Finite Group Databasebeta

← C61×#25053 #29528486

Subgroups — C61×#25053 #29528486

Order 15616.

736 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3098C212yesmaximal, complemented
2C61×#3061C211yesmaximal, characteristic
3C61×#2951C211yesmaximal, characteristic, complemented
4C61×#2078C212yesmaximal, complemented
5C61×#2039C212yesmaximal, complemented
6C61×#1974C211yesmaximal, characteristic, complemented
7C61×#1952C211yesmaximal, characteristic, complemented
8C61×#1859C212yesmaximal, complemented
9C61×#1845C211yesmaximal, characteristic, complemented
10C61×#1816C211yesmaximal, characteristic, complemented
11C61×#1764C211yesmaximal, characteristic, complemented
12C2×#135×C61C2211yescharacteristic
13C2×#131×C61C2211yescharacteristic
14C61×#537C2212yes—
15C61×#520C2212yes—
16C61×#485—22no—
17C61×#484—22no—
18C61×#482—22no—
19C61×#480—22no—
20C61×#468—22no—
21C61×#467—21no—
22C61×#466—21no—
23C61×#440—22no—
24C4×Q16×C61—21no—
25C4×D8×C61—21no—
26C2×#108×C61C2211yescharacteristic
27C61×#428C2212yes—
28C2×#107×C61C2211yescharacteristic
29C2×#107×C61C2211yescharacteristic
30C2×#107×C61C2212yes—
31C2×#104×C61C2211yescharacteristic
32C2×#104×C61C2212yes—
33C61×#417C2212yes—
34C61×#417C2212yes—
35C61×#417C2212yes—
36C61×#416C2211yescharacteristic
37C61×#408C2212yes—
38C61×#405C2211yescharacteristic
39C2×C4×C8×C61C2211yescharacteristic
40C61×#384C2212yes—
41C61×#343C2212yes—
42C61×#343C2212yes—
43C61×#341C2211yescharacteristic
44C61×#339C2211yescharacteristic
45C2×#41×C61C2311yescharacteristic
46C2×#41×C61C2312yes—
47#135×C61—22no—
48#135×C61—22no—
49C2×Q16×C61D411yescharacteristic
50C2×SD16×C61D412yes—
51C2×D8×C61D411yescharacteristic
52#131×C61—22no—
53#131×C61—22no—
54C2×M16×C61—21no—
55C2×M16×C61C2311yescharacteristic
56C2×M16×C61C2311yescharacteristic
57C2×M16×C61C2312yes—
58C22×C8×C61—21no—
59C22×C8×C61C2311yescharacteristic
60C22×C8×C61C2311yescharacteristic
61C22⋊Q8×C61—22no—
62C22⋊Q8×C61—22no—
63#121×C61—22no—
64#121×C61—22no—
65#121×C61—42no—
66C4×Q8×C61—22no—
67C4×D4×C61—22no—
68C4×D4×C61—42no—
69#117×C61—22no—
70#117×C61C2311yescharacteristic
71C2×C4⋊C4×C61—22no—
72C2×C4⋊C4×C61—42no—
73C2×C4⋊C4×C61C2312yes—
74C2×C4⋊C4×C61C2312yes—
75C2×C42×C61C2311yescharacteristic
76#108×C61—22no—
77#107×C61—21no—
78#107×C61—21no—
79#107×C61—21no—
80#107×C61—21no—
81#107×C61—22no—
82#107×C61—22no—
83#107×C61—22no—
84#106×C61—22no—
85#104×C61—22no—
86#104×C61—24no—
87#103×C61—22no—
88#103×C61—22no—
89#103×C61—22no—
90#103×C61D411yescharacteristic
91#103×C61D411yescharacteristic
92#102×C61—22no—
93#102×C61—22no—
94#102×C61—22no—
95#102×C61D411yescharacteristic
96#102×C61D411yescharacteristic
97C22⋊C8×C61—22no—
98C22⋊C8×C61—22no—
99#97×C61—21no—
100C4×C8×C61—21no—
101C4×C8×C61—22no—
102#41×C61—22no—
103#41×C61—21no—
104#41×C61—21no—
105#41×C61—21no—
106#41×C61—22no—
107#41×C61—22no—
108#41×C61—21no—
109#41×C61—22no—
110C2×Q8×C61C2×D411yescharacteristic
111C2×Q8×C61C2×D412yes—
112C2×D4×C61—22no—
113C2×D4×C61—21no—
114C2×D4×C61—42no—
115C2×D4×C61C2×D411yescharacteristic
116C2×D4×C61C2×D412yes—
117C22×C4×C61—21no—
118C22×C4×C61—22no—
119C22×C4×C61—21no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—42no—
123C22×C4×C61C2411yescharacteristic
124Q16×C61—22no—
125SD16×C61—24no—
126D8×C61—22no—
127M16×C61—22no—
128M16×C61—21no—
129M16×C61—22no—
130M16×C61—21no—
131M16×C61—21no—
132M16×C61—21no—
133M16×C61—42no—
134C2×C8×C61—21no—
135C2×C8×C61—21no—
136C2×C8×C61—21no—
137C2×C8×C61—22no—
138C2×C8×C61—21no—
139C2×C8×C61—42no—
140C2×C8×C61C2×D411yescharacteristic
141C2×C8×C61C2×D411yescharacteristic
142C2×C8×C61C2×D411yescharacteristic
143C2×C8×C61C2×D411yescharacteristic
144C2×C8×C61#4112yes—
145C2×C8×C61#4112yes—
146C4⋊C4×C61—22no—
147C4⋊C4×C61—22no—
148C4⋊C4×C61—22no—
149C4⋊C4×C61—22no—
150C4⋊C4×C61—42no—
151C4⋊C4×C61—42no—
152C4⋊C4×C61—84no—
153C4⋊C4×C61C2×D411yescharacteristic
154C4⋊C4×C61C2×D411yescharacteristic
155C22⋊C4×C61—21no—
156C22⋊C4×C61—42no—
157C22⋊C4×C61—42no—
158C22⋊C4×C61—42no—
159C42×C61—21no—
160C42×C61—21no—
161C42×C61—42no—
162C42×C61#4112yes—
163C23×C61—22no—
164C23×C61—21no—
165C23×C61H(5,𝔽2)11yescharacteristic
166Q8×C61—22no—
167Q8×C61—21no—
168Q8×C61—21no—
169Q8×C61—22no—
170D4×C61—22no—
171D4×C61—21no—
172D4×C61—21no—
173D4×C61—22no—
174D4×C61—42no—
175D4×C61—41no—
176D4×C61—42no—
177D4×C61—41no—
178D4×C61—162no—
179C2×C4×C61—22no—
180C2×C4×C61—22no—
181C2×C4×C61—22no—
182C2×C4×C61—21no—
183C2×C4×C61—21no—
184C2×C4×C61—22no—
185C2×C4×C61—21no—
186C2×C4×C61—41no—
187C2×C4×C61—42no—
188C2×C4×C61—42no—
189C2×C4×C61—41no—
190C2×C4×C61—42no—
191C2×C4×C61—42no—
192C2×C4×C61—82no—
193C2×C4×C61—82no—
194C2×C4×C61—162no—
195C2×C4×C61C22×D411yescharacteristic
196C2×C4×C61C22×D411yescharacteristic
197C2×C4×C61C2×#4111yescharacteristic
198C2×C4×C61C2×#4111yescharacteristic
199C2×C4×C61C2×#4111yescharacteristic
200C2×C4×C612−1+411yescharacteristic
201C8×C61—21no—
202C8×C61—21no—
203C8×C61—41no—
204C8×C61—42no—
205C8×C61—41no—
206C8×C61#12312yes—
207C8×C61#12312yes—
208#25053C6111yesmaximal, characteristic, direct product factor, Sylow
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—41no—
212C22×C61—42no—
213C22×C61—42no—
214C22×C61—41no—
215C22×C61—42no—
216C22×C61—41no—
217C22×C61#54211yescharacteristic
218C22×C61D4211yescharacteristic
219C22×C61#55311yescharacteristic
220C4×C61—24no—
221C4×C61—42no—
222C4×C61—41no—
223C4×C61—41no—
224C4×C61—41no—
225C4×C61—82no—
226C4×C61—82no—
227C4×C61C2×#12311yescharacteristic
228C4×C61#53211yescharacteristic
229C4×C61#54711yescharacteristic
230C4×C61#54711yescharacteristic
231#3098C2×C6112yescomplemented
232#3061C2×C6111yescharacteristic
233#2951C2×C6111yescharacteristic, complemented
234#2078C2×C6112yescomplemented
235#2039C2×C6112yescomplemented
236#1974C2×C6111yescharacteristic, complemented
237#1952C2×C6111yescharacteristic, complemented
238#1859C2×C6112yescomplemented
239#1845C2×C6111yescharacteristic, complemented
240#1816C2×C6111yescharacteristic, complemented
241#1764C2×C6111yescharacteristic, complemented
242C2×C61—21no—
243C2×C61—21no—
244C2×C61—82no—
245C2×C61—81no—
246C2×C61#242211yescharacteristic
247C2×C61#329211yescharacteristic
248C2×C61#329311yescharacteristic
249C2×#135C22×C6111yescharacteristic
250C2×#131C22×C6111yescharacteristic
251#537C22×C6112yes—
252#520C22×C6112yes—
253#485—22no—
254#484—22no—
255#482—22no—
256#480—22no—
257#468—22no—
258#467—21no—
259#466—21no—
260#440—22no—
261C4×Q16—21no—
262C4×D8—21no—
263C2×#108C22×C6111yescharacteristic
264#428C22×C6112yes—
265C2×#107C22×C6111yescharacteristic
266C2×#107C22×C6112yes—
267C2×#107C22×C6111yescharacteristic
268C2×#104C22×C6112yes—
269C2×#104C22×C6111yescharacteristic
270#417C22×C6112yes—
271#417C22×C6112yes—
272#417C22×C6112yes—
273#416C22×C6111yescharacteristic
274#408C22×C6112yes—
275#405C22×C6111yescharacteristic
276C2×C4×C8C22×C6111yescharacteristic
277#384C22×C6112yes—
278#343C22×C6112yes—
279#343C22×C6112yes—
280#341C22×C6111yescharacteristic
281#339C22×C6111yescharacteristic
282C61#2505311yescharacteristic, direct product factor, Sylow
283C2×#41C23×C6112yes—
284C2×#41C23×C6111yescharacteristic
285#135—22no—
286#135—22no—
287C2×Q16D4×C6111yescharacteristic
288C2×SD16D4×C6112yes—
289C2×D8D4×C6111yescharacteristic
290#131—22no—
291#131—22no—
292C2×M16—21no—
293C2×M16C23×C6111yescharacteristic
294C2×M16C23×C6111yescharacteristic
295C2×M16C23×C6112yes—
296C22×C8—21no—
297C22×C8C23×C6111yescharacteristic
298C22×C8C23×C6111yescharacteristic
299C22⋊Q8—22no—
300C22⋊Q8—22no—
301#121—22no—
302#121—22no—
303#121—42no—
304C4×Q8—22no—
305C4×D4—22no—
306C4×D4—42no—
307#117—22no—
308#117C23×C6111yescharacteristic
309C2×C4⋊C4—22no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4C23×C6112yes—
312C2×C4⋊C4C23×C6112yes—
313C2×C42C23×C6111yescharacteristic
314#108—22no—
315#107—21no—
316#107—21no—
317#107—21no—
318#107—21no—
319#107—22no—
320#107—22no—
321#107—22no—
322#106—22no—
323#104—24no—
324#104—22no—
325#103—22no—
326#103—22no—
327#103—22no—
328#103D4×C6111yescharacteristic
329#103D4×C6111yescharacteristic
330#102—22no—
331#102—22no—
332#102—22no—
333#102D4×C6111yescharacteristic
334#102D4×C6111yescharacteristic
335C22⋊C8—22no—
336C22⋊C8—22no—
337#97—21no—
338C4×C8—21no—
339C4×C8—22no—
340#41—22no—
341#41—21no—
342#41—21no—
343#41—21no—
344#41—22no—
345#41—22no—
346#41—22no—
347#41—21no—
348C2×Q8C2×D4×C6111yescharacteristic
349C2×Q8C2×D4×C6112yes—
350C2×D4—22no—
351C2×D4—21no—
352C2×D4—42no—
353C2×D4C2×D4×C6111yescharacteristic
354C2×D4C2×D4×C6112yes—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—42no—
361C22×C4C24×C6111yescharacteristic
362Q16—22no—
363SD16—24no—
364D8—22no—
365M16—22no—
366M16—21no—
367M16—22no—
368M16—21no—
369M16—21no—
370M16—21no—
371M16—42no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—22no—
376C2×C8—21no—
377C2×C8—42no—
378C2×C8C2×D4×C6111yescharacteristic
379C2×C8C2×D4×C6111yescharacteristic
380C2×C8C2×D4×C6111yescharacteristic
381C2×C8C2×D4×C6111yescharacteristic
382C2×C8#41×C6112yes—
383C2×C8#41×C6112yes—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—42no—
389C4⋊C4—42no—
390C4⋊C4—84no—
391C4⋊C4C2×D4×C6111yescharacteristic
392C4⋊C4C2×D4×C6111yescharacteristic
393C22⋊C4—21no—
394C22⋊C4—42no—
395C22⋊C4—42no—
396C22⋊C4—42no—
397C42—21no—
398C42—21no—
399C42—42no—
400C42#41×C6112yes—
401C23—22no—
402C23—21no—
403C23H(5,𝔽2)×C6111yescharacteristic
404Q8—21no—
405Q8—21no—
406Q8—22no—
407Q8—22no—
408D4—21no—
409D4—21no—
410D4—22no—
411D4—22no—
412D4—42no—
413D4—41no—
414D4—42no—
415D4—41no—
416D4—162no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—22no—
423C2×C4—21no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—82no—
431C2×C4—82no—
432C2×C4—162no—
433C2×C4C22×D4×C6111yescharacteristic
434C2×C4C22×D4×C6111yescharacteristic
435C2×C4C2×#41×C6111yescharacteristic
436C2×C4C2×#41×C6111yescharacteristic
437C2×C4C2×#41×C6111yescharacteristic
438C2×C42−1+4×C6111yescharacteristic
439C8—21no—
440C8—21no—
441C8—42no—
442C8—41no—
443C8—41no—
444C8#123×C6112yes—
445C8#123×C6112yes—
446C22—21no—
447C22—21no—
448C22—42no—
449C22—41no—
450C22—42no—
451C22—41no—
452C22—42no—
453C22—41no—
454C22C61×#54211yescharacteristic
455C22D42×C6111yescharacteristic
456C22C61×#55311yescharacteristic
457C4—24no—
458C4—41no—
459C4—41no—
460C4—42no—
461C4—41no—
462C4—82no—
463C4—82no—
464C4C2×#123×C6111yescharacteristic
465C4C61×#53211yescharacteristic
466C4C61×#54711yescharacteristic
467C4C61×#54711yescharacteristic
468C2—21no—
469C2—21no—
470C2—82no—
471C2—81no—
472C2C61×#242211yescharacteristic
473C2C61×#329211yescharacteristic
474C2C61×#329311yescharacteristic
subgroupG/H
center, socleC22×C61D42
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#3061C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C22×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3098C2semidirect
3. C61×#2951C2semidirect
4. C61×#2078C2semidirect
5. C61×#2039C2semidirect
6. C61×#1974C2semidirect
7. C61×#1952C2semidirect
8. C61×#1859C2semidirect
9. C61×#1845C2semidirect
10. C61×#1816C2semidirect
11. C61×#1764C2semidirect
208. #25053C61direct (N × H)
231. #3098C2×C61semidirect
233. #2951C2×C61semidirect
234. #2078C2×C61semidirect
235. #2039C2×C61semidirect
236. #1974C2×C61semidirect
237. #1952C2×C61semidirect
238. #1859C2×C61semidirect
239. #1845C2×C61semidirect
240. #1816C2×C61semidirect
241. #1764C2×C61semidirect
282. C61#25053direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#30982
C61×#30612
C61×#29512
C61×#20782
C61×#20392
C61×#19742
C61×#19522
C61×#18592
C61×#18452
C61×#18162
C61×#17642
#2505361