Finite Group Databasebeta

← #29594429

Subgroups — #29594429

Order 15616.

240 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 63 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#21448042C211yesmaximal, characteristic, complemented
2#21447638C211yesmaximal, characteristic, complemented
3#21445209C211yesmaximal, characteristic, complemented
4#21445171C211yesmaximal, characteristic
5#21443890C211yesmaximal, characteristic, complemented
6#21443873C211yesmaximal, characteristic, complemented
7C61×#1361C211yesmaximal, characteristic, complemented
8C2×C16×D61—21no—
9#16840167C2211yescharacteristic
10#16839968—21no—
11#16839954—21no—
12C8×D244C2211yescharacteristic
13#16839563—21no—
14#16839563—21no—
15#16839541—21no—
16C4×#11758185C2211yescharacteristic
17#16839515C2211yescharacteristic
18#16839509—21no—
19#16839506—21no—
20C61×#493C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C61×#335C2211yescharacteristic
23C2×#11758190—41no—
24C2×#11758199—41no—
25C2×C8×D61—21no—
26#14519777—21no—
27C4×D244D411yescharacteristic
28C2×#11758185D411yescharacteristic
29C2×#11758185D411yescharacteristic
30C16×D61—42no—
31#14519711—21no—
32#14519711—21no—
33C4⋊#92418—21no—
34C4⋊#92418D411yescharacteristic
35#14519702—41no—
36#14519698—41no—
37#14519689—21no—
38C2×D8×C61—21no—
39C2×D8×C61—21no—
40#127×C61—21no—
41C2×C16×C61—21no—
42C4⋊C8×C61—21no—
43C4×C8×C61C2311yescharacteristic
44C2×D4×C61—41no—
45C2×D4×C61—41no—
46C2×D4×C61—41no—
47C2×D244D811yescharacteristic
48C2×C4×D61—21no—
49C2×Dic122—41no—
50D8×C61—41no—
51D8×C61—41no—
52D8×C61—81no—
53C2×C8×C61—41no—
54C2×C8×C61C2×D411yescharacteristic
55C2×C8×C61#4111yescharacteristic
56C42×C61C2×D411yescharacteristic
57#11758199—82no—
58#11758198—21no—
59C4⋊Dic61—41no—
60C4⋊Dic61—41no—
61C4⋊Dic61D811yescharacteristic
62C2×#92418—21no—
63C2×#92418—41no—
64#11758190—82no—
65C8×D61—41no—
66C8×D61—41no—
67C16×C61—41no—
68#11758185—21no—
69#11758185—21no—
70C23×C61—81no—
71C22×D61—21no—
72D4×C61—81no—
73D4×C61—81no—
74D4×C61—81no—
75D4×C61—81no—
76D4×C61—161no—
77C2×C4×C61#12111yescharacteristic
78C2×C4×C61C2×D811yescharacteristic
79C2×C4×C61#13511yescharacteristic
80C2×Dic61—21no—
81C2×Dic61—81no—
82D244—21no—
83D244D1612yes—
84C4×D61—41no—
85C4×D61—41no—
86Dic122—81no—
87Dic122—81no—
88C8×C61—21no—
89C8×C61—81no—
90C8×C61#13511yescharacteristic
91C8×C61AGL(1,ℤ/8)11yescharacteristic
92#92418—41no—
93#92418—81no—
94#12467—611nomaximal, Sylow
95C22×C61—161no—
96C22×C61—161no—
97C22×C61—161no—
98C22×C61#46611yescharacteristic
99C2×D61—22no—
100C2×D61—41no—
101C2×D61—41no—
102C4×C61—21no—
103C4×C61#46311yescharacteristic
104C4×C61#47111yescharacteristic
105C4×C61C2×D1611yescharacteristic
106C4×C61#50811yescharacteristic
107Dic61—41no—
108Dic61—161no—
109#2240—611no—
110D4×C16—611no—
111#1673—611no—
112#1667—611no—
113#1371—611no—
114#1364—611no—
115#1361D6111yescharacteristic, complemented
116C2×C61—321no—
117C2×C61#168111yescharacteristic
118C2×C61#221511yescharacteristic
119C2×C61#222311yescharacteristic
120D61—42no—
121C22×C16—1221no—
122#500—611no—
123#493C2×D6111yescharacteristic
124#461—1221no—
125#459—1221no—
126C8×D4—611no—
127C4⋊C16C2×D6111yescharacteristic
128#357—1221no—
129#357—1221no—
130C22⋊C16—1221no—
131C4×C16—611no—
132#335—611no—
133#335C2×D6111yescharacteristic
134#332—1221no—
135#331—1221no—
136C61#1246711yescharacteristic, complemented, Sylow
137C2×SD16—2441no—
138C2×D8—21no—
139C2×D8—21no—
140C2×D8—2441no—
141C22×C8—1221no—
142C4⋊Q8—1221no—
143#127—21no—
144C4×D4—611no—
145C2×C16—21no—
146C2×C16—611no—
147C2×C16—611no—
148C2×C16—2442no—
149#107—1221no—
150#107—1221no—
151C4⋊C8—21no—
152C4⋊C8—611no—
153C4⋊C8—1221no—
154#103—2441no—
155#102—2441no—
156C22⋊C8—1221no—
157C4×C8C22×D6111yescharacteristic
158C2×Q8—2441no—
159C2×D4—41no—
160C2×D4—41no—
161C2×D4—41no—
162C2×D4—611no—
163C22×C4—1221no—
164SD16—4882no—
165D8—41no—
166D8—41no—
167D8—81no—
168D8—4882no—
169C2×C8—41no—
170C2×C8—1221no—
171C2×C8—2441no—
172C2×C8—2441no—
173C2×C8—2441no—
174C2×C8#1175822211yescharacteristic
175C2×C8D4×D6111yescharacteristic
176C4⋊C4—611no—
177C4⋊C4—2441no—
178C4⋊C4—2441no—
179C22⋊C4—1221no—
180C42D4×D6111yescharacteristic
181C16—41no—
182C16—1221no—
183C16—1221no—
184C23—81no—
185C23—1221no—
186Q8—4881no—
187Q8—4881no—
188D4—81no—
189D4—81no—
190D4—81no—
191D4—81no—
192D4—161no—
193D4—612no—
194D4—1221no—
195C2×C4—1221no—
196C2×C4—4881no—
197C2×C4—2441no—
198C2×C4—2441no—
199C2×C4#1451975011yescharacteristic
200C2×C4D8×D6111yescharacteristic
201C2×C4#1451979811yescharacteristic
202C8—21no—
203C8—81no—
204C8—4881no—
205C8—2441no—
206C8#1451979811yescharacteristic
207C8#1451980111yescharacteristic
208C22—161no—
209C22—161no—
210C22—161no—
211C22—1222no—
212C22—2441no—
213C22—2441no—
214C22#1683999711yescharacteristic
215C4—21no—
216C4—9761no—
217C4—2441no—
218C4#1683997611yescharacteristic
219C4#1684002411yescharacteristic
220C4D16×D6111yescharacteristic
221C4#1684019311yescharacteristic
222C2—321no—
223C2—2442no—
224C2#2144525511yescharacteristic
225C2#2144790411yescharacteristic
226C2#2144794811yescharacteristic
subgroupG/H
centerC22#16839997
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1361C2
socleC22×C61#466
prime radical#21445171C2
hypercenter#1361D61
hypocenterC61#12467
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
1. #21448042C2semidirect
2. #21447638C2semidirect
3. #21445209C2semidirect
5. #21443890C2semidirect
6. #21443873C2semidirect
7. C61×#1361C2semidirect
115. #1361D61semidirect
136. C61#12467semidirect

Maximal subgroups

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

subgroupindex
#214480422
#214476382
#214452092
#214451712
#214438902
#214438732
C61×#13612
#1246761