Finite Group Databasebeta

← #29680550

Subgroups — #29680550

Order 15616.

982 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C8×D61C211yesmaximal, characteristic
2#21448224C212yesmaximal
3#21445979C211yesmaximal, characteristic, complemented
4#21445946C212yesmaximal, complemented
5#21445845C214yesmaximal
6#107×Dic61C214yesmaximal, complemented
7C61×#1845C211yesmaximal, characteristic, complemented
8C22×C8×D61C2212yes—
9C2×#14519735—22no—
10C2×C42×D61C2211yescharacteristic
11C2×#14519711C2214yes—
12C2×C4×#92418C2211yescharacteristic
13C2×C8×Dic61C2212yes—
14C4×C8×D61C418yescomplemented
15#16839632C2212yes—
16#16839627—22no—
17#16839619—22no—
18#16839619C2214yes—
19C4⋊C4×Dic61—22no—
20C4⋊C4×Dic61C2214yes—
21#16839524C2218yes—
22C2×#107×C61C2214yes—
23C2×C4×C8×C61C2211yescharacteristic
24C61×#384C2212yes—
25C22×C4×D61D411yescharacteristic
26C22×C4×D61D411yescharacteristic
27C22×C4×D61C2311yescharacteristic
28C22×#92418C2312yes—
29C2×C8×D61—24no—
30C2×C8×D61—24no—
31C2×C8×D61C2×C418yes—
32#14519735—48no—
33C2×C4⋊Dic61—22no—
34C2×C4⋊Dic61—22no—
35C2×C4⋊Dic61C2314yes—
36C2×#11758198—24no—
37C2×C4×Dic61—24no—
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61C2311yescharacteristic
41C42×D61C2×C414yes—
42C42×D61Q814yes—
43#14519711—28no—
44C4×#92418C2×C414yes—
45C8×Dic61C2×C418yes—
46#14519684—24no—
47#14519684—24no—
48C22×C8×C61C2312yes—
49C2×C4⋊C4×C61—22no—
50C2×C4⋊C4×C61—22no—
51C2×C4⋊C4×C61C2314yes—
52C2×C42×C61C2311yescharacteristic
53#107×C61—28no—
54C4×C8×C61C2×C414yes—
55C23×D61C2×D411yescharacteristic
56C22×C4×C61—24no—
57C22×C4×C61C2×D411yescharacteristic
58C22×C4×C61C2×D411yescharacteristic
59C22×C4×C61C2411yescharacteristic
60C22×Dic61—24no—
61C22×Dic61C2×D411yescharacteristic
62C22×Dic61C2×D411yescharacteristic
63C22×Dic61C2×D411yescharacteristic
64C2×C4×D61—22no—
65C2×C4×D61—22no—
66C2×C4×D61—22no—
67C2×C4×D61—22no—
68C2×C4×D61C4⋊C414yes—
69C2×C4×D61C4⋊C414yes—
70C2×C4×D61D814yes—
71C2×C4×D61Q1614yes—
72C2×C4×D61C22×C412yes—
73C2×C4×D61C2×Q812yes—
74C2×C8×C61C22×C414yes—
75C2×C8×C61#4114yes—
76C2×C8×C61#4114yes—
77C4⋊C4×C61—28no—
78C4⋊C4×C61—44no—
79C4⋊C4×C61—44no—
80C42×C61C22×C412yes—
81C42×C61C2×Q812yes—
82#11758198—48no—
83C4⋊Dic61—28no—
84C4⋊Dic61—44no—
85C4⋊Dic61—44no—
86C4×Dic61—48no—
87C4×Dic61C4⋊C414yes—
88C4×Dic61C4⋊C414yes—
89C4×Dic61C22×C412yes—
90C4×Dic61C2×Q812yes—
91C2×#92418—22no—
92C2×#92418—22no—
93C2×#92418C22×C414yes—
94C8×D61—216no—
95C23×C61C22×D411yescharacteristic
96C22×D61—21no—
97C22×D61—21no—
98C22×D61—21no—
99C22×D61—21no—
100C22×D61C2×C4⋊C412yes—
101C22×D61C2×D812yes—
102C22×D61C2×Q1612yes—
103C2×C4×C61—44no—
104C2×C4×C61—44no—
105C2×C4×C61—44no—
106C2×C4×C61C2×C4⋊C412yes—
107C2×C4×C61C2×C4⋊C412yes—
108C2×C4×C61C2×D812yes—
109C2×C4×C61C2×Q1612yes—
110C2×C4×C61#13512yes—
111C2×C4×C61#13512yes—
112C2×C4×C61C23×C411yescharacteristic
113C2×C4×C61C22×Q811yescharacteristic
114C2×C4×C61C2×#4112yes—
115C2×C4×C61C2×#4112yes—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—44no—
121C2×Dic61—44no—
122C2×Dic61—44no—
123C2×Dic61C2×C4⋊C412yes—
124C2×Dic61C2×C4⋊C412yes—
125C2×Dic61C2×C4⋊C412yes—
126C2×Dic61C2×D812yes—
127C2×Dic61C2×Q1612yes—
128C4×D61—24no—
129C4×D61—24no—
130C4×D61—28no—
131C4×D61#107116yescomplemented
132C8×C61#11718yescomplemented
133#92418—24no—
134#20817—611nomaximal, Sylow
135C22×C61C22×C4⋊C411yescharacteristic
136C22×C61#53211yescharacteristic
137C22×C61#53211yescharacteristic
138C22×C61C22×D811yescharacteristic
139C22×C61C22×Q1611yescharacteristic
140C22×C61C2×#13511yescharacteristic
141C22×C61C2×#13511yescharacteristic
142C2×D61—22no—
143C2×D61—22no—
144C2×D61—22no—
145C2×D61—22no—
146C2×D61—22no—
147C2×D61—22no—
148C2×D61C2×#10714yes—
149C4×C61—84no—
150C4×C61C2×#10714yes—
151C4×C61#42714yes—
152C4×C61C2×#11712yes—
153C4×C61#53312yes—
154Dic61—22no—
155Dic61—22no—
156Dic61—84no—
157Dic61C2×#10714yes—
158C22×C4×C8—611no—
159#2285—612no—
160#1845—611no—
161#1845D6111yescharacteristic, complemented
162#1834—612no—
163#1808—614no—
164C4×#107—614no—
165C2×C61#228511yescharacteristic
166C2×C61C22×#10711yescharacteristic
167C2×C61C2×#42711yescharacteristic
168C2×C61#316911yescharacteristic
169C2×C61#316911yescharacteristic
170C2×C61#317011yescharacteristic
171C2×C61#317011yescharacteristic
172D61—24no—
173C23×C8—612no—
174C2×#117—1222no—
175C22×C42—611no—
176C2×#107—614no—
177C2×#107C2×D6114yes—
178C2×C4×C8—612no—
179C2×C4×C8—611no—
180C2×C4×C8—618no—
181C2×C4×C8C2×D6111yescharacteristic
182#384—612no—
183#384C2×D6112yes—
184#382—1222no—
185#380—614no—
186#380—1222no—
187C4×C4⋊C4—614no—
188C4×C4⋊C4—1222no—
189#340—618no—
190C61#2081711yescharacteristic, complemented, Sylow
191C23×C4—611no—
192C23×C4—611no—
193C23×C4—611no—
194C22×C8—612no—
195C22×C8—618no—
196C22×C8—1224no—
197C22×C8—1224no—
198C22×C8C22×D6112yes—
199#117—2448no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—614no—
203C2×C4⋊C4—1222no—
204C2×C4⋊C4—1222no—
205C2×C4⋊C4C22×D6114yes—
206C2×C22⋊C4—1224no—
207C2×C42—611no—
208C2×C42—611no—
209C2×C42—611no—
210C2×C42—614no—
211C2×C42—614no—
212C2×C42—1224no—
213C2×C42C22×D6111yescharacteristic
214#107—28no—
215#107—1228no—
216C4×C8—618no—
217C4×C8—614no—
218C4×C8C4×D6114yes—
219#95—1224no—
220#95—1224no—
221C24—611no—
222C22×C4—24no—
223C22×C4—611no—
224C22×C4—614no—
225C22×C4—614no—
226C22×C4—614no—
227C22×C4—611no—
228C22×C4—611no—
229C22×C4—612no—
230C22×C4—612no—
231C22×C4—614no—
232C22×C4—1222no—
233C22×C4—1222no—
234C22×C4—1222no—
235C22×C4—1222no—
236C22×C4—1224no—
237C22×C4D4×D6111yescharacteristic
238C22×C4D4×D6111yescharacteristic
239C22×C4C23×D6111yescharacteristic
240C2×C8—614no—
241C2×C8—1222no—
242C2×C8—1222no—
243C2×C8—12216no—
244C2×C8C2×C4×D6114yes—
245C2×C8#1175822414yes—
246C2×C8#1175822614yes—
247C4⋊C4—28no—
248C4⋊C4—44no—
249C4⋊C4—44no—
250C4⋊C4—1228no—
251C4⋊C4—2444no—
252C4⋊C4—2444no—
253C22⋊C4—2448no—
254C42—612no—
255C42—612no—
256C42—614no—
257C42—614no—
258C42—2448no—
259C42C2×C4×D6112yes—
260C42Q8×D6112yes—
261C23—612no—
262C23—612no—
263C23—612no—
264C23—1221no—
265C23—1221no—
266C23—1221no—
267C23—1221no—
268C23C2×D4×D6111yescharacteristic
269C2×C4—44no—
270C2×C4—44no—
271C2×C4—44no—
272C2×C4—612no—
273C2×C4—612no—
274C2×C4—612no—
275C2×C4—6116no—
276C2×C4—612no—
277C2×C4—612no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—1224no—
283C2×C4—1228no—
284C2×C4—1224no—
285C2×C4—2444no—
286C2×C4—2444no—
287C2×C4—2444no—
288C2×C4C4⋊C4×D6112yes—
289C2×C4C4⋊C4×D6112yes—
290C2×C4D8×D6112yes—
291C2×C4Q16×D6112yes—
292C2×C4#1451979612yes—
293C2×C4#1451980012yes—
294C2×C4C22×C4×D6111yescharacteristic
295C2×C4C2×Q8×D6111yescharacteristic
296C2×C4C2×#1175822412yes—
297C2×C4C2×#1175822612yes—
298C8—1224no—
299C8#1451973518yescomplemented
300C22—614no—
301C22—1222no—
302C22—1222no—
303C22—1222no—
304C22—1222no—
305C22—1222no—
306C22—1222no—
307C22C2×C4⋊C4×D6111yescharacteristic
308C22#1684031011yescharacteristic
309C22#1684031311yescharacteristic
310C22C2×D8×D6111yescharacteristic
311C22C2×Q16×D6111yescharacteristic
312C22C2×#1451979611yescharacteristic
313C22C2×#1451980011yescharacteristic
314C4—84no—
315C4—614no—
316C4—1222no—
317C4—1222no—
318C4—4884no—
319C4#107×D6114yes—
320C4#1683979914yes—
321C4C2×#1451973512yes—
322C4#1684031712yes—
323C2—1224no—
324C2#2144822411yescharacteristic
325C2C2×#107×D6111yescharacteristic
326C2C2×#1683979911yescharacteristic
327C2#2145639611yescharacteristic
328C2#2145639911yescharacteristic
329C2#2145640311yescharacteristic
330C2#2145640611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1845C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenter#1845D61
hypocenterC61#20817
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1845

Complements

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

NH ≅ G/Ntype
3. #21445979C2semidirect
4. #21445946C2semidirect
6. #107×Dic61C2semidirect
7. C61×#1845C2semidirect
14. C4×C8×D61C4semidirect
131. C4×D61#107semidirect
132. C8×C61#117semidirect
161. #1845D61semidirect
190. C61#20817semidirect
299. C8#14519735semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C8×D612
#214482242
#214459792
#214459462
#214458452
#107×Dic612
C61×#18452
#2081761