Finite Group Databasebeta

← #11787112

Subgroups — #11787112

Order 1152.

649 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
1#10596290C211yesmaximal, characteristic
2C3×#5240C211yesmaximal, characteristic
3C3×#5234C211yesmaximal, characteristic
4#10591116C212yesmaximal, complemented
5#10589170C212yesmaximal, complemented
6#70044—31nomaximal
7#70002—31nomaximal
8C2×C32×#41C2211yescharacteristic
9#64157—24no—
10C2×#3748—22no—
11C2×#3748C2212yes—
12C3×#926C2212yes—
13C2×C3×#208C2211yescharacteristic
14C22×C3×C3⋊C8C2211yescharacteristic
15C3×#834C414yes—
16C3×#830—22no—
17Dic3⋊(C3⋊C8)—24no—
18#5819—31no—
19#5819—31no—
20#5819—61no—
21C3×#410—31no—
22C3×#408—31no—
23#5240D311yescharacteristic
24#5234D311yescharacteristic
25#5102—32no—
26#4999—32no—
27#4559—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—24no—
37#3748—22no—
38#3748—22no—
39C2×C3⋊(C3⋊C8)—24no—
40C2×C3⋊(C3⋊C8)D414yes—
41C3×#217C2×C414yes—
42C3×C4⋊Dic3—22no—
43C3×C4×Dic3—22no—
44C3×#208—22no—
45C2×C3×C3⋊C8—22no—
46C2×C3×C3⋊C8—21no—
47C2×C3×C3⋊C8—21no—
48#1868—91noSylow
49C2×C3×#41—21no—
50C2×C3×#41C2×D311yescharacteristic
51C2×C3×#41C2×D311yescharacteristic
52C2×C3×M16—31no—
53C22×C3×C8—31no—
54C3×#117—32no—
55#948—64no—
56#948—64no—
57#948—68no—
58#926C2×D312yes—
59C2×#208—32no—
60C2×#208—32no—
61C2×#208—62no—
62C2×#208—64no—
63C2×#208—62no—
64C2×#208—62no—
65C2×#208C2×D311yescharacteristic
66C22×C3⋊C8C2×D311yescharacteristic
67C3×#99—34no—
68C3×C22⋊C8—62no—
69#834Dic314yes—
70#830—22no—
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)—24no—
87C3×C3⋊C8—41no—
88C3×C3⋊C8—41no—
89#568—91no—
90#424—92no—
91#410—31no—
92#408—31no—
93#344—92no—
94C3×#41—24no—
95C3×#41—24no—
96C3×#41—22no—
97C3×#41—22no—
98C3×#41—22no—
99C3×#41—22no—
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—62no—
116C2×C3×C8—61no—
117C2×C3×C8—61no—
118C2×C3×C8—62no—
119C3×C4⋊C4—62no—
120C3×C22⋊C4—34no—
121C3×C42—62no—
122#217C2×Dic314yes—
123C4⋊Dic3—22no—
124C4×Dic3—22no—
125#208—22no—
126#208—64no—
127#208—68no—
128#208—64no—
129#208—64no—
130#208—64no—
131#208—62no—
132#208—62no—
133#208—62no—
134#208—62no—
135C2×C3⋊C8—22no—
136C2×C3⋊C8—21no—
137C2×C3⋊C8—21no—
138C2×C3⋊C8—34no—
139C2×C3⋊C8—34no—
140C2×C3⋊C8—64no—
141C2×C3⋊C8—68no—
142C2×C3⋊C8—64no—
143C2×C3⋊C8—64no—
144C22×C32—22no—
145C22×C32—41no—
146C22×C32—42no—
147C22×C32C2×C4⋊C411yescharacteristic
148C22×C32C4×D412yes—
149C32×C4—22no—
150C32×C4#12011yescharacteristic
151C32×C4C22⋊Q812yes—
152C32×C4#12311yescharacteristic
153C3×Dic3—44no—
154C2×#41D3211yescharacteristic
155#131—184no—
156C2×M16—31no—
157C2×M16—92no—
158C2×M16—182no—
159C22×C8—31no—
160#117—32no—
161C4⋊C8—184no—
162#99—34no—
163C22⋊C8—62no—
164C23×C3—22no—
165C23×C3—21no—
166C23×C3Dic3⋊C412yes—
167C23×C3C4⋊Dic312yes—
168C23×C3C2×C4×D311yescharacteristic
169C23×C3C22×Dic311yescharacteristic
170C3×Q8—24no—
171C3×Q8—22no—
172C3×Q8—22no—
173C3×D4—28no—
174C3×D4—24no—
175C3×D4—24no—
176C3×D4—24no—
177C3×D4—22no—
178C3×D4—22no—
179C2×C3×C4—24no—
180C2×C3×C4—24no—
181C2×C3×C4—22no—
182C2×C3×C4—22no—
183C2×C3×C4—22no—
184C2×C3×C4—22no—
185C2×C3×C4—22no—
186C2×C3×C4—22no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—22no—
190C2×C3×C4—64no—
191C2×C3×C4Dic3⋊C412yes—
192C2×C3×C4C4⋊Dic312yes—
193C2×C3×C4C2×Dic611yescharacteristic
194C2×C3×C4C2×Dic611yescharacteristic
195C2×C3×C4C2×D1211yescharacteristic
196C2×C3×C4D3×D412yes—
197C2×C3×C4D3×D412yes—
198C2×C3×C4#23712yes—
199C2×C3×C4#23712yes—
200C2×C3×C4C2×#6711yescharacteristic
201C2×Dic3—24no—
202C3×C8—121no—
203C3×C8—121no—
204C3⋊C8—41no—
205C3⋊C8—41no—
206C3⋊C8—68no—
207C3⋊C8—64no—
208C3⋊C8—64no—
209C2×C32—22no—
210C2×C32—21no—
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—62no—
221M16—184no—
222M16—182no—
223M16—182no—
224C2×C8—61no—
225C2×C8—61no—
226C2×C8—62no—
227C2×C8—94no—
228C2×C8—184no—
229C4⋊C4—62no—
230C22⋊C4—34no—
231C42—62no—
232C22×C3—24no—
233C22×C3—22no—
234C22×C3—22no—
235C22×C3—21no—
236C22×C3—22no—
237C22×C3—41no—
238C22×C3—41no—
239C22×C3—42no—
240C22×C3—42no—
241C22×C3—81no—
242C22×C3—82no—
243C22×C3#67⋊C412yes—
244C22×C3C2×Dic3⋊C411yescharacteristic
245C22×C3C2×C4⋊Dic311yescharacteristic
246C22×C3D4×Dic312yes—
247C3×C4—24no—
248C3×C4—22no—
249C3×C4—22no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—22no—
253C3×C4—124no—
254C3×C4#87812yes—
255C3×C4#87812yes—
256C3×C4#88211yescharacteristic
257C3×C4#88611yescharacteristic
258C3×C4#93511yescharacteristic
259C3×C4#93711yescharacteristic
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#380512yes—
272C2×C4C2×#62611yescharacteristic
273C2×C4C2×#62711yescharacteristic
274C2×C4#381112yes—
275C8—121no—
276C8—121no—
277C8—184no—
278C2×C3—22no—
279C2×C3—21no—
280C2×C3—22no—
281C2×C3—21no—
282C2×C3—21no—
283C2×C3—41no—
284C2×C3—42no—
285C2×C3—44no—
286C2×C3—42no—
287C2×C3—42no—
288C2×C3#494611yescharacteristic
289C2×C3#495011yescharacteristic
290C22—22no—
291C22—41no—
292C22—42no—
293C22C2×Dic3⋊Dic311yescharacteristic
294C22#67⋊Dic312yes—
295C4—22no—
296C4—124no—
297C4#6396211yescharacteristic
298C4#6398111yescharacteristic
299C4#6398212yes—
300C3—21no—
301C3#7000211yescharacteristic, complemented
302C3#7004411yescharacteristic, complemented
303C2—22no—
304C2—21no—
305C2—42no—
306C2#1059171911yescharacteristic
subgroupG/H
centerC4#63981
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. #10591116C2semidirect
5. #10589170C2semidirect
261. C32#1868semidirect
301. C3#70002semidirect
302. C3#70044semidirect

Maximal subgroups

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

subgroupindex
#105962902
C3×#52402
C3×#52342
#105911162
#105891702
#700443
#700023