Finite Group Databasebeta

← #29593693

Subgroups — #29593693

Order 15616.

298 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 67 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#21458712C211yesmaximal, characteristic, complemented
2#21447856C211yesmaximal, characteristic
3#21445176C211yesmaximal, characteristic
4#21443874C211yesmaximal, characteristic, complemented
5#21443799C211yesmaximal, characteristic, complemented
6#21443784C211yesmaximal, characteristic, complemented
7C61×#2240C211yesmaximal, characteristic
8#16840487—21no—
9C2×#14519721—21no—
10#16840163—21no—
11#16840068—22no—
12#16840044—21no—
13#16839959—21no—
14C8×Dic122C2211yescharacteristic
15C4×Dic244C2211yescharacteristic
16#16839856—21no—
17C4⋊#11758185C2211yescharacteristic
18#16839563—21no—
19#16839515C2211yescharacteristic
20#16839506—21no—
21C61×#500C2211yescharacteristic
22C61×#493C2211yescharacteristic
23C61×#357—22no—
24C4×C16×C61C2211yescharacteristic
25C2×Dic244D411yescharacteristic
26C2×#11758200—41no—
27#14519775—41no—
28#14519768—22no—
29#14519767—42no—
30Q8×Dic61—41no—
31C4×Dic122—21no—
32C4×Dic122D411yescharacteristic
33#14519742—22no—
34#14519721—42no—
35C2×#11758185—21no—
36#14519711D411yescharacteristic
37#14519708—22no—
38C4⋊#92418—21no—
39C4⋊#92418D411yescharacteristic
40#14519706—21no—
41#14519702—21no—
42#14519700—22no—
43#14519698—41no—
44C8×Dic61—21no—
45C2×D8×C61—21no—
46C2×D8×C61—21no—
47C4⋊Q8×C61—21no—
48#127×C61—21no—
49C2×C16×C61—21no—
50#107×C61—21no—
51#107×C61D412yes—
52C4×C8×C61C2311yescharacteristic
53C2×Q8×C61—41no—
54C2×D4×C61—41no—
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C2×Dic122—21no—
58C2×Dic122D811yescharacteristic
59D8×C61—42no—
60D8×C61—41no—
61D8×C61—41no—
62C2×C8×C61C2×D411yescharacteristic
63C2×C8×C61C2×D411yescharacteristic
64C4⋊C4×C61—22no—
65C4⋊C4×C61—41no—
66C42×C61C2×D411yescharacteristic
67#11758200—82no—
68C4⋊Dic61—21no—
69C4⋊Dic61—42no—
70C4⋊Dic61D811yescharacteristic
71#11758196—21no—
72#11758196—42no—
73#11758196—42no—
74#11758196—41no—
75C4×Dic61—21no—
76C4×Dic61—42no—
77C4×Dic61—41no—
78C2×#92418—21no—
79C2×#92418—41no—
80Dic244—21no—
81Dic244SD1612yescomplemented
82C16×C61—41no—
83#11758185—41no—
84C23×C61—81no—
85Q8×C61—81no—
86Q8×C61—81no—
87D4×C61—81no—
88D4×C61—81no—
89D4×C61—81no—
90D4×C61—81no—
91D4×C61—161no—
92C2×C4×C61—42no—
93C2×C4×C61#12011yescharacteristic
94C2×C4×C61C2×D811yescharacteristic
95C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—41no—
99C2×Dic61—41no—
100Dic122—22no—
101Dic122—21no—
102Dic122—21no—
103Dic122—41no—
104C8×C61—21no—
105C8×C61C2×SD1611yescharacteristic
106C8×C61#13711yescharacteristic
107#92418—41no—
108#92418—81no—
109#12353—611nomaximal, Sylow
110C22×C61—161no—
111C22×C61—161no—
112C22×C61—161no—
113C22×C61#44711yescharacteristic
114C4×C61—21no—
115C4×C61—82no—
116C4×C61#44811yescharacteristic
117C4×C61#45411yescharacteristic
118C4×C61#50811yescharacteristic
119C4×C61#50911yescharacteristic
120Dic61—42no—
121Dic61—41no—
122Dic61—41no—
123Dic61—81no—
124#3383—611no—
125#2240D6111yescharacteristic
126#2207—611no—
127#1668—611no—
128#1364—611no—
129Q8⋊C16—611no—
130#1332—611no—
131C2×C61—321no—
132C2×C61#162711yescharacteristic
133C2×C61#218611yescharacteristic
134C2×C61#219311yescharacteristic
135#557—1221no—
136C2×SD32—1221no—
137#500C2×D6111yescharacteristic
138#499—1221no—
139#493C2×D6111yescharacteristic
140#479—1222no—
141#475—1221no—
142#460—1221no—
143C8×Q8—611no—
144C4×Q16—611no—
145C4×Q16—1221no—
146C4⋊C16—611no—
147#357—22no—
148#357—1221no—
149C4×C16C2×D6111yescharacteristic
150#335—611no—
151#331—1221no—
152C61#1235311yescharacteristic, complemented, Sylow
153C2×Q16—611no—
154C2×SD16—2441no—
155C2×D8—21no—
156C2×D8—21no—
157C4⋊Q8—21no—
158C4⋊Q8—2441no—
159#127—21no—
160#125—1222no—
161#125—2442no—
162C4×Q8—611no—
163C4×Q8—1222no—
164C4×Q8—1221no—
165C4×Q8—2441no—
166SD32—2442no—
167C2×C16—21no—
168C2×C16—1221no—
169#107—21no—
170#107—611no—
171#107C22⋊D6112yes—
172#106—1222no—
173C4⋊C8—611no—
174C4⋊C8—1221no—
175C4⋊C8—1221no—
176#103—1222no—
177#103—1221no—
178#102—2441no—
179C4×C8—1221no—
180C4×C8C22×D6111yescharacteristic
181C2×Q8—41no—
182C2×Q8—611no—
183C2×Q8—1221no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—41no—
187Q16—612no—
188Q16—1221no—
189SD16—4882no—
190D8—42no—
191D8—41no—
192D8—41no—
193C2×C8—1221no—
194C2×C8—2441no—
195C2×C8D4×D6111yescharacteristic
196C2×C8C2×C22⋊D6111yescharacteristic
197C4⋊C4—22no—
198C4⋊C4—41no—
199C4⋊C4—611no—
200C4⋊C4—1221no—
201C4⋊C4—1221no—
202C4⋊C4—2442no—
203C4⋊C4—2442no—
204C4⋊C4—2442no—
205C4⋊C4—2441no—
206C42—1221no—
207C42—2442no—
208C42—2441no—
209C42D4×D6111yescharacteristic
210C16—41no—
211C16—2441no—
212C23—81no—
213Q8—81no—
214Q8—81no—
215Q8—1221no—
216Q8—1222no—
217Q8—1221no—
218Q8—2441no—
219D4—81no—
220D4—81no—
221D4—81no—
222D4—81no—
223D4—161no—
224C2×C4—42no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—2441no—
228C2×C4—2441no—
229C2×C4#1451974511yescharacteristic
230C2×C4D8×D6111yescharacteristic
231C2×C4#1451980111yescharacteristic
232C8—21no—
233C8—4881no—
234C8—2441no—
235C8SD16×D6111yescharacteristic
236C8#1451980611yescharacteristic
237C22—161no—
238C22—161no—
239C22—161no—
240C22#1683989411yescharacteristic
241C4—21no—
242C4—82no—
243C4—4881no—
244C4—2442no—
245C4—2441no—
246C4—2441no—
247C4#1683989911yescharacteristic
248C4#1683993411yescharacteristic
249C4#1684019111yescharacteristic
250C4#1684019611yescharacteristic
251C2—321no—
252C2#2144491911yescharacteristic
253C2#2144773911yescharacteristic
254C2#2144778211yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2240C2
socleC22×C61#447
prime radicalC61×#493C22
hypercenter#2240D61
hypocenterC61#12353
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2240

Complements

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

NH ≅ G/Ntype
1. #21458712C2semidirect
4. #21443874C2semidirect
5. #21443799C2semidirect
6. #21443784C2semidirect
81. Dic244SD16semidirect
152. C61#12353semidirect

Maximal subgroups

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

subgroupindex
#214587122
#214478562
#214451762
#214438742
#214437992
#214437842
C61×#22402
#1235361