Finite Group Databasebeta

← #121×Dic283 #49123775

Subgroups — #121×Dic283 #49123775

Order 36224.

824 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic283C212yesmaximal, complemented
2C2×D4×Dic283C211yesmaximal, characteristic, complemented
3C22×C4×Dic283C211yesmaximal, characteristic, complemented
4#31826368C211yesmaximal, characteristic, complemented
5#31826364C211yesmaximal, characteristic, complemented
6#31826358C212yesmaximal, complemented
7#31826345C212yesmaximal, complemented
8#31826325C211yesmaximal, characteristic, complemented
9C4⋊C4×Dic283C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic283C212yesmaximal, complemented
11C2×#121×C283C211yesmaximal, characteristic
12C23×Dic283C2212yes—
13C23×Dic283C2211yescharacteristic
14C23×Dic283C2211yescharacteristic
15D4×Dic283—28no—
16D4×Dic283—24no—
17C2×C4⋊Dic283C2211yescharacteristic
18C2×C4⋊Dic283C2211yescharacteristic
19C2×C4⋊Dic283C2212yes—
20C2×C22⋊Dic283C2212yes—
21C2×C22⋊Dic283C2212yes—
22C2×C22⋊Dic283C2212yes—
23C2×C22⋊Dic283C2212yes—
24C2×C4×Dic283—24no—
25C2×C4×Dic283C2211yescharacteristic
26C2×C4×Dic283C2212yes—
27C2×C4×Dic283C2211yescharacteristic
28C2×C4×Dic283C2211yescharacteristic
29C2×C4×Dic283C2211yescharacteristic
30C283⋊#95C2212yes—
31C283⋊#95C2212yes—
32C283⋊#95C2212yes—
33C22×D4×C283C2212yes—
34C22×D4×C283C2211yescharacteristic
35C23×C4×C283C2211yescharacteristic
36#121×C283C418yescomplemented
37C2×C4⋊C4×C283C2211yescharacteristic
38C2×C22⋊C4×C283C2212yes—
39C22×Dic283—22no—
40C22×Dic283—22no—
41C22×Dic283—22no—
42C22×Dic283—22no—
43C22×Dic283—24no—
44C22×Dic283—24no—
45C22×Dic283—24no—
46C22×Dic283—22no—
47C22×Dic283D414yescomplemented
48C22×Dic283C2312yes—
49C22×Dic283C2312yes—
50C22×Dic283C2311yescharacteristic
51C22×Dic283C2311yescharacteristic
52C22×Dic283C2311yescharacteristic
53C22×Dic283C2311yescharacteristic
54C4⋊Dic283—24no—
55C4⋊Dic283—22no—
56C4⋊Dic283—22no—
57C22⋊Dic283—24no—
58C22⋊Dic283—24no—
59C22⋊Dic283—24no—
60C22⋊Dic283—24no—
61C4×Dic283—22no—
62C4×Dic283—22no—
63C4×Dic283—24no—
64C4×Dic283—22no—
65C4×Dic283D414yescomplemented
66C24×C283C2312yes—
67C24×C283C2311yescharacteristic
68C2×D4×C283—24no—
69C2×D4×C283—24no—
70C2×D4×C283—22no—
71C2×D4×C283—22no—
72C2×D4×C283C2×C418yescomplemented
73C2×D4×C283C2×C414yescomplemented
74C22×C4×C283—22no—
75C22×C4×C283—22no—
76C22×C4×C283C2×C414yescomplemented
77C22×C4×C283C2311yescharacteristic
78C22×C4×C283C2312yes—
79C22×C4×C283C2311yescharacteristic
80C4⋊C4×C283C2×C414yescomplemented
81C22⋊C4×C283C2×C418yescomplemented
82C2×Dic283—28no—
83C2×Dic283—21no—
84C2×Dic283—21no—
85C2×Dic283—21no—
86C2×Dic283—21no—
87C2×Dic283—21no—
88C2×Dic283—21no—
89C2×Dic283—28no—
90C2×Dic283—22no—
91C2×Dic283—22no—
92C2×Dic283—22no—
93C2×Dic283—22no—
94C2×Dic283—22no—
95C2×Dic283—22no—
96C2×Dic283—48no—
97C2×Dic283C2×D412yes—
98C2×Dic283C2×D412yes—
99C2×Dic283C2×D412yes—
100C2×Dic283C2×D412yes—
101C2×Dic283#4112yes—
102C2×Dic283#4112yes—
103C23×C283—21no—
104C23×C283—21no—
105C23×C283—21no—
106C23×C283—21no—
107C23×C283—22no—
108C23×C283—22no—
109C23×C283—22no—
110C23×C283—22no—
111C23×C283—22no—
112C23×C283—22no—
113C23×C283C22×C414yes—
114C23×C283C22×C412yes—
115C23×C283C2×D412yes—
116C23×C283#4112yes—
117C23×C283C2411yescharacteristic
118D4×C283—216no—
119D4×C283—28no—
120C2×C4×C283—21no—
121C2×C4×C283—22no—
122C2×C4×C283—21no—
123C2×C4×C283—22no—
124C2×C4×C283—28no—
125C2×C4×C283C22×C412yes—
126C2×C4×C283C22×C414yes—
127C2×C4×C283C22×C412yes—
128C2×C4×C283C2×D412yes—
129C2×C4×C283#4112yes—
130C22×C283—22no—
131C22×C283—22no—
132C22×C283—22no—
133C22×C283—22no—
134C22×C283—22no—
135C22×C283—22no—
136C22×C283—24no—
137C22×C283—24no—
138C22×C283—24no—
139C22×C283—42no—
140C22×C283—42no—
141C22×C283—42no—
142C22×C283—42no—
143C22×C283C4×D414yescomplemented
144C22×C283C23×C411yescharacteristic
145C22×C283C22×D411yescharacteristic
146C22×C283C22×D411yescharacteristic
147C22×C283C2×#4111yescharacteristic
148C22×C283C2×#4111yescharacteristic
149C22×C283C2×#4111yescharacteristic
150C22×C283C2×#4111yescharacteristic
151C4×C283—22no—
152C4×C283—24no—
153C4×C283C4×D414yescomplemented
154Dic283—22no—
155Dic283—22no—
156Dic283—22no—
157Dic283—42no—
158Dic283—42no—
159Dic283#12114yesdirect product factor
160C2×C283—24no—
161C2×C283—44no—
162C2×C283C2×C4×D411yescharacteristic
163C2×C283C2×C4×D411yescharacteristic
164C2×C283C4×#4111yescharacteristic
165C2×C283C2×#12111yescharacteristic
166C2×C283#52511yescharacteristic
167C2×C283#52911yescharacteristic
168C2×C283#53211yescharacteristic
169C283C4×#12111yescharacteristic, complemented, Sylow
170C4×#121—2831nomaximal, Sylow
171C2×#121D28311yescharacteristic
172C2×C4×D4—2831no—
173C2×C4×D4—2832no—
174C22×C42—2831no—
175#390—2831no—
176#389—2831no—
177#388—2832no—
178#386—2832no—
179#380—2831no—
180C4×C4⋊C4—2831no—
181C4×C22⋊C4—2832no—
182C22×D4C2×D28312yes—
183C22×D4C2×D28311yescharacteristic
184C23×C4—2831no—
185C23×C4—2832no—
186C23×C4—2831no—
187C23×C4C2×D28311yescharacteristic
188#121Dic28318yesdirect product factor
189C4×D4—5664no—
190C4×D4—5668no—
191C2×C4⋊C4—2831no—
192C2×C4⋊C4—2832no—
193C2×C4⋊C4—2831no—
194C2×C4⋊C4C2×D28311yescharacteristic
195C2×C22⋊C4—2832no—
196C2×C22⋊C4—2832no—
197C2×C22⋊C4—2832no—
198C2×C22⋊C4—2832no—
199C2×C22⋊C4C2×D28312yes—
200C2×C42—2831no—
201C2×C42—2832no—
202C2×C42—2831no—
203C2×C42—2831no—
204C2×C42—2831no—
205C2×C42—5664no—
206#95—2832no—
207#95—2832no—
208#95—2832no—
209C24C22×D28312yes—
210C24C22×D28311yescharacteristic
211C2×D4—24no—
212C2×D4—24no—
213C2×D4—22no—
214C2×D4—22no—
215C2×D4C2×Dic28318yescomplemented
216C2×D4C2×Dic28314yescomplemented
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—2831no—
220C22×C4—2834no—
221C22×C4—2831no—
222C22×C4—2831no—
223C22×C4—2831no—
224C22×C4—2832no—
225C22×C4—2832no—
226C22×C4—5662no—
227C22×C4—5662no—
228C22×C4—5662no—
229C22×C4—5662no—
230C22×C4—5664no—
231C22×C4—5664no—
232C22×C4—5664no—
233C22×C4—5662no—
234C22×C4C2×Dic28314yescomplemented
235C22×C4C22×D28311yescharacteristic
236C22×C4C22×D28312yes—
237C22×C4C22×D28311yescharacteristic
238C4⋊C4—5664no—
239C4⋊C4—5662no—
240C4⋊C4—5662no—
241C4⋊C4C2×Dic28314yescomplemented
242C22⋊C4—5664no—
243C22⋊C4—5664no—
244C22⋊C4—5664no—
245C22⋊C4—5664no—
246C22⋊C4C2×Dic28318yescomplemented
247C42—2834no—
248C42—5662no—
249C42—5662no—
250C42—5664no—
251C42—5662no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—22no—
257C23—22no—
258C23—22no—
259C23—22no—
260C23—22no—
261C23—22no—
262C23C22×Dic28314yes—
263C23C22×Dic28312yes—
264C23D4×D28312yes—
265C23#1798539112yes—
266C23C23×D28311yescharacteristic
267D4—216no—
268D4—28no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—28no—
274C2×C4—2832no—
275C2×C4—2832no—
276C2×C4—2832no—
277C2×C4—2832no—
278C2×C4—2832no—
279C2×C4—2832no—
280C2×C4—5668no—
281C2×C4—5668no—
282C2×C4—5661no—
283C2×C4—5661no—
284C2×C4—5661no—
285C2×C4—5661no—
286C2×C4—5661no—
287C2×C4—5661no—
288C2×C4—5662no—
289C2×C4—5662no—
290C2×C4—5662no—
291C2×C4—5662no—
292C2×C4—5662no—
293C2×C4—5662no—
294C2×C4—11328no—
295C2×C4C22×Dic28312yes—
296C2×C4C22×Dic28314yes—
297C2×C4C22×Dic28312yes—
298C2×C4D4×D28312yes—
299C2×C4#1798539112yes—
300C22—22no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—24no—
307C22—24no—
308C22—24no—
309C22—42no—
310C22—42no—
311C22—42no—
312C22—42no—
313C22D4×Dic28314yescomplemented
314C22C23×Dic28311yescharacteristic
315C22C2×D4×D28311yescharacteristic
316C22C2×D4×D28311yescharacteristic
317C22#41×D28311yescharacteristic
318C22#41×D28311yescharacteristic
319C22C2×#1798539111yescharacteristic
320C22C2×#1798539111yescharacteristic
321C4—22no—
322C4—24no—
323C4—2834no—
324C4—5662no—
325C4—5662no—
326C4—5662no—
327C4—11322no—
328C4—11322no—
329C4D4×Dic28314yescomplemented
330C2—24no—
331C2—44no—
332C2C2×D4×Dic28311yescharacteristic
333C2C2×D4×Dic28311yescharacteristic
334C2#41×Dic28311yescharacteristic
335C2#121×D28311yescharacteristic
336C2#3182697511yescharacteristic
337C2#3182699611yescharacteristic
338C2#3182701011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting, prime radicalC2×#121×C283C2
socle, cosocleC23×C283C24
hypercenterC2×#121D283
hypocenterC283C4×#121
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic283C2semidirect
2. C2×D4×Dic283C2semidirect
3. C22×C4×Dic283C2semidirect
4. #31826368C2semidirect
5. #31826364C2semidirect
6. #31826358C2semidirect
7. #31826345C2semidirect
8. #31826325C2semidirect
9. C4⋊C4×Dic283C2semidirect
10. C22⋊C4×Dic283C2semidirect
36. #121×C283C4semidirect
47. C22×Dic283D4semidirect
65. C4×Dic283D4semidirect
72. C2×D4×C283C2×C4semidirect
73. C2×D4×C283C2×C4semidirect
76. C22×C4×C283C2×C4semidirect
80. C4⋊C4×C283C2×C4semidirect
81. C22⋊C4×C283C2×C4semidirect
143. C22×C283C4×D4semidirect
153. C4×C283C4×D4semidirect
159. Dic283#121direct (N × H)
169. C283C4×#121semidirect
188. #121Dic283direct (N × H)
215. C2×D4C2×Dic283semidirect
216. C2×D4C2×Dic283semidirect
234. C22×C4C2×Dic283semidirect
241. C4⋊C4C2×Dic283semidirect
246. C22⋊C4C2×Dic283semidirect
313. C22D4×Dic283semidirect
329. C4D4×Dic283semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic2832
C22×C4×Dic2832
#318263682
#318263642
#318263582
#318263452
#318263252
C4⋊C4×Dic2832
C22⋊C4×Dic2832
C2×#121×C2832
C4×#121283