Finite Group Databasebeta

← #29593340

Subgroups — #29593340

Order 15616.

376 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 55 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#21456619C211yesmaximal, characteristic
2#21448034C212yesmaximal, complemented
3#21447335C211yesmaximal, characteristic, complemented
4#21443811C212yesmaximal, complemented
5C61×#1320C211yesmaximal, characteristic, complemented
6C2×#14519751—21no—
7#16840081—22no—
8#16840015—21no—
9#16840015C2212yes—
10#16839898—22no—
11#16839811C2211yescharacteristic, complemented
12#16839810—21no—
13#16839726—21no—
14#16839585—22no—
15#16839576—22no—
16#16839520C2211yescharacteristic, complemented
17C61×#407C2211yescharacteristic
18C61×#349C2212yescomplemented
19C22×D244—21no—
20C22×C22⋊D61—41no—
21C2×D488—21no—
22C2×D488D412yes—
23C2×#11758194—21no—
24C2×#11758194—21no—
25#14519751—22no—
26#14519751—22no—
27#14519751—41no—
28#14519751—41no—
29C2×C4⋊Dic61—21no—
30C2×#11758198—41no—
31#14519713—22no—
32#14519712—42no—
33#14519709—21no—
34#14519709D412yes—
35#14519699—22no—
36#14519699—22no—
37C22⋊#92418—42no—
38C23×C4×C61D411yescharacteristic
39C2×M16×C61D411yescharacteristic
40C2×M16×C61C2311yescharacteristic
41M32×C61—22no—
42C22⋊C8×C61—22no—
43C24×C61SD1611yescharacteristic
44C23×D61—41no—
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61—41no—
48C22×C4×C61—41no—
49C22×C4×C61SD1611yescharacteristic
50C22×C4×C61C2×D411yescharacteristic
51C2×C22⋊D61—42no—
52C2×C22⋊D61—42no—
53C2×C22⋊D61—84no—
54C22×Dic61—41no—
55C2×D244—22no—
56C2×D244—41no—
57C2×D244—81no—
58C2×D244—81no—
59M16×C61—41no—
60M16×C61—41no—
61C2×C8×C61—21no—
62C2×C8×C61C2×D412yes—
63#11758198—42no—
64#11758198—42no—
65C4⋊Dic61—22no—
66C4⋊Dic61—41no—
67#11758194—41no—
68#11758194—41no—
69#11758194—41no—
70#11758194—41no—
71C2×#92418—22no—
72C2×#92418—41no—
73D488—42no—
74D488—81no—
75C16×C61—42no—
76C23×C61—21no—
77C23×C61—42no—
78C23×C61—41no—
79C23×C61C2×SD1611yescharacteristic
80C22×D61—42no—
81C22×D61—82no—
82C22×D61—82no—
83C22×D61—82no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—41no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—81no—
91C2×C4×C61#12011yescharacteristic
92C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
93C22⋊D61—84no—
94C22⋊D61—84no—
95C2×Dic61—42no—
96C2×Dic61—82no—
97D244—42no—
98D244—42no—
99D244—82no—
100C8×C61—22no—
101C8×C61—41no—
102#92418—42no—
103#92418—81no—
104#12298—611nomaximal, Sylow
105C22×C61—22no—
106C22×C61—21no—
107C22×C61—41no—
108C22×C61—41no—
109C22×C61—42no—
110C22×C61—41no—
111C22×C61—81no—
112C22×C61#45011yescharacteristic
113C2×D61—82no—
114C2×D61—82no—
115C2×D61—82no—
116C2×D61—164no—
117C4×C61—21no—
118C4×C61—41no—
119C4×C61#45311yescharacteristic
120C4×C61#45811yescharacteristic
121Dic61—82no—
122#3192—611no—
123#2238—612no—
124#2091—611no—
125#1341—612no—
126#1320D6111yescharacteristic, complemented
127C2×C61—21no—
128C2×C61—42no—
129C2×C61—41no—
130C2×C61#161311yescharacteristic
131D61—162no—
132C2×#121—1221no—
133#481—1222no—
134#469—612no—
135#469—1221no—
136#447—1222no—
137#430—611no—
138#430—1221no—
139#407—1221no—
140#407C2×D6111yescharacteristic
141#365—1222no—
142#361—1222no—
143#349C2×D6112yescomplemented
144#338—611no—
145C61#1229811yescharacteristic, complemented, Sylow
146C22×D4—1221no—
147C22×D4—2441no—
148C23×C4D24411yescharacteristic
149C2×D8—612no—
150C2×D8—1221no—
151C2×M16—1221no—
152C2×M16—1221no—
153C2×M16D24411yescharacteristic
154C2×M16C22×D6111yescharacteristic
155#121—1222no—
156#121—1222no—
157#121—2441no—
158#121—2441no—
159C2×C4⋊C4—1221no—
160C2×C22⋊C4—2441no—
161M32—22no—
162#108—1222no—
163#108—2442no—
164#106—612no—
165#106—1221no—
166#102—1222no—
167#102—1222no—
168C22⋊C8—22no—
169C22⋊C8—2442no—
170C24—2441no—
171C24#1175819011yescharacteristic
172C2×D4—1222no—
173C2×D4—4881no—
174C2×D4—4881no—
175C2×D4—4884no—
176C2×D4—2441no—
177C2×D4—2442no—
178C2×D4—2442no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—2441no—
184C22×C4#1175819011yescharacteristic
185C22×C4C2×D24411yescharacteristic
186D8—4881no—
187D8—2442no—
188M16—41no—
189M16—41no—
190M16—2441no—
191M16—2441no—
192M16—2441no—
193M16—2441no—
194C2×C8—21no—
195C2×C8—1222no—
196C2×C8—2441no—
197C2×C8D4×D6112yes—
198C4⋊C4—1222no—
199C4⋊C4—2441no—
200C22⋊C4—2442no—
201C22⋊C4—2442no—
202C16—42no—
203C23—21no—
204C23—41no—
205C23—42no—
206C23—4882no—
207C23—4882no—
208C23—4882no—
209C23—2442no—
210C23C2×#1175819011yescharacteristic
211D4—4882no—
212D4—4884no—
213D4—4884no—
214D4—2442no—
215D4—2442no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—81no—
223C2×C4—4882no—
224C2×C4—2442no—
225C2×C4#1451974711yescharacteristic
226C2×C4#1451980511yescharacteristic
227C8—22no—
228C8—41no—
229C8—4881no—
230C8—2442no—
231C22—22no—
232C22—21no—
233C22—41no—
234C22—41no—
235C22—42no—
236C22—41no—
237C22—81no—
238C22—9764no—
239C22—4882no—
240C22—4882no—
241C22—4882no—
242C22#1683991511yescharacteristic
243C4—21no—
244C4—41no—
245C4—4882no—
246C4#1683993211yescharacteristic
247C4#1683995311yescharacteristic
248C2—21no—
249C2—42no—
250C2—41no—
251C2—9762no—
252C2#2144484111yescharacteristic
subgroupG/H
centerC2#21444841
commutator, cosocleC2×M16×C61C23
FrattiniC2×M16C22×D61
FittingC61×#1320C2
socleC2×C61#1613
prime radical#21456619C2
hypercenter#1320D61
hypocenterC61#12298
LCSG ▷ C2×M16×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1320

Complements

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

NH ≅ G/Ntype
2. #21448034C2semidirect
3. #21447335C2semidirect
4. #21443811C2semidirect
5. C61×#1320C2semidirect
11. #16839811C22semidirect
16. #16839520C22semidirect
18. C61×#349C22semidirect
126. #1320D61semidirect
143. #349C2×D61semidirect
145. C61#12298semidirect

Maximal subgroups

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

subgroupindex
#214566192
#214480342
#214473352
#214438112
C61×#13202
#1229861