Finite Group Databasebeta

← #29594434

Subgroups — #29594434

Order 15616.

234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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
1C16×D244C211yesmaximal, characteristic, complemented
2#21445215C211yesmaximal, characteristic, complemented
3#21445171C211yesmaximal, characteristic
4#21443893C211yesmaximal, characteristic, complemented
5#21443877C211yesmaximal, characteristic, complemented
6#21443865C211yesmaximal, characteristic, complemented
7C61×#2240C211yesmaximal, characteristic, complemented
8C2×C16×D61—21no—
9#16840049—21no—
10#16839954—21no—
11C8×D244C2211yescharacteristic
12C4⋊#11758185C2211yescharacteristic
13#16839541—21no—
14#16839515C2211yescharacteristic
15#16839515C2211yescharacteristic
16#16839511—21no—
17#16839506—21no—
18C61×#500C2211yescharacteristic
19C61×#493C2211yescharacteristic
20C61×#357—21no—
21C61×#357—21no—
22C4×C16×C61C2211yescharacteristic
23C2×#11758199—41no—
24C2×C8×D61—21no—
25C4×D244D411yescharacteristic
26C2×#11758185—21no—
27C16×D61—42no—
28#14519708—41no—
29C4⋊#92418—21no—
30C4⋊#92418—21no—
31C4⋊#92418D411yescharacteristic
32#14519698—41no—
33#14519697—41no—
34#14519689—21no—
35C2×D8×C61—21no—
36C2×D8×C61—21no—
37C4⋊Q8×C61—21no—
38#127×C61—21no—
39C2×C16×C61D411yescharacteristic
40C2×C16×C61D411yescharacteristic
41#107×C61—21no—
42#107×C61—21no—
43C4×C8×C61C2311yescharacteristic
44C2×Q8×C61—41no—
45C2×D4×C61—41no—
46C2×D4×C61—41no—
47C2×D4×C61—41no—
48C2×D244D811yescharacteristic
49C2×C4×D61—21no—
50D8×C61—41no—
51D8×C61—41no—
52D8×C61—81no—
53C2×C8×C61C2×D411yescharacteristic
54C2×C8×C61#4111yescharacteristic
55C4⋊C4×C61—41no—
56C4⋊C4×C61—41no—
57C42×C61C2×D411yescharacteristic
58#11758199—82no—
59#11758198—21no—
60C4⋊Dic61D811yescharacteristic
61C2×#92418—21no—
62C2×#92418—41no—
63C2×#92418—41no—
64C8×D61—41no—
65C8×D61—41no—
66C16×C61—21no—
67C16×C61—21no—
68#11758185—41no—
69C23×C61—81no—
70C22×D61—21no—
71Q8×C61—161no—
72D4×C61—81no—
73D4×C61—81no—
74D4×C61—81no—
75D4×C61—81no—
76D4×C61—161no—
77C2×C4×C61—81no—
78C2×C4×C61#12111yescharacteristic
79C2×C4×C61C2×D811yescharacteristic
80C2×C4×C61#13511yescharacteristic
81C2×Dic61—21no—
82D244—21no—
83D244SD3212yes—
84C4×D61—41no—
85C4×D61—41no—
86C8×C61—21no—
87C8×C61#13511yescharacteristic
88C8×C61AGL(1,ℤ/8)11yescharacteristic
89#92418—41no—
90#92418—81no—
91#92418—81no—
92#12468—611nomaximal, Sylow
93C22×C61—161no—
94C22×C61—161no—
95C22×C61—161no—
96C22×C61#46611yescharacteristic
97C2×D61—22no—
98C2×D61—41no—
99C2×D61—41no—
100C4×C61—21no—
101C4×C61—161no—
102C4×C61#46311yescharacteristic
103C4×C61#47111yescharacteristic
104C4×C61C2×SD3211yescharacteristic
105C4×C61#50811yescharacteristic
106Dic61—41no—
107#2240D6111yescharacteristic, complemented
108D4×C16—611no—
109#1675—611no—
110#1667—611no—
111#1372—611no—
112#1365—611no—
113#1361—611no—
114C2×C61—321no—
115C2×C61#168111yescharacteristic
116C2×C61#221711yescharacteristic
117C2×C61#222111yescharacteristic
118D61—42no—
119C22×C16—1221no—
120#500C2×D6111yescharacteristic
121#493C2×D6111yescharacteristic
122#476—1221no—
123#459—1221no—
124C8×D4—611no—
125C4⋊C16—611no—
126#357—21no—
127#357—21no—
128C22⋊C16—1221no—
129C4×C16C2×D6111yescharacteristic
130#335—611no—
131#335—611no—
132#333—1221no—
133#331—1221no—
134C61#1246811yescharacteristic, complemented, Sylow
135C2×D8—21no—
136C2×D8—21no—
137C2×D8—2441no—
138C22×C8—1221no—
139C4⋊Q8—21no—
140#127—21no—
141C4×D4—611no—
142C2×C16—1221no—
143C2×C16—2442no—
144C2×C16C22⋊D6111yescharacteristic
145C2×C16C22⋊D6111yescharacteristic
146#107—21no—
147#107—21no—
148#106—2441no—
149C4⋊C8—611no—
150C4⋊C8—1221no—
151C4⋊C8—1221no—
152#102—2441no—
153#102—2441no—
154C22⋊C8—1221no—
155C4×C8C22×D6111yescharacteristic
156C2×Q8—41no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—41no—
160C2×D4—611no—
161C22×C4—1221no—
162D8—41no—
163D8—41no—
164D8—81no—
165D8—4882no—
166C2×C8—1221no—
167C2×C8—2441no—
168C2×C8—2441no—
169C2×C8—2441no—
170C2×C8—2441no—
171C2×C8#1175822411yescharacteristic
172C2×C8C2×C22⋊D6111yescharacteristic
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—611no—
176C22⋊C4—1221no—
177C42D4×D6111yescharacteristic
178C16—21no—
179C16—21no—
180C16—2441no—
181C23—81no—
182C23—1221no—
183Q8—161no—
184D4—81no—
185D4—81no—
186D4—81no—
187D4—81no—
188D4—161no—
189D4—612no—
190D4—1221no—
191C2×C4—81no—
192C2×C4—1221no—
193C2×C4—2441no—
194C2×C4—2441no—
195C2×C4#1451974811yescharacteristic
196C2×C4D8×D6111yescharacteristic
197C2×C4#1451979611yescharacteristic
198C8—21no—
199C8—4881no—
200C8—4881no—
201C8—2441no—
202C8#1451979711yescharacteristic
203C8#1451980211yescharacteristic
204C22—161no—
205C22—161no—
206C22—161no—
207C22—1222no—
208C22—2441no—
209C22—2441no—
210C22#1683999511yescharacteristic
211C4—21no—
212C4—161no—
213C4—2441no—
214C4#1683997411yescharacteristic
215C4#1684002211yescharacteristic
216C4SD32×D6111yescharacteristic
217C4#1684019311yescharacteristic
218C2—321no—
219C2—2442no—
220C2#2144525311yescharacteristic
221C2#2144791211yescharacteristic
222C2#2144793611yescharacteristic
subgroupG/H
centerC22#16839995
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2240C2
socleC22×C61#466
prime radical#21445171C2
hypercenter#2240D61
hypocenterC61#12468
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. C16×D244C2semidirect
2. #21445215C2semidirect
4. #21443893C2semidirect
5. #21443877C2semidirect
6. #21443865C2semidirect
7. C61×#2240C2semidirect
107. #2240D61semidirect
134. C61#12468semidirect

Maximal subgroups

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

subgroupindex
C16×D2442
#214452152
#214451712
#214438932
#214438772
#214438652
C61×#22402
#1246861