Finite Group Databasebeta

← #30604154

Subgroups — #30604154

Order 15616.

280 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 64 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#21460768C212yesmaximal, complemented
3#21460754C212yesmaximal
4#21454468C211yesmaximal, characteristic
5#16840685—22no—
6#16840658C2214yes—
7#16840654—22no—
8C4×#11758222C411yescharacteristic
9#16839824—22no—
10#16839817—22no—
11#16839788C411yescharacteristic
12#16839788C2211yescharacteristic
13#16839728C411yescharacteristic
14#16839728C2211yescharacteristic
15C4×#11758194C2211yescharacteristic
16C2×#97×C61C411yescharacteristic
17#14519851—24no—
18C2×#11758222C2×C411yescharacteristic
19C2×#11758194C2×C411yescharacteristic
20C2×#11758194C2311yescharacteristic
21C4×Dic122—21no—
22C4×D244—21no—
23C4×C22⋊D61—22no—
24#14519736C2×C411yescharacteristic
25#14519734—21no—
26C42×D61—21no—
27#14519706—22no—
28#14519706—22no—
29#14519689—22no—
30#14519689—22no—
31#14519688D412yes—
32C4×#92418D412yes—
33C22×C8×C61C2×C411yescharacteristic
34C22×C8×C61C2×C411yescharacteristic
35C2×C42×C61C2×C411yescharacteristic
36#97×C61—21no—
37#97×C61—21no—
38C22×C4×C61—21no—
39C22×C4×C61C22×C411yescharacteristic
40C2×C22⋊D61—21no—
41#11758222—41no—
42#11758222—41no—
43C2×D244M1611yescharacteristic
44C2×C4×D61—21no—
45C2×C4×D61—22no—
46C2×Dic122M1611yescharacteristic
47C2×C8×C61—21no—
48C2×C8×C61—21no—
49C2×C8×C61—41no—
50C2×C8×C61—41no—
51C42×C61—21no—
52C42×C61C22⋊C411yescharacteristic
53C42×C61C22⋊C411yescharacteristic
54C22⋊Dic61M1612yes—
55#11758198—22no—
56C4⋊Dic61—21no—
57#11758196—22no—
58C4×Dic61—22no—
59C4×Dic61—21no—
60#11758194—41no—
61#11758194—41no—
62C2×#92418C22⋊C412yes—
63C2×#92418C2×D412yes—
64#11758187—44no—
65C23×C61C2×M1611yescharacteristic
66C22×D61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—81no—
72C2×C4×C61C2×C22⋊C411yescharacteristic
73C2×C4×C61C2×M1611yescharacteristic
74C22⋊D61—42no—
75C2×Dic61—21no—
76C2×Dic61—22no—
77D244—41no—
78C4×D61—41no—
79C4×D61—41no—
80C4×D61—82no—
81Dic122—41no—
82C8×C61—41no—
83C8×C61—41no—
84#92418—22no—
85#92418—22no—
86#11523—611nomaximal, Sylow
87C22×C61—21no—
88C22×C61—41no—
89C22×C61#40711yescharacteristic
90C2×D61—42no—
91C2×D61—41no—
92C4×C61—21no—
93C4×C61—41no—
94C4×C61—41no—
95C4×C61#41011yescharacteristic
96C4×C61#41311yescharacteristic
97Dic61—42no—
98Dic61—41no—
99#2923—611no—
100#2165—612no—
101#1328—612no—
102#1321—612no—
103C2×C61—21no—
104C2×C61—41no—
105C2×C61#146411yescharacteristic
106D61—81no—
107C4×#41—611no—
108#433—1222no—
109#432—1222no—
110#424—611no—
111#424—611no—
112#408—611no—
113#408—611no—
114C4×M16—611no—
115C2×#97#692311yescharacteristic
116#364—1222no—
117#349—614no—
118#347—1222no—
119C61#1152311yescharacteristic, complemented, Sylow
120C2×#41—611no—
121C2×M16—611no—
122C2×M16—611no—
123C22×C8C2×#692311yescharacteristic
124C22×C8C2×#692311yescharacteristic
125C4×Q8—1221no—
126C4×D4—1221no—
127C4×D4—1222no—
128#117—611no—
129#117—1221no—
130C2×C42—1221no—
131C2×C42C2×#692311yescharacteristic
132M32—1224no—
133C4⋊C8—1222no—
134C4⋊C8—1222no—
135C22⋊C8—1222no—
136C22⋊C8—1222no—
137#97—21no—
138#97—21no—
139#97—612no—
140C4×C8—612no—
141#41—2441no—
142#41—2441no—
143C2×Q8—611no—
144C2×D4—611no—
145C2×D4—1221no—
146C22×C4—21no—
147C22×C4—1222no—
148C22×C4—1221no—
149C22×C4C22×#692311yescharacteristic
150M16—2441no—
151M16—2441no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—41no—
155C2×C8—41no—
156C2×C8—612no—
157C2×C8—612no—
158C4⋊C4—1222no—
159C4⋊C4—1221no—
160C22⋊C4—612no—
161C22⋊C4—1222no—
162C42—21no—
163C42—1222no—
164C42—1221no—
165C42C22⋊#692311yescharacteristic
166C42C22⋊#692311yescharacteristic
167C16—2444no—
168C23—1221no—
169C23D61⋊M1611yescharacteristic
170Q8—2441no—
171D4—2441no—
172D4—2442no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—81no—
178C2×C4—1222no—
179C2×C4—1221no—
180C2×C4—4882no—
181C2×C4—2441no—
182C2×C4—2441no—
183C2×C4C2×C22⋊#692311yescharacteristic
184C2×C4D61⋊M1611yescharacteristic
185C8—41no—
186C8—41no—
187C8—1222no—
188C8—1222no—
189C22—21no—
190C22—41no—
191C22—2442no—
192C22—2441no—
193C22#1684073411yescharacteristic
194C4—21no—
195C4—41no—
196C4—41no—
197C4—2442no—
198C4—2441no—
199C4#1684074111yescharacteristic
200C4#1684074811yescharacteristic
201C2—21no—
202C2—41no—
203C2—4881no—
204C2#2146107211yescharacteristic
subgroupG/H
centerC4#16840741
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#97×C61C4
socleC2×C61#1464
prime radicalC2×#11758222C2×C4
cosocleC2×#11758194C23
hypercenterC2×#97#6923
hypocenterC61#11523
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C42 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
1. #21462188C2semidirect
2. #21460768C2semidirect
119. C61#11523semidirect

Maximal subgroups

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

subgroupindex
#214621882
#214607682
#214607542
#214544682
#1152361