Finite Group Databasebeta

← #30595010

Subgroups — #30595010

Order 15616.

196 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 36 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#21460916C211yesmaximal, characteristic
2#21460750C211yesmaximal, characteristic
3#21446967C211yesmaximal, characteristic
4C2×#14519838—21no—
5#16840607—21no—
6C2×#14519700—21no—
7#16839668C2211yescharacteristic
8#16839524—21no—
9#16839517C411yescharacteristic
10C2×#125×C61C411yescharacteristic
11C2×#11758217—41no—
12#14519838—22no—
13#14519838—41no—
14C22⋊#92420—41no—
15C22×Dic122D411yescharacteristic
16C22×#92418—21no—
17C2×C4⋊Dic61D411yescharacteristic
18#14519700—42no—
19#14519684—41no—
20#125×C61—42no—
21C2×C4⋊C4×C61—21no—
22C2×C4⋊C4×C61—41no—
23C2×C42×C61C2×C411yescharacteristic
24C22×C4×C61—21no—
25C22×C4×C61—41no—
26C22×C4×C61C22⋊C411yescharacteristic
27C22×Dic61—21no—
28C22×Dic61—21no—
29C2×Dic122—21no—
30C2×Dic122—41no—
31C2×Dic122—41no—
32C2×Dic122SD1611yescharacteristic
33C2×Dic122Q1611yescharacteristic
34#11758217—42no—
35#11758217—81no—
36C2×#92420—81no—
37C2×#92420—81no—
38C4⋊C4×C61—22no—
39C4⋊C4×C61—41no—
40C4⋊C4×C61—42no—
41C4⋊C4×C61—42no—
42C42×C61—41no—
43C4⋊Dic61—41no—
44C2×#92418—41no—
45C2×#92418—41no—
46C2×#92418—41no—
47C23×C61#9911yescharacteristic
48C2×C4×C61—21no—
49C2×C4×C61—21no—
50C2×C4×C61—41no—
51C2×C4×C61—41no—
52C2×C4×C61—41no—
53C2×C4×C61—42no—
54C2×C4×C61—81no—
55C2×C4×C61—81no—
56C2×C4×C61#10311yescharacteristic
57C2×C4×C61#10411yescharacteristic
58C2×Dic61—21no—
59C2×Dic61—21no—
60C2×Dic61—41no—
61C2×Dic61—41no—
62C2×Dic61—41no—
63C2×Dic61—81no—
64Dic122—41no—
65Dic122—41no—
66Dic122—81no—
67#92420—82no—
68#92420—161no—
69#92418—81no—
70#7429—611nomaximal, Sylow
71C22×C61—21no—
72C22×C61—21no—
73C22×C61#32811yescharacteristic
74C22×C61AΣL(1,𝔽16)11yescharacteristic
75C22×C61#35411yescharacteristic
76C4×C61—21no—
77C4×C61—21no—
78C4×C61—81no—
79C4×C61—82no—
80Dic61—41no—
81Dic61—41no—
82Dic61—81no—
83#2026—611no—
84#1394—611no—
85#1319—611no—
86C2×C61—21no—
87C2×C61—21no—
88C2×C61#135111yescharacteristic
89C2×C61#141311yescharacteristic
90C2×C61#141411yescharacteristic
91C2×#125#692311yescharacteristic
92C2×#103—1221no—
93C2×#101—1221no—
94#391—611no—
95#340—1221no—
96#336—611no—
97#324—1221no—
98C61#742911yescharacteristic, complemented, Sylow
99C22×Q8—611no—
100C2×M16—2441no—
101C22×C8—1221no—
102#125—42no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—611no—
106C2×C42C2×#692311yescharacteristic
107#103—2442no—
108#101—1222no—
109#101—2441no—
110C22⋊C8—2441no—
111#95—2441no—
112C2×Q8—611no—
113C2×Q8—611no—
114C2×Q8—1221no—
115C2×Q8—2441no—
116C2×Q8—2441no—
117C22×C4—21no—
118C22×C4—41no—
119C22×C4—1221no—
120C22×C4—1221no—
121C22×C4C22⋊#692311yescharacteristic
122M16—4881no—
123M16—2442no—
124C2×C8—4881no—
125C2×C8—4881no—
126C2×C8—2441no—
127C2×C8—2441no—
128C2×C8—2441no—
129C4⋊C4—22no—
130C4⋊C4—41no—
131C4⋊C4—42no—
132C4⋊C4—42no—
133C4⋊C4—2441no—
134C42—41no—
135C23#1451983511yescharacteristic
136Q8—4881no—
137Q8—2441no—
138Q8—2441no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—42no—
145C2×C4—81no—
146C2×C4—81no—
147C2×C4—1221no—
148C2×C4—1221no—
149C2×C4—4881no—
150C2×C4—2441no—
151C2×C4—2441no—
152C2×C4—2441no—
153C2×C4#1451984011yescharacteristic
154C2×C4#1451984211yescharacteristic
155C8—9761no—
156C8—4881no—
157C8—4882no—
158C22—21no—
159C22—21no—
160C22#1684061611yescharacteristic
161C22#1684066211yescharacteristic
162C22#1684066811yescharacteristic
163C4—21no—
164C4—21no—
165C4—81no—
166C4—82no—
167C4—4881no—
168C4—2441no—
169C4—2441no—
170C2—21no—
171C2—21no—
172C2#2146081411yescharacteristic
173C2#2146096211yescharacteristic
174C2#2146096411yescharacteristic
subgroupG/H
centerC22#16840668
commutatorC2×C42×C61C2×C4
FrattiniC2×C42C2×#6923
FittingC2×#125×C61C4
socleC22×C61#354
prime radicalC23×C61#99
cosocle#16839668C22
hypercenterC2×#125#6923
hypocenterC61#7429
LCSG ▷ C2×C42×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
98. C61#7429semidirect

Maximal subgroups

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

subgroupindex
#214609162
#214607502
#214469672
#742961