Finite Group Databasebeta

← #30597305

Subgroups — #30597305

Order 15616.

942 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 942 conjugacy classes of subgroups — too many to draw. Only its 148 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⋊#407C212yesmaximal
2#21460722C214yesmaximal, complemented
3#381×D61C211yesmaximal, characteristic
4C2×D61⋊M16—22no—
5#16840734—22no—
6#16840733—22no—
7#16840733C414yescomplemented
8#16840732C2214yes—
9D61⋊(C22⋊C8)—22no—
10D61⋊(C22⋊C8)C414yescomplemented
11C23×C4×D61C2211yescharacteristic
12C2×C22⋊C4×D61C412yes—
13#16839625C411yescharacteristic
14#16839624—22no—
15#16839623C2212yes—
16#95×D61—22no—
17C61×#381C411yescharacteristic
18C2×#11758213—24no—
19D61⋊M16—48no—
20C2×#11758217—24no—
21C2×D61⋊C8—24no—
22#14519834—24no—
23#14519834—24no—
24C22⋊#92420—24no—
25C22⋊#92420C2×C418yescomplemented
26C24×D61C2×C411yescharacteristic
27C23×Dic61C2311yescharacteristic
28C22×C4×D61—22no—
29C22×C4×D61—44no—
30C22×C4×D61C2×C412yes—
31C22×C4×D61C2×C412yes—
32C22×C4×D61D412yes—
33C22×C4×D61D412yes—
34C22×C4×D61D412yes—
35C22×C4×D61Q812yes—
36C2×C22⋊Dic61C2×C412yes—
37C2×#11758198—22no—
38C22⋊C4×D61—44no—
39#14519684—22no—
40#14519684—24no—
41C23×C4×C61C2×C411yescharacteristic
42C2×C22⋊C4×C61C2×C412yes—
43#95×C61—22no—
44C24×C61C22×C411yescharacteristic
45C23×D61—24no—
46C23×D61—44no—
47C23×D61C4212yes—
48C23×D61C22⋊C411yescharacteristic
49C23×D61C22⋊C411yescharacteristic
50C23×D61C4⋊C412yes—
51C22×C4×C61—22no—
52C22×C4×C61—42no—
53C22×C4×C61C4211yescharacteristic
54C22×C4×C61C4211yescharacteristic
55C22×C4×C61C22⋊C412yes—
56C22×C4×C61C4⋊C412yes—
57C22×Dic61—22no—
58C22×Dic61—42no—
59C22×Dic61C22×C412yes—
60C22×Dic61C2×D412yes—
61C22×Dic61C2×D411yescharacteristic
62C22×Dic61C2×Q811yescharacteristic
63C2×C4×D61—28no—
64C2×C4×D61—44no—
65C2×C4×D61—44no—
66C2×C4×D61—44no—
67C2×C4×D61—44no—
68C2×C4×D61—44no—
69C2×C4×D61—48no—
70C2×C4×D61—44no—
71C2×C4×D61C22⋊C412yes—
72C2×C4×D61C22⋊C412yes—
73C2×C4×D61C22⋊C412yes—
74C2×C4×D61C22⋊C412yes—
75C2×C4×D61C4⋊C412yes—
76C2×C4×D61C4⋊C412yes—
77C2×C4×D61C4⋊C412yes—
78C2×C4×D61C4⋊C412yes—
79#11758217—48no—
80C2×#92420—28no—
81#11758213—48no—
82D61⋊C8—48no—
83C22⋊C4×C61—42no—
84C22⋊Dic61—42no—
85#11758198—44no—
86C23×C61—22no—
87C23×C61—42no—
88C23×C61C2×C4211yescharacteristic
89C23×C61C2×C22⋊C411yescharacteristic
90C23×C61C2×C4⋊C411yescharacteristic
91C22×D61—22no—
92C22×D61—24no—
93C22×D61—24no—
94C22×D61—24no—
95C22×D61—24no—
96C22×D61—24no—
97C22×D61—42no—
98C22×D61—42no—
99C22×D61—42no—
100C22×D61—416no—
101C22×D61#9512yes—
102C22×D61#9512yes—
103C22×D61#9914yes—
104C2×C4×C61—24no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—42no—
108C2×C4×C61—44no—
109C2×C4×C61—42no—
110C2×C4×C61#9512yes—
111C2×C4×C61#9512yes—
112C2×Dic61—24no—
113C2×Dic61—42no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—44no—
117C2×Dic61—42no—
118C2×Dic61C2×C22⋊C412yes—
119C2×Dic61C2×C4⋊C412yes—
120C4×D61—24no—
121C4×D61—24no—
122C4×D61—24no—
123C4×D61—24no—
124C4×D61—42no—
125C4×D61—42no—
126C4×D61—42no—
127C4×D61—42no—
128C4×D61—88no—
129#92420—48no—
130#8114—611nomaximal, Sylow
131C22×C61—22no—
132C22×C61—21no—
133C22×C61—21no—
134C22×C61—22no—
135C22×C61—22no—
136C22×C61—44no—
137C22×C61C2×#9511yescharacteristic
138C22×C61C2×#9912yes—
139C2×D61—28no—
140C2×D61—22no—
141C2×D61—22no—
142C2×D61—22no—
143C2×D61—22no—
144C2×D61—44no—
145C2×D61—48no—
146C2×D61—48no—
147C2×D61#34214yes—
148C2×D61#34414yes—
149C4×C61—22no—
150C4×C61—22no—
151C4×C61—82no—
152Dic61—22no—
153Dic61—22no—
154Dic61—82no—
155C2×#407—612no—
156C2×#381—611no—
157#1306—614no—
158C2×C61—22no—
159C2×C61—41no—
160C2×C61—41no—
161C2×C61C2×#34211yescharacteristic
162C2×C61C2×#34412yes—
163D61—24no—
164D61—24no—
165C24×C4—611no—
166C22×M16—1222no—
167C22×C22⋊C4—612no—
168#407—614no—
169#407—614no—
170#407—1222no—
171#407—1222no—
172C2×C22⋊C8—614no—
173C2×C22⋊C8—1222no—
174#381—611no—
175#381—612no—
176#381—1222no—
177#381#692311yescharacteristic
178C2×#95—1222no—
179C61#811411yescharacteristic, complemented, Sylow
180C25—611no—
181C23×C4—611no—
182C23×C4—612no—
183C23×C4—612no—
184C23×C4—612no—
185C23×C4—612no—
186C23×C4—612no—
187C23×C4—612no—
188C23×C4—1222no—
189C23×C4—2444no—
190C23×C4C2×#692311yescharacteristic
191C2×M16—1224no—
192C2×M16—1224no—
193C2×M16—2448no—
194C22×C8—1224no—
195C2×C22⋊C4—612no—
196C2×C22⋊C4—1222no—
197C2×C22⋊C4—2444no—
198C2×C22⋊C4C2×#692312yes—
199C22⋊C8—618no—
200C22⋊C8—1224no—
201C22⋊C8—1224no—
202C22⋊C8—1224no—
203#95—22no—
204#95—1224no—
205#95—1222no—
206C24—611no—
207C24—611no—
208C24—612no—
209C24—612no—
210C24—1224no—
211C24—2444no—
212C24C22×#692311yescharacteristic
213C22×C4—22no—
214C22×C4—42no—
215C22×C4—612no—
216C22×C4—612no—
217C22×C4—611no—
218C22×C4—611no—
219C22×C4—612no—
220C22×C4—612no—
221C22×C4—612no—
222C22×C4—612no—
223C22×C4—612no—
224C22×C4—612no—
225C22×C4—612no—
226C22×C4—612no—
227C22×C4—1228no—
228C22×C4—1222no—
229C22×C4—2444no—
230C22×C4—2444no—
231C22×C4—2444no—
232C22×C4—2444no—
233C22×C4—2444no—
234C22×C4—2444no—
235C22×C4—2448no—
236C22×C4—2442no—
237C22×C4C4×#692311yescharacteristic
238C22×C4C4×#692311yescharacteristic
239C22×C4C4⋊#692312yes—
240C22×C4C22⋊#692312yes—
241M16—2448no—
242M16—2448no—
243C2×C8—1228no—
244C2×C8—2448no—
245C22⋊C4—42no—
246C22⋊C4—2444no—
247C22⋊C4—2442no—
248C23—22no—
249C23—42no—
250C23—612no—
251C23—612no—
252C23—614no—
253C23—1224no—
254C23—1224no—
255C23—1224no—
256C23—1224no—
257C23—1224no—
258C23—1222no—
259C23—2442no—
260C23—2442no—
261C23—2442no—
262C23—24416no—
263C23C2×C4×#692311yescharacteristic
264C23C2×C22⋊#692311yescharacteristic
265C23C2×C4⋊#692311yescharacteristic
266C2×C4—24no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—44no—
271C2×C4—42no—
272C2×C4—612no—
273C2×C4—612no—
274C2×C4—1224no—
275C2×C4—1224no—
276C2×C4—1224no—
277C2×C4—1224no—
278C2×C4—1224no—
279C2×C4—4888no—
280C2×C4—2442no—
281C2×C4—2442no—
282C2×C4—2442no—
283C2×C4—2442no—
284C2×C4—2441no—
285C2×C4—2442no—
286C2×C4—2441no—
287C2×C4—2444no—
288C2×C4—2442no—
289C2×C4(C2×#6923)⋊C412yes—
290C2×C4(C2×#6923)⋊C412yes—
291C8—2448no—
292C22—22no—
293C22—21no—
294C22—21no—
295C22—22no—
296C22—22no—
297C22—44no—
298C22—614no—
299C22—614no—
300C22—1228no—
301C22—1222no—
302C22—1222no—
303C22—1222no—
304C22—1222no—
305C22—2444no—
306C22—2448no—
307C22—2448no—
308C22C2×(C2×#6923)⋊C411yescharacteristic
309C22D61⋊#9912yes—
310C4—22no—
311C4—22no—
312C4—82no—
313C4—1222no—
314C4—1222no—
315C4—4882no—
316C2—22no—
317C2—41no—
318C2—41no—
319C2—1224no—
320C2—1224no—
321C2#2146151611yescharacteristic
322C2#2146152712yes—
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC61×#381C4
socleC22×C61C2×#95
prime radicalC24×D61C2×C4
cosocleC23×Dic61C23
hypercenter#381#6923
hypocenterC61#8114
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
2. #21460722C2semidirect
7. #16840733C4semidirect
10. D61⋊(C22⋊C8)C4semidirect
25. C22⋊#92420C2×C4semidirect
179. C61#8114semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
#214607222
#381×D612
#811461