Finite Group Databasebeta

← #29576049

Subgroups — #29576049

Order 15616.

578 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 111 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#21454457C211yesmaximal, characteristic, complemented
2#21451569C211yesmaximal, characteristic
3#21444486C212yesmaximal, complemented
4#21443678C212yesmaximal, complemented
5C61×#1458C211yesmaximal, characteristic, complemented
6C2×#14519774C2211yescharacteristic
7C2×#14519751—21no—
8#16839823—24no—
9#16839786C2212yes—
10#16839726—21no—
11C4×#11758194—21no—
12#16839679—21no—
13#16839679C412yes—
14#16839671—21no—
15#16839671C412yes—
16#16839664—21no—
17#16839628C2211yescharacteristic
18#16839505—24no—
19C2×#117×C61C2211yescharacteristic
20C61×#431C2212yes—
21C61×#324—21no—
22C61×#323—21no—
23C22×D244—21no—
24C22×D244—21no—
25C22×D244C2×C412yes—
26C22×C22⋊D61—22no—
27C2×#11758194—22no—
28#14519774—22no—
29#14519774—22no—
30#14519751—44no—
31C2×C4⋊Dic61—21no—
32C2×#11758198—22no—
33C2×#11758198—22no—
34C2×#11758198—22no—
35C4⋊#92418—22no—
36C4⋊#92418D414yescomplemented
37C22⋊#92418—24no—
38#14519688—22no—
39C4×#92418—22no—
40#14519684—21no—
41#14519684C2×C412yes—
42C23×C4×C61D411yescharacteristic
43#117×C61—22no—
44#117×C61—22no—
45C2×C4⋊C4×C61C2×C411yescharacteristic
46C2×C4⋊C4×C61D411yescharacteristic
47C2×C22⋊C4×C61C2×C411yescharacteristic
48C2×C22⋊C4×C61D411yescharacteristic
49C2×C42×C61D411yescharacteristic
50C2×C42×C61C2311yescharacteristic
51C4⋊C8×C61—22no—
52C22⋊C8×C61—22no—
53C4×C8×C61—22no—
54C24×C61C22⋊C411yescharacteristic
55C23×D61—22no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—22no—
59C22×C4×C61—22no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C2×C22⋊D61—44no—
67C2×C22⋊D61—82no—
68C2×C22⋊D61—82no—
69C22×Dic61—22no—
70C2×D244—24no—
71C2×D244—41no—
72C2×D244—42no—
73C2×D244—41no—
74C2×D244—42no—
75C2×D244—42no—
76C2×D244—82no—
77C2×D244—82no—
78C2×C8×C61—42no—
79C4⋊C4×C61—22no—
80C4⋊C4×C61—22no—
81C22⋊C4×C61—22no—
82C22⋊C4×C61—22no—
83C42×C61—21no—
84C42×C61—21no—
85C42×C61C2×D412yes—
86C42×C61#4112yes—
87#11758198—44no—
88#11758198—82no—
89#11758198—82no—
90C4⋊Dic61—42no—
91#11758194—42no—
92#11758194—42no—
93C2×#92418—24no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—41no—
98C23×C61—41no—
99C23×C61C2×C22⋊C411yescharacteristic
100C22×D61—42no—
101C22×D61—42no—
102C22×D61—42no—
103C22×D61—42no—
104C22×D61—42no—
105C22×D61—42no—
106C22×D61—42no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—42no—
115C2×C4×C61—42no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61C4×D412yes—
119C2×C4×C61#12011yescharacteristic
120C2×C4×C61#12112yes—
121C2×C4×C61#12311yescharacteristic
122C2×C4×C61#13512yes—
123C2×C4×C61AGL(1,ℤ/8)12yes—
124C22⋊D61—88no—
125C2×Dic61—42no—
126C2×Dic61—42no—
127C2×Dic61—42no—
128D244—84no—
129D244—84no—
130D244—82no—
131D244—82no—
132C8×C61—82no—
133#92418—44no—
134#9198—611nomaximal, Sylow
135C22×C61—21no—
136C22×C61—21no—
137C22×C61—42no—
138C22×C61—41no—
139C22×C61—41no—
140C22×C61—41no—
141C22×C61—81no—
142C22×C61#38611yescharacteristic
143C22×C61#41611yescharacteristic
144C22×C61#41811yescharacteristic
145C2×D61—82no—
146C2×D61—82no—
147C2×D61—82no—
148C2×D61—82no—
149C2×D61—82no—
150C2×D61—82no—
151C2×D61—82no—
152C4×C61—22no—
153C4×C61—22no—
154C4×C61—41no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61#44912yes—
158C4×C61#48212yes—
159Dic61—82no—
160#2921—611no—
161#2619—611no—
162#1545—612no—
163#1458D6111yescharacteristic, complemented
164#1286—612no—
165C2×C61—21no—
166C2×C61—21no—
167C2×C61—81no—
168C2×C61#187511yescharacteristic
169C2×C61#191011yescharacteristic
170C2×C61#191411yescharacteristic
171D61—162no—
172C2×#127—611no—
173C2×#121—1221no—
174C2×#117C2×D6111yescharacteristic
175#433—1224no—
176#431C2×D6112yes—
177#423—612no—
178#407—1221no—
179C4×M16—1221no—
180#394—612no—
181#394—1221no—
182#392—612no—
183#392—1221no—
184#390—1221no—
185#382—611no—
186#331—1224no—
187#324—21no—
188#323—21no—
189C61#919811yescharacteristic, complemented, Sylow
190C22×D4—612no—
191C22×D4—1222no—
192C22×D4—1221no—
193C22×D4—1221no—
194C23×C4D24411yescharacteristic
195C2×M16—1222no—
196#127—1222no—
197#127—1222no—
198#121—2444no—
199#117—22no—
200#117—22no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4C4×D6111yescharacteristic
203C2×C4⋊C4C22⋊D6111yescharacteristic
204C2×C22⋊C4—1222no—
205C2×C22⋊C4—1222no—
206C2×C22⋊C4—1222no—
207C2×C22⋊C4C4×D6111yescharacteristic
208C2×C22⋊C4C22⋊D6111yescharacteristic
209C2×C42D24411yescharacteristic
210C2×C42C22×D6111yescharacteristic
211C4⋊C8—22no—
212C4⋊C8—614no—
213C4⋊C8—1222no—
214C22⋊C8—22no—
215C22⋊C8—1224no—
216#97—1222no—
217C4×C8—22no—
218C4×C8—1222no—
219#95—612no—
220#95—1221no—
221C24—1222no—
222C24#1175819811yescharacteristic
223C2×D4—1224no—
224C2×D4—4882no—
225C2×D4—4882no—
226C2×D4—4882no—
227C2×D4—4882no—
228C2×D4—2444no—
229C2×D4—2441no—
230C2×D4—2442no—
231C2×D4—2441no—
232C2×D4—2442no—
233C2×D4—2442no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—1222no—
239C22×C4#1175819811yescharacteristic
240C22×C4#1175819811yescharacteristic
241C22×C4#1175819811yescharacteristic
242C22×C4C2×C4×D6111yescharacteristic
243C22×C4C2×D24411yescharacteristic
244C22×C4C2×C22⋊D6111yescharacteristic
245M16—2442no—
246M16—2442no—
247C2×C8—42no—
248C2×C8—1224no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—2442no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C22⋊C4—4882no—
255C22⋊C4—4882no—
256C22⋊C4—2444no—
257C42—21no—
258C42—21no—
259C42D4×D6112yes—
260C42#1175822412yes—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—41no—
266C23—2442no—
267C23—2442no—
268C23—2442no—
269C23—2442no—
270C23—2442no—
271C23—2442no—
272C23—2442no—
273C23C2×#1175819811yescharacteristic
274D4—4884no—
275D4—4884no—
276D4—4888no—
277D4—4882no—
278D4—4882no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—2442no—
291C2×C4—2442no—
292C2×C4—2442no—
293C2×C4#1451973712yes—
294C2×C4#1451974711yescharacteristic
295C2×C4#1451974912yes—
296C2×C4#1451976111yescharacteristic
297C2×C4#1451979912yes—
298C2×C4#1451980512yes—
299C8—82no—
300C8—2444no—
301C22—21no—
302C22—21no—
303C22—42no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22—4882no—
309C22—4882no—
310C22—4882no—
311C22—4882no—
312C22—4882no—
313C22—4882no—
314C22—4882no—
315C22#1683963911yescharacteristic
316C22#1683975911yescharacteristic
317C22#1683976811yescharacteristic
318C4—22no—
319C4—22no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—4882no—
324C4#1683990912yes—
325C4#1684008712yes—
326C2—21no—
327C2—21no—
328C2—81no—
329C2—9762no—
330C2#2144613911yescharacteristic
331C2#2144634411yescharacteristic
332C2#2144636411yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1458C2
socleC22×C61#386
prime radical#21451569C2
cosocleC2×C42×C61C23
hypercenter#1458D61
hypocenterC61#9198
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
1. #21454457C2semidirect
3. #21444486C2semidirect
4. #21443678C2semidirect
5. C61×#1458C2semidirect
36. C4⋊#92418D4semidirect
163. #1458D61semidirect
189. C61#9198semidirect

Maximal subgroups

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

subgroupindex
#214544572
#214515692
#214444862
#214436782
C61×#14582
#919861