Finite Group Databasebeta

← #30603893

Subgroups — #30603893

Order 15616.

454 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 90 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⋊#324C212yesmaximal
2#21460761C212yesmaximal, complemented
3#21460760C212yesmaximal, complemented
4#21448444C211yesmaximal, characteristic
5D61⋊(C22⋊C8)—22no—
6#16840608—22no—
7#16840607C2214yes—
8C2×#14519735C411yescharacteristic
9C2×#14519734C411yescharacteristic
10C2×C4⋊C4×D61C2211yescharacteristic
11#16839659—22no—
12#16839636—22no—
13#16839632C2211yescharacteristic
14#16839631C411yescharacteristic
15#16839627C2211yescharacteristic
16C61×#382C411yescharacteristic
17C2×D61⋊C8—42no—
18#14519834—42no—
19C22⋊#92420—24no—
20C22×C4×D61C2×C411yescharacteristic
21C22×C4×D61D412yes—
22#14519735—42no—
23#14519734—22no—
24#14519734C814yescomplemented
25C2×C4⋊Dic61—22no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×C4⋊Dic61C2311yescharacteristic
28C2×#11758196—21no—
29C2×#11758196—22no—
30C2×#11758196D412yes—
31C4⋊C4×D61—42no—
32C2×#11758198—21no—
33C2×#11758198—21no—
34C2×C4×Dic61—21no—
35C2×C4×Dic61C2×C411yescharacteristic
36#14519684—22no—
37C2×C4⋊C4×C61C2×C411yescharacteristic
38C2×C4⋊C4×C61C2×C411yescharacteristic
39C2×C42×C61C2×C411yescharacteristic
40#95×C61—22no—
41C23×D61C22⋊C411yescharacteristic
42C22×C4×C61—21no—
43C22×C4×C61—21no—
44C22×C4×C61C22⋊C412yes—
45C22×C4×C61C22×C411yescharacteristic
46C22×Dic61—21no—
47C22×Dic61—21no—
48C22×Dic61C22⋊C411yescharacteristic
49C22×Dic61C2×D412yes—
50C2×C4×D61—22no—
51C2×C4×D61—22no—
52C2×C4×D61—22no—
53C2×C4×D61—22no—
54C2×C4×D61—82no—
55C2×C4×D61C2×C812yes—
56C2×C4×D61M1612yes—
57C2×#92420—44no—
58D61⋊C8—84no—
59C4⋊C4×C61—41no—
60C4⋊C4×C61—41no—
61C42×C61—21no—
62C42×C61C2×C812yescomplemented
63#11758198—24no—
64#11758198—42no—
65C4⋊Dic61—41no—
66C4⋊Dic61—41no—
67C4⋊Dic61—82no—
68#11758196—24no—
69#11758196—42no—
70#11758196—82no—
71C4×Dic61—21no—
72C4×Dic61—42no—
73C4×Dic61C2×C812yescomplemented
74C23×C61C2×C22⋊C411yescharacteristic
75C22×D61—41no—
76C22×D61—41no—
77C22×D61C22⋊C812yes—
78C22×D61#9912yes—
79C22×D61#10112yes—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—41no—
85C2×C4×C61—41no—
86C2×C4×C61—42no—
87C2×C4×C61—42no—
88C2×C4×C61—41no—
89C2×C4×C61C22×C811yescharacteristic
90C2×C4×C61C2×M1611yescharacteristic
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—41no—
96C2×Dic61—41no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61—41no—
100C2×Dic61C22⋊C812yes—
101C4×D61—24no—
102C4×D61—24no—
103C4×D61—44no—
104C4×D61—82no—
105#92420—84no—
106#11448—611nomaximal, Sylow
107C22×C61—21no—
108C22×C61—21no—
109C22×C61C2×C22⋊C811yescharacteristic
110C22×C61C2×#9911yescharacteristic
111C22×C61C2×#10111yescharacteristic
112C2×D61—22no—
113C2×D61—22no—
114C2×D61—42no—
115C2×D61—42no—
116C2×D61#32414yes—
117C4×C61—21no—
118C4×C61—21no—
119C4×C61—42no—
120C4×C61—42no—
121C4×C61—81no—
122Dic61—22no—
123Dic61—42no—
124Dic61—42no—
125Dic61—81no—
126#2317—611no—
127C2×#324—612no—
128#1325—612no—
129#1324—612no—
130C2×C61—21no—
131C2×C61—21no—
132C2×C61C2×#32411yescharacteristic
133C2×C61#212711yescharacteristic
134C2×C61#213311yescharacteristic
135D61—24no—
136C2×#117—611no—
137C2×#117—611no—
138C22×C4⋊C4—611no—
139C2×C22⋊C8—1222no—
140#389—1222no—
141#385—1222no—
142#384—611no—
143#384—611no—
144#382—611no—
145#382#692311yescharacteristic
146#324—614no—
147#324—1222no—
148C61#1144811yescharacteristic, complemented, Sylow
149C23×C4—611no—
150C23×C4—612no—
151C22×C8—2442no—
152#117—614no—
153#117—1222no—
154#117—2442no—
155C2×C4⋊C4—612no—
156C2×C4⋊C4—611no—
157C2×C4⋊C4—611no—
158C2×C4⋊C4—1221no—
159C2×C4⋊C4—1222no—
160C2×C4⋊C4—1222no—
161C2×C4⋊C4—2442no—
162C2×C4⋊C4C2×#692311yescharacteristic
163C2×C4⋊C4C2×#692311yescharacteristic
164C2×C22⋊C4—1221no—
165C2×C22⋊C4—1221no—
166C2×C42—611no—
167C2×C42—1221no—
168C2×C42C2×#692311yescharacteristic
169C22⋊C8—1224no—
170C22⋊C8—2442no—
171#95—22no—
172#95—1222no—
173C24—611no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—611no—
177C22×C4—612no—
178C22×C4—612no—
179C22×C4—612no—
180C22×C4—1222no—
181C22×C4—1222no—
182C22×C4—1222no—
183C22×C4—1222no—
184C22×C4—1221no—
185C22×C4—1221no—
186C22×C4—4882no—
187C22×C4C22⋊#692312yes—
188C22×C4C22×#692311yescharacteristic
189C2×C8—4884no—
190C2×C8—2444no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—1224no—
194C4⋊C4—4882no—
195C4⋊C4—4882no—
196C4⋊C4—2442no—
197C4⋊C4—2441no—
198C4⋊C4—2441no—
199C22⋊C4—1224no—
200C22⋊C4—2442no—
201C42—21no—
202C42—612no—
203C42—1221no—
204C42—2442no—
205C42D61⋊C812yescomplemented
206C23—612no—
207C23—612no—
208C23—612no—
209C23—2441no—
210C23—2441no—
211C23C2×C22⋊#692311yescharacteristic
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—41no—
221C2×C4—612no—
222C2×C4—1224no—
223C2×C4—1224no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—1222no—
227C2×C4—1222no—
228C2×C4—4882no—
229C2×C4—2444no—
230C2×C4—2442no—
231C2×C4—2441no—
232C2×C4—2441no—
233C2×C4—2441no—
234C2×C4—2442no—
235C2×C4C2×D61⋊C811yescharacteristic
236C2×C4D61⋊M1611yescharacteristic
237C8—4884no—
238C22—21no—
239C22—21no—
240C22—614no—
241C22—1222no—
242C22—1222no—
243C22—2442no—
244C22—2442no—
245C22D61⋊(C22⋊C8)11yescharacteristic
246C22D61⋊#9911yescharacteristic
247C22D61⋊#10111yescharacteristic
248C4—21no—
249C4—21no—
250C4—42no—
251C4—42no—
252C4—81no—
253C4—1222no—
254C4—4881no—
255C4—2442no—
256C4—2442no—
257C2—21no—
258C2—21no—
259C2—1224no—
260C2D61⋊#32411yescharacteristic
261C2#2146209711yescharacteristic
262C2#2146211511yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊Dic61C23
hypercenter#382#6923
hypocenterC61#11448
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #21460761C2semidirect
3. #21460760C2semidirect
24. #14519734C8semidirect
62. C42×C61C2×C8semidirect
73. C4×Dic61C2×C8semidirect
148. C61#11448semidirect
205. C42D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3242
#214607612
#214607602
#214484442
#1144861