Finite Group Databasebeta

← D61×#1357 #29591215

Subgroups — D61×#1357 #29591215

Order 15616.

494 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 91 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#493×D61C211yesmaximal, characteristic
2#364×D61C212yesmaximal, complemented
3#21443856C211yesmaximal, characteristic, complemented
4#21443855C212yesmaximal, complemented
5C61×#1357C211yesmaximal, characteristic, complemented
6C2×D8×D61—22no—
7#127×D61C412yes—
8M32×D61—22no—
9#16840139C2211yescharacteristic
10#16840138C412yes—
11#16840137—22no—
12C4×C8×D61C2211yescharacteristic
13#16839583C2212yescomplemented
14#16839582—22no—
15C61×#493C2211yescharacteristic
16C61×#364C2212yescomplemented
17C2×D4×D61—22no—
18C2×D4×D61—42no—
19C2×D488—22no—
20C2×#11758199—24no—
21D8×D61—42no—
22D8×D61—42no—
23D8×D61—42no—
24D8×D61—42no—
25C2×C8×D61D412yes—
26#14519774C2×C412yes—
27#14519773—22no—
28#14519773—42no—
29C42×D61C2×C411yescharacteristic
30#14519717—22no—
31#14519716—42no—
32C16×D61—42no—
33C4×#92418C2×C411yescharacteristic
34C8×Dic61D412yes—
35C2×D8×C61—22no—
36#127×C61C2×C412yes—
37M32×C61—22no—
38C4×C8×C61C2311yescharacteristic
39C23×D61—42no—
40C2×D4×C61—22no—
41C2×D4×C61—42no—
42C2×C22⋊D61—44no—
43C2×C22⋊D61—42no—
44D4×D61—44no—
45D4×D61—44no—
46D4×D61—88no—
47C2×D244—22no—
48C2×D244—42no—
49C2×C4×D61—21no—
50C2×C4×D61C22⋊C411yescharacteristic
51D8×C61—42no—
52D8×C61—42no—
53C2×C8×C61C2×D412yes—
54C42×C61C22×C411yescharacteristic
55#11758199—44no—
56#11758199—44no—
57C4×Dic61—21no—
58C4×Dic61C22⋊C411yescharacteristic
59C2×#92418C22⋊C412yes—
60D488—42no—
61D488—42no—
62C8×D61D812yes—
63C8×D61D812yes—
64C8×D61SD1612yes—
65C8×D61SD1612yes—
66C16×C61—42no—
67#11758185—42no—
68C23×C61—42no—
69C22×D61—42no—
70C22×D61—88no—
71C22×D61—82no—
72C22×D61—82no—
73C22×D61#10011yescharacteristic
74D4×C61—44no—
75D4×C61—84no—
76C2×C4×C61—21no—
77C2×C4×C61C2×C22⋊C411yescharacteristic
78C22⋊D61—88no—
79C22⋊D61—84no—
80C2×Dic61—21no—
81C2×Dic61#10011yescharacteristic
82D244—44no—
83D244—84no—
84C4×D61—24no—
85C4×D61#10212yes—
86C4×D61#10212yes—
87C8×C61C2×D812yes—
88C8×C61C2×SD1612yes—
89#92418#10212yes—
90#92418#10212yes—
91C2×#1357—611nomaximal, Sylow
92C22×C61—84no—
93C22×C61—82no—
94C22×C61C2×#10011yescharacteristic
95C2×D61—22no—
96C2×D61—84no—
97C2×D61—82no—
98C2×D61—164no—
99C2×D61—164no—
100C2×D61#33111yescharacteristic
101C2×D61#33111yescharacteristic
102C4×C61—22no—
103C4×C61C2×#10212yes—
104Dic61—22no—
105Dic61#33112yes—
106C2×#493—611no—
107C2×#364—612no—
108#1357—611no—
109#1357—612no—
110#1357D6111yescharacteristic, direct product factor
111C2×C61—21no—
112C2×C61—162no—
113C2×C61C2×#33111yescharacteristic
114D61—21no—
115D61—162no—
116D61#135712yesdirect product factor
117C22×D8—1222no—
118C2×#127—612no—
119C2×M32—1222no—
120#493—612no—
121#493—611no—
122#493—1222no—
123#493C2×D6111yescharacteristic
124C2×C4×C8—611no—
125#364—612no—
126#364—1222no—
127#364C2×D6112yescomplemented
128C61C2×#135711yescharacteristic, complemented, Sylow
129C22×D4—1222no—
130C22×D4—2442no—
131C2×D8—22no—
132C2×D8—1224no—
133C2×D8—1222no—
134C2×D8—2442no—
135C2×D8—2442no—
136C2×D8—2442no—
137C2×D8—2442no—
138C22×C8—612no—
139#127—612no—
140#127—1222no—
141#127—2442no—
142#127C4×D6112yes—
143C2×C42—611no—
144M32—22no—
145M32—1222no—
146M32—2442no—
147C2×C16—2442no—
148C4×C8—612no—
149C4×C8—611no—
150C4×C8C22×D6111yescharacteristic
151C24—2442no—
152C2×D4—22no—
153C2×D4—42no—
154C2×D4—1222no—
155C2×D4—4888no—
156C2×D4—2442no—
157C2×D4—2444no—
158C2×D4—2444no—
159C2×D4—2442no—
160C2×D4—2444no—
161C22×C4—611no—
162C22×C4—1221no—
163D8—42no—
164D8—42no—
165D8—2444no—
166D8—2444no—
167D8—2442no—
168D8—2442no—
169C2×C8—612no—
170C2×C8—612no—
171C2×C8—612no—
172C2×C8—612no—
173C2×C8—612no—
174C2×C8D4×D6112yes—
175C42—611no—
176C42—1221no—
177C42C2×C4×D6111yescharacteristic
178C16—42no—
179C16—2442no—
180C23—42no—
181C23—611no—
182C23—4882no—
183C23—4882no—
184C23—4888no—
185C23—2442no—
186D4—44no—
187D4—84no—
188D4—4884no—
189D4—4884no—
190D4—4888no—
191D4—2444no—
192C2×C4—21no—
193C2×C4—611no—
194C2×C4—612no—
195C2×C4—612no—
196C2×C4—1224no—
197C2×C4—1221no—
198C2×C4C22⋊C4×D6111yescharacteristic
199C8—612no—
200C8—612no—
201C8D8×D6112yes—
202C8SD16×D6112yes—
203C22—84no—
204C22—82no—
205C22—611no—
206C22—611no—
207C22—1222no—
208C22—9764no—
209C22—9764no—
210C22—4884no—
211C22—4882no—
212C22#100×D6111yescharacteristic
213C4—22no—
214C4—612no—
215C4—1222no—
216C4#102×D6112yes—
217C2—21no—
218C2—162no—
219C2—612no—
220C2—1221no—
221C2—9762no—
222C2#331×D6111yescharacteristic
subgroupG/H
centerC2#331×D61
commutatorC42×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#1357C2
socleC2×C61C2×#331
prime radical#493×D61C2
cosocleC4×C8×C61C23
hypercenter#1357D61
hypocenterC61C2×#1357
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1357

Complements

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

NH ≅ G/Ntype
2. #364×D61C2semidirect
3. #21443856C2semidirect
4. #21443855C2semidirect
5. C61×#1357C2semidirect
13. #16839583C22semidirect
16. C61×#364C22semidirect
110. #1357D61direct (N × H)
116. D61#1357direct (N × H)
127. #364C2×D61semidirect
128. C61C2×#1357semidirect

Maximal subgroups

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

subgroupindex
#493×D612
#364×D612
#214438562
#214438552
C61×#13572
C2×#135761