Finite Group Databasebeta

← #29583043

Subgroups — #29583043

Order 15616.

416 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 123 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#21451061C211yesmaximal, characteristic
2#21446768C212yesmaximal
3#21443702C211yesmaximal, characteristic
4#21443659C212yesmaximal
5C61×#1956C211yesmaximal, characteristic
6C2×C4⋊#92418C2212yes—
7#16839701—22no—
8#16839661—22no—
9#16839627—22no—
10C4×C4⋊Dic61C2212yes—
11#16839524—22no—
12#16839524—22no—
13C2×C4⋊Q8×C61C2211yescharacteristic
14C2×#103×C61—22no—
15C2×C4×C8×C61C2211yescharacteristic
16C61×#384C2211yescharacteristic
17C22×#92418—22no—
18C2×C4⋊Dic61—22no—
19C2×C4⋊Dic61D412yes—
20C2×C4⋊Dic61D412yes—
21C2×C4×Dic61—22no—
22C4⋊#92418—22no—
23C4⋊#92418—22no—
24#14519684—22no—
25#14519684—24no—
26#14519684—22no—
27C22×Q8×C61—21no—
28C22×C8×C61—21no—
29C4⋊Q8×C61—22no—
30C4⋊Q8×C61—21no—
31C4⋊Q8×C61Q812yes—
32C2×C4⋊C4×C61—22no—
33C2×C4⋊C4×C61—22no—
34C2×C4⋊C4×C61D412yes—
35C2×C42×C61C2311yescharacteristic
36#103×C61—44no—
37C4×C8×C61—22no—
38C2×Q8×C61—22no—
39C2×Q8×C61—42no—
40C2×Q8×C61—42no—
41C2×Q8×C61—41no—
42C22×C4×C61—22no—
43C22×C4×C61—41no—
44C22×C4×C61C2×D411yescharacteristic
45C22×C4×C61C2×D412yes—
46C22×Dic61—22no—
47C22×Dic61—22no—
48C2×C8×C61—22no—
49C2×C8×C61—41no—
50C2×C8×C61—41no—
51C4⋊C4×C61—24no—
52C4⋊C4×C61—42no—
53C4⋊C4×C61—42no—
54C4⋊C4×C61—42no—
55C4⋊C4×C61—42no—
56C42×C61C2×Q811yescharacteristic
57C42×C61#4111yescharacteristic
58C42×C61#4112yes—
59C4⋊Dic61—22no—
60C4⋊Dic61—22no—
61C4⋊Dic61—22no—
62C4⋊Dic61—22no—
63C4⋊Dic61—82no—
64C4×Dic61—42no—
65C4×Dic61—42no—
66C2×#92418—42no—
67C2×#92418—42no—
68C2×#92418—42no—
69C23×C61#12011yescharacteristic
70Q8×C61—44no—
71Q8×C61—82no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—42no—
75C2×C4×C61—44no—
76C2×C4×C61—42no—
77C2×C4×C61—81no—
78C2×C4×C61—81no—
79C2×C4×C61C22⋊Q811yescharacteristic
80C2×C4×C61C22⋊Q812yes—
81C2×C4×C61#12411yescharacteristic
82C2×C4×C61#12412yes—
83C2×C4×C61#13512yes—
84C2×C4×C61#13512yes—
85C2×C4×C61#13712yes—
86C2×C4×C61#13712yes—
87C2×Dic61—42no—
88C2×Dic61—42no—
89C2×Dic61—42no—
90C2×Dic61—42no—
91C2×Dic61—42no—
92C2×Dic61—42no—
93C8×C61—42no—
94#92418—82no—
95#10352—611nomaximal, Sylow
96C22×C61#39311yescharacteristic
97C22×C61#45212yes—
98C22×C61#45212yes—
99C22×C61#45311yescharacteristic
100C22×C61#45411yescharacteristic
101C4×C61—21no—
102C4×C61—21no—
103C4×C61—82no—
104C4×C61—82no—
105C4×C61#47912yes—
106C4×C61#47912yes—
107C4×C61#48812yes—
108C4×C61#49112yes—
109Dic61—82no—
110Dic61—82no—
111#2571—611no—
112#1987—612no—
113#1956D6111yescharacteristic
114#1296—611no—
115#1279—612no—
116C2×C61#163011yescharacteristic
117C2×C61#163411yescharacteristic
118C2×C61#163812yes—
119C2×C61#202612yes—
120C2×C61#202711yescharacteristic
121C2×C4⋊Q8C2×D6111yescharacteristic
122C2×C4⋊C8—612no—
123C2×#103—22no—
124C2×C4×C8C2×D6111yescharacteristic
125#400—1222no—
126#389—1222no—
127#384C2×D6111yescharacteristic
128#382—1222no—
129C4×C4⋊C4—612no—
130#340—1222no—
131#340—1222no—
132C61#1035211yescharacteristic, complemented, Sylow
133C22×Q8—21no—
134C22×C8—21no—
135C22×C8—1222no—
136C4⋊Q8—21no—
137C4⋊Q8—22no—
138C4⋊Q8Dic12212yes—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—612no—
142C2×C4⋊C4—612no—
143C2×C4⋊C4—1222no—
144C2×C4⋊C4C22⋊D6112yes—
145C2×C42—1222no—
146C2×C42C22×D6111yescharacteristic
147C4⋊C8—1222no—
148C4⋊C8—1222no—
149#103—44no—
150C4×C8—22no—
151#95—1222no—
152#95—1224no—
153#95—1222no—
154C2×Q8—22no—
155C2×Q8—42no—
156C2×Q8—42no—
157C2×Q8—41no—
158C22×C4—22no—
159C22×C4—41no—
160C22×C4—1222no—
161C22×C4—1222no—
162C22×C4D4×D6112yes—
163C22×C4C2×C22⋊D6111yescharacteristic
164C2×C8—22no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—2442no—
168C2×C8—2442no—
169C2×C8—2442no—
170C4⋊C4—24no—
171C4⋊C4—42no—
172C4⋊C4—42no—
173C4⋊C4—42no—
174C4⋊C4—42no—
175C4⋊C4—1222no—
176C4⋊C4—1222no—
177C4⋊C4—1222no—
178C4⋊C4—1222no—
179C4⋊C4—4882no—
180C42—2442no—
181C42—2442no—
182C42C2×Dic12211yescharacteristic
183C42#1175822211yescharacteristic
184C42#1175822412yes—
185C23#1451974511yescharacteristic
186Q8—44no—
187Q8—82no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—44no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—81no—
194C2×C4—81no—
195C2×C4—2442no—
196C2×C4—2442no—
197C2×C4—2442no—
198C2×C4—2442no—
199C2×C4—2442no—
200C2×C4—2442no—
201C2×C4#1451975412yes—
202C2×C4#1451975611yescharacteristic
203C2×C4#1451976312yes—
204C2×C4#1451976411yescharacteristic
205C2×C4#1451979812yes—
206C2×C4#1451980012yes—
207C2×C4#1451980612yes—
208C2×C4#1451980912yes—
209C8—42no—
210C8—4882no—
211C22#1683967411yescharacteristic
212C22#1683992112yes—
213C22#1683992312yes—
214C22#1683992911yescharacteristic
215C22#1683993411yescharacteristic
216C4—21no—
217C4—21no—
218C4—82no—
219C4—82no—
220C4—4882no—
221C4—4882no—
222C4#1684006712yes—
223C4#1684007112yes—
224C4#1684011812yes—
225C4#1684012912yes—
226C2#2144493811yescharacteristic
227C2#2144496211yescharacteristic
228C2#2144498812yes—
229C2#2144696812yes—
230C2#2144697511yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1956C2
socle, prime radicalC23×C61#120
hypercenter#1956D61
hypocenterC61#10352
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
132. C61#10352semidirect

Maximal subgroups

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

subgroupindex
#214510612
#214467682
#214437022
#214436592
C61×#19562
#1035261