Finite Group Databasebeta

← #30594535

Subgroups — #30594535

Order 15616.

322 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 58 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#21461078C211yesmaximal, characteristic
2#21461074C211yesmaximal, characteristic
3#21446111C211yesmaximal, characteristic
4#16840783—21no—
5#16840733—21no—
6#16840608C412yes—
7#16840606C412yes—
8#16840605—21no—
9#16840605—21no—
10C2×C4×C22⋊D61C2211yescharacteristic
11C2×C22⋊#92418C411yescharacteristic
12C2×#14519689—21no—
13#16839516—21no—
14C23×C8×C61C411yescharacteristic
15C2×#11758213—41no—
16C4⋊#92420—41no—
17#14519834—41no—
18C22⋊#92420—22no—
19C22⋊#92420—22no—
20#14519832—41no—
21C22×C22⋊D61Q811yescharacteristic
22C22×C4×D61D411yescharacteristic
23C22×#92418—21no—
24C4×C22⋊D61—41no—
25C4×C22⋊D61—41no—
26C2×#11758196C2×C411yescharacteristic
27C2×C22⋊Dic61D411yescharacteristic
28C2×#11758198C2×C411yescharacteristic
29C2×C4×Dic61D411yescharacteristic
30C22⋊#92418—41no—
31#14519689—42no—
32C23×C4×C61C2×C411yescharacteristic
33C22×C8×C61—21no—
34C22×C8×C61—42no—
35C22×C8×C61—41no—
36C24×C61C4⋊C411yescharacteristic
37C23×D61C4⋊C411yescharacteristic
38C22×C4×C61—21no—
39C22×C4×C61—21no—
40C22×C4×C61—41no—
41C22×C4×C61—41no—
42C22×C4×C61C4211yescharacteristic
43C22×C4×C61C22⋊C411yescharacteristic
44C2×C22⋊D61—21no—
45C2×C22⋊D61—21no—
46C2×C22⋊D61—41no—
47C2×C22⋊D61—41no—
48C22×Dic61C22⋊C411yescharacteristic
49C22×Dic61C22⋊C411yescharacteristic
50C22×Dic61C4⋊C411yescharacteristic
51C2×C4×D61—21no—
52C2×C4×D61—21no—
53C2×C4×D61—41no—
54C2×C4×D61—41no—
55C2×#92420—42no—
56C2×#92420—42no—
57#11758213—81no—
58#11758213—81no—
59C2×C8×C61—22no—
60C2×C8×C61—41no—
61C2×C8×C61—42no—
62C2×C8×C61—41no—
63C2×C8×C61—42no—
64C22⋊Dic61—41no—
65#11758198—41no—
66#11758196—41no—
67C4×Dic61—21no—
68C4×Dic61—21no—
69C2×#92418—41no—
70C2×#92418—41no—
71C2×#92418—41no—
72C23×C61—21no—
73C23×C61—21no—
74C23×C61—41no—
75C23×C61—41no—
76C23×C61#9511yescharacteristic
77C23×C61#10811yescharacteristic
78C23×C61#10811yescharacteristic
79C22×D61—21no—
80C22×D61—21no—
81C22×D61—21no—
82C22×D61—41no—
83C22×D61—41no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—42no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C2×C4×C61#9911yescharacteristic
92C2×C4×C61#9911yescharacteristic
93C22⋊D61—42no—
94C22⋊D61—42no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—41no—
101C2×Dic61—41no—
102C4×D61—41no—
103C4×D61—41no—
104C4×D61—81no—
105#92420—82no—
106#92420—82no—
107C8×C61—42no—
108#92418—81no—
109#7247—611nomaximal, Sylow
110C22×C61—21no—
111C22×C61—21no—
112C22×C61—21no—
113C22×C61—21no—
114C22×C61—41no—
115C22×C61—41no—
116C22×C61—42no—
117C22×C61—41no—
118C22×C61—41no—
119C22×C61#33811yescharacteristic
120C22×C61#34111yescharacteristic
121C22×C61#34211yescharacteristic
122C2×D61—42no—
123C2×D61—41no—
124C2×D61—41no—
125C2×D61—41no—
126C2×D61—81no—
127C4×C61—21no—
128C4×C61—41no—
129C4×C61AΣL(1,𝔽16)11yescharacteristic
130C4×C61#35211yescharacteristic
131Dic61—41no—
132Dic61—41no—
133Dic61—41no—
134#1869—611no—
135#1466—611no—
136#1465—611no—
137C2×C61—21no—
138C2×C61—21no—
139C2×C61—41no—
140C2×C61—41no—
141C2×C61#129311yescharacteristic
142C2×C61#139011yescharacteristic
143C2×C61#139511yescharacteristic
144D61—81no—
145C23×C8#692311yescharacteristic
146C2×C4×D4—611no—
147#432—1221no—
148#407—1221no—
149C2×C22⋊C8—611no—
150C2×C22⋊C8—1221no—
151#336—1221no—
152#324—612no—
153#323—612no—
154#323—1221no—
155#323—1221no—
156C61#724711yescharacteristic, complemented, Sylow
157C22×D4—611no—
158C23×C4—611no—
159C23×C4C2×#692311yescharacteristic
160C2×M16—2441no—
161C22×C8—21no—
162C22×C8—42no—
163C22×C8—41no—
164C22×C8—1221no—
165C4×D4—2441no—
166C4×D4—2441no—
167C2×C4⋊C4—611no—
168C2×C22⋊C4—611no—
169C2×C22⋊C4—611no—
170C2×C42—611no—
171C4⋊C8—2441no—
172C22⋊C8—1222no—
173C22⋊C8—1222no—
174C22⋊C8—2442no—
175C22⋊C8—2441no—
176C22⋊C8—2441no—
177#97—2441no—
178C24—611no—
179C24C4⋊#692311yescharacteristic
180C2×D4—1221no—
181C2×D4—1221no—
182C2×D4—2441no—
183C2×D4—2441no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—611no—
189C22×C4—611no—
190C22×C4—611no—
191C22×C4—1221no—
192C22×C4—1221no—
193C22×C4—2441no—
194C22×C4—2441no—
195C22×C4C4×#692311yescharacteristic
196C22×C4C22⋊#692311yescharacteristic
197M16—4881no—
198M16—4881no—
199C2×C8—22no—
200C2×C8—41no—
201C2×C8—42no—
202C2×C8—41no—
203C2×C8—42no—
204C2×C8—2441no—
205C2×C8—2441no—
206C2×C8—2442no—
207C2×C8—2442no—
208C2×C8—2441no—
209C4⋊C4—2441no—
210C22⋊C4—2441no—
211C22⋊C4—2441no—
212C42—1221no—
213C42—1221no—
214C23—21no—
215C23—21no—
216C23—41no—
217C23—41no—
218C23—1221no—
219C23—1221no—
220C23—1221no—
221C23—2441no—
222C23—2441no—
223C23(C2×#6923)⋊C411yescharacteristic
224C23#1451984711yescharacteristic
225C23#1451984811yescharacteristic
226D4—2442no—
227D4—2442no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—42no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—1221no—
236C2×C4—1221no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—4881no—
241C2×C4—2441no—
242C2×C4—2441no—
243C2×C4—2441no—
244C2×C4—2441no—
245C2×C4#1451983511yescharacteristic
246C2×C4#1451983611yescharacteristic
247C8—42no—
248C8—4881no—
249C8—4882no—
250C8—4882no—
251C22—21no—
252C22—21no—
253C22—21no—
254C22—21no—
255C22—41no—
256C22—41no—
257C22—42no—
258C22—41no—
259C22—41no—
260C22—4881no—
261C22—2442no—
262C22—2441no—
263C22—2441no—
264C22—2441no—
265C22#1684063111yescharacteristic
266C22#1684063811yescharacteristic
267C22#1684064011yescharacteristic
268C4—21no—
269C4—41no—
270C4—2441no—
271C4—2441no—
272C4—2441no—
273C4#1684066211yescharacteristic
274C4#1684066411yescharacteristic
275C2—21no—
276C2—21no—
277C2—41no—
278C2—41no—
279C2—4881no—
280C2#2146069111yescharacteristic
281C2#2146090311yescharacteristic
282C2#2146091911yescharacteristic
subgroupG/H
centerC22#16840640
commutatorC22×C4×C61C42
FrattiniC23×C4C2×#6923
FittingC23×C8×C61C4
socleC22×C61#342
prime radicalC22×C22⋊D61Q8
cosocleC2×C4×C22⋊D61C22
hypercenterC23×C8#6923
hypocenterC61#7247
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
156. C61#7247semidirect

Maximal subgroups

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

subgroupindex
#214610782
#214610742
#214461112
#724761