Finite Group Databasebeta

← #30606302

Subgroups — #30606302

Order 15616.

1026 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 152 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
1C22×#14519836C212yesmaximal
2#21460913C214yesmaximal, complemented
3#21448399C211yesmaximal, characteristic
4C22×C22⋊#6923—22no—
5C2×#14519836—22no—
6C2×#14519836—24no—
7C2×#14519836C418yescomplemented
8C2×#14519836C2214yes—
9C23×D244C2211yescharacteristic
10C2×#14519736C411yescharacteristic, complemented
11#16839664C412yescomplemented
12#16839664C2212yes—
13#16839663—22no—
14#16839617—22no—
15C2×#117×C61C411yescharacteristic, complemented
16C23×#6923—42no—
17C2×C22⋊#6923—28no—
18C2×C22⋊#6923—24no—
19C2×C22⋊#6923—44no—
20C2×C22⋊#6923—42no—
21#14519836—28no—
22#14519836—24no—
23#14519836C2×C418yescomplemented
24C24×D61D412yes—
25C22×D244—42no—
26C22×D244—42no—
27C22×D244C2×C411yescharacteristic
28C22×D244C2×C414yes—
29C22×D244D412yes—
30C22×D244D412yes—
31C22×D244Q812yes—
32C22×D244C2311yescharacteristic
33#14519736—42no—
34C2×C4⋊Dic61C2×C412yescomplemented
35C2×C22⋊Dic61—21no—
36C2×#11758198—24no—
37C2×#11758198—24no—
38C2×C4×Dic61—21no—
39C23×C4×C61C2×C411yescharacteristic
40#117×C61—42no—
41C2×C4⋊C4×C61—21no—
42C2×C22⋊C4×C61—21no—
43C2×C42×C61C2×C412yescomplemented
44C24×C61C22⋊C411yescharacteristic
45C23×D61—22no—
46C23×D61—24no—
47C23×D61—22no—
48C23×D61—84no—
49C23×D61C22⋊C412yes—
50C23×D61C22⋊C414yes—
51C23×D61C4⋊C414yes—
52C23×D61C2×D412yes—
53C22×#6923—48no—
54C22×#6923—44no—
55C22×#6923—88no—
56C22×C4×C61—22no—
57C22×C4×C61—22no—
58C22×C4×C61—22no—
59C22×C4×C61C4212yes—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C4⋊C412yes—
62C22×C4×C61C22×C411yescharacteristic
63C22×Dic61—22no—
64C2×D244—41no—
65C2×D244—41no—
66C2×D244—44no—
67C2×D244—44no—
68C2×D244—42no—
69C2×D244—42no—
70C2×D244—44no—
71C2×D244—44no—
72C2×D244—41no—
73C2×D244—41no—
74C2×D244C4212yes—
75C2×D244C22⋊C414yes—
76C2×D244C4⋊C414yes—
77C2×D244C4⋊C412yes—
78C2×D244C22×C412yes—
79C2×D244C2×D411yescharacteristic
80C2×D244C2×Q811yescharacteristic
81C22⋊#6923—28no—
82C22⋊#6923—48no—
83C22⋊#6923—44no—
84C4⋊C4×C61—42no—
85C22⋊C4×C61—42no—
86C42×C61—42no—
87C22⋊Dic61—42no—
88#11758198—84no—
89#11758198—84no—
90C4⋊Dic61—42no—
91C4×Dic61—42no—
92C23×C61—42no—
93C23×C61#9512yes—
94C23×C61#9912yes—
95C23×C61#9912yes—
96C23×C61C2×C22⋊C411yescharacteristic
97C22×D61—24no—
98C22×D61—24no—
99C22×D61—22no—
100C22×D61—22no—
101C22×D61—24no—
102C22×D61—24no—
103C22×D61—22no—
104C22×D61—22no—
105C22×D61—48no—
106C22×D61—44no—
107C22×D61—44no—
108C22×D61—84no—
109C22×D61—84no—
110C22×D61—84no—
111C22×D61—88no—
112C22×D61#9514yes—
113C22×D61C2×C22⋊C412yes—
114C22×D61C2×C4⋊C412yes—
115C2×#6923—48no—
116C2×#6923—816no—
117C2×#6923—88no—
118C2×C4×C61—24no—
119C2×C4×C61—24no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—42no—
125C2×C4×C61—42no—
126C2×C4×C61—42no—
127C2×C4×C61#9512yes—
128C2×C4×C61C2×C4211yescharacteristic
129C2×C4×C61C2×C4⋊C411yescharacteristic
130C2×Dic61—44no—
131C2×Dic61—42no—
132D244—42no—
133D244—44no—
134D244—44no—
135D244—42no—
136D244—42no—
137D244—41no—
138D244—41no—
139#12582—611nomaximal, Sylow
140C22×C61—22no—
141C22×C61—24no—
142C22×C61—42no—
143C22×C61—42no—
144C22×C61#34214yes—
145C22×C61C2×#9511yescharacteristic
146C22×C61C2×#9911yescharacteristic
147C22×C61C2×#9911yescharacteristic
148C2×D61—22no—
149C2×D61—24no—
150C2×D61—22no—
151C2×D61—48no—
152C2×D61—48no—
153C2×D61—44no—
154C2×D61—44no—
155C2×D61—44no—
156C2×D61—42no—
157C2×D61—42no—
158C2×D61—82no—
159C2×D61—82no—
160C2×D61—84no—
161C2×D61—84no—
162#6923—88no—
163C4×C61—22no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—82no—
167Dic61—82no—
168C22×#99—612no—
169#2309—611no—
170#1393—614no—
171C2×C61—21no—
172C2×C61—21no—
173C2×C61—24no—
174C2×C61C2×#34211yescharacteristic
175C2×C61#212712yes—
176D61—42no—
177D61—44no—
178D61—42no—
179C23×D4—611no—
180C2×#117—611no—
181C2×#117#692311yescharacteristic, complemented
182C22×C22⋊C4—1222no—
183C2×#99—618no—
184C2×#99—614no—
185C2×#99—1224no—
186C2×#99—1222no—
187#390—612no—
188#390—612no—
189#390—1222no—
190#379—1222no—
191C61#1258211yescharacteristic, complemented, Sylow
192C25—612no—
193C22×D4—614no—
194C22×D4—612no—
195C22×D4—612no—
196C22×D4—612no—
197C22×D4—611no—
198C22×D4—611no—
199C22×D4—2442no—
200C22×D4—2442no—
201C23×C4—2442no—
202C23×C4C2×#692311yescharacteristic
203#117—42no—
204#117—2442no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—612no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—1228no—
209C2×C22⋊C4—1224no—
210C2×C22⋊C4—1224no—
211C2×C22⋊C4—1224no—
212C2×C22⋊C4—1221no—
213C2×C22⋊C4—2444no—
214C2×C22⋊C4—2442no—
215C2×C42—1221no—
216C2×C42C2×#692312yescomplemented
217#99—618no—
218#99—1228no—
219#99—1224no—
220C24—614no—
221C24—614no—
222C24—612no—
223C24—612no—
224C24—1224no—
225C24—1222no—
226C24—1222no—
227C24—4884no—
228C24C22⋊#692311yescharacteristic
229C2×D4—614no—
230C2×D4—614no—
231C2×D4—612no—
232C2×D4—612no—
233C2×D4—611no—
234C2×D4—612no—
235C2×D4—611no—
236C2×D4—2441no—
237C2×D4—2441no—
238C2×D4—2442no—
239C2×D4—2442no—
240C2×D4—2441no—
241C2×D4—2441no—
242C2×D4—2444no—
243C2×D4—2444no—
244C2×D4—2444no—
245C2×D4—2444no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—1222no—
250C22×C4—4888no—
251C22×C4—2444no—
252C22×C4—2448no—
253C22×C4C4×#692312yes—
254C22×C4C4⋊#692312yes—
255C22×C4C22⋊#692311yescharacteristic
256C22×C4C22×#692311yescharacteristic
257C4⋊C4—42no—
258C4⋊C4—2442no—
259C22⋊C4—42no—
260C22⋊C4—1228no—
261C22⋊C4—4884no—
262C22⋊C4—4884no—
263C22⋊C4—2444no—
264C22⋊C4—2448no—
265C22⋊C4—2442no—
266C42—42no—
267C42—2442no—
268C23—42no—
269C23—614no—
270C23—612no—
271C23—612no—
272C23—1222no—
273C23—1222no—
274C23—1224no—
275C23—1224no—
276C23—1222no—
277C23—1222no—
278C23—1224no—
279C23—1224no—
280C23—4884no—
281C23—4888no—
282C23—4884no—
283C23—4884no—
284C23—2444no—
285C23—2444no—
286C23—2448no—
287C23(C2×#6923)⋊C412yes—
288C23#1451983512yes—
289C23#1451983612yes—
290C23C2×C22⋊#692311yescharacteristic
291D4—2444no—
292D4—2444no—
293D4—2442no—
294D4—2442no—
295D4—2441no—
296D4—2442no—
297D4—2441no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—48816no—
308C2×C4—4888no—
309C2×C4—2444no—
310C2×C4—2448no—
311C2×C4—2442no—
312C2×C4(C2×#6923)⋊C412yes—
313C2×C4C2×C4×#692311yescharacteristic
314C2×C4C2×C4⋊#692311yescharacteristic
315C22—22no—
316C22—24no—
317C22—42no—
318C22—42no—
319C22—1222no—
320C22—1224no—
321C22—1222no—
322C22—4884no—
323C22—4884no—
324C22—4882no—
325C22—4882no—
326C22—2442no—
327C22—2444no—
328C22—2442no—
329C22—2448no—
330C22—2448no—
331C22—2444no—
332C22—2444no—
333C22#1684064014yes—
334C22C2×(C2×#6923)⋊C411yescharacteristic
335C22C2×#1451983511yescharacteristic
336C22C2×#1451983611yescharacteristic
337C4—22no—
338C4—21no—
339C4—21no—
340C4—82no—
341C4—4888no—
342C4—4882no—
343C2—21no—
344C2—24no—
345C2—21no—
346C2—2442no—
347C2—2444no—
348C2—2442no—
349C2C2×#1684064011yescharacteristic
350C2#2146209612yes—
subgroupG/H
centerC22C2×#14519836
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#99
prime radicalC23×D244C22
cosocleC22×D244C23
hypercenterC2×#117#6923
hypocenterC61#12582
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #21460913C2semidirect
7. C2×#14519836C4semidirect
10. C2×#14519736C4semidirect
11. #16839664C4semidirect
15. C2×#117×C61C4semidirect
23. #14519836C2×C4semidirect
34. C2×C4⋊Dic61C2×C4semidirect
43. C2×C42×C61C2×C4semidirect
181. C2×#117#6923semidirect
191. C61#12582semidirect
216. C2×C42C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C22×#145198362
#214609132
#214483992
#1258261