Finite Group Databasebeta

← #29593899

Subgroups — #29593899

Order 15616.

294 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458809C211yesmaximal, characteristic
2#21448046C211yesmaximal, characteristic, complemented
3#21447957C211yesmaximal, characteristic
4#21445214C211yesmaximal, characteristic, complemented
5#21443797C211yesmaximal, characteristic, complemented
6#21443779C211yesmaximal, characteristic
7C61×#1362C211yesmaximal, characteristic, complemented
8#16840486—21no—
9#16840167C2211yescharacteristic
10#16840147—21no—
11#16839986—22no—
12#16839973—21no—
13#16839964—21no—
14C8×Dic122C2211yescharacteristic
15Q16×Dic61—21no—
16C4×D488C2211yescharacteristic
17#16839588—21no—
18#16839566—22no—
19#16839564—21no—
20C4×#11758185C2211yescharacteristic
21#16839509—21no—
22C61×#494C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×Dic244—41no—
26C2×#11758201—22no—
27C2×D488D411yescharacteristic
28#14519777—21no—
29#14519772—42no—
30#14519766—22no—
31#14519757—41no—
32Q8×Dic61—22no—
33C4×Dic122D411yescharacteristic
34C4×D244—21no—
35#14519735—41no—
36C2×#11758185—21no—
37#14519711—21no—
38#14519711—21no—
39#14519711D411yescharacteristic
40C4⋊#92418D411yescharacteristic
41#14519706—21no—
42#14519702—41no—
43#14519701—22no—
44#14519699—21no—
45C8×Dic61—21no—
46C2×Q16×C61—21no—
47C2×Q16×C61D412yes—
48C4⋊Q8×C61—21no—
49C2×C16×C61—21no—
50C4⋊C8×C61—21no—
51C4×C8×C61C2311yescharacteristic
52C2×Q8×C61—22no—
53C2×D244—21no—
54C2×C4×D61—41no—
55C2×Dic122—41no—
56C2×Dic122D811yescharacteristic
57Q16×C61—42no—
58Q16×C61—41no—
59Q16×C61—41no—
60C2×C8×C61—41no—
61C2×C8×C61C2×D411yescharacteristic
62C2×C8×C61C2×D411yescharacteristic
63C4⋊C4×C61—41no—
64C4⋊C4×C61—41no—
65C42×C61C2×D411yescharacteristic
66#11758201—82no—
67#11758198—42no—
68#11758198—42no—
69#11758198—41no—
70C4⋊Dic61—21no—
71C4⋊Dic61—42no—
72C4⋊Dic61—41no—
73C4⋊Dic61—41no—
74C4⋊Dic61D811yescharacteristic
75#11758196—21no—
76C4×Dic61—21no—
77C4×Dic61—42no—
78C2×#92418—21no—
79Dic244—82no—
80D488—21no—
81D488—21no—
82C16×C61—41no—
83#11758185—41no—
84C22×D61—41no—
85Q8×C61—42no—
86Q8×C61—42no—
87C2×C4×C61—42no—
88C2×C4×C61#12011yescharacteristic
89C2×C4×C61C2×D811yescharacteristic
90C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—41no—
94C2×Dic61—81no—
95D244—41no—
96D244—41no—
97C4×D61—81no—
98C4×D61—81no—
99Dic122—21no—
100Dic122—21no—
101Dic122—81no—
102Dic122—81no—
103C8×C61—21no—
104C8×C61—81no—
105C8×C61#13511yescharacteristic
106C8×C61#13711yescharacteristic
107#92418—41no—
108#12383—611nomaximal, Sylow
109C22×C61#44711yescharacteristic
110C2×D61—81no—
111C2×D61—81no—
112C2×D61—81no—
113C4×C61—21no—
114C4×C61—82no—
115C4×C61#45211yescharacteristic
116C4×C61#45511yescharacteristic
117C4×C61#50811yescharacteristic
118C4×C61#50911yescharacteristic
119Dic61—41no—
120Dic61—41no—
121Dic61—81no—
122Dic61—161no—
123#3393—611no—
124#2241—611no—
125#2224—611no—
126#1674—611no—
127#1362D6111yescharacteristic, complemented
128Q8⋊C16—611no—
129#1331—611no—
130C2×C61#164111yescharacteristic
131C2×C61#218611yescharacteristic
132C2×C61#219511yescharacteristic
133D61—161no—
134#556—1221no—
135#500—611no—
136#495—1221no—
137#494C2×D6111yescharacteristic
138#464—1222no—
139#462—1221no—
140#461—1221no—
141C8×Q8—611no—
142C4×Q16—1221no—
143C4×D8—611no—
144#366—1221no—
145C4⋊C16C2×D6111yescharacteristic
146#358—1222no—
147#357—1221no—
148C4×C16—611no—
149#335C2×D6111yescharacteristic
150#332—1221no—
151C61#1238311yescharacteristic, complemented, Sylow
152C2×Q16—21no—
153C2×Q16—2441no—
154C2×Q16D24412yes—
155C2×SD16—1222no—
156C2×D8—611no—
157C4⋊Q8—21no—
158C4⋊Q8—1221no—
159#126—2442no—
160#124—1222no—
161C22⋊Q8—2441no—
162C4×Q8—611no—
163C4×Q8—1222no—
164C4×D4—1221no—
165#117—2441no—
166C2×C16—21no—
167C2×C16—1221no—
168#107—611no—
169#107—1221no—
170#107—1221no—
171C4⋊C8—21no—
172C4⋊C8—611no—
173C4⋊C8—1221no—
174#103—1222no—
175#103—2441no—
176#102—1221no—
177C4×C8—1221no—
178C4×C8C22×D6111yescharacteristic
179C2×Q8—22no—
180C2×Q8—611no—
181C2×Q8—2441no—
182C2×D4—1221no—
183C22×C4—2441no—
184Q16—42no—
185Q16—41no—
186Q16—41no—
187Q16—4882no—
188SD16—4882no—
189D8—1221no—
190D8—1221no—
191C2×C8—41no—
192C2×C8—1221no—
193C2×C8C2×D24411yescharacteristic
194C2×C8D4×D6111yescharacteristic
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—611no—
198C4⋊C4—1221no—
199C4⋊C4—1221no—
200C4⋊C4—2442no—
201C4⋊C4—2441no—
202C4⋊C4—2441no—
203C22⋊C4—2442no—
204C22⋊C4—2442no—
205C22⋊C4—2441no—
206C42—1221no—
207C42—2442no—
208C42D4×D6111yescharacteristic
209C16—41no—
210C16—2441no—
211C23—2441no—
212Q8—42no—
213Q8—42no—
214Q8—1221no—
215Q8—1221no—
216Q8—4881no—
217Q8—4881no—
218D4—2441no—
219D4—2441no—
220C2×C4—42no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—4881no—
224C2×C4—4881no—
225C2×C4—4881no—
226C2×C4—2441no—
227C2×C4#1451974711yescharacteristic
228C2×C4D8×D6111yescharacteristic
229C2×C4#1451980411yescharacteristic
230C8—21no—
231C8—81no—
232C8—2441no—
233C8#1451979611yescharacteristic
234C8#1451980611yescharacteristic
235C22—4881no—
236C22—4881no—
237C22—4881no—
238C22#1683989711yescharacteristic
239C4—21no—
240C4—82no—
241C4—9761no—
242C4—4881no—
243C4—2441no—
244C4—2441no—
245C4#1683992511yescharacteristic
246C4#1683994211yescharacteristic
247C4#1684019511yescharacteristic
248C4#1684019911yescharacteristic
249C2—9761no—
250C2#2144501311yescharacteristic
251C2#2144774511yescharacteristic
252C2#2144780011yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1362C2
socleC22×C61#447
prime radicalC2×D488D4
hypercenter#1362D61
hypocenterC61#12383
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
2. #21448046C2semidirect
4. #21445214C2semidirect
5. #21443797C2semidirect
7. C61×#1362C2semidirect
127. #1362D61semidirect
151. C61#12383semidirect

Maximal subgroups

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

subgroupindex
#214588092
#214480462
#214479572
#214452142
#214437972
#214437792
C61×#13622
#1238361