Finite Group Databasebeta

← #29580676

Subgroups — #29580676

Order 15616.

502 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 79 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#21455767C212yesmaximal
2#21453856C211yesmaximal, characteristic
3#21444351C212yesmaximal
4#21443727C211yesmaximal, characteristic
5C61×#1820C211yesmaximal, characteristic
6C2×#14519756C2212yes—
7#16840103—24no—
8#16840097—22no—
9#16840092—22no—
10#16839805—22no—
11#16839770—22no—
12#16839726C2212yes—
13#16839702—22no—
14#16839687—22no—
15#16839683—22no—
16#16839498—24no—
17C2×#117×C61C2211yescharacteristic
18C61×#381C2211yescharacteristic
19C61×#381C2211yescharacteristic
20C61×#342—22no—
21C22×Dic122D412yes—
22C2×#11758194—22no—
23#14519756—22no—
24#14519756—22no—
25#14519756—22no—
26#14519756—22no—
27C2×C4⋊Dic61—22no—
28C2×C4⋊Dic61D412yes—
29C2×#11758196—22no—
30C2×C22⋊Dic61—22no—
31#14519710—24no—
32#14519708—24no—
33#14519700—24no—
34#14519700—24no—
35C22⋊#92418—22no—
36C22⋊#92418D414yes—
37#14519684—24no—
38#14519684—22no—
39C23×C4×C61C2311yescharacteristic
40#117×C61—22no—
41#117×C61—22no—
42C2×C4⋊C4×C61D412yes—
43C2×C22⋊C4×C61—21no—
44C2×C22⋊C4×C61—21no—
45C2×C22⋊C4×C61D412yes—
46C2×C42×C61—21no—
47#95×C61—22no—
48#95×C61—22no—
49C24×C61C2×D411yescharacteristic
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—42no—
53C22×C4×C61—41no—
54C22×C4×C61C2×D412yes—
55C22×C4×C61C2×D411yescharacteristic
56C22×C4×C61C2×D412yes—
57C22×C4×C61#4111yescharacteristic
58C22×Dic61—22no—
59C22×Dic61—22no—
60C2×Dic122—22no—
61C2×Dic122—22no—
62C2×Dic122—44no—
63C4⋊C4×C61—22no—
64C4⋊C4×C61—22no—
65C22⋊C4×C61—41no—
66C22⋊C4×C61—41no—
67C22⋊C4×C61—42no—
68C22⋊C4×C61—42no—
69C42×C61—42no—
70C22⋊Dic61—42no—
71C22⋊Dic61—42no—
72C4⋊Dic61—22no—
73C4⋊Dic61—22no—
74C4⋊Dic61—82no—
75#11758196—42no—
76#11758196—42no—
77#11758194—44no—
78C2×#92418—24no—
79C23×C61—22no—
80C23×C61—42no—
81C23×C61#12011yescharacteristic
82C23×C61#12111yescharacteristic
83C23×C61#12711yescharacteristic
84C2×C4×C61—24no—
85C2×C4×C61—41no—
86C2×C4×C61—42no—
87C2×C4×C61—41no—
88C2×C4×C61—44no—
89C2×C4×C61—42no—
90C2×C4×C61—42no—
91C2×C4×C61—82no—
92C2×C4×C61—81no—
93C2×C4×C61—82no—
94C2×C4×C61#12012yes—
95C2×C4×C61#12112yes—
96C2×Dic61—44no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61—44no—
100Dic122—44no—
101Dic122—82no—
102#92418—44no—
103#9985—611nomaximal, Sylow
104C22×C61—22no—
105C22×C61—22no—
106C22×C61—22no—
107C22×C61—21no—
108C22×C61—21no—
109C22×C61—82no—
110C22×C61#39211yescharacteristic
111C22×C61#45812yes—
112C4×C61—22no—
113C4×C61—22no—
114C4×C61—82no—
115C4×C61—82no—
116C4×C61—161no—
117Dic61—82no—
118Dic61—82no—
119#3095—612no—
120#2817—611no—
121#1820D6111yescharacteristic
122#1511—612no—
123#1306—611no—
124C2×C61—22no—
125C2×C61—41no—
126C2×C61—41no—
127C2×C61#200912yes—
128C2×C61#202211yescharacteristic
129C2×C22⋊Q8—612no—
130C2×#117C2×D6111yescharacteristic
131#485—1224no—
132#484—1222no—
133#483—1222no—
134#428—1222no—
135#419—1222no—
136#407—612no—
137#400—1222no—
138#397—1222no—
139#395—1222no—
140#381C2×D6111yescharacteristic
141#381C2×D6111yescharacteristic
142#342—22no—
143#328—1224no—
144C61#998511yescharacteristic, complemented, Sylow
145C22×Q8—612no—
146C23×C4C22×D6111yescharacteristic
147C2×M16—1222no—
148C22⋊Q8—1222no—
149C22⋊Q8—1222no—
150C22⋊Q8—1222no—
151C22⋊Q8—1222no—
152#117—22no—
153#117—22no—
154C2×C4⋊C4—612no—
155C2×C4⋊C4—1222no—
156C2×C4⋊C4—1222no—
157C2×C4⋊C4D24412yes—
158C2×C22⋊C4—21no—
159C2×C22⋊C4—21no—
160C2×C22⋊C4—1222no—
161C2×C22⋊C4C22⋊D6112yes—
162C2×C42—21no—
163#107—1224no—
164#106—1224no—
165#103—1224no—
166#103—1224no—
167C22⋊C8—614no—
168C22⋊C8—1222no—
169#95—22no—
170#95—22no—
171#95—1224no—
172#95—1222no—
173C24C2×C22⋊D6111yescharacteristic
174C2×Q8—1222no—
175C2×Q8—1222no—
176C2×Q8—2444no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—42no—
180C22×C4—41no—
181C22×C4—1222no—
182C22×C4—1222no—
183C22×C4C2×D24411yescharacteristic
184C22×C4#1175822211yescharacteristic
185C22×C4D4×D6112yes—
186C22×C4D4×D6112yes—
187M16—2444no—
188C2×C8—1224no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—1222no—
192C4⋊C4—1222no—
193C4⋊C4—4882no—
194C4⋊C4—2442no—
195C4⋊C4—2442no—
196C22⋊C4—41no—
197C22⋊C4—41no—
198C22⋊C4—42no—
199C22⋊C4—42no—
200C22⋊C4—2442no—
201C22⋊C4—2442no—
202C42—42no—
203C23—22no—
204C23—42no—
205C23#1451974511yescharacteristic
206C23#1451975111yescharacteristic
207C23#1451977311yescharacteristic
208Q8—4882no—
209Q8—2444no—
210C2×C4—24no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—44no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—82no—
218C2×C4—81no—
219C2×C4—82no—
220C2×C4—2444no—
221C2×C4—2444no—
222C2×C4—2442no—
223C2×C4—2442no—
224C2×C4#1451974712yes—
225C2×C4#1451975012yes—
226C8—2444no—
227C22—22no—
228C22—21no—
229C22—21no—
230C22—22no—
231C22—22no—
232C22—82no—
233C22#1683967111yescharacteristic
234C22#1683995112yes—
235C4—22no—
236C4—22no—
237C4—82no—
238C4—82no—
239C4—161no—
240C4—4882no—
241C4—4882no—
242C2—22no—
243C2—41no—
244C2—41no—
245C2#2144687812yes—
246C2#2144695011yescharacteristic
subgroupG/H
centerC22#16839671
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1820C2
socleC22×C61#392
prime radicalC24×C61C2×D4
hypercenter#1820D61
hypocenterC61#9985
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
144. C61#9985semidirect

Maximal subgroups

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

subgroupindex
#214557672
#214538562
#214443512
#214437272
C61×#18202
#998561