Finite Group Databasebeta

← #29566633

Subgroups — #29566633

Order 15616.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#21445885C211yesmaximal, characteristic
2#21443743C211yesmaximal, characteristic
3C61×#1314C211yesmaximal, characteristic
4C22×C4×Dic61C411yescharacteristic
5C2×C22⋊#92418C411yescharacteristic
6C22⋊#11758185—21no—
7#16839516—21no—
8#16839516—21no—
9C2×C22⋊C8×C61C2211yescharacteristic
10C61×C22⋊C16—21no—
11C23×Dic61C811yescharacteristic
12C23×Dic61C811yescharacteristic
13C22×#92418—21no—
14C2×C4×Dic61—21no—
15C2×C4×Dic61—21no—
16C2×C4×Dic61—41no—
17C2×C4×Dic61—41no—
18C2×#11758185—41no—
19C22⋊#92418—41no—
20C23×C4×C61C2×C411yescharacteristic
21C22×C8×C61D411yescharacteristic
22C22×C8×C61D411yescharacteristic
23C2×C16×C61—41no—
24C22⋊C8×C61—41no—
25C24×C61C2×C811yescharacteristic
26C22×C4×C61—21no—
27C22×C4×C61—21no—
28C22×C4×C61—41no—
29C22×C4×C61—41no—
30C22×C4×C61C22⋊C411yescharacteristic
31C22×C4×C61M1611yescharacteristic
32C22×Dic61—21no—
33C22×Dic61—21no—
34C22×Dic61—21no—
35C22×Dic61—42no—
36C22×Dic61—41no—
37C22×Dic61—41no—
38C22×Dic61—41no—
39C22×Dic61C1612yescomplemented
40C2×C8×C61—21no—
41C2×C8×C61—21no—
42C2×C8×C61—41no—
43C2×C8×C61—41no—
44C4×Dic61—42no—
45C4×Dic61—41no—
46C4×Dic61—41no—
47C2×#92418—41no—
48C2×#92418—41no—
49C2×#92418—41no—
50C16×C61—81no—
51#11758185—81no—
52C23×C61—21no—
53C23×C61—21no—
54C23×C61—41no—
55C23×C61—41no—
56C23×C61C22⋊C811yescharacteristic
57C23×C61C2×C1611yescharacteristic
58C23×C61M3211yescharacteristic
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—21no—
62C2×C4×C61—42no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61#9911yescharacteristic
67C2×C4×C61#10011yescharacteristic
68C2×Dic61—22no—
69C2×Dic61—22no—
70C2×Dic61—42no—
71C2×Dic61—41no—
72C2×Dic61—42no—
73C2×Dic61—41no—
74C2×Dic61—41no—
75C2×Dic61—41no—
76C2×Dic61—42no—
77C2×Dic61—42no—
78C8×C61—41no—
79C8×C61—41no—
80#92418—81no—
81#7055—611nomaximal, Sylow
82C22×C61—21no—
83C22×C61—21no—
84C22×C61—21no—
85C22×C61—21no—
86C22×C61—41no—
87C22×C61—41no—
88C22×C61—42no—
89C22×C61—41no—
90C22×C61—41no—
91C22×C61#32311yescharacteristic
92C22×C61C22⋊C1611yescharacteristic
93C22×C61#34911yescharacteristic
94C4×C61—21no—
95C4×C61—41no—
96C4×C61#35211yescharacteristic
97C4×C61#35211yescharacteristic
98Dic61—42no—
99Dic61—42no—
100#1817—611no—
101#1314—611no—
102#1314D6111yescharacteristic
103C2×C61—21no—
104C2×C61—21no—
105C2×C61—41no—
106C2×C61—41no—
107C2×C61#131411yescharacteristic
108C2×C61#131711yescharacteristic
109C2×C61#132011yescharacteristic
110C22×C42—611no—
111C2×C22⋊C8—611no—
112C2×C22⋊C8C2×D6111yescharacteristic
113C22⋊C16—21no—
114C22⋊C16—1221no—
115#336—1221no—
116#336—1221no—
117C61#705511yescharacteristic, complemented, Sylow
118C23×C4—611no—
119C23×C4—611no—
120C23×C4C4×D6111yescharacteristic
121C22×C8—1221no—
122C22×C8D24411yescharacteristic
123C22×C8C22⋊D6111yescharacteristic
124C2×C42—1221no—
125C2×C42—1221no—
126C2×C42—2441no—
127C2×C42—2441no—
128C2×C16—41no—
129C2×C16—2441no—
130C22⋊C8—41no—
131C22⋊C8—2441no—
132C24C8×D6111yescharacteristic
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—41no—
136C22×C4—41no—
137C22×C4—612no—
138C22×C4—1221no—
139C22×C4—1221no—
140C22×C4—1221no—
141C22×C4—2442no—
142C22×C4—2441no—
143C22×C4—2441no—
144C22×C4—2441no—
145C22×C4#1175818911yescharacteristic
146C22×C4#1175819811yescharacteristic
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—41no—
150C2×C8—41no—
151C2×C8—2441no—
152C2×C8—2441no—
153C2×C8—2441no—
154C42—2442no—
155C42—2441no—
156C42—2441no—
157C16—81no—
158C16—4881no—
159C23—21no—
160C23—21no—
161C23—41no—
162C23—41no—
163C23#1451968911yescharacteristic
164C23C16×D6111yescharacteristic
165C23#1451971611yescharacteristic
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—1222no—
174C2×C4—1222no—
175C2×C4—2442no—
176C2×C4—2441no—
177C2×C4—2442no—
178C2×C4—2441no—
179C2×C4—2441no—
180C2×C4—2441no—
181C2×C4—2442no—
182C2×C4—2442no—
183C2×C4#1451969111yescharacteristic
184C2×C4#1451969311yescharacteristic
185C8—41no—
186C8—41no—
187C8—4881no—
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—41no—
193C22—41no—
194C22—42no—
195C22—41no—
196C22—41no—
197C22#1683948511yescharacteristic
198C22#1683954111yescharacteristic
199C22#1683954311yescharacteristic
200C4—21no—
201C4—41no—
202C4—2442no—
203C4—2442no—
204C4#1683955111yescharacteristic
205C4#1683955311yescharacteristic
206C2—21no—
207C2—21no—
208C2—41no—
209C2—41no—
210C2#2144374211yescharacteristic
211C2#2144374811yescharacteristic
212C2#2144375411yescharacteristic
subgroupG/H
centerC2×C4#14519691
commutatorC23×C61C2×C16
FrattiniC2×C22⋊C8C2×D61
FittingC61×#1314C2
socleC22×C61#323
prime radicalC24×C61C2×C8
cosocleC2×C22⋊C8×C61C22
hypercenter#1314D61
hypocenterC61#7055
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
39. C22×Dic61C16semidirect
117. C61#7055semidirect

Maximal subgroups

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

subgroupindex
#214458852
#214437432
C61×#13142
#705561