Finite Group Databasebeta

← #81515

Subgroups — #81515

Order 384.

420 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5627C211yesmaximal, characteristic
2D3×#117C211yesmaximal, characteristic, complemented
3C3×#485C211yesmaximal, characteristic, complemented
4#5045C211yesmaximal, characteristic, complemented
5#5003C211yesmaximal, characteristic, complemented
6#4882C211yesmaximal, characteristic, complemented
7#4880C211yesmaximal, characteristic, complemented
8#4863C211yesmaximal, characteristic, complemented
9#4860C211yesmaximal, characteristic, complemented
10#4811C211yesmaximal, characteristic, complemented
11#4805C211yesmaximal, characteristic, complemented
12#4804C211yesmaximal, characteristic, complemented
13#4804C211yesmaximal, characteristic, complemented
14#4737C211yesmaximal, characteristic, complemented
15D3×C22⋊C8C211yesmaximal, characteristic, complemented
16#3091—31nomaximal, Sylow
17C2×#239C2211yescharacteristic
18C22×C4×D3C2211yescharacteristic
19C3×C22⋊Q8C2211yescharacteristic
20C3×#117C2211yescharacteristic
21#946C2211yescharacteristic
22#930C2211yescharacteristic
23#926C2211yescharacteristic
24C2×D3×C8C2211yescharacteristic
25C2×D3×C8C2211yescharacteristic
26#895C2211yescharacteristic
27#894—21no—
28#893—21no—
29#892C2211yescharacteristic
30#892C2211yescharacteristic
31#892C2211yescharacteristic
32D3×C4⋊C4C2211yescharacteristic
33D3×C4⋊C4C2211yescharacteristic
34#882—21no—
35#67⋊C4—21no—
36D3×C22⋊C4—21no—
37#877—21no—
38#872—21no—
39C42×D3—21no—
40C3×#107C2211yescharacteristic, complemented
41C3×#106C2211yescharacteristic, complemented
42C3×#103C2211yescharacteristic, complemented
43C3×#103C2211yescharacteristic, complemented
44C3×C22⋊C8C2211yescharacteristic
45#835C2211yescharacteristic, complemented
46#835C2211yescharacteristic, complemented
47#830C2211yescharacteristic
48#821C2211yescharacteristic, complemented
49#821C2211yescharacteristic, complemented
50(C2×D3)⋊C8C2211yescharacteristic
51(C2×D3)⋊C8C2211yescharacteristic
52#818C2211yescharacteristic, complemented
53#817C2211yescharacteristic, complemented
54#809C2211yescharacteristic, complemented
55#809C2211yescharacteristic, complemented
56#808C2211yescharacteristic, complemented
57#808C2211yescharacteristic, complemented
58#807C2211yescharacteristic, complemented
59#807C2211yescharacteristic, complemented
60#525—31no—
61C2×#117—31no—
62#485—31no—
63#485D311yescharacteristic, complemented
64#484—31no—
65#483—31no—
66#482—31no—
67#482—31no—
68#481—31no—
69#480—31no—
70#427—31no—
71#427—31no—
72#416—31no—
73#416—31no—
74C2×C22⋊C8—31no—
75C23×D3D411yescharacteristic
76C2×C3×Q8C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C2×#67—21no—
79C22×Dic3D411yescharacteristic
80#239—22no—
81#239—22no—
82C2×D12—21no—
83C2×D12—21no—
84C2×D12C2311yescharacteristic
85C2×C4×D3—22no—
86C2×C4×D3—22no—
87C2×C4×D3—21no—
88C2×C4×D3—21no—
89C2×C4×D3—21no—
90C2×C4×D3D411yescharacteristic
91C2×C4×D3D411yescharacteristic
92C2×C4×D3C2311yescharacteristic
93C2×C4×D3C2311yescharacteristic
94C2×C3×C8C2311yescharacteristic
95C2×C3×C8C2311yescharacteristic
96C3×C4⋊C4—21no—
97C3×C4⋊C4C2311yescharacteristic
98C3×C4⋊C4C2311yescharacteristic
99C3×C4⋊C4C2311yescharacteristic
100C3×C22⋊C4—21no—
101C3×C22⋊C4—21no—
102C3×C42—21no—
103#217—21no—
104(C2×D3)⋊C4—21no—
105(C2×D3)⋊C4—21no—
106(C2×D3)⋊C4—21no—
107(C2×D3)⋊C4—21no—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110C4⋊Dic3C2311yescharacteristic
111C4⋊Dic3C2311yescharacteristic
112C4⋊Dic3C2311yescharacteristic
113Dic3⋊C4—21no—
114Dic3⋊C4—21no—
115Dic3⋊C4—21no—
116C4×Dic3—21no—
117C4×Dic3—21no—
118C4×Dic3—21no—
119C4×Dic3—21no—
120C2×C3⋊C8C2311yescharacteristic
121C2×C3⋊C8C2311yescharacteristic
122D3×C8—22no—
123D3×C8—22no—
124C2×#41—31no—
125C23×C4—31no—
126C22×C8—31no—
127C22×C8—31no—
128#123—61no—
129C22⋊Q8—31no—
130C22⋊Q8C2×D311yescharacteristic
131#121—31no—
132#121—31no—
133#120—61no—
134C4×D4—61no—
135C4×D4—61no—
136#117—31no—
137#117—31no—
138#117—31no—
139#117—31no—
140#117—61no—
141#117—61no—
142#117C2×D311yescharacteristic
143C2×C4⋊C4—31no—
144C2×C4⋊C4—31no—
145C2×C22⋊C4—61no—
146C2×C42—61no—
147#107—31no—
148#107—31no—
149#107—31no—
150#107C2×D311yescharacteristic, complemented
151#106—31no—
152#106—31no—
153#106—31no—
154#106C2×D311yescharacteristic, complemented
155#103—31no—
156#103—31no—
157#103C2×D311yescharacteristic, complemented
158#103C2×D311yescharacteristic, complemented
159#102—31no—
160#102—31no—
161#102—31no—
162#102—31no—
163C22⋊C8—31no—
164C22⋊C8—31no—
165C22⋊C8—31no—
166C22⋊C8C2×D311yescharacteristic
167C23×C3C2×D411yescharacteristic
168C22×D3—22no—
169C22×D3—22no—
170C22×D3—21no—
171C22×D3—41no—
172C22×D3C2×D411yescharacteristic
173C22×D3C2×D411yescharacteristic
174C3×Q8—21no—
175C3×Q8—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4C2×D411yescharacteristic
183C2×C3×C4C2411yescharacteristic
184#67—42no—
185C2×Dic3—22no—
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3C2×D411yescharacteristic
190C2×Dic3C2×D411yescharacteristic
191D12—21no—
192D12—21no—
193D12—42no—
194D12—42no—
195C4×D3—22no—
196C4×D3—21no—
197C4×D3—21no—
198C4×D3—22no—
199C4×D3—42no—
200C4×D3—42no—
201C4×D3—42no—
202C4×D3#4112yes—
203C4×D3#4112yes—
204C3×C8—21no—
205C3×C8—21no—
206C3⋊C8—21no—
207C3⋊C8—21no—
208C24—31no—
209#41—62no—
210#41—62no—
211C2×Q8C22×D311yescharacteristic
212C2×D4—31no—
213C2×D4—61no—
214C2×D4—61no—
215C2×D4—61no—
216C22×C4—31no—
217C22×C4—31no—
218C22×C4—31no—
219C22×C4—31no—
220C22×C4—31no—
221C22×C4—62no—
222C22×C4—62no—
223C22×C4—61no—
224C22×C4—61no—
225C22×C4—61no—
226C22×C4C22×D311yescharacteristic
227C2×C8—31no—
228C2×C8—31no—
229C2×C8—62no—
230C2×C8—62no—
231C2×C8C22×D311yescharacteristic
232C2×C8C22×D311yescharacteristic
233C4⋊C4—21no—
234C4⋊C4—31no—
235C4⋊C4—31no—
236C4⋊C4—31no—
237C4⋊C4—61no—
238C4⋊C4—61no—
239C4⋊C4—61no—
240C4⋊C4C22×D311yescharacteristic
241C4⋊C4C22×D311yescharacteristic
242C4⋊C4C22×D311yescharacteristic
243C22⋊C4—21no—
244C22⋊C4—21no—
245C22⋊C4—61no—
246C22⋊C4—61no—
247C22⋊C4—61no—
248C22⋊C4—61no—
249C22⋊C4—61no—
250C22⋊C4—61no—
251C22⋊C4—61no—
252C42—21no—
253C42—61no—
254C42—61no—
255C42—61no—
256C42—61no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3C22×D411yescharacteristic
261C2×D3—21no—
262C2×D3—21no—
263C2×D3—21no—
264C2×D3—21no—
265C2×D3—44no—
266C2×D3—41no—
267C2×D3—41no—
268C2×D3—41no—
269C2×D3#12312yes—
270C2×D3#13512yes—
271C3×C4—21no—
272C3×C4—41no—
273C3×C4—41no—
274C3×C4—41no—
275C3×C4—41no—
276C3×C4C2×#4111yescharacteristic
277C3×C4C2×#4111yescharacteristic
278Dic3—21no—
279Dic3—41no—
280Dic3—41no—
281Dic3—41no—
282Dic3#12312yes—
283C23—31no—
284C23—31no—
285C23—62no—
286C23—62no—
287C23—61no—
288C23—121no—
289C23D3×D411yescharacteristic
290Q8—21no—
291Q8—21no—
292D4—61no—
293D4—61no—
294D4—122no—
295D4—122no—
296D4—122no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—31no—
304C2×C4—32no—
305C2×C4—32no—
306C2×C4—31no—
307C2×C4—62no—
308C2×C4—62no—
309C2×C4—62no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4—61no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—122no—
316C2×C4—122no—
317C2×C4—122no—
318C2×C4D3×D411yescharacteristic
319C2×C4C23×D311yescharacteristic
320C8—21no—
321C8—21no—
322C8—61no—
323C8—61no—
324C2×C3—41no—
325C2×C3C2×#12311yescharacteristic
326C2×C3C2×#13511yescharacteristic
327C2×C3#57511yescharacteristic
328D3—22no—
329D3—22no—
330D3—81no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—32no—
335C22—32no—
336C22—61no—
337C22—61no—
338C22—61no—
339C22—61no—
340C22—124no—
341C22—121no—
342C22—121no—
343C22—121no—
344C22C2×D3×D411yescharacteristic
345C4—21no—
346C4—32no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—61no—
352C4—121no—
353C4—121no—
354C4—121no—
355C4D3×#4111yescharacteristic
356C4D3×#4111yescharacteristic
357C3#309111yescharacteristic, complemented, Sylow
358C2—41no—
359C2—62no—
360C2—62no—
361C2—241no—
362C2D3×#12311yescharacteristic
363C2D3×#13511yescharacteristic
364C2#577711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#485C2
socleC22×C3C22×D4
prime radical#5627C2
hypercenter#485D3
hypocenterC3#3091
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
2. D3×#117C2semidirect
3. C3×#485C2semidirect
4. #5045C2semidirect
5. #5003C2semidirect
6. #4882C2semidirect
7. #4880C2semidirect
8. #4863C2semidirect
9. #4860C2semidirect
10. #4811C2semidirect
11. #4805C2semidirect
12. #4804C2semidirect
13. #4804C2semidirect
14. #4737C2semidirect
15. D3×C22⋊C8C2semidirect
40. C3×#107C22semidirect
41. C3×#106C22semidirect
42. C3×#103C22semidirect
43. C3×#103C22semidirect
45. #835C22semidirect
46. #835C22semidirect
48. #821C22semidirect
49. #821C22semidirect
52. #818C22semidirect
53. #817C22semidirect
54. #809C22semidirect
55. #809C22semidirect
56. #808C22semidirect
57. #808C22semidirect
58. #807C22semidirect
59. #807C22semidirect
63. #485D3semidirect
150. #107C2×D3semidirect
154. #106C2×D3semidirect
157. #103C2×D3semidirect
158. #103C2×D3semidirect
357. C3#3091semidirect

Maximal subgroups

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

subgroupindex
#56272
D3×#1172
C3×#4852
#50452
#50032
#48822
#48802
#48632
#48602
#48112
#48052
#48042
#47372
D3×C22⋊C82
#30913