Finite Group Databasebeta

← #29591200

Subgroups — #29591200

Order 15616.

296 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 75 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#21456469C211yesmaximal, characteristic
2#21447424C211yesmaximal, characteristic, complemented
3#21443851C214yesmaximal, complemented
4C61×#2166C211yesmaximal, characteristic, complemented
5#16840367C412yes—
6C2×#14519717—21no—
7#16840164C411yescharacteristic
8#16840139C411yescharacteristic
9#16840127C2212yes—
10#16840015—21no—
11#16839998—21no—
12#16839875—21no—
13C4×D488—21no—
14#16839540—21no—
15#16839540C2212yes—
16C61×#405C2211yescharacteristic
17C61×#364—21no—
18C61×#349—21no—
19C61×#347C2212yes—
20C2×D488—21no—
21C2×D488—21no—
22#14519774C2×C412yes—
23#14519769C2×C412yes—
24#14519762—42no—
25#14519751—22no—
26#14519750—42no—
27C4×D244—22no—
28#14519717—22no—
29#14519717—22no—
30C2×#11758185—22no—
31#14519711—21no—
32#14519709—21no—
33#14519699—22no—
34#14519699—22no—
35C2×M16×C61D411yescharacteristic
36C22×C8×C61D411yescharacteristic
37#117×C61C2×C411yescharacteristic
38M32×C61—22no—
39#97×C61D411yescharacteristic
40#97×C61C2311yescharacteristic
41C4×C8×C61C2×C411yescharacteristic
42C4×C8×C61D411yescharacteristic
43C22×C4×C61C22⋊C411yescharacteristic
44C2×C22⋊D61—42no—
45C2×D244—22no—
46C2×D244—42no—
47C2×C4×D61—42no—
48M16×C61—41no—
49C2×C8×C61—21no—
50C2×C8×C61—21no—
51C2×C8×C61C22⋊C411yescharacteristic
52C2×C8×C61C22⋊C411yescharacteristic
53C2×C8×C61C2×D411yescharacteristic
54C2×C8×C61C2×D411yescharacteristic
55C4⋊C4×C61—21no—
56C22⋊C4×C61—21no—
57C42×C61C22⋊C411yescharacteristic
58C42×C61C22×C411yescharacteristic
59#11758198—42no—
60#11758198—42no—
61C4⋊Dic61—22no—
62#11758196—42no—
63D488—42no—
64D488—41no—
65D488—41no—
66C16×C61—42no—
67#11758185—24no—
68C23×C61#10011yescharacteristic
69C22×D61—42no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61#10011yescharacteristic
75C2×C4×C61C2×C22⋊C411yescharacteristic
76C22⋊D61—162no—
77C2×Dic61—42no—
78D244—42no—
79D244—42no—
80D244—162no—
81C4×D61—162no—
82C8×C61—21no—
83C8×C61—21no—
84C8×C61—21no—
85C8×C61#10411yescharacteristic
86C8×C61#10411yescharacteristic
87#11913—611nomaximal, Sylow
88C22×C61—21no—
89C22×C61—41no—
90C22×C61C2×#10011yescharacteristic
91C2×D61—82no—
92C2×D61—82no—
93C2×D61—82no—
94C4×C61—21no—
95C4×C61—41no—
96C4×C61—41no—
97C4×C61C2×#10411yescharacteristic
98C4×C61#42111yescharacteristic
99Dic61—82no—
100#3176—611no—
101#2166D6111yescharacteristic, complemented
102#2110—611no—
103#1355—614no—
104C2×C61—21no—
105C2×C61—41no—
106C2×C61#153011yescharacteristic
107D61—162no—
108#540—612no—
109C2×M32—1221no—
110#499—611no—
111#493—611no—
112#490—612no—
113#469—1221no—
114#466—1221no—
115#442—1221no—
116C4×D8—1221no—
117#405C2×D6111yescharacteristic
118#364—21no—
119#349—21no—
120#347—612no—
121#347—1221no—
122#347C2×D6112yes—
123C61#1191311yescharacteristic, complemented, Sylow
124C2×D8—1221no—
125C2×D8—1221no—
126C2×M16C22⋊D6111yescharacteristic
127C22×C8D24411yescharacteristic
128#127—612no—
129#125—612no—
130#123—2442no—
131#121—1222no—
132#121—2442no—
133C4×D4—1222no—
134#117C4×D6111yescharacteristic
135M32—22no—
136M32—1222no—
137M32—1222no—
138C2×C16—1222no—
139#107—1221no—
140#106—1221no—
141#102—1222no—
142#102—1222no—
143#97D24411yescharacteristic
144#97C22×D6111yescharacteristic
145C4×C8C4×D6111yescharacteristic
146C4×C8C22⋊D6111yescharacteristic
147C2×D4—1222no—
148C2×D4—2442no—
149C2×D4—2442no—
150C22×C4—2442no—
151C22×C4#1175819811yescharacteristic
152D8—2442no—
153D8—2441no—
154D8—2441no—
155M16—41no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8#1175819811yescharacteristic
159C2×C8#1175819811yescharacteristic
160C2×C8C2×D24411yescharacteristic
161C2×C8C2×C22⋊D6111yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—1222no—
164C4⋊C4—2442no—
165C22⋊C4—21no—
166C22⋊C4—2442no—
167C22⋊C4—2442no—
168C42#1175819811yescharacteristic
169C42C2×C4×D6111yescharacteristic
170C16—42no—
171C16—1224no—
172C23—2442no—
173C23#1451969311yescharacteristic
174D4—9762no—
175D4—9762no—
176D4—2442no—
177D4—2442no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—9762no—
183C2×C4—2442no—
184C2×C4#1451969311yescharacteristic
185C2×C4C2×#1175819811yescharacteristic
186C8—21no—
187C8—21no—
188C8—21no—
189C8#1451970311yescharacteristic
190C8#1451970311yescharacteristic
191C22—21no—
192C22—41no—
193C22—4882no—
194C22—4882no—
195C22—4882no—
196C22C2×#1451969311yescharacteristic
197C4—21no—
198C4—41no—
199C4—41no—
200C4—4882no—
201C4C2×#1451970311yescharacteristic
202C4#1683978011yescharacteristic
203C2—21no—
204C2—41no—
205C2—9762no—
206C2#2144443111yescharacteristic
subgroupG/H
centerC2#21444431
commutatorC42×C61C22×C4
Frattini#97C22×D61
FittingC61×#2166C2
socleC2×C61#1530
prime radical#21456469C2
cosocle#97×C61C23
hypercenter#2166D61
hypocenterC61#11913
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2166

Complements

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

NH ≅ G/Ntype
2. #21447424C2semidirect
3. #21443851C2semidirect
4. C61×#2166C2semidirect
101. #2166D61semidirect
123. C61#11913semidirect

Maximal subgroups

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

subgroupindex
#214564692
#214474242
#214438512
C61×#21662
#1191361