Finite Group Databasebeta

← #29593072

Subgroups — #29593072

Order 15616.

342 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 59 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#21444861C212yesmaximal
3#21443845C212yesmaximal
4#21443765C211yesmaximal, characteristic
5C61×#2060C211yesmaximal, characteristic
6#16840095—22no—
7#16839701—21no—
8#16839701C2212yes—
9#16839661—22no—
10#16839627—22no—
11C4×C4⋊Dic61—21no—
12#16839499—22no—
13#16839488C2212yes—
14C61×#544C2211yescharacteristic
15C61×#428—21no—
16C61×#384C2211yescharacteristic
17C61×#343C2211yescharacteristic
18C61×#339—21no—
19C2×C4⋊Dic61—21no—
20C2×C4⋊Dic61—21no—
21C2×C4⋊Dic61—21no—
22C2×C4⋊Dic61D412yes—
23C2×C4×Dic61—22no—
24#14519710—42no—
25#14519701—42no—
26C22⋊#92418—22no—
27#14519684—21no—
28#14519684—22no—
29#14519684—22no—
30#14519684—22no—
31#14519684D412yes—
32C2×M16×C61—21no—
33C4⋊Q8×C61—41no—
34#125×C61—41no—
35C22⋊Q8×C61—22no—
36#117×C61—21no—
37C2×C4⋊C4×C61—22no—
38C2×C4⋊C4×C61D411yescharacteristic
39C2×C4⋊C4×C61C2311yescharacteristic
40C2×C42×C61D411yescharacteristic
41#107×C61—41no—
42#106×C61—41no—
43C2×Q8×C61—22no—
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61C2×D411yescharacteristic
47C22×C4×C61C2×D412yes—
48C22×Dic61—22no—
49C22×Dic61—22no—
50M16×C61—22no—
51M16×C61—41no—
52C2×C8×C61—41no—
53C4⋊C4×C61—21no—
54C4⋊C4×C61—21no—
55C4⋊C4×C61—22no—
56C4⋊C4×C61—41no—
57C4⋊C4×C61—44no—
58C4⋊C4×C61—42no—
59C4⋊C4×C61—41no—
60C22⋊C4×C61—41no—
61C42×C61—21no—
62C42×C61—41no—
63C42×C61Q1612yes—
64C4⋊Dic61—42no—
65C4⋊Dic61—42no—
66C4⋊Dic61—42no—
67C4⋊Dic61—81no—
68C4×Dic61—44no—
69C2×#92418—42no—
70C23×C61#12011yescharacteristic
71Q8×C61—82no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—22no—
78C2×C4×C61—42no—
79C2×C4×C61—42no—
80C2×C4×C61—41no—
81C2×C4×C61—41no—
82C2×C4×C61—41no—
83C2×C4×C61C2×Q1611yescharacteristic
84C2×C4×C61#13711yescharacteristic
85C2×Dic61—42no—
86C2×Dic61—42no—
87C2×Dic61—42no—
88C2×Dic61—42no—
89C2×Dic61—42no—
90C2×Dic61—42no—
91C8×C61—42no—
92#92418—82no—
93#12257—611nomaximal, Sylow
94C22×C61—21no—
95C22×C61—21no—
96C22×C61#45111yescharacteristic
97C22×C61#45611yescharacteristic
98C22×C61B(4,𝔽2)11yescharacteristic
99C4×C61—24no—
100C4×C61—21no—
101C4×C61—21no—
102C4×C61—42no—
103C4×C61—81no—
104C4×C61—81no—
105C4×C61—81no—
106Dic61—82no—
107Dic61—82no—
108#2571—611no—
109#2060D6111yescharacteristic
110#1617—612no—
111#1353—612no—
112#1325—611no—
113C2×C61—21no—
114C2×C61—21no—
115C2×C61#160511yescharacteristic
116C2×C61#219811yescharacteristic
117C2×C61#220411yescharacteristic
118#544C2×D6111yescharacteristic
119#484—1222no—
120#428—21no—
121#400—612no—
122#400—1221no—
123#389—1222no—
124#384C2×D6111yescharacteristic
125#382—1222no—
126C4×C4⋊C4—1221no—
127#343C2×D6111yescharacteristic
128#339—21no—
129#328—1222no—
130#324—612no—
131C61#1225711yescharacteristic, complemented, Sylow
132C2×M16—21no—
133C4⋊Q8—41no—
134#125—41no—
135C22⋊Q8—22no—
136#117—21no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—612no—
139C2×C4⋊C4—1221no—
140C2×C4⋊C4—1221no—
141C2×C4⋊C4—1221no—
142C2×C4⋊C4C22⋊D6111yescharacteristic
143C2×C4⋊C4C22×D6111yescharacteristic
144C2×C42—1222no—
145C2×C42C22⋊D6111yescharacteristic
146#107—41no—
147#107—2442no—
148#106—41no—
149#103—2442no—
150C22⋊C8—1222no—
151#95—612no—
152#95—1221no—
153#95—1222no—
154#95—1222no—
155#95—1222no—
156C2×Q8—22no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—1222no—
160C22×C4—1222no—
161C22×C4D4×D6112yes—
162C22×C4C2×C22⋊D6111yescharacteristic
163M16—22no—
164M16—41no—
165C2×C8—41no—
166C2×C8—2442no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—22no—
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—44no—
173C4⋊C4—42no—
174C4⋊C4—4881no—
175C4⋊C4—2442no—
176C4⋊C4—2442no—
177C4⋊C4—2442no—
178C22⋊C4—41no—
179C42—21no—
180C42—41no—
181C42—2444no—
182C42#1175820212yes—
183C23#1451974511yescharacteristic
184Q8—82no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—2442no—
197C2×C4—2442no—
198C2×C4—2442no—
199C2×C4—2442no—
200C2×C4—2442no—
201C2×C4—2442no—
202C2×C4C2×#1175820211yescharacteristic
203C2×C4#1451980711yescharacteristic
204C8—42no—
205C8—4882no—
206C22—21no—
207C22—21no—
208C22#1683991711yescharacteristic
209C22#1683994411yescharacteristic
210C22#1683994811yescharacteristic
211C4—24no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—81no—
216C4—81no—
217C4—81no—
218C4—4882no—
219C4—4882no—
220C2—21no—
221C2—21no—
222C2#2144479211yescharacteristic
223C2#2144781411yescharacteristic
224C2#2144784411yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2060C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#2060D61
hypocenterC61#12257
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2060

Complements

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

NH ≅ G/Ntype
131. C61#12257semidirect

Maximal subgroups

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

subgroupindex
#214510612
#214448612
#214438452
#214437652
C61×#20602
#1225761