Finite Group Databasebeta

← #30595161

Subgroups — #30595161

Order 15616.

274 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 42 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#21461823C211yesmaximal, characteristic
2#21461323C211yesmaximal, characteristic
3#21447483C211yesmaximal, characteristic
4#16840842C411yescharacteristic, complemented
5#16840780—21no—
6#16840760—21no—
7#16840743C411yescharacteristic, complemented
8#16840633—21no—
9#16840622C412yescomplemented
10#16840620—21no—
11#16840311C2211yescharacteristic
12#16839734—21no—
13#16839557C411yescharacteristic, complemented
14#16839554—21no—
15C61×#354C411yescharacteristic, complemented
16#14519865—42no—
17D61⋊M16—21no—
18D61⋊M16—41no—
19#14519856—21no—
20#14519844—22no—
21#14519841—42no—
22#14519836—41no—
23#14519834—41no—
24C4×#92420—41no—
25C2×#11758226C2×C411yescharacteristic
26C2×#11758224D411yescharacteristic
27#14519775C2×C411yescharacteristic
28#14519773D411yescharacteristic
29#14519765Q811yescharacteristic
30#14519750—41no—
31#14519737—41no—
32#14519733—41no—
33C42×D61D411yescharacteristic
34#14519692—21no—
35#14519691—41no—
36#124×C61C2×C411yescharacteristic
37#99×C61—21no—
38C2×Q8×C61C4211yescharacteristic
39C2×D4×C61C22⋊C411yescharacteristic
40C2×C22⋊D61—21no—
41C2×C22⋊D61—41no—
42C22×Dic61—21no—
43#11758226—41no—
44#11758226—41no—
45#11758224—41no—
46#11758224—41no—
47C2×D244—21no—
48C2×D244C4⋊C411yescharacteristic
49C2×C4×D61—21no—
50C2×C4×D61—21no—
51C2×C4×D61C22⋊C411yescharacteristic
52C2×Dic122C4⋊C411yescharacteristic
53C22⋊#6923—41no—
54#11758217—41no—
55C2×#92420—42no—
56C4⋊#6923—41no—
57C4×#6923—41no—
58#11758213—22no—
59#11758213—42no—
60D61⋊C8—41no—
61D61⋊C8—42no—
62C22⋊C4×C61—41no—
63C22⋊C4×C61—41no—
64C42×C61C4⋊C411yescharacteristic
65C22⋊Dic61—41no—
66#11758198—41no—
67#11758196—41no—
68#11758196—81no—
69C4×Dic61—21no—
70C4×Dic61—81no—
71C4×Dic61C22⋊C411yescharacteristic
72C23×C61—21no—
73C22×D61—21no—
74C22×D61#9911yescharacteristic
75C2×#6923—81no—
76Q8×C61—41no—
77D4×C61—41no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—81no—
81C2×C4×C61#9511yescharacteristic
82C22⋊D61—82no—
83C22⋊D61—81no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—41no—
87C2×Dic61—41no—
88C2×Dic61—81no—
89C2×Dic61#9911yescharacteristic
90D244—41no—
91D244—42no—
92C4×D61—21no—
93C4×D61—21no—
94C4×D61—42no—
95C4×D61—41no—
96C4×D61—41no—
97Dic122—41no—
98#92420—42no—
99#92420—82no—
100#7490—611nomaximal, Sylow
101C22×C61—41no—
102C22×C61—81no—
103C22×C61#34211yescharacteristic
104C2×D61—21no—
105C2×D61—41no—
106C2×D61—41no—
107C2×D61—81no—
108#6923—161no—
109C4×C61—21no—
110C4×C61—41no—
111C4×C61—41no—
112C4×C61—161no—
113Dic61—22no—
114Dic61—41no—
115Dic61—161no—
116Dic61AΣL(1,𝔽16)11yescharacteristic
117Dic61#35211yescharacteristic
118#2126—611no—
119#1884—611no—
120#1543—611no—
121C2×C61—21no—
122C2×C61—81no—
123C2×C61#139011yescharacteristic
124D61—41no—
125D61—81no—
126#568—611no—
127#532—611no—
128#431—1221no—
129#421—1221no—
130#410—611no—
131#410—1221no—
132#354—611no—
133#354#692311yescharacteristic, complemented
134#353—1221no—
135#339—1221no—
136#333—612no—
137#331—1221no—
138C61#749011yescharacteristic, complemented, Sylow
139C2×#41—611no—
140C2×#41—611no—
141#131—2442no—
142C2×M16—1221no—
143C2×M16—2441no—
144C4⋊Q8—611no—
145#127—611no—
146#124—611no—
147#124C2×#692311yescharacteristic
148#121—2441no—
149C4×D4—2441no—
150#117—1221no—
151#117—2441no—
152C2×C42—611no—
153C4⋊C8—1222no—
154#104—2442no—
155#99—21no—
156#99—1221no—
157#99—2441no—
158#99—2441no—
159C22⋊C8—2441no—
160C4×C8—2441no—
161#41—2441no—
162#41—2441no—
163#41—2441no—
164#41—2441no—
165C2×Q8—611no—
166C2×Q8C4×#692311yescharacteristic
167C2×D4—611no—
168C2×D4—1221no—
169C2×D4—1221no—
170C2×D4—2441no—
171C2×D4C22⋊#692311yescharacteristic
172C22×C4—611no—
173C22×C4—1221no—
174C22×C4—1221no—
175C22×C4—1221no—
176M16—1222no—
177M16—2441no—
178M16—2442no—
179C2×C8—2442no—
180C2×C8—2441no—
181C2×C8—2442no—
182C4⋊C4—4881no—
183C4⋊C4—2441no—
184C4⋊C4—2441no—
185C22⋊C4—41no—
186C22⋊C4—41no—
187C22⋊C4—2441no—
188C22⋊C4—2441no—
189C22⋊C4—2441no—
190C42—611no—
191C42—1221no—
192C42—4881no—
193C42—2441no—
194C42C4⋊#692311yescharacteristic
195C23—21no—
196C23—611no—
197C23—1221no—
198Q8—41no—
199Q8—2441no—
200D4—41no—
201D4—4882no—
202D4—4881no—
203D4—2441no—
204D4—2442no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—81no—
208C2×C4—611no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—4881no—
214C2×C4—4881no—
215C2×C4—2441no—
216C2×C4—2441no—
217C2×C4—2442no—
218C2×C4—2441no—
219C2×C4—2441no—
220C2×C4(C2×#6923)⋊C411yescharacteristic
221C8—4882no—
222C8—2442no—
223C22—41no—
224C22—81no—
225C22—1221no—
226C22—4881no—
227C22—2441no—
228C22—2441no—
229C22#1684063911yescharacteristic
230C4—21no—
231C4—41no—
232C4—41no—
233C4—161no—
234C4—611no—
235C4—611no—
236C4—1222no—
237C4—9761no—
238C4—9761no—
239C4—2441no—
240C2—21no—
241C2—81no—
242C2—4881no—
243C2—2441no—
244C2#2146090211yescharacteristic
subgroupG/H
centerC2#21460902
commutatorC2×Q8×C61C42
Frattini#124C2×#6923
FittingC61×#354C4
socleC2×C61#1390
prime radical, cosocle#16840311C22
hypercenter#354#6923
hypocenterC61#7490
LCSG ▷ C2×Q8×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #354

Complements

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

NH ≅ G/Ntype
4. #16840842C4semidirect
7. #16840743C4semidirect
9. #16840622C4semidirect
13. #16839557C4semidirect
15. C61×#354C4semidirect
133. #354#6923semidirect
138. C61#7490semidirect

Maximal subgroups

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

subgroupindex
#214618232
#214613232
#214474832
#749061