Finite Group Databasebeta

← #29593376

Subgroups — #29593376

Order 15616.

262 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 262 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#21457273C211yesmaximal, characteristic
2#21448038C212yesmaximal
3#21443812C212yesmaximal
4#21443772C211yesmaximal, characteristic
5C61×#2103C211yesmaximal, characteristic
6#16840374—21no—
7#16840070—22no—
8#16840020C2212yes—
9#16840003—21no—
10#16839973—22no—
11#16839586—22no—
12#16839577—22no—
13#16839544C2212yes—
14C61×#430C2211yescharacteristic
15C61×#424C2211yescharacteristic
16C61×#344—21no—
17C61×#341—21no—
18C61×#338C2211yescharacteristic
19C2×Dic244—21no—
20C2×Dic244D412yes—
21#14519777—21no—
22#14519770—42no—
23#14519769—21no—
24#14519767—42no—
25#14519756—22no—
26C4×Dic122—22no—
27#14519717—22no—
28#14519711—21no—
29#14519709D412yes—
30#14519702—22no—
31#14519702—22no—
32C2×M16×C61—21no—
33C2×M16×C61—21no—
34C2×M16×C61C2311yescharacteristic
35C22×C8×C61D411yescharacteristic
36#117×C61D411yescharacteristic
37#108×C61—22no—
38C4⋊C8×C61—22no—
39C22×C4×C61C2×D411yescharacteristic
40C2×Dic122—22no—
41M16×C61—41no—
42M16×C61—41no—
43M16×C61—41no—
44M16×C61—41no—
45M16×C61—41no—
46C2×C8×C61—21no—
47C2×C8×C61—41no—
48C2×C8×C61—41no—
49C2×C8×C61—41no—
50C2×C8×C61C2×D412yes—
51C4⋊C4×C61—21no—
52C22⋊C4×C61SD1612yes—
53C42×C61—21no—
54C22⋊Dic61—42no—
55C4⋊Dic61—22no—
56C4⋊Dic61—42no—
57#11758196—42no—
58#11758196—42no—
59#11758196—42no—
60C4×Dic61—42no—
61Dic244—42no—
62Dic244—81no—
63#11758185—42no—
64C23×C61C2×SD1611yescharacteristic
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—22no—
68C2×C4×C61#12011yescharacteristic
69C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
70C2×Dic61—42no—
71C2×Dic61—42no—
72Dic122—42no—
73Dic122—42no—
74C8×C61—22no—
75C8×C61—41no—
76C8×C61—81no—
77C8×C61—81no—
78#12305—611nomaximal, Sylow
79C22×C61—21no—
80C22×C61—41no—
81C22×C61#45011yescharacteristic
82C4×C61—21no—
83C4×C61—42no—
84C4×C61#45411yescharacteristic
85C4×C61#45811yescharacteristic
86Dic61—82no—
87Dic61—82no—
88#3261—611no—
89#2239—612no—
90#2103D6111yescharacteristic
91#1342—612no—
92#1328—611no—
93C2×C61—21no—
94C2×C61—41no—
95C2×C61#161611yescharacteristic
96#541—1221no—
97#479—1222no—
98#470—612no—
99#467—1221no—
100#462—1222no—
101#430C2×D6111yescharacteristic
102#424C2×D6111yescharacteristic
103#365—1222no—
104#362—1222no—
105#349—612no—
106#344—21no—
107#341—21no—
108#338C2×D6111yescharacteristic
109C61#1230511yescharacteristic, complemented, Sylow
110C2×Q16—612no—
111C2×Q16—1221no—
112C2×M16—21no—
113C2×M16—21no—
114C2×M16C22×D6111yescharacteristic
115C22×C8C22⋊D6111yescharacteristic
116C4⋊Q8—1221no—
117#126—2442no—
118#125—1221no—
119#125—2442no—
120C22⋊Q8—1222no—
121C4×Q8—1222no—
122#117C22⋊D6111yescharacteristic
123M32—1222no—
124#108—22no—
125#107—1221no—
126#106—612no—
127C4⋊C8—22no—
128#103—1222no—
129#103—1222no—
130C2×Q8—1222no—
131C22×C4C2×C22⋊D6111yescharacteristic
132Q16—4881no—
133Q16—2442no—
134M16—41no—
135M16—41no—
136M16—41no—
137M16—41no—
138M16—41no—
139C2×C8—21no—
140C2×C8—41no—
141C2×C8—41no—
142C2×C8—41no—
143C2×C8D4×D6112yes—
144C4⋊C4—21no—
145C4⋊C4—1222no—
146C4⋊C4—2442no—
147C4⋊C4—2442no—
148C4⋊C4—2442no—
149C4⋊C4—2442no—
150C22⋊C4—2442no—
151C22⋊C4#1175820112yes—
152C42—21no—
153C42—2442no—
154C16—2442no—
155C23C2×#1175820111yescharacteristic
156Q8—2442no—
157Q8—2442no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—2442no—
162C2×C4—2442no—
163C2×C4#1451974511yescharacteristic
164C2×C4#1451980211yescharacteristic
165C8—22no—
166C8—41no—
167C8—81no—
168C8—81no—
169C22—21no—
170C22—41no—
171C22#1683991211yescharacteristic
172C4—21no—
173C4—42no—
174C4—4882no—
175C4—4882no—
176C4#1683993411yescharacteristic
177C4#1683995111yescharacteristic
178C2—21no—
179C2—41no—
180C2#2144485511yescharacteristic
subgroupG/H
centerC2#21444855
commutator, cosocleC2×M16×C61C23
FrattiniC2×M16C22×D61
FittingC61×#2103C2
socleC2×C61#1616
prime radicalC23×C61C2×SD16
hypercenter#2103D61
hypocenterC61#12305
LCSG ▷ C2×M16×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2103

Complements

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

NH ≅ G/Ntype
109. C61#12305semidirect

Maximal subgroups

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

subgroupindex
#214572732
#214480382
#214438122
#214437722
C61×#21032
#1230561