Finite Group Databasebeta

← #30595194

Subgroups — #30595194

Order 15616.

348 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C2×#16840667C212yesmaximal
2#21446625C211yesmaximal, characteristic
3C2×#14519836—22no—
4#16840667—22no—
5#16840667C414yescomplemented
6C2×#14519774C2211yescharacteristic
7C2×#14519699—22no—
8#16839632C411yescharacteristic, complemented
9C2×C4×C8×C61C411yescharacteristic, complemented
10C2×C22⋊#6923—42no—
11#14519836—24no—
12#14519836—42no—
13C22×D244—41no—
14C22×D244D412yes—
15#14519774—41no—
16#14519774C2×C412yes—
17#14519774D411yescharacteristic
18#14519774Q811yescharacteristic
19C2×C4⋊Dic61—21no—
20C2×C4⋊Dic61—41no—
21#14519699—44no—
22C22×C8×C61—21no—
23C2×C42×C61C2×C411yescharacteristic
24C4×C8×C61—41no—
25C23×D61—22no—
26C22×#6923—82no—
27C22×C4×C61—21no—
28C22×C4×C61C22⋊C411yescharacteristic
29C22×Dic61—41no—
30C2×D244—22no—
31C2×D244—42no—
32C2×D244—42no—
33C2×D244—42no—
34C2×D244—41no—
35C2×D244—41no—
36C2×D244—82no—
37C2×D244—82no—
38C2×D244C22⋊C412yes—
39C2×D244C4⋊C412yes—
40C22⋊#6923—44no—
41C22⋊#6923—82no—
42C2×C8×C61—22no—
43C2×C8×C61—41no—
44C2×C8×C61—41no—
45C42×C61—21no—
46C42×C61C4211yescharacteristic
47C42×C61C4⋊C411yescharacteristic
48C4⋊Dic61—42no—
49C4⋊Dic61—82no—
50C23×C61#9911yescharacteristic
51C22×D61—22no—
52C22×D61—22no—
53C22×D61—42no—
54C22×D61—42no—
55C22×D61—82no—
56C22×D61—82no—
57C2×#6923—84no—
58C2×#6923—162no—
59C2×#6923—162no—
60C2×C4×C61—22no—
61C2×C4×C61—22no—
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61#9511yescharacteristic
67C2×C4×C61#9911yescharacteristic
68C2×Dic61—82no—
69C2×Dic61—81no—
70D244—42no—
71D244—42no—
72D244—82no—
73D244—84no—
74D244—82no—
75D244—82no—
76C8×C61—42no—
77#7498—611nomaximal, Sylow
78C22×C61—21no—
79C22×C61—21no—
80C22×C61#34211yescharacteristic
81C22×C61#35311yescharacteristic
82C22×C61#35411yescharacteristic
83C2×D61—42no—
84C2×D61—42no—
85C2×D61—82no—
86C2×D61—82no—
87C2×D61—82no—
88C2×D61—82no—
89C2×D61—162no—
90#6923—164no—
91C4×C61—22no—
92C4×C61—22no—
93C4×C61—21no—
94C4×C61—21no—
95Dic61—161no—
96C2×#353—612no—
97#1957—611no—
98C2×C61—21no—
99C2×C61—21no—
100C2×C61#139311yescharacteristic
101C2×C61#140811yescharacteristic
102C2×C61#140911yescharacteristic
103D61—82no—
104D61—82no—
105C2×#127—611no—
106C2×#102—1222no—
107C2×#99—1222no—
108C2×C4×C8#692311yescharacteristic, complemented
109#384—611no—
110#353—614no—
111#353—1222no—
112C61#749811yescharacteristic, complemented, Sylow
113C22×D4—612no—
114C22×D4—2441no—
115C22×C8—21no—
116#127—612no—
117#127—611no—
118#127—611no—
119#127—2441no—
120C2×C4⋊C4—1221no—
121C2×C4⋊C4—2441no—
122C2×C22⋊C4—2442no—
123C2×C42C2×#692311yescharacteristic
124#102—2444no—
125#99—1224no—
126#99—2442no—
127C4×C8—41no—
128C24—1222no—
129C2×D4—612no—
130C2×D4—612no—
131C2×D4—1222no—
132C2×D4—4882no—
133C2×D4—4882no—
134C2×D4—2442no—
135C2×D4—2441no—
136C2×D4—2441no—
137C2×D4—2442no—
138C2×D4—2442no—
139C22×C4—21no—
140C22×C4—4882no—
141C22×C4—2441no—
142C22×C4C22⋊#692311yescharacteristic
143C2×C8—22no—
144C2×C8—41no—
145C2×C8—41no—
146C4⋊C4—4882no—
147C4⋊C4—2442no—
148C22⋊C4—4882no—
149C22⋊C4—2444no—
150C42—21no—
151C42C4×#692311yescharacteristic
152C42C4⋊#692311yescharacteristic
153C23—1222no—
154C23—1222no—
155C23—4882no—
156C23—4882no—
157C23—2442no—
158C23—2442no—
159C23#1451983611yescharacteristic
160D4—4884no—
161D4—4882no—
162D4—4882no—
163D4—4882no—
164D4—2442no—
165D4—2442no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—9762no—
173C2×C4—9762no—
174C2×C4—4882no—
175C2×C4—4884no—
176C2×C4—4881no—
177C2×C4(C2×#6923)⋊C411yescharacteristic
178C2×C4#1451983511yescharacteristic
179C8—42no—
180C22—21no—
181C22—21no—
182C22—9762no—
183C22—4882no—
184C22—4882no—
185C22—4882no—
186C22—4882no—
187C22—2442no—
188C22—2442no—
189C22#1684064011yescharacteristic
190C22#1684066711yescharacteristic
191C22#1684066911yescharacteristic
192C4—22no—
193C4—22no—
194C4—21no—
195C4—21no—
196C4—9764no—
197C4—9761no—
198C2—21no—
199C2—21no—
200C2—4882no—
201C2—4882no—
202C2#2146091311yescharacteristic
203C2#2146095111yescharacteristic
204C2#2146095311yescharacteristic
subgroupG/H
centerC22#16840667
commutatorC42×C61C42
FrattiniC2×C42C2×#6923
FittingC2×C4×C8×C61C4
socleC22×C61#353
prime radical, cosocleC2×#14519774C22
hypercenterC2×C4×C8#6923
hypocenterC61#7498
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
5. #16840667C4semidirect
8. #16839632C4semidirect
9. C2×C4×C8×C61C4semidirect
108. C2×C4×C8#6923semidirect
112. C61#7498semidirect

Maximal subgroups

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

subgroupindex
C2×#168406672
#214466252
#749861