Finite Group Databasebeta

← #30608576

Subgroups — #30608576

Order 15616.

182 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 50 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#21462223C211yesmaximal, characteristic
2#21462216C211yesmaximal, characteristic, complemented
3#21460985C211yesmaximal, characteristic, complemented
4#21460975C211yesmaximal, characteristic, complemented
5#21460972C211yesmaximal, characteristic
6#21460928C211yesmaximal, characteristic, complemented
7#21448135C211yesmaximal, characteristic
8#16840804—21no—
9Q16×#6923—21no—
10#16840695C2211yescharacteristic
11#16840691C2211yescharacteristic
12#16840689C2211yescharacteristic
13#16840676—21no—
14#16840675—21no—
15#16840649C2211yescharacteristic
16#16840191C2211yescharacteristic
17Q32×D61C2211yescharacteristic
18Dic976C411yescharacteristic, complemented
19#16839602C411yescharacteristic, complemented
20#16839600C411yescharacteristic, complemented
21#16839595C2211yescharacteristic
22C61×SD64C411yescharacteristic, complemented
23#14519864—41no—
24Q8×#6923—41no—
25D61⋊C16D411yescharacteristic
26#14519848—21no—
27#14519846—21no—
28#14519841—41no—
29#14519840—41no—
30C8×#6923D411yescharacteristic
31#14519827—21no—
32#14519796—21no—
33Q16×D61—21no—
34Dic488C2×C411yescharacteristic
35Dic488C2×C411yescharacteristic
36#14519723—21no—
37#14519721—21no—
38C16×D61C2311yescharacteristic
39#14519683C2×C411yescharacteristic
40Q32×C61C2×C411yescharacteristic
41D16×C61C2×C411yescharacteristic
42C32×C61C2×C411yescharacteristic
43Q8×D61—41no—
44#11758224—41no—
45#11758217—81no—
46C2×#92420—81no—
47C4⋊#6923—41no—
48C4⋊#6923—81no—
49C4×#6923—81no—
50C4×#6923D811yescharacteristic
51#11758213—41no—
52D61⋊C8D811yescharacteristic
53Q16×C61—21no—
54D8×C61—21no—
55#11758202—41no—
56#11758200—41no—
57Dic244—21no—
58Dic244—21no—
59C8×D61C2×D411yescharacteristic
60#11758187—21no—
61C16×C61C22×C411yescharacteristic
62#11758185#4111yescharacteristic
63C2×#6923—21no—
64C2×#6923—81no—
65Q8×C61—41no—
66D4×C61—41no—
67C22⋊D61—81no—
68C2×Dic61—81no—
69C4×D61—81no—
70C4×D61C2×D811yescharacteristic
71Dic122—41no—
72Dic122—41no—
73Dic122—81no—
74#92420—21no—
75#92420—81no—
76C8×C61C4×D411yescharacteristic
77#92418#13511yescharacteristic
78#13657—611nomaximal, Sylow
79C22×C61—81no—
80C2×D61#50911yescharacteristic
81#6923—41no—
82#6923—161no—
83C4×C61—81no—
84C4×C61C4×D811yescharacteristic
85Dic61—81no—
86Dic61—81no—
87Dic61#50911yescharacteristic
88#2264—611no—
89#2179—611no—
90#2176—611no—
91#1426—611no—
92#1420—611no—
93#1418—611no—
94#1398—611no—
95C2×C61—161no—
96C2×C61#217711yescharacteristic
97D61—21no—
98#508—611no—
99C2×Q32—611no—
100#443—1221no—
101C4×Q16—1221no—
102Q64—611no—
103Q64—611no—
104SD64—611no—
105SD64#692311yescharacteristic, complemented
106M64—611no—
107M64—611no—
108#368—611no—
109#367—611no—
110#359—1221no—
111#358—1221no—
112#346—611no—
113C61#1365711yescharacteristic, complemented, Sylow
114#135—1221no—
115C2×Q16—1221no—
116#131—2441no—
117C4×Q8—2441no—
118Q32—611no—
119Q32—611no—
120Q32—1221no—
121Q32C2×#692311yescharacteristic
122SD32—1221no—
123D16C2×#692311yescharacteristic
124C2×C16—611no—
125C2×C16—611no—
126#108—1221no—
127#107—1221no—
128#104—2441no—
129#103—2441no—
130C4×C8—611no—
131C32—611no—
132C32—1221no—
133C32C2×#692311yescharacteristic
134#41—2441no—
135C2×Q8—2441no—
136Q16—21no—
137Q16—1221no—
138Q16—1221no—
139Q16—2441no—
140SD16—2441no—
141D8—21no—
142M16—4881no—
143M16—2441no—
144C2×C8—611no—
145C2×C8—611no—
146C2×C8—4881no—
147C4⋊C4—4881no—
148C4⋊C4—2441no—
149C42—611no—
150C42—4881no—
151C16—611no—
152C16—1221no—
153C16C22×#692311yescharacteristic
154Q8—41no—
155Q8—4881no—
156Q8—2441no—
157Q8—2441no—
158D4—41no—
159D4—4881no—
160C2×C4—611no—
161C2×C4—1221no—
162C2×C4—4881no—
163C2×C4—4881no—
164C2×C4—4881no—
165C8—611no—
166C8—1221no—
167C8—4881no—
168C8D4×#692311yescharacteristic
169C22—81no—
170C22—611no—
171C4—81no—
172C4—611no—
173C4—9761no—
174C4—4881no—
175C4—4881no—
176C4—2441no—
177C4D8×#692311yescharacteristic
178C2—161no—
179C2—1221no—
180C2#2146221711yescharacteristic
subgroupG/H
centerC2#21462217
commutatorC16×C61C22×C4
FrattiniC16C22×#6923
FittingC61×SD64C4
socleC2×C61#2177
prime radical#16840191C22
cosocleC16×D61C23
hypercenterSD64#6923
hypocenterC61#13657
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
2. #21462216C2semidirect
3. #21460985C2semidirect
4. #21460975C2semidirect
6. #21460928C2semidirect
18. Dic976C4semidirect
19. #16839602C4semidirect
20. #16839600C4semidirect
22. C61×SD64C4semidirect
105. SD64#6923semidirect
113. C61#13657semidirect

Maximal subgroups

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

subgroupindex
#214622232
#214622162
#214609852
#214609752
#214609722
#214609282
#214481352
#1365761