Finite Group Databasebeta

← #30597291

Subgroups — #30597291

Order 15616.

942 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 942 conjugacy classes of subgroups — too many to draw. Only its 152 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×D61D411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C22×C4×D61D412yes—
36C22×C4×D61Q811yescharacteristic
37C22×C4×D61Q811yescharacteristic
38C2×C22⋊Dic61C2×C412yes—
39C2×#11758198—22no—
40C22⋊C4×D61—44no—
41#14519684—22no—
42#14519684—24no—
43C23×C4×C61C2×C411yescharacteristic
44C2×C22⋊C4×C61C2×C412yes—
45#95×C61—22no—
46C24×C61C22×C411yescharacteristic
47C23×D61—24no—
48C23×D61—44no—
49C23×D61C4211yescharacteristic
50C23×D61C4211yescharacteristic
51C23×D61C22⋊C411yescharacteristic
52C23×D61C22⋊C411yescharacteristic
53C23×D61C4⋊C411yescharacteristic
54C23×D61C4⋊C411yescharacteristic
55C22×C4×C61—22no—
56C22×C4×C61—42no—
57C22×C4×C61C4212yes—
58C22×C4×C61C22⋊C412yes—
59C22×C4×C61C4⋊C411yescharacteristic
60C22×C4×C61C4⋊C411yescharacteristic
61C22×Dic61—22no—
62C22×Dic61—42no—
63C22×Dic61C22×C412yes—
64C22×Dic61C2×D412yes—
65C22×Dic61C2×D411yescharacteristic
66C22×Dic61C2×Q811yescharacteristic
67C2×C4×D61—28no—
68C2×C4×D61—44no—
69C2×C4×D61—44no—
70C2×C4×D61—42no—
71C2×C4×D61—42no—
72C2×C4×D61—42no—
73C2×C4×D61—42no—
74C2×C4×D61—44no—
75C2×C4×D61—48no—
76C2×C4×D61—44no—
77C2×C4×D61C22⋊C412yes—
78C2×C4×D61C22⋊C412yes—
79C2×C4×D61C22⋊C412yes—
80C2×C4×D61C22⋊C412yes—
81C2×C4×D61C4⋊C412yes—
82C2×C4×D61C4⋊C412yes—
83C2×C4×D61C4⋊C412yes—
84C2×C4×D61C4⋊C412yes—
85#11758217—48no—
86C2×#92420—28no—
87#11758213—48no—
88D61⋊C8—48no—
89C22⋊C4×C61—42no—
90C22⋊Dic61—42no—
91#11758198—44no—
92C23×C61—22no—
93C23×C61—42no—
94C23×C61C2×C4211yescharacteristic
95C23×C61C2×C22⋊C411yescharacteristic
96C23×C61C2×C4⋊C411yescharacteristic
97C22×D61—24no—
98C22×D61—22no—
99C22×D61—22no—
100C22×D61—22no—
101C22×D61—22no—
102C22×D61—22no—
103C22×D61—24no—
104C22×D61—24no—
105C22×D61—42no—
106C22×D61—42no—
107C22×D61—42no—
108C22×D61—416no—
109C22×D61#9511yescharacteristic
110C22×D61#9511yescharacteristic
111C22×D61#9511yescharacteristic
112C22×D61#9511yescharacteristic
113C22×D61#9914yes—
114C2×C4×C61—24no—
115C2×C4×C61—42no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—44no—
119C2×C4×C61—42no—
120C2×C4×C61#9512yes—
121C2×C4×C61#9512yes—
122C2×Dic61—24no—
123C2×Dic61—42no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—44no—
127C2×Dic61—42no—
128C2×Dic61C2×C22⋊C412yes—
129C2×Dic61C2×C4⋊C412yes—
130C4×D61—24no—
131C4×D61—24no—
132C4×D61—24no—
133C4×D61—24no—
134C4×D61—42no—
135C4×D61—42no—
136C4×D61—42no—
137C4×D61—42no—
138C4×D61—88no—
139#92420—48no—
140C2×#1306—611nomaximal, Sylow
141C22×C61—22no—
142C22×C61—21no—
143C22×C61—21no—
144C22×C61—22no—
145C22×C61—22no—
146C22×C61—44no—
147C22×C61C2×#9511yescharacteristic
148C22×C61C2×#9912yes—
149C2×D61—22no—
150C2×D61—28no—
151C2×D61—21no—
152C2×D61—21no—
153C2×D61—22no—
154C2×D61—22no—
155C2×D61—44no—
156C2×D61—44no—
157C2×D61—44no—
158C2×D61—44no—
159C2×D61—44no—
160C2×D61#34212yes—
161C2×D61#34212yes—
162C2×D61#34414yes—
163C4×C61—22no—
164C4×C61—22no—
165C4×C61—82no—
166Dic61—22no—
167Dic61—22no—
168Dic61—82no—
169C2×#407—612no—
170C2×#381—611no—
171#1306—614no—
172C2×C61—22no—
173C2×C61—41no—
174C2×C61—41no—
175C2×C61C2×#34211yescharacteristic
176C2×C61C2×#34412yes—
177D61—22no—
178D61—41no—
179D61—41no—
180D61#130614yescomplemented
181C24×C4—611no—
182C22×M16—1222no—
183C22×C22⋊C4—612no—
184#407—614no—
185#407—614no—
186#407—1222no—
187#407—1222no—
188C2×C22⋊C8—614no—
189C2×C22⋊C8—1222no—
190#381—611no—
191#381—612no—
192#381—1222no—
193#381#692311yescharacteristic
194C2×#95—1222no—
195C61C2×#130611yescharacteristic, complemented, Sylow
196C25—611no—
197C23×C4—611no—
198C23×C4—612no—
199C23×C4—612no—
200C23×C4—612no—
201C23×C4—611no—
202C23×C4—611no—
203C23×C4—611no—
204C23×C4—611no—
205C23×C4—612no—
206C23×C4—1222no—
207C23×C4—2444no—
208C23×C4C2×#692311yescharacteristic
209C2×M16—1224no—
210C2×M16—1224no—
211C2×M16—2448no—
212C22×C8—1224no—
213C2×C22⋊C4—612no—
214C2×C22⋊C4—1222no—
215C2×C22⋊C4—2444no—
216C2×C22⋊C4C2×#692312yes—
217C22⋊C8—618no—
218C22⋊C8—1224no—
219C22⋊C8—1224no—
220C22⋊C8—1224no—
221#95—22no—
222#95—1224no—
223#95—1222no—
224C24—611no—
225C24—611no—
226C24—611no—
227C24—611no—
228C24—611no—
229C24—611no—
230C24—1224no—
231C24—2444no—
232C24C22×#692311yescharacteristic
233C22×C4—22no—
234C22×C4—42no—
235C22×C4—612no—
236C22×C4—612no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—612no—
240C22×C4—612no—
241C22×C4—612no—
242C22×C4—612no—
243C22×C4—612no—
244C22×C4—612no—
245C22×C4—612no—
246C22×C4—612no—
247C22×C4—1228no—
248C22×C4—1222no—
249C22×C4—2444no—
250C22×C4—2444no—
251C22×C4—2444no—
252C22×C4—2442no—
253C22×C4—2442no—
254C22×C4—2442no—
255C22×C4—2442no—
256C22×C4—2444no—
257C22×C4—2448no—
258C22×C4—2442no—
259C22×C4C4×#692312yes—
260C22×C4C4⋊#692311yescharacteristic
261C22×C4C4⋊#692311yescharacteristic
262C22×C4C22⋊#692312yes—
263M16—2448no—
264M16—2448no—
265C2×C8—1228no—
266C2×C8—2448no—
267C22⋊C4—42no—
268C22⋊C4—2444no—
269C22⋊C4—2442no—
270C23—22no—
271C23—42no—
272C23—611no—
273C23—614no—
274C23—611no—
275C23—611no—
276C23—611no—
277C23—1224no—
278C23—1222no—
279C23—1222no—
280C23—1222no—
281C23—1222no—
282C23—1224no—
283C23—1224no—
284C23—1222no—
285C23—2442no—
286C23—2442no—
287C23—2442no—
288C23—24416no—
289C23C2×C4×#692311yescharacteristic
290C23C2×C22⋊#692311yescharacteristic
291C23C2×C4⋊#692311yescharacteristic
292C2×C4—24no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—44no—
297C2×C4—42no—
298C2×C4—612no—
299C2×C4—612no—
300C2×C4—1224no—
301C2×C4—1224no—
302C2×C4—1224no—
303C2×C4—1224no—
304C2×C4—1224no—
305C2×C4—4888no—
306C2×C4—2442no—
307C2×C4—2442no—
308C2×C4—2442no—
309C2×C4—2442no—
310C2×C4—2441no—
311C2×C4—2442no—
312C2×C4—2441no—
313C2×C4—2444no—
314C2×C4—2442no—
315C2×C4(C2×#6923)⋊C412yes—
316C2×C4(C2×#6923)⋊C412yes—
317C8—2448no—
318C22—22no—
319C22—21no—
320C22—21no—
321C22—22no—
322C22—22no—
323C22—44no—
324C22—612no—
325C22—614no—
326C22—612no—
327C22—1228no—
328C22—1222no—
329C22—1221no—
330C22—1221no—
331C22—1222no—
332C22—1222no—
333C22—2444no—
334C22—2444no—
335C22—2444no—
336C22—2444no—
337C22—2444no—
338C22C2×(C2×#6923)⋊C411yescharacteristic
339C22D61⋊#9912yes—
340C4—22no—
341C4—22no—
342C4—82no—
343C4—1222no—
344C4—1222no—
345C4—4882no—
346C2—22no—
347C2—41no—
348C2—41no—
349C2—614no—
350C2—1222no—
351C2—2441no—
352C2—2441no—
353C2#2146151611yescharacteristic
354C2#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
hypocenterC61C2×#1306
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
180. D61#1306semidirect
195. C61C2×#1306semidirect

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
C2×#130661