Finite Group Databasebeta

← #30594405

Subgroups — #30594405

Order 15616.

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

normal subgroups only

This group has 248 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#21462056C211yesmaximal, characteristic
2#21461574C211yesmaximal, characteristic
3#21447432C211yesmaximal, characteristic
4D61⋊M32—21no—
5#16840748C411yescharacteristic
6#16840741C411yescharacteristic
7#16840725—21no—
8#16840659—21no—
9#16840658C412yescomplemented
10#16840644—21no—
11C2×#14519783C2211yescharacteristic
12C2×#14519717C411yescharacteristic, complemented
13#16839541—21no—
14#16839541—21no—
15C22×C16×C61C411yescharacteristic, complemented
16D61⋊M16—21no—
17#14519856—21no—
18#14519852—41no—
19#14519851—22no—
20D61⋊C16—41no—
21#14519838—21no—
22#14519837C812yes—
23#14519836—21no—
24#14519835C812yes—
25#14519831—41no—
26C8×#6923—41no—
27C2×#11758222C2×C411yescharacteristic
28#14519783—41no—
29#14519783—41no—
30C2×#11758194C2×C411yescharacteristic
31C2×#11758189D411yescharacteristic
32C2×#11758189Q811yescharacteristic
33C2×C8×D61D411yescharacteristic
34C2×C8×D61D411yescharacteristic
35#14519717—41no—
36C2×#11758185—21no—
37C22×C8×C61C2×C411yescharacteristic
38C2×C16×C61—21no—
39C2×C16×C61—41no—
40C22×C4×C61C4211yescharacteristic
41C2×C22⋊D61C2×C811yescharacteristic
42C2×C22⋊D61C2×C811yescharacteristic
43#11758222—41no—
44#11758222—41no—
45C2×D244M1611yescharacteristic
46C2×C4×D61C22⋊C411yescharacteristic
47C2×C4×D61C4⋊C411yescharacteristic
48C2×Dic122M1611yescharacteristic
49C22⋊#6923—22no—
50#11758217—22no—
51C4⋊#6923—41no—
52C4×#6923—41no—
53#11758213—41no—
54D61⋊C8—41no—
55C2×C8×C61—21no—
56C2×C8×C61—21no—
57C2×C8×C61C22⋊C411yescharacteristic
58C2×C8×C61C4⋊C411yescharacteristic
59#11758194—41no—
60C2×#92418C22⋊C411yescharacteristic
61C2×#92418C4⋊C411yescharacteristic
62#11758189—41no—
63#11758189—41no—
64C8×D61—21no—
65C8×D61—21no—
66C8×D61—21no—
67C8×D61—21no—
68#11758187—42no—
69C16×C61—41no—
70#11758185—41no—
71C23×C61C4×C811yescharacteristic
72C22×D61C22⋊C811yescharacteristic
73C22×D61C4⋊C811yescharacteristic
74C2×#6923—42no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61#9511yescharacteristic
78C2×C4×C61#9711yescharacteristic
79C22⋊D61—41no—
80C22⋊D61—41no—
81C2×Dic61C22⋊C811yescharacteristic
82C2×Dic61C4⋊C811yescharacteristic
83D244—41no—
84C4×D61—21no—
85C4×D61—21no—
86C4×D61—21no—
87C4×D61—21no—
88Dic122—41no—
89#92420—42no—
90C8×C61—21no—
91C8×C61#9911yescharacteristic
92C8×C61#9911yescharacteristic
93#92418—21no—
94#92418—21no—
95#7207—611nomaximal, Sylow
96C22×C61—21no—
97C22×C61—41no—
98C22×C61#33611yescharacteristic
99C2×D61—21no—
100C2×D61—21no—
101C2×D61—41no—
102C2×D61—41no—
103#6923—82no—
104C4×C61—21no—
105C4×C61#34211yescharacteristic
106C4×C61#34411yescharacteristic
107Dic61—21no—
108Dic61—21no—
109#2115—611no—
110#2113—611no—
111#1757—611no—
112C2×C61—21no—
113C2×C61—41no—
114C2×C61#128211yescharacteristic
115D61—41no—
116D61—41no—
117C2×#131—611no—
118C2×M32—611no—
119C2×M32—1221no—
120C22×C16#692311yescharacteristic, complemented
121#413—611no—
122#410—611no—
123#405—1221no—
124#349—612no—
125#349—1221no—
126C22⋊C16—1221no—
127C22⋊C16—1221no—
128#344—1221no—
129C61#720711yescharacteristic, complemented, Sylow
130C2×#41—611no—
131#131—2441no—
132#131—2441no—
133C2×M16—611no—
134C2×M16—611no—
135C2×M16—611no—
136C2×M16—1221no—
137C22×C8—611no—
138C22×C8—611no—
139C22×C8C2×#692311yescharacteristic
140#117—1221no—
141M32—1222no—
142M32—2441no—
143M32—2441no—
144C2×C16—21no—
145C2×C16—41no—
146C2×C16—1221no—
147C2×C16—2441no—
148#101—1221no—
149#100—612no—
150#99—612no—
151#99—1221no—
152#97—2441no—
153C4×C8—2441no—
154#41—2441no—
155#41—2441no—
156C2×Q8—611no—
157C2×D4—611no—
158C2×D4—611no—
159C2×D4—611no—
160C22×C4—611no—
161C22×C4—611no—
162C22×C4C4×#692311yescharacteristic
163M16—1222no—
164M16—2441no—
165M16—2441no—
166M16—2441no—
167M16—2441no—
168C2×C8—21no—
169C2×C8—21no—
170C2×C8—611no—
171C2×C8—611no—
172C2×C8—1221no—
173C2×C8—1221no—
174C2×C8—1221no—
175C2×C8—1221no—
176C2×C8—2441no—
177C2×C8C4⋊#692311yescharacteristic
178C2×C8C22⋊#692311yescharacteristic
179C4⋊C4—2441no—
180C22⋊C4—1222no—
181C42—2441no—
182C16—41no—
183C16—2442no—
184C16—2441no—
185C23—611no—
186C23—611no—
187C23C8×#692311yescharacteristic
188Q8—2441no—
189D4—2441no—
190D4—2441no—
191D4—2441no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—611no—
195C2×C4—611no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—1221no—
199C2×C4—1221no—
200C2×C4—2442no—
201C2×C4(C2×#6923)⋊C411yescharacteristic
202C2×C4#1451983111yescharacteristic
203C8—21no—
204C8—1221no—
205C8—1221no—
206C8—2442no—
207C8#1451983511yescharacteristic
208C8#1451983611yescharacteristic
209C22—21no—
210C22—41no—
211C22—1221no—
212C22—1221no—
213C22—2441no—
214C22—2441no—
215C22(C2×#6923)⋊C811yescharacteristic
216C4—21no—
217C4—1221no—
218C4—1221no—
219C4—4882no—
220C4#1684064011yescharacteristic
221C4#1684064411yescharacteristic
222C2—21no—
223C2—41no—
224C2—2441no—
225C2—2441no—
226C2#2146066111yescharacteristic
subgroupG/H
centerC8#14519835
commutatorC23×C61C4×C8
FrattiniC22×C8C2×#6923
FittingC22×C16×C61C4
socleC2×C61#1282
prime radicalC2×#11758222C2×C4
cosocleC2×#14519783C22
hypercenterC22×C16#6923
hypocenterC61#7207
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C8 ◁ C2×C8 ◁ C22×C8 ◁ C22×C16

Complements

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

NH ≅ G/Ntype
9. #16840658C4semidirect
12. C2×#14519717C4semidirect
15. C22×C16×C61C4semidirect
120. C22×C16#6923semidirect
129. C61#7207semidirect

Maximal subgroups

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

subgroupindex
#214620562
#214615742
#214474322
#720761