Finite Group Databasebeta

← #30594389

Subgroups — #30594389

Order 15616.

364 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C4×#14519837C211yesmaximal, characteristic
2#21461054C211yesmaximal, characteristic
3#21446111C211yesmaximal, characteristic
4C2×#14519837C412yes—
5D61⋊(C22⋊C8)—21no—
6C4×#11758217—21no—
7#16840642—21no—
8#16840608—21no—
9#16840605C412yes—
10C2×C4×C22⋊D61C2211yescharacteristic
11C2×C22⋊#92418C411yescharacteristic
12C2×#14519689—21no—
13#16839516—21no—
14C23×C8×C61C411yescharacteristic
15C2×#11758217—22no—
16C2×D61⋊C8—41no—
17#14519837—22no—
18#14519837C814yescomplemented
19#14519834—41no—
20C22⋊#92420—22no—
21#14519832—41no—
22C4×#92420—41no—
23C22×C22⋊D61C2×C411yescharacteristic
24C22×C4×D61D411yescharacteristic
25C22×#92418—21no—
26C4×C22⋊D61—41no—
27C4×C22⋊D61—41no—
28C2×#11758196D411yescharacteristic
29C2×C22⋊Dic61C2×C411yescharacteristic
30C2×#11758198Q811yescharacteristic
31C2×C4×Dic61D411yescharacteristic
32C22⋊#92418—41no—
33#14519689—42no—
34C23×C4×C61C2×C411yescharacteristic
35C22×C8×C61—21no—
36C22×C8×C61—42no—
37C22×C8×C61—41no—
38C24×C61C4211yescharacteristic
39C23×D61C4⋊C411yescharacteristic
40C22×C4×C61—21no—
41C22×C4×C61—21no—
42C22×C4×C61—41no—
43C22×C4×C61—41no—
44C22×C4×C61C22⋊C411yescharacteristic
45C22×C4×C61C4⋊C411yescharacteristic
46C2×C22⋊D61—41no—
47C2×C22⋊D61—41no—
48C2×C22⋊D61C2×C812yes—
49C2×C22⋊D61M1612yes—
50C22×Dic61C22⋊C411yescharacteristic
51C22×Dic61C22⋊C411yescharacteristic
52C22×Dic61C4⋊C411yescharacteristic
53C2×C4×D61—21no—
54C2×C4×D61—21no—
55C2×C4×D61—41no—
56C2×C4×D61—41no—
57#11758217—24no—
58#11758217—42no—
59C2×#92420—42no—
60C2×#92420—42no—
61D61⋊C8—81no—
62D61⋊C8—81no—
63C2×C8×C61—22no—
64C2×C8×C61—41no—
65C2×C8×C61—42no—
66C2×C8×C61—41no—
67C2×C8×C61—42no—
68C22⋊Dic61—41no—
69#11758198—41no—
70#11758196—41no—
71C4×Dic61—21no—
72C4×Dic61—21no—
73C2×#92418—41no—
74C2×#92418—41no—
75C2×#92418—41no—
76C23×C61—21no—
77C23×C61—21no—
78C23×C61—41no—
79C23×C61—41no—
80C23×C61#9511yescharacteristic
81C23×C61C4×C811yescharacteristic
82C23×C61#9711yescharacteristic
83C22×D61—21no—
84C22×D61—21no—
85C22×D61—41no—
86C22×D61—41no—
87C22×D61C4⋊C812yes—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—42no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61#9911yescharacteristic
96C2×C4×C61#9911yescharacteristic
97C22⋊D61—42no—
98C22⋊D61—42no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61C22⋊C812yes—
106C4×D61—41no—
107C4×D61—41no—
108C4×D61—81no—
109#92420—44no—
110#92420—82no—
111C8×C61—42no—
112#92418—81no—
113#7203—611nomaximal, Sylow
114C22×C61—21no—
115C22×C61—21no—
116C22×C61—21no—
117C22×C61—21no—
118C22×C61—41no—
119C22×C61—41no—
120C22×C61—42no—
121C22×C61—41no—
122C22×C61—41no—
123C22×C61#33611yescharacteristic
124C22×C61#34211yescharacteristic
125C22×C61#34411yescharacteristic
126C2×D61—22no—
127C2×D61—41no—
128C2×D61—41no—
129C2×D61—42no—
130C2×D61—81no—
131C4×C61—21no—
132C4×C61—41no—
133C4×C61AΣL(1,𝔽16)11yescharacteristic
134C4×C61#35211yescharacteristic
135Dic61—22no—
136Dic61—41no—
137Dic61—41no—
138#1869—611no—
139C4×#100—611no—
140#1459—611no—
141C2×C61—21no—
142C2×C61—21no—
143C2×C61—41no—
144C2×C61—41no—
145C2×C61#128211yescharacteristic
146C2×C61#139011yescharacteristic
147C2×C61#139211yescharacteristic
148D61—42no—
149C23×C8#692311yescharacteristic
150C2×C4×D4—611no—
151C2×#100—612no—
152C2×C22⋊C8—611no—
153C2×C22⋊C8—1221no—
154C2×C22⋊C8—1221no—
155C4×M16—1221no—
156#343—1221no—
157#336—1221no—
158#324—1221no—
159#323—612no—
160C61#720311yescharacteristic, complemented, Sylow
161C22×D4—611no—
162C23×C4—611no—
163C23×C4C2×#692311yescharacteristic
164C2×M16—1222no—
165C22×C8—21no—
166C22×C8—42no—
167C22×C8—41no—
168C22×C8—1221no—
169C22×C8—2441no—
170C4×D4—2441no—
171C4×D4—2441no—
172C2×C4⋊C4—611no—
173C2×C22⋊C4—611no—
174C2×C22⋊C4—611no—
175C2×C42—611no—
176#100—614no—
177#100—1222no—
178C22⋊C8—1222no—
179C22⋊C8—2442no—
180C22⋊C8—2441no—
181C22⋊C8—2441no—
182#97—2441no—
183C4×C8—2441no—
184C24—611no—
185C24C4×#692311yescharacteristic
186C2×D4—612no—
187C2×D4—612no—
188C2×D4—2441no—
189C2×D4—2441no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—611no—
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—1221no—
198C22×C4—1221no—
199C22×C4—2441no—
200C22×C4—2441no—
201C22×C4C4⋊#692311yescharacteristic
202C22×C4C22⋊#692311yescharacteristic
203M16—1224no—
204M16—2442no—
205C2×C8—22no—
206C2×C8—41no—
207C2×C8—42no—
208C2×C8—41no—
209C2×C8—42no—
210C2×C8—4881no—
211C2×C8—4881no—
212C2×C8—2441no—
213C2×C8—2441no—
214C2×C8—2442no—
215C2×C8—2441no—
216C2×C8—2442no—
217C4⋊C4—2441no—
218C22⋊C4—2441no—
219C22⋊C4—2441no—
220C42—1221no—
221C42—1221no—
222C23—21no—
223C23—21no—
224C23—41no—
225C23—41no—
226C23—612no—
227C23—1221no—
228C23—1221no—
229C23—2441no—
230C23—2441no—
231C23(C2×#6923)⋊C411yescharacteristic
232C23C8×#692311yescharacteristic
233C23#1451983111yescharacteristic
234D4—2442no—
235D4—2442no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—612no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—4881no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4#1451983511yescharacteristic
254C2×C4#1451983611yescharacteristic
255C8—42no—
256C8—4881no—
257C8—4882no—
258C8—2444no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—41no—
264C22—41no—
265C22—42no—
266C22—41no—
267C22—41no—
268C22—1222no—
269C22—4881no—
270C22—2442no—
271C22—2441no—
272C22—2441no—
273C22(C2×#6923)⋊C811yescharacteristic
274C22#1684064011yescharacteristic
275C22#1684064411yescharacteristic
276C4—21no—
277C4—41no—
278C4—1222no—
279C4—2441no—
280C4—2441no—
281C4#1684066211yescharacteristic
282C4#1684066411yescharacteristic
283C2—21no—
284C2—21no—
285C2—41no—
286C2—41no—
287C2—2442no—
288C2#2146066111yescharacteristic
289C2#2146090311yescharacteristic
290C2#2146091011yescharacteristic
subgroupG/H
centerC2×C4#14519835
commutatorC23×C61C4×C8
FrattiniC23×C4C2×#6923
FittingC23×C8×C61C4
socleC22×C61#342
prime radicalC22×C22⋊D61C2×C4
cosocleC2×C4×C22⋊D61C22
hypercenterC23×C8#6923
hypocenterC61#7203
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
18. #14519837C8semidirect
160. C61#7203semidirect

Maximal subgroups

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

subgroupindex
C4×#145198372
#214610542
#214461112
#720361