Finite Group Databasebeta

← #30595214

Subgroups — #30595214

Order 15616.

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

normal subgroups only

This group has 336 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#21446643C211yesmaximal, characteristic
3C2×#14519836—22no—
4#16840667—22no—
5#16840667C414yescomplemented
6C2×#14519774C2211yescharacteristic
7C2×#14519699—22no—
8#16839628C411yescharacteristic, complemented
9C2×#97×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—
20#14519699—44no—
21#14519684—41no—
22C22×C8×C61—21no—
23C2×C42×C61C2×C411yescharacteristic
24#97×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—84no—
37C2×D244C22⋊C412yes—
38C2×D244C4⋊C412yes—
39C22⋊#6923—44no—
40C22⋊#6923—82no—
41C2×C8×C61—22no—
42C2×C8×C61—41no—
43C2×C8×C61—41no—
44C42×C61—21no—
45C42×C61C4211yescharacteristic
46C42×C61C4⋊C411yescharacteristic
47C4⋊Dic61—42no—
48C23×C61#9911yescharacteristic
49C22×D61—22no—
50C22×D61—22no—
51C22×D61—42no—
52C22×D61—42no—
53C22×D61—84no—
54C2×#6923—84no—
55C2×#6923—164no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—42no—
61C2×C4×C61#9511yescharacteristic
62C2×C4×C61#9911yescharacteristic
63C2×Dic61—82no—
64C2×Dic61—81no—
65D244—42no—
66D244—42no—
67D244—82no—
68D244—84no—
69D244—82no—
70D244—82no—
71C8×C61—42no—
72#7504—611nomaximal, Sylow
73C22×C61—22no—
74C22×C61#34211yescharacteristic
75C22×C61#35311yescharacteristic
76C22×C61#35411yescharacteristic
77C2×D61—42no—
78C2×D61—42no—
79C2×D61—84no—
80C2×D61—82no—
81C2×D61—82no—
82C2×D61—162no—
83#6923—164no—
84C4×C61—21no—
85C4×C61—21no—
86C4×C61—41no—
87C4×C61—41no—
88Dic61—161no—
89C2×#353—612no—
90#1961—611no—
91C2×C61—21no—
92C2×C61—21no—
93C2×C61#139311yescharacteristic
94C2×C61#141212yes—
95D61—82no—
96D61—82no—
97C2×#127—611no—
98C2×#102—1222no—
99C2×#99—1222no—
100C2×#97#692311yescharacteristic, complemented
101#382—611no—
102#353—614no—
103#353—1222no—
104C61#750411yescharacteristic, complemented, Sylow
105C22×D4—612no—
106C22×D4—2441no—
107C22×C8—21no—
108#127—612no—
109#127—611no—
110#127—611no—
111#127—2441no—
112C2×C4⋊C4—1221no—
113C2×C22⋊C4—2442no—
114C2×C42C2×#692311yescharacteristic
115#102—2444no—
116#99—1224no—
117#99—2442no—
118#97—41no—
119#95—2441no—
120C24—1222no—
121C2×D4—612no—
122C2×D4—612no—
123C2×D4—1222no—
124C2×D4—4884no—
125C2×D4—2442no—
126C2×D4—2441no—
127C2×D4—2441no—
128C2×D4—2442no—
129C2×D4—2442no—
130C22×C4—21no—
131C22×C4—4882no—
132C22×C4—2441no—
133C22×C4C22⋊#692311yescharacteristic
134C2×C8—22no—
135C2×C8—41no—
136C2×C8—41no—
137C4⋊C4—2442no—
138C22⋊C4—4882no—
139C22⋊C4—2444no—
140C42—21no—
141C42C4×#692311yescharacteristic
142C42C4⋊#692311yescharacteristic
143C23—1222no—
144C23—1222no—
145C23—4884no—
146C23—2442no—
147C23—2442no—
148C23#1451983611yescharacteristic
149D4—4882no—
150D4—4884no—
151D4—4882no—
152D4—4882no—
153D4—2442no—
154D4—2442no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—42no—
160C2×C4—9764no—
161C2×C4—4882no—
162C2×C4—4884no—
163C2×C4—4881no—
164C2×C4(C2×#6923)⋊C411yescharacteristic
165C2×C4#1451983511yescharacteristic
166C8—42no—
167C22—22no—
168C22—9762no—
169C22—4882no—
170C22—4882no—
171C22—4884no—
172C22—2442no—
173C22—2442no—
174C22#1684064011yescharacteristic
175C22#1684066711yescharacteristic
176C22#1684066911yescharacteristic
177C4—21no—
178C4—21no—
179C4—41no—
180C4—41no—
181C4—9761no—
182C4—9764no—
183C2—21no—
184C2—21no—
185C2—4882no—
186C2—4882no—
187C2#2146091311yescharacteristic
188C2#2146096012yes—
subgroupG/H
centerC22#16840669
commutatorC42×C61C42
FrattiniC2×C42C2×#6923
FittingC2×#97×C61C4
socleC22×C61#354
prime radical, cosocleC2×#14519774C22
hypercenterC2×#97#6923
hypocenterC61#7504
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
5. #16840667C4semidirect
8. #16839628C4semidirect
9. C2×#97×C61C4semidirect
100. C2×#97#6923semidirect
104. C61#7504semidirect

Maximal subgroups

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

subgroupindex
C2×#168406672
#214466432
#750461