Finite Group Databasebeta

← #30595208

Subgroups — #30595208

Order 15616.

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

normal subgroups only

This group has 286 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#21461948C211yesmaximal, characteristic
3#355×D61C211yesmaximal, characteristic
4C2×#14519840—21no—
5C2×#14519839—21no—
6D61⋊#99—21no—
7C4×D61⋊C8C411yescharacteristic, complemented
8#16840706C411yescharacteristic, complemented
9#16840669C412yescomplemented
10#16840668—21no—
11#124×D61C2211yescharacteristic
12#101×D61—21no—
13#16839559C411yescharacteristic, complemented
14#16839558—21no—
15C61×#355C411yescharacteristic, complemented
16C2×D61⋊C8—21no—
17C2×C4⋊#6923—21no—
18C2×C22⋊#6923—41no—
19#14519840—42no—
20#14519839—42no—
21#14519836—22no—
22#14519835—41no—
23C4×#92420—41no—
24(C2×#6923)⋊C4—41no—
25C2×Q8×D61D411yescharacteristic
26C2×D4×D61D411yescharacteristic
27M16×D61—41no—
28#14519766D411yescharacteristic
29#14519765C2×C411yescharacteristic
30#14519764Q811yescharacteristic
31#14519763—41no—
32C22⋊C4×D61—41no—
33C42×D61C2×C411yescharacteristic
34#14519696—21no—
35#14519695—41no—
36#124×C61C2×C411yescharacteristic
37#101×C61—21no—
38C23×D61—21no—
39C22×#6923—41no—
40C22×#6923—81no—
41C2×Q8×C61C22⋊C411yescharacteristic
42C2×D4×C61C4⋊C411yescharacteristic
43C2×C22⋊D61—21no—
44Q8×D61—41no—
45Q8×D61—41no—
46D4×D61—41no—
47D4×D61—41no—
48C2×D244C22⋊C411yescharacteristic
49C2×C4×D61—21no—
50C2×C4×D61—21no—
51C2×C4×D61C22⋊C411yescharacteristic
52C2×Dic122—21no—
53C2×Dic122C4⋊C411yescharacteristic
54C22⋊#6923—42no—
55C22⋊#6923—81no—
56C2×#92420—41no—
57C4⋊#6923—41no—
58C4⋊#6923—41no—
59D61⋊C8—22no—
60D61⋊C8—41no—
61M16×C61—41no—
62C22⋊C4×C61—41no—
63C42×C61C4211yescharacteristic
64C22⋊Dic61—41no—
65#11758198—41no—
66#11758198—41no—
67C4×Dic61—21no—
68C4×Dic61C4⋊C411yescharacteristic
69#11758194—41no—
70#11758189—81no—
71C8×D61—81no—
72C23×C61—21no—
73C22×D61—21no—
74C22×D61—41no—
75C22×D61—41no—
76C22×D61—82no—
77C22×D61#9911yescharacteristic
78C2×#6923—82no—
79C2×#6923—82no—
80C2×#6923—81no—
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—41no—
98Dic122—81no—
99#92420—42no—
100C8×C61—81no—
101#92418—81no—
102#7502—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×D61#35311yescharacteristic
112C2×D61#35411yescharacteristic
113#6923—161no—
114#6923—162no—
115C4×C61—21no—
116C4×C61—41no—
117C4×C61—41no—
118Dic61—21no—
119Dic61—41no—
120Dic61—41no—
121C2×#355—611no—
122C2×#354—611no—
123#1958—611no—
124C2×C61—21no—
125C2×C61—81no—
126C2×C61#139311yescharacteristic
127D61—21no—
128D61—81no—
129D61#141412yes—
130C2×#124—611no—
131C2×#103—1221no—
132C2×#102—1221no—
133C2×#101—1221no—
134C2×#99—1221no—
135C2×C4×C8—611no—
136#382—611no—
137#355—611no—
138#355—1221no—
139#355#692311yescharacteristic, complemented
140#354—612no—
141#354—1221no—
142C61#750211yescharacteristic, complemented, Sylow
143C22×Q8—611no—
144C22×D4—611no—
145C2×M16—2441no—
146C22×C8—1221no—
147#124—611no—
148#124—611no—
149#124—611no—
150#124—2441no—
151#124C2×#692311yescharacteristic
152C2×C4⋊C4—1221no—
153C2×C22⋊C4—2441no—
154C2×C22⋊C4—2441no—
155C2×C42—611no—
156#103—2442no—
157#102—2442no—
158#101—21no—
159#101—1221no—
160#101—2441no—
161#99—1222no—
162#99—2441no—
163C4×C8—2441no—
164#95—2441no—
165C24—1221no—
166C2×Q8—611no—
167C2×Q8—1221no—
168C2×Q8—2441no—
169C2×Q8—2441no—
170C2×Q8C22⋊#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—
180C22×C4—2441no—
181M16—41no—
182M16—4881no—
183M16—2441no—
184C2×C8—1222no—
185C2×C8—4881no—
186C2×C8—2441no—
187C2×C8—2441no—
188C4⋊C4—2441no—
189C4⋊C4—2441no—
190C22⋊C4—41no—
191C22⋊C4—4881no—
192C22⋊C4—2441no—
193C22⋊C4—2441no—
194C22⋊C4—2441no—
195C22⋊C4—2442no—
196C42—611no—
197C42—1221no—
198C42C4×#692311yescharacteristic
199C23—21no—
200C23—611no—
201C23—1221no—
202C23—4882no—
203C23—2441no—
204C23—2441no—
205Q8—41no—
206Q8—4881no—
207Q8—2441no—
208D4—41no—
209D4—4881no—
210D4—2441no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—611no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—9762no—
219C2×C4—4881no—
220C2×C4—4882no—
221C2×C4—4882no—
222C2×C4—2441no—
223C2×C4—2441no—
224C2×C4—2442no—
225C2×C4(C2×#6923)⋊C411yescharacteristic
226C8—81no—
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—9761no—
244C4—9762no—
245C4—2441no—
246C4—2441no—
247C2—21no—
248C2—81no—
249C2—612no—
250C2—1221no—
251C2—4881no—
252C2#2146091211yescharacteristic
subgroupG/H
centerC2#21460912
commutatorC42×C61C42
Frattini#124C2×#6923
FittingC61×#355C4
socleC2×C61#1393
prime radicalC2×D4×D61D4
cosocle#124×D61C22
hypercenter#355#6923
hypocenterC61#7502
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #355

Complements

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

NH ≅ G/Ntype
7. C4×D61⋊C8C4semidirect
8. #16840706C4semidirect
9. #16840669C4semidirect
13. #16839559C4semidirect
15. C61×#355C4semidirect
139. #355#6923semidirect
142. C61#7502semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3542
#214619482
#355×D612
#750261