Finite Group Databasebeta

← #30594819

Subgroups — #30594819

Order 15616.

342 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 40 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#21460749C211yesmaximal, characteristic, complemented
2#21460639C211yesmaximal, characteristic, complemented
3#21445780C211yesmaximal, characteristic
4#16840628—21no—
5#16840607—21no—
6C2×#14519825C411yescharacteristic
7C2×#14519703—21no—
8#16839764—21no—
9#16839669C2211yescharacteristic
10C2×#101×C61C411yescharacteristic
11C22×#92420—41no—
12C22⋊#92420—41no—
13#14519825—21no—
14#14519825—42no—
15#14519825—41no—
16#14519825C812yescomplemented
17C2×#11758226—41no—
18C2×#11758222—21no—
19C2×#11758222—41no—
20C2×Q8×D61—41no—
21C2×C4⋊Dic61D411yescharacteristic
22C2×C4×Dic61D411yescharacteristic
23#14519703—42no—
24#14519702—41no—
25#14519699—41no—
26#14519684—41no—
27C22×Q8×C61C2×C411yescharacteristic
28C2×M16×C61—21no—
29#101×C61—41no—
30C2×Q8×C61—21no—
31C2×Q8×C61—41no—
32C2×Q8×C61—41no—
33C2×Q8×C61C2×C811yescharacteristic
34C2×Q8×C61M1611yescharacteristic
35C22×C4×C61—21no—
36C22×C4×C61C22⋊C411yescharacteristic
37C2×C22⋊D61—41no—
38C22×Dic61—21no—
39C22×Dic61—21no—
40#11758226—42no—
41#11758226—42no—
42#11758226—44no—
43Q8×D61—42no—
44Q8×D61—42no—
45Q8×D61—44no—
46#11758222—22no—
47#11758222—22no—
48#11758222—41no—
49#11758222—42no—
50#11758222—42no—
51#11758222—41no—
52#11758222—42no—
53#11758222—42no—
54C2×D244—21no—
55C2×D244—41no—
56C2×C4×D61—41no—
57C2×C4×D61—42no—
58C2×Dic122—21no—
59C2×Dic122—41no—
60C2×#92420—42no—
61C2×#92420—81no—
62C2×#92420—81no—
63C2×#92420—81no—
64M16×C61—41no—
65M16×C61—41no—
66C2×C8×C61—41no—
67C4⋊Dic61—41no—
68C4×Dic61—41no—
69C23×C61#9911yescharacteristic
70C22×D61—41no—
71Q8×C61—42no—
72Q8×C61—41no—
73Q8×C61—41no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61C22⋊C811yescharacteristic
81C2×C4×C61#10011yescharacteristic
82C22⋊D61—42no—
83C22⋊D61—42no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—41no—
87C2×Dic61—41no—
88C2×Dic61—41no—
89C2×Dic61—41no—
90C2×Dic61—81no—
91D244—22no—
92D244—41no—
93D244—42no—
94D244—42no—
95C4×D61—42no—
96C4×D61—42no—
97C4×D61—44no—
98C4×D61—44no—
99Dic122—22no—
100Dic122—41no—
101Dic122—42no—
102Dic122—42no—
103#92420—82no—
104#92420—161no—
105C8×C61—81no—
106#7345—611nomaximal, Sylow
107C22×C61—21no—
108C22×C61—21no—
109C22×C61#32311yescharacteristic
110C22×C61AΣL(1,𝔽16)11yescharacteristic
111C22×C61AΣL(1,𝔽16)11yescharacteristic
112C2×D61—42no—
113C2×D61—81no—
114C2×D61—81no—
115C4×C61—21no—
116C4×C61—21no—
117C4×C61—41no—
118C4×C61—41no—
119Dic61—41no—
120Dic61—41no—
121Dic61—42no—
122Dic61—81no—
123#1793—611no—
124#1319—611no—
125#1272—611no—
126C2×C61—21no—
127C2×C61—21no—
128C2×C61#131611yescharacteristic
129C2×C61#140411yescharacteristic
130C2×C61#140511yescharacteristic
131D61—82no—
132C2×2−1+4—611no—
133C2×#104—1221no—
134#417—1221no—
135C2×#101#692311yescharacteristic
136#391—611no—
137#336—1221no—
138#324—1221no—
139C61#734511yescharacteristic, complemented, Sylow
1402−1+4—612no—
1412−1+4—1221no—
1422−1+4—2441no—
1432−1+4—2442no—
144C2×#41—1221no—
145C2×#41—2441no—
146C2×#41—2441no—
147C22×Q8—2441no—
148C22×Q8C2×#692311yescharacteristic
149C2×M16—21no—
150C22×C8—2441no—
151C2×C4⋊C4—611no—
152C2×C42—611no—
153#104—2442no—
154#103—2441no—
155#102—2441no—
156#101—41no—
157C22⋊C8—2441no—
158#95—2441no—
159#41—1222no—
160#41—1222no—
161#41—2441no—
162#41—2442no—
163#41—2442no—
164#41—2442no—
165#41—2442no—
166#41—2442no—
167#41—2442no—
168#41—2444no—
169#41—2441no—
170C2×Q8—21no—
171C2×Q8—41no—
172C2×Q8—41no—
173C2×Q8—1221no—
174C2×Q8—2441no—
175C2×Q8—2442no—
176C2×Q8—2442no—
177C2×Q8—2444no—
178C2×Q8D61⋊C811yescharacteristic
179C2×Q8#1175821311yescharacteristic
180C2×D4—1221no—
181C2×D4—2441no—
182C2×D4—2441no—
183C22×C4—21no—
184C22×C4—1221no—
185C22×C4—1221no—
186C22×C4—2441no—
187C22×C4—2442no—
188C22×C4C22⋊#692311yescharacteristic
189M16—41no—
190M16—41no—
191C2×C8—41no—
192C2×C8—4881no—
193C2×C8—4881no—
194C2×C8—4881no—
195C2×C8—2442no—
196C4⋊C4—2441no—
197C42—2441no—
198C23—2441no—
199C23#1451983611yescharacteristic
200Q8—41no—
201Q8—41no—
202Q8—42no—
203Q8—1222no—
204Q8—2441no—
205Q8—2442no—
206Q8—2442no—
207D4—1222no—
208D4—2441no—
209D4—2442no—
210D4—2442no—
211D4—2442no—
212D4—2442no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—4881no—
222C2×C4—2442no—
223C2×C4—2442no—
224C2×C4—2444no—
225C2×C4—2444no—
226C2×C4—2441no—
227C2×C4—2441no—
228C2×C4—2441no—
229C2×C4—2441no—
230C2×C4#1451983411yescharacteristic
231C2×C4#1451983711yescharacteristic
232C8—81no—
233C8—9761no—
234C8—4882no—
235C22—21no—
236C22—21no—
237C22—4881no—
238C22—4881no—
239C22—2442no—
240C22#1684060611yescharacteristic
241C22#1684066311yescharacteristic
242C22#1684066311yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—41no—
247C4—4881no—
248C4—2441no—
249C4—2441no—
250C4—2442no—
251C2—21no—
252C2—21no—
253C2—4882no—
254C2#2146074411yescharacteristic
255C2#2146094311yescharacteristic
256C2#2146094511yescharacteristic
subgroupG/H
centerC22#16840663
commutatorC2×Q8×C61C2×C8
FrattiniC22×Q8C2×#6923
FittingC2×#101×C61C4
socleC22×C61AΣL(1,𝔽16)
prime radicalC2×#14519825C4
cosocle#16839669C22
hypercenterC2×#101#6923
hypocenterC61#7345
LCSG ▷ C2×Q8×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
1. #21460749C2semidirect
2. #21460639C2semidirect
16. #14519825C8semidirect
139. C61#7345semidirect

Maximal subgroups

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

subgroupindex
#214607492
#214606392
#214457802
#734561