Finite Group Databasebeta

← #29593377

Subgroups — #29593377

Order 15616.

262 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 59 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#21448036C212yesmaximal
2#21447399C211yesmaximal, characteristic
3#21443813C212yesmaximal
4#21443772C211yesmaximal, characteristic
5C61×#3261C211yesmaximal, characteristic
6#16839811C2211yescharacteristic
7#16839584—22no—
8#16839578—22no—
9#16839544C2212yes—
10#16839532—21no—
11#16839527—21no—
12#16839520C2211yescharacteristic
13C61×#541—21no—
14C61×#479—22no—
15C61×#470C2212yes—
16C61×#467—21no—
17C61×#462—22no—
18C61×#424C2211yescharacteristic
19C2×#11758194—21no—
20C2×#11758194—21no—
21#14519717—22no—
22#14519713—22no—
23C2×Q16×C61—21no—
24C2×Q16×C61D412yes—
25C2×M16×C61C2311yescharacteristic
26C22×C8×C61D411yescharacteristic
27C4⋊Q8×C61—21no—
28#126×C61—42no—
29#125×C61—21no—
30#125×C61—42no—
31C22⋊Q8×C61—22no—
32C4×Q8×C61—22no—
33#117×C61D411yescharacteristic
34#107×C61—21no—
35#106×C61D412yes—
36C4⋊C8×C61—22no—
37#103×C61—22no—
38#103×C61—22no—
39C2×Q8×C61—22no—
40C22×C4×C61C2×D411yescharacteristic
41Q16×C61—42no—
42Q16×C61—81no—
43M16×C61—41no—
44C2×C8×C61—21no—
45C2×C8×C61—41no—
46C2×C8×C61C2×D412yes—
47C4⋊C4×C61—21no—
48C4⋊C4×C61—22no—
49C4⋊C4×C61—42no—
50C4⋊C4×C61—42no—
51C4⋊C4×C61—42no—
52C4⋊C4×C61—42no—
53C22⋊C4×C61—42no—
54C22⋊C4×C61SD1612yes—
55C42×C61—21no—
56C42×C61—42no—
57#11758194—41no—
58#11758194—41no—
59#11758194—41no—
60#11758194—41no—
61C2×#92418—41no—
62C2×#92418—41no—
63#11758185—42no—
64C23×C61C2×SD1611yescharacteristic
65Q8×C61—42no—
66Q8×C61—42no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—22no—
70C2×C4×C61—42no—
71C2×C4×C61—42no—
72C2×C4×C61#12011yescharacteristic
73C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
74C8×C61—22no—
75C8×C61—41no—
76#92418—81no—
77#92418—81no—
78#12305—611nomaximal, Sylow
79C22×C61—21no—
80C22×C61—41no—
81C22×C61#45011yescharacteristic
82C4×C61—21no—
83C4×C61—42no—
84C4×C61—82no—
85C4×C61—82no—
86C4×C61#45411yescharacteristic
87C4×C61#45811yescharacteristic
88#3261D6111yescharacteristic
89#2239—612no—
90#2103—611no—
91#1342—612no—
92#1328—611no—
93C2×C61—21no—
94C2×C61—41no—
95C2×C61#161611yescharacteristic
96#541—21no—
97#479—22no—
98#470C2×D6112yes—
99#467—21no—
100#462—22no—
101#430—611no—
102#424C2×D6111yescharacteristic
103#365—1222no—
104#362—1222no—
105#349—612no—
106#344—1221no—
107#341—1221no—
108#338—611no—
109C61#1230511yescharacteristic, complemented, Sylow
110C2×Q16—21no—
111C2×Q16C22⋊D6112yes—
112C2×M16—1221no—
113C2×M16—1221no—
114C2×M16C22×D6111yescharacteristic
115C22×C8C22⋊D6111yescharacteristic
116C4⋊Q8—21no—
117#126—42no—
118#125—21no—
119#125—42no—
120C22⋊Q8—22no—
121C4×Q8—22no—
122#117C22⋊D6111yescharacteristic
123M32—1222no—
124#108—1222no—
125#107—21no—
126#106C22⋊D6112yes—
127C4⋊C8—22no—
128#103—22no—
129#103—22no—
130C2×Q8—22no—
131C22×C4C2×C22⋊D6111yescharacteristic
132Q16—42no—
133Q16—81no—
134M16—41no—
135M16—2441no—
136M16—2441no—
137M16—2441no—
138M16—2441no—
139C2×C8—21no—
140C2×C8—41no—
141C2×C8—2441no—
142C2×C8—2441no—
143C2×C8C2×C22⋊D6112yes—
144C4⋊C4—21no—
145C4⋊C4—22no—
146C4⋊C4—42no—
147C4⋊C4—42no—
148C4⋊C4—42no—
149C4⋊C4—42no—
150C22⋊C4—42no—
151C22⋊C4#1175820012yes—
152C42—21no—
153C42—42no—
154C16—2442no—
155C23C2×#1175820011yescharacteristic
156Q8—42no—
157Q8—42no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4#1451974611yescharacteristic
164C2×C4#1451980311yescharacteristic
165C8—22no—
166C8—41no—
167C8—4881no—
168C8—4881no—
169C22—21no—
170C22—41no—
171C22#1683991311yescharacteristic
172C4—21no—
173C4—42no—
174C4—82no—
175C4—82no—
176C4#1683993511yescharacteristic
177C4#1683995211yescharacteristic
178C2—21no—
179C2—41no—
180C2#2144485611yescharacteristic
subgroupG/H
centerC2#21444856
commutator, cosocleC2×M16×C61C23
FrattiniC2×M16C22×D61
FittingC61×#3261C2
socleC2×C61#1616
prime radicalC23×C61C2×SD16
hypercenter#3261D61
hypocenterC61#12305
LCSG ▷ C2×M16×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3261

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
#214480362
#214473992
#214438132
#214437722
C61×#32612
#1230561