Finite Group Databasebeta

← #29589488

Subgroups — #29589488

Order 15616.

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

normal subgroups only

This group has 460 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#21444156C212yesmaximal
3#21443763C211yesmaximal, characteristic, complemented
4#21443752C212yesmaximal, complemented
5C61×#1324C211yesmaximal, characteristic, complemented
6C2×#14519765C411yescharacteristic
7C2×#14519742C411yescharacteristic
8C2×#14519739C2211yescharacteristic
9#16839724—22no—
10#16839667C2211yescharacteristic
11#16839663C411yescharacteristic
12#16839651—22no—
13#16839609—22no—
14C42×Dic61C411yescharacteristic
15#16839488C2212yes—
16#16839485—22no—
17C61×#382C2211yescharacteristic
18C61×#324C2212yes—
19C22×Dic122C2×C411yescharacteristic
20C22×D244C2×C411yescharacteristic
21C22×C4×D61D412yes—
22C2×#11758189—42no—
23#14519765—22no—
24#14519765—22no—
25#14519742—41no—
26#14519742—41no—
27#14519739—41no—
28#14519739—41no—
29C2×#11758196—21no—
30C2×#11758198—22no—
31C2×#11758198—22no—
32C2×#11758198D412yes—
33C2×C4×Dic61—21no—
34C2×C4×Dic61—21no—
35C2×C4×Dic61—21no—
36C2×C4×Dic61C2×C411yescharacteristic
37C2×C4×Dic61C2×C411yescharacteristic
38C22⋊#92418—22no—
39#14519689—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×D61C22⋊C412yes—
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61C22×C411yescharacteristic
50C22×C4×C61C2×D412yes—
51C22×Dic61—21no—
52C22×Dic61—21no—
53C22×Dic61C22⋊C411yescharacteristic
54C22×Dic61C22⋊C411yescharacteristic
55C2×D244—21no—
56C2×D244—21no—
57C2×D244—41no—
58C2×D244—41no—
59C2×C4×D61—22no—
60C2×C4×D61—22no—
61C2×C4×D61—44no—
62C2×Dic122—21no—
63C2×Dic122—41no—
64C2×Dic122—41no—
65C2×Dic122M1612yescomplemented
66C2×C8×C61—42no—
67C4⋊C4×C61—41no—
68C4⋊C4×C61—41no—
69C42×C61—21no—
70C42×C61M1612yescomplemented
71#11758198—28no—
72#11758198—42no—
73#11758198—44no—
74#11758196—42no—
75C4×Dic61—21no—
76C4×Dic61—21no—
77C4×Dic61—42no—
78C4×Dic61—42no—
79C4×Dic61—41no—
80C4×Dic61—41no—
81C4×Dic61—41no—
82C2×#92418—42no—
83#11758189—84no—
84C23×C61C2×C22⋊C411yescharacteristic
85C22×D61—22no—
86C22×D61—22no—
87C22×D61—22no—
88C22×D61—42no—
89C22×D61—42no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61—42no—
97C2×C4×C61—42no—
98C2×C4×C61—41no—
99C2×C4×C61C2×M1611yescharacteristic
100C2×C4×C61C2×M1611yescharacteristic
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—21no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61#9911yescharacteristic
111C2×Dic61#9911yescharacteristic
112D244—42no—
113D244—42no—
114C4×D61—44no—
115C4×D61—82no—
116Dic122—42no—
117Dic122—42no—
118C8×C61—82no—
119#92418—82no—
120#11531—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—21no—
123C22×C61#40711yescharacteristic
124C22×C61C2×#9911yescharacteristic
125C22×C61#41311yescharacteristic
126C2×D61—44no—
127C2×D61—42no—
128C2×D61—42no—
129C2×D61—42no—
130C2×D61—82no—
131C4×C61—21no—
132C4×C61—21no—
133C4×C61—42no—
134C4×C61—42no—
135C4×C61—81no—
136Dic61—21no—
137Dic61—42no—
138Dic61—41no—
139Dic61—42no—
140Dic61#35412yes—
141C4×#124—611no—
142#1465—612no—
143#1324—611no—
144#1324D6111yescharacteristic, complemented
145#1319—612no—
146C2×C61—21no—
147C2×C61—21no—
148C2×C61#146511yescharacteristic
149C2×C61C2×#35411yescharacteristic
150C2×C61#213211yescharacteristic
151D61—82no—
152C2×#124—611no—
153C2×C4×Q8—611no—
154C2×C4×D4—611no—
155#407—1222no—
156#391—611no—
157#390—611no—
158#388—1222no—
159#382C2×D6111yescharacteristic
160C4×C22⋊C4—1222no—
161C43—611no—
162#324—612no—
163#324C2×D6112yes—
164#323—1222no—
165C61#1153111yescharacteristic, complemented, Sylow
166C22×Q8—611no—
167C22×D4—611no—
168C23×C4—612no—
169C2×M16—2442no—
170#124—1222no—
171#124—1222no—
172C4×Q8—2441no—
173C4×Q8—2441no—
174C4×D4—2441no—
175C4×D4—2441no—
176C2×C4⋊C4—1221no—
177C2×C4⋊C4C4×D6111yescharacteristic
178C2×C4⋊C4C22×D6111yescharacteristic
179C2×C22⋊C4—612no—
180C2×C22⋊C4—1222no—
181C2×C22⋊C4—1222no—
182C2×C42—611no—
183C2×C42—611no—
184C2×C42—1221no—
185C2×C42—1221no—
186C2×C42—1221no—
187C2×C42C4×D6111yescharacteristic
188C22⋊C8—22no—
189C22⋊C8—1222no—
190C22⋊C8—2442no—
191#95—22no—
192#95—1222no—
193C24—612no—
194C2×Q8—612no—
195C2×Q8—1221no—
196C2×Q8—2441no—
197C2×Q8—2441no—
198C2×D4—1221no—
199C2×D4—1221no—
200C2×D4—2441no—
201C2×D4—2441no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—611no—
205C22×C4—611no—
206C22×C4—1222no—
207C22×C4—1222no—
208C22×C4—1221no—
209C22×C4—1221no—
210C22×C4—2444no—
211C22×C4C2×C4×D6111yescharacteristic
212C22×C4D4×D6112yes—
213M16—4884no—
214C2×C8—42no—
215C2×C8—2442no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—2442no—
219C22⋊C4—1228no—
220C22⋊C4—2442no—
221C22⋊C4—2444no—
222C42—21no—
223C42—1221no—
224C42—1221no—
225C42—2441no—
226C42—2441no—
227C42—2441no—
228C42—2442no—
229C42—2442no—
230C42#1175818912yescomplemented
231C23—1222no—
232C23—1222no—
233C23—1222no—
234C23—2442no—
235C23—2442no—
236C23C22⋊C4×D6111yescharacteristic
237Q8—2442no—
238Q8—2442no—
239D4—2442no—
240D4—2442no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—611no—
251C2×C4—611no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—1222no—
255C2×C4—1221no—
256C2×C4—4882no—
257C2×C4—2444no—
258C2×C4—2441no—
259C2×C4—2441no—
260C2×C4—2441no—
261C2×C4—2441no—
262C2×C4—2441no—
263C2×C4M16×D6111yescharacteristic
264C2×C4C2×#1175818911yescharacteristic
265C8—82no—
266C8—4882no—
267C22—21no—
268C22—21no—
269C22—4882no—
270C22—2444no—
271C22—2442no—
272C22—2442no—
273C22—2442no—
274C22#1683972411yescharacteristic
275C22#99×D6111yescharacteristic
276C22#1683974511yescharacteristic
277C4—21no—
278C4—21no—
279C4—42no—
280C4—42no—
281C4—81no—
282C4—612no—
283C4—1221no—
284C4—2442no—
285C4—2442no—
286C4—2441no—
287C2—21no—
288C2—21no—
289C2—4882no—
290C2#2144415611yescharacteristic
291C2#354×D6111yescharacteristic
292C2#2144750111yescharacteristic
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#11531
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
3. #21443763C2semidirect
4. #21443752C2semidirect
5. C61×#1324C2semidirect
65. C2×Dic122M16semidirect
70. C42×C61M16semidirect
144. #1324D61semidirect
165. C61#11531semidirect
230. C42#11758189semidirect

Maximal subgroups

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

subgroupindex
#214483582
#214441562
#214437632
#214437522
C61×#13242
#1153161