Finite Group Databasebeta

← #29573550

Subgroups — #29573550

Order 15616.

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

normal subgroups only

This group has 394 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#21448422C211yesmaximal, characteristic
2#21444149C211yesmaximal, characteristic
3#21443726C212yesmaximal
4#21443724C212yesmaximal
5C61×#1463C211yesmaximal, characteristic
6#16839726C2212yes—
7#16839648—22no—
8#16839648—22no—
9#16839625C412yes—
10#16839622C2211yescharacteristic
11#16839622C2211yescharacteristic
12C4×C22⋊Dic61C412yes—
13#16839488—22no—
14C22×C4⋊C4×C61C2211yescharacteristic
15C61×#407C2212yes—
16C61×#324—22no—
17C2×#11758194—22no—
18C2×C4⋊Dic61—21no—
19C2×C4⋊Dic61—21no—
20C2×C22⋊Dic61C2×C412yes—
21C2×C22⋊Dic61C2×C412yes—
22C2×C4×Dic61—22no—
23C22⋊#92418—22no—
24C22⋊#92418—22no—
25#14519684—22no—
26#14519684—24no—
27#14519684—21no—
28#14519684—21no—
29C23×C4×C61C2×C411yescharacteristic
30C23×C4×C61C2×C411yescharacteristic
31C23×C4×C61C2311yescharacteristic
32C2×M16×C61—22no—
33C2×C4⋊C4×C61—22no—
34C2×C4⋊C4×C61—22no—
35C2×C4⋊C4×C61D412yes—
36C2×C4⋊C4×C61D412yes—
37C22⋊C8×C61—22no—
38C22⋊C8×C61—22no—
39C24×C61C22×C411yescharacteristic
40C22×C4×C61—21no—
41C22×C4×C61—21no—
42C22×C4×C61—21no—
43C22×C4×C61—21no—
44C22×C4×C61—41no—
45C22×C4×C61—41no—
46C22×C4×C61—81no—
47C22×C4×C61—81no—
48C22×C4×C61C22⋊C412yes—
49C22×C4×C61C22⋊C412yes—
50C22×C4×C61C2×D411yescharacteristic
51C22×C4×C61C2×D411yescharacteristic
52C22×C4×C61#4112yes—
53C22×C4×C61#4112yes—
54C22×Dic61—22no—
55C22×Dic61—22no—
56M16×C61—82no—
57C2×C8×C61—42no—
58C4⋊C4×C61—24no—
59C4⋊C4×C61—24no—
60C22⋊Dic61—42no—
61C22⋊Dic61—42no—
62C4⋊Dic61—81no—
63C4⋊Dic61—81no—
64C4×Dic61—82no—
65#11758194—82no—
66C2×#92418—42no—
67C23×C61—21no—
68C23×C61—21no—
69C23×C61—41no—
70C23×C61—41no—
71C23×C61C2×C22⋊C411yescharacteristic
72C23×C61#11711yescharacteristic
73C23×C61#11711yescharacteristic
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—42no—
79C2×C4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61—42no—
82C2×C4×C61—42no—
83C2×C4×C61—42no—
84C2×C4×C61—42no—
85C2×C4×C61—81no—
86C2×C4×C61—81no—
87C2×C4×C61#12312yes—
88C2×C4×C61#12312yes—
89C2×Dic61—42no—
90C2×Dic61—42no—
91C2×Dic61—42no—
92C2×Dic61—42no—
93C2×Dic61—42no—
94C2×Dic61—42no—
95C8×C61—82no—
96#92418—82no—
97#8758—611nomaximal, Sylow
98C22×C61—21no—
99C22×C61—21no—
100C22×C61—21no—
101C22×C61—21no—
102C22×C61—21no—
103C22×C61—21no—
104C22×C61—21no—
105C22×C61—21no—
106C22×C61—42no—
107C22×C61—42no—
108C22×C61#38111yescharacteristic
109C22×C61#41311yescharacteristic
110C22×C61#41311yescharacteristic
111C4×C61—22no—
112C4×C61—22no—
113C4×C61—42no—
114C4×C61—42no—
115Dic61—82no—
116Dic61—82no—
117#2313—611no—
118#1463—611no—
119#1463D6111yescharacteristic
120#1305—612no—
121#1305—612no—
122C2×C61—21no—
123C2×C61—21no—
124C2×C61—41no—
125C2×C61—41no—
126C2×C61#182211yescharacteristic
127C2×C61#182811yescharacteristic
128C2×C61#183011yescharacteristic
129C22×C4⋊C4C2×D6111yescharacteristic
130#407—612no—
131#407C2×D6112yes—
132#387—1222no—
133#387—1222no—
134#381—612no—
135#380—611no—
136#380—611no—
137C4×C22⋊C4—612no—
138#324—22no—
139#324—1222no—
140C61#875811yescharacteristic, complemented, Sylow
141C23×C4C4×D6111yescharacteristic
142C23×C4C4×D6111yescharacteristic
143C23×C4C22×D6111yescharacteristic
144C2×M16—22no—
145C2×M16—1222no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—1221no—
149C2×C4⋊C4—1221no—
150C2×C4⋊C4D24412yes—
151C2×C4⋊C4C22⋊D6112yes—
152C2×C22⋊C4—612no—
153C2×C22⋊C4—612no—
154C2×C42—1222no—
155C22⋊C8—22no—
156C22⋊C8—22no—
157C22⋊C8—1222no—
158C22⋊C8—1222no—
159#95—1222no—
160#95—1224no—
161#95—1221no—
162#95—1221no—
163C24C2×C4×D6111yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—81no—
171C22×C4—81no—
172C22×C4—1222no—
173C22×C4—1222no—
174C22×C4#1175819812yes—
175C22×C4#1175819812yes—
176C22×C4C2×D24411yescharacteristic
177C22×C4#1175822412yes—
178C22×C4#1175822412yes—
179C22×C4C2×C22⋊D6111yescharacteristic
180M16—82no—
181M16—4882no—
182C2×C8—42no—
183C2×C8—2442no—
184C4⋊C4—24no—
185C4⋊C4—24no—
186C4⋊C4—4881no—
187C4⋊C4—4881no—
188C22⋊C4—2442no—
189C22⋊C4—2442no—
190C42—4882no—
191C23—21no—
192C23—21no—
193C23—41no—
194C23—41no—
195C23C2×#1175819811yescharacteristic
196C23#1451973311yescharacteristic
197C23#1451973311yescharacteristic
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—81no—
210C2×C4—81no—
211C2×C4—2442no—
212C2×C4—2442no—
213C2×C4—2442no—
214C2×C4—2442no—
215C2×C4—2442no—
216C2×C4—2442no—
217C2×C4#1451975812yes—
218C2×C4#1451976112yes—
219C8—82no—
220C8—4882no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—42no—
230C22—42no—
231C22#1683962311yescharacteristic
232C22#1683974411yescharacteristic
233C22#1683974411yescharacteristic
234C4—22no—
235C4—22no—
236C4—42no—
237C4—42no—
238C4—4882no—
239C4—4882no—
240C2—21no—
241C2—21no—
242C2—41no—
243C2—41no—
244C2#2144590011yescharacteristic
245C2#2144592511yescharacteristic
246C2#2144593111yescharacteristic
subgroupG/H
centerC22#16839623
commutator, prime radicalC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1463C2
socleC22×C61#381
cosocleC23×C4×C61C23
hypercenter#1463D61
hypocenterC61#8758
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
140. C61#8758semidirect

Maximal subgroups

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

subgroupindex
#214484222
#214441492
#214437262
#214437242
C61×#14632
#875861