Finite Group Databasebeta

← #29594436

Subgroups — #29594436

Order 15616.

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

normal subgroups only

This group has 234 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#21445219C211yesmaximal, characteristic, complemented
4#21445171C211yesmaximal, characteristic
5#21443892C211yesmaximal, characteristic, complemented
6#21443876C211yesmaximal, characteristic, complemented
7C61×#1361C211yesmaximal, characteristic, complemented
8C2×C16×D61—21no—
9#16840167C2211yescharacteristic
10#16840053—21no—
11#16839954—21no—
12C8×D244C2211yescharacteristic
13#16839563—21no—
14#16839563—21no—
15#16839541—21no—
16C4×#11758185C2211yescharacteristic
17#16839515C2211yescharacteristic
18#16839510—21no—
19#16839506—21no—
20C61×#493C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C61×#335C2211yescharacteristic
23C2×#11758199—41no—
24C2×C8×D61—21no—
25#14519777—21no—
26C4×D244D411yescharacteristic
27C2×#11758185D411yescharacteristic
28C2×#11758185D411yescharacteristic
29C16×D61—42no—
30#14519711—21no—
31#14519711—21no—
32#14519709—41no—
33C4⋊#92418—21no—
34C4⋊#92418D411yescharacteristic
35#14519699—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—
64C8×D61—41no—
65C8×D61—41no—
66C16×C61—41no—
67#11758185—21no—
68#11758185—21no—
69C23×C61—81no—
70C22×D61—21no—
71D4×C61—81no—
72D4×C61—81no—
73D4×C61—81no—
74D4×C61—81no—
75D4×C61—161no—
76C2×C4×C61#12111yescharacteristic
77C2×C4×C61C2×D811yescharacteristic
78C2×C4×C61#13511yescharacteristic
79C2×Dic61—21no—
80C2×Dic61—81no—
81D244—21no—
82D244SD3212yes—
83C4×D61—41no—
84C4×D61—41no—
85Dic122—161no—
86C8×C61—21no—
87C8×C61—81no—
88C8×C61#13511yescharacteristic
89C8×C61AGL(1,ℤ/8)11yescharacteristic
90#92418—41no—
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#46311yescharacteristic
102C4×C61#47111yescharacteristic
103C4×C61C2×SD3211yescharacteristic
104C4×C61#50811yescharacteristic
105Dic61—41no—
106Dic61—161no—
107#2240—611no—
108D4×C16—611no—
109#1675—611no—
110#1667—611no—
111#1372—611no—
112#1365—611no—
113#1361D6111yescharacteristic, complemented
114C2×C61—321no—
115C2×C61#168111yescharacteristic
116C2×C61#221711yescharacteristic
117C2×C61#222111yescharacteristic
118D61—42no—
119C22×C16—1221no—
120#500—611no—
121#493C2×D6111yescharacteristic
122#476—1221no—
123#459—1221no—
124C8×D4—611no—
125C4⋊C16C2×D6111yescharacteristic
126#357—1221no—
127#357—1221no—
128C22⋊C16—1221no—
129C4×C16—611no—
130#335—611no—
131#335C2×D6111yescharacteristic
132#333—1221no—
133#331—1221no—
134C61#1246811yescharacteristic, complemented, Sylow
135C2×D8—21no—
136C2×D8—21no—
137C2×D8—2441no—
138C22×C8—1221no—
139C4⋊Q8—1221no—
140#127—21no—
141C4×D4—611no—
142C2×C16—21no—
143C2×C16—611no—
144C2×C16—611no—
145C2×C16—2442no—
146#107—1221no—
147#107—1221no—
148#106—2441no—
149C4⋊C8—21no—
150C4⋊C8—611no—
151C4⋊C8—1221no—
152#102—2441no—
153#102—2441no—
154C22⋊C8—1221no—
155C4×C8C22×D6111yescharacteristic
156C2×Q8—2441no—
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—41no—
167C2×C8—1221no—
168C2×C8—2441no—
169C2×C8—2441no—
170C2×C8—2441no—
171C2×C8#1175822211yescharacteristic
172C2×C8D4×D6111yescharacteristic
173C4⋊C4—611no—
174C4⋊C4—2441no—
175C4⋊C4—2441no—
176C22⋊C4—1221no—
177C42D4×D6111yescharacteristic
178C16—41no—
179C16—1221no—
180C16—1221no—
181C23—81no—
182C23—1221no—
183Q8—9761no—
184D4—81no—
185D4—81no—
186D4—81no—
187D4—81no—
188D4—161no—
189D4—612no—
190D4—1221no—
191C2×C4—1221no—
192C2×C4—4881no—
193C2×C4—2441no—
194C2×C4—2441no—
195C2×C4#1451975011yescharacteristic
196C2×C4D8×D6111yescharacteristic
197C2×C4#1451979811yescharacteristic
198C8—21no—
199C8—81no—
200C8—4881no—
201C8—2441no—
202C8#1451979811yescharacteristic
203C8#1451980111yescharacteristic
204C22—161no—
205C22—161no—
206C22—161no—
207C22—1222no—
208C22—2441no—
209C22—2441no—
210C22#1683999711yescharacteristic
211C4—21no—
212C4—9761no—
213C4—2441no—
214C4#1683997611yescharacteristic
215C4#1684002411yescharacteristic
216C4SD32×D6111yescharacteristic
217C4#1684019111yescharacteristic
218C2—321no—
219C2—2442no—
220C2#2144525511yescharacteristic
221C2#2144791411yescharacteristic
222C2#2144793811yescharacteristic
subgroupG/H
centerC22#16839997
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1361C2
socleC22×C61#466
prime radical#21445171C2
hypercenter#1361D61
hypocenterC61#12468
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. #21445219C2semidirect
5. #21443892C2semidirect
6. #21443876C2semidirect
7. C61×#1361C2semidirect
113. #1361D61semidirect
134. C61#12468semidirect

Maximal subgroups

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

subgroupindex
#214480422
#214476382
#214452192
#214451712
#214438922
#214438762
C61×#13612
#1246861