Finite Group Databasebeta

← #29583156

Subgroups — #29583156

Order 15616.

364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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#21449124C211yesmaximal, characteristic
2#21444318C212yesmaximal
3#21443720C212yesmaximal
4#21443648C211yesmaximal, characteristic
5C61×#1995C211yesmaximal, characteristic
6#16839815C2212yes—
7#16839704—22no—
8#16839696—22no—
9C4×#11758196—22no—
10C4×C4⋊Dic61C2212yes—
11#16839499—22no—
12#16839499—22no—
13C61×#533C2211yescharacteristic
14C61×#423C2211yescharacteristic
15C61×#376C2211yescharacteristic
16C61×#339—22no—
17C2×C4⋊Dic61—22no—
18C2×#11758196—22no—
19C2×#11758196—22no—
20C2×C4×Dic61—22no—
21C4⋊#92418—22no—
22C22⋊#92418—22no—
23C4×#92418—22no—
24#14519684—22no—
25#14519684—22no—
26#14519684D412yes—
27#14519684D412yes—
28C2×M16×C61—21no—
29C4⋊Q8×C61Q812yes—
30#125×C61—21no—
31C22⋊Q8×C61—22no—
32C4×Q8×C61—22no—
33#117×C61—21no—
34C2×C42×C61D412yes—
35C2×C42×C61C2311yescharacteristic
36C4⋊C8×C61—22no—
37#95×C61—22no—
38C2×Q8×C61—22no—
39C22×C4×C61—22no—
40C22×C4×C61C2×D412yes—
41C22×C4×C61C2×D411yescharacteristic
42C22×Dic61—22no—
43C22×Dic61—22no—
44M16×C61—42no—
45C2×C8×C61—41no—
46C4⋊C4×C61—22no—
47C4⋊C4×C61—22no—
48C4⋊C4×C61—42no—
49C22⋊C4×C61—41no—
50C42×C61—22no—
51C42×C61—22no—
52C42×C61—41no—
53C42×C61C2×Q811yescharacteristic
54C42×C61#4111yescharacteristic
55C42×C61#4112yes—
56C4⋊Dic61—44no—
57#11758196—44no—
58#11758196—44no—
59C4×Dic61—42no—
60C4×Dic61—42no—
61C2×#92418—42no—
62C23×C61#12011yescharacteristic
63Q8×C61—82no—
64C2×C4×C61—42no—
65C2×C4×C61—42no—
66C2×C4×C61—42no—
67C2×C4×C61—42no—
68C2×C4×C61—42no—
69C2×C4×C61C22⋊Q812yes—
70C2×C4×C61C22⋊Q811yescharacteristic
71C2×C4×C61#12412yes—
72C2×C4×C61#12411yescharacteristic
73C2×C4×C61#13512yes—
74C2×C4×C61#13712yes—
75C2×Dic61—24no—
76C2×Dic61—42no—
77C2×Dic61—42no—
78C2×Dic61—42no—
79C2×Dic61—42no—
80C2×Dic61—42no—
81C8×C61—81no—
82#92418—82no—
83#10373—611nomaximal, Sylow
84C22×C61—22no—
85C22×C61#39311yescharacteristic
86C22×C61#45212yes—
87C4×C61—22no—
88C4×C61—22no—
89C4×C61—82no—
90C4×C61—82no—
91C4×C61#47912yes—
92C4×C61#48811yescharacteristic
93C4×C61#49111yescharacteristic
94Dic61—44no—
95Dic61—82no—
96#2402—611no—
97#1995D6111yescharacteristic
98#1503—612no—
99#1303—612no—
100#1274—611no—
101C2×C61—22no—
102C2×C61#202611yescharacteristic
103C2×C61#203112yes—
104#533C2×D6111yescharacteristic
105#431—612no—
106#423C2×D6111yescharacteristic
107#400—1222no—
108#398—1222no—
109C4×C4⋊C4—612no—
110C4×C4⋊C4—1222no—
111#376C2×D6111yescharacteristic
112#339—22no—
113#328—1222no—
114#328—1222no—
115C61#1037311yescharacteristic, complemented, Sylow
116C2×M16—21no—
117C4⋊Q8Dic12212yes—
118#125—21no—
119C22⋊Q8—22no—
120C4×Q8—22no—
121#117—21no—
122C2×C4⋊C4—1222no—
123C2×C4⋊C4—1222no—
124C2×C4⋊C4—1222no—
125C2×C42—1222no—
126C2×C42C22⋊D6112yes—
127C2×C42C22×D6111yescharacteristic
128C4⋊C8—22no—
129C4⋊C8—1222no—
130C22⋊C8—1222no—
131C4×C8—1222no—
132#95—22no—
133#95—612no—
134#95—612no—
135#95—1222no—
136#95—1222no—
137C2×Q8—22no—
138C22×C4—22no—
139C22×C4—1222no—
140C22×C4—1222no—
141C22×C4D4×D6112yes—
142C22×C4C2×C22⋊D6111yescharacteristic
143M16—42no—
144C2×C8—41no—
145C2×C8—2442no—
146C4⋊C4—22no—
147C4⋊C4—22no—
148C4⋊C4—42no—
149C4⋊C4—2444no—
150C4⋊C4—2444no—
151C4⋊C4—2444no—
152C22⋊C4—41no—
153C42—22no—
154C42—22no—
155C42—41no—
156C42—2442no—
157C42—2442no—
158C42C2×Dic12211yescharacteristic
159C42#1175822211yescharacteristic
160C42#1175822412yes—
161C23#1451974511yescharacteristic
162Q8—82no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—1224no—
169C2×C4—2442no—
170C2×C4—2442no—
171C2×C4—2442no—
172C2×C4—2442no—
173C2×C4—2442no—
174C2×C4#1451975412yes—
175C2×C4#1451975611yescharacteristic
176C2×C4#1451976312yes—
177C2×C4#1451976411yescharacteristic
178C2×C4#1451979712yes—
179C2×C4#1451980812yes—
180C8—81no—
181C8—4882no—
182C22—22no—
183C22#1683967411yescharacteristic
184C22#1683992212yes—
185C4—22no—
186C4—22no—
187C4—82no—
188C4—82no—
189C4—4882no—
190C4—2444no—
191C4#1684006912yes—
192C4#1684011611yescharacteristic
193C4#1684013011yescharacteristic
194C2—22no—
195C2#2144697011yescharacteristic
196C2#2144698912yes—
subgroupG/H
centerC2×C4#14519764
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1995C2
socleC22×C61#393
prime radicalC23×C61#120
hypercenter#1995D61
hypocenterC61#10373
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
115. C61#10373semidirect

Maximal subgroups

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

subgroupindex
#214491242
#214443182
#214437202
#214436482
C61×#19952
#1037361