Finite Group Databasebeta

← #29583157

Subgroups — #29583157

Order 15616.

364 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 89 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#21446800C211yesmaximal, characteristic
3#21444319C212yesmaximal
4#21443721C212yesmaximal
5C61×#1274C211yesmaximal, characteristic
6#16840319C2211yescharacteristic
7#16839786C2211yescharacteristic
8#16839704—22no—
9#16839696—22no—
10C4×#11758196—22no—
11C4×C4⋊Dic61C2212yes—
12#16839522—22no—
13#16839500—22no—
14#16839500—22no—
15C61×#431C2212yes—
16C61×#376C2211yescharacteristic
17C2×#11758194—21no—
18#14519777Q812yes—
19#14519769—21no—
20#14519756—22no—
21C4×Dic122—22no—
22#14519736—21no—
23C2×C4⋊Dic61—22no—
24C2×#11758196—22no—
25C2×#11758196—22no—
26C2×C4×Dic61—22no—
27C4⋊#92418—22no—
28#14519684—22no—
29#14519684—22no—
30#14519684D412yes—
31#14519684D412yes—
32C2×C42×C61D412yes—
33C2×C42×C61C2311yescharacteristic
34C4⋊C8×C61—22no—
35C22⋊C8×C61—22no—
36C4×C8×C61—22no—
37#95×C61—22no—
38C22×C4×C61—22no—
39C22×C4×C61C2×D412yes—
40C22×C4×C61C2×D411yescharacteristic
41C22×Dic61—22no—
42C22×Dic61—22no—
43C2×Dic122—22no—
44C2×C8×C61—42no—
45C42×C61—22no—
46C42×C61—22no—
47C42×C61C2×Q811yescharacteristic
48C42×C61#4112yes—
49C42×C61#4111yescharacteristic
50C22⋊Dic61—41no—
51C4⋊Dic61—22no—
52C4⋊Dic61—22no—
53C4⋊Dic61—44no—
54#11758196—44no—
55#11758196—44no—
56#11758196—42no—
57C4×Dic61—41no—
58C4×Dic61—42no—
59C4×Dic61—42no—
60#11758194—42no—
61C2×#92418—41no—
62C23×C61#12011yescharacteristic
63C2×C4×C61—42no—
64C2×C4×C61—42no—
65C2×C4×C61—42no—
66C2×C4×C61—42no—
67C2×C4×C61C22⋊Q812yes—
68C2×C4×C61C22⋊Q811yescharacteristic
69C2×C4×C61#12412yes—
70C2×C4×C61#12411yescharacteristic
71C2×C4×C61#13512yes—
72C2×C4×C61#13712yes—
73C2×Dic61—24no—
74C2×Dic61—42no—
75C2×Dic61—42no—
76C2×Dic61—42no—
77C2×Dic61—42no—
78C2×Dic61—42no—
79C2×Dic61—42no—
80Dic122—82no—
81C8×C61—82no—
82#92418—81no—
83#10373—611nomaximal, Sylow
84C22×C61—22no—
85C22×C61#39311yescharacteristic
86C22×C61#45212yes—
87C4×C61—22no—
88C4×C61—22no—
89C4×C61—82no—
90C4×C61#47912yes—
91C4×C61#48811yescharacteristic
92C4×C61#49111yescharacteristic
93Dic61—44no—
94Dic61—82no—
95Dic61—82no—
96#2402—611no—
97#1995—611no—
98#1503—612no—
99#1303—612no—
100#1274D6111yescharacteristic
101C2×C61—22no—
102C2×C61#202611yescharacteristic
103C2×C61#203112yes—
104#533—611no—
105#431C2×D6112yes—
106#423—611no—
107#400—1222no—
108#398—1222no—
109C4×C4⋊C4—612no—
110C4×C4⋊C4—1222no—
111#376C2×D6111yescharacteristic
112#339—1222no—
113#328—1222no—
114#328—1222no—
115C61#1037311yescharacteristic, complemented, Sylow
116C2×M16—1221no—
117C4⋊Q8—612no—
118#125—1221no—
119C22⋊Q8—1222no—
120C4×Q8—1222no—
121#117—1221no—
122C2×C4⋊C4—1222no—
123C2×C4⋊C4—1222no—
124C2×C4⋊C4—1222no—
125C2×C42—1222no—
126C2×C42D24412yes—
127C2×C42C22×D6111yescharacteristic
128C4⋊C8—22no—
129C4⋊C8—1222no—
130C22⋊C8—22no—
131C4×C8—22no—
132#95—22no—
133#95—612no—
134#95—612no—
135#95—1222no—
136#95—1222no—
137C2×Q8—1222no—
138C22×C4—22no—
139C22×C4—1222no—
140C22×C4—1222no—
141C22×C4C2×D24411yescharacteristic
142C22×C4D4×D6112yes—
143M16—2442no—
144C2×C8—42no—
145C2×C8—2441no—
146C4⋊C4—1222no—
147C4⋊C4—1222no—
148C4⋊C4—2444no—
149C4⋊C4—2444no—
150C4⋊C4—2444no—
151C4⋊C4—2442no—
152C22⋊C4—2441no—
153C42—22no—
154C42—22no—
155C42—2442no—
156C42—2441no—
157C42—2442no—
158C42#1175822212yes—
159C42#1175822411yescharacteristic
160C42Q8×D6111yescharacteristic
161C23#1451974711yescharacteristic
162Q8—4882no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—1224no—
168C2×C4—2442no—
169C2×C4—2442no—
170C2×C4—2442no—
171C2×C4—2442no—
172C2×C4—2442no—
173C2×C4—2442no—
174C2×C4#1451975512yes—
175C2×C4#1451975711yescharacteristic
176C2×C4#1451976312yes—
177C2×C4#1451976511yescharacteristic
178C2×C4#1451979912yes—
179C2×C4#1451981012yes—
180C8—82no—
181C8—4881no—
182C22—22no—
183C22#1683967511yescharacteristic
184C22#1683992612yes—
185C4—22no—
186C4—22no—
187C4—82no—
188C4—4882no—
189C4—4882no—
190C4—2444no—
191C4#1684007012yes—
192C4#1684011711yescharacteristic
193C4#1684013111yescharacteristic
194C2—22no—
195C2#2144697111yescharacteristic
196C2#2144699012yes—
subgroupG/H
centerC2×C4#14519765
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1274C2
socleC22×C61#393
prime radicalC23×C61#120
hypercenter#1274D61
hypocenterC61#10373
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

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
#214468002
#214443192
#214437212
C61×#12742
#1037361