Finite Group Databasebeta

← #30605167

Subgroups — #30605167

Order 15616.

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

normal subgroups only

This group has 586 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#21461718C211yesmaximal, characteristic
2#21461069C211yesmaximal, characteristic
3#21460819C214yesmaximal, complemented
4C2×#16839683C211yesmaximal, characteristic
5#16840732—21no—
6#16840732—21no—
7#16840642—21no—
8#16840642C2212yes—
9#16840608—21no—
10#16840608C2212yes—
11C23×Dic122C411yescharacteristic
12C22×C4⋊Dic61—21no—
13C22×#11758196C2211yescharacteristic
14#16839683—21no—
15#16839683—21no—
16#16839683C412yes—
17#16839683C2212yes—
18C2×#14519684—21no—
19C2×#95×C61C411yescharacteristic
20C2×#11758217—22no—
21C2×#11758217—41no—
22C22⋊#92420—22no—
23C22⋊#92420—41no—
24C22⋊#92420—41no—
25C22⋊#92420—41no—
26C22×Dic122—21no—
27C22×Dic122—41no—
28C22×Dic122—41no—
29C22×Dic122—44no—
30C22×Dic122C2×C412yes—
31C23×Dic61—21no—
32C23×Dic61D411yescharacteristic
33C23×Dic61D411yescharacteristic
34C2×C4⋊Dic61—22no—
35C2×C4⋊Dic61—22no—
36C2×C4⋊Dic61—44no—
37C2×#11758196—41no—
38C2×#11758196—41no—
39C2×#11758196C2×C411yescharacteristic
40C2×#11758196D411yescharacteristic
41C2×#11758196D411yescharacteristic
42C2×#11758196C2311yescharacteristic
43#14519684—22no—
44#14519684—22no—
45C23×C4×C61—21no—
46C23×C4×C61C2×C411yescharacteristic
47#95×C61—21no—
48#95×C61C2×C412yes—
49C24×C61C22⋊C411yescharacteristic
50C22×C4×C61—24no—
51C22×C4×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61—22no—
54C22×C4×C61—42no—
55C22×C4×C61—42no—
56C22×C4×C61—42no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22×C411yescharacteristic
59C22×Dic61—24no—
60C22×Dic61—21no—
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61—22no—
64C22×Dic61—21no—
65C22×Dic61—22no—
66C22×Dic61—41no—
67C22×Dic61—42no—
68C22×Dic61—41no—
69C22×Dic61—41no—
70C22×Dic61—42no—
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C2×Dic122—44no—
76C2×Dic122—42no—
77C2×Dic122—44no—
78C2×Dic122—48no—
79C2×Dic122—42no—
80C2×Dic122—44no—
81C2×Dic122—44no—
82#11758217—42no—
83#11758217—42no—
84#11758217—82no—
85C2×#92420—42no—
86C2×#92420—42no—
87C4⋊Dic61—44no—
88C4⋊Dic61—44no—
89#11758196—41no—
90#11758196—41no—
91#11758196—41no—
92#11758196—41no—
93C23×C61—22no—
94C23×C61—22no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61#9911yescharacteristic
98C23×C61#9911yescharacteristic
99C23×C61C2×C22⋊C411yescharacteristic
100C2×C4×C61—24no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—42no—
104C2×C4×C61—42no—
105C2×C4×C61—48no—
106C2×C4×C61—42no—
107C2×C4×C61—42no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—24no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—42no—
119C2×Dic61—42no—
120C2×Dic61—42no—
121C2×Dic61—44no—
122C2×Dic61—42no—
123C2×Dic61—44no—
124C2×Dic61—42no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—81no—
128C2×Dic61#13712yes—
129Dic122—48no—
130Dic122—44no—
131Dic122—44no—
132#92420—82no—
133#92420—82no—
134#11815—611nomaximal, Sylow
135C22×C61—24no—
136C22×C61—24no—
137C22×C61—21no—
138C22×C61—21no—
139C22×C61—21no—
140C22×C61—21no—
141C22×C61—21no—
142C22×C61—21no—
143C22×C61AΣL(1,𝔽16)12yes—
144C22×C61#35612yes—
145C22×C61C2×#9911yescharacteristic
146C22×C61#41911yescharacteristic
147C22×C61#42111yescharacteristic
148C4×C61—44no—
149C4×C61—41no—
150C4×C61—41no—
151Dic61—22no—
152Dic61—41no—
153Dic61—44no—
154Dic61—41no—
155Dic61—41no—
156C2×#395—611no—
157#1821—611no—
158#1463—611no—
159#1354—614no—
160C2×C61—21no—
161C2×C61—22no—
162C2×C61—22no—
163C2×C61—21no—
164C2×C61#151111yescharacteristic
165C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
166C2×C61C2×#35611yescharacteristic
167C23×Q8—611no—
168C22×C4⋊C4—611no—
169C22×C4⋊C4—1221no—
170#407—1221no—
171#407—1221no—
172#395—612no—
173#395—612no—
174#395—1221no—
175#395—1221no—
176C2×#95—1221no—
177C2×#95#692311yescharacteristic
178#343—612no—
179#343—1221no—
180#324—612no—
181#324—1221no—
182C61#1181511yescharacteristic, complemented, Sylow
183C22×Q8—612no—
184C22×Q8—1221no—
185C22×Q8—2441no—
186C22×Q8—2441no—
187C22×Q8—2444no—
188C23×C4—21no—
189C23×C4—611no—
190C23×C4—611no—
191C23×C4—1221no—
192C23×C4C2×#692311yescharacteristic
193C2×M16—1222no—
194C2×M16—2441no—
195C2×C4⋊C4—611no—
196C2×C4⋊C4—611no—
197C2×C4⋊C4—611no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4—1222no—
200C2×C4⋊C4—1222no—
201C2×C4⋊C4—2441no—
202C2×C4⋊C4—2441no—
203C2×C4⋊C4—2444no—
204C22⋊C8—1222no—
205C22⋊C8—2441no—
206C22⋊C8—2441no—
207C22⋊C8—2441no—
208#95—21no—
209#95—1222no—
210#95—1222no—
211#95C2×#692312yes—
212C24C22⋊#692311yescharacteristic
213C2×Q8—2442no—
214C2×Q8—2442no—
215C2×Q8—2444no—
216C2×Q8—2444no—
217C2×Q8—2448no—
218C2×Q8—2444no—
219C2×Q8—2444no—
220C22×C4—24no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—611no—
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—1222no—
232C22×C4—1221no—
233C22×C4—1224no—
234C22×C4—1221no—
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4—1222no—
238C22×C4—2441no—
239C22×C4—2442no—
240C22×C4—2442no—
241C22×C4—2441no—
242C22×C4—2441no—
243C22×C4C22⋊#692311yescharacteristic
244C22×C4C22×#692311yescharacteristic
245M16—4882no—
246M16—2442no—
247M16—2442no—
248C2×C8—2442no—
249C2×C8—2442no—
250C4⋊C4—2441no—
251C4⋊C4—2441no—
252C4⋊C4—2441no—
253C4⋊C4—2441no—
254C4⋊C4—2444no—
255C4⋊C4—2444no—
256C23—21no—
257C23—21no—
258C23—22no—
259C23—22no—
260C23#1451983611yescharacteristic
261C23#1451983611yescharacteristic
262C23C2×C22⋊#692311yescharacteristic
263Q8—2444no—
264Q8—2448no—
265Q8—2444no—
266C2×C4—24no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—48no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—612no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—1224no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—4881no—
286C2×C4—2442no—
287C2×C4—2442no—
288C2×C4—2442no—
289C2×C4—2444no—
290C2×C4—2442no—
291C2×C4—2442no—
292C2×C4—2444no—
293C2×C4—2441no—
294C2×C4—2441no—
295C8—4882no—
296C8—4882no—
297C22—24no—
298C22—24no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22#1684066312yes—
306C22#1684067312yes—
307C22C2×#1451983611yescharacteristic
308C22#1684075511yescharacteristic
309C22#1684076011yescharacteristic
310C4—44no—
311C4—41no—
312C4—41no—
313C4—1222no—
314C4—2441no—
315C4—2441no—
316C4—2444no—
317C4—2441no—
318C2—21no—
319C2—21no—
320C2—22no—
321C2—22no—
322C2#2146122711yescharacteristic
323C2C2×#1684066311yescharacteristic
324C2C2×#1684067311yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#95×C61C4
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×#11758196C23
hypercenterC2×#95#6923
hypocenterC61#11815
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. #21460819C2semidirect
182. C61#11815semidirect

Maximal subgroups

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

subgroupindex
#214617182
#214610692
#214608192
C2×#168396832
#1181561