Finite Group Databasebeta

← #30604328

Subgroups — #30604328

Order 15616.

424 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461076C211yesmaximal, characteristic
2#21461056C211yesmaximal, characteristic
3#21460759C214yesmaximal, complemented
4#21450988C211yesmaximal, characteristic
5#16840733—21no—
6D61⋊(C22⋊C8)—21no—
7#16840607C2212yes—
8#16840607C2212yes—
9#16840606—21no—
10#16840606—21no—
11C2×#14519777C411yescharacteristic
12C2×C4×D244C2211yescharacteristic
13#16839675—21no—
14#16839675—21no—
15#16839664C412yes—
16#16839628C2212yes—
17#16839619—21no—
18#16839619—21no—
19C4×C4⋊C4×C61C411yescharacteristic
20C2×#11758213—41no—
21C2×D61⋊C8—41no—
22#14519834—41no—
23#14519834—41no—
24C22⋊#92420—22no—
25C22⋊#92420—22no—
26C22×Dic122—21no—
27C22×D244C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30#14519777—41no—
31#14519777—41no—
32C4×D244—41no—
33C4×D244—41no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C412yes—
36C2×C4⋊Dic61C2311yescharacteristic
37C2×#11758198—22no—
38C2×#11758198—22no—
39C2×#11758198D411yescharacteristic
40C2×#11758198D411yescharacteristic
41#14519684—22no—
42#14519684—22no—
43C2×C4⋊C4×C61—21no—
44C2×C42×C61C2×C412yes—
45C2×C42×C61C2×C411yescharacteristic
46#95×C61—21no—
47C23×D61C22⋊C411yescharacteristic
48C23×D61C22⋊C411yescharacteristic
49C22×C4×C61—22no—
50C22×C4×C61C22⋊C411yescharacteristic
51C22×C4×C61C22⋊C411yescharacteristic
52C22×C4×C61C22×C411yescharacteristic
53C22×Dic61—22no—
54C22×Dic61C2×D411yescharacteristic
55C22×Dic61C2×D411yescharacteristic
56C2×D244—22no—
57C2×D244—22no—
58C2×D244—41no—
59C2×C4×D61—21no—
60C2×C4×D61—21no—
61C2×C4×D61—21no—
62C2×C4×D61—21no—
63C2×C4×D61—42no—
64C2×C4×D61—42no—
65C2×Dic122—42no—
66C2×Dic122—82no—
67C2×#92420—42no—
68C2×#92420—42no—
69#11758213—82no—
70D61⋊C8—82no—
71C4⋊C4×C61—42no—
72C42×C61—21no—
73C42×C61—21no—
74C42×C61—24no—
75#11758198—41no—
76#11758198—41no—
77#11758198—82no—
78#11758198—82no—
79C4⋊Dic61—41no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82C4⋊Dic61—42no—
83C23×C61C2×C22⋊C411yescharacteristic
84C22×D61—21no—
85C22×D61—21no—
86C22×D61—21no—
87C22×D61—21no—
88C22×D61—21no—
89C22×D61—41no—
90C22×D61—41no—
91C22×D61—41no—
92C22×D61—41no—
93C22×D61#10112yes—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—22no—
97C2×C4×C61—21no—
98C2×C4×C61—41no—
99C2×C4×C61—42no—
100C2×C4×C61—42no—
101C2×C4×C61—42no—
102C2×C4×C61#9911yescharacteristic
103C2×C4×C61#9911yescharacteristic
104C2×C4×C61#13112yes—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61—42no—
110C2×Dic61—42no—
111C2×Dic61—42no—
112D244—44no—
113C4×D61—42no—
114C4×D61—42no—
115C4×D61—81no—
116C4×D61—81no—
117Dic122—84no—
118#92420—82no—
119#92420—82no—
120#11569—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—21no—
123C22×C61#40811yescharacteristic
124C22×C61C2×#9911yescharacteristic
125C22×C61C2×#10111yescharacteristic
126C2×D61—22no—
127C2×D61—41no—
128C2×D61—41no—
129C2×D61—42no—
130C2×D61—42no—
131C2×D61—41no—
132C2×D61—41no—
133C2×D61—41no—
134C2×D61—81no—
135C2×D61—81no—
136C4×C61—21no—
137C4×C61—22no—
138C4×C61—41no—
139C4×C61—82no—
140C4×C61#35412yes—
141Dic61—41no—
142Dic61—41no—
143Dic61—82no—
144#2563—611no—
145#1465—611no—
146#1459—611no—
147#1324—614no—
148C2×C61—21no—
149C2×C61—21no—
150C2×C61#147211yescharacteristic
151C2×C61C2×#35411yescharacteristic
152C2×C61#213411yescharacteristic
153D61—42no—
154D61—81no—
155C2×C4⋊Q8—611no—
156C2×C4×D4—611no—
157#407—1221no—
158C2×C22⋊C8—1221no—
159#393—1221no—
160#393—1221no—
161#390—612no—
162#382—612no—
163#380—1221no—
164#380—1221no—
165C4×C4⋊C4#692311yescharacteristic
166#324—612no—
167#324—612no—
168#323—1221no—
169#323—1221no—
170C61#1156911yescharacteristic, complemented, Sylow
171C22×Q8—1221no—
172C22×D4—611no—
173C23×C4—611no—
174C23×C4—611no—
175C2×M16—2441no—
176C22×C8—2441no—
177C4⋊Q8—2441no—
178C4⋊Q8—2441no—
179C4×D4—2441no—
180C4×D4—2441no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—611no—
183C2×C4⋊C4—612no—
184C2×C4⋊C4—1221no—
185C2×C22⋊C4—611no—
186C2×C22⋊C4—611no—
187C2×C22⋊C4—1222no—
188C2×C22⋊C4—1222no—
189C2×C42C2×#692312yes—
190C2×C42C2×#692311yescharacteristic
191C22⋊C8—1222no—
192C22⋊C8—1222no—
193C22⋊C8—2441no—
194C22⋊C8—2441no—
195#95—21no—
196#95—1222no—
197#95—1222no—
198C24—611no—
199C24—611no—
200C2×Q8—4882no—
201C2×Q8—2442no—
202C2×D4—1222no—
203C2×D4—1222no—
204C2×D4—2441no—
205C22×C4—22no—
206C22×C4—611no—
207C22×C4—611no—
208C22×C4—1221no—
209C22×C4—1221no—
210C22×C4—1221no—
211C22×C4—1221no—
212C22×C4—1222no—
213C22×C4—2442no—
214C22×C4—2442no—
215C22×C4C22⋊#692311yescharacteristic
216C22×C4C22⋊#692311yescharacteristic
217C22×C4C22×#692311yescharacteristic
218M16—4882no—
219C2×C8—4882no—
220C2×C8—2442no—
221C2×C8—2442no—
222C4⋊C4—42no—
223C4⋊C4—2441no—
224C4⋊C4—2442no—
225C4⋊C4—2441no—
226C4⋊C4—2441no—
227C22⋊C4—4882no—
228C22⋊C4—4882no—
229C22⋊C4—2441no—
230C22⋊C4—2441no—
231C42—21no—
232C42—21no—
233C42—24no—
234C23—612no—
235C23—1221no—
236C23—1221no—
237C23—1221no—
238C23—1221no—
239C23—1221no—
240C23—2441no—
241C23—2441no—
242C23—2441no—
243C23—2441no—
244C23C2×C22⋊#692311yescharacteristic
245Q8—4884no—
246D4—2444no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—4881no—
258C2×C4—4881no—
259C2×C4—2442no—
260C2×C4—2442no—
261C2×C4—2442no—
262C2×C4—2442no—
263C2×C4—2442no—
264C2×C4—2441no—
265C2×C4—2441no—
266C2×C4#1451983611yescharacteristic
267C2×C4#1451983611yescharacteristic
268C2×C4#1451986412yes—
269C8—4882no—
270C8—4882no—
271C22—21no—
272C22—21no—
273C22—1222no—
274C22—4881no—
275C22—4881no—
276C22—2442no—
277C22—2442no—
278C22—2441no—
279C22—2441no—
280C22—2441no—
281C22—2441no—
282C22—2441no—
283C22#1684073611yescharacteristic
284C22C2×#1451983611yescharacteristic
285C22D61⋊#10111yescharacteristic
286C4—21no—
287C4—22no—
288C4—41no—
289C4—82no—
290C4—4882no—
291C4—2441no—
292C4—2441no—
293C4#1684066912yes—
294C2—21no—
295C2—21no—
296C2—4881no—
297C2—2442no—
298C2#2146109711yescharacteristic
299C2C2×#1684066911yescharacteristic
300C2#2146212011yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC22×C61C2×#99
prime radicalC22×D244C2×C4
cosocleC2×C4⋊Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#11569
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460759C2semidirect
170. C61#11569semidirect

Maximal subgroups

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

subgroupindex
#214610762
#214610562
#214607592
#214509882
#1156961