Finite Group Databasebeta

← #29589484

Subgroups — #29589484

Order 15616.

444 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 77 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#21448358C211yesmaximal, characteristic
2#21444161C212yesmaximal, complemented
3#21443763C211yesmaximal, characteristic, complemented
4#21443750C212yesmaximal
5C61×#1324C211yesmaximal, characteristic, complemented
6C2×#14519765C411yescharacteristic
7C2×#14519742C2211yescharacteristic
8C2×#14519739C411yescharacteristic
9#16839816—22no—
10#16839667C411yescharacteristic
11#16839663C2211yescharacteristic
12#16839651—22no—
13#16839609—22no—
14C42×Dic61C411yescharacteristic
15#16839488C2212yes—
16#16839487—22no—
17C61×#382C2211yescharacteristic
18C61×#324C2212yes—
19C22×Dic122C2×C411yescharacteristic
20C22×D244C2×C411yescharacteristic
21C22×C4×D61—21no—
22#14519765—22no—
23#14519765—22no—
24#14519742—41no—
25#14519742—41no—
26#14519739—41no—
27#14519739—41no—
28C2×#11758196D412yes—
29C2×#11758198—22no—
30C2×#11758198—22no—
31C2×#11758198—21no—
32C2×C4×Dic61—21no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61C2×C411yescharacteristic
35C2×C4×Dic61C2×C411yescharacteristic
36C2×C4×Dic61D412yes—
37#14519706—42no—
38C22⋊#92418—22no—
39#14519687—42no—
40#14519684—22no—
41C2×C4⋊C4×C61C2×C411yescharacteristic
42C2×C4⋊C4×C61C2311yescharacteristic
43C2×C42×C61C2×C411yescharacteristic
44C22⋊C8×C61—22no—
45#95×C61—22no—
46C23×D61—21no—
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61C22×C411yescharacteristic
50C22×C4×C61C2×D412yes—
51C22×Dic61—21no—
52C22×Dic61C22⋊C412yes—
53C22×Dic61C22⋊C411yescharacteristic
54C22×Dic61C22⋊C411yescharacteristic
55C2×D244—21no—
56C2×D244—41no—
57C2×D244—41no—
58C2×D244M1612yes—
59C2×C4×D61—44no—
60C2×C4×D61—41no—
61C2×C4×D61—41no—
62C2×Dic122—21no—
63C2×Dic122—21no—
64C2×Dic122—41no—
65C2×Dic122—41no—
66C2×C8×C61—42no—
67C4⋊C4×C61—41no—
68C4⋊C4×C61—41no—
69C42×C61—21no—
70C42×C61M1612yes—
71#11758198—28no—
72#11758198—44no—
73#11758198—42no—
74#11758196—42no—
75C4×Dic61—22no—
76C4×Dic61—22no—
77C4×Dic61—21no—
78C4×Dic61—21no—
79C4×Dic61—42no—
80C4×Dic61—42no—
81C4×Dic61—41no—
82C2×#92418—42no—
83C23×C61C2×C22⋊C411yescharacteristic
84C22×D61—22no—
85C22×D61—42no—
86C22×D61—42no—
87C22×D61—41no—
88C22×D61—41no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61—41no—
98C2×C4×C61C2×M1611yescharacteristic
99C2×C4×C61C2×M1611yescharacteristic
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—21no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61#9911yescharacteristic
110C2×Dic61#9911yescharacteristic
111D244—42no—
112D244—42no—
113C4×D61—82no—
114C4×D61—82no—
115Dic122—42no—
116Dic122—42no—
117C8×C61—82no—
118#92418—82no—
119#11530—611nomaximal, Sylow
120C22×C61—21no—
121C22×C61—21no—
122C22×C61#40711yescharacteristic
123C22×C61C2×#9911yescharacteristic
124C22×C61#41311yescharacteristic
125C2×D61—44no—
126C2×D61—42no—
127C2×D61—82no—
128C2×D61—81no—
129C2×D61—81no—
130C4×C61—21no—
131C4×C61—21no—
132C4×C61—42no—
133C4×C61—42no—
134C4×C61—81no—
135Dic61—21no—
136Dic61—42no—
137Dic61—41no—
138Dic61—42no—
139Dic61#35512yes—
140C4×#124—611no—
141#1467—612no—
142#1324—611no—
143#1324D6111yescharacteristic, complemented
144#1318—612no—
145C2×C61—21no—
146C2×C61—21no—
147C2×C61#146511yescharacteristic
148C2×C61#212611yescharacteristic
149C2×C61C2×#35511yescharacteristic
150D61—82no—
151C2×#124—611no—
152C2×C4×Q8—611no—
153C2×C4×D4—611no—
154#432—1222no—
155#391—611no—
156#390—611no—
157#388—1222no—
158#382C2×D6111yescharacteristic
159C4×C22⋊C4—1222no—
160C43—611no—
161#324—612no—
162#324—1222no—
163#324C2×D6112yes—
164C61#1153011yescharacteristic, complemented, Sylow
165C22×Q8—611no—
166C22×D4—611no—
167C23×C4—1221no—
168#124—1222no—
169#124—1222no—
170C4×Q8—2441no—
171C4×Q8—2441no—
172C4×D4—2441no—
173C4×D4—2441no—
174C2×C4⋊C4—612no—
175C2×C4⋊C4C4×D6111yescharacteristic
176C2×C4⋊C4C22×D6111yescharacteristic
177C2×C22⋊C4—1222no—
178C2×C22⋊C4—1221no—
179C2×C22⋊C4—1222no—
180C2×C42—611no—
181C2×C42—612no—
182C2×C42—611no—
183C2×C42—1221no—
184C2×C42—1221no—
185C2×C42C4×D6111yescharacteristic
186C4⋊C8—2442no—
187C22⋊C8—22no—
188C22⋊C8—1222no—
189#97—2442no—
190#95—22no—
191#95—1222no—
192C24—1221no—
193C2×Q8—1221no—
194C2×Q8—1221no—
195C2×Q8—2441no—
196C2×Q8—2441no—
197C2×D4—612no—
198C2×D4—1221no—
199C2×D4—2441no—
200C2×D4—2441no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—611no—
204C22×C4—612no—
205C22×C4—611no—
206C22×C4—1221no—
207C22×C4—2441no—
208C22×C4—2441no—
209C22×C4—2444no—
210C22×C4C2×C4×D6111yescharacteristic
211C22×C4D4×D6112yes—
212C2×C8—42no—
213C2×C8—2442no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—2442no—
217C22⋊C4—1228no—
218C22⋊C4—2442no—
219C22⋊C4—2444no—
220C42—21no—
221C42—1222no—
222C42—1222no—
223C42—1221no—
224C42—1221no—
225C42—2441no—
226C42—2442no—
227C42—2442no—
228C42#1175818912yes—
229C23—1222no—
230C23—2442no—
231C23—2442no—
232C23—2441no—
233C23—2441no—
234C23C22⋊C4×D6111yescharacteristic
235Q8—2442no—
236Q8—2442no—
237D4—2442no—
238D4—2442no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—611no—
249C2×C4—611no—
250C2×C4—1222no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4—1221no—
254C2×C4—1222no—
255C2×C4—1222no—
256C2×C4—4882no—
257C2×C4—4882no—
258C2×C4—2441no—
259C2×C4—2441no—
260C2×C4—2441no—
261C2×C4M16×D6111yescharacteristic
262C2×C4C2×#1175818911yescharacteristic
263C8—82no—
264C8—4882no—
265C22—21no—
266C22—21no—
267C22—4882no—
268C22—4881no—
269C22—4881no—
270C22—2444no—
271C22—2442no—
272C22#1683972411yescharacteristic
273C22#99×D6111yescharacteristic
274C22#1683974511yescharacteristic
275C4—21no—
276C4—21no—
277C4—42no—
278C4—42no—
279C4—81no—
280C4—612no—
281C4—1221no—
282C4—2442no—
283C4—2441no—
284C4—2442no—
285C2—21no—
286C2—21no—
287C2—4882no—
288C2#2144415611yescharacteristic
289C2#2144748311yescharacteristic
290C2#355×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1324C2
socleC22×C61C2×#99
prime radicalC22×D244C2×C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1324D61
hypocenterC61#11530
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
2. #21444161C2semidirect
3. #21443763C2semidirect
5. C61×#1324C2semidirect
143. #1324D61semidirect
164. C61#11530semidirect

Maximal subgroups

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

subgroupindex
#214483582
#214441612
#214437632
#214437502
C61×#13242
#1153061