Finite Group Databasebeta

← #29591528

Subgroups — #29591528

Order 15616.

292 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 79 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#21447635C211yesmaximal, characteristic, complemented
3#21443881C212yesmaximal, complemented
4#21443855C212yesmaximal, complemented
5C61×#2153C211yesmaximal, characteristic, complemented
6#16840367C412yes—
7#16840164C2211yescharacteristic
8#16840139C2211yescharacteristic
9#16840127C412yes—
10#16840015—21no—
11#16839998—21no—
12#16839875—21no—
13C4×D488—21no—
14#16839583C2212yes—
15#16839544—21no—
16#16839540—21no—
17C2×M32×C61—21no—
18C61×#405C2211yescharacteristic
19C61×#364—21no—
20C61×#364C2212yes—
21C2×D488—21no—
22C2×D488—21no—
23#14519774C2×C412yes—
24#14519769C2×C412yes—
25#14519762—42no—
26#14519751—22no—
27#14519750—42no—
28C4×D244—22no—
29#14519717—22no—
30#14519711—21no—
31#14519709—21no—
32#14519699—22no—
33#14519699—22no—
34C2×M16×C61D411yescharacteristic
35C22×C8×C61D411yescharacteristic
36#117×C61C2×C411yescharacteristic
37M32×C61—22no—
38M32×C61—41no—
39C2×C16×C61—41no—
40#97×C61C2×C411yescharacteristic
41#97×C61D411yescharacteristic
42C4×C8×C61D411yescharacteristic
43C4×C8×C61C2311yescharacteristic
44C22×C4×C61C22⋊C411yescharacteristic
45C2×C22⋊D61—42no—
46C2×D244—22no—
47C2×D244—42no—
48C2×C4×D61—42no—
49M16×C61—22no—
50C2×C8×C61—21no—
51C2×C8×C61—21no—
52C2×C8×C61C22⋊C411yescharacteristic
53C2×C8×C61C22⋊C411yescharacteristic
54C2×C8×C61C2×D411yescharacteristic
55C2×C8×C61C2×D411yescharacteristic
56C4⋊C4×C61—21no—
57C22⋊C4×C61—21no—
58C42×C61C22⋊C411yescharacteristic
59C42×C61C22×C411yescharacteristic
60#11758198—42no—
61#11758198—42no—
62C4⋊Dic61—22no—
63#11758196—42no—
64D488—42no—
65D488—41no—
66D488—41no—
67C16×C61—42no—
68#11758185—42no—
69C23×C61#10011yescharacteristic
70C22×D61—42no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61#10011yescharacteristic
76C2×C4×C61C2×C22⋊C411yescharacteristic
77C22⋊D61—162no—
78C2×Dic61—42no—
79D244—42no—
80D244—42no—
81D244—162no—
82C4×D61—162no—
83C8×C61—21no—
84C8×C61—21no—
85C8×C61#13512yes—
86C8×C61AGL(1,ℤ/8)11yescharacteristic
87C8×C61#13711yescharacteristic
88#11989—611nomaximal, Sylow
89C22×C61—21no—
90C22×C61—41no—
91C22×C61C2×#10011yescharacteristic
92C2×D61—82no—
93C2×D61—82no—
94C2×D61—82no—
95C4×C61—21no—
96C4×C61—41no—
97C4×C61—41no—
98C4×C61#41611yescharacteristic
99C4×C61#41711yescharacteristic
100Dic61—82no—
101#3176—611no—
102#2166—611no—
103#2153D6111yescharacteristic, complemented
104#1366—612no—
105#1357—612no—
106C2×C61—21no—
107C2×C61—41no—
108C2×C61#155111yescharacteristic
109D61—162no—
110#540—612no—
111C2×M32—21no—
112#499—611no—
113#493—611no—
114#490—612no—
115#469—1221no—
116#466—1221no—
117#442—1221no—
118C4×D8—1221no—
119#405C2×D6111yescharacteristic
120#364—21no—
121#364—612no—
122#364C2×D6112yes—
123#349—1221no—
124#347—1221no—
125C61#1198911yescharacteristic, complemented, Sylow
126C2×D8—1221no—
127C2×D8—1221no—
128C2×M16D24411yescharacteristic
129C22×C8C22⋊D6111yescharacteristic
130#127—612no—
131#125—612no—
132#123—2442no—
133#121—1222no—
134#121—2442no—
135C4×D4—1222no—
136#117C4×D6111yescharacteristic
137M32—22no—
138M32—41no—
139M32—1222no—
140C2×C16—41no—
141#107—1221no—
142#106—1221no—
143#102—1222no—
144#102—1222no—
145#97C4×D6111yescharacteristic
146#97D24411yescharacteristic
147C4×C8C22⋊D6111yescharacteristic
148C4×C8C22×D6111yescharacteristic
149C2×D4—1222no—
150C2×D4—2442no—
151C2×D4—2442no—
152C22×C4—2442no—
153C22×C4#1175819811yescharacteristic
154D8—2441no—
155D8—2442no—
156D8—2441no—
157M16—22no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8#1175819811yescharacteristic
161C2×C8#1175819811yescharacteristic
162C2×C8C2×D24411yescharacteristic
163C2×C8C2×C22⋊D6111yescharacteristic
164C4⋊C4—21no—
165C4⋊C4—1222no—
166C4⋊C4—2442no—
167C22⋊C4—21no—
168C22⋊C4—2442no—
169C22⋊C4—2442no—
170C42#1175819811yescharacteristic
171C42C2×C4×D6111yescharacteristic
172C16—42no—
173C16—2442no—
174C23—2442no—
175C23#1451969311yescharacteristic
176D4—9762no—
177D4—9762no—
178D4—2442no—
179D4—2442no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—9762no—
185C2×C4—2442no—
186C2×C4#1451969311yescharacteristic
187C2×C4C2×#1175819811yescharacteristic
188C8—21no—
189C8—21no—
190C8#1451979912yes—
191C8#1451980311yescharacteristic
192C8#1451980811yescharacteristic
193C22—21no—
194C22—41no—
195C22—4882no—
196C22—4882no—
197C22—4882no—
198C22C2×#1451969311yescharacteristic
199C4—21no—
200C4—41no—
201C4—41no—
202C4—4882no—
203C4#1683975911yescharacteristic
204C4#1683976111yescharacteristic
205C2—21no—
206C2—41no—
207C2—9762no—
208C2#2144451211yescharacteristic
subgroupG/H
centerC2#21444512
commutatorC42×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#2153C2
socleC2×C61#1551
prime radical#21456469C2
cosocleC4×C8×C61C23
hypercenter#2153D61
hypocenterC61#11989
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2153

Complements

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

NH ≅ G/Ntype
2. #21447635C2semidirect
3. #21443881C2semidirect
4. #21443855C2semidirect
5. C61×#2153C2semidirect
103. #2153D61semidirect
125. C61#11989semidirect

Maximal subgroups

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

subgroupindex
#214564692
#214476352
#214438812
#214438552
C61×#21532
#1198961