristic
164C3×Dic3—81no—
165C3×Dic3—81no—
166C4⋊Q8—31no—
167C4⋊Q8—31no—
168C4×Q8D3211yescharacteristic
169#107—61no—
170#106—61no—
171C4⋊C8—31no—
172C4⋊C8—31no—
173C4⋊C8—91no—
174C4⋊C8—181no—
175#103—61no—
176#103—61no—
177#103—181no—
178#103—181no—
179C4×C8—91no—
180C4×C8—181no—
181C3×Q8—22no—
182C3×Q8—21no—
183C3×Q8—21no—
184C3×Q8—22no—
185C3×Q8—121no—
186C3×Q8—121no—
187C3×Q8—241no—
188C3×Q8#21612yes—
189C3×Q8#21612yes—
190C2×C3×C4—22no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—22no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—121no—
200C2×C3×C4—121no—
201C2×C3×C4D3×D411yescharacteristic
202C2×C3×C4D3×D411yescharacteristic
203C2×C3×C4#23711yescharacteristic
204C2×C3×C4#23711yescharacteristic
205C2×C3×C4C2×#6711yescharacteristic
206C2×C3×C4C2×#6711yescharacteristic
207C2×Dic3—41no—
208C2×Dic3—41no—
209Dic6—41no—
210Dic6—41no—
211Dic6—81no—
212C3×C8—121no—
213C3×C8—121no—
214C3⋊C8—41no—
215C3⋊C8—41no—
216C3⋊C8—62no—
217C3⋊C8—61no—
218C3⋊C8—61no—
219C3⋊C8—61no—
220C3⋊C8—61no—
221C3⋊C8—121no—
222C3⋊C8—122no—
223C3⋊C8—121no—
224C3⋊C8—121no—
225C2×C32#46411yescharacteristic
226C2×C32#46711yescharacteristic
227C2×C32#47111yescharacteristic
228C2×Q8—61no—
229C2×Q8—61no—
230C2×Q8#62511yescharacteristic
231C2×C8—61no—
232C2×C8—61no—
233C2×C8—91no—
234C2×C8—91no—
235C2×C8—181no—
236C4⋊C4—21no—
237C4⋊C4—61no—
238C4⋊C4—61no—
239C4⋊C4—61no—
240C4⋊C4—61no—
241C4⋊C4#62511yescharacteristic
242C42—21no—
243C42C2×D3211yescharacteristic
244C22×C3—21no—
245C22×C3#93911yescharacteristic
246C22×C3#93911yescharacteristic
247C3×C4—24no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—22no—
251C3×C4—22no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—41no—
257C3×C4—42no—
258C3×C4—41no—
259C3×C4—41no—
260C3×C4—241no—
261C3×C4—241no—
262C3×C4#91511yescharacteristic
263C3×C4#91611yescharacteristic
264C3×C4#91811yescharacteristic
265C3×C4#91911yescharacteristic
266C3×C4C2×#21611yescharacteristic
267C3×C4C2×#21611yescharacteristic
268C3×C4#95011yescharacteristic
269C3×C4#95011yescharacteristic
270Dic3—81no—
271Dic3—81no—
272C32#168411yescharacteristic, complemented, Sylow
273Q8—21no—
274Q8—121no—
275Q8—121no—
276Q8—241no—
277Q8#371812yes—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—121no—
281C2×C4—121no—
282C2×C4#380511yescharacteristic
283C2×C4C2×#62511yescharacteristic
284C2×C4#381111yescharacteristic
285C8—121no—
286C8—121no—
287C8—181no—
288C8—181no—
289C8—361no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3#505111yescharacteristic
294C2×C3#505111yescharacteristic
295C2×C3#516611yescharacteristic
296C2×C3#518511yescharacteristic
297C2×C3#520011yescharacteristic
298C2×C3#520311yescharacteristic
299C22#6398011yescharacteristic
300C4—21no—
301C4—22no—
302C4—41no—
303C4—241no—
304C4—241no—
305C4#6382211yescharacteristic
306C4C2×#371811yescharacteristic
307C4#6395011yescharacteristic
308C4#6395111yescharacteristic
309C3—21no—
310C3#7111911yescharacteristic, complemented
311C3#7115111yescharacteristic, complemented
312C2#1059118811yescharacteristic
313C2#1059161211yescharacteristic
314C2#1059168111yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socle, prime radicalC22×C32#121
hypercenterC4×Q8D32
hypocenterC32#1684
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
272. C32#1684semidirect
310. C3#71119semidirect
311. C3#71151semidirect

Maximal subgroups

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

subgroupindex
Q8×C3⋊(C3⋊C8)2
C3×#50212
C3×#50202
#105902902
#105891002
#105890952
#105890922
#711513
#711193