Finite Group Databasebeta

← #30608573

Subgroups — #30608573

Order 15616.

184 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 52 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#21462220C211yesmaximal, characteristic, complemented
2#21462218C211yesmaximal, characteristic, complemented
3#21460982C211yesmaximal, characteristic, complemented
4#21460971C211yesmaximal, characteristic, complemented
5#21460970C211yesmaximal, characteristic, complemented
6#21460925C211yesmaximal, characteristic, complemented
7#21448127C211yesmaximal, characteristic
8#16840806—21no—
9#16840804—21no—
10D61⋊C32C2211yescharacteristic
11#16840690C2211yescharacteristic
12#16840690C2211yescharacteristic
13#16840677—21no—
14#16840676—21no—
15C16×#6923C2211yescharacteristic
16#16840195C2211yescharacteristic
17#16840191C2211yescharacteristic
18#16839602C411yescharacteristic, complemented
19#16839601C411yescharacteristic, complemented
20#16839597C411yescharacteristic, complemented
21C32×D61C2211yescharacteristic
22C61×SD64C411yescharacteristic, complemented
23#14519865—41no—
24#14519864—41no—
25D61⋊C16D411yescharacteristic
26#14519848—21no—
27#14519848—21no—
28#14519842—41no—
29#14519841—41no—
30C8×#6923D411yescharacteristic
31#14519827—21no—
32#14519800—21no—
33#14519796—21no—
34Dic488C2×C411yescharacteristic
35#14519721—21no—
36#14519720—21no—
37D976C2×C411yescharacteristic
38C16×D61C2311yescharacteristic
39#14519683C2×C411yescharacteristic
40Q32×C61C2×C411yescharacteristic
41D16×C61C2×C411yescharacteristic
42C32×C61C2×C411yescharacteristic
43#11758226—41no—
44#11758224—41no—
45#11758217—81no—
46C2×#92420—81no—
47C4×#6923D811yescharacteristic
48#11758213—41no—
49#11758213—41no—
50#11758213—81no—
51D61⋊C8—81no—
52D61⋊C8D811yescharacteristic
53Q16×C61—21no—
54D8×C61—21no—
55#11758201—41no—
56#11758200—41no—
57Dic244—21no—
58D488—21no—
59C8×D61C2×D411yescharacteristic
60#11758187—21no—
61C16×C61C22×C411yescharacteristic
62#11758185#4111yescharacteristic
63C2×#6923—21no—
64Q8×C61—41no—
65D4×C61—41no—
66C22⋊D61—81no—
67C2×Dic61—81no—
68D244—41no—
69D244—81no—
70C4×D61—81no—
71C4×D61C2×D811yescharacteristic
72Dic122—41no—
73#92420—81no—
74#92420—81no—
75#92420D1611yescharacteristic
76#92420D1611yescharacteristic
77C8×C61C4×D411yescharacteristic
78#92418#13511yescharacteristic
79#13656—611nomaximal, Sylow
80C22×C61—81no—
81C2×D61—81no—
82C2×D61#50811yescharacteristic
83#6923—41no—
84C4×C61—81no—
85C4×C61C4×D811yescharacteristic
86Dic61—81no—
87Dic61C2×D1611yescharacteristic
88#2262—611no—
89#2178—611no—
90#2178—611no—
91#1425—611no—
92#1417—611no—
93#1417—611no—
94#1397—611no—
95C2×C61—161no—
96C2×C61C4×D1611yescharacteristic
97D61—21no—
98D61—161no—
99#508—611no—
100#508—611no—
101#443—1221no—
102#443—1221no—
103Q64—611no—
104SD64—611no—
105SD64#692311yescharacteristic, complemented
106D32—611no—
107C2×C32—611no—
108C2×C32—611no—
109#368—611no—
110#368—611no—
111#359—1221no—
112#359—1221no—
113C4×C16—611no—
114C61#1365611yescharacteristic, complemented, Sylow
115#135—1221no—
116#135—1221no—
117#131—2441no—
118#131—2441no—
119Q32—611no—
120Q32C2×#692311yescharacteristic
121SD32—1221no—
122SD32—1221no—
123D16—611no—
124D16C2×#692311yescharacteristic
125C2×C16—611no—
126C2×C16—611no—
127#108—1221no—
128#108—1221no—
129#104—2441no—
130#104—2441no—
131C4×C8—611no—
132C32—611no—
133C32—1221no—
134C32C2×#692311yescharacteristic
135#41—2441no—
136#41—2441no—
137Q16—21no—
138Q16—1221no—
139SD16—2441no—
140SD16—2441no—
141D8—21no—
142D8—1221no—
143M16—4881no—
144M16—4881no—
145M16—2441no—
146M16—2441no—
147C2×C8—611no—
148C2×C8—611no—
149C2×C8—4881no—
150C2×C8—4881no—
151C42—611no—
152C16—611no—
153C16—1221no—
154C16C22×#692311yescharacteristic
155Q8—41no—
156Q8—2441no—
157D4—41no—
158D4—4881no—
159D4—4881no—
160D4—2441no—
161C2×C4—611no—
162C2×C4—1221no—
163C2×C4—4881no—
164C2×C4—4881no—
165C8—611no—
166C8—611no—
167C8—611no—
168C8—4881no—
169C8—4881no—
170C8D4×#692311yescharacteristic
171C22—81no—
172C22—611no—
173C22—4881no—
174C4—81no—
175C4—611no—
176C4—4881no—
177C4—2441no—
178C4D8×#692311yescharacteristic
179C2—161no—
180C2—1221no—
181C2—9761no—
182C2D16×#692311yescharacteristic
subgroupG/H
centerC2D16×#6923
commutatorC16×C61C22×C4
FrattiniC16C22×#6923
FittingC61×SD64C4
socleC2×C61C4×D16
prime radical#21448127C2
cosocleC16×D61C23
hypercenterSD64#6923
hypocenterC61#13656
LCSG ▷ C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ SD64

Complements

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

NH ≅ G/Ntype
1. #21462220C2semidirect
2. #21462218C2semidirect
3. #21460982C2semidirect
4. #21460971C2semidirect
5. #21460970C2semidirect
6. #21460925C2semidirect
18. #16839602C4semidirect
19. #16839601C4semidirect
20. #16839597C4semidirect
22. C61×SD64C4semidirect
105. SD64#6923semidirect
114. C61#13656semidirect

Maximal subgroups

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

subgroupindex
#214622202
#214622182
#214609822
#214609712
#214609702
#214609252
#214481272
#1365661