Finite Group Databasebeta

← #11787111

Subgroups — #11787111

Order 1152.

599 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5819C211yesmaximal, characteristic
2#10592933C211yesmaximal, characteristic
3C3×#5240C211yesmaximal, characteristic
4#10591117C212yesmaximal, complemented
5#10589169C212yesmaximal, complemented
6#72026—31nomaximal
7#70044—31nomaximal
8C2×C32×#41C2211yescharacteristic
9C2×#3748C2211yescharacteristic
10C22×C3⋊(C3⋊C8)C2211yescharacteristic
11C3×#948—24no—
12C3×#926C2212yes—
13C2×C3×#208—22no—
14C2×C3×#208C2212yes—
15#63657—22no—
16C3×#834C414yes—
17Dic3⋊(C3⋊C8)—24no—
18C3×#568—31no—
19#5819D311yescharacteristic
20C3×#410—31no—
21#5240D311yescharacteristic
22#5234—31no—
23#5234—31no—
24#5234—61no—
25#5119—32no—
26#4999—32no—
27#4556—32no—
28#4533—32no—
29C32×#41—22no—
30C32×#41—22no—
31C2×C32×Q8Q811yescharacteristic
32C2×C32×D4C2×C412yes—
33C2×C32×D4Q811yescharacteristic
34C22×C32×C4D412yes—
35C22×C32×C4C2311yescharacteristic
36#3748—22no—
37C2×C3⋊(C3⋊C8)—21no—
38C2×C3⋊(C3⋊C8)—21no—
39C2×C3⋊(C3⋊C8)—22no—
40C3×#217C2×C414yes—
41C3×C4⋊Dic3—22no—
42C3×C4×Dic3—22no—
43C3×#208—24no—
44C3×#208—22no—
45C3×#208—22no—
46C2×C3×C3⋊C8—24no—
47C2×C3×C3⋊C8D414yes—
48#1868—91noSylow
49C2×C3×#41—21no—
50C2×C3×#41C2×D311yescharacteristic
51C2×C3×#41C2×D311yescharacteristic
52C3×#131—64no—
53C2×C3×M16—32no—
54C2×C3×M16—62no—
55C3×#117—32no—
56#948—24no—
57#926C2×D312yes—
58C2×#208—22no—
59C2×#208—31no—
60C2×#208—31no—
61C2×#208—61no—
62C2×#208C2×D312yes—
63C22×C3⋊C8—31no—
64C22×C3⋊C8—31no—
65C22×C3⋊C8—61no—
66C3×#99—34no—
67#834Dic314yes—
68#830—64no—
69#830—62no—
70#830—62no—
71Dic3⋊C8—64no—
72C4⋊(C3⋊C8)—64no—
73C23×C32C4⋊C412yes—
74C23×C32C22×C411yescharacteristic
75C32×Q8—22no—
76C32×D4—24no—
77C32×D4—22no—
78C2×C32×C4—22no—
79C2×C32×C4—22no—
80C2×C32×C4C4⋊C412yes—
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4C2×D412yes—
83C2×C32×C4C2×Q811yescharacteristic
84C2×C32×C4#4112yes—
85C2×C3×Dic3—24no—
86C3⋊(C3⋊C8)—41no—
87C3⋊(C3⋊C8)—41no—
88C3×C3⋊C8—24no—
89#568—31no—
90#424—92no—
91#410—31no—
92#408—91no—
93#344—92no—
94C3×#41—22no—
95C3×#41—22no—
96C3×#41—22no—
97C3×#41—22no—
98C3×#41—42no—
99C3×#41—42no—
100C2×C3×Q8—21no—
101C2×C3×Q8Dic611yescharacteristic
102C2×C3×Q8Dic611yescharacteristic
103C2×C3×D4—22no—
104C2×C3×D4—21no—
105C2×C3×D4Dic611yescharacteristic
106C2×C3×D4Dic611yescharacteristic
107C2×C3×D4C4×D312yes—
108C2×C3×D4C2×Dic312yes—
109C22×C3×C4—22no—
110C22×C3×C4—21no—
111C22×C3×C4D1212yes—
112C22×C3×C4#6712yes—
113C22×C3×C4C22×D311yescharacteristic
114C22×C3×C4C22×D311yescharacteristic
115C3×M16—64no—
116C3×M16—62no—
117C3×M16—62no—
118C2×C3×C8—34no—
119C2×C3×C8—64no—
120C3×C4⋊C4—62no—
121C3×C22⋊C4—34no—
122C3×C42—62no—
123#217C2×Dic314yes—
124C4⋊Dic3—22no—
125C4×Dic3—22no—
126#208—24no—
127#208—22no—
128#208—22no—
129#208—62no—
130#208—62no—
131#208—122no—
132C2×C3⋊C8—24no—
133C2×C3⋊C8—62no—
134C2×C3⋊C8—62no—
135C2×C3⋊C8—61no—
136C2×C3⋊C8—61no—
137C2×C3⋊C8—62no—
138C2×C3⋊C8—62no—
139C2×C3⋊C8—61no—
140C2×C3⋊C8—61no—
141C2×C3⋊C8—122no—
142C2×C3⋊C8#6714yes—
143C22×C32—22no—
144C22×C32—41no—
145C22×C32—42no—
146C22×C32C2×C4⋊C411yescharacteristic
147C22×C32C4×D412yes—
148C32×C4—22no—
149C32×C4#12011yescharacteristic
150C32×C4C22⋊Q812yes—
151C32×C4#12311yescharacteristic
152C3×Dic3—44no—
153C2×#41D3211yescharacteristic
154#131—64no—
155C2×M16—32no—
156C2×M16—62no—
157C2×M16—91no—
158C22×C8—91no—
159#117—32no—
160C4⋊C8—184no—
161#99—34no—
162C22⋊C8—182no—
163C23×C3—22no—
164C23×C3—21no—
165C23×C3Dic3⋊C412yes—
166C23×C3C4⋊Dic312yes—
167C23×C3C2×C4×D311yescharacteristic
168C23×C3C22×Dic311yescharacteristic
169C3×Q8—22no—
170C3×Q8—22no—
171C3×Q8—42no—
172C3×D4—24no—
173C3×D4—24no—
174C3×D4—22no—
175C3×D4—22no—
176C3×D4—42no—
177C3×D4—44no—
178C2×C3×C4—22no—
179C2×C3×C4—22no—
180C2×C3×C4—22no—
181C2×C3×C4—22no—
182C2×C3×C4—22no—
183C2×C3×C4—22no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—22no—
187C2×C3×C4—42no—
188C2×C3×C4—42no—
189C2×C3×C4—64no—
190C2×C3×C4Dic3⋊C412yes—
191C2×C3×C4C4⋊Dic312yes—
192C2×C3×C4C2×Dic611yescharacteristic
193C2×C3×C4C2×Dic611yescharacteristic
194C2×C3×C4C2×D1211yescharacteristic
195C2×C3×C4#23512yes—
196C2×C3×C4D3×D412yes—
197C2×C3×C4#23712yes—
198C2×C3×C4C2×#6711yescharacteristic
199C2×C3×C4C2×#6712yes—
200C2×Dic3—24no—
201C3×C8—64no—
202C3⋊C8—24no—
203C3⋊C8—122no—
204C3⋊C8—122no—
205C3⋊C8—121no—
206C3⋊C8—121no—
207C3⋊C8—121no—
208C3⋊C8—121no—
209C2×C32—21no—
210C2×C32—22no—
211C2×C32—42no—
212C2×C32#38511yescharacteristic
213#41—22no—
214#41—22no—
215C2×Q8#62711yescharacteristic
216C2×D4D3×Dic312yes—
217C2×D4#62711yescharacteristic
218C22×C4#62612yes—
219C22×C4C2×D3211yescharacteristic
220M16—64no—
221M16—62no—
222M16—62no—
223M16—182no—
224C2×C8—34no—
225C2×C8—64no—
226C2×C8—181no—
227C2×C8—181no—
228C2×C8—182no—
229C4⋊C4—62no—
230C22⋊C4—34no—
231C42—62no—
232C22×C3—22no—
233C22×C3—22no—
234C22×C3—21no—
235C22×C3—22no—
236C22×C3—42no—
237C22×C3—41no—
238C22×C3—41no—
239C22×C3—42no—
240C22×C3—42no—
241C22×C3—42no—
242C22×C3—44no—
243C22×C3C2×Dic3⋊C411yescharacteristic
244C22×C3C2×C4⋊Dic311yescharacteristic
245C22×C3C4×#6712yes—
246C22×C3D4×Dic312yes—
247C3×C4—22no—
248C3×C4—22no—
249C3×C4—22no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—42no—
253C3×C4—124no—
254C3×C4#87812yes—
255C3×C4#88211yescharacteristic
256C3×C4#88611yescharacteristic
257C3×C4#92412yes—
258C3×C4#92911yescharacteristic
259C3×C4#95311yescharacteristic
260Dic3—44no—
261C32#186811yescharacteristic, complemented, Sylow
262C23Dic3⋊Dic312yes—
263C23C2×D3×Dic311yescharacteristic
264Q8—22no—
265D4—24no—
266D4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—64no—
270C2×C4Dic3⋊Dic312yes—
271C2×C4#380412yes—
272C2×C4C2×#62611yescharacteristic
273C2×C4C2×#62711yescharacteristic
274C2×C4D3×#6712yes—
275C8—64no—
276C8—361no—
277C8—361no—
278C2×C3—22no—
279C2×C3—22no—
280C2×C3—21no—
281C2×C3—22no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—42no—
285C2×C3—42no—
286C2×C3—42no—
287C2×C3—82no—
288C2×C3#495011yescharacteristic
289C2×C3#521011yescharacteristic
290C22—22no—
291C22—41no—
292C22—42no—
293C22C2×Dic3⋊Dic311yescharacteristic
294C22Dic3×#6712yes—
295C4—22no—
296C4—124no—
297C4#6396412yes—
298C4#6396611yescharacteristic
299C4#6397711yescharacteristic
300C3—21no—
301C3#7004411yescharacteristic, complemented
302C3#7202611yescharacteristic, complemented
303C2—22no—
304C2—21no—
305C2—42no—
306C2#1059171811yescharacteristic
subgroupG/H
centerC4#63977
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC2×C32#385
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1868
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #10591117C2semidirect
5. #10589169C2semidirect
261. C32#1868semidirect
301. C3#70044semidirect
302. C3#72026semidirect

Maximal subgroups

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

subgroupindex
C3×#58192
#105929332
C3×#52402
#105911172
#105891692
#720263
#700443