Finite Group Databasebeta

← #82557

Subgroups — #82557

Order 384.

484 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#520C211yesmaximal, characteristic, complemented
2C2×#950C211yesmaximal, characteristic
3#5523C211yesmaximal, characteristic, complemented
4#5232C211yesmaximal, characteristic, complemented
5C4×#216C212yesmaximal, complemented
6#5026C212yesmaximal, complemented
7#5018C212yesmaximal, complemented
8C4×#213C212yesmaximal, complemented
9#4997C211yesmaximal, characteristic, complemented
10#4966C211yesmaximal, characteristic, complemented
11C2×#807C211yesmaximal, characteristic, complemented
12#2951—31nomaximal, Sylow
13C2×C3×#41C2211yescharacteristic
14C2×#235C2211yescharacteristic
15C3×C4×Q8C2212yes—
16C3×C4×D4—22no—
17C3×C4×D4C2212yes—
18C3×#117—21no—
19C3×#117C2211yescharacteristic
20C2×C3×C4⋊C4—21no—
21C2×C3×C4⋊C4C2211yescharacteristic
22#950C418yescomplemented
23C2×#216C2211yescharacteristic
24C2×#215C2211yescharacteristic
25C2×#214C2211yescharacteristic
26C2×#213C2211yescharacteristic
27C2×C4⋊Dic3C2211yescharacteristic
28C2×#208C2211yescharacteristic
29C22×C3⋊C8C2211yescharacteristic
30#892—21no—
31D3×C4⋊C4—21no—
32#67⋊C4—22no—
33C4×D12C2212yes—
34C4×Dic6C2212yes—
35#835C2212yes—
36#832C2212yes—
37#810C2212yes—
38#809C2212yes—
39#807C2212yes—
40#807C2212yes—
41#803C2212yes—
42C4×C3⋊C8C2212yes—
43C2×#135—31no—
44#520—31no—
45#520D311yescharacteristic, complemented
46#440—32no—
47#440—32no—
48C4×Q16—32no—
49C4×D8—32no—
50C2×#107—31no—
51#417—31no—
52#417—31no—
53#405—31no—
54C3×#41—22no—
55C3×#41C2×C414yescomplemented
56C2×C3×Q8C2311yescharacteristic
57C2×C3×D4—21no—
58C2×C3×D4C2311yescharacteristic
59C22×C3×C4—21no—
60C22×C3×C4—21no—
61C22×C3×C4—22no—
62C22×C3×C4C2311yescharacteristic
63C2×#67—21no—
64C22×Dic3—21no—
65#235—22no—
66#235C2×C414yescomplemented
67C2×D12C2311yescharacteristic
68C2×C4×D3—21no—
69C2×C4×D3—22no—
70C2×Dic6C2311yescharacteristic
71C3×C4⋊C4—21no—
72C3×C4⋊C4—22no—
73C3×C4⋊C4D411yescharacteristic
74C3×C4⋊C4D411yescharacteristic
75C3×C4⋊C4C2312yes—
76C3×C22⋊C4—22no—
77C3×C22⋊C4D412yes—
78C3×C42—22no—
79C3×C42C2312yes—
80#216C2×C414yescomplemented
81#215C2×C414yescomplemented
82#214C2×C414yescomplemented
83#213C2×C414yescomplemented
84(C2×D3)⋊C4—22no—
85C4⋊Dic3—21no—
86C4⋊Dic3C2312yes—
87Dic3⋊C4—22no—
88C4×Dic3—22no—
89#208—22no—
90C2×C3⋊C8C2×C414yescomplemented
91C2×C3⋊C8C2312yes—
92C2×C3⋊C8C2311yescharacteristic
93C2×C3⋊C8C2311yescharacteristic
94C2×#41—31no—
95C2×#41C2×D311yescharacteristic
96#135—38no—
97C2×Q16—31no—
98C2×SD16—31no—
99C2×SD16—31no—
100C2×D8—31no—
101C2×M16—31no—
102C22×C8—31no—
103C4×Q8—32no—
104C4×Q8C2×D312yes—
105C4×D4—22no—
106C4×D4—32no—
107C4×D4—62no—
108C4×D4C2×D312yes—
109#117—21no—
110#117—61no—
111#117C2×D311yescharacteristic
112C2×C4⋊C4—21no—
113C2×C4⋊C4—31no—
114C2×C4⋊C4—61no—
115C2×C4⋊C4C2×D311yescharacteristic
116#107—32no—
117#107—32no—
118#103—32no—
119#103—32no—
120#102—32no—
121#102—32no—
122#97—32no—
123C4×C8—32no—
124C23×C3—21no—
125C23×C3C2×D411yescharacteristic
126C22×D3—21no—
127C3×Q8—21no—
128C3×Q8C22×C412yes—
129C3×D4—24no—
130C3×D4—21no—
131C3×D4C22×C412yes—
132C2×C3×C4—21no—
133C2×C3×C4—24no—
134C2×C3×C4—22no—
135C2×C3×C4—82no—
136C2×C3×C4—81no—
137C2×C3×C4C22×C412yes—
138C2×C3×C4C2×D412yes—
139C2×C3×C4C2×D412yes—
140C2×C3×C4C2×D411yescharacteristic
141C2×C3×C4#4112yes—
142C2×C3×C4C2411yescharacteristic
143#67—24no—
144C2×Dic3—21no—
145C2×Dic3—22no—
146C2×Dic3—81no—
147D12—21no—
148D12C22×C412yes—
149C4×D3—24no—
150C4×D3—82no—
151Dic6—21no—
152Dic6C22×C412yes—
153C3⋊C8—22no—
154C3⋊C8C22×C412yes—
155C3⋊C8C22×C412yes—
156#41—22no—
157#41—34no—
158#41—62no—
159#41C4×D314yescomplemented
160C2×Q8—31no—
161C2×Q8C22×D311yescharacteristic
162C2×D4—21no—
163C2×D4—31no—
164C2×D4—61no—
165C2×D4C22×D311yescharacteristic
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—22no—
169C22×C4—61no—
170C22×C4—61no—
171C22×C4—62no—
172C22×C4C22×D311yescharacteristic
173Q16—34no—
174SD16—34no—
175SD16—34no—
176D8—34no—
177M16—62no—
178C2×C8—34no—
179C2×C8—31no—
180C2×C8—31no—
181C2×C8—32no—
182C4⋊C4—21no—
183C4⋊C4—22no—
184C4⋊C4—32no—
185C4⋊C4—61no—
186C4⋊C4—62no—
187C4⋊C4#6711yescharacteristic
188C4⋊C4#6711yescharacteristic
189C4⋊C4C22×D312yes—
190C22⋊C4—22no—
191C22⋊C4—62no—
192C22⋊C4#6712yes—
193C42—22no—
194C42—62no—
195C42C22×D312yes—
196C22×C3—21no—
197C22×C3—21no—
198C22×C3—22no—
199C22×C3—41no—
200C22×C3—41no—
201C22×C3C4×D412yes—
202C22×C3C22×D411yescharacteristic
203C2×D3—22no—
204C2×D3—41no—
205C2×D3—41no—
206C3×C4—22no—
207C3×C4—22no—
208C3×C4—22no—
209C3×C4—42no—
210C3×C4C4×D412yes—
211C3×C4C23×C411yescharacteristic
212C3×C4C2×#4111yescharacteristic
213Dic3—22no—
214Dic3—42no—
215C23—21no—
216C23—61no—
217C23C2×#6711yescharacteristic
218Q8—21no—
219Q8—32no—
220Q8—61no—
221Q8C2×C4×D312yes—
222D4—24no—
223D4—21no—
224D4—32no—
225D4—64no—
226D4—61no—
227D4C2×C4×D312yes—
228C2×C4—21no—
229C2×C4—24no—
230C2×C4—22no—
231C2×C4—61no—
232C2×C4—64no—
233C2×C4—62no—
234C2×C4—82no—
235C2×C4—81no—
236C2×C4—242no—
237C2×C4—241no—
238C2×C4C2×C4×D312yes—
239C2×C4#23512yes—
240C2×C4C2×#6712yes—
241C2×C4C2×#6712yes—
242C2×C4C2×#6711yescharacteristic
243C2×C4C23×D311yescharacteristic
244C8—32no—
245C8—32no—
246C8—62no—
247C2×C3—22no—
248C2×C3—42no—
249C2×C3C2×C4×D411yescharacteristic
250C2×C3#57611yescharacteristic
251C2×C3#57811yescharacteristic
252D3—42no—
253C22—21no—
254C22—21no—
255C22—22no—
256C22—41no—
257C22—41no—
258C22—62no—
259C22—121no—
260C22—121no—
261C22C4×#6712yes—
262C22C22×#6711yescharacteristic
263C4—22no—
264C4—22no—
265C4—22no—
266C4—42no—
267C4—62no—
268C4—122no—
269C4C4×#6712yes—
270C4C22×C4×D311yescharacteristic
271C4C2×#23511yescharacteristic
272C3#295111yescharacteristic, complemented, Sylow
273C2—22no—
274C2—42no—
275C2—122no—
276C2C2×C4×#6711yescharacteristic
277C2#583511yescharacteristic
278C2#583811yescharacteristic
subgroupG/H
centerC22C22×#67
commutatorC3×C4C23×C4
FrattiniC2×C4C23×D3
FittingC3×#520C2
socleC22×C3C22×D4
prime radicalC2×#950C2
cosocleC2×C3×C4C24
hypercenter#520D3
hypocenterC3#2951
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. C3×#520C2semidirect
3. #5523C2semidirect
4. #5232C2semidirect
5. C4×#216C2semidirect
6. #5026C2semidirect
7. #5018C2semidirect
8. C4×#213C2semidirect
9. #4997C2semidirect
10. #4966C2semidirect
11. C2×#807C2semidirect
22. #950C4semidirect
45. #520D3semidirect
55. C3×#41C2×C4semidirect
66. #235C2×C4semidirect
80. #216C2×C4semidirect
81. #215C2×C4semidirect
82. #214C2×C4semidirect
83. #213C2×C4semidirect
90. C2×C3⋊C8C2×C4semidirect
159. #41C4×D3semidirect
272. C3#2951semidirect

Maximal subgroups

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

subgroupindex
C3×#5202
C2×#9502
#55232
#52322
C4×#2162
#50262
#50182
C4×#2132
#49972
#49662
C2×#8072
#29513