Finite Group Databasebeta

← #30595211

Subgroups — #30595211

Order 15616.

270 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 46 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#21462112C211yesmaximal, characteristic
2#21462092C211yesmaximal, characteristic
3#21446650C211yesmaximal, characteristic
4#16840748—21no—
5#16840741—21no—
6#16840673C412yescomplemented
7#16840671—21no—
8#16840669—21no—
9#16840667C412yescomplemented
10#16840312C2211yescharacteristic
11C2×#14519703—21no—
12C2×#14519703—21no—
13#16839608C411yescharacteristic, complemented
14C61×#423C411yescharacteristic, complemented
15D61⋊M16—41no—
16#14519856—41no—
17#14519838—22no—
18#14519837—41no—
19#14519836—22no—
20#14519835—41no—
21C2×#11758222D411yescharacteristic
22C2×#11758222D411yescharacteristic
23#14519777C2×C411yescharacteristic
24#14519774C2×C411yescharacteristic
25#14519765D411yescharacteristic
26#14519765Q811yescharacteristic
27#14519751—41no—
28C4×D244—41no—
29C2×C4×Dic61—21no—
30#14519703—42no—
31#14519703—42no—
32#14519684—41no—
33C2×M16×C61—21no—
34C2×C42×C61C2×C411yescharacteristic
35C4⋊C8×C61—41no—
36C22×C4×C61—21no—
37C22×C4×C61C22⋊C411yescharacteristic
38C2×C22⋊D61—21no—
39C2×C22⋊D61—21no—
40C22×Dic61—41no—
41#11758222—41no—
42#11758222—41no—
43#11758222—41no—
44#11758222—41no—
45C2×D244—41no—
46C2×D244C22⋊C411yescharacteristic
47C2×D244C4⋊C411yescharacteristic
48C2×C4×D61—21no—
49C2×C4×D61—21no—
50C2×Dic122C22⋊C411yescharacteristic
51C2×Dic122C4⋊C411yescharacteristic
52C22⋊#6923—42no—
53#11758217—42no—
54C4⋊#6923—81no—
55C4×#6923—81no—
56#11758213—81no—
57D61⋊C8—81no—
58M16×C61—41no—
59M16×C61—41no—
60C2×C8×C61—41no—
61C42×C61—21no—
62C42×C61C4211yescharacteristic
63C42×C61C4⋊C411yescharacteristic
64#11758198—41no—
65#11758198—41no—
66C4⋊Dic61—41no—
67C4×Dic61—22no—
68C4×Dic61—41no—
69C23×C61#9911yescharacteristic
70C22×D61—21no—
71C22×D61—21no—
72C2×#6923—82no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—81no—
78C2×C4×C61#9511yescharacteristic
79C2×C4×C61#9911yescharacteristic
80C22⋊D61—81no—
81C22⋊D61—81no—
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—42no—
85C2×Dic61—82no—
86D244—41no—
87D244—41no—
88D244—82no—
89C4×D61—41no—
90C4×D61—41no—
91C4×D61—41no—
92C4×D61—41no—
93Dic122—41no—
94Dic122—41no—
95#92420—82no—
96C8×C61—81no—
97#7503—611nomaximal, Sylow
98C22×C61—21no—
99C22×C61—41no—
100C22×C61#34211yescharacteristic
101C2×D61—41no—
102C2×D61—41no—
103C2×D61—81no—
104C2×D61—81no—
105#6923—162no—
106C4×C61—21no—
107C4×C61—41no—
108C4×C61—41no—
109C4×C61#35311yescharacteristic
110C4×C61#35411yescharacteristic
111Dic61—41no—
112Dic61—41no—
113Dic61—82no—
114#2132—611no—
115#2126—611no—
116#1963—611no—
117C2×C61—21no—
118C2×C61—41no—
119C2×C61#139311yescharacteristic
120D61—81no—
121D61—81no—
122#532—611no—
123#423#692311yescharacteristic, complemented
124C2×#104—1221no—
125C2×#104—1221no—
126#413—1221no—
127#410—1221no—
128#376—611no—
129#356—612no—
130#355—1221no—
131#354—1221no—
132#353—612no—
133C61#750311yescharacteristic, complemented, Sylow
134C2×#41—611no—
135C2×#41—611no—
136C2×M16—21no—
137C2×M16—2441no—
138C4⋊Q8—611no—
139#127—611no—
140#124—611no—
141#124—611no—
142#121—2441no—
143C4×D4—2441no—
144#117—2441no—
145C2×C42—1221no—
146C2×C42C2×#692311yescharacteristic
147C4⋊C8—41no—
148#104—2442no—
149#104—2442no—
150#101—1222no—
151#100—2441no—
152#99—1222no—
153#99—2441no—
154#95—2441no—
155#41—2441no—
156#41—2441no—
157#41—2441no—
158#41—2441no—
159C2×Q8—611no—
160C2×Q8—611no—
161C2×D4—611no—
162C2×D4—611no—
163C2×D4—1221no—
164C2×D4—1221no—
165C2×D4—2441no—
166C22×C4—21no—
167C22×C4—1221no—
168C22×C4—1221no—
169C22×C4—2441no—
170C22×C4C22⋊#692311yescharacteristic
171M16—41no—
172M16—41no—
173M16—4881no—
174M16—2442no—
175C2×C8—41no—
176C2×C8—4881no—
177C4⋊C4—4881no—
178C4⋊C4—2441no—
179C22⋊C4—2441no—
180C22⋊C4—2441no—
181C22⋊C4—2442no—
182C42—21no—
183C42—1222no—
184C42—4881no—
185C42—2441no—
186C42C4×#692311yescharacteristic
187C42C4⋊#692311yescharacteristic
188C23—1221no—
189C23—1221no—
190C23#1451983611yescharacteristic
191Q8—2441no—
192Q8—2441no—
193D4—4882no—
194D4—4881no—
195D4—4881no—
196D4—2441no—
197D4—2441no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—81no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—4882no—
206C2×C4—4882no—
207C2×C4—2442no—
208C2×C4—2441no—
209C2×C4—2441no—
210C2×C4—2441no—
211C2×C4—2441no—
212C2×C4(C2×#6923)⋊C411yescharacteristic
213C2×C4#1451983511yescharacteristic
214C8—81no—
215C8—4882no—
216C22—21no—
217C22—41no—
218C22—4881no—
219C22—4881no—
220C22—2441no—
221C22—2441no—
222C22#1684064011yescharacteristic
223C4—21no—
224C4—41no—
225C4—41no—
226C4—9762no—
227C4—4882no—
228C4—2441no—
229C4—2441no—
230C4#1684066611yescharacteristic
231C4#1684066811yescharacteristic
232C2—21no—
233C2—41no—
234C2—4881no—
235C2—4881no—
236C2#2146091411yescharacteristic
subgroupG/H
centerC4#16840668
commutatorC42×C61C42
FrattiniC2×C42C2×#6923
FittingC61×#423C4
socleC2×C61#1393
prime radical, cosocle#16840312C22
hypercenter#423#6923
hypocenterC61#7503
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
6. #16840673C4semidirect
9. #16840667C4semidirect
13. #16839608C4semidirect
14. C61×#423C4semidirect
123. #423#6923semidirect
133. C61#7503semidirect

Maximal subgroups

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

subgroupindex
#214621122
#214620922
#214466502
#750361