Finite Group Databasebeta

← #30605545

Subgroups — #30605545

Order 15616.

400 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 86 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
1D61⋊#364C212yesmaximal, complemented
2#21460828C212yesmaximal, complemented
3#21460827C212yesmaximal, complemented
4#21456242C211yesmaximal, characteristic
5D61⋊M32—22no—
6#16840685C2214yes—
7#16840684—22no—
8C2×#14519798—22no—
9#16840313C411yescharacteristic
10#16840310C411yescharacteristic
11#16840143—22no—
12#16840141C2211yescharacteristic
13#16840138C2211yescharacteristic
14#16840135C411yescharacteristic
15C4×C8×D61C2211yescharacteristic
16C61×#492C411yescharacteristic
17#14519852—42no—
18#14519851—24no—
19D61⋊C16—42no—
20C2×#11758226—21no—
21C2×#11758224—21no—
22#14519798—42no—
23#14519798—42no—
24#14519798—42no—
25#14519798—42no—
26C2×#11758202—22no—
27C2×#11758190—22no—
28C2×#11758199—22no—
29C2×C8×D61D412yes—
30#14519777C2×C411yescharacteristic
31#14519774C2×C411yescharacteristic
32#14519766—21no—
33#14519764—21no—
34#14519752—41no—
35#14519748—41no—
36D4×Dic61—41no—
37#14519739—41no—
38C42×D61C2×C411yescharacteristic
39C4×#92418C2311yescharacteristic
40C8×Dic61D412yes—
41C2×SD16×C61—22no—
42C4⋊Q8×C61C2×C411yescharacteristic
43#127×C61C2×C411yescharacteristic
44C4×C8×C61C2×C411yescharacteristic
45C2×Q8×C61—21no—
46C2×D4×C61—21no—
47C2×D4×C61—41no—
48C2×C22⋊D61—41no—
49C22×Dic61—41no—
50#11758226—42no—
51#11758226—42no—
52#11758224—42no—
53#11758224—42no—
54C2×D244—21no—
55C2×D244—41no—
56C2×D244—41no—
57C2×C4×D61—21no—
58C2×C4×D61—41no—
59C2×C4×D61C22⋊C411yescharacteristic
60C2×Dic122—21no—
61SD16×C61—42no—
62SD16×C61—42no—
63C2×C8×C61C22⋊C412yes—
64C4⋊C4×C61—41no—
65C42×C61C22×C411yescharacteristic
66C22⋊Dic61—42no—
67#11758202—42no—
68#11758202—42no—
69#11758199—42no—
70#11758199—42no—
71#11758198—42no—
72C4⋊Dic61—41no—
73C4×Dic61—21no—
74C4×Dic61C22⋊C411yescharacteristic
75C2×#92418C2×D412yes—
76#11758190—42no—
77#11758190—42no—
78C8×D61D812yes—
79C8×D61D812yes—
80C8×D61SD1612yes—
81C8×D61SD1612yes—
82#11758187—44no—
83C23×C61—41no—
84C22×D61—41no—
85C22×D61#10011yescharacteristic
86Q8×C61—42no—
87D4×C61—42no—
88D4×C61—82no—
89C2×C4×C61—21no—
90C2×C4×C61—41no—
91C2×C4×C61C2×C22⋊C411yescharacteristic
92C22⋊D61—82no—
93C2×Dic61—21no—
94C2×Dic61—41no—
95C2×Dic61—81no—
96C2×Dic61—81no—
97C2×Dic61#10011yescharacteristic
98D244—42no—
99D244—82no—
100D244—82no—
101C4×D61—42no—
102C4×D61—81no—
103C4×D61—81no—
104C4×D61#10212yes—
105C4×D61#10212yes—
106Dic122—42no—
107C8×C61#10212yes—
108C8×C61#10212yes—
109#92418C2×D812yes—
110#92418C2×SD1612yes—
111#11920—611nomaximal, Sylow
112C22×C61—82no—
113C22×C61—81no—
114C22×C61C2×#10011yescharacteristic
115C2×D61—41no—
116C2×D61—82no—
117C2×D61—81no—
118C2×D61#33112yes—
119C4×C61—22no—
120C4×C61—81no—
121C4×C61C2×#10212yes—
122Dic61—41no—
123Dic61—81no—
124Dic61#33111yescharacteristic
125Dic61#33111yescharacteristic
126#3147—611no—
127C2×#364—612no—
128#1358—612no—
129#1357—612no—
130C2×C61—21no—
131C2×C61—161no—
132C2×C61C2×#33111yescharacteristic
133D61—22no—
134D61—161no—
135C2×#135—1222no—
136#532—611no—
137#532—611no—
138C2×M32—1222no—
139#495—1222no—
140#494—611no—
141#493—611no—
142#492—611no—
143#492#692311yescharacteristic
144C2×C4×C8—611no—
145#364—614no—
146#364—1222no—
147C61#1192011yescharacteristic, complemented, Sylow
148C2×#41—1221no—
149C2×#41—1221no—
150#135—2442no—
151#135—2442no—
152#135—2442no—
153#135—2442no—
154C2×Q16—1222no—
155C2×SD16—22no—
156C2×SD16—1222no—
157C2×D8—1222no—
158C22×C8—612no—
159C4⋊Q8—611no—
160C4⋊Q8C2×#692311yescharacteristic
161#127—611no—
162#127C2×#692311yescharacteristic
163#124—1221no—
164#124—1221no—
165#121—2441no—
166#121—2441no—
167C4×D4—2441no—
168C4×D4—2441no—
169C2×C42—611no—
170M32—1224no—
171M32—2442no—
172C2×C16—2442no—
173C4×C8—612no—
174C4×C8—611no—
175C4×C8C2×#692311yescharacteristic
176#41—2442no—
177#41—2442no—
178#41—2442no—
179#41—2442no—
180C2×Q8—21no—
181C2×Q8—1221no—
182C2×D4—21no—
183C2×D4—41no—
184C2×D4—1221no—
185C2×D4—2441no—
186C2×D4—2441no—
187C2×D4—2441no—
188C22×C4—611no—
189C22×C4—1221no—
190C22×C4—2441no—
191C22×C4—2441no—
192Q16—2442no—
193Q16—2442no—
194SD16—42no—
195SD16—42no—
196SD16—2442no—
197SD16—2442no—
198D8—2442no—
199D8—2442no—
200C2×C8—612no—
201C2×C8—612no—
202C2×C8—612no—
203C2×C8—612no—
204C2×C8—612no—
205C2×C8C22⋊#692312yes—
206C4⋊C4—41no—
207C4⋊C4—2441no—
208C22⋊C4—2442no—
209C22⋊C4—2442no—
210C42—611no—
211C42—1221no—
212C42C22×#692311yescharacteristic
213C16—2444no—
214C23—41no—
215C23—611no—
216C23—2441no—
217Q8—42no—
218Q8—2442no—
219D4—42no—
220D4—82no—
221D4—4882no—
222D4—4882no—
223D4—4882no—
224D4—2442no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—611no—
228C2×C4—612no—
229C2×C4—612no—
230C2×C4—1221no—
231C2×C4—4881no—
232C2×C4—4881no—
233C2×C4—4881no—
234C2×C4—4881no—
235C2×C4—2442no—
236C2×C4—2441no—
237C2×C4C2×C22⋊#692311yescharacteristic
238C8—612no—
239C8—612no—
240C8#1451983912yes—
241C8#1451983912yes—
242C22—82no—
243C22—81no—
244C22—612no—
245C22—4882no—
246C22—4881no—
247C22—2441no—
248C22D61⋊#10011yescharacteristic
249C4—22no—
250C4—81no—
251C4—611no—
252C4—611no—
253C4—4881no—
254C4—2441no—
255C4C2×#1451983912yes—
256C2—21no—
257C2—161no—
258C2—1222no—
259C2—9761no—
260C2D61⋊#33111yescharacteristic
subgroupG/H
centerC2D61⋊#331
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#492C4
socleC2×C61C2×#331
prime radical#21456242C2
cosocleC4×#92418C23
hypercenter#492#6923
hypocenterC61#11920
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #492

Complements

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

NH ≅ G/Ntype
1. D61⋊#364C2semidirect
2. #21460828C2semidirect
3. #21460827C2semidirect
147. C61#11920semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3642
#214608282
#214608272
#214562422
#1192061