Finite Group Databasebeta

← #30595177

Subgroups — #30595177

Order 15616.

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

normal subgroups only

This group has 270 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#21461822C211yesmaximal, characteristic
2#21461308C211yesmaximal, characteristic
3#21447481C211yesmaximal, characteristic
4#16840840C411yescharacteristic, complemented
5#16840785—21no—
6#16840760—21no—
7#16840742C411yescharacteristic, complemented
8#16840633—21no—
9#16840617—21no—
10#16840617C412yescomplemented
11#16840310C2211yescharacteristic
12#16839734—21no—
13#16839556—21no—
14#16839555C411yescharacteristic, complemented
15C61×#353C411yescharacteristic, complemented
16#14519864—42no—
17D61⋊M16—21no—
18C2×#11758217—41no—
19#14519856—21no—
20#14519844—41no—
21#14519841—42no—
22#14519835—41no—
23#14519834—41no—
24#14519832—22no—
25C2×#11758224C2×C411yescharacteristic
26C2×#11758224D411yescharacteristic
27#14519777Q811yescharacteristic
28#14519764C2×C411yescharacteristic
29#14519764D411yescharacteristic
30#14519748—41no—
31D4×Dic61—41no—
32#14519733—41no—
33C42×D61D411yescharacteristic
34#14519692—21no—
35#14519691—41no—
36#127×C61C2×C411yescharacteristic
37#99×C61—21no—
38C2×D4×C61—41no—
39C2×D4×C61C4211yescharacteristic
40C2×D4×C61C22⋊C411yescharacteristic
41C2×C22⋊D61—21no—
42C2×C22⋊D61—21no—
43C22×Dic61—21no—
44C22×Dic61—21no—
45#11758224—41no—
46#11758224—41no—
47#11758224—41no—
48#11758224—41no—
49C2×C4×D61—21no—
50C2×C4×D61C22⋊C411yescharacteristic
51C2×Dic122C4⋊C411yescharacteristic
52C2×Dic122C4⋊C411yescharacteristic
53C22⋊#6923—41no—
54#11758217—41no—
55#11758217—42no—
56C2×#92420—42no—
57C2×#92420—42no—
58C4⋊#6923—41no—
59C4×#6923—41no—
60#11758213—22no—
61D61⋊C8—41no—
62C22⋊C4×C61—41no—
63C42×C61C4⋊C411yescharacteristic
64C22⋊Dic61—41no—
65C22⋊Dic61—41no—
66C22⋊Dic61—41no—
67C4⋊Dic61—41no—
68#11758196—81no—
69C4×Dic61—21no—
70C4×Dic61—81no—
71C4×Dic61C22⋊C411yescharacteristic
72C23×C61—21no—
73C23×C61—21no—
74C22×D61#9911yescharacteristic
75C2×#6923—81no—
76D4×C61—41no—
77D4×C61—41no—
78D4×C61—82no—
79C2×C4×C61—21no—
80C2×C4×C61—81no—
81C2×C4×C61#9511yescharacteristic
82C22⋊D61—42no—
83C22⋊D61—81no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—41no—
88C2×Dic61—41no—
89C2×Dic61—41no—
90C2×Dic61—41no—
91C2×Dic61—81no—
92C2×Dic61#9911yescharacteristic
93C4×D61—21no—
94C4×D61—21no—
95C4×D61—81no—
96Dic122—41no—
97Dic122—41no—
98#92420—42no—
99#92420—82no—
100#7494—611nomaximal, Sylow
101C22×C61—41no—
102C22×C61—41no—
103C22×C61—81no—
104C22×C61—81no—
105C22×C61#34211yescharacteristic
106C2×D61—21no—
107C2×D61—41no—
108#6923—161no—
109C4×C61—21no—
110C4×C61—41no—
111C4×C61—161no—
112Dic61—41no—
113Dic61—41no—
114Dic61—41no—
115Dic61—161no—
116Dic61AΣL(1,𝔽16)11yescharacteristic
117Dic61#35211yescharacteristic
118#2126—611no—
119#1884—611no—
120#1536—611no—
121C2×C61—21no—
122C2×C61—81no—
123C2×C61—81no—
124C2×C61#139011yescharacteristic
125D61—41no—
126#568—611no—
127#532—611no—
128#432—1221no—
129#421—1221no—
130#410—611no—
131#410—1221no—
132#354—1221no—
133#353—611no—
134#353#692311yescharacteristic, complemented
135#339—1221no—
136#329—612no—
137#329—1221no—
138C61#749411yescharacteristic, complemented, Sylow
139C2×#41—611no—
140C2×#41—611no—
141#131—2442no—
142C2×M16—1221no—
143C2×M16—2441no—
144C4⋊Q8—611no—
145#127C2×#692311yescharacteristic
146#124—611no—
147#124—611no—
148#121—2441no—
149C4×D4—2441no—
150#117—1221no—
151#117—2441no—
152C2×C42—611no—
153C4⋊C8—2441no—
154#104—2442no—
155#99—21no—
156#99—1221no—
157#99—2441no—
158#99—2441no—
159C22⋊C8—2441no—
160#97—1222no—
161#41—2441no—
162#41—2441no—
163#41—2441no—
164#41—2441no—
165C2×Q8—611no—
166C2×Q8—611no—
167C2×D4—41no—
168C2×D4—1221no—
169C2×D4—1221no—
170C2×D4C4×#692311yescharacteristic
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—2441no—
187C22⋊C4—2441no—
188C22⋊C4—2441no—
189C22⋊C4—2441no—
190C42—611no—
191C42—1221no—
192C42—4881no—
193C42—2441no—
194C42C4⋊#692311yescharacteristic
195C23—21no—
196C23—21no—
197C23—611no—
198Q8—2441no—
199Q8—2441no—
200D4—41no—
201D4—41no—
202D4—82no—
203D4—4881no—
204D4—2442no—
205C2×C4—21no—
206C2×C4—81no—
207C2×C4—611no—
208C2×C4—1221no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—4881no—
214C2×C4—4881no—
215C2×C4—4881no—
216C2×C4—2441no—
217C2×C4—2441no—
218C2×C4—2441no—
219C2×C4—2441no—
220C2×C4(C2×#6923)⋊C411yescharacteristic
221C8—4882no—
222C8—2442no—
223C22—41no—
224C22—41no—
225C22—81no—
226C22—81no—
227C22—1221no—
228C22—2441no—
229C22#1684063911yescharacteristic
230C4—21no—
231C4—41no—
232C4—161no—
233C4—611no—
234C4—611no—
235C4—9761no—
236C4—9761no—
237C4—2441no—
238C4—2441no—
239C4—2441no—
240C2—21no—
241C2—81no—
242C2—81no—
243C2—2441no—
244C2#2146090211yescharacteristic
subgroupG/H
centerC2#21460902
commutatorC2×D4×C61C42
Frattini#127C2×#6923
FittingC61×#353C4
socleC2×C61#1390
prime radical, cosocle#16840310C22
hypercenter#353#6923
hypocenterC61#7494
LCSG ▷ C2×D4×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #353

Complements

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

NH ≅ G/Ntype
4. #16840840C4semidirect
7. #16840742C4semidirect
10. #16840617C4semidirect
14. #16839555C4semidirect
15. C61×#353C4semidirect
134. #353#6923semidirect
138. C61#7494semidirect

Maximal subgroups

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

subgroupindex
#214618222
#214613082
#214474812
#749461