Finite Group Databasebeta

← #29599909

Subgroups — #29599909

Order 15616.

276 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 83 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#21447434C211yesmaximal, characteristic
2#21445874C212yesmaximal
3#21443921C211yesmaximal, characteristic, complemented
4#21443916C212yesmaximal, complemented
5C61×#2161C211yesmaximal, characteristic, complemented
6C2×#14519783C2211yescharacteristic
7C22×#11758185C2211yescharacteristic
8#16839800C2212yes—
9#16839778—22no—
10#16839541—22no—
11#16839533—22no—
12C2×M32×C61C2211yescharacteristic
13C2×#108×C61C2212yes—
14C61×#368—22no—
15C2×#11758222D411yescharacteristic
16#14519783—22no—
17#14519783—22no—
18C2×#11758194D411yescharacteristic
19C2×#11758189—21no—
20C2×C8×D61—21no—
21#14519736—22no—
22C2×#11758185—21no—
23C2×#11758185—22no—
24#14519711—22no—
25#14519709—22no—
26#14519703—44no—
27C2×M16×C61—22no—
28C22×C8×C61C2311yescharacteristic
29M32×C61—22no—
30C2×C16×C61D412yes—
31#108×C61—22no—
32#108×C61—22no—
33C22×C4×C61C2×D411yescharacteristic
34C2×C22⋊D61—21no—
35#11758222—22no—
36#11758222—22no—
37C2×D244Q1611yescharacteristic
38C2×C4×D61—21no—
39C2×Dic122Q1611yescharacteristic
40M16×C61—42no—
41M16×C61—42no—
42C2×C8×C61—42no—
43C2×C8×C61C2×D411yescharacteristic
44C2×C8×C61#4112yes—
45C2×C8×C61#4112yes—
46C2×C8×C61#4111yescharacteristic
47C22⋊Dic61—42no—
48C4⋊Dic61—42no—
49C4×Dic61—42no—
50#11758194—22no—
51C2×#92418—21no—
52#11758189—42no—
53C8×D61—41no—
54C8×D61—41no—
55C16×C61—22no—
56#11758185—41no—
57C23×C61#13511yescharacteristic
58C22×D61—21no—
59C2×C4×C61#12111yescharacteristic
60C2×C4×C61#12312yes—
61C2×C4×C61C2×Q1611yescharacteristic
62C2×C4×C61AGL(1,ℤ/8)12yes—
63C22⋊D61—42no—
64C2×Dic61—21no—
65C2×Dic61—82no—
66D244—22no—
67C4×D61—41no—
68C4×D61—41no—
69Dic122—22no—
70C8×C61—82no—
71C8×C61#12311yescharacteristic
72C8×C61#12411yescharacteristic
73C8×C61#12612yes—
74#92418—41no—
75#13499—611nomaximal, Sylow
76C22×C61—41no—
77C22×C61#46711yescharacteristic
78C22×C61#48212yes—
79C2×D61—42no—
80C2×D61—41no—
81C4×C61#39711yescharacteristic
82C4×C61#46911yescharacteristic
83C4×C61#48412yes—
84Dic61—41no—
85Dic61—162no—
86#2161D6111yescharacteristic, complemented
87#2113—611no—
88#1814—612no—
89#1384—611no—
90#1382—612no—
91C2×C61—22no—
92C2×C61—21no—
93C2×C61#207611yescharacteristic
94D61—81no—
95C2×#131—611no—
96C2×M32C2×D6111yescharacteristic
97C22×C16—611no—
98C2×#108C2×D6112yes—
99#427—612no—
100#421—1222no—
101#368—22no—
102C22⋊C16—1222no—
103#344—1222no—
104C61#1349911yescharacteristic, complemented, Sylow
105C2×#41—611no—
106#131—1222no—
107#131—1222no—
108C2×M16—22no—
109C2×M16—611no—
110C2×M16—1221no—
111C22×C8—1221no—
112C22×C8C22×D6111yescharacteristic
113#117—1222no—
114M32—22no—
115C2×C16—1222no—
116C2×C16—1221no—
117C2×C16C22⋊D6112yes—
118#108—22no—
119#108—22no—
120#107—1222no—
121#106—1222no—
122#104—2444no—
123#41—1222no—
124#41—1222no—
125C2×Q8—611no—
126C2×D4—611no—
127C2×D4—1221no—
128C22×C4—1221no—
129C22×C4D4×D6111yescharacteristic
130M16—42no—
131M16—42no—
132M16—1222no—
133M16—2442no—
134C2×C8—42no—
135C2×C8—1221no—
136C2×C8—2441no—
137C2×C8—2441no—
138C2×C8#1175822212yes—
139C2×C8#1175822411yescharacteristic
140C2×C8#1175822612yes—
141C2×C8C2×C22⋊D6111yescharacteristic
142C4⋊C4—2442no—
143C22⋊C4—2442no—
144C42—2442no—
145C16—22no—
146C16—2441no—
147C23—1221no—
148C23#1451980011yescharacteristic
149Q8—1222no—
150D4—1222no—
151D4—2442no—
152C2×C4—1221no—
153C2×C4—4882no—
154C2×C4—2441no—
155C2×C4—2441no—
156C2×C4#1451974811yescharacteristic
157C2×C4#1451976212yes—
158C2×C4Q16×D6111yescharacteristic
159C2×C4#1451980112yes—
160C8—82no—
161C8—2441no—
162C8#1451976011yescharacteristic
163C8#1451976611yescharacteristic
164C8#1451977212yes—
165C22—41no—
166C22—2442no—
167C22—2441no—
168C22#1684000011yescharacteristic
169C22#1684008912yes—
170C4—9762no—
171C4—2441no—
172C4#1683968811yescharacteristic
173C4#1684001211yescharacteristic
174C4#1684009912yes—
175C2—22no—
176C2—21no—
177C2—4881no—
178C2#2144724811yescharacteristic
subgroupG/H
centerC4#16840012
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#2161C2
socleC2×C61#2076
prime radicalC2×#11758222D4
hypercenter#2161D61
hypocenterC61#13499
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2161

Complements

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

NH ≅ G/Ntype
3. #21443921C2semidirect
4. #21443916C2semidirect
5. C61×#2161C2semidirect
86. #2161D61semidirect
104. C61#13499semidirect

Maximal subgroups

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

subgroupindex
#214474342
#214458742
#214439212
#214439162
C61×#21612
#1349961