Finite Group Databasebeta

← #30604212

Subgroups — #30604212

Order 15616.

334 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 70 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#21462193C212yesmaximal, complemented
2#21460754C212yesmaximal, complemented
3#21460751C212yesmaximal, complemented
4#21454522C211yesmaximal, characteristic
5#16840684—22no—
6#16840658C2214yes—
7#16840655—22no—
8C2×#14519783C411yescharacteristic
9#16840273C411yescharacteristic
10#16839838—22no—
11#16839831—22no—
12#16839788C411yescharacteristic
13#16839728C2211yescharacteristic
14#16839726C2211yescharacteristic
15#16839717C2211yescharacteristic
16C22×M16×C61C411yescharacteristic
17#14519851—24no—
18C2×#11758222C2×C411yescharacteristic
19#14519783—42no—
20C2×#11758194C2×C411yescharacteristic
21C2×#11758194C2311yescharacteristic
22C2×#11758189—21no—
23C2×C8×D61—21no—
24#14519760—21no—
25#14519756—21no—
26#14519751—21no—
27#14519746—21no—
28C4×C22⋊D61—22no—
29#14519736C2×C411yescharacteristic
30#14519706—22no—
31C22⋊#92418—22no—
32#14519689—22no—
33#14519687D412yes—
34C8×Dic61D412yes—
35C23×C4×C61C2×C411yescharacteristic
36C2×M16×C61—21no—
37C2×M16×C61—21no—
38C2×M16×C61—42no—
39C22×C8×C61C2×C411yescharacteristic
40C22×C8×C61C2×C411yescharacteristic
41C24×C61M1611yescharacteristic
42C22×C4×C61—21no—
43C22×C4×C61—21no—
44C22×C4×C61—41no—
45C22×C4×C61—41no—
46C22×C4×C61M1611yescharacteristic
47C22×C4×C61C22×C411yescharacteristic
48C2×C22⋊D61—21no—
49C2×C22⋊D61—22no—
50#11758222—41no—
51#11758222—41no—
52C2×D244M1611yescharacteristic
53C2×C4×D61—21no—
54C2×Dic122M1611yescharacteristic
55M16×C61—42no—
56M16×C61—42no—
57C2×C8×C61—22no—
58C2×C8×C61—21no—
59C2×C8×C61—41no—
60C2×C8×C61C22⋊C411yescharacteristic
61C2×C8×C61C22⋊C411yescharacteristic
62C22⋊Dic61—22no—
63C22⋊Dic61—21no—
64#11758198—22no—
65C4⋊Dic61—21no—
66#11758196—22no—
67C4×Dic61C22⋊C412yes—
68#11758194—41no—
69#11758194—41no—
70C2×#92418—21no—
71C2×#92418C2×D412yes—
72#11758189—42no—
73C8×D61—42no—
74#11758187—44no—
75C23×C61—21no—
76C23×C61—41no—
77C23×C61—81no—
78C23×C61C2×M1611yescharacteristic
79C22×D61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—42no—
84C2×C4×C61—41no—
85C2×C4×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61C2×C22⋊C411yescharacteristic
88C2×C4×C61C2×M1611yescharacteristic
89C22⋊D61—42no—
90C22⋊D61—82no—
91C2×Dic61—22no—
92C2×Dic61—21no—
93D244—41no—
94C4×D61—41no—
95C4×D61—41no—
96Dic122—41no—
97C8×C61—21no—
98C8×C61—41no—
99C8×C61#10012yes—
100#92418—22no—
101#92418—41no—
102#11538—611nomaximal, Sylow
103C22×C61—21no—
104C22×C61—41no—
105C22×C61—41no—
106C22×C61—41no—
107C22×C61—41no—
108C22×C61—82no—
109C22×C61#40711yescharacteristic
110C2×D61—42no—
111C2×D61—41no—
112C4×C61—21no—
113C4×C61—41no—
114C4×C61#41011yescharacteristic
115C4×C61C2×#10011yescharacteristic
116Dic61—42no—
117Dic61—41no—
118#2930—611no—
119#2166—612no—
120#1321—612no—
121#1320—612no—
122C2×C61—21no—
123C2×C61—41no—
124C2×C61—81no—
125C2×C61#146611yescharacteristic
126D61—81no—
127C2×#131—611no—
128C22×M16#692311yescharacteristic
129#525—611no—
130#436—1222no—
131#435—1222no—
132#424—611no—
133#408—611no—
134#407—611no—
135#405—611no—
136#364—1222no—
137#349—614no—
138#347—1222no—
139C61#1153811yescharacteristic, complemented, Sylow
140C2×#41—611no—
141C23×C4C2×#692311yescharacteristic
142#131—2442no—
143C2×M16—21no—
144C2×M16—21no—
145C2×M16—42no—
146C2×M16—611no—
147C2×M16—611no—
148C2×M16—1221no—
149C22×C8—1221no—
150C22×C8C2×#692311yescharacteristic
151C22×C8C2×#692311yescharacteristic
152#123—1221no—
153C22⋊Q8—1221no—
154#121—1221no—
155#120—1221no—
156C4×D4—1222no—
157#117—611no—
158M32—1224no—
159C4⋊C8—1222no—
160C22⋊C8—1222no—
161C22⋊C8—1222no—
162#97—612no—
163C4×C8—612no—
164C24#1175821311yescharacteristic
165#41—2441no—
166#41—2441no—
167C2×Q8—611no—
168C2×D4—611no—
169C2×D4—1222no—
170C2×D4—1221no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—1221no—
176C22×C4#1175821311yescharacteristic
177C22×C4C22×#692311yescharacteristic
178M16—42no—
179M16—42no—
180M16—2441no—
181M16—2442no—
182M16—2441no—
183C2×C8—22no—
184C2×C8—21no—
185C2×C8—41no—
186C2×C8—612no—
187C2×C8—1221no—
188C2×C8—2442no—
189C2×C8C22⋊#692311yescharacteristic
190C2×C8C22⋊#692311yescharacteristic
191C4⋊C4—1222no—
192C4⋊C4—1221no—
193C22⋊C4—1222no—
194C22⋊C4—1222no—
195C22⋊C4—1221no—
196C42—612no—
197C16—2444no—
198C23—21no—
199C23—41no—
200C23—81no—
201C23—1221no—
202C23C2×#1175821311yescharacteristic
203Q8—2441no—
204D4—4882no—
205D4—2441no—
206D4—2442no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—1222no—
215C2×C4—1221no—
216C2×C4—2441no—
217C2×C4—2441no—
218C2×C4C2×C22⋊#692311yescharacteristic
219C2×C4D61⋊M1611yescharacteristic
220C8—21no—
221C8—41no—
222C8—1222no—
223C8—2441no—
224C8#1451983712yes—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—82no—
231C22—2442no—
232C22—2441no—
233C22#1684073311yescharacteristic
234C4—21no—
235C4—41no—
236C4—2442no—
237C4—2441no—
238C4#1684074111yescharacteristic
239C4C2×#1451983711yescharacteristic
240C2—21no—
241C2—41no—
242C2—81no—
243C2—4881no—
244C2#2146107811yescharacteristic
subgroupG/H
centerC4#16840741
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×M16×C61C4
socleC2×C61#1466
prime radical#16840273C4
cosocleC2×#11758194C23
hypercenterC22×M16#6923
hypocenterC61#11538
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C8 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
1. #21462193C2semidirect
2. #21460754C2semidirect
3. #21460751C2semidirect
139. C61#11538semidirect

Maximal subgroups

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

subgroupindex
#214621932
#214607542
#214607512
#214545222
#1153861