Finite Group Databasebeta

← #30605729

Subgroups — #30605729

Order 15616.

412 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 64 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#21462188C212yesmaximal, complemented
2#21460829C212yesmaximal, complemented
3#21460827C212yesmaximal, complemented
4#21456269C211yesmaximal, characteristic
5#16840685C2214yescomplemented
6#16840658—22no—
7#16840654—22no—
8C2×#14519803—22no—
9#16840312C411yescharacteristic
10#16840149—22no—
11#16840138C411yescharacteristic
12#16840138C2211yescharacteristic
13#16840134C411yescharacteristic
14#16840134C2211yescharacteristic
15C4×#11758194C2211yescharacteristic
16C2×#127×C61C411yescharacteristic
17#14519851—24no—
18C2×#11758222—21no—
19#14519803—48no—
20C2×#11758200—22no—
21C2×#11758200—22no—
22C2×#11758199—22no—
23C2×#11758199—22no—
24C2×#11758194D412yes—
25#14519777C2×C411yescharacteristic
26#14519774C2×C411yescharacteristic
27#14519765—21no—
28#14519751—41no—
29C4×D244—41no—
30#14519688D412yes—
31C4×#92418C2×C411yescharacteristic
32C4×#92418C2311yescharacteristic
33C22×D4×C61—21no—
34C22×D4×C61—41no—
35#127×C61—21no—
36#127×C61—41no—
37#127×C61C2×C411yescharacteristic
38#127×C61C2×C411yescharacteristic
39C2×C42×C61C2×C411yescharacteristic
40C24×C61—41no—
41C2×D4×C61—21no—
42C2×D4×C61—21no—
43C2×D4×C61—44no—
44C2×D4×C61—42no—
45C2×D4×C61—41no—
46C2×D4×C61—41no—
47C2×D4×C61—41no—
48C2×D4×C61—84no—
49C22×C4×C61—21no—
50C22×C4×C61C22⋊C411yescharacteristic
51C2×C22⋊D61—41no—
52#11758222—44no—
53C2×D244—21no—
54C2×D244—41no—
55C2×C4×D61—41no—
56C2×Dic122—21no—
57C42×C61—21no—
58C42×C61C22⋊C411yescharacteristic
59C42×C61C22×C411yescharacteristic
60#11758200—44no—
61#11758200—44no—
62#11758199—44no—
63#11758199—44no—
64#11758198—42no—
65C4⋊Dic61—41no—
66#11758194—24no—
67C2×#92418C22⋊C412yes—
68C2×#92418C2×D412yes—
69#11758187—44no—
70C23×C61—41no—
71C23×C61—41no—
72C23×C61—82no—
73C23×C61—84no—
74C23×C61#10011yescharacteristic
75C22×D61—41no—
76D4×C61—42no—
77D4×C61—42no—
78D4×C61—82no—
79D4×C61—82no—
80D4×C61—82no—
81D4×C61—84no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61—42no—
86C2×C4×C61#10011yescharacteristic
87C2×C4×C61C2×C22⋊C411yescharacteristic
88C22⋊D61—82no—
89C2×Dic61—41no—
90D244—42no—
91D244—82no—
92C4×D61—82no—
93Dic122—42no—
94#92418—22no—
95#92418AGL(1,ℤ/8)14yes—
96#11992—611nomaximal, Sylow
97C22×C61—21no—
98C22×C61—41no—
99C22×C61—82no—
100C22×C61—82no—
101C22×C61—81no—
102C22×C61—81no—
103C22×C61—164no—
104C22×C61C2×#10011yescharacteristic
105C2×D61—82no—
106C2×D61—81no—
107C4×C61—22no—
108C4×C61—21no—
109C4×C61—41no—
110C4×C61#41812yes—
111Dic61—81no—
112#3151—611no—
113#2165—612no—
114#1359—612no—
115#1357—612no—
116C2×C61—21no—
117C2×C61—41no—
118C2×C61—161no—
119C2×C61—161no—
120C2×C61#155511yescharacteristic
121D61—161no—
122C2×AGL(1,ℤ/8)—1222no—
123#532—611no—
124C2×#127#692311yescharacteristic
125#496—1222no—
126#493—611no—
127#493—611no—
128#492—611no—
129#492—611no—
130C4×M16—611no—
131#364—614no—
132#349—1222no—
133#347—1222no—
134C61#1199211yescharacteristic, complemented, Sylow
135C2×#41—1221no—
136C22×D4—21no—
137C22×D4—41no—
138AGL(1,ℤ/8)—2448no—
139C2×SD16—1222no—
140C2×SD16—1222no—
141C2×D8—1222no—
142C2×D8—1222no—
143C2×M16—612no—
144C4⋊Q8—611no—
145#127—21no—
146#127—41no—
147#127—611no—
148#127C2×#692311yescharacteristic
149#127C2×#692311yescharacteristic
150#124—1221no—
151#121—2441no—
152C4×D4—2441no—
153C2×C42C2×#692311yescharacteristic
154M32—1224no—
155#97—612no—
156C4×C8—611no—
157C4×C8—611no—
158C24—41no—
159#41—2444no—
160C2×Q8—1221no—
161C2×D4—21no—
162C2×D4—21no—
163C2×D4—44no—
164C2×D4—41no—
165C2×D4—41no—
166C2×D4—42no—
167C2×D4—41no—
168C2×D4—84no—
169C2×D4—1221no—
170C2×D4—2441no—
171C2×D4—2441no—
172C22×C4—21no—
173C22×C4—2441no—
174C22×C4C22⋊#692311yescharacteristic
175SD16—2444no—
176SD16—2444no—
177D8—2444no—
178D8—2444no—
179M16—1224no—
180C2×C8—612no—
181C2×C8—612no—
182C4⋊C4—2441no—
183C22⋊C4—2442no—
184C42—21no—
185C42C22⋊#692311yescharacteristic
186C42C22×#692311yescharacteristic
187C16—2444no—
188C23—41no—
189C23—41no—
190C23—82no—
191C23—84no—
192C23—2441no—
193C23#1451983711yescharacteristic
194Q8—2442no—
195D4—42no—
196D4—42no—
197D4—82no—
198D4—82no—
199D4—82no—
200D4—84no—
201D4—4882no—
202D4—4882no—
203D4—2442no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—42no—
208C2×C4—4882no—
209C2×C4—2441no—
210C2×C4#1451983711yescharacteristic
211C2×C4C2×C22⋊#692311yescharacteristic
212C8—614no—
213C8—1222no—
214C22—21no—
215C22—41no—
216C22—82no—
217C22—82no—
218C22—81no—
219C22—81no—
220C22—164no—
221C22—4882no—
222C22—4881no—
223C22C2×#1451983711yescharacteristic
224C4—22no—
225C4—21no—
226C4—41no—
227C4—4881no—
228C4#1684075412yes—
229C2—21no—
230C2—41no—
231C2—161no—
232C2—161no—
233C2—9761no—
234C2#2146134611yescharacteristic
subgroupG/H
centerC2#21461346
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC2×#127×C61C4
socleC2×C61#1555
prime radical#21456269C2
cosocleC4×#92418C23
hypercenterC2×#127#6923
hypocenterC61#11992
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #21462188C2semidirect
2. #21460829C2semidirect
3. #21460827C2semidirect
5. #16840685C22semidirect
134. C61#11992semidirect

Maximal subgroups

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

subgroupindex
#214621882
#214608292
#214608272
#214562692
#1199261