Finite Group Databasebeta

← #29573475

Subgroups — #29573475

Order 15616.

514 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 155 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
1C2×#16839488C212yesmaximal
2#21443667C214yesmaximal
3C61×#2274C211yesmaximal, characteristic
4C2×C22⋊#92418C2214yes—
5#16839488—22no—
6#16839488—22no—
7C2×#117×C61C411yescharacteristic
8C2×#117×C61C411yescharacteristic
9C22×C4⋊C4×C61C2211yescharacteristic
10C4×C4⋊C4×C61—22no—
11C4×C4⋊C4×C61—22no—
12C4×C22⋊C4×C61C412yes—
13C4×C22⋊C4×C61C2212yes—
14C22×#92418—24no—
15C22⋊#92418—24no—
16C22⋊#92418—24no—
17C23×C4×C61C2×C411yescharacteristic
18C23×C4×C61C2×C411yescharacteristic
19C23×C4×C61C2311yescharacteristic
20#117×C61—22no—
21#117×C61—24no—
22#117×C61C814yescomplemented
23C2×C4⋊C4×C61—21no—
24C2×C4⋊C4×C61—21no—
25C2×C4⋊C4×C61—24no—
26C2×C4⋊C4×C61D412yes—
27C2×C4⋊C4×C61D412yes—
28C2×C22⋊C4×C61C2×C412yes—
29C2×C22⋊C4×C61C2×C412yes—
30C2×C42×C61—21no—
31C2×C42×C61—21no—
32C2×C42×C61—22no—
33C2×C42×C61—22no—
34#95×C61—22no—
35#95×C61—22no—
36C24×C61C22×C411yescharacteristic
37C22×C4×C61—22no—
38C22×C4×C61—22no—
39C22×C4×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61—22no—
42C22×C4×C61—81no—
43C22×C4×C61—81no—
44C22×C4×C61C22⋊C411yescharacteristic
45C22×C4×C61C22⋊C411yescharacteristic
46C22×C4×C61C22⋊C412yes—
47C22×C4×C61C2×C812yes—
48C22×C4×C61M1612yes—
49C22×C4×C61C2×D412yes—
50C22×C4×C61#4114yes—
51C4⋊C4×C61—24no—
52C4⋊C4×C61—24no—
53C4⋊C4×C61—24no—
54C4⋊C4×C61—24no—
55C22⋊C4×C61—22no—
56C22⋊C4×C61—22no—
57C22⋊C4×C61C2×C814yes—
58C22⋊C4×C61M1614yes—
59C42×C61—24no—
60C42×C61—24no—
61C42×C61—82no—
62C42×C61—82no—
63C2×#92418—44no—
64C2×#92418—84no—
65C23×C61—41no—
66C23×C61—41no—
67C23×C61C2×C22⋊C411yescharacteristic
68C23×C61#11712yes—
69C23×C61C22×C811yescharacteristic
70C23×C61C2×M1611yescharacteristic
71C23×C61C2×M1612yes—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—24no—
77C2×C4×C61—24no—
78C2×C4×C61—22no—
79C2×C4×C61—24no—
80C2×C4×C61—24no—
81C2×C4×C61—44no—
82C2×C4×C61—42no—
83C2×C4×C61—42no—
84C2×C4×C61—42no—
85C2×C4×C61—42no—
86C2×C4×C61—42no—
87C2×C4×C61—42no—
88C2×C4×C61—82no—
89C2×C4×C61C22⋊C812yes—
90C2×C4×C61C22⋊C812yes—
91C2×C4×C61#12314yes—
92#92418—84no—
93#8735—611nomaximal, Sylow
94C22×C61—21no—
95C22×C61—22no—
96C22×C61—21no—
97C22×C61—22no—
98C22×C61—41no—
99C22×C61—41no—
100C22×C61—42no—
101C22×C61#38111yescharacteristic
102C22×C61C2×C22⋊C811yescharacteristic
103C22×C61#40711yescharacteristic
104C22×C61#43112yes—
105C22×C61#43212yes—
106C4×C61—22no—
107C4×C61—22no—
108C4×C61—24no—
109C4×C61—44no—
110C4×C61—44no—
111C4×C61—42no—
112#2274D6111yescharacteristic
113C2×#324—612no—
114#1282—614no—
115C2×C61—21no—
116C2×C61—21no—
117C2×C61—22no—
118C2×C61—22no—
119C2×C61#181711yescharacteristic
120C2×C61#182811yescharacteristic
121C2×C61#183011yescharacteristic
122C2×#117Dic6111yescharacteristic
123C2×#117Dic6111yescharacteristic
124C22×C4⋊C4C2×D6111yescharacteristic
125C2×C22⋊C8—614no—
126C4×C4⋊C4—22no—
127C4×C4⋊C4—22no—
128C4×C22⋊C4Dic6112yes—
129C4×C22⋊C4C2×D6112yes—
130#324—1222no—
131#324—1222no—
132C61#873511yescharacteristic, complemented, Sylow
133C23×C4C2×Dic6111yescharacteristic
134C23×C4C2×Dic6111yescharacteristic
135C23×C4C22×D6111yescharacteristic
136C22×C8—1224no—
137#117—22no—
138#117—24no—
139#117#9241814yescomplemented
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—24no—
143C2×C4⋊C4C22⋊D6112yes—
144C2×C4⋊C4C22⋊D6112yes—
145C2×C22⋊C4C2×Dic6112yes—
146C2×C22⋊C4C2×Dic6112yes—
147C2×C42—21no—
148C2×C42—21no—
149C2×C42—22no—
150C2×C42—22no—
151C22⋊C8—1224no—
152C22⋊C8—1224no—
153#95—22no—
154#95—22no—
155C24C22×Dic6111yescharacteristic
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—81no—
162C22×C4—81no—
163C22×C4C2×#9241812yes—
164C22×C4#1175819412yes—
165C22×C4C22⋊Dic6111yescharacteristic
166C22×C4C22⋊Dic6111yescharacteristic
167C22×C4C22⋊Dic6112yes—
168C22×C4#1175822214yes—
169C22×C4C2×C22⋊D6112yes—
170C2×C8—4884no—
171C2×C8—2444no—
172C4⋊C4—24no—
173C4⋊C4—24no—
174C4⋊C4—24no—
175C4⋊C4—24no—
176C22⋊C4—22no—
177C22⋊C4—22no—
178C22⋊C4C2×#9241814yes—
179C22⋊C4#1175819414yes—
180C42—24no—
181C42—24no—
182C42—82no—
183C42—82no—
184C23—41no—
185C23—41no—
186C23C2×C22⋊Dic6111yescharacteristic
187C23#1451973612yes—
188C23C22×#9241811yescharacteristic
189C23C2×#1175819411yescharacteristic
190C23C2×#1175819412yes—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—24no—
194C2×C4—24no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—24no—
198C2×C4—24no—
199C2×C4—22no—
200C2×C4—42no—
201C2×C4—44no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—82no—
208C2×C4C22⋊#9241812yes—
209C2×C4C22⋊#9241812yes—
210C2×C4#1451976014yes—
211C8—4884no—
212C22—21no—
213C22—22no—
214C22—21no—
215C22—22no—
216C22—41no—
217C22—41no—
218C22—42no—
219C22#1683962511yescharacteristic
220C22C2×C22⋊#9241811yescharacteristic
221C22#1683972611yescharacteristic
222C22#1683981512yes—
223C22#1683981912yes—
224C4—24no—
225C4—22no—
226C4—22no—
227C4—44no—
228C4—44no—
229C4—42no—
230C2—21no—
231C2—21no—
232C2—22no—
233C2—22no—
234C2#2144588711yescharacteristic
235C2#2144592711yescharacteristic
236C2#2144593311yescharacteristic
subgroupG/H
centerC22#16839625
commutatorC23×C61C22×C8
FrattiniC23×C4C22×D61
FittingC61×#2274C2
socleC22×C61#381
prime radicalC24×C61C22×C4
cosocleC23×C4×C61C23
hypercenter#2274D61
hypocenterC61#8735
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2274

Complements

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

NH ≅ G/Ntype
22. #117×C61C8semidirect
132. C61#8735semidirect
139. #117#92418semidirect

Maximal subgroups

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

subgroupindex
C2×#168394882
#214436672
C61×#22742
#873561