Finite Group Databasebeta

← D61×#1348 #29590234

Subgroups — D61×#1348 #29590234

Order 15616.

506 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 101 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#467×D61C211yesmaximal, characteristic
2C22⋊C16×D61C211yesmaximal, characteristic
3#340×D61C211yesmaximal, characteristic
4#21443832C211yesmaximal, characteristic, complemented
5#21443831C211yesmaximal, characteristic, complemented
6#21443830C211yesmaximal, characteristic, complemented
7C61×#1348C211yesmaximal, characteristic, complemented
8C2×Q16×D61C411yescharacteristic, complemented
9C22×C8×D61C2211yescharacteristic
10C22⋊Q8×D61—21no—
11C2×C4⋊C4×D61—21no—
12C2×C16×D61—21no—
13#16840004C411yescharacteristic, complemented
14#16840003C2211yescharacteristic
15#16840002—21no—
16#16840001—21no—
17#16840000C411yescharacteristic, complemented
18#107×D61C411yescharacteristic, complemented
19#103×D61—21no—
20C22⋊#11758185C2211yescharacteristic
21#16839541—21no—
22#16839525C2211yescharacteristic
23#16839524—21no—
24C61×#467C2211yescharacteristic
25C61×C22⋊C16C2211yescharacteristic
26C61×#340C2211yescharacteristic
27C2×Q8×D61—21no—
28C22×C4×D61—41no—
29C22×C4×D61D411yescharacteristic
30C2×Dic244C2×C411yescharacteristic, complemented
31C2×#11758202—21no—
32Q16×D61—42no—
33C22×#92418D411yescharacteristic
34C2×C8×D61—42no—
35C2×C8×D61C2×C411yescharacteristic
36C2×C8×D61C2×C411yescharacteristic
37C2×C8×D61D411yescharacteristic
38C2×C8×D61D411yescharacteristic
39#14519757—21no—
40#14519756—21no—
41#14519755—41no—
42#14519754—41no—
43#14519753—21no—
44C2×C4⋊Dic61—21no—
45C2×#11758196—41no—
46C4⋊C4×D61—24no—
47C4⋊C4×D61—21no—
48C4⋊C4×D61—42no—
49C4⋊C4×D61—41no—
50C22⋊C4×D61—41no—
51C2×#11758185—21no—
52C16×D61—42no—
53#14519711C2×C411yescharacteristic, complemented
54#14519710—21no—
55#14519702—21no—
56#14519701—21no—
57#14519700—21no—
58C2×Q16×C61C2×C411yescharacteristic, complemented
59C22×C8×C61C2311yescharacteristic
60C22⋊Q8×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C16×C61—21no—
63#107×C61C2×C411yescharacteristic, complemented
64#103×C61—21no—
65C23×D61D811yescharacteristic
66C2×Q8×C61—21no—
67C22×C4×C61—41no—
68C22×C4×C61C2×D411yescharacteristic
69C22×Dic61—41no—
70C22×Dic61D811yescharacteristic
71Q8×D61—42no—
72Q8×D61—42no—
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—44no—
76C2×C4×D61—41no—
77C2×C4×D61—41no—
78C2×C4×D61—82no—
79C2×C4×D61—82no—
80C2×C4×D61C22⋊C411yescharacteristic
81C2×C4×D61C22⋊C411yescharacteristic
82C2×C4×D61SD1611yescharacteristic
83C2×C4×D61SD1611yescharacteristic
84C2×Dic122—21no—
85C2×Dic122—41no—
86Q16×C61—41no—
87C2×C8×C61—41no—
88C2×C8×C61C22×C411yescharacteristic
89C2×C8×C61C2×D411yescharacteristic
90C4⋊C4×C61—22no—
91C4⋊C4×C61—21no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C22⋊C4×C61—41no—
95C22⋊Dic61—41no—
96#11758202—42no—
97#11758198—41no—
98#11758198—41no—
99C4⋊Dic61—22no—
100C4⋊Dic61—21no—
101C4⋊Dic61—41no—
102C4⋊Dic61—41no—
103#11758196—44no—
104#11758196—41no—
105#11758196—41no—
106#11758196—41no—
107C2×#92418—41no—
108C2×#92418C22⋊C411yescharacteristic
109C2×#92418C22⋊C411yescharacteristic
110Dic244—41no—
111C8×D61—22no—
112C8×D61—22no—
113C8×D61—41no—
114C8×D61—41no—
115C16×C61—41no—
116#11758185—41no—
117C23×C61C2×D811yescharacteristic
118C22×D61—22no—
119C22×D61—22no—
120C22×D61#10211yescharacteristic
121C22×D61#10211yescharacteristic
122C22×D61SD3212yes—
123C22×D61Q3212yes—
124Q8×C61—41no—
125Q8×C61—41no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—42no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—81no—
132C2×C4×C61—81no—
133C2×C4×C61C2×C22⋊C411yescharacteristic
134C2×C4×C61C2×SD1611yescharacteristic
135C2×Dic61—22no—
136C2×Dic61—42no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—81no—
140C2×Dic61—81no—
141C2×Dic61#10211yescharacteristic
142C2×Dic61#10211yescharacteristic
143C4×D61—22no—
144C4×D61—21no—
145C4×D61—21no—
146C4×D61—22no—
147C4×D61—88no—
148C4×D61—82no—
149C4×D61—82no—
150C4×D61#9912yes—
151C4×D61#10412yes—
152Dic122—41no—
153Dic122—41no—
154Dic122—82no—
155C8×C61—21no—
156C8×C61—21no—
157#92418—21no—
158#92418—21no—
159C2×#1348—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61C2×#10211yescharacteristic
163C22×C61C2×SD3211yescharacteristic
164C22×C61C2×Q3211yescharacteristic
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—24no—
168C2×D61—24no—
169C2×D61#32712yes—
170C2×D61#35812yes—
171C2×D61#35812yes—
172C2×D61#36012yes—
173C4×C61—21no—
174C4×C61—82no—
175C4×C61—81no—
176C4×C61—81no—
177C4×C61C2×#9911yescharacteristic
178C4×C61C2×#10411yescharacteristic
179Dic61—21no—
180Dic61—82no—
181Dic61—81no—
182Dic61—81no—
183Dic61#32712yes—
184C2×#467—611no—
185C2×C22⋊C16—611no—
186C2×#340—611no—
187#1348—611no—
188#1348—611no—
189#1348—611no—
190#1348D6111yescharacteristic, direct product factor
191C2×C61—21no—
192C2×C61—21no—
193C2×C61C2×#32711yescharacteristic
194C2×C61C2×#35811yescharacteristic
195C2×C61C2×#36011yescharacteristic
196D61—22no—
197D61#134814yesdirect product factor
198C22×Q16—611no—
199C23×C8—611no—
200C2×C22⋊Q8—1221no—
201C22×C4⋊C4—1221no—
202C22×C16—1221no—
203#467—611no—
204#467—611no—
205#467—611no—
206#467—1221no—
207#467—1221no—
208#467C2×D6111yescharacteristic
209C2×#107—611no—
210C2×#103—1221no—
211C22⋊C16—611no—
212C22⋊C16—1221no—
213C22⋊C16C2×D6111yescharacteristic
214#340—611no—
215#340—1221no—
216#340C2×D6111yescharacteristic
217C61C2×#134811yescharacteristic, complemented, Sylow
218C22×Q8—1221no—
219C23×C4—611no—
220C23×C4—2441no—
221C2×Q16—611no—
222C2×Q16—1221no—
223C2×Q16—2442no—
224C2×Q16C4×D6111yescharacteristic, complemented
225C22×C8—611no—
226C22×C8—611no—
227C22×C8—611no—
228C22×C8—611no—
229C22×C8—611no—
230C22×C8—2442no—
231C22×C8C22×D6111yescharacteristic
232C22⋊Q8—21no—
233C22⋊Q8—1221no—
234C22⋊Q8—1221no—
235C22⋊Q8—1221no—
236C22⋊Q8—2441no—
237C22⋊Q8—2441no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4—1224no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—2441no—
243C2×C4⋊C4—2442no—
244C2×C4⋊C4—2441no—
245C2×C22⋊C4—2441no—
246C2×C16—21no—
247C2×C16—1221no—
248C2×C16—2442no—
249#107—611no—
250#107—1221no—
251#107C4×D6111yescharacteristic, complemented
252#103—21no—
253#103—1221no—
254#103—1221no—
255#103—1221no—
256C24—611no—
257C2×Q8—21no—
258C2×Q8—1221no—
259C2×Q8—2441no—
260C2×Q8—2442no—
261C2×Q8—2442no—
262C22×C4—41no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—1222no—
269C22×C4—1222no—
270C22×C4—4882no—
271C22×C4—4882no—
272C22×C4—2441no—
273C22×C4—2441no—
274C22×C4—2444no—
275C22×C4—2441no—
276C22×C4D4×D6111yescharacteristic
277Q16—41no—
278Q16—2441no—
279Q16—2442no—
280C2×C8—41no—
281C2×C8—611no—
282C2×C8—611no—
283C2×C8—1222no—
284C2×C8—1222no—
285C2×C8—2441no—
286C2×C8—2441no—
287C2×C8—2441no—
288C2×C8C2×C4×D6111yescharacteristic
289C2×C8D4×D6111yescharacteristic
290C4⋊C4—22no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—1222no—
295C4⋊C4—1221no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C4⋊C4—2444no—
301C4⋊C4—2441no—
302C22⋊C4—41no—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C16—41no—
307C16—2441no—
308C23—611no—
309C23—611no—
310C23—612no—
311C23—612no—
312C23—1222no—
313C23—1222no—
314C23D8×D6111yescharacteristic
315Q8—41no—
316Q8—41no—
317Q8—4882no—
318Q8—2441no—
319Q8—2441no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—611no—
328C2×C4—612no—
329C2×C4—612no—
330C2×C4—611no—
331C2×C4—1222no—
332C2×C4—1222no—
333C2×C4—1222no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—4882no—
337C2×C4—4882no—
338C2×C4—4888no—
339C2×C4—4881no—
340C2×C4—4881no—
341C2×C4—2442no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4C22⋊C4×D6111yescharacteristic
345C2×C4SD16×D6111yescharacteristic
346C8—21no—
347C8—21no—
348C8—1221no—
349C8—1221no—
350C22—21no—
351C22—21no—
352C22—612no—
353C22—612no—
354C22—612no—
355C22—612no—
356C22—1224no—
357C22—1224no—
358C22—1221no—
359C22—1221no—
360C22#102×D6111yescharacteristic
361C22SD32×D6111yescharacteristic
362C22Q32×D6111yescharacteristic
363C4—21no—
364C4—82no—
365C4—81no—
366C4—81no—
367C4—612no—
368C4—1221no—
369C4—4882no—
370C4—4881no—
371C4—4881no—
372C4#99×D6111yescharacteristic
373C4#104×D6111yescharacteristic
374C2—21no—
375C2—21no—
376C2—614no—
377C2—1222no—
378C2#327×D6111yescharacteristic
379C2#358×D6111yescharacteristic
380C2#360×D6111yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1348C2
socleC22×C61C2×#102
prime radicalC23×D61D8
cosocleC22×C8×C61C23
hypercenter#1348D61
hypocenterC61C2×#1348
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1348

Complements

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

NH ≅ G/Ntype
4. #21443832C2semidirect
5. #21443831C2semidirect
6. #21443830C2semidirect
7. C61×#1348C2semidirect
8. C2×Q16×D61C4semidirect
13. #16840004C4semidirect
17. #16840000C4semidirect
18. #107×D61C4semidirect
30. C2×Dic244C2×C4semidirect
53. #14519711C2×C4semidirect
58. C2×Q16×C61C2×C4semidirect
63. #107×C61C2×C4semidirect
190. #1348D61direct (N × H)
197. D61#1348direct (N × H)
217. C61C2×#1348semidirect
224. C2×Q16C4×D61semidirect
251. #107C4×D61semidirect

Maximal subgroups

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

subgroupindex
#467×D612
C22⋊C16×D612
#340×D612
#214438322
#214438312
#214438302
C61×#13482
C2×#134861