Finite Group Databasebeta

← #29569267

Subgroups — #29569267

Order 15616.

422 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 87 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#21447347C211yesmaximal, characteristic
2#21447227C212yesmaximal, complemented
3#21443645C212yesmaximal, complemented
4#21443640C211yesmaximal, characteristic
5C61×#2804C211yesmaximal, characteristic
6C2×#14519710—21no—
7C2×#14519701—22no—
8C2×#14519698—21no—
9#16839632C2211yescharacteristic
10#16839524—22no—
11#16839517C2212yes—
12#16839517C2211yescharacteristic
13C61×#400—21no—
14C61×#393—22no—
15C61×#391C2212yes—
16C61×#390C2211yescharacteristic
17C61×#386—21no—
18C61×#385—22no—
19C22×#92418—21no—
20C22×#92418—22no—
21C2×C4⋊Dic61—21no—
22C2×C4⋊Dic61—22no—
23#14519710—42no—
24#14519701—44no—
25#14519698—42no—
26C22×Q8×C61D412yes—
27C22×D4×C61D411yescharacteristic
28C23×C4×C61—21no—
29C2×C4⋊C4×C61—21no—
30C2×C4⋊C4×C61D412yes—
31C2×C4⋊C4×C61D411yescharacteristic
32C2×C22⋊C4×C61—22no—
33C2×C22⋊C4×C61—22no—
34C2×C22⋊C4×C61—21no—
35C2×C42×C61C2311yescharacteristic
36#95×C61—22no—
37#95×C61—21no—
38#95×C61—22no—
39#95×C61—22no—
40C24×C61—21no—
41C2×Q8×C61—22no—
42C2×Q8×C61—22no—
43C2×Q8×C61—42no—
44C2×Q8×C61—42no—
45C2×D4×C61—21no—
46C2×D4×C61—41no—
47C2×D4×C61—41no—
48C2×D4×C61Q1612yes—
49C22×C4×C61—22no—
50C22×C4×C61—21no—
51C22×C4×C61—22no—
52C22×C4×C61—81no—
53C22×C4×C61—82no—
54C22×C4×C61C2×D411yescharacteristic
55C22×C4×C61C2×D412yes—
56C22×Dic61—41no—
57C4⋊C4×C61—42no—
58C4⋊C4×C61—41no—
59C4⋊C4×C61—81no—
60C22⋊C4×C61—42no—
61C22⋊C4×C61—42no—
62C22⋊C4×C61—82no—
63C22⋊C4×C61—81no—
64C42×C61—41no—
65C4⋊Dic61—41no—
66C4⋊Dic61—41no—
67C4⋊Dic61—42no—
68C4⋊Dic61—42no—
69C2×#92418—22no—
70C2×#92418—41no—
71C2×#92418—41no—
72C2×#92418—42no—
73C2×#92418—42no—
74C2×#92418—42no—
75C23×C61—22no—
76C23×C61—42no—
77C23×C61—41no—
78C23×C61—42no—
79C23×C61—41no—
80C23×C61#12011yescharacteristic
81Q8×C61—44no—
82Q8×C61—82no—
83D4×C61—42no—
84D4×C61—81no—
85C2×C4×C61—21no—
86C2×C4×C61—22no—
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61—42no—
90C2×C4×C61—42no—
91C2×C4×C61—41no—
92C2×C4×C61—42no—
93C2×C4×C61—42no—
94C2×C4×C61—42no—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61—84no—
98C2×C4×C61C2×Q1611yescharacteristic
99C2×C4×C61#13512yes—
100C2×C4×C61AGL(1,ℤ/8)12yes—
101C2×C4×C61#13711yescharacteristic
102C2×Dic61—82no—
103C2×Dic61—81no—
104#92418—42no—
105#92418—82no—
106#7821—611nomaximal, Sylow
107C22×C61—42no—
108C22×C61—44no—
109C22×C61—82no—
110C22×C61—81no—
111C22×C61—81no—
112C22×C61#44912yes—
113C22×C61#45111yescharacteristic
114C22×C61#45311yescharacteristic
115C22×C61#45512yes—
116C22×C61#45811yescharacteristic
117C4×C61—22no—
118C4×C61—22no—
119C4×C61—21no—
120C4×C61—21no—
121C4×C61—82no—
122C4×C61—81no—
123C4×C61—82no—
124Dic61—161no—
125#2804D6111yescharacteristic
126#2093—611no—
127#2072—612no—
128#1272—612no—
129#1270—611no—
130C2×C61—82no—
131C2×C61#161212yes—
132C2×C61#161411yescharacteristic
133C2×C61#162011yescharacteristic
134C2×C61#164412yes—
135C2×C61#165911yescharacteristic
136C2×#107—1221no—
137C2×#103—1222no—
138C2×#102—1221no—
139#400—21no—
140#393—22no—
141#391C2×D6112yes—
142#390C2×D6111yescharacteristic
143#386—21no—
144#385—22no—
145#384—611no—
146#340—1222no—
147#336—612no—
148#336—611no—
149C61#782111yescharacteristic, complemented, Sylow
150C22×Q8C22⋊D6112yes—
151C22×D4C22⋊D6111yescharacteristic
152C23×C4—21no—
153C22×C8—1221no—
154C22×C8—1222no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—1222no—
157C2×C4⋊C4—1221no—
158C2×C4⋊C4C22⋊D6112yes—
159C2×C4⋊C4C22⋊D6111yescharacteristic
160C2×C22⋊C4—22no—
161C2×C22⋊C4—22no—
162C2×C22⋊C4—21no—
163C2×C42C22×D6111yescharacteristic
164#107—2442no—
165#103—2444no—
166#102—2442no—
167#95—22no—
168#95—21no—
169#95—22no—
170#95—22no—
171C24—21no—
172C2×Q8—22no—
173C2×Q8—22no—
174C2×Q8—42no—
175C2×Q8—42no—
176C2×D4—21no—
177C2×D4—41no—
178C2×D4—41no—
179C2×D4#1175820212yes—
180C22×C4—22no—
181C22×C4—21no—
182C22×C4—22no—
183C22×C4—82no—
184C22×C4—81no—
185C22×C4—2441no—
186C22×C4C2×C22⋊D6111yescharacteristic
187C22×C4C2×C22⋊D6112yes—
188C2×C8—1222no—
189C2×C8—2442no—
190C2×C8—2442no—
191C2×C8—2442no—
192C2×C8—2441no—
193C2×C8—2441no—
194C4⋊C4—41no—
195C4⋊C4—42no—
196C4⋊C4—81no—
197C4⋊C4—2441no—
198C4⋊C4—2441no—
199C4⋊C4—2442no—
200C4⋊C4—2442no—
201C22⋊C4—42no—
202C22⋊C4—42no—
203C22⋊C4—82no—
204C22⋊C4—81no—
205C42—41no—
206C23—22no—
207C23—42no—
208C23—41no—
209C23—42no—
210C23—41no—
211C23#1451974611yescharacteristic
212Q8—44no—
213Q8—82no—
214D4—42no—
215D4—81no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—84no—
229C2×C4—4882no—
230C2×C4—4881no—
231C2×C4C2×#1175820211yescharacteristic
232C2×C4#1451979712yes—
233C2×C4#1451980212yes—
234C2×C4#1451980811yescharacteristic
235C8—4882no—
236C8—2442no—
237C22—44no—
238C22—42no—
239C22—81no—
240C22—81no—
241C22—82no—
242C22#1683990712yes—
243C22#1683991811yescharacteristic
244C22#1683993011yescharacteristic
245C22#1683994012yes—
246C22#1683995211yescharacteristic
247C4—22no—
248C4—22no—
249C4—21no—
250C4—21no—
251C4—82no—
252C4—81no—
253C4—82no—
254C4—9761no—
255C2—82no—
256C2#2144483312yes—
257C2#2144484411yescharacteristic
258C2#2144487811yescharacteristic
259C2#2144503312yes—
260C2#2144512511yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2804C2
socleC23×C61#120
prime radicalC22×D4×C61D4
hypercenter#2804D61
hypocenterC61#7821
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2804

Complements

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

NH ≅ G/Ntype
2. #21447227C2semidirect
3. #21443645C2semidirect
149. C61#7821semidirect

Maximal subgroups

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

subgroupindex
#214473472
#214472272
#214436452
#214436402
C61×#28042
#782161