Finite Group Databasebeta

← #81436

Subgroups — #81436

Order 384.

342 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5642C211yesmaximal, characteristic
2#5513C211yesmaximal, characteristic
3C3×#483C211yesmaximal, characteristic, complemented
4#5051C211yesmaximal, characteristic, complemented
5C2×#807C211yesmaximal, characteristic, complemented
6#4868C211yesmaximal, characteristic, complemented
7#4860C211yesmaximal, characteristic, complemented
8#4858C211yesmaximal, characteristic, complemented
9#4857C211yesmaximal, characteristic, complemented
10#4815C211yesmaximal, characteristic, complemented
11#4813C211yesmaximal, characteristic, complemented
12#4799C211yesmaximal, characteristic, complemented
13#4790C211yesmaximal, characteristic, complemented
14#67⋊C8C211yesmaximal, characteristic
15#4721C211yesmaximal, characteristic, complemented
16#3336—31nomaximal, Sylow
17C3×C22⋊Q8C2211yescharacteristic
18C2×C3×C4⋊C4C2211yescharacteristic
19#946C2211yescharacteristic
20Q8×Dic3C2211yescharacteristic
21C2×#216C2211yescharacteristic
22#929—21no—
23C4×#67C2211yescharacteristic
24#926—21no—
25C2×C4⋊Dic3C2211yescharacteristic
26#924C2211yescharacteristic
27C22×C3⋊C8C2211yescharacteristic
28C2×D3×C8C2211yescharacteristic
29#898—21no—
30#898—21no—
31#897C2211yescharacteristic
32#892C2211yescharacteristic
33#892C2211yescharacteristic
34#890—21no—
35#890C2211yescharacteristic
36#890C2211yescharacteristic
37#889—21no—
38#887C2211yescharacteristic
39#886—21no—
40#877—21no—
41C3×#106C2211yescharacteristic
42C3×#106C2211yescharacteristic
43C3×#103C2211yescharacteristic
44C3×#103C2211yescharacteristic
45C3×C22⋊C8C2211yescharacteristic
46#835C2211yescharacteristic
47(C2×D3)⋊C8C2211yescharacteristic
48#817C2211yescharacteristic
49#817C2211yescharacteristic
50#816C2211yescharacteristic
51#816C2211yescharacteristic
52Dic3⋊C8C2211yescharacteristic
53C8×Dic3C2211yescharacteristic
54#810C2211yescharacteristic
55#807C2211yescharacteristic
56#807C2211yescharacteristic
57#807C2211yescharacteristic
58#807C2211yescharacteristic
59#807C2211yescharacteristic
60#552—31no—
61#552—31no—
62#499—31no—
63#485—31no—
64#485—31no—
65#483—31no—
66#483D311yescharacteristic, complemented
67#479—31no—
68#479—31no—
69#467—31no—
70#467—31no—
71C4×Q16—31no—
72C8×D4—31no—
73#427—31no—
74C2×#107—31no—
75C2×C3×Q8C2311yescharacteristic
76C22×C3×C4—21no—
77C22×C3×C4C2311yescharacteristic
78C2×#67D411yescharacteristic
79C22×Dic3—21no—
80C2×C4×D3C2311yescharacteristic
81C2×Dic6C2311yescharacteristic
82C2×C3×C8C2311yescharacteristic
83C2×C3×C8C2311yescharacteristic
84C3×C4⋊C4—21no—
85C3×C4⋊C4—21no—
86C3×C4⋊C4C2311yescharacteristic
87C3×C4⋊C4C2311yescharacteristic
88C3×C4⋊C4C2311yescharacteristic
89C3×C22⋊C4—21no—
90#217—21no—
91#217D411yescharacteristic
92#216—22no—
93(C2×D3)⋊C4—21no—
94(C2×D3)⋊C4—21no—
95(C2×D3)⋊C4—21no—
96(C2×D3)⋊C4—21no—
97(C2×D3)⋊C4D411yescharacteristic
98C4⋊Dic3—21no—
99C4⋊Dic3—21no—
100C4⋊Dic3—21no—
101C4⋊Dic3—21no—
102C4⋊Dic3—21no—
103C4⋊Dic3C2311yescharacteristic
104C4⋊Dic3C2311yescharacteristic
105C4⋊Dic3C2311yescharacteristic
106Dic3⋊C4—21no—
107Dic3⋊C4—21no—
108Dic3⋊C4—21no—
109Dic3⋊C4—21no—
110Dic3⋊C4—21no—
111Dic3⋊C4D411yescharacteristic
112C4×Dic3—21no—
113C4×Dic3—21no—
114C4×Dic3—21no—
115C4×Dic3—21no—
116C4×Dic3C2311yescharacteristic
117C2×C3⋊C8—22no—
118C2×C3⋊C8C2311yescharacteristic
119C2×C3⋊C8C2311yescharacteristic
120D3×C8—22no—
121C2×Q16—31no—
122C22×C8—31no—
123C22×C8—31no—
124#126—61no—
125#126—61no—
126#125—31no—
127#125—31no—
128#125—61no—
129#125—61no—
130#123—61no—
131#123—61no—
132C22⋊Q8—31no—
133C22⋊Q8—31no—
134C22⋊Q8—31no—
135C22⋊Q8C2×D311yescharacteristic
136C4×Q8—31no—
137C4×Q8—31no—
138C4×D4—31no—
139#117—31no—
140#117—31no—
141#117—61no—
142#117—61no—
143C2×C4⋊C4—31no—
144C2×C4⋊C4C2×D311yescharacteristic
145#107—31no—
146#107—31no—
147#107—31no—
148#107—31no—
149#107—31no—
150#106—31no—
151#106—31no—
152#106C2×D311yescharacteristic
153#106C2×D311yescharacteristic
154C4⋊C8—31no—
155#103—31no—
156#103—31no—
157#103—31no—
158#103—31no—
159#103C2×D311yescharacteristic
160#103C2×D311yescharacteristic
161C22⋊C8—31no—
162C22⋊C8C2×D311yescharacteristic
163C4×C8—31no—
164C23×C3C2×D411yescharacteristic
165C22×D3C2×D411yescharacteristic
166C3×Q8—21no—
167C3×Q8—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—42no—
175C2×C3×C4C2×D411yescharacteristic
176C2×C3×C4C2411yescharacteristic
177#67—22no—
178C2×Dic3—21no—
179C2×Dic3—21no—
180C2×Dic3—21no—
181C2×Dic3—21no—
182C2×Dic3—42no—
183C2×Dic3C2×D411yescharacteristic
184C2×Dic3C2×D411yescharacteristic
185C2×Dic3C2×D411yescharacteristic
186C4×D3—21no—
187C4×D3—21no—
188Dic6—21no—
189Dic6—21no—
190C3×C8—21no—
191C3×C8—21no—
192C3⋊C8—21no—
193C3⋊C8#4112yes—
194C2×Q8—31no—
195C2×Q8C22×D311yescharacteristic
196C2×D4—31no—
197C22×C4—21no—
198C22×C4—31no—
199C22×C4—61no—
200C22×C4C22×D311yescharacteristic
201Q16—62no—
202C2×C8—31no—
203C2×C8—31no—
204C2×C8—62no—
205C2×C8—62no—
206C2×C8C22×D311yescharacteristic
207C2×C8C22×D311yescharacteristic
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—31no—
211C4⋊C4—31no—
212C4⋊C4—31no—
213C4⋊C4—31no—
214C4⋊C4—61no—
215C4⋊C4—61no—
216C4⋊C4—61no—
217C4⋊C4—61no—
218C4⋊C4—61no—
219C4⋊C4—61no—
220C4⋊C4—61no—
221C4⋊C4—61no—
222C4⋊C4—61no—
223C4⋊C4—61no—
224C4⋊C4C22×D311yescharacteristic
225C4⋊C4C22×D311yescharacteristic
226C4⋊C4C22×D311yescharacteristic
227C22⋊C4—21no—
228C22⋊C4—31no—
229C22⋊C4—31no—
230C22⋊C4—61no—
231C22⋊C4—61no—
232C22⋊C4—61no—
233C22⋊C4—61no—
234C22⋊C4—61no—
235C42—31no—
236C42—61no—
237C42—61no—
238C42—61no—
239C42—61no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3#13512yes—
243C22×C3C22×D411yescharacteristic
244C2×D3—21no—
245C2×D3—21no—
246C2×D3—21no—
247C3×C4—21no—
248C3×C4—41no—
249C3×C4—41no—
250C3×C4—41no—
251C3×C4—41no—
252C3×C4C2×#4111yescharacteristic
253C3×C42−1+411yescharacteristic
254Dic3—21no—
255Dic3—21no—
256Dic3—21no—
257Dic3—41no—
258Dic3—41no—
259Dic3—41no—
260Dic3—41no—
261C23—31no—
262C23D3×D411yescharacteristic
263Q8—21no—
264Q8—21no—
265Q8—61no—
266Q8—61no—
267D4—62no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—31no—
275C2×C4—31no—
276C2×C4—31no—
277C2×C4—42no—
278C2×C4—61no—
279C2×C4—61no—
280C2×C4—61no—
281C2×C4—61no—
282C2×C4—61no—
283C2×C4—61no—
284C2×C4—122no—
285C2×C4D3×D411yescharacteristic
286C2×C4C23×D311yescharacteristic
287C8—21no—
288C8—21no—
289C8—32no—
290C8—61no—
291C2×C3—22no—
292C2×C3#54711yescharacteristic
293C2×C3C2×#13511yescharacteristic
294C2×C3#57811yescharacteristic
295D3—41no—
296C22—21no—
297C22—21no—
298C22—61no—
299C22—61no—
300C22—61no—
301C22#91612yes—
302C22C2×D3×D411yescharacteristic
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—61no—
309C4—61no—
310C4—61no—
311C4—121no—
312C4—121no—
313C4—121no—
314C4—121no—
315C4D3×#4111yescharacteristic
316C4#101011yescharacteristic
317C3#333611yescharacteristic, complemented, Sylow
318C2—22no—
319C2—121no—
320C2#565511yescharacteristic
321C2C2×#91611yescharacteristic
322C2#577911yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#483C2
socleC22×C3C22×D4
prime radicalC2×#67D4
hypercenter#483D3
hypocenterC3#3336
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. C3×#483C2semidirect
4. #5051C2semidirect
5. C2×#807C2semidirect
6. #4868C2semidirect
7. #4860C2semidirect
8. #4858C2semidirect
9. #4857C2semidirect
10. #4815C2semidirect
11. #4813C2semidirect
12. #4799C2semidirect
13. #4790C2semidirect
15. #4721C2semidirect
66. #483D3semidirect
317. C3#3336semidirect

Maximal subgroups

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

subgroupindex
#56422
#55132
C3×#4832
#50512
C2×#8072
#48682
#48602
#48582
#48572
#48152
#48132
#47992
#47902
#67⋊C82
#47212
#33363