Finite Group Databasebeta

← #29569269

Subgroups — #29569269

Order 15616.

422 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 83 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#21453765C211yesmaximal, characteristic
2#21447347C211yesmaximal, characteristic
3#21447229C212yesmaximal, complemented
4#21443644C212yesmaximal, complemented
5C61×#1270C211yesmaximal, characteristic
6C2×#14519710—21no—
7C2×#14519702—22no—
8C2×#14519698—21no—
9#16839701—21no—
10#16839674—22no—
11#16839668C2212yes—
12#16839642—21no—
13#16839637—22no—
14#16839632C2211yescharacteristic
15#16839525—22no—
16#16839517C2211yescharacteristic
17C61×#390C2211yescharacteristic
18C61×#336C2212yes—
19C22×Dic122D412yes—
20C23×Dic61—21no—
21C22×#92418—21no—
22C2×C4⋊Dic61—21no—
23C2×C4⋊Dic61—22no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61D412yes—
26C2×C22⋊Dic61—22no—
27C2×C22⋊Dic61—21no—
28#14519710—42no—
29#14519702—44no—
30#14519698—42no—
31#14519684—22no—
32#14519684—21no—
33#14519684—22no—
34#14519684—22no—
35C22×D4×C61D411yescharacteristic
36C22×C8×C61—22no—
37C2×C4⋊C4×C61D411yescharacteristic
38C2×C22⋊C4×C61—22no—
39C2×C42×C61C2311yescharacteristic
40C24×C61—21no—
41C2×D4×C61—21no—
42C2×D4×C61—41no—
43C2×D4×C61—41no—
44C2×D4×C61Q1612yes—
45C22×C4×C61—21no—
46C22×C4×C61C2×D411yescharacteristic
47C22×C4×C61C2×D412yes—
48C22×Dic61—22no—
49C22×Dic61—22no—
50C22×Dic61—41no—
51C22×Dic61—81no—
52C22×Dic61—82no—
53C2×Dic122—22no—
54C2×Dic122—22no—
55C2×Dic122—42no—
56C2×Dic122—42no—
57C2×C8×C61—42no—
58C2×C8×C61—42no—
59C2×C8×C61—42no—
60C4⋊C4×C61—41no—
61C22⋊C4×C61—42no—
62C22⋊C4×C61—42no—
63C42×C61—41no—
64C22⋊Dic61—82no—
65C22⋊Dic61—81no—
66C4⋊Dic61—42no—
67C4⋊Dic61—41no—
68C4⋊Dic61—41no—
69C4⋊Dic61—42no—
70C4⋊Dic61—42no—
71C4⋊Dic61—81no—
72C2×#92418—22no—
73C2×#92418—41no—
74C2×#92418—41no—
75C23×C61—22no—
76C23×C61—42no—
77C23×C61—41no—
78C23×C61—42no—
79C23×C61—41no—
80C23×C61#12011yescharacteristic
81D4×C61—42no—
82D4×C61—81no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61—21no—
86C2×C4×C61—22no—
87C2×C4×C61—42no—
88C2×C4×C61—41no—
89C2×C4×C61C2×Q1611yescharacteristic
90C2×C4×C61#13512yes—
91C2×C4×C61AGL(1,ℤ/8)12yes—
92C2×C4×C61#13711yescharacteristic
93C2×Dic61—42no—
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61—84no—
100C2×Dic61—82no—
101C2×Dic61—81no—
102Dic122—44no—
103Dic122—82no—
104C8×C61—82no—
105#92418—42no—
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—81no—
122Dic61—82no—
123Dic61—82no—
124Dic61—161no—
125#2804—611no—
126#2093—611no—
127#2072—612no—
128#1272—612no—
129#1270D6111yescharacteristic
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—1221no—
140#393—1222no—
141#391—612no—
142#390C2×D6111yescharacteristic
143#386—1221no—
144#385—1222no—
145#384—611no—
146#340—1222no—
147#336—611no—
148#336C2×D6112yes—
149C61#782111yescharacteristic, complemented, Sylow
150C22×Q8—612no—
151C22×D4D24411yescharacteristic
152C23×C4—1221no—
153C22×C8—22no—
154C22×C8—1221no—
155C2×C4⋊C4—612no—
156C2×C4⋊C4—1221no—
157C2×C4⋊C4—1221no—
158C2×C4⋊C4—1222no—
159C2×C4⋊C4D24411yescharacteristic
160C2×C22⋊C4—22no—
161C2×C22⋊C4—1222no—
162C2×C22⋊C4—1221no—
163C2×C42C22×D6111yescharacteristic
164#107—2442no—
165#103—2444no—
166#102—2442no—
167#95—1222no—
168#95—1221no—
169#95—1222no—
170#95—1222no—
171C24—21no—
172C2×Q8—1222no—
173C2×Q8—1222no—
174C2×Q8—2442no—
175C2×Q8—2442no—
176C2×D4—21no—
177C2×D4—41no—
178C2×D4—41no—
179C2×D4Dic24412yes—
180C22×C4—21no—
181C22×C4—1222no—
182C22×C4—1222no—
183C22×C4—4882no—
184C22×C4—4881no—
185C22×C4—2441no—
186C22×C4C2×D24411yescharacteristic
187C22×C4D4×D6112yes—
188C2×C8—42no—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—1222no—
192C2×C8—2441no—
193C2×C8—2441no—
194C4⋊C4—41no—
195C4⋊C4—4881no—
196C4⋊C4—2441no—
197C4⋊C4—2441no—
198C4⋊C4—2442no—
199C4⋊C4—2442no—
200C4⋊C4—2442no—
201C22⋊C4—42no—
202C22⋊C4—42no—
203C22⋊C4—4882no—
204C22⋊C4—4881no—
205C42—41no—
206C23—22no—
207C23—42no—
208C23—41no—
209C23—42no—
210C23—41no—
211C23#1451974711yescharacteristic
212Q8—4882no—
213Q8—2444no—
214D4—42no—
215D4—81no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4—4882no—
223C2×C4—4881no—
224C2×C4—4884no—
225C2×C4—2442no—
226C2×C4—2442no—
227C2×C4—2442no—
228C2×C4—2442no—
229C2×C4—2442no—
230C2×C4—2442no—
231C2×C4C2×Dic24411yescharacteristic
232C2×C4#1451979812yes—
233C2×C4#1451980112yes—
234C2×C4#1451981011yescharacteristic
235C8—82no—
236C8—2442no—
237C22—44no—
238C22—42no—
239C22—81no—
240C22—81no—
241C22—82no—
242C22#1683990812yes—
243C22#1683992011yescharacteristic
244C22#1683993211yescharacteristic
245C22#1683994112yes—
246C22#1683995311yescharacteristic
247C4—22no—
248C4—22no—
249C4—21no—
250C4—21no—
251C4—81no—
252C4—9761no—
253C4—4882no—
254C4—4882no—
255C2—82no—
256C2#2144483412yes—
257C2#2144484611yescharacteristic
258C2#2144487911yescharacteristic
259C2#2144503612yes—
260C2#2144512611yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1270C2
socleC23×C61#120
prime radicalC22×D4×C61D4
hypercenter#1270D61
hypocenterC61#7821
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
3. #21447229C2semidirect
4. #21443644C2semidirect
149. C61#7821semidirect

Maximal subgroups

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

subgroupindex
#214537652
#214473472
#214472292
#214436442
C61×#12702
#782161