Finite Group Databasebeta

← #29594415

Subgroups — #29594415

Order 15616.

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

normal subgroups only

This group has 196 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#21448060C211yesmaximal, characteristic, complemented
2#21447996C211yesmaximal, characteristic, complemented
3#21447892C211yesmaximal, characteristic
4#21447660C211yesmaximal, characteristic, complemented
5#21443886C211yesmaximal, characteristic, complemented
6#21443881C211yesmaximal, characteristic, complemented
7C61×#1357C211yesmaximal, characteristic, complemented
8#16840198—21no—
9#16840180—21no—
10#16840164C2211yescharacteristic
11#16839880C2211yescharacteristic
12#16839585—21no—
13#16839583C2211yescharacteristic
14#16839575—21no—
15#16839573—21no—
16#16839563—21no—
17#16839563—21no—
18#16839547—21no—
19#16839538C2211yescharacteristic
20C61×#493C2211yescharacteristic
21C61×#364C2211yescharacteristic
22C61×#364C2211yescharacteristic
23#14519799D411yescharacteristic
24#14519783—21no—
25#14519769—21no—
26#14519721—41no—
27#14519718—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×D8×C61—21no—
38C2×D8×C61—21no—
39#127×C61—21no—
40M32×C61—21no—
41M32×C61—21no—
42C4×C8×C61C2311yescharacteristic
43C2×D4×C61—41no—
44C2×D4×C61—81no—
45#11758222—21no—
46D8×C61—41no—
47D8×C61—41no—
48D8×C61—41no—
49D8×C61—41no—
50C2×C8×C61C2×D411yescharacteristic
51C2×C8×C61C2×D411yescharacteristic
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—
66C23×C61—81no—
67D4×C61—81no—
68D4×C61—81no—
69D4×C61—162no—
70C2×C4×C61—21no—
71C2×C4×C61#12111yescharacteristic
72C22⋊D61—41no—
73C2×Dic61—81no—
74D244—21no—
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—162no—
84C22×C61—161no—
85C22×C61#47211yescharacteristic
86C2×D61—41no—
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#1369—611no—
97#1366—611no—
98#1357D6111yescharacteristic, complemented
99C2×C61—21no—
100C2×C61—321no—
101C2×C61#167711yescharacteristic
102D61—81no—
103#509—1221no—
104#504—1221no—
105#499—611no—
106#493C2×D6111yescharacteristic
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#346—611no—
118C61#1246511yescharacteristic, complemented, Sylow
119#135—611no—
120C2×D8—21no—
121C2×D8—21no—
122#131—1221no—
123#127—21no—
124#125—1221no—
125SD32—2441no—
126D16—2441no—
127M32—21no—
128M32—21no—
129M32—1221no—
130M32—2441no—
131C2×C16—611no—
132C2×C16—611no—
133C2×C16—2441no—
134#108—611no—
135#107—1221no—
136#106—1221no—
137#104—1221no—
138C4×C8C22×D6111yescharacteristic
139#41—1221no—
140C2×D4—41no—
141C2×D4—81no—
142Q16—611no—
143SD16—1221no—
144D8—41no—
145D8—41no—
146D8—41no—
147D8—41no—
148D8—611no—
149M16—1221no—
150M16—2441no—
151C2×C8—2441no—
152C2×C8D4×D6111yescharacteristic
153C2×C8D4×D6111yescharacteristic
154C4⋊C4—4881no—
155C4⋊C4—2441no—
156C42#1175822211yescharacteristic
157C16—41no—
158C16—41no—
159C16—1221no—
160C16—1221no—
161C16—2441no—
162C23—81no—
163Q8—1221no—
164D4—81no—
165D4—81no—
166D4—162no—
167D4—1221no—
168D4—2441no—
169C2×C4—21no—
170C2×C4—4881no—
171C2×C4—2441no—
172C2×C4#1451975011yescharacteristic
173C8—2441no—
174C8SD16×D6111yescharacteristic
175C8#1451979611yescharacteristic
176C8#1451979811yescharacteristic
177C8#1451980111yescharacteristic
178C22—162no—
179C22—161no—
180C22—2441no—
181C22#1684003111yescharacteristic
182C4—41no—
183C4—9761no—
184C4—2441no—
185C4#1683997611yescharacteristic
186C4#1683999011yescharacteristic
187C2—21no—
188C2—321no—
189C2—4881no—
190C2#2144522711yescharacteristic
subgroupG/H
centerC2#21445227
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1357C2
socleC2×C61#1677
prime radical#21447892C2
hypercenter#1357D61
hypocenterC61#12465
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1357

Complements

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

NH ≅ G/Ntype
1. #21448060C2semidirect
2. #21447996C2semidirect
4. #21447660C2semidirect
5. #21443886C2semidirect
6. #21443881C2semidirect
7. C61×#1357C2semidirect
98. #1357D61semidirect
118. C61#12465semidirect

Maximal subgroups

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

subgroupindex
#214480602
#214479962
#214478922
#214476602
#214438862
#214438812
C61×#13572
#1246561