Finite Group Databasebeta

← #29594422

Subgroups — #29594422

Order 15616.

186 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 53 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#21448064C211yesmaximal, characteristic, complemented
2#21447996C211yesmaximal, characteristic
3#21447897C211yesmaximal, characteristic
4#21447660C211yesmaximal, characteristic
5#21443886C211yesmaximal, characteristic, complemented
6#21443881C211yesmaximal, characteristic, complemented
7C61×#1358C211yesmaximal, characteristic, complemented
8#16840203—21no—
9#16840180—21no—
10#16840164C2211yescharacteristic
11#16839880C2211yescharacteristic
12#16839585—21no—
13#16839583C2211yescharacteristic
14#16839578—21no—
15#16839573—21no—
16#16839566—21no—
17#16839566—21no—
18#16839547—21no—
19#16839538C2211yescharacteristic
20C61×#494C2211yescharacteristic
21C61×#364C2211yescharacteristic
22C61×#364C2211yescharacteristic
23#14519799D411yescharacteristic
24#14519783—21no—
25#14519769—21no—
26#14519723—41no—
27#14519720—41no—
28#14519717—21no—
29#14519716—41no—
30C2×#11758185D411yescharacteristic
31C2×#11758185D411yescharacteristic
32C16×D61—41no—
33#14519713D411yescharacteristic
34#14519711—21no—
35#14519709—21no—
36#14519705—21no—
37C2×Q16×C61—21no—
38C2×Q16×C61—21no—
39C4⋊Q8×C61—21no—
40M32×C61—21no—
41M32×C61—21no—
42C4×C8×C61C2311yescharacteristic
43C2×Q8×C61—41no—
44#11758222—21no—
45Q16×C61—41no—
46Q16×C61—41no—
47Q16×C61—41no—
48Q16×C61—41no—
49C2×C8×C61C2×D411yescharacteristic
50C2×C8×C61C2×D411yescharacteristic
51C4⋊C4×C61—81no—
52C42×C61#4111yescharacteristic
53C4⋊Dic61—41no—
54#11758196—81no—
55#11758194—21no—
56Dic244SD1611yescharacteristic
57D488SD1611yescharacteristic
58#11758190—21no—
59#11758189—41no—
60C8×D61—41no—
61C16×C61—41no—
62C16×C61—41no—
63#11758185—21no—
64#11758185—21no—
65#11758185—41no—
66Q8×C61—81no—
67Q8×C61—81no—
68C2×C4×C61—21no—
69C2×C4×C61—81no—
70C2×C4×C61#12111yescharacteristic
71C22⋊D61—41no—
72C2×Dic61—81no—
73D244—21no—
74C4×D61—41no—
75Dic122—21no—
76C8×C61C2×SD1611yescharacteristic
77C8×C61#13511yescharacteristic
78C8×C61#13511yescharacteristic
79C8×C61AGL(1,ℤ/8)11yescharacteristic
80#92418—41no—
81#12466—611nomaximal, Sylow
82C22×C61#47211yescharacteristic
83C2×D61—41no—
84C4×C61—41no—
85C4×C61—161no—
86C4×C61#46311yescharacteristic
87C4×C61#46511yescharacteristic
88Dic61—41no—
89Dic61—161no—
90#2245—611no—
91#2231—611no—
92#2214—611no—
93#2171—611no—
94#1369—611no—
95#1366—611no—
96#1358D6111yescharacteristic, complemented
97C2×C61—21no—
98C2×C61#167711yescharacteristic
99D61—81no—
100#510—1221no—
101#504—1221no—
102#499—611no—
103#494C2×D6111yescharacteristic
104#443—611no—
105#365—1221no—
106#364—611no—
107#364C2×D6111yescharacteristic
108#364C2×D6111yescharacteristic
109#362—1221no—
110#360—1221no—
111#358—1221no—
112#358—1221no—
113#350—1221no—
114#346—611no—
115C61#1246611yescharacteristic, complemented, Sylow
116#135—611no—
117C2×Q16—21no—
118C2×Q16—21no—
119#131—1221no—
120C4⋊Q8—21no—
121#125—1221no—
122Q32—2441no—
123SD32—2441no—
124M32—21no—
125M32—21no—
126M32—1221no—
127M32—2441no—
128C2×C16—611no—
129C2×C16—611no—
130C2×C16—2441no—
131#108—611no—
132#107—1221no—
133#106—1221no—
134#104—1221no—
135C4×C8C22×D6111yescharacteristic
136#41—1221no—
137C2×Q8—41no—
138Q16—41no—
139Q16—41no—
140Q16—41no—
141Q16—41no—
142Q16—611no—
143SD16—1221no—
144D8—611no—
145M16—1221no—
146M16—2441no—
147C2×C8—2441no—
148C2×C8D4×D6111yescharacteristic
149C2×C8D4×D6111yescharacteristic
150C4⋊C4—81no—
151C4⋊C4—4881no—
152C4⋊C4—2441no—
153C42#1175822211yescharacteristic
154C16—41no—
155C16—41no—
156C16—1221no—
157C16—1221no—
158C16—2441no—
159Q8—81no—
160Q8—81no—
161Q8—1221no—
162D4—1221no—
163D4—2441no—
164C2×C4—21no—
165C2×C4—81no—
166C2×C4—4881no—
167C2×C4—2441no—
168C2×C4#1451975011yescharacteristic
169C8—2441no—
170C8SD16×D6111yescharacteristic
171C8#1451979611yescharacteristic
172C8#1451979811yescharacteristic
173C8#1451980111yescharacteristic
174C22—2441no—
175C22#1684003111yescharacteristic
176C4—41no—
177C4—161no—
178C4—9761no—
179C4—2441no—
180C4#1683997611yescharacteristic
181C4#1683999011yescharacteristic
182C2—21no—
183C2—4881no—
184C2#2144522711yescharacteristic
subgroupG/H
centerC2#21445227
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1358C2
socleC2×C61#1677
prime radical#14519799D4
hypercenter#1358D61
hypocenterC61#12466
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1358

Complements

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

NH ≅ G/Ntype
1. #21448064C2semidirect
5. #21443886C2semidirect
6. #21443881C2semidirect
7. C61×#1358C2semidirect
96. #1358D61semidirect
115. C61#12466semidirect

Maximal subgroups

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

subgroupindex
#214480642
#214479962
#214478972
#214476602
#214438862
#214438812
C61×#13582
#1246661