Finite Group Databasebeta

← #30594658

Subgroups — #30594658

Order 15616.

324 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 58 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#21461058C211yesmaximal, characteristic
2#21461054C211yesmaximal, characteristic
3#21446114C211yesmaximal, characteristic
4#16840779—21no—
5D61⋊(C22⋊C8)—21no—
6#16840608C412yes—
7#16840606C412yes—
8#16840605—21no—
9#16840605—21no—
10C22×#11758194C411yescharacteristic
11C2×C4×C22⋊D61C2211yescharacteristic
12C2×#14519689—21no—
13#16839516—21no—
14C2×C22⋊C8×C61C411yescharacteristic
15C2×D61⋊C8—41no—
16#14519844—41no—
17#14519834—41no—
18C22⋊#92420—22no—
19C22⋊#92420—22no—
20C4×#92420—41no—
21C22×C22⋊D61Q811yescharacteristic
22C22×C4×D61D411yescharacteristic
23C2×#11758194—42no—
24C2×#11758194—41no—
25C22×#92418—21no—
26C4×C22⋊D61—41no—
27C4×C22⋊D61—41no—
28C2×#11758196C2×C411yescharacteristic
29C2×C22⋊Dic61D411yescharacteristic
30C2×#11758198C2×C411yescharacteristic
31C2×C4×Dic61D411yescharacteristic
32#14519689—42no—
33C23×C4×C61C2×C411yescharacteristic
34C22×C8×C61—21no—
35C22⋊C8×C61—41no—
36C24×C61C4⋊C411yescharacteristic
37C23×D61C4⋊C411yescharacteristic
38C22×C4×C61—21no—
39C22×C4×C61—21no—
40C22×C4×C61—41no—
41C22×C4×C61—41no—
42C22×C4×C61C4211yescharacteristic
43C22×C4×C61C22⋊C411yescharacteristic
44C2×C22⋊D61—22no—
45C2×C22⋊D61—22no—
46C2×C22⋊D61—41no—
47C22×Dic61C22⋊C411yescharacteristic
48C22×Dic61C22⋊C411yescharacteristic
49C22×Dic61C4⋊C411yescharacteristic
50C2×C4×D61—21no—
51C2×C4×D61—21no—
52C2×C4×D61—41no—
53C2×C4×D61—41no—
54C2×#92420—42no—
55C2×#92420—42no—
56D61⋊C8—81no—
57D61⋊C8—81no—
58C2×C8×C61—41no—
59C2×C8×C61—41no—
60C2×C8×C61—41no—
61C22⋊Dic61—41no—
62#11758198—41no—
63#11758196—41no—
64C4×Dic61—21no—
65C4×Dic61—21no—
66#11758194—42no—
67#11758194—42no—
68C2×#92418—22no—
69C2×#92418—41no—
70C2×#92418—41no—
71C23×C61—21no—
72C23×C61—21no—
73C23×C61—21no—
74C23×C61—41no—
75C23×C61—41no—
76C23×C61#9511yescharacteristic
77C22×D61—21no—
78C22×D61—21no—
79C22×D61—41no—
80C22×D61—41no—
81C22×D61#10812yes—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—42no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61—41no—
89C2×C4×C61#9911yescharacteristic
90C2×C4×C61#9911yescharacteristic
91C22⋊D61—44no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—41no—
97C2×Dic61—41no—
98C2×Dic61#10812yes—
99C4×D61—41no—
100C4×D61—41no—
101C4×D61—81no—
102#92420—82no—
103#92420—82no—
104C8×C61—81no—
105#92418—42no—
106#7285—611nomaximal, Sylow
107C22×C61—21no—
108C22×C61—21no—
109C22×C61—41no—
110C22×C61—41no—
111C22×C61—41no—
112C22×C61—81no—
113C22×C61—81no—
114C22×C61#34111yescharacteristic
115C22×C61#34111yescharacteristic
116C22×C61#34211yescharacteristic
117C2×D61—22no—
118C2×D61—41no—
119C2×D61—41no—
120C2×D61—42no—
121C2×D61—81no—
122C4×C61—21no—
123C4×C61—41no—
124C4×C61AΣL(1,𝔽16)11yescharacteristic
125C4×C61#35211yescharacteristic
126Dic61—22no—
127Dic61—41no—
128Dic61—41no—
129#1870—611no—
130#1460—611no—
131#1459—611no—
132C2×C61—21no—
133C2×C61—21no—
134C2×C61—81no—
135C2×C61#129811yescharacteristic
136C2×C61#139011yescharacteristic
137C2×C61#139511yescharacteristic
138D61—42no—
139C22×M16—611no—
140C2×C4×D4—611no—
141#431—1221no—
142C2×C22⋊C8—1221no—
143C2×C22⋊C8—1221no—
144C2×C22⋊C8#692311yescharacteristic
145#336—1221no—
146#324—612no—
147#323—612no—
148#323—1221no—
149#323—1221no—
150C61#728511yescharacteristic, complemented, Sylow
151C22×D4—611no—
152C23×C4—611no—
153C23×C4C2×#692311yescharacteristic
154C2×M16—2442no—
155C2×M16—2441no—
156C22×C8—21no—
157C22×C8—1221no—
158C22×C8—2441no—
159C4×D4—2441no—
160C4×D4—2441no—
161C2×C4⋊C4—611no—
162C2×C22⋊C4—611no—
163C2×C22⋊C4—611no—
164C2×C42—611no—
165C4⋊C8—2441no—
166C22⋊C8—41no—
167C22⋊C8—1222no—
168C22⋊C8—1222no—
169C22⋊C8—2442no—
170C22⋊C8—2441no—
171C4×C8—2441no—
172C24—611no—
173C24C4⋊#692311yescharacteristic
174C2×D4—1222no—
175C2×D4—1222no—
176C2×D4—2441no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—611no—
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—1221no—
185C22×C4—1221no—
186C22×C4—2441no—
187C22×C4—2441no—
188C22×C4C4×#692311yescharacteristic
189C22×C4C22⋊#692311yescharacteristic
190M16—2442no—
191M16—2442no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—1222no—
196C2×C8—4881no—
197C2×C8—4881no—
198C2×C8—2442no—
199C2×C8—2442no—
200C2×C8—2441no—
201C2×C8—2441no—
202C4⋊C4—2441no—
203C22⋊C4—2441no—
204C22⋊C4—2441no—
205C42—1221no—
206C42—1221no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—41no—
211C23—41no—
212C23—612no—
213C23—1221no—
214C23—1221no—
215C23—2441no—
216C23—2441no—
217C23(C2×#6923)⋊C411yescharacteristic
218D4—2444no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—612no—
227C2×C4—1221no—
228C2×C4—1221no—
229C2×C4—1221no—
230C2×C4—1221no—
231C2×C4—4881no—
232C2×C4—2441no—
233C2×C4—2441no—
234C2×C4—2441no—
235C2×C4—2441no—
236C2×C4#1451983511yescharacteristic
237C2×C4#1451983611yescharacteristic
238C8—81no—
239C8—4882no—
240C8—4882no—
241C8—2442no—
242C22—21no—
243C22—21no—
244C22—41no—
245C22—41no—
246C22—41no—
247C22—81no—
248C22—81no—
249C22—1222no—
250C22—4881no—
251C22—2442no—
252C22—2441no—
253C22—2441no—
254C22#1684063711yescharacteristic
255C22#1684063711yescharacteristic
256C22#1684064011yescharacteristic
257C4—21no—
258C4—41no—
259C4—1222no—
260C4—2441no—
261C4—2441no—
262C4#1684066311yescharacteristic
263C4#1684066511yescharacteristic
264C2—21no—
265C2—21no—
266C2—81no—
267C2—2442no—
268C2#2146070111yescharacteristic
269C2#2146090411yescharacteristic
270C2#2146091911yescharacteristic
subgroupG/H
centerC2×C4#14519836
commutatorC22×C4×C61C42
FrattiniC23×C4C2×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61#342
prime radicalC22×C22⋊D61Q8
cosocleC2×C4×C22⋊D61C22
hypercenterC2×C22⋊C8#6923
hypocenterC61#7285
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
150. C61#7285semidirect

Maximal subgroups

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

subgroupindex
#214610582
#214610542
#214461142
#728561