Finite Group Databasebeta

← #30595014

Subgroups — #30595014

Order 15616.

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

normal subgroups only

This group has 206 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#21460917C211yesmaximal, characteristic
2#21460640C211yesmaximal, characteristic
3#21446981C211yesmaximal, characteristic
4C2×#14519838—21no—
5#16840628—21no—
6#16840393C411yescharacteristic
7#16839772—21no—
8#16839667C2211yescharacteristic
9#16839523—21no—
10C61×#343C411yescharacteristic
11C2×#11758217—41no—
12C22×#92420—41no—
13#14519838—22no—
14#14519838—41no—
15C22×Dic122D411yescharacteristic
16#14519776—41no—
17#14519768—41no—
18#14519756—41no—
19#14519736—21no—
20C2×C4×Dic61D411yescharacteristic
21#14519702—41no—
22#14519702—41no—
23#14519684—41no—
24C2×M16×C61—21no—
25C2×C4⋊C4×C61C2×C411yescharacteristic
26C22×C4×C61—21no—
27C22×C4×C61C22⋊C411yescharacteristic
28C22×Dic61—21no—
29C22×Dic61—21no—
30C2×Dic122—21no—
31C2×Dic122—41no—
32C2×Dic122—41no—
33C2×Dic122—41no—
34C2×Dic122SD1611yescharacteristic
35C2×Dic122Q1611yescharacteristic
36#11758217—42no—
37#11758217—81no—
38C2×#92420—42no—
39C2×#92420—81no—
40C2×#92420—81no—
41C2×#92420—81no—
42M16×C61—41no—
43M16×C61—41no—
44C2×C8×C61—41no—
45C4⋊C4×C61—41no—
46C22⋊Dic61—41no—
47C4⋊Dic61—21no—
48C4⋊Dic61—21no—
49C4⋊Dic61—41no—
50#11758196—42no—
51C4×Dic61—41no—
52C4×Dic61—41no—
53C23×C61#9911yescharacteristic
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—41no—
57C2×C4×C61—81no—
58C2×C4×C61#10311yescharacteristic
59C2×C4×C61#10411yescharacteristic
60C2×Dic61—21no—
61C2×Dic61—21no—
62C2×Dic61—21no—
63C2×Dic61—21no—
64C2×Dic61—41no—
65C2×Dic61—41no—
66C2×Dic61—41no—
67C2×Dic61—41no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70Dic122—41no—
71Dic122—41no—
72Dic122—81no—
73Dic122—161no—
74#92420—82no—
75#92420—82no—
76C8×C61—81no—
77#7431—611nomaximal, Sylow
78C22×C61—21no—
79C22×C61—21no—
80C22×C61#32811yescharacteristic
81C22×C61AΣL(1,𝔽16)11yescharacteristic
82C22×C61#35411yescharacteristic
83C4×C61—21no—
84C4×C61—21no—
85C4×C61—81no—
86Dic61—41no—
87Dic61—41no—
88Dic61—41no—
89Dic61—41no—
90Dic61—81no—
91Dic61—81no—
92#2028—611no—
93#1394—611no—
94#1272—611no—
95C2×C61—21no—
96C2×C61—21no—
97C2×C61#135111yescharacteristic
98C2×C61#140311yescharacteristic
99C2×C61#140511yescharacteristic
100#544—611no—
101#419—1221no—
102C2×#101—1221no—
103#391—611no—
104#343#692311yescharacteristic
105#339—1221no—
106#336—1221no—
107C61#743111yescharacteristic, complemented, Sylow
108C22×Q8—611no—
109C2×M16—21no—
110C2×M16—2441no—
111C22×C8—2441no—
112C4⋊Q8—2441no—
113#125—2441no—
114C22⋊Q8—2441no—
115#117—1221no—
116C2×C4⋊C4C2×#692311yescharacteristic
117C2×C42—611no—
118#103—2441no—
119#103—2441no—
120#101—1222no—
121#101—2441no—
122#95—2441no—
123C2×Q8—611no—
124C2×Q8—611no—
125C2×Q8—1221no—
126C2×Q8—2441no—
127C2×Q8—2441no—
128C2×Q8—2441no—
129C22×C4—21no—
130C22×C4—1221no—
131C22×C4—1221no—
132C22×C4C22⋊#692311yescharacteristic
133M16—41no—
134M16—41no—
135M16—4881no—
136M16—2442no—
137C2×C8—41no—
138C2×C8—4881no—
139C2×C8—4881no—
140C2×C8—4881no—
141C2×C8—2442no—
142C4⋊C4—41no—
143C4⋊C4—1221no—
144C4⋊C4—1221no—
145C4⋊C4—2441no—
146C4⋊C4—2442no—
147C22⋊C4—2441no—
148C42—2441no—
149C42—2441no—
150C23#1451983611yescharacteristic
151Q8—9761no—
152Q8—4881no—
153Q8—2441no—
154Q8—2441no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—81no—
159C2×C4—1221no—
160C2×C4—1221no—
161C2×C4—1221no—
162C2×C4—1221no—
163C2×C4—2441no—
164C2×C4—2441no—
165C2×C4—2441no—
166C2×C4—2441no—
167C2×C4—2441no—
168C2×C4—2441no—
169C2×C4#1451984011yescharacteristic
170C2×C4#1451984111yescharacteristic
171C8—81no—
172C8—4882no—
173C8—4882no—
174C22—21no—
175C22—21no—
176C22#1684061511yescharacteristic
177C22#1684066311yescharacteristic
178C22#1684066911yescharacteristic
179C4—21no—
180C4—21no—
181C4—81no—
182C4—4881no—
183C4—4881no—
184C4—2441no—
185C4—2441no—
186C4—2441no—
187C4—2441no—
188C2—21no—
189C2—21no—
190C2#2146081311yescharacteristic
191C2#2146094111yescharacteristic
192C2#2146094511yescharacteristic
subgroupG/H
centerC22#16840663
commutatorC2×C4⋊C4×C61C2×C4
FrattiniC2×C4⋊C4C2×#6923
FittingC61×#343C4
socleC22×C61AΣL(1,𝔽16)
prime radicalC23×C61#99
cosocle#16839667C22
hypercenter#343#6923
hypocenterC61#7431
LCSG ▷ C2×C4⋊C4×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4 ◁ #343

Complements

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

NH ≅ G/Ntype
107. C61#7431semidirect

Maximal subgroups

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

subgroupindex
#214609172
#214606402
#214469812
#743161