Finite Group Databasebeta

← #29600853

Subgroups — #29600853

Order 15616.

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

normal subgroups only

This group has 204 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×#16839600C211yesmaximal, characteristic, complemented
2C2×C32×D61C211yesmaximal, characteristic, complemented
3#21447911C211yesmaximal, characteristic, complemented
4#21447902C211yesmaximal, characteristic
5#21444020C211yesmaximal, characteristic, complemented
6#21444001C211yesmaximal, characteristic, complemented
7C61×#1415C211yesmaximal, characteristic, complemented
8C2×Dic488C2211yescharacteristic
9C2×C16×D61C2211yescharacteristic
10#16840004—21no—
11#16839995—21no—
12#16839600—22no—
13C2×#14519683C2211yescharacteristic
14C32×D61—22no—
15#16839588C2211yescharacteristic
16#16839565—21no—
17#16839563—21no—
18C2×D16×C61C2211yescharacteristic
19C2×C32×C61C2211yescharacteristic
20C61×#366C2211yescharacteristic
21C2×Dic244—21no—
22C2×C8×D61D411yescharacteristic
23#14519757—41no—
24#14519748—41no—
25Dic488—21no—
26Dic488—21no—
27C2×#11758185D411yescharacteristic
28C16×D61—21no—
29C16×D61—21no—
30#14519711—21no—
31#14519700—41no—
32#14519698—41no—
33#14519683D412yescomplemented
34C2×D8×C61—21no—
35D16×C61—21no—
36D16×C61—21no—
37C2×C16×C61C2311yescharacteristic
38#107×C61—21no—
39C32×C61—21no—
40C2×D4×C61—41no—
41C2×C22⋊D61—81no—
42C2×C4×D61D811yescharacteristic
43C2×Dic122—41no—
44D8×C61—41no—
45D8×C61—41no—
46C2×C8×C61C2×D411yescharacteristic
47C4⋊C4×C61—41no—
48C22⋊Dic61—81no—
49#11758198—81no—
50C4⋊Dic61—41no—
51C4⋊Dic61—81no—
52C2×#92418D811yescharacteristic
53Dic244—41no—
54Dic244—41no—
55C8×D61—21no—
56C8×D61—21no—
57C16×C61C2×D411yescharacteristic
58C16×C61#4111yescharacteristic
59#11758185—21no—
60C23×C61—81no—
61C22×D61D1611yescharacteristic
62D4×C61—81no—
63D4×C61—81no—
64C2×C4×C61—81no—
65C2×C4×C61C2×D811yescharacteristic
66C22⋊D61—162no—
67C2×Dic61—81no—
68C2×Dic61—81no—
69C2×Dic61D1611yescharacteristic
70C4×D61—21no—
71C4×D61—21no—
72Dic122—81no—
73Dic122—81no—
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×SD64—611no—
92C22×C32—611no—
93#2216—611no—
94#2215—611no—
95#1424—611no—
96#1416—611no—
97#1415D6111yescharacteristic, complemented
98C2×C61—321no—
99C2×C61#221511yescharacteristic
100C2×C61C2×SD6411yescharacteristic
101C2×C61#226211yescharacteristic
102D61—22no—
103C2×Q32—611no—
104C2×D16C2×D6111yescharacteristic
105C22×C16—611no—
106#467—1221no—
107#466—1221no—
108SD64—1222no—
109C2×C32—611no—
110C2×C32—1222no—
111C2×C32C2×D6111yescharacteristic
112#366—611no—
113#366C2×D6111yescharacteristic
114#358—1221no—
115#357—1221no—
116C61#1369611yescharacteristic, complemented, Sylow
117C2×Q16—1221no—
118C2×D8—21no—
119C22×C8—611no—
120C22⋊Q8—2441no—
121#121—2441no—
122Q32—1221no—
123Q32—1221no—
124D16—21no—
125D16—21no—
126C2×C16—611no—
127C2×C16—1221no—
128C2×C16—1221no—
129C2×C16C22×D6111yescharacteristic
130#107—21no—
131#107—1221no—
132#103—2441no—
133#102—2441no—
134C32—21no—
135C32—612no—
136C2×Q8—2441no—
137C2×D4—41no—
138C2×D4—4881no—
139C22×C4—611no—
140Q16—2441no—
141Q16—2441no—
142D8—41no—
143D8—41no—
144C2×C8—611no—
145C2×C8—1221no—
146C2×C8—1221no—
147C2×C8D4×D6111yescharacteristic
148C4⋊C4—41no—
149C4⋊C4—4881no—
150C4⋊C4—2441no—
151C22⋊C4—4881no—
152C22⋊C4—4881no—
153C16—1221no—
154C16#1175822211yescharacteristic
155C16D4×D6111yescharacteristic
156C23—81no—
157C23—611no—
158Q8—4881no—
159Q8—4881no—
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#1451975011yescharacteristic
172C8#1451979811yescharacteristic
173C22—161no—
174C22—161no—
175C22—161no—
176C22—612no—
177C22—1221no—
178C22—1221no—
179C22D16×D6111yescharacteristic
180C4—161no—
181C4—1221no—
182C4—9761no—
183C4—9761no—
184C4#1683999711yescharacteristic
185C4#1684019311yescharacteristic
186C2—321no—
187C2—1222no—
188C2#2144790411yescharacteristic
189C2SD64×D6111yescharacteristic
190C2#2144812511yescharacteristic
subgroupG/H
centerC22D16×D61
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#1415C2
socleC22×C61C2×D16
prime radical#21447902C2
hypercenter#1415D61
hypocenterC61#13696
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×#16839600C2semidirect
2. C2×C32×D61C2semidirect
3. #21447911C2semidirect
5. #21444020C2semidirect
6. #21444001C2semidirect
7. C61×#1415C2semidirect
33. #14519683D4semidirect
84. C2×D61SD64semidirect
97. #1415D61semidirect
116. C61#13696semidirect

Maximal subgroups

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

subgroupindex
C2×#168396002
C2×C32×D612
#214479112
#214479022
#214440202
#214440012
C61×#14152
#1369661