Finite Group Databasebeta

← D61⋊#1829 #30615126

Subgroups — D61⋊#1829 #30615126

Order 15616.

1434 conjugacy classes of subgroups; only the 262 normal subgroups are shown.

normal subgroups only

This group has 1434 conjugacy classes of subgroups — too many to draw. Only its 262 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
1C2×D61⋊#100C212yesmaximal
2#21461732C218yesmaximal, complemented
3#21461527C214yesmaximal, complemented
4#518×D61C211yesmaximal, characteristic
5C2×D61⋊M16C2214yes—
6D61⋊#100—24no—
7D61⋊#100—24no—
8C2×#14519837C2218yes—
9#16840643C22116yescomplemented
10C22×D4×D61C2211yescharacteristic
11#16840237C411yescharacteristic
12#16840236C412yes—
13#16840235C2214yes—
14#16840234—24no—
15C4×D4×D61—24no—
16#117×D61C2212yes—
17C2×C22⋊C4×D61C414yes—
18C61×#518C411yescharacteristic
19C2×#11758213—24no—
20D61⋊M16—24no—
21D61⋊M16—24no—
22D61⋊M16—24no—
23D61⋊M16—24no—
24C2×#11758217C2318yes—
25C2×D61⋊C8—24no—
26#14519837—216no—
27C24×D61C2×C412yes—
28C22×D244C2×C411yescharacteristic
29C22×C22⋊D61C2312yes—
30C2×D4×D61—24no—
31C2×D4×D61—24no—
32C2×D4×D61D414yes—
33C2×D4×D61D414yes—
34C22×C4×D61—24no—
35C22×C4×D61C2311yescharacteristic
36C4×D244—24no—
37D4×Dic61—24no—
38#14519739—24no—
39C4×C22⋊D61—28no—
40#14519737—28no—
41#14519736C2×C412yes—
42#14519735—22no—
43#14519734—22no—
44#14519733C2314yes—
45C4⋊C4×D61—22no—
46C2×C22⋊Dic61C2×C414yes—
47C2×#11758198—24no—
48C22⋊C4×D61—24no—
49C22⋊C4×D61—24no—
50C22⋊C4×D61C2×C414yes—
51C22⋊C4×D61C2×C418yes—
52C42×D61—22no—
53C22×D4×C61C2×C411yescharacteristic
54C4×D4×C61—24no—
55#117×C61C2×C412yes—
56C2×C22⋊C4×C61C2×C414yes—
57C24×C61C22×C412yes—
58C23×D61—24no—
59C23×D61—24no—
60C23×D61—84no—
61C23×D61C22⋊C414yes—
62C23×D61C22⋊C414yes—
63C23×D61C22×C412yes—
64C23×D61C22×C411yescharacteristic
65C2×D4×C61—24no—
66C2×D4×C61C22⋊C414yes—
67C22×C4×C61—24no—
68C22×C4×C61C22×C411yescharacteristic
69C2×C22⋊D61—28no—
70C2×C22⋊D61C2×D418yes—
71C22×Dic61—24no—
72C22×Dic61C2411yescharacteristic
73D4×D61—28no—
74D4×D61—28no—
75D4×D61—28no—
76D4×D61—28no—
77C2×D244—24no—
78C2×D244C22⋊C414yes—
79C2×C4×D61—24no—
80C2×C4×D61—28no—
81C2×C4×D61—88no—
82C2×C4×D61C2×D412yes—
83C2×C4×D61C2×D412yes—
84C2×C4×D61#4114yes—
85C2×C4×D61#4114yes—
86#11758217—28no—
87#11758217—28no—
88C2×#92420—28no—
89#11758213—44no—
90#11758213—44no—
91D61⋊C8—44no—
92D61⋊C8—44no—
93C4⋊C4×C61—22no—
94C22⋊C4×C61—24no—
95C22⋊C4×C61C22×C414yes—
96C42×C61—22no—
97C22⋊Dic61—24no—
98C22⋊Dic61C22×C414yes—
99#11758198—24no—
100#11758198—28no—
101C4⋊Dic61—22no—
102#11758196—24no—
103C4×Dic61—22no—
104C4×Dic61—24no—
105C23×C61—24no—
106C23×C61—82no—
107C23×C61C2×C22⋊C414yes—
108C23×C61C23×C411yescharacteristic
109C22×D61—24no—
110C22×D61—24no—
111C22×D61—24no—
112C22×D61—28no—
113C22×D61—42no—
114C22×D61—48no—
115C22×D61—88no—
116C22×D61—88no—
117C22×D61—84no—
118C22×D61—82no—
119C22×D61C2×C22⋊C411yescharacteristic
120C22×D61C2×C22⋊C414yes—
121C22×D61C2×C22⋊C411yescharacteristic
122C22×D61#11712yes—
123C22×D61#11712yes—
124D4×C61—28no—
125C2×C4×C61—24no—
126C2×C4×C61—84no—
127C2×C4×C61C2×C22⋊C412yes—
128C2×C4×C61#11714yes—
129C22⋊D61—216no—
130C2×Dic61—24no—
131C2×Dic61—84no—
132C2×Dic61C22×D412yes—
133C2×Dic61C2×#4114yes—
134D244—28no—
135C4×D61—48no—
136C4×D61—88no—
137C4×D61#12314yes—
138C4×D61#12314yes—
139C4×D61#12314yes—
140C4×D61#12314yes—
141#92420—48no—
142C2×#1829—611nomaximal, Sylow
143C22×C61—24no—
144C22×C61—41no—
145C22×C61—44no—
146C22×C61—84no—
147C22×C61C22×C22⋊C411yescharacteristic
148C22×C61C2×#11712yes—
149C2×D61—22no—
150C2×D61—24no—
151C2×D61—24no—
152C2×D61—41no—
153C2×D61—42no—
154C2×D61—48no—
155C2×D61—48no—
156C2×D61—44no—
157C2×D61—88no—
158C2×D61—84no—
159C2×D61#38111yescharacteristic
160C2×D61#38112yes—
161C2×D61#38111yescharacteristic
162C4×C61—44no—
163C4×C61#38114yes—
164Dic61—44no—
165Dic61C2×#12314yes—
166C2×#518—611no—
167C22×#100—612no—
168#1829—618no—
169C2×#344—614no—
170C2×C61—21no—
171C2×C61—22no—
172C2×C61—44no—
173C2×C61C2×#38111yescharacteristic
174D61—21no—
175D61—22no—
176D61—44no—
177D61#182912yescomplemented
178C23×D4—611no—
179C22×M16—614no—
180#518—611no—
181#518—612no—
182#518—614no—
183#518—1224no—
184#518#692311yescharacteristic
185C2×C4×D4—1224no—
186C2×#117—612no—
187C22×C22⋊C4—614no—
188C2×#100—618no—
189C2×#100—1224no—
190C2×#100—1224no—
191#344—6116no—
192C61C2×#182911yescharacteristic, complemented, Sylow
193C25—612no—
194C22×D4—612no—
195C22×D4—614no—
196C22×D4—614no—
197C22×D4—611no—
198C22×D4—1224no—
199C22×D4—1224no—
200C22×D4C2×#692311yescharacteristic
201C23×C4—611no—
202C23×C4—1224no—
203C2×M16—618no—
204C2×M16—1224no—
205C2×M16—1224no—
206C2×M16—1224no—
207C2×M16—1224no—
208C2×M16—1224no—
209C22×C8—1224no—
210C4×D4—24no—
211C4×D4—1224no—
212C4×D4—1228no—
213C4×D4—1224no—
214C4×D4—1228no—
215C4×D4—1224no—
216#117—612no—
217#117—614no—
218#117—1222no—
219#117—1222no—
220#117C2×#692312yes—
221C2×C4⋊C4—1222no—
222C2×C22⋊C4—614no—
223C2×C22⋊C4—614no—
224C2×C22⋊C4—618no—
225C2×C22⋊C4—1224no—
226C2×C22⋊C4—1224no—
227C2×C22⋊C4—1224no—
228C2×C22⋊C4C2×#692314yes—
229C2×C42—1222no—
230#100—12216no—
231C24—611no—
232C24—614no—
233C24—612no—
234C24—614no—
235C24—1224no—
236C24—1224no—
237C24—4884no—
238C24C22×#692312yes—
239C2×D4—24no—
240C2×D4—618no—
241C2×D4—614no—
242C2×D4—1228no—
243C2×D4—1228no—
244C2×D4—1228no—
245C2×D4—1228no—
246C2×D4—1228no—
247C2×D4—1224no—
248C2×D4C22⋊#692314yes—
249C22×C4—24no—
250C22×C4—611no—
251C22×C4—612no—
252C22×C4—612no—
253C22×C4—614no—
254C22×C4—614no—
255C22×C4—1228no—
256C22×C4—1224no—
257C22×C4—1224no—
258C22×C4—4888no—
259C22×C4C22×#692311yescharacteristic
260M16—1228no—
261M16—1228no—
262M16—2444no—
263M16—2444no—
264C2×C8—1228no—
265C2×C8—2444no—
266C2×C8—2444no—
267C4⋊C4—22no—
268C4⋊C4—1224no—
269C4⋊C4—1222no—
270C22⋊C4—24no—
271C22⋊C4—614no—
272C22⋊C4—1224no—
273C22⋊C4—1228no—
274C22⋊C4—1224no—
275C22⋊C4C22×#692314yes—
276C42—22no—
277C42—1224no—
278C42—1222no—
279C23—24no—
280C23—82no—
281C23—611no—
282C23—612no—
283C23—611no—
284C23—612no—
285C23—614no—
286C23—1228no—
287C23—1224no—
288C23—1224no—
289C23—1224no—
290C23—4882no—
291C23—4884no—
292C23—4888no—
293C23—4888no—
294C23—2442no—
295C23—2448no—
296C23C2×C22⋊#692314yes—
297C23C23×#692311yescharacteristic
298D4—28no—
299D4—12216no—
300D4—1228no—
301C2×C4—24no—
302C2×C4—84no—
303C2×C4—612no—
304C2×C4—614no—
305C2×C4—614no—
306C2×C4—614no—
307C2×C4—614no—
308C2×C4—614no—
309C2×C4—1224no—
310C2×C4—4888no—
311C2×C4—4884no—
312C2×C4—2448no—
313C2×C4C2×C22⋊#692312yes—
314C2×C4#1451985614yes—
315C8—2448no—
316C22—24no—
317C22—41no—
318C22—44no—
319C22—84no—
320C22—611no—
321C22—612no—
322C22—611no—
323C22—1222no—
324C22—1224no—
325C22—1224no—
326C22—4884no—
327C22—4888no—
328C22—2441no—
329C22—2442no—
330C22—2444no—
331C22—2448no—
332C22—2448no—
333C22C22×C22⋊#692311yescharacteristic
334C22C2×#1451985612yes—
335C4—44no—
336C4—614no—
337C4—2444no—
338C4#1684070514yes—
339C2—21no—
340C2—22no—
341C2—44no—
342C2—612no—
343C2—1222no—
344C2—1221no—
345C2—2444no—
346C2C2×#1684070511yescharacteristic
subgroupG/H
centerC2C2×#16840705
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC61×#518C4
socleC2×C61C2×#381
prime radicalC22×D4×D61C22
cosocleC22×Dic61C24
hypercenter#518#6923
hypocenterC61C2×#1829
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #21461732C2semidirect
3. #21461527C2semidirect
9. #16840643C22semidirect
177. D61#1829semidirect
192. C61C2×#1829semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊#1002
#214617322
#214615272
#518×D612
C2×#182961