Finite Group Databasebeta

← #29583251

Subgroups — #29583251

Order 15616.

414 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 73 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#21451484C211yesmaximal, characteristic
2#21445916C212yesmaximal
3#21445894C211yesmaximal, characteristic
4#21443673C212yesmaximal
5C61×#1306C211yesmaximal, characteristic
6C2×#14519736C2211yescharacteristic
7#16839698—21no—
8#16839674—21no—
9#16839666—22no—
10#16839649—22no—
11#16839625C2211yescharacteristic
12C4×C22⋊Dic61C2212yes—
13#16839528—21no—
14#16839528—21no—
15#16839523—22no—
16#16839523—22no—
17C61×#407C2212yes—
18C61×#381C2211yescharacteristic
19C22×Dic122—21no—
20#14519736—22no—
21#14519736—22no—
22C2×C4⋊Dic61—21no—
23C2×C4⋊Dic61Q812yescomplemented
24C2×#11758196—22no—
25C2×C22⋊Dic61—22no—
26C2×C22⋊Dic61—21no—
27C2×C22⋊Dic61—21no—
28C2×C4×Dic61—21no—
29C2×C4×Dic61D412yes—
30C2×C4×Dic61D412yes—
31#14519684—21no—
32#14519684—21no—
33#14519684—22no—
34#14519684—22no—
35#14519684—22no—
36C23×C4×C61C2311yescharacteristic
37C2×M16×C61—22no—
38C2×C22⋊C4×C61D411yescharacteristic
39C2×C22⋊C4×C61D411yescharacteristic
40C22⋊C8×C61—22no—
41C22⋊C8×C61—22no—
42#95×C61—22no—
43C24×C61C2×D411yescharacteristic
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61—41no—
47C22×C4×C61—41no—
48C22×C4×C61C2×D412yes—
49C22×C4×C61C2×Q811yescharacteristic
50C22×C4×C61#4112yes—
51C22×C4×C61#4111yescharacteristic
52C22×Dic61—22no—
53C22×Dic61—22no—
54C22×Dic61—22no—
55C22×Dic61—41no—
56C2×Dic122—44no—
57C2×Dic122—81no—
58M16×C61—42no—
59M16×C61—42no—
60C2×C8×C61—42no—
61C22⋊C4×C61—41no—
62C22⋊C4×C61—41no—
63C22⋊Dic61—44no—
64C22⋊Dic61—41no—
65C22⋊Dic61—41no—
66C22⋊Dic61—41no—
67C22⋊Dic61—41no—
68C4⋊Dic61—24no—
69C4⋊Dic61—81no—
70#11758196—44no—
71C4×Dic61—42no—
72C4×Dic61—42no—
73C4×Dic61—42no—
74C23×C61—21no—
75C23×C61—21no—
76C23×C61—42no—
77C23×C61#12011yescharacteristic
78C23×C61C22⋊Q811yescharacteristic
79C23×C61#12411yescharacteristic
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—41no—
83C2×C4×C61—41no—
84C2×C4×C61—42no—
85C2×C4×C61—42no—
86C2×C4×C61—42no—
87C2×C4×C61—41no—
88C2×C4×C61—41no—
89C2×C4×C61C22⋊Q812yes—
90C2×C4×C61#12412yes—
91C2×Dic61—24no—
92C2×Dic61—42no—
93C2×Dic61—42no—
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97C2×Dic61—42no—
98C2×Dic61—82no—
99C2×Dic61—81no—
100C2×Dic61—82no—
101Dic122—84no—
102C8×C61—82no—
103#10387—611nomaximal, Sylow
104C22×C61—22no—
105C22×C61—21no—
106C22×C61—21no—
107C22×C61—22no—
108C22×C61—22no—
109C22×C61—81no—
110C22×C61—81no—
111C22×C61#39311yescharacteristic
112C22×C61#45811yescharacteristic
113C22×C61#45811yescharacteristic
114C4×C61—22no—
115C4×C61—22no—
116C4×C61—81no—
117C4×C61—81no—
118Dic61—44no—
119Dic61—82no—
120Dic61—82no—
121Dic61—161no—
122#2607—611no—
123#1826—612no—
124#1820—611no—
125#1306D6111yescharacteristic
126#1284—612no—
127C2×C61—21no—
128C2×C61—21no—
129C2×C61—41no—
130C2×C61—41no—
131C2×C61#203011yescharacteristic
132C2×C61#203112yes—
133C2×#117—611no—
134#407C2×D6112yes—
135#399—1221no—
136#393—1221no—
137#391—1222no—
138#387—1222no—
139#381—611no—
140#381C2×D6111yescharacteristic
141C4×C22⋊C4—612no—
142#342—1221no—
143#342—1221no—
144#339—1222no—
145#339—1222no—
146C61#1038711yescharacteristic, complemented, Sylow
147C22×Q8—1221no—
148C23×C4C22×D6111yescharacteristic
149C2×M16—22no—
150#117—1222no—
151#117—1222no—
152C2×C4⋊C4—612no—
153C2×C4⋊C4—1221no—
154C2×C4⋊C4—1222no—
155C2×C22⋊C4—1221no—
156C2×C22⋊C4—1222no—
157C2×C22⋊C4—1221no—
158C2×C22⋊C4D24411yescharacteristic
159C2×C22⋊C4D24411yescharacteristic
160C2×C42—612no—
161C2×C42—612no—
162C2×C42—1221no—
163C22⋊C8—22no—
164C22⋊C8—22no—
165#95—22no—
166#95—1221no—
167#95—1222no—
168#95—1221no—
169#95—1222no—
170#95—1222no—
171C24C2×D24411yescharacteristic
172C2×Q8—4881no—
173C2×Q8—2444no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—1222no—
179C22×C4—1222no—
180C22×C4—1222no—
181C22×C4—2441no—
182C22×C4#1175822212yes—
183C22×C4D4×D6112yes—
184C22×C4#1175822411yescharacteristic
185C22×C4Q8×D6111yescharacteristic
186M16—42no—
187M16—42no—
188C2×C8—42no—
189C4⋊C4—1224no—
190C4⋊C4—4881no—
191C4⋊C4—2444no—
192C22⋊C4—41no—
193C22⋊C4—41no—
194C22⋊C4—2444no—
195C22⋊C4—2441no—
196C22⋊C4—2441no—
197C22⋊C4—2441no—
198C22⋊C4—2441no—
199C42—2442no—
200C42—2442no—
201C42—2442no—
202C23—21no—
203C23—21no—
204C23—42no—
205C23#1451974711yescharacteristic
206C23#1451975711yescharacteristic
207C23#1451976511yescharacteristic
208Q8—4884no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—1224no—
219C2×C4—4881no—
220C2×C4—4882no—
221C2×C4—4882no—
222C2×C4—2442no—
223C2×C4—2442no—
224C2×C4—2442no—
225C2×C4—2442no—
226C2×C4—2442no—
227C2×C4—2442no—
228C2×C4#1451975512yes—
229C2×C4#1451976312yes—
230C8—82no—
231C22—22no—
232C22—21no—
233C22—21no—
234C22—22no—
235C22—22no—
236C22—81no—
237C22—81no—
238C22#1683967511yescharacteristic
239C22#1683995311yescharacteristic
240C22#1683995311yescharacteristic
241C4—22no—
242C4—22no—
243C4—81no—
244C4—81no—
245C4—9761no—
246C4—4882no—
247C4—4882no—
248C4—2444no—
249C2—21no—
250C2—21no—
251C2—41no—
252C2—41no—
253C2#2144698711yescharacteristic
254C2#2144699412yes—
subgroupG/H
centerC22#16839675
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1306C2
socleC22×C61#393
prime radicalC24×C61C2×D4
hypercenter#1306D61
hypocenterC61#10387
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
23. C2×C4⋊Dic61Q8semidirect
146. C61#10387semidirect

Maximal subgroups

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

subgroupindex
#214514842
#214459162
#214458942
#214436732
C61×#13062
#1038761