Finite Group Databasebeta

← #29600848

Subgroups — #29600848

Order 15616.

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

normal subgroups only

This group has 194 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×#16839602C211yesmaximal, characteristic, complemented
2C2×C32×D61C211yesmaximal, characteristic
3#21447911C211yesmaximal, characteristic
4#21447907C211yesmaximal, characteristic
5#21444018C211yesmaximal, characteristic, complemented
6#21444001C211yesmaximal, characteristic, complemented
7C61×#1416C211yesmaximal, characteristic, complemented
8C2×Dic488C2211yescharacteristic
9C2×C16×D61C2211yescharacteristic
10#16840004—21no—
11#16840000—21no—
12#16839602—22no—
13C2×#14519683C2211yescharacteristic
14C32×D61—22no—
15#16839588C2211yescharacteristic
16#16839566—21no—
17#16839565—21no—
18C2×Q32×C61C2211yescharacteristic
19C2×C32×C61C2211yescharacteristic
20C61×#366C2211yescharacteristic
21C2×Dic244—21no—
22C2×C8×D61D411yescharacteristic
23#14519757—41no—
24#14519753—41no—
25Dic488—21no—
26Dic488—21no—
27C2×#11758185D411yescharacteristic
28C16×D61—21no—
29C16×D61—21no—
30#14519711—21no—
31#14519701—41no—
32#14519700—41no—
33#14519683D412yes—
34C2×Q16×C61—21no—
35Q32×C61—21no—
36Q32×C61—21no—
37C2×C16×C61C2311yescharacteristic
38#107×C61—21no—
39C32×C61—21no—
40C2×Q8×C61—41no—
41C2×C4×D61D811yescharacteristic
42C2×Dic122—41no—
43Q16×C61—41no—
44Q16×C61—41no—
45C2×C8×C61C2×D411yescharacteristic
46C4⋊C4×C61—41no—
47#11758198—81no—
48#11758198—81no—
49C4⋊Dic61—41no—
50C4⋊Dic61—81no—
51#11758196—81no—
52C2×#92418D811yescharacteristic
53Dic244—41no—
54Dic244—41no—
55C8×D61—21no—
56C8×D61—21no—
57C16×C61C2×D411yescharacteristic
58C16×C61#4111yescharacteristic
59#11758185—21no—
60C22×D61D1611yescharacteristic
61Q8×C61—81no—
62Q8×C61—81no—
63C2×C4×C61—81no—
64C2×C4×C61—81no—
65C2×C4×C61C2×D811yescharacteristic
66C2×Dic61—81no—
67C2×Dic61—81no—
68C2×Dic61D1611yescharacteristic
69C4×D61—21no—
70C4×D61—21no—
71Dic122—81no—
72Dic122—81no—
73C8×C61#12111yescharacteristic
74C8×C61#13511yescharacteristic
75#92418—21no—
76#13695—611nomaximal, Sylow
77C22×C61C2×D1611yescharacteristic
78C2×D61—21no—
79C2×D61—21no—
80C2×D61Q6412yescomplemented
81C4×C61—161no—
82C4×C61—161no—
83C4×C61#46611yescharacteristic
84C4×C61#50811yescharacteristic
85Dic61—21no—
86Dic61—161no—
87Dic61—161no—
88C2×Q64—611no—
89C22×C32—611no—
90#2216—611no—
91#2216—611no—
92#1423—611no—
93#1416—611no—
94#1416D6111yescharacteristic, complemented
95C2×C61#221511yescharacteristic
96C2×C61C2×Q6411yescharacteristic
97C2×C61#226211yescharacteristic
98D61—22no—
99C2×Q32—611no—
100C2×Q32C2×D6111yescharacteristic
101C22×C16—611no—
102#467—1221no—
103#467—1221no—
104Q64—1222no—
105C2×C32—611no—
106C2×C32—1222no—
107C2×C32C2×D6111yescharacteristic
108#366—611no—
109#366C2×D6111yescharacteristic
110#358—1221no—
111#358—1221no—
112C61#1369511yescharacteristic, complemented, Sylow
113C2×Q16—21no—
114C2×Q16—1221no—
115C22×C8—611no—
116C22⋊Q8—2441no—
117C22⋊Q8—2441no—
118Q32—21no—
119Q32—21no—
120Q32—1221no—
121Q32—1221no—
122C2×C16—611no—
123C2×C16—1221no—
124C2×C16—1221no—
125C2×C16C22×D6111yescharacteristic
126#107—21no—
127#107—1221no—
128#103—2441no—
129#103—2441no—
130C32—21no—
131C32—612no—
132C2×Q8—41no—
133C2×Q8—2441no—
134C22×C4—611no—
135Q16—41no—
136Q16—41no—
137Q16—2441no—
138Q16—2441no—
139C2×C8—611no—
140C2×C8—1221no—
141C2×C8—1221no—
142C2×C8D4×D6111yescharacteristic
143C4⋊C4—41no—
144C4⋊C4—4881no—
145C4⋊C4—4881no—
146C4⋊C4—2441no—
147C22⋊C4—4881no—
148C22⋊C4—4881no—
149C16—1221no—
150C16#1175822211yescharacteristic
151C16D4×D6111yescharacteristic
152C23—611no—
153Q8—81no—
154Q8—81no—
155Q8—4881no—
156Q8—4881no—
157C2×C4—81no—
158C2×C4—81no—
159C2×C4—611no—
160C2×C4—1221no—
161C2×C4—1221no—
162C2×C4—4881no—
163C2×C4—4881no—
164C2×C4D8×D6111yescharacteristic
165C8—1221no—
166C8#1451975011yescharacteristic
167C8#1451979811yescharacteristic
168C22—612no—
169C22—1221no—
170C22—1221no—
171C22D16×D6111yescharacteristic
172C4—161no—
173C4—161no—
174C4—1221no—
175C4—9761no—
176C4—9761no—
177C4#1683999711yescharacteristic
178C4#1684019311yescharacteristic
179C2—1222no—
180C2#2144790411yescharacteristic
181C2Q64×D6111yescharacteristic
182C2#2144812711yescharacteristic
subgroupG/H
centerC22D16×D61
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#1416C2
socleC22×C61C2×D16
prime radicalC22×D61D16
hypercenter#1416D61
hypocenterC61#13695
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1416

Complements

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

NH ≅ G/Ntype
1. C2×#16839602C2semidirect
5. #21444018C2semidirect
6. #21444001C2semidirect
7. C61×#1416C2semidirect
80. C2×D61Q64semidirect
94. #1416D61semidirect
112. C61#13695semidirect

Maximal subgroups

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

subgroupindex
C2×#168396022
C2×C32×D612
#214479112
#214479072
#214440182
#214440012
C61×#14162
#1369561