Finite Group Databasebeta

← #29594417

Subgroups — #29594417

Order 15616.

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

normal subgroups only

This group has 196 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#21448061C211yesmaximal, characteristic, complemented
2#21447996C211yesmaximal, characteristic, complemented
3#21447896C211yesmaximal, characteristic
4#21447662C211yesmaximal, characteristic, complemented
5#21443879C211yesmaximal, characteristic, complemented
6#21443855C211yesmaximal, characteristic, complemented
7C61×#1369C211yesmaximal, characteristic, complemented
8#16840200—21no—
9#16840178—21no—
10#16840164C2211yescharacteristic
11#16840139C2211yescharacteristic
12#16839880C2211yescharacteristic
13#16839585—21no—
14#16839583C2211yescharacteristic
15#16839576—21no—
16#16839573—21no—
17#16839564—21no—
18#16839564—21no—
19#16839545—21no—
20C61×#364C2211yescharacteristic
21C61×#364C2211yescharacteristic
22C61×#346C2211yescharacteristic
23#14519799D411yescharacteristic
24C2×D488—21no—
25C2×D488—21no—
26#14519783—21no—
27#14519774—21no—
28#14519769—21no—
29#14519722—41no—
30D976—41no—
31#14519717—21no—
32#14519716—41no—
33C16×D61—41no—
34#14519713D411yescharacteristic
35#14519711—21no—
36#14519709—21no—
37#14519705—21no—
38M32×C61—21no—
39M32×C61—21no—
40C2×C16×C61D411yescharacteristic
41C2×C16×C61D411yescharacteristic
42C4×C8×C61C2311yescharacteristic
43#11758222—21no—
44C2×D244—41no—
45C2×D244—81no—
46C2×C8×C61C2×D411yescharacteristic
47C2×C8×C61C2×D411yescharacteristic
48C42×C61#4111yescharacteristic
49C4⋊Dic61—41no—
50#11758196—81no—
51#11758194—21no—
52Dic244SD1611yescharacteristic
53D488—41no—
54D488—41no—
55D488—41no—
56D488—41no—
57D488SD1611yescharacteristic
58#11758190—21no—
59#11758189—41no—
60C8×D61—41no—
61C16×C61—21no—
62C16×C61—21no—
63C16×C61—41no—
64C16×C61—41no—
65#11758185—41no—
66C22×D61—81no—
67C2×C4×C61—21no—
68C2×C4×C61#12111yescharacteristic
69C22⋊D61—41no—
70C2×Dic61—81no—
71D244—21no—
72D244—81no—
73D244—81no—
74D244—162no—
75C4×D61—41no—
76Dic122—21no—
77C8×C61C2×SD1611yescharacteristic
78C8×C61#13511yescharacteristic
79C8×C61#13511yescharacteristic
80C8×C61AGL(1,ℤ/8)11yescharacteristic
81#92418—41no—
82#12465—611nomaximal, Sylow
83C22×C61#47211yescharacteristic
84C2×D61—41no—
85C2×D61—162no—
86C2×D61—161no—
87C4×C61—41no—
88C4×C61#46311yescharacteristic
89C4×C61#46511yescharacteristic
90Dic61—41no—
91Dic61—161no—
92#2244—611no—
93#2231—611no—
94#2213—611no—
95#2171—611no—
96#1369D6111yescharacteristic, complemented
97#1366—611no—
98#1357—611no—
99C2×C61—21no—
100C2×C61#167711yescharacteristic
101D61—81no—
102D61—321no—
103#509—1221no—
104#504—1221no—
105#499—611no—
106#493—611no—
107#443—611no—
108#365—1221no—
109#364—611no—
110#364C2×D6111yescharacteristic
111#364C2×D6111yescharacteristic
112#361—1221no—
113#360—1221no—
114#357—1221no—
115#357—1221no—
116#350—1221no—
117#346C2×D6111yescharacteristic
118C61#1246511yescharacteristic, complemented, Sylow
119#135—611no—
120C2×D8—1221no—
121C2×D8—1221no—
122#131—1221no—
123#127—1221no—
124#125—1221no—
125SD32—2441no—
126D16—2441no—
127M32—21no—
128M32—21no—
129M32—1221no—
130M32—2441no—
131C2×C16—2441no—
132C2×C16D24411yescharacteristic
133C2×C16D24411yescharacteristic
134#108—611no—
135#107—1221no—
136#106—1221no—
137#104—1221no—
138C4×C8C22×D6111yescharacteristic
139#41—1221no—
140C2×D4—4881no—
141C2×D4—2441no—
142Q16—611no—
143SD16—1221no—
144D8—611no—
145D8—2441no—
146D8—2441no—
147D8—2441no—
148D8—2441no—
149M16—1221no—
150M16—2441no—
151C2×C8—2441no—
152C2×C8C2×D24411yescharacteristic
153C2×C8D4×D6111yescharacteristic
154C4⋊C4—4881no—
155C4⋊C4—2441no—
156C42#1175822611yescharacteristic
157C16—21no—
158C16—21no—
159C16—41no—
160C16—41no—
161C16—2441no—
162C23—4881no—
163Q8—1221no—
164D4—1221no—
165D4—9762no—
166D4—4881no—
167D4—4881no—
168D4—2441no—
169C2×C4—21no—
170C2×C4—4881no—
171C2×C4—2441no—
172C2×C4#1451975211yescharacteristic
173C8—2441no—
174C8SD16×D6111yescharacteristic
175C8#1451979811yescharacteristic
176C8#1451979911yescharacteristic
177C8#1451980511yescharacteristic
178C22—9762no—
179C22—9761no—
180C22—2441no—
181C22#1684003311yescharacteristic
182C4—41no—
183C4—9761no—
184C4—2441no—
185C4#1683997811yescharacteristic
186C4#1683999211yescharacteristic
187C2—21no—
188C2—19521no—
189C2—4881no—
190C2#2144522911yescharacteristic
subgroupG/H
centerC2#21445229
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1369C2
socleC2×C61#1677
prime radical#21447896C2
hypercenter#1369D61
hypocenterC61#12465
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1369

Complements

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

NH ≅ G/Ntype
1. #21448061C2semidirect
2. #21447996C2semidirect
4. #21447662C2semidirect
5. #21443879C2semidirect
6. #21443855C2semidirect
7. C61×#1369C2semidirect
96. #1369D61semidirect
118. C61#12465semidirect

Maximal subgroups

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

subgroupindex
#214480612
#214479962
#214478962
#214476622
#214438792
#214438552
C61×#13692
#1246561