Finite Group Databasebeta

← #30606044

Subgroups — #30606044

Order 15616.

234 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 62 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#21461469C211yesmaximal, characteristic, complemented
2#21461415C211yesmaximal, characteristic, complemented
3#21460845C211yesmaximal, characteristic, complemented
4#21460777C211yesmaximal, characteristic, complemented
5#21460777C211yesmaximal, characteristic, complemented
6#21460738C211yesmaximal, characteristic, complemented
7#21447695C211yesmaximal, characteristic
8#16840797—21no—
9D4×#92420—21no—
10#16840651C2211yescharacteristic
11#16840623C2211yescharacteristic
12#16840623C2211yescharacteristic
13D4⋊#92420—21no—
14D4⋊#92420—21no—
15#16840603C2211yescharacteristic
16D8×Dic61C2211yescharacteristic
17D8×Dic61C2211yescharacteristic
18#16839590C411yescharacteristic
19#16839563C411yescharacteristic
20#16839563C411yescharacteristic
21#16839537C2211yescharacteristic
22C2×D16×C61C411yescharacteristic
23C2×#11758217—41no—
24C22×#92420—41no—
25C2×#11758187—21no—
26C4⋊#92420—21no—
27C4⋊#92420—21no—
28C22⋊#92420—41no—
29C22⋊#92420—41no—
30C4×#92420D411yescharacteristic
31C4×#92420D411yescharacteristic
32D4×Dic61—21no—
33D4×Dic61—21no—
34C2×#11758185C2×C411yescharacteristic
35#14519711C2×C411yescharacteristic
36#14519711C2×C411yescharacteristic
37#14519698—21no—
38#14519698—21no—
39C8×Dic61C2311yescharacteristic
40C2×D8×C61C2×C411yescharacteristic
41C2×D8×C61C2×C411yescharacteristic
42D16×C61—22no—
43C2×C16×C61C2×C411yescharacteristic
44C2×D4×C61—21no—
45C2×D4×C61—21no—
46C22×Dic61—41no—
47C22×Dic61—41no—
48#11758217—82no—
49C2×#92420—21no—
50C2×#92420—21no—
51C2×#92420—41no—
52C2×#92420—41no—
53C2×#92420—82no—
54D8×C61—21no—
55D8×C61—21no—
56D8×C61—21no—
57D8×C61M1612yescomplemented
58C2×C8×C61C22×C411yescharacteristic
59C22⋊Dic61—41no—
60C22⋊Dic61—41no—
61C4⋊Dic61—21no—
62C4⋊Dic61—21no—
63C4×Dic61C2×D411yescharacteristic
64C2×#92418#4111yescharacteristic
65#11758187—22no—
66C16×C61—21no—
67#11758185—21no—
68C23×C61—41no—
69C23×C61—41no—
70D4×C61—22no—
71D4×C61—41no—
72D4×C61—41no—
73D4×C61—41no—
74C2×C4×C61C4×D411yescharacteristic
75C2×Dic61—41no—
76C2×Dic61—41no—
77C2×Dic61—81no—
78C2×Dic61—81no—
79C2×Dic61—81no—
80C2×Dic61—81no—
81C2×Dic61AGL(1,ℤ/8)11yescharacteristic
82C2×Dic61AGL(1,ℤ/8)11yescharacteristic
83#92420—41no—
84#92420—41no—
85#92420—81no—
86#92420—81no—
87C8×C61C2×M1611yescharacteristic
88C8×C61#13111yescharacteristic
89#92418—21no—
90#12078—611nomaximal, Sylow
91C22×C61—42no—
92C22×C61—81no—
93C22×C61—81no—
94C22×C61—81no—
95C22×C61—81no—
96C22×C61—81no—
97C22×C61#44211yescharacteristic
98C4×C61#43511yescharacteristic
99C4×C61#44311yescharacteristic
100Dic61—21no—
101Dic61—21no—
102Dic61—81no—
103Dic61—81no—
104#2177—611no—
105#1594—611no—
106#1580—611no—
107#1368—611no—
108#1333—611no—
109#1333—611no—
110#1313—611no—
111C2×C61—82no—
112C2×C61—161no—
113C2×C61#158611yescharacteristic
114C2×C61AGL(1,ℤ/16)11yescharacteristic
115C2×C61AGL(1,ℤ/16)11yescharacteristic
116C2×D16#692311yescharacteristic
117C4×D8—611no—
118C4×D8—611no—
119#436—1221no—
120C8×D4—1221no—
121#367—611no—
122#357—611no—
123#357—611no—
124#346—611no—
125#346—611no—
126#334—611no—
127#334—611no—
128D4⋊C8—1221no—
129D4⋊C8—1221no—
130#322—611no—
131C61#1207811yescharacteristic, complemented, Sylow
132C2×D8C2×#692311yescharacteristic
133C2×D8C2×#692311yescharacteristic
134C2×M16—2441no—
135C22×C8—2441no—
136C4×D4—1221no—
137C4×D4—1221no—
138D16—22no—
139C2×C16—611no—
140C2×C16—1221no—
141C2×C16C2×#692311yescharacteristic
142#107—611no—
143#107—611no—
144C4⋊C8—1221no—
145C4⋊C8—1221no—
146#102—1221no—
147#102—1221no—
148C22⋊C8—2441no—
149C22⋊C8—2441no—
150C4×C8—611no—
151C4×C8—611no—
152C4×C8—611no—
153C2×D4—21no—
154C2×D4—21no—
155C22×C4—2441no—
156C22×C4—2441no—
157D8—21no—
158D8—21no—
159D8—21no—
160D8#1175821712yescomplemented
161M16—4882no—
162C2×C8—611no—
163C2×C8—1221no—
164C2×C8—1221no—
165C2×C8—4882no—
166C2×C8—2441no—
167C2×C8—2441no—
168C2×C8C22×#692311yescharacteristic
169C4⋊C4—1221no—
170C4⋊C4—1221no—
171C22⋊C4—2441no—
172C22⋊C4—2441no—
173C42—611no—
174C16—21no—
175C16—1222no—
176C16—1221no—
177C23—41no—
178C23—41no—
179D4—22no—
180D4—41no—
181D4—41no—
182D4—41no—
183C2×C4—611no—
184C2×C4—611no—
185C2×C4—4881no—
186C2×C4—4881no—
187C2×C4—4881no—
188C2×C4—4881no—
189C2×C4—2441no—
190C2×C4—2441no—
191C2×C4D4×#692311yescharacteristic
192C8—1221no—
193C8—4881no—
194C8—4881no—
195C8—2441no—
196C8—2441no—
197C8C2×#1175821711yescharacteristic
198C8#1451986411yescharacteristic
199C22—42no—
200C22—81no—
201C22—81no—
202C22—81no—
203C22—81no—
204C22—81no—
205C22#1684080311yescharacteristic
206C4—1221no—
207C4—1221no—
208C4—4881no—
209C4—4881no—
210C4#1684079311yescharacteristic
211C4#1684080411yescharacteristic
212C2—82no—
213C2—161no—
214C2#2146144011yescharacteristic
215C2#2146222811yescharacteristic
216C2#2146222911yescharacteristic
subgroupG/H
centerC22#16840803
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
Fitting, prime radicalC2×D16×C61C4
socleC22×C61#442
cosocleC8×Dic61C23
hypercenterC2×D16#6923
hypocenterC61#12078
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #21461469C2semidirect
2. #21461415C2semidirect
3. #21460845C2semidirect
4. #21460777C2semidirect
5. #21460777C2semidirect
6. #21460738C2semidirect
57. D8×C61M16semidirect
131. C61#12078semidirect
160. D8#11758217semidirect

Maximal subgroups

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

subgroupindex
#214614692
#214614152
#214608452
#214607772
#214607382
#214476952
#1207861