Finite Group Databasebeta

← #30594601

Subgroups — #30594601

Order 15616.

218 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 54 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#21462036C211yesmaximal, characteristic
2#21461742C211yesmaximal, characteristic
3#347×D61C211yesmaximal, characteristic
4D61⋊M32—21no—
5#16840708C411yescharacteristic
6#16840706C411yescharacteristic
7#16840655—21no—
8#16840654C412yescomplemented
9#16840636—21no—
10#16840636—21no—
11M32×D61—21no—
12#97×D61C2211yescharacteristic
13#16839540C411yescharacteristic, complemented
14#16839539—21no—
15C61×#347C411yescharacteristic, complemented
16C2×C4⋊#6923—21no—
17C2×C4⋊#6923—21no—
18C2×C4⋊#6923—41no—
19#14519852—22no—
20#14519851—22no—
21D61⋊C16—22no—
22(C2×#6923)⋊C4—41no—
23C2×C8×D61D411yescharacteristic
24C2×C8×D61D411yescharacteristic
25C42×D61C2×C411yescharacteristic
26#14519717—21no—
27#14519716—22no—
28C16×D61—22no—
29#14519688C2×C411yescharacteristic
30#14519687D411yescharacteristic
31#14519687Q811yescharacteristic
32M32×C61—21no—
33#97×C61C2×C411yescharacteristic
34C22×#6923—41no—
35C22×#6923—41no—
36C2×C4×D61—21no—
37C2×C4×D61C22⋊C411yescharacteristic
38C4⋊#6923—41no—
39C4⋊#6923—41no—
40C4⋊#6923—41no—
41C4⋊#6923—41no—
42C4⋊#6923—82no—
43C2×C8×C61C22⋊C411yescharacteristic
44C2×C8×C61C4⋊C411yescharacteristic
45C42×C61C4211yescharacteristic
46C4×Dic61—21no—
47C4×Dic61C4⋊C411yescharacteristic
48C2×#92418C22⋊C411yescharacteristic
49C2×#92418C4⋊C411yescharacteristic
50C8×D61—21no—
51C8×D61—21no—
52C8×D61—21no—
53C8×D61—21no—
54#11758187—24no—
55C16×C61—22no—
56#11758185—22no—
57C22×D61#10011yescharacteristic
58C2×#6923—82no—
59C2×#6923—81no—
60C2×#6923—81no—
61C2×#6923—81no—
62C2×#6923—81no—
63C2×C4×C61—21no—
64C2×C4×C61#9511yescharacteristic
65C2×Dic61—21no—
66C2×Dic61#10111yescharacteristic
67C4×D61—41no—
68C4×D61—41no—
69C4×D61#10411yescharacteristic
70C4×D61#10411yescharacteristic
71C4×D61#10411yescharacteristic
72C4×D61#10411yescharacteristic
73C8×C61—21no—
74C8×C61—21no—
75#92418—21no—
76#92418—21no—
77#7266—611nomaximal, Sylow
78C22×C61#34311yescharacteristic
79C2×D61—21no—
80C2×D61—21no—
81C2×D61#32911yescharacteristic
82C2×D61#32911yescharacteristic
83#6923—161no—
84#6923—161no—
85C4×C61—41no—
86C4×C61#33911yescharacteristic
87C4×C61#33911yescharacteristic
88Dic61—41no—
89Dic61#33011yescharacteristic
90Dic61#33011yescharacteristic
91C2×#347—611no—
92C2×#347—611no—
93#1836—611no—
94C2×C61—21no—
95C2×C61#129511yescharacteristic
96D61—21no—
97D61#135511yescharacteristic
98D61#135611yescharacteristic
99C2×M32—1221no—
100C2×M32—1221no—
101C2×#97—611no—
102#384—611no—
103#382—611no—
104#347—612no—
105#347—611no—
106#347—1221no—
107#347—1221no—
108#347#692311yescharacteristic, complemented
109#340—1221no—
110#340—1221no—
111C61#726611yescharacteristic, complemented, Sylow
112C22×C8—611no—
113C22×C8—611no—
114C2×C4⋊C4—1221no—
115C2×C4⋊C4—1221no—
116C2×C4⋊C4—2441no—
117C2×C42—611no—
118M32—21no—
119M32—1222no—
120M32—1222no—
121M32—1222no—
122M32—1221no—
123C2×C16—1222no—
124C2×C16—1222no—
125#97—611no—
126#97—611no—
127#97—611no—
128#97C2×#692311yescharacteristic
129#95—2441no—
130C22×C4—611no—
131C22×C4—1221no—
132C22×C4—2441no—
133C22×C4—2441no—
134C2×C8—611no—
135C2×C8—611no—
136C2×C8—1221no—
137C2×C8—1221no—
138C2×C8—1221no—
139C2×C8—1221no—
140C2×C8C4⋊#692311yescharacteristic
141C2×C8C22⋊#692311yescharacteristic
142C4⋊C4—4882no—
143C4⋊C4—2441no—
144C4⋊C4—2441no—
145C4⋊C4—2441no—
146C4⋊C4—2441no—
147C42—611no—
148C42—1221no—
149C42C4×#692311yescharacteristic
150C16—22no—
151C16—1222no—
152C16—1224no—
153C23—611no—
154C2×C4—21no—
155C2×C4—611no—
156C2×C4—611no—
157C2×C4—611no—
158C2×C4—611no—
159C2×C4—611no—
160C2×C4—1221no—
161C2×C4—4881no—
162C2×C4—4881no—
163C2×C4—4882no—
164C2×C4—4881no—
165C2×C4—4881no—
166C2×C4—2441no—
167C2×C4—2441no—
168C2×C4(C2×#6923)⋊C411yescharacteristic
169C8—21no—
170C8—21no—
171C8—1221no—
172C8—1221no—
173C22—611no—
174C22—611no—
175C22—1221no—
176C22—1221no—
177C22#1684064111yescharacteristic
178C4—41no—
179C4—611no—
180C4—611no—
181C4—9761no—
182C4—9761no—
183C4—2441no—
184C4#1684063311yescharacteristic
185C4#1684063411yescharacteristic
186C2—21no—
187C2—611no—
188C2—611no—
189C2—1221no—
190C2#2146069611yescharacteristic
subgroupG/H
centerC2#21460696
commutatorC42×C61C42
Frattini#97C2×#6923
FittingC61×#347C4
socleC2×C61#1295
prime radicalC22×D61#100
cosocle#97×D61C22
hypercenter#347#6923
hypocenterC61#7266
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #347

Complements

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

NH ≅ G/Ntype
8. #16840654C4semidirect
13. #16839540C4semidirect
15. C61×#347C4semidirect
108. #347#6923semidirect
111. C61#7266semidirect

Maximal subgroups

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

subgroupindex
#214620362
#214617422
#347×D612
#726661