Finite Group Databasebeta

← #29593699

Subgroups — #29593699

Order 15616.

298 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 69 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#21458708C211yesmaximal, characteristic, complemented
2#21448043C211yesmaximal, characteristic
3#21447859C211yesmaximal, characteristic
4#21445180C211yesmaximal, characteristic
5#21443875C211yesmaximal, characteristic, complemented
6#21443799C211yesmaximal, characteristic, complemented
7C61×#1332C211yesmaximal, characteristic, complemented
8#16840491—21no—
9C2×#14519720—21no—
10#16840167C2211yescharacteristic
11#16840163—21no—
12#16840139C2211yescharacteristic
13#16840071—22no—
14#16840047—21no—
15#16839963—21no—
16C8×Dic122C2211yescharacteristic
17Q16×Dic61—21no—
18C4⋊#11758185C2211yescharacteristic
19#16839564—22no—
20#16839562—21no—
21#16839505—21no—
22C4×Q16×C61C2211yescharacteristic
23C4×C16×C61C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×#11758190—41no—
26C2×D488—21no—
27C2×D488—21no—
28#14519777—21no—
29#14519777—41no—
30#14519774—21no—
31#14519768—22no—
32#14519768—42no—
33Q8×Dic61—22no—
34C4×Dic122—41no—
35C4×Dic122D411yescharacteristic
36#14519720—42no—
37C2×#11758185—21no—
38#14519711—21no—
39#14519711D412yes—
40#14519708—22no—
41C4⋊#92418D411yescharacteristic
42#14519706—21no—
43#14519701—22no—
44#14519699—41no—
45C8×Dic61—21no—
46C2×Q16×C61D411yescharacteristic
47C4×Q8×C61—21no—
48C2×C16×C61—21no—
49#107×C61D411yescharacteristic
50C4⋊C8×C61—21no—
51#103×C61—21no—
52C4×C8×C61C2311yescharacteristic
53C2×Q8×C61—21no—
54C2×D244—41no—
55C2×D244—41no—
56C2×D244—41no—
57C2×Dic122—41no—
58C2×Dic122D811yescharacteristic
59Q16×C61—21no—
60Q16×C61SD1612yescomplemented
61C2×C8×C61—41no—
62C2×C8×C61C2×D411yescharacteristic
63C2×C8×C61C2×D411yescharacteristic
64C4⋊C4×C61—21no—
65C4⋊C4×C61—41no—
66C42×C61—41no—
67C42×C61C2×D411yescharacteristic
68C4⋊Dic61—22no—
69C4⋊Dic61—42no—
70C4⋊Dic61—42no—
71C4⋊Dic61—41no—
72C4⋊Dic61D811yescharacteristic
73#11758196—21no—
74#11758196—42no—
75C4×Dic61—21no—
76C4×Dic61—42no—
77C2×#92418—21no—
78D488—42no—
79D488—41no—
80D488—41no—
81#11758190—82no—
82C16×C61—41no—
83#11758185—41no—
84C22×D61—81no—
85Q8×C61—22no—
86Q8×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61—41no—
89C2×C4×C61#12011yescharacteristic
90C2×C4×C61C2×D811yescharacteristic
91C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—42no—
95D244—81no—
96D244—81no—
97D244—81no—
98D244—81no—
99D244—161no—
100Dic122—21no—
101Dic122—21no—
102Dic122—81no—
103Dic122—81no—
104C8×C61—21no—
105C8×C61—81no—
106C8×C61C2×SD1611yescharacteristic
107C8×C61#13711yescharacteristic
108#92418—41no—
109#12353—611nomaximal, Sylow
110C22×C61#44711yescharacteristic
111C2×D61—161no—
112C2×D61—161no—
113C2×D61—161no—
114C4×C61—21no—
115C4×C61—42no—
116C4×C61—81no—
117C4×C61#44811yescharacteristic
118C4×C61#45411yescharacteristic
119C4×C61#50811yescharacteristic
120C4×C61#50911yescharacteristic
121Dic61—41no—
122Dic61—41no—
123Dic61—82no—
124#3383—611no—
125#2240—611no—
126#2207—611no—
127#1668—611no—
128#1364—611no—
129Q8⋊C16—611no—
130#1332D6111yescharacteristic, complemented
131C2×C61#162711yescharacteristic
132C2×C61#218611yescharacteristic
133C2×C61#219311yescharacteristic
134D61—321no—
135#557—1221no—
136C2×SD32—1221no—
137#500—611no—
138#499—1221no—
139#493—611no—
140#479—1222no—
141#475—1221no—
142#460—1221no—
143C8×Q8—611no—
144C4×Q16—1221no—
145C4×Q16C2×D6111yescharacteristic
146C4⋊C16—611no—
147#357—1222no—
148#357—1221no—
149C4×C16C2×D6111yescharacteristic
150#335C2×D6111yescharacteristic
151#331—1221no—
152C61#1235311yescharacteristic, complemented, Sylow
153C2×Q16D24411yescharacteristic
154C2×SD16—2441no—
155C2×D8—1221no—
156C2×D8—1221no—
157C4⋊Q8—1221no—
158C4⋊Q8—2441no—
159#127—1221no—
160#125—1222no—
161#125—2442no—
162C4×Q8—21no—
163C4×Q8—611no—
164C4×Q8—1222no—
165C4×Q8—2441no—
166SD32—2442no—
167C2×C16—21no—
168C2×C16—1221no—
169#107—612no—
170#107—1221no—
171#107D24411yescharacteristic
172#106—1222no—
173C4⋊C8—21no—
174C4⋊C8—611no—
175C4⋊C8—1221no—
176#103—21no—
177#103—1222no—
178#102—2441no—
179C4×C8—1221no—
180C4×C8C22×D6111yescharacteristic
181C2×Q8—21no—
182C2×Q8—611no—
183C2×Q8—2441no—
184C2×D4—2441no—
185C2×D4—2441no—
186C2×D4—2441no—
187Q16—21no—
188Q16#1175819012yescomplemented
189SD16—4882no—
190D8—2442no—
191D8—2441no—
192D8—2441no—
193C2×C8—41no—
194C2×C8—1221no—
195C2×C8C2×D24411yescharacteristic
196C2×C8D4×D6111yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—41no—
199C4⋊C4—611no—
200C4⋊C4—1221no—
201C4⋊C4—1222no—
202C4⋊C4—2442no—
203C4⋊C4—2442no—
204C4⋊C4—2442no—
205C4⋊C4—2441no—
206C42—41no—
207C42—1221no—
208C42—2442no—
209C42D4×D6111yescharacteristic
210C16—41no—
211C16—2441no—
212C23—4881no—
213Q8—22no—
214Q8—41no—
215Q8—1221no—
216Q8—1221no—
217Q8—4881no—
218Q8—4881no—
219D4—9761no—
220D4—4881no—
221D4—4881no—
222D4—4881no—
223D4—4881no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—2442no—
229C2×C4#1451974711yescharacteristic
230C2×C4D8×D6111yescharacteristic
231C2×C4#1451980411yescharacteristic
232C8—21no—
233C8—81no—
234C8—2441no—
235C8C2×#1175819011yescharacteristic
236C8#1451981011yescharacteristic
237C22—9761no—
238C22—9761no—
239C22—9761no—
240C22#1683989711yescharacteristic
241C4—21no—
242C4—42no—
243C4—81no—
244C4—4882no—
245C4—2441no—
246C4—2441no—
247C4#1683990311yescharacteristic
248C4#1683993611yescharacteristic
249C4#1684019511yescharacteristic
250C4#1684019911yescharacteristic
251C2—19521no—
252C2#2144492511yescharacteristic
253C2#2144774511yescharacteristic
254C2#2144778411yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1332C2
socleC22×C61#447
prime radical#16840139C22
hypercenter#1332D61
hypocenterC61#12353
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1332

Complements

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

NH ≅ G/Ntype
1. #21458708C2semidirect
5. #21443875C2semidirect
6. #21443799C2semidirect
7. C61×#1332C2semidirect
60. Q16×C61SD16semidirect
130. #1332D61semidirect
152. C61#12353semidirect
188. Q16#11758190semidirect

Maximal subgroups

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

subgroupindex
#214587082
#214480432
#214478592
#214451802
#214438752
#214437992
C61×#13322
#1235361