Finite Group Databasebeta

← #29567048

Subgroups — #29567048

Order 15616.

276 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 67 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#21445902C211yesmaximal, characteristic
2#21445585C211yesmaximal, characteristic
3C61×#1464C211yesmaximal, characteristic
4#16839726—21no—
5C2×C22⋊#92418—21no—
6C2×#14519688C411yescharacteristic
7C2×C4×#92418C411yescharacteristic
8#16839531—21no—
9#16839531C412yes—
10#16839517—21no—
11C2×#117×C61C2211yescharacteristic
12C61×#432—21no—
13C61×#324—21no—
14C61×#323C412yes—
15C2×#11758194—22no—
16C22×#92418—21no—
17C22×#92418—21no—
18C22⋊#92418—24no—
19C22⋊#92418—41no—
20C22⋊#92418—41no—
21#14519688—41no—
22C4×#92418—41no—
23C23×C4×C61D411yescharacteristic
24#117×C61—41no—
25#117×C61—41no—
26C2×C4⋊C4×C61C2×C411yescharacteristic
27C2×C4⋊C4×C61D411yescharacteristic
28C2×C22⋊C4×C61C2×C411yescharacteristic
29C2×C22⋊C4×C61Q811yescharacteristic
30C2×C42×C61C2×C411yescharacteristic
31C2×C42×C61D411yescharacteristic
32C4⋊C8×C61—41no—
33C22⋊C8×C61—22no—
34#97×C61—41no—
35C24×C61C4⋊C411yescharacteristic
36C22×C4×C61—21no—
37C22×C4×C61—21no—
38C22×C4×C61—22no—
39C22×C4×C61—41no—
40C22×C4×C61C4211yescharacteristic
41C22×C4×C61C22⋊C411yescharacteristic
42C22×C4×C61C22⋊C411yescharacteristic
43C22×C4×C61C22⋊C411yescharacteristic
44C22×C4×C61C4⋊C411yescharacteristic
45C22×C4×C61C4⋊C411yescharacteristic
46C2×C8×C61—42no—
47C4⋊C4×C61—41no—
48C4⋊C4×C61—41no—
49C22⋊C4×C61—41no—
50C22⋊C4×C61—41no—
51C42×C61—21no—
52C42×C61—21no—
53C42×C61—21no—
54C42×C61—21no—
55#11758194—42no—
56#11758194—42no—
57C2×#92418—22no—
58C2×#92418—22no—
59C2×#92418—41no—
60C2×#92418—41no—
61C2×#92418—41no—
62C2×#92418—41no—
63C2×#92418—42no—
64C23×C61—21no—
65C23×C61—21no—
66C23×C61—21no—
67C23×C61—41no—
68C23×C61—41no—
69C23×C61#9511yescharacteristic
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—42no—
79C2×C4×C61—42no—
80C2×C4×C61—41no—
81C2×C4×C61—41no—
82C2×C4×C61—41no—
83C2×C4×C61—41no—
84C2×C4×C61#9911yescharacteristic
85C2×C4×C61#9911yescharacteristic
86C2×C4×C61#10412yes—
87C8×C61—82no—
88#92418—42no—
89#92418—42no—
90#92418—82no—
91#7216—611nomaximal, Sylow
92C22×C61—21no—
93C22×C61—21no—
94C22×C61—42no—
95C22×C61—41no—
96C22×C61—41no—
97C22×C61—41no—
98C22×C61—81no—
99C22×C61H(3,ℤ/4)11yescharacteristic
100C22×C61#33911yescharacteristic
101C22×C61#34211yescharacteristic
102C4×C61—21no—
103C4×C61—21no—
104C4×C61—22no—
105C4×C61—41no—
106C4×C61—41no—
107C4×C61—41no—
108C4×C61—41no—
109#1822—611no—
110#1750—611no—
111#1464D6111yescharacteristic
112C2×C61—21no—
113C2×C61—21no—
114C2×C61—81no—
115C2×C61#128411yescharacteristic
116C2×C61#139211yescharacteristic
117C2×C61#139511yescharacteristic
118C2×#117C2×D6111yescharacteristic
119#432—21no—
120#407—1221no—
121C2×C22⋊C8—1221no—
122C2×#97—611no—
123C2×C4×C8—611no—
124#343—612no—
125#343—1221no—
126#336—1221no—
127#324—21no—
128#323Dic6112yes—
129C61#721611yescharacteristic, complemented, Sylow
130C23×C4D24411yescharacteristic
131C2×M16—1222no—
132C22×C8—1221no—
133C22×C8—1221no—
134#117—41no—
135#117—41no—
136C2×C4⋊C4C4×D6111yescharacteristic
137C2×C4⋊C4C22⋊D6111yescharacteristic
138C2×C22⋊C4Dic12211yescharacteristic
139C2×C22⋊C4C2×Dic6111yescharacteristic
140C2×C42C4×D6111yescharacteristic
141C2×C42C22⋊D6111yescharacteristic
142C4⋊C8—41no—
143C22⋊C8—22no—
144C22⋊C8—1224no—
145C22⋊C8—2441no—
146C22⋊C8—2441no—
147#97—41no—
148#97—2441no—
149C4×C8—2441no—
150C24C4⋊Dic6111yescharacteristic
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—22no—
154C22×C4—41no—
155C22×C4C4×Dic6111yescharacteristic
156C22×C4#1175819611yescharacteristic
157C22×C4#1175819611yescharacteristic
158C22×C4#1175819811yescharacteristic
159C22×C4#1175819811yescharacteristic
160C22×C4C22⋊Dic6111yescharacteristic
161M16—2442no—
162M16—2442no—
163C2×C8—42no—
164C2×C8—1222no—
165C2×C8—1222no—
166C2×C8—2442no—
167C2×C8—2441no—
168C2×C8—2441no—
169C2×C8—2441no—
170C2×C8—2441no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C22⋊C4—41no—
174C22⋊C4—41no—
175C42—21no—
176C42—21no—
177C42—21no—
178C42—21no—
179C23—21no—
180C23—21no—
181C23—21no—
182C23—41no—
183C23—41no—
184C23#1451968411yescharacteristic
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4#1451969111yescharacteristic
200C2×C4#1451969111yescharacteristic
201C2×C4#1451970312yes—
202C8—82no—
203C8—4882no—
204C8—2442no—
205C8—2442no—
206C22—21no—
207C22—21no—
208C22—42no—
209C22—41no—
210C22—41no—
211C22—41no—
212C22—81no—
213C22#1683951911yescharacteristic
214C22#1683952311yescharacteristic
215C22#1683952811yescharacteristic
216C4—22no—
217C4—21no—
218C4—21no—
219C4—41no—
220C4—41no—
221C4—41no—
222C4—41no—
223C2—21no—
224C2—21no—
225C2—81no—
226C2#2144367311yescharacteristic
227C2#2144394111yescharacteristic
228C2#2144394711yescharacteristic
subgroupG/H
centerC22#16839528
commutatorC22×C4×C61C42
FrattiniC2×#117C2×D61
FittingC61×#1464C2
socleC22×C61#342
prime radicalC24×C61C4⋊C4
cosocleC2×#117×C61C22
hypercenter#1464D61
hypocenterC61#7216
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
129. C61#7216semidirect

Maximal subgroups

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

subgroupindex
#214459022
#214455852
C61×#14642
#721661