Finite Group Databasebeta

← #30604149

Subgroups — #30604149

Order 15616.

284 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 66 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#21462189C212yesmaximal, complemented
2#21460766C212yesmaximal, complemented
3#21460751C212yesmaximal
4#21454454C211yesmaximal, characteristic
5#16840684—22no—
6#16840658C2214yes—
7#16840655—22no—
8C2×#14519736C411yescharacteristic
9#16839820—22no—
10#16839820—22no—
11#16839785C411yescharacteristic
12#16839785C2211yescharacteristic
13#16839726C2211yescharacteristic
14M16×Dic61C411yescharacteristic
15M16×Dic61C2211yescharacteristic
16C61×#407C411yescharacteristic
17#14519851—24no—
18C2×#11758194C2×C411yescharacteristic
19C2×#11758194C2311yescharacteristic
20#14519736—21no—
21#14519736—21no—
22#14519736—22no—
23C2×C4⋊Dic61—21no—
24C2×C22⋊Dic61—21no—
25C2×C4×Dic61C2×C411yescharacteristic
26C2×C4×Dic61C2×C411yescharacteristic
27#14519706—22no—
28#14519706—22no—
29C22⋊#92418—22no—
30#14519687—21no—
31#14519687D412yes—
32C8×Dic61—21no—
33C8×Dic61D412yes—
34C23×C4×C61C2×C411yescharacteristic
35C2×M16×C61C2×C411yescharacteristic
36C2×M16×C61C2×C411yescharacteristic
37C22⋊C8×C61—22no—
38C24×C61M1611yescharacteristic
39C22×C4×C61—21no—
40C22×C4×C61—21no—
41C22×C4×C61—41no—
42C22×C4×C61—41no—
43C22×C4×C61M1611yescharacteristic
44C22×C4×C61C22×C411yescharacteristic
45C22×Dic61—21no—
46C22×Dic61—21no—
47M16×C61—41no—
48M16×C61—41no—
49C2×C8×C61—21no—
50C2×C8×C61C22⋊C412yes—
51C22⋊Dic61—22no—
52C22⋊Dic61—22no—
53C4⋊Dic61—22no—
54C4⋊Dic61—22no—
55C4×Dic61—21no—
56C4×Dic61—21no—
57C4×Dic61C22⋊C411yescharacteristic
58C4×Dic61C22⋊C411yescharacteristic
59C4×Dic61M1612yes—
60#11758194—41no—
61#11758194—41no—
62C2×#92418—21no—
63C2×#92418C2×D412yes—
64#11758187—44no—
65C23×C61—21no—
66C23×C61—41no—
67C23×C61—81no—
68C23×C61C2×M1611yescharacteristic
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—42no—
73C2×C4×C61—41no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61C2×C22⋊C411yescharacteristic
77C2×C4×C61C2×M1611yescharacteristic
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—22no—
81C2×Dic61—81no—
82C2×Dic61—81no—
83C8×C61—22no—
84C8×C61—41no—
85#92418—22no—
86#92418—41no—
87#11522—611nomaximal, Sylow
88C22×C61—21no—
89C22×C61—41no—
90C22×C61—42no—
91C22×C61—41no—
92C22×C61—82no—
93C22×C61#40711yescharacteristic
94C4×C61—21no—
95C4×C61—41no—
96C4×C61#41011yescharacteristic
97C4×C61#41311yescharacteristic
98Dic61—41no—
99Dic61—41no—
100Dic61—42no—
101#2921—611no—
102#2165—612no—
103#1327—612no—
104#1320—612no—
105C2×C61—21no—
106C2×C61—41no—
107C2×C61—81no—
108C2×C61#146411yescharacteristic
109C2×#117—611no—
110#433—1222no—
111#433—1222no—
112#423—611no—
113#423—611no—
114#407—611no—
115#407#692311yescharacteristic
116C4×M16—611no—
117C4×M16—611no—
118#364—1222no—
119#349—614no—
120#347—1222no—
121C61#1152211yescharacteristic, complemented, Sylow
122C23×C4C2×#692311yescharacteristic
123C2×M16—611no—
124C2×M16—611no—
125C2×M16C2×#692311yescharacteristic
126C2×M16C2×#692311yescharacteristic
127#117—1221no—
128#117—1221no—
129#117—1222no—
130C2×C4⋊C4—1221no—
131C2×C22⋊C4—1221no—
132C2×C42—611no—
133C2×C42—611no—
134M32—1224no—
135C4⋊C8—1222no—
136C4⋊C8—1222no—
137C22⋊C8—22no—
138C22⋊C8—1222no—
139#97—612no—
140#97—1221no—
141C4×C8—612no—
142C4×C8—1221no—
143C24#1175821311yescharacteristic
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—41no—
147C22×C4—41no—
148C22×C4—1221no—
149C22×C4—1221no—
150C22×C4#1175821311yescharacteristic
151C22×C4C22×#692311yescharacteristic
152M16—41no—
153M16—41no—
154M16—2441no—
155M16—2441no—
156C2×C8—21no—
157C2×C8—612no—
158C2×C8—1221no—
159C2×C8C22⋊#692312yes—
160C4⋊C4—1222no—
161C4⋊C4—1222no—
162C22⋊C4—1222no—
163C22⋊C4—1222no—
164C42—611no—
165C42—611no—
166C42—612no—
167C42—1221no—
168C42—1221no—
169C16—2444no—
170C23—21no—
171C23—41no—
172C23—81no—
173C23C2×#1175821311yescharacteristic
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—1221no—
182C2×C4—1221no—
183C2×C4—1222no—
184C2×C4—4881no—
185C2×C4—4881no—
186C2×C4C2×C22⋊#692311yescharacteristic
187C2×C4D61⋊M1611yescharacteristic
188C8—22no—
189C8—41no—
190C8—1222no—
191C8—2441no—
192C22—21no—
193C22—41no—
194C22—42no—
195C22—41no—
196C22—82no—
197C22#1684073311yescharacteristic
198C4—21no—
199C4—41no—
200C4—2441no—
201C4—2441no—
202C4—2442no—
203C4#1684074211yescharacteristic
204C4#1684074911yescharacteristic
205C2—21no—
206C2—41no—
207C2—81no—
208C2#2146107111yescharacteristic
subgroupG/H
centerC4#16840742
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#407C4
socleC2×C61#1464
prime radicalC24×C61M16
cosocleC2×#11758194C23
hypercenter#407#6923
hypocenterC61#11522
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #21462189C2semidirect
2. #21460766C2semidirect
121. C61#11522semidirect

Maximal subgroups

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

subgroupindex
#214621892
#214607662
#214607512
#214544542
#1152261