Finite Group Databasebeta

← #30595184

Subgroups — #30595184

Order 15616.

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

normal subgroups only

This group has 280 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
1D61⋊#355C211yesmaximal, characteristic
2#21461824C211yesmaximal, characteristic
3#21444441C211yesmaximal, characteristic
4#16840829C411yescharacteristic
5#16840755—21no—
6D61⋊#101—21no—
7D61⋊#100C411yescharacteristic
8#16840671—21no—
9#16840670C412yescomplemented
10#16840633—21no—
11#124×D61C2211yescharacteristic
12#16839817—21no—
13#16839502C411yescharacteristic, complemented
14#16839501—21no—
15C61×#329C411yescharacteristic, complemented
16D61⋊M16—21no—
17D61⋊M16—41no—
18D4×#6923—42no—
19#14519856—21no—
20C2×C22⋊#6923—41no—
21#14519840—42no—
22#14519838—22no—
23#14519838—41no—
24#14519837—41no—
25C2×Q8×D61D411yescharacteristic
26C2×D4×D61C2×C411yescharacteristic
27#14519766Q811yescharacteristic
28#14519765D411yescharacteristic
29#14519764C2×C411yescharacteristic
30#14519763—41no—
31C22⋊C4×D61—41no—
32C42×D61D411yescharacteristic
33#14519706—41no—
34#14519689—41no—
35#14519688—21no—
36#124×C61C2×C411yescharacteristic
37#97×C61—21no—
38C23×D61—21no—
39C22×#6923—42no—
40C2×Q8×C61C4⋊C411yescharacteristic
41C2×D4×C61C4211yescharacteristic
42C2×C22⋊D61—21no—
43Q8×D61—41no—
44Q8×D61—41no—
45D4×D61—41no—
46D4×D61—41no—
47C2×D244C4⋊C411yescharacteristic
48C2×C4×D61—21no—
49C2×C4×D61—21no—
50C2×C4×D61C22⋊C411yescharacteristic
51C2×Dic122—21no—
52C2×Dic122C22⋊C411yescharacteristic
53C22⋊#6923—41no—
54C22⋊#6923—42no—
55#11758217—42no—
56#11758217—41no—
57C4⋊#6923—22no—
58C4×#6923—41no—
59#11758213—41no—
60#11758213—81no—
61D61⋊C8—41no—
62D61⋊C8—81no—
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—
72C23×C61—21no—
73C22×D61—21no—
74C22×D61—41no—
75C22×D61—41no—
76C22×D61—82no—
77C22×D61#9911yescharacteristic
78C2×#6923—42no—
79C2×#6923—162no—
80Q8×C61—41no—
81D4×C61—41no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61#9511yescharacteristic
85C22⋊D61—42no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61#9911yescharacteristic
89D244—41no—
90C4×D61—21no—
91C4×D61—21no—
92C4×D61—41no—
93C4×D61—41no—
94C4×D61—81no—
95Dic122—41no—
96Dic122—81no—
97#92420—81no—
98#92420—82no—
99C8×C61—81no—
100#92418—81no—
101#7495—611nomaximal, Sylow
102C22×C61—41no—
103C22×C61—81no—
104C22×C61#34211yescharacteristic
105C2×D61—41no—
106C2×D61—41no—
107C2×D61—82no—
108C2×D61—81no—
109C2×D61—161no—
110C2×D61AΣL(1,𝔽16)11yescharacteristic
111C2×D61#35211yescharacteristic
112#6923—82no—
113C4×C61—21no—
114C4×C61—41no—
115C4×C61—41no—
116Dic61—21no—
117Dic61—41no—
118Dic61—41no—
119C2×#355—611no—
120#1885—611no—
121#1533—611no—
122C2×C61—21no—
123C2×C61—81no—
124C2×C61#139011yescharacteristic
125D61—21no—
126D61—21no—
127D61—81no—
128C2×#124—611no—
129#518—611no—
130#432—1221no—
131#419—1221no—
132C2×#101—1221no—
133C2×#100—611no—
134#355—612no—
135#355—1221no—
136#339—1221no—
137#329—611no—
138#329—1221no—
139#329#692311yescharacteristic, complemented
140C61#749511yescharacteristic, complemented, Sylow
141C22×Q8—611no—
142C22×D4—611no—
143C2×M16—1221no—
144C2×M16—2441no—
145#124—611no—
146#124—611no—
147#124—611no—
148#124—2441no—
149#124C2×#692311yescharacteristic
150C4×D4—2442no—
151#117—1221no—
152C2×C22⋊C4—2441no—
153C2×C22⋊C4—2441no—
154C2×C42—611no—
155C4⋊C8—2441no—
156#103—2442no—
157#101—1222no—
158#101—2441no—
159#100—2441no—
160C22⋊C8—2441no—
161#97—21no—
162#97—1221no—
163C24—1221no—
164C2×Q8—611no—
165C2×Q8—1221no—
166C2×Q8—2441no—
167C2×Q8—2441no—
168C2×Q8C4⋊#692311yescharacteristic
169C2×D4—611no—
170C2×D4—1221no—
171C2×D4—2441no—
172C2×D4—2441no—
173C2×D4C4×#692311yescharacteristic
174C22×C4—611no—
175C22×C4—1221no—
176C22×C4—1221no—
177C22×C4—2442no—
178M16—4881no—
179M16—2441no—
180M16—2442no—
181M16—2441no—
182C2×C8—41no—
183C2×C8—4881no—
184C2×C8—2441no—
185C2×C8—2441no—
186C4⋊C4—1222no—
187C22⋊C4—41no—
188C22⋊C4—2441no—
189C22⋊C4—2441no—
190C22⋊C4—2441no—
191C22⋊C4—2441no—
192C22⋊C4—2442no—
193C42—611no—
194C42—1221no—
195C42—2441no—
196C42C22⋊#692311yescharacteristic
197C23—21no—
198C23—611no—
199C23—1221no—
200C23—4882no—
201C23—2441no—
202C23—2441no—
203Q8—41no—
204Q8—4881no—
205Q8—2441no—
206D4—41no—
207D4—2441no—
208D4—2442no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—611no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—9762no—
217C2×C4—4881no—
218C2×C4—2441no—
219C2×C4—2441no—
220C2×C4—2442no—
221C2×C4(C2×#6923)⋊C411yescharacteristic
222C8—81no—
223C8—4881no—
224C8—4881no—
225C8—4882no—
226C22—41no—
227C22—81no—
228C22—611no—
229C22—611no—
230C22—9761no—
231C22—4881no—
232C22—4882no—
233C22—2441no—
234C22—2441no—
235C22#1684063911yescharacteristic
236C4—21no—
237C4—41no—
238C4—41no—
239C4—1221no—
240C4—4882no—
241C4—2441no—
242C4—2441no—
243C2—21no—
244C2—81no—
245C2—1221no—
246C2—1221no—
247C2—4881no—
248C2#2146090511yescharacteristic
subgroupG/H
centerC2#21460905
commutatorC2×D4×C61C42
Frattini#124C2×#6923
FittingC61×#329C4
socleC2×C61#1390
prime radicalC2×D4×D61C2×C4
cosocle#124×D61C22
hypercenter#329#6923
hypocenterC61#7495
LCSG ▷ C2×D4×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
9. #16840670C4semidirect
13. #16839502C4semidirect
15. C61×#329C4semidirect
139. #329#6923semidirect
140. C61#7495semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3552
#214618242
#214444412
#749561