Finite Group Databasebeta

← #30599362

Subgroups — #30599362

Order 15616.

398 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 72 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#21461718C212yesmaximal
2#21460722C214yesmaximal
3#21448421C211yesmaximal, characteristic
4#16840732C2214yes—
5#16840642—22no—
6#16840642—22no—
7C22×#11758196C2211yescharacteristic
8#16839649—22no—
9#16839643—22no—
10#16839623C2212yes—
11#16839622C411yescharacteristic
12C22⋊C4×Dic61C412yes—
13C61×#380C411yescharacteristic
14C2×#11758217—24no—
15C22⋊#92420—28no—
16C23×Dic61C2×C411yescharacteristic
17C23×Dic61C2311yescharacteristic
18C2×C4⋊Dic61—21no—
19C2×#11758196—24no—
20C2×#11758196D412yes—
21C2×#11758196D412yes—
22C2×C22⋊Dic61C2×C412yes—
23C2×C4×Dic61—22no—
24#14519684—21no—
25#14519684—22no—
26#14519684—24no—
27C23×C4×C61C2×C411yescharacteristic
28C2×C4⋊C4×C61—21no—
29C2×C22⋊C4×C61C2×C412yes—
30#95×C61—21no—
31C24×C61C22×C411yescharacteristic
32C22×C4×C61—22no—
33C22×C4×C61—22no—
34C22×C4×C61—81no—
35C22×C4×C61C22⋊C411yescharacteristic
36C22×C4×C61C22⋊C411yescharacteristic
37C22×Dic61—22no—
38C22×Dic61—22no—
39C22×Dic61—41no—
40C22×Dic61—41no—
41C22×Dic61—81no—
42C22×Dic61C22⋊C412yes—
43C22×Dic61C2×D412yes—
44C22×Dic61#4114yes—
45#11758217—44no—
46#11758217—44no—
47C2×#92420—44no—
48C4⋊C4×C61—81no—
49C22⋊C4×C61—42no—
50C22⋊Dic61—42no—
51C4⋊Dic61—81no—
52#11758196—24no—
53#11758196—24no—
54C4×Dic61—82no—
55C23×C61—21no—
56C23×C61—21no—
57C23×C61—41no—
58C23×C61—41no—
59C23×C61C2×C22⋊C411yescharacteristic
60C23×C61#11712yes—
61C2×C4×C61—21no—
62C2×C4×C61—21no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—42no—
66C2×C4×C61—42no—
67C2×C4×C61—42no—
68C2×C4×C61—82no—
69C2×Dic61—22no—
70C2×Dic61—22no—
71C2×Dic61—22no—
72C2×Dic61—44no—
73C2×Dic61—42no—
74C2×Dic61—42no—
75C2×Dic61—42no—
76C2×Dic61—42no—
77C2×Dic61—82no—
78C2×Dic61#12314yes—
79#92420—84no—
80#8755—611nomaximal, Sylow
81C22×C61—21no—
82C22×C61—21no—
83C22×C61—22no—
84C22×C61—22no—
85C22×C61—22no—
86C22×C61—42no—
87C22×C61—42no—
88C22×C61#38111yescharacteristic
89C22×C61#41011yescharacteristic
90C22×C61#41011yescharacteristic
91C4×C61—41no—
92C4×C61—41no—
93C4×C61—82no—
94Dic61—24no—
95Dic61—42no—
96Dic61—82no—
97#2313—611no—
98#1821—612no—
99#1306—614no—
100C2×C61—21no—
101C2×C61—21no—
102C2×C61—42no—
103C2×C61#182011yescharacteristic
104C2×C61#182911yescharacteristic
105C2×C61#183011yescharacteristic
106C22×C4⋊C4—611no—
107#407—614no—
108#387—1222no—
109#387—1222no—
110#381—612no—
111#380—611no—
112#380#692311yescharacteristic
113C4×C22⋊C4—612no—
114#343—1222no—
115#343—1222no—
116C61#875511yescharacteristic, complemented, Sylow
117C23×C4—611no—
118C23×C4—611no—
119C23×C4C2×#692311yescharacteristic
120C2×M16—1224no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—612no—
123C2×C4⋊C4—612no—
124C2×C4⋊C4—1224no—
125C2×C4⋊C4—1221no—
126C2×C22⋊C4—612no—
127C2×C22⋊C4C2×#692312yes—
128C2×C42—1222no—
129C22⋊C8—1228no—
130#95—21no—
131#95—1222no—
132#95—1224no—
133#95—1221no—
134C24C22×#692311yescharacteristic
135C22×C4—22no—
136C22×C4—22no—
137C22×C4—81no—
138C22×C4—612no—
139C22×C4—614no—
140C22×C4—612no—
141C22×C4—1222no—
142C22×C4—1222no—
143C22×C4—4881no—
144C22×C4—2441no—
145C22×C4—2441no—
146C22×C4C22⋊#692311yescharacteristic
147C22×C4C22⋊#692311yescharacteristic
148M16—2444no—
149M16—2444no—
150C2×C8—2444no—
151C4⋊C4—81no—
152C4⋊C4—1224no—
153C4⋊C4—1224no—
154C4⋊C4—4881no—
155C22⋊C4—42no—
156C22⋊C4—2442no—
157C42—4882no—
158C23—21no—
159C23—21no—
160C23—41no—
161C23—41no—
162C23C2×C22⋊#692311yescharacteristic
163C23#1451985612yes—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—82no—
172C2×C4—614no—
173C2×C4—1222no—
174C2×C4—1222no—
175C2×C4—1222no—
176C2×C4—4882no—
177C2×C4—2444no—
178C2×C4—2442no—
179C2×C4—2442no—
180C2×C4—2442no—
181C2×C4—2442no—
182C8—4884no—
183C22—21no—
184C22—21no—
185C22—22no—
186C22—22no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22#1684070511yescharacteristic
191C22#1684074211yescharacteristic
192C22#1684074311yescharacteristic
193C4—41no—
194C4—41no—
195C4—82no—
196C4—1224no—
197C4—4882no—
198C4—2442no—
199C2—21no—
200C2—21no—
201C2—42no—
202C2#2146171711yescharacteristic
203C2#2146173211yescharacteristic
204C2#2146173311yescharacteristic
subgroupG/H
centerC22#16840705
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC61×#380C4
socleC22×C61#381
cosocleC23×Dic61C23
hypercenter#380#6923
hypocenterC61#8755
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #380

Complements

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

NH ≅ G/Ntype
116. C61#8755semidirect

Maximal subgroups

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

subgroupindex
#214617182
#214607222
#214484212
#875561