Finite Group Databasebeta

← #30604365

Subgroups — #30604365

Order 15616.

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

normal subgroups only

This group has 552 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#21461074C211yesmaximal, characteristic
2#21461058C211yesmaximal, characteristic
3#21460763C214yesmaximal, complemented
4#21449185C211yesmaximal, characteristic
5#16840779—21no—
6#16840733—21no—
7#16840608—21no—
8#16840606—21no—
9#16840605C2212yes—
10#16840605C2212yes—
11C23×Dic122C411yescharacteristic
12C2×#14519757—21no—
13C2×C4×C22⋊D61C2211yescharacteristic
14#16839683—21no—
15#16839675—21no—
16#16839667—21no—
17#16839639C412yes—
18#16839637C2212yes—
19C61×#380C411yescharacteristic
20C2×#11758213—41no—
21#14519844—41no—
22#14519834—41no—
23C22⋊#92420—22no—
24C22⋊#92420—22no—
25C4×#92420—41no—
26C22×Dic122—21no—
27C22×Dic122—21no—
28C22×Dic122—44no—
29C22×Dic122—41no—
30C22×Dic122—41no—
31C22×C22⋊D61C2×C411yescharacteristic
32C23×Dic61C2×C412yes—
33C22×C4×D61D411yescharacteristic
34#14519757—44no—
35C4×C22⋊D61—41no—
36C4×C22⋊D61—41no—
37C2×C4⋊Dic61—22no—
38C2×#11758196D411yescharacteristic
39C2×C22⋊Dic61C2311yescharacteristic
40C2×#11758198—22no—
41C2×#11758198D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43#14519684—22no—
44#14519684—22no—
45C23×C4×C61C2×C411yescharacteristic
46C2×C4⋊C4×C61—21no—
47C2×C22⋊C4×C61C2×C412yes—
48#95×C61—21no—
49C24×C61C22×C411yescharacteristic
50C23×D61C22⋊C411yescharacteristic
51C22×C4×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61—22no—
54C22×C4×C61—42no—
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22⋊C411yescharacteristic
57C2×C22⋊D61—22no—
58C2×C22⋊D61—22no—
59C2×C22⋊D61—41no—
60C22×Dic61—22no—
61C22×Dic61—44no—
62C22×Dic61—42no—
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C2×C4×D61—21no—
67C2×C4×D61—21no—
68C2×C4×D61—42no—
69C2×Dic122—24no—
70C2×Dic122—44no—
71C2×Dic122—42no—
72C2×Dic122—42no—
73C2×Dic122—48no—
74C2×Dic122—44no—
75C2×Dic122—41no—
76C2×Dic122—41no—
77C2×Dic122—44no—
78C2×#92420—42no—
79C2×#92420—42no—
80#11758213—82no—
81C4⋊C4×C61—42no—
82C22⋊C4×C61—24no—
83C22⋊Dic61—41no—
84#11758198—41no—
85#11758198—44no—
86C4⋊Dic61—44no—
87#11758196—41no—
88C4×Dic61—21no—
89C4×Dic61—21no—
90C23×C61—21no—
91C23×C61—21no—
92C23×C61—41no—
93C23×C61—41no—
94C23×C61C2×C22⋊C411yescharacteristic
95C23×C61#13112yes—
96C22×D61—21no—
97C22×D61—21no—
98C22×D61—21no—
99C22×D61—41no—
100C22×D61—41no—
101C2×C4×C61—22no—
102C2×C4×C61—21no—
103C2×C4×C61—42no—
104C2×C4×C61—42no—
105C2×C4×C61—41no—
106C2×C4×C61—42no—
107C2×C4×C61—42no—
108C2×C4×C61—42no—
109C2×C4×C61#9911yescharacteristic
110C2×C4×C61#9911yescharacteristic
111C22⋊D61—44no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—24no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—42no—
118C2×Dic61—44no—
119C2×Dic61—42no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—44no—
123C2×Dic61#10112yes—
124C4×D61—42no—
125C4×D61—81no—
126Dic122—44no—
127Dic122—48no—
128Dic122—44no—
129#92420—82no—
130#92420—82no—
131#11580—611nomaximal, Sylow
132C22×C61—21no—
133C22×C61—21no—
134C22×C61—22no—
135C22×C61—42no—
136C22×C61—42no—
137C22×C61—41no—
138C22×C61—41no—
139C22×C61#40811yescharacteristic
140C22×C61C2×#9911yescharacteristic
141C22×C61C2×#10111yescharacteristic
142C2×D61—42no—
143C2×D61—41no—
144C2×D61—41no—
145C2×D61—41no—
146C2×D61—81no—
147C4×C61—21no—
148C4×C61—41no—
149C4×C61—82no—
150C4×C61AΣL(1,𝔽16)12yes—
151Dic61—22no—
152Dic61—41no—
153Dic61—44no—
154Dic61—41no—
155#2409—611no—
156#1465—611no—
157#1460—611no—
158#1326—614no—
159C2×C61—21no—
160C2×C61—21no—
161C2×C61—42no—
162C2×C61#147211yescharacteristic
163C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
164C2×C61#212311yescharacteristic
165D61—81no—
166C23×Q8—611no—
167C2×C22⋊Q8—1221no—
168C2×C4×D4—611no—
169#431—1221no—
170#407—1221no—
171#395—1221no—
172#393—1221no—
173#391—1221no—
174#386—612no—
175#385—612no—
176#380#692311yescharacteristic
177#324—1221no—
178#323—612no—
179#323—612no—
180#323—1221no—
181C61#1158011yescharacteristic, complemented, Sylow
182C22×Q8—1221no—
183C22×Q8—1221no—
184C22×Q8—2441no—
185C22×Q8—2441no—
186C22×Q8—2444no—
187C22×D4—611no—
188C23×C4—611no—
189C23×C4—612no—
190C23×C4C2×#692311yescharacteristic
191C2×M16—2441no—
192C22⋊Q8—2444no—
193C4×D4—2441no—
194C4×D4—2441no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—611no—
197C2×C4⋊C4—1222no—
198C2×C22⋊C4—611no—
199C2×C22⋊C4—611no—
200C2×C22⋊C4—1222no—
201C2×C22⋊C4C2×#692312yes—
202C2×C42—611no—
203C4⋊C8—2441no—
204C22⋊C8—1222no—
205C22⋊C8—1222no—
206C22⋊C8—2441no—
207C4×C8—2441no—
208#95—21no—
209#95—1222no—
210#95—1222no—
211C24—611no—
212C24C22×#692311yescharacteristic
213C2×Q8—1224no—
214C2×Q8—2442no—
215C2×Q8—2442no—
216C2×Q8—2444no—
217C2×Q8—2444no—
218C2×Q8—2448no—
219C2×Q8—2444no—
220C2×Q8—2441no—
221C2×Q8—2441no—
222C2×D4—1222no—
223C2×D4—1222no—
224C2×D4—2441no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—42no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—611no—
232C22×C4—1222no—
233C22×C4—1221no—
234C22×C4—1221no—
235C22×C4—2442no—
236C22×C4—2444no—
237C22×C4—2442no—
238C22×C4C22⋊#692311yescharacteristic
239C22×C4C22⋊#692311yescharacteristic
240M16—4882no—
241C2×C8—2442no—
242C2×C8—2442no—
243C4⋊C4—42no—
244C4⋊C4—2441no—
245C4⋊C4—2444no—
246C22⋊C4—24no—
247C22⋊C4—2441no—
248C22⋊C4—2444no—
249C22⋊C4—2441no—
250C42—1221no—
251C42—1221no—
252C23—21no—
253C23—21no—
254C23—41no—
255C23—41no—
256C23—1221no—
257C23—1221no—
258C23—1221no—
259C23—2441no—
260C23—2441no—
261C23C2×C22⋊#692311yescharacteristic
262C23#1451986412yes—
263Q8—2444no—
264Q8—2448no—
265Q8—2444no—
266D4—2444no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—612no—
276C2×C4—1221no—
277C2×C4—1221no—
278C2×C4—1224no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—4881no—
282C2×C4—2442no—
283C2×C4—2444no—
284C2×C4—2442no—
285C2×C4—2442no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2444no—
289C2×C4#1451983611yescharacteristic
290C2×C4#1451983611yescharacteristic
291C8—4882no—
292C8—4882no—
293C22—21no—
294C22—21no—
295C22—22no—
296C22—42no—
297C22—42no—
298C22—41no—
299C22—41no—
300C22—4881no—
301C22—2442no—
302C22—2441no—
303C22—2441no—
304C22—2441no—
305C22#1684073611yescharacteristic
306C22C2×#1451983611yescharacteristic
307C22D61⋊#10111yescharacteristic
308C4—21no—
309C4—41no—
310C4—82no—
311C4—1222no—
312C4—2441no—
313C4—2444no—
314C4—2441no—
315C4#1684066312yes—
316C2—21no—
317C2—21no—
318C2—42no—
319C2—4881no—
320C2#2146109711yescharacteristic
321C2C2×#1684066311yescharacteristic
322C2#2146208311yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC61×#380C4
socleC22×C61C2×#99
prime radicalC22×C22⋊D61C2×C4
cosocleC2×C22⋊Dic61C23
hypercenter#380#6923
hypocenterC61#11580
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #21460763C2semidirect
181. C61#11580semidirect

Maximal subgroups

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

subgroupindex
#214610742
#214610582
#214607632
#214491852
#1158061