Finite Group Databasebeta

← #29594420

Subgroups — #29594420

Order 15616.

186 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 55 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#21447992C211yesmaximal, characteristic
2#21447897C211yesmaximal, characteristic
3#21447662C211yesmaximal, characteristic
4#21443887C211yesmaximal, characteristic, complemented
5#21443880C211yesmaximal, characteristic, complemented
6#21443858C211yesmaximal, characteristic, complemented
7C61×#2245C211yesmaximal, characteristic, complemented
8#16840203—21no—
9#16840178—21no—
10#16839880C2211yescharacteristic
11#16839584—21no—
12#16839583C2211yescharacteristic
13#16839583C2211yescharacteristic
14#16839583C2211yescharacteristic
15#16839578—21no—
16#16839571—21no—
17#16839545—21no—
18C61×#499C2211yescharacteristic
19C61×#494C2211yescharacteristic
20C61×#358—21no—
21C61×#358—21no—
22C61×#346C2211yescharacteristic
23#14519799D411yescharacteristic
24#14519783—21no—
25#14519723—41no—
26#14519720—41no—
27#14519717—21no—
28#14519717—21no—
29#14519717—21no—
30#14519716—41no—
31C16×D61—41no—
32#14519713D411yescharacteristic
33#14519705—21no—
34C2×Q16×C61—21no—
35C2×Q16×C61—21no—
36C4⋊Q8×C61—21no—
37#125×C61—21no—
38C2×C16×C61D411yescharacteristic
39C2×C16×C61D411yescharacteristic
40#107×C61—21no—
41#106×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—41no—
52C4⋊C4×C61—81no—
53C4⋊C4×C61—81no—
54C42×C61#4111yescharacteristic
55#11758194—21no—
56Dic244SD1611yescharacteristic
57D488SD1611yescharacteristic
58#11758190—21no—
59#11758189—41no—
60C8×D61—41no—
61C16×C61—21no—
62C16×C61—21no—
63#11758185—41no—
64#11758185—41no—
65#11758185—41no—
66Q8×C61—81no—
67Q8×C61—81no—
68C2×C4×C61—21no—
69C2×C4×C61—81no—
70C2×C4×C61—81no—
71C2×C4×C61#12111yescharacteristic
72C22⋊D61—41no—
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—161no—
87C4×C61#46311yescharacteristic
88C4×C61#46511yescharacteristic
89Dic61—41no—
90#2245D6111yescharacteristic, complemented
91#2231—611no—
92#2214—611no—
93#2171—611no—
94#1369—611no—
95#1366—611no—
96#1358—611no—
97C2×C61—21no—
98C2×C61#167711yescharacteristic
99D61—81no—
100#510—1221no—
101#504—1221no—
102#499C2×D6111yescharacteristic
103#494C2×D6111yescharacteristic
104#443—611no—
105#365—1221no—
106#364—611no—
107#364—611no—
108#364—611no—
109#362—1221no—
110#360—1221no—
111#358—21no—
112#358—21no—
113#350—1221no—
114#346C2×D6111yescharacteristic
115C61#1246611yescharacteristic, complemented, Sylow
116#135—611no—
117C2×Q16—21no—
118C2×Q16—21no—
119#131—1221no—
120C4⋊Q8—21no—
121#125—21no—
122Q32—2441no—
123SD32—2441no—
124M32—1221no—
125M32—1221no—
126M32—1221no—
127M32—2441no—
128C2×C16—2441no—
129C2×C16C22⋊D6111yescharacteristic
130C2×C16C22⋊D6111yescharacteristic
131#108—611no—
132#107—21no—
133#106—21no—
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×C8C2×C22⋊D6111yescharacteristic
150C4⋊C4—41no—
151C4⋊C4—81no—
152C4⋊C4—81no—
153C42#1175822411yescharacteristic
154C16—21no—
155C16—21no—
156C16—2441no—
157C16—2441no—
158C16—2441no—
159Q8—81no—
160Q8—81no—
161Q8—1221no—
162D4—1221no—
163D4—2441no—
164C2×C4—21no—
165C2×C4—81no—
166C2×C4—81no—
167C2×C4—2441no—
168C2×C4#1451974811yescharacteristic
169C8—2441no—
170C8SD16×D6111yescharacteristic
171C8#1451979711yescharacteristic
172C8#1451979811yescharacteristic
173C8#1451980211yescharacteristic
174C22—2441no—
175C22#1684002911yescharacteristic
176C4—41no—
177C4—161no—
178C4—161no—
179C4—2441no—
180C4#1683997411yescharacteristic
181C4#1683998811yescharacteristic
182C2—21no—
183C2—4881no—
184C2#2144522511yescharacteristic
subgroupG/H
centerC2#21445225
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2245C2
socleC2×C61#1677
prime radical#14519799D4
hypercenter#2245D61
hypocenterC61#12466
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2245

Complements

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

NH ≅ G/Ntype
4. #21443887C2semidirect
5. #21443880C2semidirect
6. #21443858C2semidirect
7. C61×#2245C2semidirect
90. #2245D61semidirect
115. C61#12466semidirect

Maximal subgroups

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

subgroupindex
#214479922
#214478972
#214476622
#214438872
#214438802
#214438582
C61×#22452
#1246661