Finite Group Databasebeta

← #29583087

Subgroups — #29583087

Order 15616.

400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 89 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#21454091C211yesmaximal, characteristic
2#21446792C212yesmaximal
3#21446638C211yesmaximal, characteristic
4#21443701C212yesmaximal
5C61×#1295C211yesmaximal, characteristic
6C2×#14519777C2211yescharacteristic
7C2×#14519700—21no—
8C2×#14519700—21no—
9C2×#14519688C2211yescharacteristic
10#16839704—22no—
11#16839701—21no—
12#16839683—22no—
13#16839682—21no—
14#16839628C2212yes—
15#16839525—22no—
16#16839525—22no—
17C2×#97×C61C2212yes—
18C61×#382C2211yescharacteristic
19C22×Dic122—21no—
20C22×Dic122—21no—
21C22×#92418—21no—
22#14519777—22no—
23#14519777—21no—
24#14519777Q812yescomplemented
25C2×C4⋊Dic61—22no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61D412yes—
28C2×C4⋊Dic61D412yes—
29C2×#11758196—22no—
30#14519700—42no—
31#14519700—42no—
32#14519688—22no—
33#14519684—21no—
34#14519684—22no—
35#14519684—21no—
36#14519684—22no—
37#14519684—22no—
38C22×C8×C61—22no—
39C2×C4⋊C4×C61D411yescharacteristic
40C2×C4⋊C4×C61D411yescharacteristic
41C2×C42×C61C2311yescharacteristic
42#97×C61—22no—
43#97×C61—22no—
44#95×C61—22no—
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61C2×D411yescharacteristic
48C22×C4×C61C2×D412yes—
49C22×Dic61—22no—
50C22×Dic61—22no—
51C22×Dic61—41no—
52C2×Dic122—22no—
53C2×Dic122—41no—
54C2×Dic122—41no—
55C2×Dic122—41no—
56C2×Dic122—41no—
57C2×Dic122—41no—
58C2×Dic122—81no—
59C2×Dic122—82no—
60C2×C8×C61—24no—
61C2×C8×C61—42no—
62C2×C8×C61—42no—
63C4⋊C4×C61—41no—
64C4⋊C4×C61—41no—
65C42×C61C2×Q811yescharacteristic
66C42×C61#4112yes—
67C42×C61#4111yescharacteristic
68C4⋊Dic61—24no—
69C4⋊Dic61—42no—
70C4⋊Dic61—42no—
71C4⋊Dic61—42no—
72C4⋊Dic61—81no—
73#11758196—82no—
74C2×#92418—22no—
75C2×#92418—41no—
76C2×#92418—41no—
77C23×C61#12011yescharacteristic
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—41no—
83C2×C4×C61—41no—
84C2×C4×C61—42no—
85C2×C4×C61—42no—
86C2×C4×C61C22⋊Q812yes—
87C2×C4×C61C22⋊Q811yescharacteristic
88C2×C4×C61#12412yes—
89C2×C4×C61#12411yescharacteristic
90C2×Dic61—42no—
91C2×Dic61—42no—
92C2×Dic61—42no—
93C2×Dic61—42no—
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97C2×Dic61—81no—
98C2×Dic61—81no—
99Dic122—42no—
100Dic122—42no—
101Dic122—81no—
102Dic122—81no—
103Dic122—84no—
104C8×C61—44no—
105#92418—42no—
106#10359—611nomaximal, Sylow
107C22×C61#39311yescharacteristic
108C22×C61#45311yescharacteristic
109C22×C61#45411yescharacteristic
110C22×C61#45512yes—
111C22×C61#45612yes—
112C4×C61—21no—
113C4×C61—21no—
114C4×C61—22no—
115C4×C61—22no—
116C4×C61—81no—
117C4×C61—81no—
118Dic61—82no—
119Dic61—82no—
120Dic61—82no—
121#2844—611no—
122#1993—612no—
123#1960—611no—
124#1295—612no—
125#1295D6111yescharacteristic
126C2×C61#165911yescharacteristic
127C2×C61#166011yescharacteristic
128C2×C61#166412yes—
129C2×C61#202711yescharacteristic
130C2×C61#202812yes—
131C2×C4⋊Q8—611no—
132C2×#103—1221no—
133C2×#103—1221no—
134C2×#97—611no—
135C2×#97C2×D6112yes—
136#400—1222no—
137#400—1221no—
138#395—1222no—
139#395—1221no—
140#382—612no—
141#382C2×D6111yescharacteristic
142#340—1222no—
143#340—1222no—
144C61#1035911yescharacteristic, complemented, Sylow
145C22×Q8—1221no—
146C22×Q8—1221no—
147C22×C8—22no—
148C22×C8—1221no—
149C4⋊Q8—612no—
150C4⋊Q8—1222no—
151C4⋊Q8—1221no—
152C2×C4⋊C4—612no—
153C2×C4⋊C4—612no—
154C2×C4⋊C4—1222no—
155C2×C4⋊C4—1222no—
156C2×C4⋊C4—1221no—
157C2×C4⋊C4D24411yescharacteristic
158C2×C4⋊C4D24411yescharacteristic
159C2×C42C22×D6111yescharacteristic
160#103—2442no—
161#103—2442no—
162#97—22no—
163#97—22no—
164#97—1222no—
165#95—22no—
166#95—1222no—
167#95—1221no—
168#95—1221no—
169#95—1222no—
170#95—1222no—
171C2×Q8—1222no—
172C2×Q8—4882no—
173C2×Q8—4881no—
174C2×Q8—2441no—
175C2×Q8—2441no—
176C2×Q8—2441no—
177C2×Q8—2441no—
178C2×Q8—2441no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—1222no—
182C22×C4—1222no—
183C22×C4—2441no—
184C22×C4C2×D24411yescharacteristic
185C22×C4D4×D6112yes—
186C2×C8—24no—
187C2×C8—42no—
188C2×C8—42no—
189C2×C8—1222no—
190C2×C8—2441no—
191C2×C8—2441no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—1224no—
195C4⋊C4—4882no—
196C4⋊C4—4881no—
197C4⋊C4—2442no—
198C4⋊C4—2442no—
199C4⋊C4—2442no—
200C42#1175822212yes—
201C42#1175822411yescharacteristic
202C42Q8×D6111yescharacteristic
203C23#1451974711yescharacteristic
204Q8—4881no—
205Q8—4881no—
206Q8—4884no—
207Q8—2442no—
208Q8—2442no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—4881no—
218C2×C4—4881no—
219C2×C4—2442no—
220C2×C4—2442no—
221C2×C4—2442no—
222C2×C4—2442no—
223C2×C4—2442no—
224C2×C4—2442no—
225C2×C4—2442no—
226C2×C4#1451975512yes—
227C2×C4#1451975711yescharacteristic
228C2×C4#1451976312yes—
229C2×C4#1451976511yescharacteristic
230C8—44no—
231C8—2442no—
232C22#1683967511yescharacteristic
233C22#1683993211yescharacteristic
234C22#1683993711yescharacteristic
235C22#1683994112yes—
236C22#1683994612yes—
237C4—21no—
238C4—21no—
239C4—22no—
240C4—22no—
241C4—81no—
242C4—81no—
243C4—4882no—
244C4—4882no—
245C4—4882no—
246C2#2144512611yescharacteristic
247C2#2144513111yescharacteristic
248C2#2144515412yes—
249C2#2144697611yescharacteristic
250C2#2144697912yes—
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socle, prime radicalC23×C61#120
hypercenter#1295D61
hypocenterC61#10359
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
24. #14519777Q8semidirect
144. C61#10359semidirect

Maximal subgroups

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

subgroupindex
#214540912
#214467922
#214466382
#214437012
C61×#12952
#1035961