Finite Group Databasebeta

← #30608582

Subgroups — #30608582

Order 15616.

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

normal subgroups only

This group has 194 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#21462222C211yesmaximal, characteristic, complemented
2#21462217C211yesmaximal, characteristic, complemented
3#21460985C211yesmaximal, characteristic, complemented
4#21460974C211yesmaximal, characteristic, complemented
5#21460973C211yesmaximal, characteristic, complemented
6#21460928C211yesmaximal, characteristic, complemented
7#21448133C211yesmaximal, characteristic
8#16840806—21no—
9D8×#6923—21no—
10#16840695C2211yescharacteristic
11#16840691C2211yescharacteristic
12#16840689C2211yescharacteristic
13#16840677—21no—
14#16840674—21no—
15#16840649C2211yescharacteristic
16#16840195C2211yescharacteristic
17D16×D61C2211yescharacteristic
18#16839599C411yescharacteristic, complemented
19D1952C411yescharacteristic, complemented
20#16839597C411yescharacteristic, complemented
21#16839595C2211yescharacteristic
22C61×SD64C411yescharacteristic, complemented
23#14519865—41no—
24D4×#6923—41no—
25D61⋊C16D411yescharacteristic
26#14519848—21no—
27#14519846—21no—
28#14519842—41no—
29#14519839—41no—
30C8×#6923D411yescharacteristic
31#14519827—21no—
32#14519800—21no—
33D8×D61—21no—
34#14519720—21no—
35D976C2×C411yescharacteristic
36D976C2×C411yescharacteristic, complemented
37#14519718—21no—
38C16×D61C2311yescharacteristic
39#14519683C2×C411yescharacteristic, complemented
40Q32×C61C2×C411yescharacteristic, complemented
41D16×C61C2×C411yescharacteristic
42C32×C61C2×C411yescharacteristic, complemented
43C22×#6923—81no—
44#11758226—41no—
45D4×D61—41no—
46C22⋊#6923—81no—
47C4⋊#6923—41no—
48C4×#6923D811yescharacteristic
49#11758213—41no—
50#11758213—81no—
51D61⋊C8—81no—
52D61⋊C8D811yescharacteristic
53Q16×C61—21no—
54D8×C61—21no—
55#11758201—41no—
56#11758199—41no—
57D488—21no—
58D488—21no—
59C8×D61C2×D411yescharacteristic
60#11758187—21no—
61C16×C61C22×C411yescharacteristic
62#11758185#4111yescharacteristic
63C22×D61—81no—
64C2×#6923—21no—
65C2×#6923—81no—
66C2×#6923—162no—
67Q8×C61—41no—
68D4×C61—41no—
69C22⋊D61—81no—
70D244—41no—
71D244—41no—
72D244—81no—
73C4×D61—81no—
74C4×D61C2×D811yescharacteristic
75#92420—21no—
76#92420—81no—
77C8×C61C4×D411yescharacteristic
78#92418#13511yescharacteristic
79#13658—611nomaximal, Sylow
80C22×C61—81no—
81C2×D61—81no—
82C2×D61—81no—
83C2×D61—161no—
84C2×D61—161no—
85C2×D61#50911yescharacteristic
86#6923—41no—
87#6923—161no—
88C4×C61—81no—
89C4×C61C4×D811yescharacteristic
90Dic61#50911yescharacteristic
91#2263—611no—
92#2179—611no—
93#2177—611no—
94#1426—611no—
95#1419—611no—
96#1418—611no—
97#1398—611no—
98C2×C61—161no—
99C2×C61#217711yescharacteristic
100D61—21no—
101D61—161no—
102D61—161no—
103#508—611no—
104C2×D16—611no—
105#443—1221no—
106C4×D8—1221no—
107SD64—611no—
108SD64#692311yescharacteristic, complemented
109D32—611no—
110D32—611no—
111M64—611no—
112M64—611no—
113#368—611no—
114#367—611no—
115#359—1221no—
116#357—1221no—
117#346—611no—
118C61#1365811yescharacteristic, complemented, Sylow
119#135—1221no—
120C2×D8—1221no—
121#131—2441no—
122C4×D4—2441no—
123Q32C2×#692311yescharacteristic, complemented
124SD32—1221no—
125D16—611no—
126D16—611no—
127D16—1221no—
128D16C2×#692311yescharacteristic
129C2×C16—611no—
130C2×C16—611no—
131#108—1221no—
132#107—1221no—
133#104—2441no—
134#102—2441no—
135C4×C8—611no—
136C32—611no—
137C32—1221no—
138C32C2×#692311yescharacteristic, complemented
139#41—2441no—
140C2×D4—2441no—
141C22×C4—4881no—
142Q16—21no—
143SD16—2441no—
144D8—21no—
145D8—1221no—
146D8—1221no—
147D8—2441no—
148M16—4881no—
149M16—2441no—
150C2×C8—611no—
151C2×C8—611no—
152C2×C8—4881no—
153C4⋊C4—2441no—
154C22⋊C4—4881no—
155C42—611no—
156C16—611no—
157C16—1221no—
158C16C22×#692311yescharacteristic
159C23—4881no—
160Q8—41no—
161D4—41no—
162D4—4881no—
163D4—4881no—
164D4—2441no—
165D4—2441no—
166C2×C4—611no—
167C2×C4—1221no—
168C2×C4—9762no—
169C2×C4—4881no—
170C2×C4—4881no—
171C8—611no—
172C8—1221no—
173C8—4881no—
174C8D4×#692311yescharacteristic
175C22—81no—
176C22—611no—
177C22—9761no—
178C22—9761no—
179C22—4881no—
180C22—4881no—
181C4—81no—
182C4—611no—
183C4—9761no—
184C4—2441no—
185C4D8×#692311yescharacteristic
186C2—161no—
187C2—1221no—
188C2—9761no—
189C2—9761no—
190C2#2146221711yescharacteristic
subgroupG/H
centerC2#21462217
commutatorC16×C61C22×C4
FrattiniC16C22×#6923
FittingC61×SD64C4
socleC2×C61#2177
prime radical#21448133C2
cosocleC16×D61C23
hypercenterSD64#6923
hypocenterC61#13658
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. #21462222C2semidirect
2. #21462217C2semidirect
3. #21460985C2semidirect
4. #21460974C2semidirect
5. #21460973C2semidirect
6. #21460928C2semidirect
18. #16839599C4semidirect
19. D1952C4semidirect
20. #16839597C4semidirect
22. C61×SD64C4semidirect
36. D976C2×C4semidirect
39. #14519683C2×C4semidirect
40. Q32×C61C2×C4semidirect
42. C32×C61C2×C4semidirect
108. SD64#6923semidirect
118. C61#13658semidirect
123. Q32C2×#6923semidirect
138. C32C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214622222
#214622172
#214609852
#214609742
#214609732
#214609282
#214481332
#1365861