Finite Group Databasebeta

← #30605523

Subgroups — #30605523

Order 15616.

296 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 62 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#21462194C211yesmaximal, characteristic, complemented
2#21462041C211yesmaximal, characteristic, complemented
3#21460821C214yesmaximal, complemented
4#21456466C211yesmaximal, characteristic
5D61⋊M32—21no—
6#16840684—21no—
7#16840659—21no—
8#16840655—21no—
9#16840654C2212yes—
10#16840654C2212yes—
11#16840366C412yes—
12#16840164C411yescharacteristic
13#16840126C2212yes—
14#16840012—21no—
15#16839995—21no—
16#16839874—21no—
17D8×Dic61—21no—
18#16839716C2211yescharacteristic
19C61×#493C411yescharacteristic
20#14519852—22no—
21#14519851—22no—
22#14519851—22no—
23D61⋊C16—22no—
24C2×#11758189D411yescharacteristic
25C2×C8×D61D411yescharacteristic
26#14519769C2×C412yes—
27#14519758—42no—
28#14519749—42no—
29#14519748—22no—
30D4×Dic61—22no—
31#14519734C2×C411yescharacteristic
32#14519711—21no—
33#14519709—21no—
34#14519698—22no—
35#14519698—22no—
36#14519688C2311yescharacteristic
37#14519687D411yescharacteristic
38C8×Dic61D411yescharacteristic
39C2×D8×C61—21no—
40C2×D8×C61—21no—
41#127×C61C2×C412yes—
42C4×C8×C61C2×C411yescharacteristic
43C2×D4×C61—22no—
44C2×D4×C61—42no—
45C2×C22⋊D61—42no—
46C22×Dic61—42no—
47C2×C4×D61C22⋊C411yescharacteristic
48D8×C61—42no—
49D8×C61—41no—
50D8×C61—41no—
51C2×C8×C61C22⋊C411yescharacteristic
52C2×C8×C61C22⋊C411yescharacteristic
53C42×C61C22×C411yescharacteristic
54C22⋊Dic61—42no—
55C22⋊Dic61—42no—
56#11758198—21no—
57C4⋊Dic61—22no—
58#11758196—21no—
59#11758196—42no—
60C4×Dic61C22⋊C411yescharacteristic
61C2×#92418C2×D411yescharacteristic
62C2×#92418C2×D411yescharacteristic
63#11758189—41no—
64C8×D61—21no—
65C8×D61—21no—
66#11758187—24no—
67#11758187—42no—
68C23×C61—42no—
69C22×D61#10011yescharacteristic
70D4×C61—42no—
71D4×C61—42no—
72D4×C61—162no—
73C2×C4×C61—21no—
74C2×C4×C61C2×C22⋊C411yescharacteristic
75C22⋊D61—162no—
76C2×Dic61—21no—
77C2×Dic61—42no—
78C2×Dic61—162no—
79C2×Dic61#10011yescharacteristic
80C4×D61—21no—
81C4×D61—21no—
82C8×C61—21no—
83C8×C61#10411yescharacteristic
84C8×C61#10411yescharacteristic
85#92418—21no—
86#92418—21no—
87#11913—611nomaximal, Sylow
88C22×C61—82no—
89C22×C61—82no—
90C22×C61—82no—
91C22×C61C2×#10011yescharacteristic
92C2×D61—21no—
93C2×D61—41no—
94C4×C61—41no—
95C4×C61C2×#10411yescharacteristic
96C4×C61#42111yescharacteristic
97Dic61—21no—
98Dic61—41no—
99Dic61—82no—
100#3176—611no—
101#2166—611no—
102#2110—611no—
103#1355—614no—
104C2×C61—21no—
105C2×C61—162no—
106C2×C61#153011yescharacteristic
107D61—41no—
108#540—612no—
109C2×M32—1221no—
110#499—611no—
111#493#692311yescharacteristic
112#490—612no—
113#469—1221no—
114#466—1221no—
115#442—1221no—
116C4×D8—1221no—
117#405—611no—
118#364—1221no—
119#349—1221no—
120#347—612no—
121#347—612no—
122#347—1221no—
123C61#1191311yescharacteristic, complemented, Sylow
124C2×D8—21no—
125C2×D8—21no—
126C2×M16—611no—
127C22×C8—611no—
128#127C2×#692312yes—
129#125—612no—
130#123—2442no—
131#121—1222no—
132#121—2442no—
133C4×D4—1222no—
134#117—611no—
135M32—1222no—
136M32—1222no—
137M32—1222no—
138C2×C16—1222no—
139#107—1221no—
140#106—1221no—
141#102—1222no—
142#102—1222no—
143#97—611no—
144#97—611no—
145C4×C8—611no—
146C4×C8C2×#692311yescharacteristic
147C2×D4—22no—
148C2×D4—42no—
149C2×D4—2442no—
150C22×C4—611no—
151C22×C4—2442no—
152D8—42no—
153D8—41no—
154D8—41no—
155M16—2441no—
156C2×C8—611no—
157C2×C8—611no—
158C2×C8—1221no—
159C2×C8—1221no—
160C2×C8C22⋊#692311yescharacteristic
161C2×C8C22⋊#692311yescharacteristic
162C4⋊C4—1221no—
163C4⋊C4—1222no—
164C4⋊C4—2442no—
165C22⋊C4—1221no—
166C22⋊C4—2442no—
167C22⋊C4—2442no—
168C42—611no—
169C42C22×#692311yescharacteristic
170C16—1224no—
171C16—2442no—
172C23—42no—
173C23—611no—
174D4—42no—
175D4—42no—
176D4—162no—
177D4—9762no—
178C2×C4—21no—
179C2×C4—611no—
180C2×C4—1221no—
181C2×C4—1221no—
182C2×C4—1221no—
183C2×C4—9762no—
184C2×C4—2442no—
185C2×C4C2×C22⋊#692311yescharacteristic
186C8—21no—
187C8—1221no—
188C8—1221no—
189C8#1451984111yescharacteristic
190C8#1451984111yescharacteristic
191C22—82no—
192C22—82no—
193C22—82no—
194C22—1221no—
195C22—2441no—
196C22D61⋊#10011yescharacteristic
197C4—41no—
198C4—1221no—
199C4—4882no—
200C4—2441no—
201C4C2×#1451984111yescharacteristic
202C4#1684076011yescharacteristic
203C2—21no—
204C2—162no—
205C2—2441no—
206C2#2146128911yescharacteristic
subgroupG/H
centerC2#21461289
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#493C4
socleC2×C61#1530
prime radical#21456466C2
cosocle#14519688C23
hypercenter#493#6923
hypocenterC61#11913
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #21462194C2semidirect
2. #21462041C2semidirect
3. #21460821C2semidirect
123. C61#11913semidirect

Maximal subgroups

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

subgroupindex
#214621942
#214620412
#214608212
#214564662
#1191361