Finite Group Databasebeta

← #30605580

Subgroups — #30605580

Order 15616.

306 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 94 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⋊(C4⋊C16)C211yesmaximal, characteristic
2#21461369C211yesmaximal, characteristic
3#21460835C214yesmaximal, complemented
4#21456330C211yesmaximal, characteristic
5C2×D61⋊C16—21no—
6#16840781—21no—
7#16840683C2212yes—
8C4⋊#11758187—21no—
9#16840625—21no—
10#16840624C2212yes—
11#16840317—21no—
12#16840167C411yescharacteristic
13#16840163—21no—
14#16840163C2212yes—
15#16840158—21no—
16#16839799—21no—
17#16839799C412yes—
18C4×C8×D61C2211yescharacteristic
19C61×#500C411yescharacteristic
20D61⋊C16—42no—
21C2×#11758187—22no—
22C4⋊#92420—22no—
23#14519834—41no—
24C4×#92420—41no—
25C2×C8×D61C2×C411yescharacteristic
26C2×C8×D61D411yescharacteristic
27#14519777—21no—
28#14519768—22no—
29#14519757—41no—
30#14519753—41no—
31Q8×Dic61—41no—
32#14519742—41no—
33#14519735—22no—
34C42×D61D411yescharacteristic
35#14519711—21no—
36#14519711C2×C412yes—
37#14519708—22no—
38#14519708—22no—
39C4×#92418D411yescharacteristic
40C8×Dic61D411yescharacteristic
41C8×Dic61C2311yescharacteristic
42C4⋊Q8×C61—21no—
43#107×C61—21no—
44#107×C61C2×C412yes—
45C4×C8×C61C2×C411yescharacteristic
46C2×Q8×C61—41no—
47C2×C4×D61C22⋊C411yescharacteristic
48C2×C4×D61D811yescharacteristic
49C2×C4×D61SD1611yescharacteristic
50C2×Dic122—41no—
51C2×#92420—42no—
52C2×C8×C61C22⋊C411yescharacteristic
53C2×C8×C61C22×C411yescharacteristic
54C4⋊C4×C61—22no—
55C4⋊C4×C61—41no—
56C42×C61C22⋊C411yescharacteristic
57#11758198—42no—
58C4⋊Dic61—22no—
59C4⋊Dic61—41no—
60C4⋊Dic61—42no—
61#11758196—42no—
62C4×Dic61—42no—
63C4×Dic61D811yescharacteristic
64C4×Dic61SD1611yescharacteristic
65C4×Dic61C2×D411yescharacteristic
66C2×#92418C22⋊C411yescharacteristic
67C2×#92418C2×D411yescharacteristic
68C8×D61—22no—
69C8×D61SD1612yes—
70C8×D61Q1612yes—
71#11758187—42no—
72C22×D61#10211yescharacteristic
73Q8×C61—82no—
74C2×C4×C61—42no—
75C2×C4×C61#10211yescharacteristic
76C2×C4×C61#10211yescharacteristic
77C2×C4×C61C2×C22⋊C411yescharacteristic
78C2×Dic61—42no—
79C2×Dic61#10211yescharacteristic
80C2×Dic61C2×D811yescharacteristic
81C2×Dic61C2×SD1611yescharacteristic
82C4×D61—22no—
83C4×D61—41no—
84C4×D61#10112yes—
85C4×D61#10312yes—
86Dic122—82no—
87#92420—82no—
88C8×C61—21no—
89C8×C61#10312yes—
90#92418—21no—
91#92418C2×SD1611yescharacteristic
92#92418C2×Q1611yescharacteristic
93#11934—611nomaximal, Sylow
94C22×C61C2×#10211yescharacteristic
95C2×D61—21no—
96C2×D61—21no—
97C2×D61#33212yes—
98C4×C61—21no—
99C4×C61—82no—
100C4×C61#35912yes—
101C4×C61C2×#10111yescharacteristic
102C4×C61C2×#10311yescharacteristic
103Dic61—21no—
104Dic61—21no—
105Dic61—82no—
106Dic61#33212yes—
107#3160—611no—
108C2×C4⋊C16—611no—
109#1564—611no—
110#1363—614no—
111C2×C61C2×#33211yescharacteristic
112C2×C61C2×#35911yescharacteristic
113C2×C61#214511yescharacteristic
114D61—22no—
115#533—1221no—
116C22×C16—1221no—
117#500—611no—
118#500#692311yescharacteristic
119#499—612no—
120#499—1221no—
121#498—1221no—
122#431—1221no—
123#427—612no—
124#427—1221no—
125C2×C4×C8—611no—
126C4⋊C16—612no—
127C4⋊C16—1221no—
128#335—1221no—
129#334—612no—
130C61#1193411yescharacteristic, complemented, Sylow
131C22×C8—611no—
132C22×C8—611no—
133C4⋊Q8—21no—
134C4⋊Q8—1221no—
135#125—1222no—
136C22⋊Q8—2441no—
137C22⋊Q8—2441no—
138C4×Q8—2441no—
139C4×Q8—2441no—
140#117—1222no—
141C2×C42—611no—
142C2×C16—1222no—
143C2×C16—2442no—
144#107—21no—
145#107—612no—
146#107—1221no—
147#107C2×#692312yes—
148#106—1222no—
149#106—1222no—
150C4⋊C8—1222no—
151C22⋊C8—2441no—
152C4×C8—611no—
153C4×C8—611no—
154C4×C8—611no—
155C4×C8—2441no—
156C4×C8C2×#692311yescharacteristic
157C2×Q8—41no—
158C2×Q8—2441no—
159C22×C4—611no—
160C22×C4—611no—
161C22×C4—611no—
162C2×C8—611no—
163C2×C8—612no—
164C2×C8—612no—
165C2×C8—611no—
166C2×C8—1222no—
167C2×C8—2442no—
168C2×C8C22⋊#692311yescharacteristic
169C2×C8C22×#692311yescharacteristic
170C4⋊C4—22no—
171C4⋊C4—41no—
172C4⋊C4—1222no—
173C4⋊C4—2442no—
174C4⋊C4—2442no—
175C4⋊C4—2441no—
176C22⋊C4—2442no—
177C42—611no—
178C42—611no—
179C42—611no—
180C42—2442no—
181C42C22⋊#692311yescharacteristic
182C16—2442no—
183C23—611no—
184Q8—82no—
185Q8—4882no—
186C2×C4—42no—
187C2×C4—611no—
188C2×C4—612no—
189C2×C4—612no—
190C2×C4—611no—
191C2×C4—611no—
192C2×C4—1222no—
193C2×C4—2441no—
194C2×C4—2442no—
195C2×C4#1451983911yescharacteristic
196C2×C4#1451983911yescharacteristic
197C2×C4C2×C22⋊#692311yescharacteristic
198C8—21no—
199C8—611no—
200C8—611no—
201C8—1221no—
202C8—4882no—
203C8#1451984012yes—
204C22—612no—
205C22—1221no—
206C22—1221no—
207C22C2×#1451983911yescharacteristic
208C4—21no—
209C4—82no—
210C4—612no—
211C4—1221no—
212C4—1221no—
213C4—4882no—
214C4#1684067612yes—
215C4D61⋊#10111yescharacteristic
216C4C2×#1451984011yescharacteristic
217C2—1222no—
218C2D61⋊#33211yescharacteristic
219C2C2×#1684067611yescharacteristic
220C2#2146214111yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#500C4
socleC22×C61C2×#102
prime radicalC22×D61#102
cosocleC8×Dic61C23
hypercenter#500#6923
hypocenterC61#11934
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #500

Complements

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

NH ≅ G/Ntype
3. #21460835C2semidirect
130. C61#11934semidirect

Maximal subgroups

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

subgroupindex
D61⋊(C4⋊C16)2
#214613692
#214608352
#214563302
#1193461