Finite Group Databasebeta

← #29593817

Subgroups — #29593817

Order 15616.

356 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 69 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#21457540C211yesmaximal, characteristic
2#21448047C211yesmaximal, characteristic, complemented
3#21447956C211yesmaximal, characteristic, complemented
4#21445209C211yesmaximal, characteristic, complemented
5#21443867C211yesmaximal, characteristic, complemented
6#21443775C211yesmaximal, characteristic, complemented
7C61×#1331C211yesmaximal, characteristic, complemented
8C2×#14519796—21no—
9#16840416—21no—
10#16840167C2211yescharacteristic
11#16840142C2211yescharacteristic
12#16840004—21no—
13#16839968—21no—
14#16839967—21no—
15#16839925—22no—
16C8×D244C2211yescharacteristic
17#16839587—21no—
18C4⋊#11758185C2211yescharacteristic
19#16839567—22no—
20#16839563—21no—
21#16839509—21no—
22C4×D8×C61C2211yescharacteristic
23C4×C16×C61C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×#11758224—22no—
26#14519796—42no—
27#14519796—42no—
28C2×Dic244—21no—
29C2×Dic244D412yes—
30C2×#11758190—41no—
31C2×#11758200—22no—
32C2×C8×D61—21no—
33#14519777—21no—
34#14519777—21no—
35#14519761—42no—
36#14519757—22no—
37#14519751—41no—
38C4×D244D411yescharacteristic
39C2×C4⋊Dic61—41no—
40C2×#11758185—21no—
41#14519711—21no—
42#14519711—21no—
43C4⋊#92418D411yescharacteristic
44#14519702—41no—
45#14519700—22no—
46#14519689—21no—
47C2×D8×C61D411yescharacteristic
48C4×D4×C61—21no—
49C2×C16×C61—21no—
50#107×C61D411yescharacteristic
51C4⋊C8×C61—21no—
52#102×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×D4×C61—21no—
55C22×C4×C61—41no—
56C2×C22⋊D61—42no—
57C22×Dic61—42no—
58#11758224—44no—
59#11758224—82no—
60C2×D244D811yescharacteristic
61C2×C4×D61—21no—
62C2×Dic122—22no—
63C2×Dic122—41no—
64D8×C61—21no—
65D8×C61SD1612yescomplemented
66C2×C8×C61—41no—
67C2×C8×C61C2×D411yescharacteristic
68C2×C8×C61C2×D411yescharacteristic
69C4⋊C4×C61—21no—
70C22⋊C4×C61—41no—
71C42×C61C2×D411yescharacteristic
72#11758200—44no—
73#11758198—21no—
74#11758198—42no—
75C4⋊Dic61—42no—
76C4⋊Dic61—41no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79C4⋊Dic61—41no—
80C4⋊Dic61D811yescharacteristic
81C2×#92418—21no—
82Dic244—42no—
83Dic244—41no—
84Dic244—41no—
85#11758190—82no—
86C8×D61—41no—
87C8×D61—41no—
88C16×C61—41no—
89#11758185—41no—
90C23×C61—41no—
91C22×D61—21no—
92D4×C61—22no—
93D4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61—81no—
96C2×C4×C61—81no—
97C2×C4×C61#12011yescharacteristic
98C2×C4×C61C2×D811yescharacteristic
99C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
100C22⋊D61—84no—
101C2×Dic61—21no—
102C2×Dic61—42no—
103C2×Dic61—84no—
104C2×Dic61—81no—
105D244—21no—
106D244—21no—
107C4×D61—41no—
108C4×D61—41no—
109Dic122—42no—
110Dic122—42no—
111Dic122—81no—
112Dic122—81no—
113C8×C61—21no—
114C8×C61—81no—
115C8×C61C2×SD1611yescharacteristic
116C8×C61AGL(1,ℤ/8)11yescharacteristic
117#92418—41no—
118#12371—611nomaximal, Sylow
119C22×C61—42no—
120C22×C61—81no—
121C22×C61—81no—
122C22×C61#44711yescharacteristic
123C2×D61—41no—
124C2×D61—41no—
125C2×D61—41no—
126C4×C61—21no—
127C4×C61—81no—
128C4×C61#45011yescharacteristic
129C4×C61#45511yescharacteristic
130C4×C61#50811yescharacteristic
131C4×C61#50911yescharacteristic
132Dic61—41no—
133Dic61—82no—
134Dic61—161no—
135#3283—611no—
136#2241—611no—
137#2224—611no—
138#1673—611no—
139#1362—611no—
140#1331D6111yescharacteristic, complemented
141D4⋊C16—611no—
142C2×C61—82no—
143C2×C61#163911yescharacteristic
144C2×C61#218611yescharacteristic
145C2×C61#219511yescharacteristic
146D61—81no—
147C2×#135—1221no—
148#547—1221no—
149#500—611no—
150#494—611no—
151#467—1221no—
152#461—1221no—
153#461—1221no—
154#452—1222no—
155C4×D8C2×D6111yescharacteristic
156C8×D4—611no—
157#366—1221no—
158C4⋊C16—611no—
159#358—1222no—
160#357—1221no—
161C4×C16C2×D6111yescharacteristic
162#335C2×D6111yescharacteristic
163#332—1221no—
164C61#1237111yescharacteristic, complemented, Sylow
165C2×#41—1222no—
166#135—2442no—
167#135—2442no—
168C2×Q16—612no—
169C2×Q16—1221no—
170C2×SD16—1222no—
171C2×SD16—2441no—
172C2×D8D24411yescharacteristic
173C22×C8—1221no—
174C4⋊Q8—1221no—
175C4⋊Q8—1221no—
176#123—2442no—
177C22⋊Q8—1222no—
178#121—2441no—
179C4×D4—21no—
180C4×D4—611no—
181C2×C4⋊C4—2441no—
182C2×C16—21no—
183C2×C16—1221no—
184#107—1221no—
185#107—1221no—
186#107D24411yescharacteristic
187C4⋊C8—21no—
188C4⋊C8—611no—
189#103—1222no—
190#103—2441no—
191#102—21no—
192C22⋊C8—1221no—
193C4×C8C22×D6111yescharacteristic
194#41—4882no—
195#41—2444no—
196C2×Q8—1222no—
197C2×Q8—2441no—
198C2×D4—21no—
199C2×D4—611no—
200C2×D4—2442no—
201C22×C4—41no—
202C22×C4—1221no—
203C22×C4—2442no—
204Q16—2442no—
205Q16—2441no—
206Q16—2441no—
207SD16—4882no—
208SD16—2444no—
209D8—21no—
210D8#1175819012yescomplemented
211C2×C8—41no—
212C2×C8—1221no—
213C2×C8—2441no—
214C2×C8—2441no—
215C2×C8C2×D24411yescharacteristic
216C2×C8D4×D6111yescharacteristic
217C4⋊C4—21no—
218C4⋊C4—611no—
219C4⋊C4—2442no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C4⋊C4—2441no—
224C22⋊C4—41no—
225C22⋊C4—1221no—
226C22⋊C4—2442no—
227C42D4×D6111yescharacteristic
228C16—41no—
229C16—2441no—
230C23—41no—
231C23—1221no—
232Q8—4881no—
233Q8—4881no—
234Q8—2442no—
235Q8—2442no—
236D4—22no—
237D4—41no—
238D4—1221no—
239D4—1221no—
240D4—4884no—
241C2×C4—41no—
242C2×C4—81no—
243C2×C4—81no—
244C2×C4—1221no—
245C2×C4—4881no—
246C2×C4—4884no—
247C2×C4—2442no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4#1451974711yescharacteristic
251C2×C4D8×D6111yescharacteristic
252C2×C4#1451980411yescharacteristic
253C8—21no—
254C8—81no—
255C8—2441no—
256C8C2×#1175819011yescharacteristic
257C8#1451980511yescharacteristic
258C22—42no—
259C22—81no—
260C22—81no—
261C22—2441no—
262C22—2441no—
263C22—2441no—
264C22#1683989711yescharacteristic
265C4—21no—
266C4—81no—
267C4—9761no—
268C4—4882no—
269C4—2441no—
270C4#1683991511yescharacteristic
271C4#1683994111yescharacteristic
272C4#1684019311yescharacteristic
273C4#1684019611yescharacteristic
274C2—82no—
275C2—4881no—
276C2#2144500111yescharacteristic
277C2#2144774311yescharacteristic
278C2#2144779811yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1331C2
socleC22×C61#447
prime radical#21457540C2
hypercenter#1331D61
hypocenterC61#12371
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1331

Complements

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

NH ≅ G/Ntype
2. #21448047C2semidirect
3. #21447956C2semidirect
4. #21445209C2semidirect
5. #21443867C2semidirect
6. #21443775C2semidirect
7. C61×#1331C2semidirect
65. D8×C61SD16semidirect
140. #1331D61semidirect
164. C61#12371semidirect
210. D8#11758190semidirect

Maximal subgroups

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

subgroupindex
#214575402
#214480472
#214479562
#214452092
#214438672
#214437752
C61×#13312
#1237161