Finite Group Databasebeta

← #30605524

Subgroups — #30605524

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#21460823C212yesmaximal, complemented
4#21460822C212yesmaximal, complemented
5#21456470C211yesmaximal, characteristic
6D61⋊M32—21no—
7#16840684—21no—
8#16840659—21no—
9#16840655—21no—
10#16840654C2211yescharacteristic
11#16840654C2211yescharacteristic
12#16840654C2212yes—
13#16840368C412yes—
14#16840139C411yescharacteristic
15#16840128C2212yes—
16#16840016—21no—
17#16839999—21no—
18#16839873—21no—
19#16839844—21no—
20#16839716C2211yescharacteristic
21C61×#499C411yescharacteristic
22#14519852—22no—
23#14519851—21no—
24#14519851—21no—
25#14519851—22no—
26D61⋊C16—22no—
27C2×D488—21no—
28C2×D488—21no—
29C2×#11758189D411yescharacteristic
30C2×C8×D61D411yescharacteristic
31#14519774C2×C412yes—
32#14519762—42no—
33#14519752—22no—
34#14519752—42no—
35#14519739—22no—
36#14519734C2×C411yescharacteristic
37#14519697—22no—
38#14519697—22no—
39#14519688C2311yescharacteristic
40#14519687D411yescharacteristic
41C8×Dic61D411yescharacteristic
42#125×C61C2×C412yes—
43#107×C61—21no—
44#106×C61—21no—
45C4×C8×C61C2×C411yescharacteristic
46C2×D244—22no—
47C2×D244—42no—
48C2×D244—42no—
49C2×C4×D61—42no—
50C2×C4×D61C22⋊C411yescharacteristic
51C2×C8×C61C22⋊C411yescharacteristic
52C2×C8×C61C22⋊C411yescharacteristic
53C4⋊C4×C61—22no—
54C4⋊C4×C61—42no—
55C42×C61C22×C411yescharacteristic
56#11758198—21no—
57#11758198—42no—
58#11758198—42no—
59#11758196—21no—
60C4×Dic61C22⋊C411yescharacteristic
61C2×#92418C2×D411yescharacteristic
62C2×#92418C2×D411yescharacteristic
63D488—42no—
64D488—41no—
65D488—41no—
66#11758189—41no—
67C8×D61—21no—
68C8×D61—21no—
69#11758187—22no—
70#11758187—22no—
71#11758187—42no—
72C22×D61—42no—
73C22×D61#10011yescharacteristic
74C2×C4×C61—21no—
75C2×C4×C61—42no—
76C2×C4×C61C2×C22⋊C411yescharacteristic
77C2×Dic61—21no—
78C2×Dic61#10011yescharacteristic
79D244—42no—
80D244—42no—
81D244—162no—
82D244—162no—
83C4×D61—21no—
84C4×D61—21no—
85C4×D61—162no—
86C8×C61—21no—
87C8×C61#10411yescharacteristic
88C8×C61#10411yescharacteristic
89#92418—21no—
90#92418—21no—
91#11913—611nomaximal, Sylow
92C22×C61C2×#10011yescharacteristic
93C2×D61—21no—
94C2×D61—41no—
95C2×D61—82no—
96C2×D61—82no—
97C2×D61—82no—
98C4×C61—41no—
99C4×C61—82no—
100C4×C61C2×#10411yescharacteristic
101C4×C61#42111yescharacteristic
102Dic61—21no—
103Dic61—41no—
104#3176—611no—
105#2166—611no—
106#2110—611no—
107#1355—612no—
108#1355—612no—
109C2×C61—21no—
110C2×C61#153011yescharacteristic
111D61—41no—
112D61—162no—
113#540—612no—
114C2×M32—1221no—
115#499#692311yescharacteristic
116#493—611no—
117#490—612no—
118#469—1221no—
119#466—1221no—
120#442—1221no—
121C4×D8—1221no—
122#405—611no—
123#364—1221no—
124#349—1221no—
125#347—611no—
126#347—611no—
127#347—612no—
128#347—1221no—
129C61#1191311yescharacteristic, complemented, Sylow
130C2×D8—1221no—
131C2×D8—1221no—
132C2×M16—611no—
133C22×C8—611no—
134#127—612no—
135#125C2×#692312yes—
136#123—2442no—
137#121—1222no—
138#121—2442no—
139C4×D4—1222no—
140#117—611no—
141M32—1221no—
142M32—1221no—
143M32—1222no—
144M32—1222no—
145C2×C16—1222no—
146#107—21no—
147#106—21no—
148#102—1222no—
149#102—1222no—
150#97—611no—
151#97—611no—
152C4×C8—611no—
153C4×C8C2×#692311yescharacteristic
154C2×D4—1222no—
155C2×D4—2442no—
156C2×D4—2442no—
157C22×C4—611no—
158C22×C4—2442no—
159D8—2442no—
160D8—2441no—
161D8—2441no—
162M16—2441no—
163C2×C8—611no—
164C2×C8—611no—
165C2×C8—1221no—
166C2×C8—1221no—
167C2×C8C22⋊#692311yescharacteristic
168C2×C8C22⋊#692311yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—42no—
171C4⋊C4—1221no—
172C22⋊C4—1221no—
173C22⋊C4—2442no—
174C22⋊C4—2442no—
175C42—611no—
176C42C22×#692311yescharacteristic
177C16—1222no—
178C16—1222no—
179C16—2442no—
180C23—611no—
181C23—2442no—
182D4—9762no—
183D4—9762no—
184D4—2442no—
185D4—2442no—
186C2×C4—21no—
187C2×C4—42no—
188C2×C4—611no—
189C2×C4—1221no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—9762no—
193C2×C4C2×C22⋊#692311yescharacteristic
194C8—21no—
195C8—1221no—
196C8—1221no—
197C8#1451984211yescharacteristic
198C8#1451984211yescharacteristic
199C22—1221no—
200C22—4882no—
201C22—4882no—
202C22—4882no—
203C22—2441no—
204C22D61⋊#10011yescharacteristic
205C4—41no—
206C4—82no—
207C4—1221no—
208C4—2441no—
209C4C2×#1451984211yescharacteristic
210C4#1684076111yescharacteristic
211C2—21no—
212C2—9762no—
213C2—2441no—
214C2#2146129011yescharacteristic
subgroupG/H
centerC2#21461290
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#499C4
socleC2×C61#1530
prime radical#21456470C2
cosocle#14519688C23
hypercenter#499#6923
hypocenterC61#11913
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #499

Complements

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

NH ≅ G/Ntype
1. #21462194C2semidirect
2. #21462041C2semidirect
3. #21460823C2semidirect
4. #21460822C2semidirect
129. C61#11913semidirect

Maximal subgroups

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

subgroupindex
#214621942
#214620412
#214608232
#214608222
#214564702
#1191361