Finite Group Databasebeta

← #30608358

Subgroups — #30608358

Order 15616.

458 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 60 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#21462092C212yesmaximal, complemented
2#21460950C214yesmaximal, complemented
3#21456269C211yesmaximal, characteristic
4#16840741—22no—
5#16840669—22no—
6#16840667C2214yescomplemented
7C2×#14519803—22no—
8#16840312C2211yescharacteristic
9#16840149—22no—
10#16840138C2212yes—
11#16840134C412yescomplemented
12C4×#11758194C411yescharacteristic, complemented
13C2×#127×C61C411yescharacteristic, complemented
14#14519856—42no—
15#14519836—24no—
16#14519835—42no—
17C2×#11758222D412yes—
18#14519803—44no—
19#14519803—44no—
20C2×#11758200—24no—
21C2×#11758199—24no—
22C2×#11758194—21no—
23#14519777C2×C411yescharacteristic
24#14519774C2311yescharacteristic
25#14519765D412yes—
26#14519751—41no—
27C4×D244—41no—
28#14519688—21no—
29C4×#92418C2×C412yes—
30C22×D4×C61—21no—
31C22×D4×C61—41no—
32#127×C61—21no—
33#127×C61—41no—
34#127×C61C2×C412yes—
35C2×C42×C61C2×C411yescharacteristic
36C24×C61—41no—
37C2×D4×C61—22no—
38C2×D4×C61—42no—
39C2×D4×C61—42no—
40C2×D4×C61—42no—
41C2×D4×C61—42no—
42C2×D4×C61—41no—
43C2×D4×C61—84no—
44C22×C4×C61—21no—
45C22×C4×C61C22⋊C411yescharacteristic
46C2×C22⋊D61—22no—
47#11758222—42no—
48#11758222—42no—
49C2×D244—41no—
50C2×D244C2×D412yes—
51C2×C4×D61—22no—
52C2×Dic122C22⋊C412yes—
53C22⋊#6923—44no—
54C4⋊#6923—82no—
55C4×#6923—82no—
56C42×C61—21no—
57C42×C61C22⋊C411yescharacteristic
58C42×C61C22×C411yescharacteristic
59#11758200—48no—
60#11758199—48no—
61#11758198—42no—
62C4⋊Dic61—41no—
63#11758194—24no—
64C2×#92418—22no—
65C23×C61—42no—
66C23×C61—81no—
67C23×C61—81no—
68C23×C61—84no—
69C23×C61#9911yescharacteristic
70C22×D61—22no—
71C2×#6923—84no—
72D4×C61—44no—
73D4×C61—84no—
74D4×C61—84no—
75D4×C61—82no—
76C2×C4×C61—21no—
77C2×C4×C61—22no—
78C2×C4×C61—21no—
79C2×C4×C61—42no—
80C2×C4×C61#9911yescharacteristic
81C2×C4×C61C2×C22⋊C411yescharacteristic
82C22⋊D61—82no—
83C2×Dic61—22no—
84D244—42no—
85D244—82no—
86C4×D61—42no—
87C4×D61—42no—
88Dic122—42no—
89#92418—24no—
90#13585—611nomaximal, Sylow
91C22×C61—21no—
92C22×C61—41no—
93C22×C61—84no—
94C22×C61—82no—
95C22×C61—162no—
96C22×C61—162no—
97C22×C61C2×#9911yescharacteristic
98C2×D61—42no—
99C2×D61—82no—
100#6923—164no—
101C4×C61—22no—
102C4×C61—21no—
103C4×C61—41no—
104C4×C61#35312yes—
105Dic61—42no—
106#3151—611no—
107#2126—612no—
108#1408—614no—
109C2×C61—21no—
110C2×C61—41no—
111C2×C61—162no—
112C2×C61C2×#35311yescharacteristic
113D61—82no—
114C2×AGL(1,ℤ/8)—1222no—
115#532—611no—
116C2×#127#692311yescharacteristic, complemented
117#496—1222no—
118#493—612no—
119#492—612no—
120#410—1222no—
121C4×M16—611no—
122#354—1222no—
123#353—614no—
124C61#1358511yescharacteristic, complemented, Sylow
125C2×#41—612no—
126C22×D4—21no—
127C22×D4—41no—
128AGL(1,ℤ/8)—2444no—
129AGL(1,ℤ/8)—2444no—
130C2×SD16—1224no—
131C2×D8—1224no—
132C2×M16—1221no—
133C4⋊Q8—611no—
134#127—21no—
135#127—41no—
136#127—611no—
137#127C2×#692312yes—
138#124—612no—
139#121—2441no—
140C4×D4—2441no—
141#117—2442no—
142C2×C42C2×#692311yescharacteristic
143#99—1224no—
144#99—2442no—
145#97—1221no—
146C4×C8—612no—
147C24—41no—
148#41—2442no—
149#41—2442no—
150C2×Q8—612no—
151C2×D4—22no—
152C2×D4—42no—
153C2×D4—42no—
154C2×D4—42no—
155C2×D4—42no—
156C2×D4—41no—
157C2×D4—84no—
158C2×D4—612no—
159C2×D4—1222no—
160C2×D4—2441no—
161C22×C4—21no—
162C22×C4—1222no—
163C22×C4C22⋊#692311yescharacteristic
164SD16—2448no—
165D8—2448no—
166M16—1224no—
167C2×C8—1222no—
168C4⋊C4—4882no—
169C4⋊C4—2441no—
170C22⋊C4—2442no—
171C22⋊C4—2444no—
172C42—21no—
173C42—4882no—
174C42C22⋊#692311yescharacteristic
175C42C22×#692311yescharacteristic
176C23—42no—
177C23—81no—
178C23—81no—
179C23—84no—
180C23—1222no—
181C23#1451983511yescharacteristic
182Q8—2442no—
183D4—44no—
184D4—84no—
185D4—84no—
186D4—82no—
187D4—4882no—
188D4—4882no—
189D4—2442no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—42no—
194C2×C4—1222no—
195C2×C4—4884no—
196C2×C4—2442no—
197C2×C4—2442no—
198C2×C4#1451983511yescharacteristic
199C2×C4C2×C22⋊#692311yescharacteristic
200C8—1224no—
201C22—21no—
202C22—41no—
203C22—84no—
204C22—82no—
205C22—162no—
206C22—162no—
207C22—4882no—
208C22—2442no—
209C22C2×#1451983511yescharacteristic
210C4—22no—
211C4—21no—
212C4—41no—
213C4—9764no—
214C4—2442no—
215C4#1684066612yes—
216C2—21no—
217C2—41no—
218C2—162no—
219C2—4882no—
220C2C2×#1684066611yescharacteristic
subgroupG/H
centerC2C2×#16840666
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC2×#127×C61C4
socleC2×C61C2×#353
prime radical#21456269C2
cosocle#14519774C23
hypercenterC2×#127#6923
hypocenterC61#13585
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #21462092C2semidirect
2. #21460950C2semidirect
6. #16840667C22semidirect
11. #16840134C4semidirect
12. C4×#11758194C4semidirect
13. C2×#127×C61C4semidirect
116. C2×#127#6923semidirect
124. C61#13585semidirect

Maximal subgroups

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

subgroupindex
#214620922
#214609502
#214562692
#1358561