Finite Group Databasebeta

← #29593075

Subgroups — #29593075

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#21447164C211yesmaximal, characteristic
3#21444863C212yesmaximal
4#21443847C212yesmaximal
5C61×#1325C211yesmaximal, characteristic
6#16840393C2211yescharacteristic
7#16840098—22no—
8#16839802—21no—
9#16839701—21no—
10#16839701C2212yes—
11#16839661—22no—
12#16839627—22no—
13C4×C4⋊Dic61—21no—
14#16839531C2211yescharacteristic
15#16839522—21no—
16#16839500—22no—
17C61×#384C2211yescharacteristic
18C61×#324C2212yes—
19C2×#11758194—21no—
20#14519776—41no—
21#14519768—41no—
22#14519756—22no—
23#14519736—21no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61D412yes—
28C2×C4×Dic61—22no—
29#14519711—42no—
30#14519710—41no—
31#14519708—41no—
32#14519702—42no—
33#14519684—21no—
34#14519684—22no—
35#14519684—22no—
36#14519684—22no—
37#14519684D412yes—
38C2×C4⋊C4×C61—22no—
39C2×C4⋊C4×C61D411yescharacteristic
40C2×C4⋊C4×C61C2311yescharacteristic
41C2×C42×C61D411yescharacteristic
42C22⋊C8×C61—22no—
43C22×C4×C61—21no—
44C22×C4×C61—21no—
45C22×C4×C61C2×D411yescharacteristic
46C22×C4×C61C2×D412yes—
47C22×Dic61—22no—
48C22×Dic61—22no—
49C2×Dic122—22no—
50C2×C8×C61—42no—
51C4⋊C4×C61—41no—
52C4⋊C4×C61—44no—
53C4⋊C4×C61—41no—
54C42×C61—21no—
55C42×C61Q1612yes—
56C22⋊Dic61—41no—
57C4⋊Dic61—21no—
58C4⋊Dic61—21no—
59C4⋊Dic61—22no—
60C4⋊Dic61—42no—
61C4⋊Dic61—42no—
62C4⋊Dic61—42no—
63C4⋊Dic61—81no—
64#11758196—42no—
65C4×Dic61—44no—
66C4×Dic61—41no—
67#11758194—22no—
68#11758194—41no—
69C2×#92418—41no—
70C23×C61#12011yescharacteristic
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—22no—
77C2×C4×C61—42no—
78C2×C4×C61—42no—
79C2×C4×C61—41no—
80C2×C4×C61C2×Q1611yescharacteristic
81C2×C4×C61#13711yescharacteristic
82C2×Dic61—42no—
83C2×Dic61—42no—
84C2×Dic61—42no—
85C2×Dic61—42no—
86C2×Dic61—42no—
87C2×Dic61—41no—
88C2×Dic61—41no—
89C2×Dic61—42no—
90Dic122—82no—
91C8×C61—82no—
92#92418—42no—
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—
104Dic61—82no—
105Dic61—81no—
106Dic61—81no—
107Dic61—82no—
108#2571—611no—
109#2060—611no—
110#1617—612no—
111#1353—612no—
112#1325D6111yescharacteristic
113C2×C61—21no—
114C2×C61—21no—
115C2×C61#160511yescharacteristic
116C2×C61#219811yescharacteristic
117C2×C61#220411yescharacteristic
118#544—611no—
119#484—1222no—
120#428—1221no—
121#400—612no—
122#400—1221no—
123#389—1222no—
124#384C2×D6111yescharacteristic
125#382—1222no—
126C4×C4⋊C4—1221no—
127#343—611no—
128#339—1221no—
129#328—1222no—
130#324C2×D6112yes—
131C61#1225711yescharacteristic, complemented, Sylow
132C2×M16—1221no—
133C4⋊Q8—2441no—
134#125—2441no—
135C22⋊Q8—1222no—
136#117—1221no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—612no—
139C2×C4⋊C4—1221no—
140C2×C4⋊C4—1221no—
141C2×C4⋊C4—1221no—
142C2×C4⋊C4D24411yescharacteristic
143C2×C4⋊C4C22×D6111yescharacteristic
144C2×C42—1222no—
145C2×C42D24411yescharacteristic
146#107—2441no—
147#107—2442no—
148#106—2441no—
149#103—2442no—
150C22⋊C8—22no—
151#95—612no—
152#95—1221no—
153#95—1222no—
154#95—1222no—
155#95—1222no—
156C2×Q8—1222no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—1222no—
160C22×C4—1222no—
161C22×C4C2×D24411yescharacteristic
162C22×C4D4×D6112yes—
163M16—1222no—
164M16—2441no—
165C2×C8—42no—
166C2×C8—2441no—
167C4⋊C4—41no—
168C4⋊C4—41no—
169C4⋊C4—44no—
170C4⋊C4—1221no—
171C4⋊C4—1221no—
172C4⋊C4—1222no—
173C4⋊C4—4881no—
174C4⋊C4—2442no—
175C4⋊C4—2442no—
176C4⋊C4—2442no—
177C4⋊C4—2442no—
178C22⋊C4—2441no—
179C42—21no—
180C42—2444no—
181C42—2441no—
182C42Dic24412yes—
183C23#1451974711yescharacteristic
184Q8—4882no—
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—2442no—
195C2×C4—2442no—
196C2×C4—2442no—
197C2×C4—2442no—
198C2×C4—2442no—
199C2×C4—2441no—
200C2×C4—2441no—
201C2×C4—2442no—
202C2×C4C2×Dic24411yescharacteristic
203C2×C4#1451981011yescharacteristic
204C8—82no—
205C8—2442no—
206C22—21no—
207C22—21no—
208C22#1683992011yescharacteristic
209C22#1683994711yescharacteristic
210C22#1683995011yescharacteristic
211C4—24no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—81no—
216C4—4882no—
217C4—4881no—
218C4—4881no—
219C4—4882no—
220C2—21no—
221C2—21no—
222C2#2144479511yescharacteristic
223C2#2144781711yescharacteristic
224C2#2144784711yescharacteristic
subgroupG/H
centerC22#16839950
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1325C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#1325D61
hypocenterC61#12257
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

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
#214471642
#214448632
#214438472
C61×#13252
#1225761