Finite Group Databasebeta

← #30598813

Subgroups — #30598813

Order 15616.

842 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 842 conjugacy classes of subgroups — too many to draw. Only its 100 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#21461718C212yesmaximal, complemented
2#21461067C212yesmaximal, complemented
3#21461066C212yesmaximal
4C22×#14519772C211yesmaximal, characteristic
5#16840732C2214yes—
6#16840642—24no—
7#16840607—24no—
8#16840606—24no—
9C2×#14519772—24no—
10C2×#14519772—24no—
11C2×#14519772—24no—
12C22×C4⋊Dic61C2211yescharacteristic
13C22×#11758196C2211yescharacteristic
14C22×#11758198C411yescharacteristic
15C22×#11758198C411yescharacteristic
16C22×#11758198C2211yescharacteristic
17C22×C4×Dic61C411yescharacteristic
18C22×C4⋊C4×C61C411yescharacteristic
19C2×#11758217—24no—
20C22⋊#92420—24no—
21C22⋊#92420—24no—
22C24×D61C2×C411yescharacteristic
23C23×Dic61C2×C411yescharacteristic
24C23×Dic61C2×C411yescharacteristic
25C23×Dic61C2311yescharacteristic
26#14519772—232no—
27C2×C4⋊Dic61—22no—
28C2×C4⋊Dic61—22no—
29C2×C4⋊Dic61D414yes—
30C2×#11758196—22no—
31C2×#11758196—22no—
32C2×#11758196D414yes—
33C2×#11758198—22no—
34C2×#11758198—22no—
35C2×#11758198—22no—
36C2×#11758198—22no—
37C2×#11758198—22no—
38C2×#11758198—22no—
39C2×#11758198—22no—
40C2×#11758198—22no—
41C2×#11758198D414yes—
42C2×C4×Dic61—22no—
43C2×C4×Dic61—22no—
44C2×C4×Dic61—22no—
45C23×C4×C61C2×C411yescharacteristic
46C23×C4×C61C2×C411yescharacteristic
47C23×C4×C61C2×C411yescharacteristic
48C2×C4⋊C4×C61—22no—
49C2×C4⋊C4×C61—22no—
50C2×C4⋊C4×C61—22no—
51C24×C61C22×C411yescharacteristic
52C23×D61—21no—
53C23×D61—21no—
54C23×D61—42no—
55C23×D61—42no—
56C23×D61—42no—
57C23×D61C22⋊C412yes—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—42no—
65C22×C4×C61—42no—
66C22×C4×C61—42no—
67C22×C4×C61C22⋊C412yes—
68C22×C4×C61C22⋊C412yes—
69C22×C4×C61C22⋊C412yes—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—42no—
75C22×Dic61—42no—
76C22×Dic61—42no—
77C22×Dic61C22⋊C412yes—
78C22×Dic61C22⋊C412yes—
79C22×Dic61C2×D412yes—
80C22×Dic61C2×D412yes—
81C22×Dic61C2×D412yes—
82#11758217—48no—
83C2×#92420—44no—
84C4⋊C4×C61—28no—
85#11758198—28no—
86#11758198—28no—
87#11758198—28no—
88C4⋊Dic61—28no—
89#11758196—28no—
90C4×Dic61—28no—
91C23×C61—22no—
92C23×C61—22no—
93C23×C61—22no—
94C23×C61C2×C22⋊C411yescharacteristic
95C23×C61C2×C22⋊C411yescharacteristic
96C23×C61C2×C22⋊C411yescharacteristic
97C22×D61—22no—
98C22×D61—24no—
99C22×D61—42no—
100C22×D61—42no—
101C22×D61—42no—
102C22×D61—42no—
103C22×D61—42no—
104C22×D61—42no—
105C22×D61—42no—
106C22×D61—42no—
107C22×D61—88no—
108C2×C4×C61—22no—
109C2×C4×C61—22no—
110C2×C4×C61—22no—
111C2×C4×C61—24no—
112C2×C4×C61—42no—
113C2×C4×C61—42no—
114C2×C4×C61—42no—
115C2×C4×C61—42no—
116C2×C4×C61—42no—
117C2×C4×C61—42no—
118C2×C4×C61—42no—
119C2×C4×C61—42no—
120C2×Dic61—24no—
121C2×Dic61—22no—
122C2×Dic61—22no—
123C2×Dic61—42no—
124C2×Dic61—42no—
125C2×Dic61—42no—
126C2×Dic61—42no—
127C2×Dic61—42no—
128C2×Dic61—42no—
129C2×Dic61—42no—
130C2×Dic61—42no—
131C2×Dic61#12014yes—
132#92420—84no—
133#8556—611nomaximal, Sylow
134C22×C61—28no—
135C22×C61—21no—
136C22×C61—21no—
137C22×C61—21no—
138C22×C61—21no—
139C22×C61—21no—
140C22×C61—21no—
141C22×C61#37911yescharacteristic
142C22×C61#41012yes—
143C22×C61#41312yes—
144C22×C61#41312yes—
145C2×D61—42no—
146C2×D61—42no—
147C2×D61—42no—
148C2×D61—84no—
149C2×D61—84no—
150C2×D61—84no—
151C4×C61—42no—
152C4×C61—42no—
153C4×C61—42no—
154Dic61—24no—
155Dic61—42no—
156Dic61—42no—
157C22×#126—611no—
158#1821—612no—
159#1463—612no—
160#1462—612no—
161C2×C61—22no—
162C2×C61—22no—
163C2×C61—22no—
164C2×C61#178211yescharacteristic
165C2×C61#178511yescharacteristic
166C2×C61#178511yescharacteristic
167D61—82no—
168C2×#126—1224no—
169C2×#126—1224no—
170C2×#126—1224no—
171C22×C4⋊C4—611no—
172C22×C4⋊C4—611no—
173C22×C4⋊C4#692311yescharacteristic
174C22×C22⋊C4—611no—
175C22×C22⋊C4—611no—
176C22×C22⋊C4—611no—
177C22×C42—611no—
178#407—614no—
179#343—1224no—
180#324—1224no—
181#323—1224no—
182C61#855611yescharacteristic, complemented, Sylow
183C25—611no—
184C23×C4—611no—
185C23×C4—611no—
186C23×C4—611no—
187C23×C4C2×#692311yescharacteristic
188C23×C4C2×#692311yescharacteristic
189C23×C4C2×#692311yescharacteristic
190C2×M16—1224no—
191#126—12232no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—614no—
196C2×C4⋊C4—614no—
197C2×C4⋊C4—1222no—
198C2×C4⋊C4—1222no—
199C2×C4⋊C4—1222no—
200C2×C4⋊C4—1222no—
201C2×C22⋊C4—614no—
202C2×C22⋊C4—1222no—
203C2×C22⋊C4—1222no—
204C2×C22⋊C4—1222no—
205C2×C22⋊C4—1222no—
206C2×C22⋊C4—1222no—
207C2×C22⋊C4—1222no—
208C2×C22⋊C4—1222no—
209C2×C22⋊C4—1222no—
210C2×C42—1222no—
211C2×C42—1222no—
212C2×C42—1222no—
213C22⋊C8—1224no—
214C22⋊C8—1224no—
215C24—612no—
216C24—1221no—
217C24—1221no—
218C24—2442no—
219C24—2442no—
220C24—2442no—
221C24C22×#692311yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—612no—
232C22×C4—612no—
233C22×C4—612no—
234C22×C4—612no—
235C22×C4—612no—
236C22×C4—1221no—
237C22×C4—1221no—
238C22×C4—1221no—
239C22×C4—1221no—
240C22×C4—2442no—
241C22×C4—2442no—
242C22×C4—2442no—
243C22×C4C22⋊#692312yes—
244C22×C4C22⋊#692312yes—
245C22×C4C22⋊#692312yes—
246M16—2448no—
247C2×C8—2444no—
248C4⋊C4—28no—
249C4⋊C4—1228no—
250C4⋊C4—1228no—
251C22⋊C4—1228no—
252C22⋊C4—1228no—
253C22⋊C4—1228no—
254C42—1228no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—1224no—
259C23—1222no—
260C23—4888no—
261C23—2442no—
262C23—2442no—
263C23—2442no—
264C23—2442no—
265C23—2442no—
266C23—2442no—
267C23—2442no—
268C23—2442no—
269C23C2×C22⋊#692311yescharacteristic
270C23C2×C22⋊#692311yescharacteristic
271C23C2×C22⋊#692311yescharacteristic
272C2×C4—24no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—614no—
285C2×C4—1224no—
286C2×C4—1222no—
287C2×C4—1222no—
288C2×C4—2442no—
289C2×C4—2442no—
290C2×C4—2442no—
291C2×C4—2442no—
292C2×C4—2442no—
293C2×C4—2442no—
294C2×C4—2442no—
295C2×C4—2442no—
296C8—4884no—
297C22—28no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—4884no—
305C22—4884no—
306C22—4884no—
307C22—2442no—
308C22—2442no—
309C22—2442no—
310C22#1684070311yescharacteristic
311C22#1684074312yes—
312C22#1684074812yes—
313C22#1684074912yes—
314C4—42no—
315C4—42no—
316C4—42no—
317C4—1224no—
318C4—2442no—
319C4—2442no—
320C2—22no—
321C2—22no—
322C2—22no—
323C2—4882no—
324C2#2146165011yescharacteristic
325C2#2146165511yescharacteristic
326C2#2146165611yescharacteristic
subgroupG/H
centerC22#16840703
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC22×C61#379
prime radicalC24×D61C2×C4
cosocleC23×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#8556
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #21461718C2semidirect
2. #21461067C2semidirect
182. C61#8556semidirect

Maximal subgroups

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

subgroupindex
#214617182
#214610672
#214610662
C22×#145197722
#855661