Finite Group Databasebeta

← #29570376

Subgroups — #29570376

Order 15616.

914 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 155 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#407×D61C212yesmaximal
2#21448199C211yesmaximal, characteristic
3#21443728C212yesmaximal, complemented
4#21443727C211yesmaximal, characteristic, complemented
5C61×#1306C211yesmaximal, characteristic, complemented
6C23×C4×D61C2211yescharacteristic
7C2×M16×D61—22no—
8C2×#14519733C412yes—
9#16839726C2212yes—
10#16839725—22no—
11#16839724—22no—
12#16839724C414yescomplemented
13C22⋊C8×D61—22no—
14C22⋊C8×D61C414yescomplemented
15#16839625C2211yescharacteristic
16#16839621—22no—
17#16839617C412yes—
18#16839609—22no—
19C61×#407C2212yes—
20C61×#381C2211yescharacteristic
21C24×D61C2×C411yescharacteristic
22C23×Dic61C2×C411yescharacteristic
23C22×C4×D61—44no—
24C22×C4×D61C2×C412yes—
25C22×C4×D61C2×C412yes—
26C22×C4×D61D412yes—
27C22×C4×D61D411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61D412yes—
30C22×C4×D61Q811yescharacteristic
31C22×C4×D61Q811yescharacteristic
32C2×#11758194—22no—
33C2×#11758189—24no—
34M16×D61—48no—
35C2×C8×D61—24no—
36#14519733—44no—
37C2×#11758196—22no—
38C2×C22⋊Dic61C2×C412yes—
39C2×#11758198—24no—
40C2×C4×Dic61—22no—
41C22⋊#92418—22no—
42C22⋊#92418C2×C414yes—
43#14519689—24no—
44#14519689—24no—
45#14519684—22no—
46C23×C4×C61C2311yescharacteristic
47C2×M16×C61—22no—
48C2×C22⋊C4×C61C2×C412yes—
49C22⋊C8×C61—22no—
50C22⋊C8×C61C2×C414yes—
51#95×C61—22no—
52C24×C61C22×C411yescharacteristic
53C23×D61—44no—
54C23×D61—42no—
55C23×D61C4212yes—
56C23×D61C22⋊C412yes—
57C23×D61C4⋊C411yescharacteristic
58C23×D61C4⋊C411yescharacteristic
59C22×C4×C61—22no—
60C22×C4×C61—42no—
61C22×C4×C61C22×C412yes—
62C22×C4×C61C2×D412yes—
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61C2×Q811yescharacteristic
65C22×Dic61—24no—
66C22×Dic61—22no—
67C22×Dic61C4211yescharacteristic
68C22×Dic61C4211yescharacteristic
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C4⋊C411yescharacteristic
72C22×Dic61C4⋊C411yescharacteristic
73C2×C4×D61—28no—
74C2×C4×D61—44no—
75C2×C4×D61—44no—
76C2×C4×D61—42no—
77C2×C4×D61—42no—
78C2×C4×D61—42no—
79C2×C4×D61—42no—
80C2×C4×D61—44no—
81C2×C4×D61C22⋊C412yes—
82C2×C4×D61C22⋊C412yes—
83C2×C4×D61C22⋊C412yes—
84C2×C4×D61C22⋊C412yes—
85C2×C4×D61C4⋊C412yes—
86C2×C4×D61C4⋊C412yes—
87C2×C4×D61C4⋊C412yes—
88C2×C4×D61C4⋊C412yes—
89M16×C61—44no—
90C2×C8×C61—24no—
91C22⋊C4×C61—42no—
92C22⋊Dic61—42no—
93#11758198—48no—
94#11758196—44no—
95C4×Dic61—44no—
96#11758194—44no—
97C2×#92418—24no—
98#11758189—48no—
99C8×D61—48no—
100C23×C61—22no—
101C23×C61—42no—
102C23×C61C2×C4211yescharacteristic
103C23×C61C2×C22⋊C411yescharacteristic
104C23×C61C2×C4⋊C411yescharacteristic
105C22×D61—24no—
106C22×D61—24no—
107C22×D61—24no—
108C22×D61—24no—
109C22×D61—42no—
110C22×D61—41no—
111C22×D61—41no—
112C22×D61—42no—
113C22×D61—42no—
114C22×D61—42no—
115C22×D61—416no—
116C22×D61#9512yes—
117C22×D61#9512yes—
118C2×C4×C61—24no—
119C2×C4×C61—42no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—44no—
123C2×C4×C61—42no—
124C2×C4×C61C2×C22⋊C412yes—
125C2×C4×C61C2×C4⋊C412yes—
126C2×Dic61—22no—
127C2×Dic61—22no—
128C2×Dic61—22no—
129C2×Dic61—22no—
130C2×Dic61—22no—
131C2×Dic61—44no—
132C2×Dic61—42no—
133C2×Dic61#9511yescharacteristic
134C2×Dic61#9511yescharacteristic
135C2×Dic61#9511yescharacteristic
136C2×Dic61#9511yescharacteristic
137C2×Dic61#9914yes—
138C4×D61—24no—
139C4×D61—24no—
140C4×D61—24no—
141C4×D61—24no—
142C4×D61—42no—
143C4×D61—42no—
144C4×D61—42no—
145C4×D61—42no—
146C8×C61—44no—
147#92418—44no—
148#8112—611nomaximal, Sylow
149C22×C61—22no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—22no—
153C22×C61—22no—
154C22×C61—44no—
155C22×C61C2×#9511yescharacteristic
156C22×C61C2×#9912yes—
157C2×D61—22no—
158C2×D61—22no—
159C2×D61—22no—
160C2×D61—22no—
161C2×D61—22no—
162C2×D61—44no—
163C2×D61—48no—
164C2×D61—48no—
165C2×D61—44no—
166C2×D61#34414yes—
167C4×C61—22no—
168C4×C61—22no—
169C4×C61—82no—
170Dic61—21no—
171Dic61—21no—
172Dic61—82no—
173Dic61#34212yes—
174Dic61#34212yes—
175C2×#407—612no—
176#2280—611no—
177#1306—612no—
178#1306—611no—
179#1306D6111yescharacteristic, complemented
180C2×C61—22no—
181C2×C61—41no—
182C2×C61—41no—
183C2×C61C2×#34211yescharacteristic
184C2×C61C2×#34412yes—
185D61—24no—
186D61—42no—
187C24×C4—611no—
188C22×M16—1222no—
189C2×#117—612no—
190#407—612no—
191#407—614no—
192#407—1222no—
193#407—1222no—
194#407C2×D6112yes—
195C2×C22⋊C8—614no—
196C2×C22⋊C8—1222no—
197#381—611no—
198#381C2×D6111yescharacteristic
199#380—1222no—
200#379—612no—
201C4×C22⋊C4—1222no—
202C61#811211yescharacteristic, complemented, Sylow
203C25—611no—
204C23×C4—611no—
205C23×C4—612no—
206C23×C4—612no—
207C23×C4—612no—
208C23×C4—612no—
209C23×C4—611no—
210C23×C4—611no—
211C23×C4—611no—
212C23×C4—611no—
213C23×C4—2444no—
214C23×C4C22×D6111yescharacteristic
215C2×M16—22no—
216C2×M16—1224no—
217C2×M16—1222no—
218C2×M16—2448no—
219C22×C8—1224no—
220#117—2444no—
221C2×C4⋊C4—1222no—
222C2×C22⋊C4—612no—
223C2×C22⋊C4—1224no—
224C2×C22⋊C4C4×D6112yes—
225C2×C42—1222no—
226C22⋊C8—22no—
227C22⋊C8—614no—
228C22⋊C8—1224no—
229C22⋊C8—1224no—
230C22⋊C8—1222no—
231C22⋊C8C4×D6114yes—
232#95—22no—
233#95—1222no—
234C24—612no—
235C24—611no—
236C24—612no—
237C24—611no—
238C24—2442no—
239C24—2444no—
240C24C2×C4×D6111yescharacteristic
241C22×C4—22no—
242C22×C4—42no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—612no—
250C22×C4—612no—
251C22×C4—612no—
252C22×C4—612no—
253C22×C4—612no—
254C22×C4—612no—
255C22×C4—612no—
256C22×C4—612no—
257C22×C4—1228no—
258C22×C4—1224no—
259C22×C4—1222no—
260C22×C4—2444no—
261C22×C4—2444no—
262C22×C4—2444no—
263C22×C4—2442no—
264C22×C4—2442no—
265C22×C4—2442no—
266C22×C4—2442no—
267C22×C4C2×C4×D6112yes—
268C22×C4D4×D6112yes—
269C22×C4D4×D6111yescharacteristic
270C22×C4Q8×D6111yescharacteristic
271M16—44no—
272M16—2448no—
273M16—2444no—
274C2×C8—24no—
275C2×C8—1224no—
276C2×C8—2448no—
277C4⋊C4—2444no—
278C22⋊C4—42no—
279C22⋊C4—2448no—
280C22⋊C4—2442no—
281C42—2444no—
282C23—22no—
283C23—42no—
284C23—612no—
285C23—612no—
286C23—1224no—
287C23—1224no—
288C23—1224no—
289C23—1224no—
290C23—2442no—
291C23—2441no—
292C23—2441no—
293C23—2442no—
294C23—2442no—
295C23—2442no—
296C23—24416no—
297C23C42×D6111yescharacteristic
298C23C22⋊C4×D6111yescharacteristic
299C23C4⋊C4×D6111yescharacteristic
300C2×C4—24no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—44no—
305C2×C4—42no—
306C2×C4—614no—
307C2×C4—611no—
308C2×C4—611no—
309C2×C4—611no—
310C2×C4—611no—
311C2×C4—1224no—
312C2×C4—1224no—
313C2×C4—1224no—
314C2×C4—1224no—
315C2×C4—1222no—
316C2×C4—1222no—
317C2×C4—1222no—
318C2×C4—1222no—
319C2×C4—1222no—
320C2×C4—2442no—
321C2×C4—2442no—
322C2×C4—2442no—
323C2×C4—2442no—
324C2×C4—2444no—
325C2×C4—2442no—
326C2×C4C22⋊C4×D6112yes—
327C2×C4C4⋊C4×D6112yes—
328C8—44no—
329C8—2444no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—22no—
335C22—44no—
336C22—614no—
337C22—1222no—
338C22—1222no—
339C22—1222no—
340C22—1222no—
341C22—1222no—
342C22—2448no—
343C22—2444no—
344C22—2448no—
345C22—2444no—
346C22#95×D6111yescharacteristic
347C22#99×D6112yes—
348C4—22no—
349C4—22no—
350C4—82no—
351C4—612no—
352C4—612no—
353C4—1221no—
354C4—1221no—
355C4—4882no—
356C2—22no—
357C2—41no—
358C2—41no—
359C2—1224no—
360C2—2442no—
361C2#342×D6111yescharacteristic
362C2#344×D6112yes—
subgroupG/H
centerC22#95×D61
commutatorC23×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#1306C2
socleC22×C61C2×#95
prime radicalC24×D61C2×C4
cosocleC23×C4×C61C23
hypercenter#1306D61
hypocenterC61#8112
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
3. #21443728C2semidirect
4. #21443727C2semidirect
5. C61×#1306C2semidirect
12. #16839724C4semidirect
14. C22⋊C8×D61C4semidirect
179. #1306D61semidirect
202. C61#8112semidirect

Maximal subgroups

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

subgroupindex
#407×D612
#214481992
#214437282
#214437272
C61×#13062
#811261