Finite Group Databasebeta

← #29566688

Subgroups — #29566688

Order 15616.

218 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 49 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#21447247C211yesmaximal, characteristic
2#21443743C211yesmaximal, characteristic
3C61×#1289C211yesmaximal, characteristic
4C2×#14519711C411yescharacteristic, complemented
5#16839622—21no—
6C22⋊#11758185—21no—
7#16839525—21no—
8#16839525C411yescharacteristic, complemented
9C2×C22⋊C8×C61C2211yescharacteristic
10C61×#380—21no—
11C2×C4⋊Dic61—21no—
12C2×C4⋊Dic61—21no—
13C2×C22⋊Dic61—41no—
14C2×#11758185—41no—
15#14519711—41no—
16#14519684—41no—
17C23×C4×C61D411yescharacteristic
18C22×C8×C61C2×C411yescharacteristic
19C22×C8×C61D411yescharacteristic
20C2×C4⋊C4×C61—41no—
21C2×C22⋊C4×C61—41no—
22C22⋊C8×C61—41no—
23#95×C61—22no—
24C24×C61D811yescharacteristic
25C22×C4×C61—21no—
26C22×C4×C61—21no—
27C22×C4×C61—41no—
28C22×C4×C61—41no—
29C22×C4×C61—42no—
30C22×C4×C61C22⋊C411yescharacteristic
31C22×C4×C61SD1611yescharacteristic
32C22×Dic61—41no—
33C22×Dic61—41no—
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C2×C8×C61—41no—
37C2×C8×C61—41no—
38C4⋊C4×C61—81no—
39C4⋊C4×C61—81no—
40C22⋊C4×C61—81no—
41C22⋊C4×C61—81no—
42C22⋊Dic61—82no—
43C4⋊Dic61—41no—
44C4⋊Dic61—41no—
45C4⋊Dic61—41no—
46C4⋊Dic61—41no—
47#11758185—81no—
48C23×C61—21no—
49C23×C61—21no—
50C23×C61—41no—
51C23×C61—41no—
52C23×C61#10211yescharacteristic
53C23×C61SD3211yescharacteristic
54C23×C61Q3211yescharacteristic
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—41no—
59C2×C4×C61—41no—
60C2×C4×C61—41no—
61C2×C4×C61—81no—
62C2×C4×C61—82no—
63C2×C4×C61—82no—
64C2×C4×C61—82no—
65C2×C4×C61#9911yescharacteristic
66C2×C4×C61#10411yescharacteristic
67C2×Dic61—81no—
68C2×Dic61—81no—
69C2×Dic61—81no—
70C2×Dic61—81no—
71C2×Dic61—81no—
72C2×Dic61—81no—
73C8×C61—41no—
74C8×C61—41no—
75#7077—611nomaximal, Sylow
76C22×C61—21no—
77C22×C61—21no—
78C22×C61—21no—
79C22×C61—21no—
80C22×C61—41no—
81C22×C61—41no—
82C22×C61—41no—
83C22×C61—41no—
84C22×C61—81no—
85C22×C61#32711yescharacteristic
86C22×C61#35811yescharacteristic
87C22×C61#36011yescharacteristic
88C4×C61—21no—
89C4×C61—41no—
90C4×C61—162no—
91C4×C61#35211yescharacteristic
92C4×C61#35411yescharacteristic
93Dic61—161no—
94Dic61—161no—
95#2076—611no—
96#1314—611no—
97#1289D6111yescharacteristic
98C2×C61—21no—
99C2×C61—21no—
100C2×C61—41no—
101C2×C61—41no—
102C2×C61#133911yescharacteristic
103C2×C61#134411yescharacteristic
104C2×C61#134811yescharacteristic
105C2×#107—611no—
106C2×C22⋊C8C2×D6111yescharacteristic
107#380—21no—
108#380—1221no—
109C22⋊C16—1221no—
110#340—611no—
111#340—1221no—
112C61#707711yescharacteristic, complemented, Sylow
113C23×C4C22⋊D6111yescharacteristic
114C22×C8C4×D6111yescharacteristic
115C22×C8D24411yescharacteristic
116C2×C4⋊C4—41no—
117C2×C4⋊C4—1221no—
118C2×C4⋊C4—1221no—
119C2×C22⋊C4—41no—
120C2×C22⋊C4—2441no—
121C2×C16—2441no—
122#107—2441no—
123C22⋊C8—41no—
124#95—22no—
125#95—2441no—
126C24#1175819911yescharacteristic
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—41no—
130C22×C4—41no—
131C22×C4—42no—
132C22×C4—2441no—
133C22×C4—2441no—
134C22×C4#1175819811yescharacteristic
135C22×C4#1175820111yescharacteristic
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—41no—
139C2×C8—41no—
140C4⋊C4—81no—
141C4⋊C4—81no—
142C4⋊C4—2441no—
143C4⋊C4—2441no—
144C4⋊C4—2441no—
145C4⋊C4—2441no—
146C22⋊C4—81no—
147C22⋊C4—81no—
148C22⋊C4—4882no—
149C16—4881no—
150C23—21no—
151C23—21no—
152C23—41no—
153C23—41no—
154C23#1451969711yescharacteristic
155C23#1451972111yescharacteristic
156C23#1451972311yescharacteristic
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—81no—
164C2×C4—82no—
165C2×C4—82no—
166C2×C4—82no—
167C2×C4—4881no—
168C2×C4—4881no—
169C2×C4—4881no—
170C2×C4—4881no—
171C2×C4—4881no—
172C2×C4—4881no—
173C2×C4#1451969111yescharacteristic
174C2×C4#1451970511yescharacteristic
175C8—41no—
176C8—41no—
177C22—21no—
178C22—21no—
179C22—21no—
180C22—21no—
181C22—41no—
182C22—41no—
183C22—41no—
184C22—41no—
185C22—81no—
186C22#1683949511yescharacteristic
187C22#1683956511yescharacteristic
188C22#1683957111yescharacteristic
189C4—21no—
190C4—41no—
191C4—162no—
192C4—9761no—
193C4—9761no—
194C4#1683955111yescharacteristic
195C4#1683955611yescharacteristic
196C2—21no—
197C2—21no—
198C2—41no—
199C2—41no—
200C2#2144380311yescharacteristic
201C2#2144381811yescharacteristic
202C2#2144383011yescharacteristic
subgroupG/H
centerC22#16839495
commutatorC22×C8×C61C2×C4
FrattiniC2×C22⋊C8C2×D61
FittingC61×#1289C2
socleC22×C61#327
prime radicalC24×C61D8
cosocleC2×C22⋊C8×C61C22
hypercenter#1289D61
hypocenterC61#7077
LCSG ▷ C22×C8×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1289

Complements

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

NH ≅ G/Ntype
4. C2×#14519711C4semidirect
8. #16839525C4semidirect
112. C61#7077semidirect

Maximal subgroups

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

subgroupindex
#214472472
#214437432
C61×#12892
#707761