Finite Group Databasebeta

← #30603922

Subgroups — #30603922

Order 15616.

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

normal subgroups only

This group has 364 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⋊#349C212yesmaximal
2#21460768C212yesmaximal, complemented
3#21460767C212yesmaximal, complemented
4#21454380C211yesmaximal, characteristic
5D61⋊M32—22no—
6#16840659—22no—
7#16840658C2214yes—
8C22×#11758189C411yescharacteristic
9C2×M16×D61C2211yescharacteristic
10#117×D61C411yescharacteristic
11#16839790C411yescharacteristic
12#16839789C2211yescharacteristic
13#16839788C2211yescharacteristic
14#16839787—22no—
15#16839784—22no—
16C61×#424C411yescharacteristic
17#14519852—42no—
18#14519851—24no—
19D61⋊C16—42no—
20C22×C4×D61C2×C411yescharacteristic
21C2×#11758194C2311yescharacteristic
22C2×#11758189—21no—
23C2×#11758189—21no—
24C2×#11758189—42no—
25C2×#11758189D412yes—
26M16×D61—42no—
27C22×#92418C2×C411yescharacteristic
28C2×C8×D61D412yes—
29#14519736C2×C411yescharacteristic
30#14519735—21no—
31#14519734—21no—
32#14519733C812yes—
33C4⋊C4×D61—21no—
34C22⋊C4×D61C812yes—
35C42×D61—21no—
36C4⋊#92418—22no—
37#14519706—22no—
38#14519706—22no—
39C2×M16×C61C2×C411yescharacteristic
40C22×C8×C61C2×C411yescharacteristic
41#117×C61C2×C411yescharacteristic
42C4⋊C8×C61—22no—
43C23×D61C2×C811yescharacteristic
44C22×C4×C61C22×C411yescharacteristic
45C22×Dic61C2×C811yescharacteristic
46C2×C4×D61—22no—
47C2×C4×D61—22no—
48C2×C4×D61—22no—
49C2×C4×D61C22⋊C411yescharacteristic
50C2×C4×D61C22⋊C411yescharacteristic
51C2×C4×D61M1611yescharacteristic
52C2×C4×D61M1611yescharacteristic
53M16×C61—41no—
54C2×C8×C61—21no—
55C2×C8×C61—41no—
56C2×C8×C61C22⋊C412yes—
57C4⋊C4×C61—21no—
58C22⋊C4×C61C2×C812yes—
59C42×C61—21no—
60C22⋊Dic61C2×C812yes—
61#11758198—22no—
62C4⋊Dic61—21no—
63#11758196—22no—
64C4×Dic61—21no—
65C4×Dic61—22no—
66#11758194—41no—
67C2×#92418—21no—
68C2×#92418—41no—
69C2×#92418C2×D412yes—
70#11758189—42no—
71#11758189—42no—
72#11758189—42no—
73C8×D61—22no—
74C8×D61—22no—
75#11758187—44no—
76C23×C61C22×C811yescharacteristic
77C22×D61—22no—
78C22×D61—81no—
79C22×D61C22⋊C811yescharacteristic
80C22×D61C22⋊C811yescharacteristic
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61C2×C22⋊C411yescharacteristic
85C2×C4×C61C2×M1611yescharacteristic
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61C22⋊C811yescharacteristic
89C2×Dic61C22⋊C811yescharacteristic
90C4×D61—22no—
91C4×D61—21no—
92C4×D61—21no—
93C4×D61—22no—
94C4×D61—82no—
95C4×D61#9912yes—
96C4×D61#10112yes—
97C8×C61—22no—
98C8×C61—41no—
99#92418—22no—
100#92418—41no—
101#11458—611nomaximal, Sylow
102C22×C61—21no—
103C22×C61—41no—
104C22×C61C2×C22⋊C811yescharacteristic
105C2×D61—21no—
106C2×D61—41no—
107C2×D61—41no—
108C2×D61—82no—
109C2×D61#32412yes—
110C4×C61—21no—
111C4×C61—42no—
112C4×C61C2×#9911yescharacteristic
113C4×C61C2×#10111yescharacteristic
114Dic61—21no—
115Dic61—42no—
116Dic61#32412yes—
117#2905—611no—
118C2×#349—612no—
119#1328—612no—
120#1328—612no—
121C2×C61—21no—
122C2×C61—41no—
123C2×C61C2×#32411yescharacteristic
124D61—22no—
125D61—41no—
126C22×M16—611no—
127C22×M16—611no—
128C2×#117—611no—
129C2×M32—1222no—
130#424—611no—
131#424—611no—
132#424—611no—
133#424—1222no—
134#424#692311yescharacteristic
135#423—1222no—
136#349—614no—
137#349—1222no—
138C61#1145811yescharacteristic, complemented, Sylow
139C23×C4—611no—
140C2×M16—611no—
141C2×M16—612no—
142C2×M16—1221no—
143C2×M16—1221no—
144C2×M16—2442no—
145C2×M16—2442no—
146C2×M16C2×#692311yescharacteristic
147C22×C8—612no—
148C22×C8—611no—
149C22×C8C2×#692311yescharacteristic
150#117—611no—
151#117—612no—
152#117—1221no—
153#117—1221no—
154#117C2×#692311yescharacteristic
155C2×C4⋊C4—1221no—
156C2×C22⋊C4—612no—
157C2×C42—1221no—
158M32—1224no—
159M32—2442no—
160C2×C16—2442no—
161C4⋊C8—22no—
162C4⋊C8—1222no—
163C4⋊C8—1222no—
164C4⋊C8—1222no—
165C24—611no—
166C22×C4—611no—
167C22×C4—611no—
168C22×C4—611no—
169C22×C4—611no—
170C22×C4—611no—
171C22×C4—1222no—
172C22×C4—1222no—
173C22×C4—1222no—
174C22×C4C22×#692311yescharacteristic
175M16—41no—
176M16—2442no—
177M16—2442no—
178M16—2442no—
179M16—2441no—
180C2×C8—21no—
181C2×C8—41no—
182C2×C8—612no—
183C2×C8—1222no—
184C2×C8—1222no—
185C2×C8—1221no—
186C2×C8—2441no—
187C2×C8C22⋊#692312yes—
188C4⋊C4—21no—
189C4⋊C4—1222no—
190C4⋊C4—1221no—
191C22⋊C4—612no—
192C22⋊C4—1222no—
193C22⋊C4D61⋊C812yes—
194C42—21no—
195C42—1222no—
196C42—1221no—
197C16—2444no—
198C23—611no—
199C23—611no—
200C23—1222no—
201C23—4881no—
202C23C2×D61⋊C811yescharacteristic
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—611no—
207C2×C4—612no—
208C2×C4—612no—
209C2×C4—611no—
210C2×C4—1222no—
211C2×C4—1222no—
212C2×C4—1222no—
213C2×C4—1221no—
214C2×C4—1221no—
215C2×C4—1222no—
216C2×C4—4882no—
217C2×C4C2×C22⋊#692311yescharacteristic
218C2×C4D61⋊M1611yescharacteristic
219C8—22no—
220C8—41no—
221C8—1222no—
222C8—2441no—
223C22—21no—
224C22—41no—
225C22—612no—
226C22—1221no—
227C22—4882no—
228C22—2441no—
229C22—2441no—
230C22D61⋊(C22⋊C8)11yescharacteristic
231C4—21no—
232C4—42no—
233C4—612no—
234C4—1221no—
235C4—2442no—
236C4D61⋊#9911yescharacteristic
237C4D61⋊#10111yescharacteristic
238C2—21no—
239C2—41no—
240C2—1222no—
241C2—2441no—
242C2D61⋊#32411yescharacteristic
subgroupG/H
centerC4D61⋊#99
commutatorC23×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#424C4
socleC2×C61C2×#324
prime radicalC23×D61C2×C8
cosocleC2×#11758194C23
hypercenter#424#6923
hypocenterC61#11458
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #21460768C2semidirect
3. #21460767C2semidirect
138. C61#11458semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3492
#214607682
#214607672
#214543802
#1145861