Finite Group Databasebeta

← #30604148

Subgroups — #30604148

Order 15616.

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

normal subgroups only

This group has 284 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#21454457C211yesmaximal, characteristic
5#16840685—22no—
6#16840658C2214yes—
7#16840654—22no—
8#16839823—22no—
9#16839823—22no—
10#16839786C411yescharacteristic
11#16839786C2211yescharacteristic
12#16839726C411yescharacteristic
13#16839726C2211yescharacteristic
14C4×#11758194C411yescharacteristic
15C4×#11758194C2211yescharacteristic
16C2×#117×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×C61C2×C411yescharacteristic
31#117×C61—21no—
32#117×C61—21no—
33#117×C61—22no—
34C2×C4⋊C4×C61—21no—
35C2×C22⋊C4×C61—21no—
36C2×C42×C61C2×C411yescharacteristic
37C2×C42×C61C2×C411yescharacteristic
38C24×C61M1611yescharacteristic
39C22×C4×C61—21no—
40C22×C4×C61—21no—
41C22×C4×C61—21no—
42C22×C4×C61—21no—
43C22×C4×C61—41no—
44C22×C4×C61—41no—
45C22×C4×C61M1611yescharacteristic
46C22×C4×C61C22×C411yescharacteristic
47C4⋊C4×C61—22no—
48C4⋊C4×C61—22no—
49C22⋊C4×C61—22no—
50C22⋊C4×C61—22no—
51C42×C61—21no—
52C42×C61—21no—
53C42×C61C22⋊C411yescharacteristic
54C42×C61C22⋊C411yescharacteristic
55C42×C61M1612yes—
56#11758194—41no—
57#11758194—41no—
58#11758194—41no—
59#11758194—41no—
60C2×#92418—21no—
61C2×#92418—21no—
62C2×#92418C22⋊C412yes—
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—21no—
73C2×C4×C61—22no—
74C2×C4×C61—21no—
75C2×C4×C61—42no—
76C2×C4×C61—41no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61—81no—
80C2×C4×C61—81no—
81C2×C4×C61C2×C22⋊C411yescharacteristic
82C2×C4×C61C2×M1611yescharacteristic
83#92418—22no—
84#92418—22no—
85#92418—41no—
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—41no—
97C4×C61—42no—
98C4×C61—41no—
99C4×C61#41011yescharacteristic
100C4×C61#41311yescharacteristic
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#692311yescharacteristic
110#433—1222no—
111#433—1222no—
112#423—611no—
113#423—611no—
114#407—611no—
115#407—611no—
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×M16—611no—
126C2×M16—611no—
127#117—22no—
128#117—21no—
129#117—21no—
130C2×C4⋊C4—21no—
131C2×C22⋊C4—21no—
132C2×C42C2×#692311yescharacteristic
133C2×C42C2×#692311yescharacteristic
134M32—1224no—
135C4⋊C8—1222no—
136C4⋊C8—1222no—
137C22⋊C8—1222no—
138C22⋊C8—1222no—
139#97—612no—
140#97—1221no—
141C4×C8—612no—
142C4×C8—1221no—
143C24#1175821711yescharacteristic
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4#1175821711yescharacteristic
151C22×C4C22×#692311yescharacteristic
152M16—2441no—
153M16—2441no—
154M16—2441no—
155M16—2441no—
156C2×C8—612no—
157C2×C8—612no—
158C2×C8—1221no—
159C2×C8—1221no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C22⋊C4—22no—
163C22⋊C4—22no—
164C42—21no—
165C42—21no—
166C42#1175821712yes—
167C42C22⋊#692311yescharacteristic
168C42C22⋊#692311yescharacteristic
169C16—2444no—
170C23—21no—
171C23—41no—
172C23—81no—
173C23C2×#1175821711yescharacteristic
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—81no—
185C2×C4—81no—
186C2×C4C2×C22⋊#692311yescharacteristic
187C2×C4C2×#1175821711yescharacteristic
188C8—1222no—
189C8—1222no—
190C8—2441no—
191C8—2441no—
192C22—21no—
193C22—41no—
194C22—42no—
195C22—41no—
196C22—82no—
197C22#1684073211yescharacteristic
198C4—21no—
199C4—42no—
200C4—41no—
201C4—41no—
202C4—41no—
203C4#1684074111yescharacteristic
204C4#1684074811yescharacteristic
205C2—21no—
206C2—41no—
207C2—81no—
208C2#2146107011yescharacteristic
subgroupG/H
centerC4#16840741
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC2×C61#1464
prime radicalC24×C61M16
cosocleC2×#11758194C23
hypercenterC2×#117#6923
hypocenterC61#11522
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C42 ◁ C2×C42 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #21462188C2semidirect
2. #21460765C2semidirect
121. C61#11522semidirect

Maximal subgroups

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

subgroupindex
#214621882
#214607652
#214607512
#214544572
#1152261