Finite Group Databasebeta

← #29600797

Subgroups — #29600797

Order 15616.

220 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C2×#16839601C211yesmaximal, characteristic, complemented
2C2×#16839600C211yesmaximal, characteristic, complemented
3#21448067C211yesmaximal, characteristic
4#21447677C211yesmaximal, characteristic, complemented
5#21444014C211yesmaximal, characteristic, complemented
6#21443996C211yesmaximal, characteristic, complemented
7C61×#1415C211yesmaximal, characteristic, complemented
8C2×Dic488C2211yescharacteristic
9C2×D976C2211yescharacteristic
10C2×#14519718—21no—
11#16840137—21no—
12#16839856—21no—
13#16839601—22no—
14#16839600—22no—
15C2×#14519683C2211yescharacteristic
16#16839565—21no—
17C16×Dic61C2211yescharacteristic
18C2×D16×C61C2211yescharacteristic
19C2×C32×C61C2211yescharacteristic
20C61×#366C2211yescharacteristic
21C2×Dic244—21no—
22C2×D488—21no—
23C2×#11758199—41no—
24#14519773—41no—
25#14519742—41no—
26Dic488—21no—
27Dic488D412yescomplemented
28D976—21no—
29D976—21no—
30#14519718—42no—
31C2×#11758185D411yescharacteristic
32#14519700—41no—
33C8×Dic61D411yescharacteristic
34#14519683—21no—
35C2×D8×C61—21no—
36D16×C61—21no—
37D16×C61—21no—
38C2×C16×C61C2311yescharacteristic
39#107×C61—21no—
40C32×C61—21no—
41C2×D4×C61—41no—
42C2×C22⋊D61—81no—
43C2×C22⋊D61—81no—
44C2×D244—41no—
45C2×Dic122—41no—
46D8×C61—41no—
47D8×C61—41no—
48C2×C8×C61C2×D411yescharacteristic
49C4⋊C4×C61—41no—
50#11758199—82no—
51#11758196—81no—
52C4×Dic61—81no—
53C4×Dic61D811yescharacteristic
54C2×#92418D811yescharacteristic
55Dic244—22no—
56Dic244—41no—
57D488—41no—
58D488—41no—
59C16×C61C2×D411yescharacteristic
60C16×C61#4111yescharacteristic
61#11758185—21no—
62C23×C61—81no—
63C22×D61—81no—
64D4×C61—81no—
65D4×C61—81no—
66C2×C4×C61—81no—
67C2×C4×C61C2×D811yescharacteristic
68C22⋊D61—162no—
69C22⋊D61—162no—
70C2×Dic61—81no—
71C2×Dic61D1611yescharacteristic
72C2×Dic61D1611yescharacteristic
73D244—81no—
74D244—81no—
75Dic122—42no—
76Dic122—81no—
77C8×C61#12111yescharacteristic
78C8×C61AGL(1,ℤ/8)11yescharacteristic
79#92418—21no—
80#13686—611nomaximal, Sylow
81C22×C61—161no—
82C22×C61—161no—
83C22×C61—161no—
84C22×C61C2×D1611yescharacteristic
85C2×D61—161no—
86C2×D61—161no—
87C2×D61—161no—
88C4×C61—161no—
89C4×C61#45911yescharacteristic
90C4×C61#50911yescharacteristic
91Dic61—21no—
92Dic61—82no—
93Dic61SD6412yescomplemented
94C2×SD64—611no—
95C2×SD64—611no—
96#2246—611no—
97C4×Q32—611no—
98C4⋊C32—611no—
99#1415—611no—
100#1415D6111yescharacteristic, complemented
101C2×C61—321no—
102C2×C61#220611yescharacteristic
103C2×C61C2×SD6411yescharacteristic
104C2×C61#226311yescharacteristic
105D61—321no—
106C2×Q32—611no—
107C2×D16—611no—
108C2×D16—1221no—
109C2×D16C2×D6111yescharacteristic
110#493—1221no—
111C4×Q16—1221no—
112SD64—1222no—
113SD64—1222no—
114C2×C32—611no—
115C2×C32C2×D6111yescharacteristic
116#366C2×D6111yescharacteristic
117#358—1221no—
118C4×C16—611no—
119C61#1368611yescharacteristic, complemented, Sylow
120C2×Q16—1221no—
121C2×D8—21no—
122C2×D8—1221no—
123C2×D8—2441no—
124#127—2441no—
125C4×Q8—2441no—
126Q32—612no—
127Q32—1221no—
128D16—21no—
129D16—21no—
130D16—1221no—
131D16—1221no—
132D16—2442no—
133C2×C16—611no—
134C2×C16C22×D6111yescharacteristic
135#107—21no—
136#103—2441no—
137C4×C8—611no—
138C32—21no—
139C32—1221no—
140C2×Q8—2441no—
141C2×D4—41no—
142C2×D4—4881no—
143C2×D4—4881no—
144C2×D4—2441no—
145Q16—1222no—
146Q16—2441no—
147D8—41no—
148D8—41no—
149D8—4882no—
150D8—2441no—
151D8—2441no—
152C2×C8—611no—
153C2×C8D4×D6111yescharacteristic
154C4⋊C4—41no—
155C4⋊C4—4881no—
156C42—611no—
157C42—4881no—
158C16—1221no—
159C16#1175822211yescharacteristic
160C16D4×D6111yescharacteristic
161C23—81no—
162C23—4881no—
163Q8—4881no—
164Q8—2442no—
165D4—81no—
166D4—81no—
167D4—9762no—
168D4—9762no—
169D4—4881no—
170D4—4881no—
171C2×C4—81no—
172C2×C4—611no—
173C2×C4—611no—
174C2×C4—4881no—
175C2×C4D8×D6111yescharacteristic
176C8—1221no—
177C8#1451975011yescharacteristic
178C8#1451980411yescharacteristic
179C22—161no—
180C22—161no—
181C22—161no—
182C22—9761no—
183C22—9761no—
184C22—9761no—
185C22D16×D6111yescharacteristic
186C4—161no—
187C4—612no—
188C4—1221no—
189C4—4882no—
190C4#1683995611yescharacteristic
191C4#1684019911yescharacteristic
192C2—321no—
193C2—19521no—
194C2#2144785311yescharacteristic
195C2SD64×D6111yescharacteristic
196C2#2144813011yescharacteristic
subgroupG/H
centerC22D16×D61
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#1415C2
socleC22×C61C2×D16
prime radical#21448067C2
hypercenter#1415D61
hypocenterC61#13686
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1415

Complements

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

NH ≅ G/Ntype
1. C2×#16839601C2semidirect
2. C2×#16839600C2semidirect
4. #21447677C2semidirect
5. #21444014C2semidirect
6. #21443996C2semidirect
7. C61×#1415C2semidirect
27. Dic488D4semidirect
93. Dic61SD64semidirect
100. #1415D61semidirect
119. C61#13686semidirect

Maximal subgroups

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

subgroupindex
C2×#168396012
C2×#168396002
#214480672
#214476772
#214440142
#214439962
C61×#14152
#1368661