Finite Group Databasebeta

← #29590714

Subgroups — #29590714

Order 15616.

488 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 79 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#21451569C211yesmaximal, characteristic
2#21445902C211yesmaximal, characteristic, complemented
3#21443823C214yesmaximal, complemented
4C61×#1464C211yesmaximal, characteristic, complemented
5C2×#14519774C411yescharacteristic
6C2×#14519751—21no—
7#16839726—21no—
8#16839679—21no—
9#16839679C2212yes—
10#16839671—21no—
11#16839671C412yes—
12#16839664—21no—
13#16839628C411yescharacteristic
14#16839531—21no—
15#16839531C2212yes—
16C2×#117×C61C2211yescharacteristic
17C61×#432—21no—
18C61×#324C2212yes—
19C61×#323—21no—
20C22×D244—21no—
21C22×D244—21no—
22C22×D244C2×C412yes—
23C22×C22⋊D61—22no—
24C2×#11758194—22no—
25#14519774—41no—
26#14519774—41no—
27#14519751—44no—
28C2×C4⋊Dic61—21no—
29C2×#11758198—22no—
30C2×#11758198—22no—
31C2×#11758198—22no—
32C22⋊#92418—41no—
33C22⋊#92418—41no—
34#14519684—21no—
35#14519684C2×C412yes—
36C23×C4×C61D411yescharacteristic
37#117×C61—41no—
38#117×C61—41no—
39C2×C4⋊C4×C61D411yescharacteristic
40C2×C4⋊C4×C61C2311yescharacteristic
41C2×C22⋊C4×C61C2×C411yescharacteristic
42C2×C22⋊C4×C61D411yescharacteristic
43C2×C42×C61C2×C411yescharacteristic
44C2×C42×C61D411yescharacteristic
45C4⋊C8×C61—41no—
46C22⋊C8×C61—22no—
47#97×C61—41no—
48C24×C61C22⋊C411yescharacteristic
49C23×D61—22no—
50C22×C4×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61—22no—
53C22×C4×C61—41no—
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22×C411yescharacteristic
58C22×C4×C61C2×D411yescharacteristic
59C22×C4×C61C2×D411yescharacteristic
60C2×C22⋊D61—44no—
61C2×C22⋊D61—82no—
62C2×C22⋊D61—82no—
63C22×Dic61—22no—
64C2×D244—42no—
65C2×D244—42no—
66C2×D244—42no—
67C2×D244—42no—
68C2×D244—41no—
69C2×D244—41no—
70C2×D244—82no—
71C2×D244—82no—
72C2×C8×C61—42no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C22⋊C4×C61—41no—
76C22⋊C4×C61—41no—
77C42×C61—21no—
78C42×C61—21no—
79C42×C61—21no—
80C42×C61—21no—
81#11758198—44no—
82#11758198—82no—
83#11758198—82no—
84C4⋊Dic61—42no—
85#11758194—42no—
86#11758194—42no—
87C2×#92418—42no—
88C23×C61—21no—
89C23×C61—21no—
90C23×C61—21no—
91C23×C61—41no—
92C23×C61—41no—
93C23×C61C2×C22⋊C411yescharacteristic
94C22×D61—42no—
95C22×D61—42no—
96C22×D61—42no—
97C22×D61—42no—
98C22×D61—42no—
99C22×D61—42no—
100C22×D61—42no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—42no—
110C2×C4×C61—42no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61#9911yescharacteristic
116C2×C4×C61#9911yescharacteristic
117C2×C4×C61AGL(1,ℤ/8)12yes—
118C22⋊D61—88no—
119C2×Dic61—42no—
120C2×Dic61—42no—
121C2×Dic61—42no—
122D244—82no—
123D244—82no—
124D244—84no—
125D244—84no—
126C8×C61—82no—
127#92418—82no—
128#11806—611nomaximal, Sylow
129C22×C61—21no—
130C22×C61—21no—
131C22×C61—42no—
132C22×C61—41no—
133C22×C61—41no—
134C22×C61—41no—
135C22×C61—81no—
136C22×C61C2×#9911yescharacteristic
137C22×C61#41811yescharacteristic
138C22×C61#42111yescharacteristic
139C2×D61—82no—
140C2×D61—82no—
141C2×D61—82no—
142C2×D61—82no—
143C2×D61—82no—
144C2×D61—82no—
145C2×D61—82no—
146C4×C61—22no—
147C4×C61—21no—
148C4×C61—21no—
149C4×C61—41no—
150C4×C61—41no—
151C4×C61—41no—
152C4×C61—41no—
153Dic61—82no—
154#2619—611no—
155#1822—611no—
156#1464D6111yescharacteristic, complemented
157#1345—614no—
158C2×C61—21no—
159C2×C61—21no—
160C2×C61—81no—
161C2×C61#151011yescharacteristic
162C2×C61#212211yescharacteristic
163C2×C61#213411yescharacteristic
164D61—162no—
165C2×#127—611no—
166C2×#121—1221no—
167C2×#117C2×D6111yescharacteristic
168#432—21no—
169#407—1221no—
170#394—612no—
171#394—1221no—
172#392—612no—
173#392—1221no—
174#390—1221no—
175#382—611no—
176#343—612no—
177#343—1221no—
178#324C2×D6112yes—
179#323—21no—
180C61#1180611yescharacteristic, complemented, Sylow
181C22×D4—612no—
182C22×D4—1222no—
183C22×D4—1221no—
184C22×D4—1221no—
185C23×C4D24411yescharacteristic
186C2×M16—1222no—
187#127—2441no—
188#127—2441no—
189#121—2444no—
190#117—41no—
191#117—41no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4D24411yescharacteristic
194C2×C4⋊C4C22×D6111yescharacteristic
195C2×C22⋊C4—1222no—
196C2×C22⋊C4—1222no—
197C2×C22⋊C4—1222no—
198C2×C22⋊C4C4×D6111yescharacteristic
199C2×C22⋊C4C22⋊D6111yescharacteristic
200C2×C42C4×D6111yescharacteristic
201C2×C42C22⋊D6111yescharacteristic
202C4⋊C8—41no—
203C22⋊C8—22no—
204C22⋊C8—2441no—
205C22⋊C8—2441no—
206#97—41no—
207#95—612no—
208#95—1221no—
209C24—1222no—
210C24#1175819811yescharacteristic
211C2×D4—4882no—
212C2×D4—4882no—
213C2×D4—4882no—
214C2×D4—4882no—
215C2×D4—2442no—
216C2×D4—2442no—
217C2×D4—2442no—
218C2×D4—2442no—
219C2×D4—2444no—
220C2×D4—2441no—
221C2×D4—2441no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—41no—
226C22×C4—1222no—
227C22×C4#1175819811yescharacteristic
228C22×C4#1175819811yescharacteristic
229C22×C4#1175819811yescharacteristic
230C22×C4C2×C4×D6111yescharacteristic
231C22×C4C2×D24411yescharacteristic
232C22×C4C2×C22⋊D6111yescharacteristic
233M16—2442no—
234M16—2442no—
235C2×C8—42no—
236C2×C8—2442no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—2442no—
240C22⋊C4—41no—
241C22⋊C4—41no—
242C22⋊C4—4882no—
243C22⋊C4—4882no—
244C22⋊C4—2444no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—2442no—
255C23—2442no—
256C23—2442no—
257C23—2442no—
258C23—2442no—
259C23—2442no—
260C23—2442no—
261C23C2×#1175819811yescharacteristic
262D4—4882no—
263D4—4882no—
264D4—4884no—
265D4—4884no—
266D4—4888no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—2442no—
282C2×C4—2442no—
283C2×C4—2442no—
284C2×C4#1451969111yescharacteristic
285C2×C4#1451969111yescharacteristic
286C2×C4#1451980512yes—
287C8—82no—
288C8—4882no—
289C22—21no—
290C22—21no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—4882no—
297C22—4882no—
298C22—4882no—
299C22—4882no—
300C22—4882no—
301C22—4882no—
302C22—4882no—
303C22C2×#1451969111yescharacteristic
304C22#1683976811yescharacteristic
305C22#1683977811yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—4882no—
314C2—21no—
315C2—21no—
316C2—81no—
317C2—9762no—
318C2#2144434911yescharacteristic
319C2#2144746811yescharacteristic
320C2#2144751011yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1464C2
socleC22×C61C2×#99
prime radical#21451569C2
cosocleC2×C4⋊C4×C61C23
hypercenter#1464D61
hypocenterC61#11806
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #21445902C2semidirect
3. #21443823C2semidirect
4. C61×#1464C2semidirect
156. #1464D61semidirect
180. C61#11806semidirect

Maximal subgroups

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

subgroupindex
#214515692
#214459022
#214438232
C61×#14642
#1180661