Finite Group Databasebeta

← #30595160

Subgroups — #30595160

Order 15616.

302 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 44 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
1D61⋊#354C211yesmaximal, characteristic
2#21461827C211yesmaximal, characteristic
3#329×D61C211yesmaximal, characteristic
4#16840830C411yescharacteristic, complemented
5#16840754—21no—
6D61⋊#101C411yescharacteristic, complemented
7D61⋊#99—21no—
8#16840669—21no—
9#16840668C412yescomplemented
10#16840633—21no—
11#124×D61C2211yescharacteristic
12#97×D61—21no—
13#16839502C411yescharacteristic, complemented
14#16839501—21no—
15C61×#329C411yescharacteristic, complemented
16D61⋊M16—21no—
17Q8×#6923—42no—
18#14519856—21no—
19#14519856—41no—
20C2×C22⋊#6923—41no—
21#14519839—42no—
22#14519838—41no—
23#14519836—22no—
24#14519835—41no—
25C2×Q8×D61C2×C411yescharacteristic
26C2×D4×D61D411yescharacteristic
27C2×C8×D61—41no—
28#14519766C2×C411yescharacteristic
29#14519765D411yescharacteristic
30#14519764Q811yescharacteristic
31#14519763—41no—
32C22⋊C4×D61—41no—
33C42×D61D411yescharacteristic
34#14519688—21no—
35#14519687—41no—
36#124×C61C2×C411yescharacteristic
37#97×C61—21no—
38C23×D61—21no—
39C22×#6923—81no—
40C2×Q8×C61C4211yescharacteristic
41C2×D4×C61C4⋊C411yescharacteristic
42C2×C22⋊D61—21no—
43Q8×D61—41no—
44Q8×D61—41no—
45D4×D61—41no—
46D4×D61—41no—
47C2×D244C22⋊C411yescharacteristic
48C2×C4×D61—21no—
49C2×C4×D61—21no—
50C2×C4×D61C22⋊C411yescharacteristic
51C2×Dic122—21no—
52C2×Dic122C4⋊C411yescharacteristic
53C22⋊#6923—41no—
54C22⋊#6923—42no—
55C22⋊#6923—81no—
56#11758217—41no—
57C4⋊#6923—22no—
58C4⋊#6923—42no—
59C4×#6923—41no—
60C4×#6923—42no—
61#11758213—41no—
62D61⋊C8—41no—
63C2×C8×C61—41no—
64C22⋊C4×C61—41no—
65C42×C61C22⋊C411yescharacteristic
66C22⋊Dic61—41no—
67#11758198—41no—
68#11758198—41no—
69C4×Dic61—21no—
70C4×Dic61C4⋊C411yescharacteristic
71C2×#92418—41no—
72C8×D61—44no—
73C23×C61—21no—
74C22×D61—21no—
75C22×D61—41no—
76C22×D61—41no—
77C22×D61—82no—
78C22×D61#9911yescharacteristic
79C2×#6923—42no—
80C2×#6923—82no—
81C2×#6923—162no—
82Q8×C61—41no—
83D4×C61—41no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61#9511yescharacteristic
87C22⋊D61—81no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61#9911yescharacteristic
91D244—41no—
92C4×D61—21no—
93C4×D61—21no—
94C4×D61—42no—
95C4×D61—41no—
96C4×D61—41no—
97Dic122—42no—
98Dic122—41no—
99#92420—81no—
100C8×C61—42no—
101#92418—42no—
102#7489—611nomaximal, Sylow
103C22×C61—41no—
104C22×C61—81no—
105C22×C61#34211yescharacteristic
106C2×D61—22no—
107C2×D61—41no—
108C2×D61—82no—
109C2×D61—81no—
110C2×D61—161no—
111C2×D61AΣL(1,𝔽16)11yescharacteristic
112C2×D61#35211yescharacteristic
113#6923—82no—
114#6923—162no—
115C4×C61—21no—
116C4×C61—41no—
117C4×C61—41no—
118Dic61—21no—
119Dic61—41no—
120Dic61—41no—
121C2×#354—611no—
122#1888—611no—
123C2×#329—611no—
124C2×C61—21no—
125C2×C61—81no—
126C2×C61#139011yescharacteristic
127D61—21no—
128D61—81no—
129D61#140412yes—
130C2×#124—611no—
131#519—611no—
132#418—1221no—
133C2×#101—611no—
134C2×#99—1221no—
135C2×#97—1221no—
136#354—612no—
137#354—1221no—
138#339—1221no—
139#329—611no—
140#329—1221no—
141#329#692311yescharacteristic, complemented
142C61#748911yescharacteristic, complemented, Sylow
143C22×Q8—611no—
144C22×D4—611no—
145C2×M16—1221no—
146C22×C8—2441no—
147#124—611no—
148#124—611no—
149#124—611no—
150#124—2441no—
151#124C2×#692311yescharacteristic
152C4×Q8—2442no—
153#117—1221no—
154#117—2441no—
155C2×C22⋊C4—2441no—
156C2×C22⋊C4—2441no—
157C2×C42—611no—
158#102—2442no—
159#101—2441no—
160#99—1222no—
161#99—2441no—
162#97—21no—
163#97—1221no—
164#97—2441no—
165C24—1221no—
166C2×Q8—611no—
167C2×Q8—1221no—
168C2×Q8—2441no—
169C2×Q8—2441no—
170C2×Q8C4×#692311yescharacteristic
171C2×D4—611no—
172C2×D4—1221no—
173C2×D4—2441no—
174C2×D4—2441no—
175C2×D4C4⋊#692311yescharacteristic
176C22×C4—611no—
177C22×C4—1221no—
178C22×C4—1221no—
179C22×C4—4881no—
180M16—2441no—
181M16—2441no—
182C2×C8—41no—
183C2×C8—2444no—
184C2×C8—2441no—
185C2×C8—2441no—
186C4⋊C4—1222no—
187C4⋊C4—2442no—
188C22⋊C4—41no—
189C22⋊C4—4881no—
190C22⋊C4—2441no—
191C22⋊C4—2441no—
192C22⋊C4—2441no—
193C22⋊C4—2442no—
194C22⋊C4—2441no—
195C42—611no—
196C42—1221no—
197C42—2441no—
198C42—2442no—
199C42C22⋊#692311yescharacteristic
200C23—21no—
201C23—611no—
202C23—1221no—
203C23—4882no—
204C23—2441no—
205C23—2441no—
206Q8—41no—
207Q8—2441no—
208Q8—2442no—
209D4—41no—
210D4—4881no—
211D4—2441no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—611no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1221no—
219C2×C4—9762no—
220C2×C4—4882no—
221C2×C4—2441no—
222C2×C4—2441no—
223C2×C4—2442no—
224C2×C4—2442no—
225C2×C4(C2×#6923)⋊C411yescharacteristic
226C8—42no—
227C8—4881no—
228C8—2442no—
229C22—41no—
230C22—81no—
231C22—611no—
232C22—611no—
233C22—1222no—
234C22—9761no—
235C22—4881no—
236C22—4882no—
237C22—2441no—
238C22#1684063911yescharacteristic
239C4—21no—
240C4—41no—
241C4—41no—
242C4—1221no—
243C4—9762no—
244C4—4882no—
245C4—2441no—
246C4—2441no—
247C2—21no—
248C2—81no—
249C2—612no—
250C2—1221no—
251C2—4881no—
252C2#2146090511yescharacteristic
subgroupG/H
centerC2#21460905
commutatorC2×Q8×C61C42
Frattini#124C2×#6923
FittingC61×#329C4
socleC2×C61#1390
prime radicalC2×D4×D61D4
cosocle#124×D61C22
hypercenter#329#6923
hypocenterC61#7489
LCSG ▷ C2×Q8×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #329

Complements

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

NH ≅ G/Ntype
4. #16840830C4semidirect
6. D61⋊#101C4semidirect
9. #16840668C4semidirect
13. #16839502C4semidirect
15. C61×#329C4semidirect
141. #329#6923semidirect
142. C61#7489semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3542
#214618272
#329×D612
#748961