Finite Group Databasebeta

← #29600851

Subgroups — #29600851

Order 15616.

204 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 59 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×C32×D61C211yesmaximal, characteristic, complemented
2#21447907C211yesmaximal, characteristic, complemented
3#21447902C211yesmaximal, characteristic
4#21444021C211yesmaximal, characteristic, complemented
5#21444000C211yesmaximal, characteristic, complemented
6#21443997C211yesmaximal, characteristic, complemented
7C2×C61×SD64C211yesmaximal, characteristic, complemented
8C2×C16×D61C2211yescharacteristic
9#16840000—21no—
10#16839995—21no—
11C2×#14519683C2211yescharacteristic
12C32×D61—22no—
13#16839588C2211yescharacteristic
14#16839588C2211yescharacteristic
15#16839566—21no—
16#16839563—21no—
17C2×Q32×C61C2211yescharacteristic
18C2×D16×C61C2211yescharacteristic
19C61×SD64—22no—
20C2×C32×C61C2211yescharacteristic
21C2×C8×D61D411yescharacteristic
22#14519753—41no—
23#14519748—41no—
24C2×#11758185D411yescharacteristic
25C16×D61—21no—
26C16×D61—21no—
27#14519711—21no—
28#14519711—21no—
29#14519701—41no—
30#14519698—41no—
31#14519683—21no—
32C2×Q16×C61—21no—
33C2×D8×C61—21no—
34Q32×C61—21no—
35Q32×C61—21no—
36D16×C61—21no—
37D16×C61—21no—
38C2×C16×C61C2311yescharacteristic
39C32×C61D412yescomplemented
40C2×Q8×C61—41no—
41C2×D4×C61—41no—
42C2×C22⋊D61—81no—
43C2×C4×D61D811yescharacteristic
44Q16×C61—41no—
45Q16×C61—41no—
46D8×C61—41no—
47D8×C61—41no—
48C2×C8×C61C2×D411yescharacteristic
49C22⋊Dic61—81no—
50#11758198—81no—
51C4⋊Dic61—41no—
52C4⋊Dic61—41no—
53#11758196—81no—
54C2×#92418D811yescharacteristic
55C8×D61—21no—
56C8×D61—21no—
57C16×C61C2×D411yescharacteristic
58C16×C61#4111yescharacteristic
59#11758185—21no—
60C23×C61—81no—
61C22×D61D1611yescharacteristic
62Q8×C61—81no—
63Q8×C61—81no—
64D4×C61—81no—
65D4×C61—81no—
66C2×C4×C61—81no—
67C2×C4×C61C2×D811yescharacteristic
68C22⋊D61—162no—
69C2×Dic61—81no—
70C2×Dic61—81no—
71C2×Dic61D1611yescharacteristic
72C4×D61—21no—
73C4×D61—21no—
74C8×C61#12111yescharacteristic
75C8×C61#13511yescharacteristic
76#92418—21no—
77#13696—611nomaximal, Sylow
78C22×C61—161no—
79C22×C61—161no—
80C22×C61—161no—
81C22×C61C2×D1611yescharacteristic
82C2×D61—21no—
83C2×D61—21no—
84C2×D61SD6412yescomplemented
85C4×C61—161no—
86C4×C61#46611yescharacteristic
87C4×C61#50811yescharacteristic
88Dic61—21no—
89Dic61—161no—
90Dic61—161no—
91C2×SD64D6111yescharacteristic, complemented
92C22×C32—611no—
93#2216—611no—
94#2215—611no—
95#1424—611no—
96#1416—611no—
97#1415—611no—
98C2×C61—321no—
99C2×C61#221511yescharacteristic
100C2×C61C2×SD6411yescharacteristic
101C2×C61#226211yescharacteristic
102D61—22no—
103C2×Q32C2×D6111yescharacteristic
104C2×D16C2×D6111yescharacteristic
105C22×C16—611no—
106#467—1221no—
107#466—1221no—
108SD64—22no—
109C2×C32—611no—
110C2×C32—1222no—
111C2×C32C2×D6111yescharacteristic
112#366—611no—
113#366—611no—
114#358—1221no—
115#357—1221no—
116C61#1369611yescharacteristic, complemented, Sylow
117C2×Q16—21no—
118C2×D8—21no—
119C22×C8—611no—
120C22⋊Q8—2441no—
121#121—2441no—
122Q32—21no—
123Q32—21no—
124D16—21no—
125D16—21no—
126C2×C16—611no—
127C2×C16—1221no—
128C2×C16—1221no—
129C2×C16C22×D6111yescharacteristic
130#107—1221no—
131#107—1221no—
132#103—2441no—
133#102—2441no—
134C32—1221no—
135C32C22⋊D6112yescomplemented
136C2×Q8—41no—
137C2×D4—41no—
138C2×D4—4881no—
139C22×C4—611no—
140Q16—41no—
141Q16—41no—
142D8—41no—
143D8—41no—
144C2×C8—611no—
145C2×C8—1221no—
146C2×C8—1221no—
147C2×C8D4×D6111yescharacteristic
148C4⋊C4—4881no—
149C4⋊C4—2441no—
150C4⋊C4—2441no—
151C22⋊C4—4881no—
152C22⋊C4—4881no—
153C16—1221no—
154C16#1175822411yescharacteristic
155C16C2×C22⋊D6111yescharacteristic
156C23—81no—
157C23—611no—
158Q8—81no—
159Q8—81no—
160D4—81no—
161D4—81no—
162D4—9762no—
163C2×C4—81no—
164C2×C4—611no—
165C2×C4—1221no—
166C2×C4—1221no—
167C2×C4—4881no—
168C2×C4—4881no—
169C2×C4D8×D6111yescharacteristic
170C8—1221no—
171C8#1451974811yescharacteristic
172C8#1451979611yescharacteristic
173C22—161no—
174C22—161no—
175C22—161no—
176C22—612no—
177C22—1221no—
178C22—1221no—
179C22D16×D6111yescharacteristic
180C4—161no—
181C4—1221no—
182C4—9761no—
183C4—9761no—
184C4#1683999511yescharacteristic
185C4#1684019111yescharacteristic
186C2—321no—
187C2—1222no—
188C2#2144790211yescharacteristic
189C2SD64×D6111yescharacteristic
190C2#2144812711yescharacteristic
subgroupG/H
centerC22D16×D61
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC2×C61×SD64C2
socleC22×C61C2×D16
prime radical#21447902C2
hypercenterC2×SD64D61
hypocenterC61#13696
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×SD64

Complements

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

NH ≅ G/Ntype
1. C2×C32×D61C2semidirect
2. #21447907C2semidirect
4. #21444021C2semidirect
5. #21444000C2semidirect
6. #21443997C2semidirect
7. C2×C61×SD64C2semidirect
39. C32×C61D4semidirect
84. C2×D61SD64semidirect
91. C2×SD64D61semidirect
116. C61#13696semidirect
135. C32C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×C32×D612
#214479072
#214479022
#214440212
#214440002
#214439972
C2×C61×SD642
#1369661