Finite Group Databasebeta

← #30604144

Subgroups — #30604144

Order 15616.

330 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 68 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#21462188C212yesmaximal, complemented
2#21460765C212yesmaximal, complemented
3#21460751C212yesmaximal
4#21454452C211yesmaximal, characteristic
5#16840685—22no—
6#16840658C2214yes—
7#16840654—22no—
8#16839819—22no—
9#16839815—22no—
10#16839786C411yescharacteristic
11#16839786C2211yescharacteristic
12#16839726C411yescharacteristic
13#16839726C2211yescharacteristic
14C4×#11758194C411yescharacteristic
15C4×#11758194C2211yescharacteristic
16C22×C42×C61C411yescharacteristic
17#14519851—24no—
18C2×#11758194C2×C411yescharacteristic
19C2×#11758194C2×C411yescharacteristic
20C2×#11758194C2×C411yescharacteristic
21C2×#11758194C2311yescharacteristic
22C4⋊#92418—22no—
23C4⋊#92418—22no—
24C22⋊#92418—22no—
25C22⋊#92418—22no—
26#14519688—21no—
27#14519688D412yes—
28C4×#92418—21no—
29C4×#92418D412yes—
30C23×C4×C61—21no—
31C23×C4×C61C2×C411yescharacteristic
32C2×C42×C61—21no—
33C2×C42×C61—21no—
34C2×C42×C61—21no—
35C2×C42×C61—21no—
36C2×C42×C61—21no—
37C2×C42×C61C2×C411yescharacteristic
38C2×C42×C61C2×C411yescharacteristic
39C24×C61M1611yescharacteristic
40C22×C4×C61—21no—
41C22×C4×C61—21no—
42C22×C4×C61—21no—
43C22×C4×C61—21no—
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61—21no—
48C22×C4×C61—44no—
49C22×C4×C61—41no—
50C22×C4×C61—41no—
51C22×C4×C61M1611yescharacteristic
52C22×C4×C61C22×C411yescharacteristic
53C42×C61—21no—
54C42×C61—21no—
55C42×C61—21no—
56C42×C61—21no—
57C42×C61—21no—
58C42×C61—21no—
59C42×C61C22⋊C411yescharacteristic
60C42×C61C22⋊C411yescharacteristic
61C42×C61M1611yescharacteristic
62C42×C61M1611yescharacteristic
63#11758194—41no—
64#11758194—41no—
65#11758194—41no—
66#11758194—41no—
67C2×#92418—21no—
68C2×#92418—21no—
69C2×#92418C22⋊C412yes—
70C2×#92418C2×D412yes—
71#11758187—44no—
72C23×C61—21no—
73C23×C61—42no—
74C23×C61—41no—
75C23×C61C2×M1611yescharacteristic
76C2×C4×C61—24no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—42no—
85C2×C4×C61—42no—
86C2×C4×C61—42no—
87C2×C4×C61—42no—
88C2×C4×C61—42no—
89C2×C4×C61—42no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61C2×C22⋊C411yescharacteristic
94C2×C4×C61C2×M1611yescharacteristic
95#92418—22no—
96#92418—22no—
97#92418—41no—
98#92418—41no—
99#11521—611nomaximal, Sylow
100C22×C61—22no—
101C22×C61—21no—
102C22×C61—41no—
103C22×C61—41no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61—41no—
107C22×C61#40711yescharacteristic
108C4×C61—22no—
109C4×C61—22no—
110C4×C61—21no—
111C4×C61—41no—
112C4×C61—41no—
113C4×C61—41no—
114C4×C61#41011yescharacteristic
115C4×C61#41311yescharacteristic
116#2920—611no—
117#2165—612no—
118#1327—612no—
119#1320—612no—
120C2×C61—21no—
121C2×C61—42no—
122C2×C61—41no—
123C2×C61#146411yescharacteristic
124C22×C42#692311yescharacteristic
125#432—1222no—
126#431—1222no—
127#423—611no—
128#423—611no—
129#407—611no—
130#407—611no—
131C4×M16—611no—
132C4×M16—611no—
133#364—1222no—
134#349—614no—
135#347—1222no—
136C61#1152111yescharacteristic, complemented, Sylow
137C23×C4—21no—
138C23×C4C2×#692311yescharacteristic
139C2×M16—611no—
140C2×M16—611no—
141C2×M16—611no—
142C2×M16—611no—
143C2×C42—21no—
144C2×C42—21no—
145C2×C42—21no—
146C2×C42—21no—
147C2×C42—21no—
148C2×C42C2×#692311yescharacteristic
149C2×C42C2×#692311yescharacteristic
150M32—1224no—
151C4⋊C8—1222no—
152C4⋊C8—1222no—
153C22⋊C8—1222no—
154C22⋊C8—1222no—
155#97—612no—
156#97—1221no—
157C4×C8—612no—
158C4×C8—1221no—
159C24#1175821711yescharacteristic
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—44no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4#1175821711yescharacteristic
172C22×C4C22×#692311yescharacteristic
173M16—2441no—
174M16—2441no—
175M16—2441no—
176M16—2441no—
177C2×C8—612no—
178C2×C8—612no—
179C2×C8—1221no—
180C2×C8—1221no—
181C42—21no—
182C42—21no—
183C42—21no—
184C42—21no—
185C42—21no—
186C42—21no—
187C42#1175821711yescharacteristic
188C42#1175821711yescharacteristic
189C42C22⋊#692311yescharacteristic
190C42C22⋊#692311yescharacteristic
191C16—2444no—
192C23—21no—
193C23—42no—
194C23—41no—
195C23C2×#1175821711yescharacteristic
196C2×C4—24no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4C2×C22⋊#692311yescharacteristic
214C2×C4C2×#1175821711yescharacteristic
215C8—1222no—
216C8—1222no—
217C8—2441no—
218C8—2441no—
219C22—22no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—42no—
224C22—42no—
225C22—41no—
226C22#1684073211yescharacteristic
227C4—22no—
228C4—22no—
229C4—21no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4#1684074111yescharacteristic
234C4#1684074811yescharacteristic
235C2—21no—
236C2—42no—
237C2—41no—
238C2#2146107011yescharacteristic
subgroupG/H
centerC4#16840741
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×C42×C61C4
socleC2×C61#1464
prime radicalC24×C61M16
cosocleC2×#11758194C23
hypercenterC22×C42#6923
hypocenterC61#11521
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C42 ◁ C2×C42 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. #21462188C2semidirect
2. #21460765C2semidirect
136. C61#11521semidirect

Maximal subgroups

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

subgroupindex
#214621882
#214607652
#214607512
#214544522
#1152161