Finite Group Databasebeta

← #29594413

Subgroups — #29594413

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#21447992C211yesmaximal, characteristic, complemented
2#21447892C211yesmaximal, characteristic
3#21447662C211yesmaximal, characteristic, complemented
4#21443887C211yesmaximal, characteristic, complemented
5#21443880C211yesmaximal, characteristic, complemented
6#21443856C211yesmaximal, characteristic, complemented
7C61×#2244C211yesmaximal, characteristic, complemented
8#16840198—21no—
9#16840178—21no—
10#16839880C2211yescharacteristic
11#16839584—21no—
12#16839583C2211yescharacteristic
13#16839583C2211yescharacteristic
14#16839583C2211yescharacteristic
15#16839575—21no—
16#16839571—21no—
17#16839545—21no—
18C61×#499C2211yescharacteristic
19C61×#493C2211yescharacteristic
20C61×#357—21no—
21C61×#357—21no—
22C61×#346C2211yescharacteristic
23#14519799D411yescharacteristic
24#14519783—21no—
25#14519721—41no—
26#14519718—41no—
27#14519717—21no—
28#14519717—21no—
29#14519717—21no—
30#14519716—41no—
31C16×D61—41no—
32#14519713D411yescharacteristic
33#14519705—21no—
34C2×D8×C61—21no—
35C2×D8×C61—21no—
36#127×C61—21no—
37#125×C61—21no—
38C2×C16×C61D411yescharacteristic
39C2×C16×C61D411yescharacteristic
40#107×C61—21no—
41#106×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
52C4⋊C4×C61—41no—
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—
66C23×C61—81no—
67D4×C61—81no—
68D4×C61—81no—
69D4×C61—162no—
70C2×C4×C61—21no—
71C2×C4×C61—81no—
72C2×C4×C61#12111yescharacteristic
73C22⋊D61—41no—
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—161no—
89C4×C61#46311yescharacteristic
90C4×C61#46511yescharacteristic
91Dic61—41no—
92#2244D6111yescharacteristic, complemented
93#2231—611no—
94#2213—611no—
95#2171—611no—
96#1369—611no—
97#1366—611no—
98#1357—611no—
99C2×C61—21no—
100C2×C61—321no—
101C2×C61#167711yescharacteristic
102D61—81no—
103#509—1221no—
104#504—1221no—
105#499C2×D6111yescharacteristic
106#493C2×D6111yescharacteristic
107#443—611no—
108#365—1221no—
109#364—611no—
110#364—611no—
111#364—611no—
112#361—1221no—
113#360—1221no—
114#357—21no—
115#357—21no—
116#350—1221no—
117#346C2×D6111yescharacteristic
118C61#1246511yescharacteristic, complemented, Sylow
119#135—611no—
120C2×D8—21no—
121C2×D8—21no—
122#131—1221no—
123#127—21no—
124#125—21no—
125SD32—2441no—
126D16—2441no—
127M32—1221no—
128M32—1221no—
129M32—1221no—
130M32—2441no—
131C2×C16—2441no—
132C2×C16C22⋊D6111yescharacteristic
133C2×C16C22⋊D6111yescharacteristic
134#108—611no—
135#107—21no—
136#106—21no—
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×C8C2×C22⋊D6111yescharacteristic
154C4⋊C4—41no—
155C4⋊C4—81no—
156C42#1175822411yescharacteristic
157C16—21no—
158C16—21no—
159C16—2441no—
160C16—2441no—
161C16—2441no—
162C23—81no—
163Q8—1221no—
164D4—81no—
165D4—81no—
166D4—162no—
167D4—1221no—
168D4—2441no—
169C2×C4—21no—
170C2×C4—81no—
171C2×C4—2441no—
172C2×C4#1451974811yescharacteristic
173C8—2441no—
174C8SD16×D6111yescharacteristic
175C8#1451979711yescharacteristic
176C8#1451979811yescharacteristic
177C8#1451980211yescharacteristic
178C22—162no—
179C22—161no—
180C22—2441no—
181C22#1684002911yescharacteristic
182C4—41no—
183C4—161no—
184C4—2441no—
185C4#1683997411yescharacteristic
186C4#1683998811yescharacteristic
187C2—21no—
188C2—321no—
189C2—4881no—
190C2#2144522511yescharacteristic
subgroupG/H
centerC2#21445225
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2244C2
socleC2×C61#1677
prime radical#21447892C2
hypercenter#2244D61
hypocenterC61#12465
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2244

Complements

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

NH ≅ G/Ntype
1. #21447992C2semidirect
3. #21447662C2semidirect
4. #21443887C2semidirect
5. #21443880C2semidirect
6. #21443856C2semidirect
7. C61×#2244C2semidirect
92. #2244D61semidirect
118. C61#12465semidirect

Maximal subgroups

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

subgroupindex
#214479922
#214478922
#214476622
#214438872
#214438802
#214438562
C61×#22442
#1246561