Finite Group Databasebeta

← #29599703

Subgroups — #29599703

Order 15616.

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

normal subgroups only

This group has 384 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#21453807C211yesmaximal, characteristic
2#21446034C212yesmaximal
3#21443946C211yesmaximal, characteristic
4#21443945C212yesmaximal
5C61×#1857C211yesmaximal, characteristic
6#16839805—22no—
7C2×#14519696C2212yes—
8#16839701—21no—
9#16839694—22no—
10#16839669C2212yes—
11#16839660—21no—
12#16839649—22no—
13#16839521—22no—
14C61×#519C2211yescharacteristic
15C61×#428—21no—
16C2×#101×C61C2211yescharacteristic
17C61×#391C2211yescharacteristic
18C61×#339—21no—
19C2×#11758194—22no—
20C2×C4⋊Dic61—21no—
21C2×C4⋊Dic61—21no—
22C2×C4⋊Dic61—21no—
23C2×C4⋊Dic61D412yes—
24C2×#11758196—22no—
25C2×C4×Dic61D412yes—
26#14519710—42no—
27#14519708—42no—
28#14519696—22no—
29#14519696Q814yes—
30#14519684—22no—
31#14519684—21no—
32#14519684—22no—
33#14519684—22no—
34C22×Q8×C61C2311yescharacteristic
35C2×M16×C61—21no—
36C4×Q8×C61—41no—
37C4×Q8×C61—41no—
38#117×C61—21no—
39#117×C61—22no—
40C2×C4⋊C4×C61D411yescharacteristic
41C2×C42×C61D411yescharacteristic
42#107×C61—41no—
43#106×C61—41no—
44#101×C61—21no—
45#101×C61Q812yes—
46#95×C61—22no—
47C2×Q8×C61—41no—
48C2×Q8×C61—41no—
49C2×Q8×C61C2×Q811yescharacteristic
50C2×Q8×C61C2×Q812yes—
51C2×Q8×C61#4111yescharacteristic
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61C2×D412yes—
55C22×C4×C61C2×D411yescharacteristic
56C22×Dic61—22no—
57C22×Dic61—22no—
58M16×C61—22no—
59M16×C61—41no—
60C2×C8×C61—41no—
61C4⋊C4×C61—21no—
62C4⋊C4×C61—21no—
63C4⋊C4×C61—22no—
64C4⋊C4×C61—22no—
65C4⋊C4×C61—41no—
66C22⋊C4×C61—41no—
67C42×C61—42no—
68C42×C61—41no—
69C42×C61—41no—
70C4⋊Dic61—42no—
71C4⋊Dic61—42no—
72C4⋊Dic61—81no—
73C4⋊Dic61—81no—
74#11758196—44no—
75C4×Dic61—42no—
76#11758194—24no—
77#11758194—42no—
78C2×#92418—42no—
79C23×C61#12011yescharacteristic
80Q8×C61—42no—
81Q8×C61—41no—
82Q8×C61—41no—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61—22no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—42no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61C22⋊Q812yes—
95C2×C4×C61C22⋊Q811yescharacteristic
96C2×C4×C61C4⋊Q811yescharacteristic
97C2×C4×C61C4⋊Q812yes—
98C2×Dic61—42no—
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61—42no—
102C2×Dic61—42no—
103C2×Dic61—42no—
104C8×C61—42no—
105#92418—44no—
106#13465—611nomaximal, Sylow
107C22×C61—21no—
108C22×C61—21no—
109C22×C61#39511yescharacteristic
110C22×C61B(4,𝔽2)11yescharacteristic
111C22×C61#45811yescharacteristic
112C4×C61—22no—
113C4×C61—21no—
114C4×C61—21no—
115C4×C61—22no—
116C4×C61—42no—
117C4×C61—81no—
118C4×C61—81no—
119C4×C61—81no—
120Dic61—82no—
121Dic61—82no—
122#2809—611no—
123#1857—612no—
124#1857D6111yescharacteristic
125#1394—612no—
126#1394—611no—
127C2×C61—21no—
128C2×C61—21no—
129C2×C61#206211yescharacteristic
130C2×C61#220311yescharacteristic
131C2×C61#220411yescharacteristic
132#519C2×D6111yescharacteristic
133#428—21no—
134#428—1222no—
135C2×#101—612no—
136C2×#101C2×D6111yescharacteristic
137#400—1221no—
138#398—1222no—
139#391—612no—
140#391C2×D6111yescharacteristic
141#389—1221no—
142#387—1222no—
143#339—21no—
144#339—1222no—
145C61#1346511yescharacteristic, complemented, Sylow
146C22×Q8C22×D6111yescharacteristic
147C2×M16—21no—
148C2×M16—1222no—
149C4×Q8—41no—
150C4×Q8—41no—
151#117—22no—
152#117—21no—
153C2×C4⋊C4—612no—
154C2×C4⋊C4—1221no—
155C2×C4⋊C4—1221no—
156C2×C4⋊C4—1222no—
157C2×C4⋊C4—1221no—
158C2×C4⋊C4C22⋊D6111yescharacteristic
159C2×C42—612no—
160C2×C42C22⋊D6111yescharacteristic
161#107—41no—
162#107—2442no—
163#106—41no—
164#106—2442no—
165#101—21no—
166#101—614no—
167#101—1222no—
168#101Dic12212yes—
169#95—22no—
170#95—1221no—
171#95—1222no—
172#95—1222no—
173#95—1222no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8C2×Dic12211yescharacteristic
177C2×Q8#1175822211yescharacteristic
178C2×Q8Q8×D6112yes—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—1222no—
182C22×C4—1222no—
183C22×C4D4×D6112yes—
184C22×C4C2×C22⋊D6111yescharacteristic
185M16—22no—
186M16—41no—
187M16—1224no—
188M16—2442no—
189C2×C8—41no—
190C2×C8—2442no—
191C4⋊C4—21no—
192C4⋊C4—22no—
193C4⋊C4—21no—
194C4⋊C4—22no—
195C4⋊C4—41no—
196C4⋊C4—4881no—
197C4⋊C4—4881no—
198C4⋊C4—2442no—
199C4⋊C4—2444no—
200C4⋊C4—2442no—
201C22⋊C4—41no—
202C42—41no—
203C42—41no—
204C42—42no—
205C42—2442no—
206C23#1451974511yescharacteristic
207Q8—41no—
208Q8—41no—
209Q8—42no—
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—41no—
220C2×C4—41no—
221C2×C4—2442no—
222C2×C4—2442no—
223C2×C4—2442no—
224C2×C4—2442no—
225C2×C4—2442no—
226C2×C4—2442no—
227C2×C4#1451975512yes—
228C2×C4#1451975611yescharacteristic
229C2×C4#1451977511yescharacteristic
230C2×C4#1451977612yes—
231C8—42no—
232C8—2444no—
233C22—21no—
234C22—21no—
235C22#1683968211yescharacteristic
236C22#1683994811yescharacteristic
237C22#1683995111yescharacteristic
238C4—21no—
239C4—22no—
240C4—21no—
241C4—22no—
242C4—42no—
243C4—81no—
244C4—81no—
245C4—81no—
246C4—4882no—
247C4—4882no—
248C2—21no—
249C2—21no—
250C2#2144717211yescharacteristic
251C2#2144783911yescharacteristic
252C2#2144784411yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC22×Q8×C61C23
FrattiniC22×Q8C22×D61
FittingC61×#1857C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#1857D61
hypocenterC61#13465
LCSG ▷ C22×Q8×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1857

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
#214460342
#214439462
#214439452
C61×#18572
#1346561