Finite Group Databasebeta

← #29599704

Subgroups — #29599704

Order 15616.

384 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 81 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#21453807C211yesmaximal, characteristic
2#21446036C212yesmaximal
3#21446033C211yesmaximal, characteristic
4#21443945C212yesmaximal
5C61×#1394C211yesmaximal, characteristic
6#16840240C2211yescharacteristic
7#16839804—22no—
8#16839802—21no—
9C2×#14519696C2211yescharacteristic
10#16839701—21no—
11#16839694—22no—
12#16839669C2212yes—
13#16839660—21no—
14#16839649—22no—
15#16839523—22no—
16#16839522—21no—
17C2×#101×C61C2212yes—
18C61×#391C2211yescharacteristic
19C2×#11758194—21no—
20Q8×Dic61—41no—
21Q8×Dic61—41no—
22#14519736—21no—
23#14519736—22no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61D412yes—
28C2×#11758196—22no—
29C2×C4×Dic61D412yes—
30#14519711—42no—
31#14519710—41no—
32#14519709—42no—
33#14519708—41no—
34#14519696—21no—
35#14519696Q812yes—
36#14519684—22no—
37#14519684—21no—
38#14519684—22no—
39#14519684—22no—
40C22×Q8×C61C2311yescharacteristic
41C2×M16×C61—22no—
42C2×C4⋊C4×C61D411yescharacteristic
43C2×C42×C61D411yescharacteristic
44#101×C61—22no—
45#101×C61Q814yes—
46#95×C61—22no—
47C2×Q8×C61—41no—
48C2×Q8×C61—41no—
49C2×Q8×C61C2×Q812yes—
50C2×Q8×C61C2×Q811yescharacteristic
51C2×Q8×C61#4111yescharacteristic
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61C2×D411yescharacteristic
55C22×C4×C61C2×D412yes—
56C22×Dic61—22no—
57C22×Dic61—22no—
58M16×C61—24no—
59M16×C61—42no—
60C2×C8×C61—42no—
61C4⋊C4×C61—41no—
62C42×C61—41no—
63C22⋊Dic61—41no—
64C4⋊Dic61—21no—
65C4⋊Dic61—22no—
66C4⋊Dic61—21no—
67C4⋊Dic61—22no—
68C4⋊Dic61—42no—
69C4⋊Dic61—42no—
70C4⋊Dic61—81no—
71C4⋊Dic61—81no—
72#11758196—44no—
73C4×Dic61—41no—
74C4×Dic61—42no—
75C4×Dic61—42no—
76#11758194—22no—
77#11758194—41no—
78C2×#92418—41no—
79C23×C61#12011yescharacteristic
80Q8×C61—41no—
81Q8×C61—42no—
82Q8×C61—41no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61—21no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—42no—
91C2×C4×C61—41no—
92C2×C4×C61C22⋊Q812yes—
93C2×C4×C61C22⋊Q811yescharacteristic
94C2×C4×C61C4⋊Q812yes—
95C2×C4×C61C4⋊Q811yescharacteristic
96C2×Dic61—42no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61—42no—
100C2×Dic61—41no—
101C2×Dic61—41no—
102C2×Dic61—42no—
103C2×Dic61—42no—
104C8×C61—44no—
105#92418—42no—
106#13465—611nomaximal, Sylow
107C22×C61—21no—
108C22×C61—21no—
109C22×C61#39511yescharacteristic
110C22×C61B(4,𝔽2)11yescharacteristic
111C22×C61#45811yescharacteristic
112C4×C61—21no—
113C4×C61—22no—
114C4×C61—22no—
115C4×C61—21no—
116C4×C61—42no—
117C4×C61—81no—
118Dic61—82no—
119Dic61—81no—
120Dic61—81no—
121Dic61—82no—
122#2809—611no—
123#1857—612no—
124#1857—611no—
125#1394—612no—
126#1394D6111yescharacteristic
127C2×C61—21no—
128C2×C61—21no—
129C2×C61#206211yescharacteristic
130C2×C61#220311yescharacteristic
131C2×C61#220411yescharacteristic
132#519—611no—
133#428—1222no—
134#428—1221no—
135C2×#101—611no—
136C2×#101C2×D6112yes—
137#400—1221no—
138#398—1222no—
139#391—612no—
140#391C2×D6111yescharacteristic
141#389—1221no—
142#387—1222no—
143#339—1222no—
144#339—1221no—
145C61#1346511yescharacteristic, complemented, Sylow
146C22×Q8C22×D6111yescharacteristic
147C2×M16—22no—
148C2×M16—1221no—
149C4×Q8—2441no—
150C4×Q8—2441no—
151#117—1221no—
152#117—1222no—
153C2×C4⋊C4—612no—
154C2×C4⋊C4—1221no—
155C2×C4⋊C4—1221no—
156C2×C4⋊C4—1222no—
157C2×C4⋊C4—1221no—
158C2×C4⋊C4D24411yescharacteristic
159C2×C42—612no—
160C2×C42D24411yescharacteristic
161#107—2441no—
162#107—2442no—
163#106—2441no—
164#106—2442no—
165#101—22no—
166#101—612no—
167#101—1221no—
168#101Dic12214yes—
169#95—22no—
170#95—1221no—
171#95—1222no—
172#95—1222no—
173#95—1222no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8C2×Dic12212yes—
177C2×Q8#1175822411yescharacteristic
178C2×Q8Q8×D6111yescharacteristic
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—1222no—
182C22×C4—1222no—
183C22×C4C2×D24411yescharacteristic
184C22×C4D4×D6112yes—
185M16—24no—
186M16—42no—
187M16—1222no—
188M16—2441no—
189C2×C8—42no—
190C2×C8—2441no—
191C4⋊C4—41no—
192C4⋊C4—1221no—
193C4⋊C4—1222no—
194C4⋊C4—1221no—
195C4⋊C4—1222no—
196C4⋊C4—4881no—
197C4⋊C4—4881no—
198C4⋊C4—2442no—
199C4⋊C4—2444no—
200C4⋊C4—2442no—
201C22⋊C4—2441no—
202C42—41no—
203C42—2442no—
204C42—2441no—
205C42—2442no—
206C23#1451974711yescharacteristic
207Q8—42no—
208Q8—41no—
209Q8—41no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—2442no—
220C2×C4—2442no—
221C2×C4—2442no—
222C2×C4—2442no—
223C2×C4—2441no—
224C2×C4—2441no—
225C2×C4—2442no—
226C2×C4—2442no—
227C2×C4#1451975412yes—
228C2×C4#1451975711yescharacteristic
229C2×C4#1451977612yes—
230C2×C4#1451977711yescharacteristic
231C8—44no—
232C8—2442no—
233C22—21no—
234C22—21no—
235C22#1683968311yescharacteristic
236C22#1683995011yescharacteristic
237C22#1683995311yescharacteristic
238C4—22no—
239C4—21no—
240C4—22no—
241C4—21no—
242C4—42no—
243C4—81no—
244C4—4882no—
245C4—4881no—
246C4—4881no—
247C4—4882no—
248C2—21no—
249C2—21no—
250C2#2144717311yescharacteristic
251C2#2144784211yescharacteristic
252C2#2144784711yescharacteristic
subgroupG/H
centerC22#16839950
commutator, cosocleC22×Q8×C61C23
FrattiniC22×Q8C22×D61
FittingC61×#1394C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#1394D61
hypocenterC61#13465
LCSG ▷ C22×Q8×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
145. C61#13465semidirect

Maximal subgroups

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

subgroupindex
#214538072
#214460362
#214460332
#214439452
C61×#13942
#1346561