Finite Group Databasebeta

← #30604150

Subgroups — #30604150

Order 15616.

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

normal subgroups only

This group has 284 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#21460766C212yesmaximal, complemented
3#21460752C212yesmaximal
4#21454455C211yesmaximal, characteristic
5#16840685—22no—
6#16840658C2214yes—
7#16840654—22no—
8C2×#14519734C411yescharacteristic
9#16839824—22no—
10#16839821—22no—
11#16839785C411yescharacteristic
12#16839785C2211yescharacteristic
13#16839725C411yescharacteristic
14#16839725C2211yescharacteristic
15C4×#11758194C2211yescharacteristic
16C4×M16×C61C411yescharacteristic
17#14519851—24no—
18C22×C4×D61C2×C411yescharacteristic
19C2×#11758194C2×C411yescharacteristic
20C2×#11758194C2311yescharacteristic
21#14519734—21no—
22#14519734—21no—
23#14519734—22no—
24C2×#11758196—21no—
25C2×#11758198—21no—
26C2×C4×Dic61C2×C411yescharacteristic
27#14519706—22no—
28#14519706—22no—
29#14519689—22no—
30#14519689—22no—
31#14519688D412yes—
32C4×#92418D412yes—
33C2×M16×C61C2×C411yescharacteristic
34C2×M16×C61C2×C411yescharacteristic
35C2×C42×C61C2×C411yescharacteristic
36#97×C61—21no—
37C4×C8×C61—21no—
38C23×D61M1611yescharacteristic
39C22×C4×C61—21no—
40C22×C4×C61C22×C411yescharacteristic
41C22×Dic61—21no—
42C22×Dic61M1611yescharacteristic
43C2×C4×D61—21no—
44C2×C4×D61—21no—
45C2×C4×D61—41no—
46C2×C4×D61—41no—
47M16×C61—41no—
48M16×C61—41no—
49C2×C8×C61—21no—
50C2×C8×C61—21no—
51C42×C61—21no—
52C42×C61C22⋊C411yescharacteristic
53C42×C61C22⋊C411yescharacteristic
54#11758198—22no—
55#11758198—22no—
56#11758196—22no—
57#11758196—22no—
58C4×Dic61—21no—
59C4×Dic61M1612yes—
60#11758194—41no—
61#11758194—41no—
62C2×#92418C22⋊C412yes—
63C2×#92418C2×D412yes—
64#11758187—44no—
65C23×C61C2×M1611yescharacteristic
66C22×D61—21no—
67C22×D61—41no—
68C22×D61—81no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—81no—
74C2×C4×C61C2×C22⋊C411yescharacteristic
75C2×C4×C61C2×M1611yescharacteristic
76C2×Dic61—22no—
77C2×Dic61—21no—
78C2×Dic61—41no—
79C2×Dic61—81no—
80C4×D61—42no—
81C4×D61—41no—
82C4×D61—41no—
83C8×C61—41no—
84C8×C61—41no—
85#92418—22no—
86#92418—22no—
87#11522—611nomaximal, Sylow
88C22×C61—21no—
89C22×C61—41no—
90C22×C61#40711yescharacteristic
91C2×D61—42no—
92C2×D61—41no—
93C2×D61—82no—
94C4×C61—21no—
95C4×C61—41no—
96C4×C61—41no—
97C4×C61#41011yescharacteristic
98C4×C61#41311yescharacteristic
99Dic61—42no—
100Dic61—41no—
101#2921—611no—
102#2165—612no—
103#1327—612no—
104#1320—612no—
105C2×C61—21no—
106C2×C61—41no—
107C2×C61#146411yescharacteristic
108D61—81no—
109C2×#117—611no—
110#433—1222no—
111#433—1222no—
112#423—611no—
113#423—611no—
114#407—611no—
115#407—611no—
116C4×M16—611no—
117C4×M16#692311yescharacteristic
118#364—1222no—
119#349—614no—
120#347—1222no—
121C61#1152211yescharacteristic, complemented, Sylow
122C23×C4—611no—
123C2×M16—611no—
124C2×M16—611no—
125C2×M16C2×#692311yescharacteristic
126C2×M16C2×#692311yescharacteristic
127#117—1222no—
128#117—1221no—
129#117—1221no—
130C2×C4⋊C4—1221no—
131C2×C22⋊C4—1221no—
132C2×C42—611no—
133C2×C42C2×#692311yescharacteristic
134M32—1224no—
135C4⋊C8—1222no—
136C4⋊C8—1222no—
137C22⋊C8—1222no—
138C22⋊C8—1222no—
139#97—21no—
140#97—612no—
141C4×C8—21no—
142C4×C8—612no—
143C24—611no—
144C22×C4—21no—
145C22×C4—611no—
146C22×C4—1221no—
147C22×C4—1221no—
148C22×C4—1221no—
149C22×C4—2441no—
150C22×C4—2441no—
151C22×C4C22×#692311yescharacteristic
152M16—41no—
153M16—41no—
154M16—2441no—
155M16—2441no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—612no—
159C2×C8—612no—
160C4⋊C4—1222no—
161C4⋊C4—1222no—
162C22⋊C4—1222no—
163C22⋊C4—1222no—
164C42—21no—
165C42—612no—
166C42—1221no—
167C42C22⋊#692311yescharacteristic
168C42C22⋊#692311yescharacteristic
169C16—2444no—
170C23—1221no—
171C23—4881no—
172C23—2441no—
173C23D61⋊M1611yescharacteristic
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—81no—
179C2×C4—1222no—
180C2×C4—1221no—
181C2×C4—4881no—
182C2×C4—2442no—
183C2×C4—2441no—
184C2×C4—2441no—
185C2×C4—2441no—
186C2×C4C2×C22⋊#692311yescharacteristic
187C2×C4D61⋊M1611yescharacteristic
188C8—41no—
189C8—41no—
190C8—1222no—
191C8—1222no—
192C22—21no—
193C22—41no—
194C22—4882no—
195C22—2442no—
196C22—2441no—
197C22#1684073411yescharacteristic
198C4—21no—
199C4—41no—
200C4—41no—
201C4—2442no—
202C4—2441no—
203C4#1684074111yescharacteristic
204C4#1684074811yescharacteristic
205C2—21no—
206C2—41no—
207C2—4881no—
208C2#2146107211yescharacteristic
subgroupG/H
centerC4#16840741
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×M16×C61C4
socleC2×C61#1464
prime radicalC23×D61M16
cosocleC2×#11758194C23
hypercenterC4×M16#6923
hypocenterC61#11522
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C42 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
1. #21462188C2semidirect
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
#214621882
#214607662
#214607522
#214544552
#1152261