Finite Group Databasebeta

← C61×#19316 #29522749

Subgroups — C61×#19316 #29522749

Order 15616.

682 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3138C211yesmaximal, characteristic, complemented
2C61×#3116C211yesmaximal, characteristic, complemented
3C61×#3038C211yesmaximal, characteristic
4C61×#2970C211yesmaximal, characteristic, complemented
5C61×#1702C212yesmaximal, complemented
6C61×#1698C212yesmaximal, complemented
7C61×#1681C212yesmaximal, complemented
8C61×#1677C212yesmaximal, complemented
9C61×#1569C211yesmaximal, characteristic, complemented
10C61×#1559C211yesmaximal, characteristic, complemented
11C61×#1555C211yesmaximal, characteristic, complemented
12C2×AGL(1,ℤ/8)×C61—21no—
13C61×#533C2211yescharacteristic
14C2×#127×C61C2211yescharacteristic
15C4×#41×C61C2211yescharacteristic
16C61×#490—21no—
17C61×#490—21no—
18C61×#486C2212yes—
19C61×#486C2212yes—
20C61×#485—21no—
21C61×#477C2211yescharacteristic, complemented
22C61×#476C2211yescharacteristic, complemented
23C61×#462C2211yescharacteristic, complemented
24C61×#461C2211yescharacteristic, complemented
25C61×#460—21no—
26C61×#460C2212yes—
27C61×#459—21no—
28C61×#459C2212yes—
29C61×#452—21no—
30C61×#446C2212yescomplemented
31C61×#441—21no—
32C61×#440—21no—
33C61×#435—22no—
34C8×D4×C61C2212yescomplemented
35C61×#432—21no—
36C61×#432C2211yescharacteristic
37C61×#432C2211yescharacteristic
38C61×#423C2211yescharacteristic
39C61×#418—22no—
40C61×#418—21no—
41C4×M16×C61C2211yescharacteristic
42C2×#97×C61—21no—
43C61×#335C2212yescomplemented
44C61×#334C2212yescomplemented
45C61×#333C2212yescomplemented
46C61×#332C2212yescomplemented
47C61×#331C2212yes—
48C61×#331C2212yes—
49C2×#41×C61D411yescharacteristic
50C22×D4×C61—21no—
51C22×D4×C61—21no—
52C22×D4×C61—21no—
53AGL(1,ℤ/8)×C61—44no—
54C2×Q16×C61—21no—
55C2×SD16×C61—22no—
56C2×SD16×C61—21no—
57C2×D8×C61—22no—
58C2×M16×C61—21no—
59C2×M16×C61D412yes—
60C22×C8×C61—22no—
61C4⋊Q8×C61C2311yescharacteristic
62C4⋊Q8×C61C2311yescharacteristic
63#127×C61—21no—
64#127×C61—21no—
65#127×C61—21no—
66#127×C61C2312yes—
67#125×C61—21no—
68C22⋊Q8×C61—21no—
69C22⋊Q8×C61—21no—
70C4×Q8×C61—21no—
71C4×Q8×C61—21no—
72C4×Q8×C61D411yescharacteristic
73C4×Q8×C61C2311yescharacteristic
74C4×D4×C61—21no—
75C4×D4×C61—21no—
76C4×D4×C61D411yescharacteristic
77C4×D4×C61C2311yescharacteristic
78#117×C61—21no—
79#117×C61—21no—
80#117×C61D411yescharacteristic
81C2×C42×C61—21no—
82C2×C42×C61C2311yescharacteristic
83#107×C61—21no—
84#106×C61—21no—
85C4⋊C8×C61—22no—
86C4⋊C8×C61—21no—
87C4⋊C8×C61C2312yes—
88C4⋊C8×C61C2311yescharacteristic
89C4⋊C8×C61C2311yescharacteristic
90C4⋊C8×C61C2312yes—
91#103×C61—21no—
92#103×C61—21no—
93#103×C61—21no—
94#102×C61—21no—
95#102×C61—22no—
96#102×C61—22no—
97#102×C61—22no—
98#102×C61—22no—
99#102×C61—22no—
100#102×C61—22no—
101C22⋊C8×C61—21no—
102C22⋊C8×C61—21no—
103C22⋊C8×C61—22no—
104#97×C61—22no—
105#97×C61—21no—
106#97×C61—21no—
107#97×C61D411yescharacteristic
108#97×C61D411yescharacteristic
109C4×C8×C61C2312yes—
110C24×C61—41no—
111#41×C61—22no—
112#41×C61—41no—
113C2×Q8×C61—21no—
114C2×Q8×C61—21no—
115C2×Q8×C61C2×D411yescharacteristic
116C2×D4×C61—21no—
117C2×D4×C61—22no—
118C2×D4×C61—22no—
119C2×D4×C61—22no—
120C2×D4×C61—42no—
121C2×D4×C61—44no—
122C2×D4×C61—42no—
123C2×D4×C61—41no—
124C2×D4×C61—41no—
125C2×D4×C61—41no—
126C2×D4×C61—82no—
127C2×D4×C61C2×D411yescharacteristic
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61#4111yescharacteristic
134Q16×C61—42no—
135SD16×C61—44no—
136SD16×C61—42no—
137D8×C61—44no—
138M16×C61—42no—
139M16×C61—42no—
140C2×C8×C61—22no—
141C2×C8×C61—21no—
142C2×C8×C61—21no—
143C2×C8×C61—22no—
144C2×C8×C61—44no—
145C2×C8×C61C2×D412yes—
146C2×C8×C61C2×D412yes—
147C4⋊C4×C61—21no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—41no—
154C4⋊C4×C61—41no—
155C4⋊C4×C61C2×D411yescharacteristic
156C4⋊C4×C61C2×D411yescharacteristic
157C22⋊C4×C61—21no—
158C22⋊C4×C61—21no—
159C22⋊C4×C61—21no—
160C22⋊C4×C61—41no—
161C42×C61—21no—
162C42×C61—21no—
163C42×C61—21no—
164C42×C61—41no—
165C42×C61C2×D411yescharacteristic
166C42×C61C2×D411yescharacteristic
167C42×C61#4111yescharacteristic
168C42×C61C2411yescharacteristic
169C23×C61—21no—
170C23×C61—42no—
171C23×C61—82no—
172C23×C61—82no—
173C23×C61—82no—
174C23×C61#12111yescharacteristic
175Q8×C61—21no—
176Q8×C61—21no—
177Q8×C61—41no—
178Q8×C61—41no—
179Q8×C61—81no—
180D4×C61—21no—
181D4×C61—42no—
182D4×C61—42no—
183D4×C61—44no—
184D4×C61—42no—
185D4×C61—82no—
186D4×C61—82no—
187D4×C61—82no—
188D4×C61—82no—
189D4×C61AGL(1,ℤ/8)12yes—
190C2×C4×C61—21no—
191C2×C4×C61—22no—
192C2×C4×C61—21no—
193C2×C4×C61—21no—
194C2×C4×C61—21no—
195C2×C4×C61—21no—
196C2×C4×C61—41no—
197C2×C4×C61—42no—
198C2×C4×C61—42no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61—81no—
202C2×C4×C61#12111yescharacteristic
203C2×C4×C61#12111yescharacteristic
204C2×C4×C61#12111yescharacteristic
205C2×C4×C61C22×D411yescharacteristic
206C2×C4×C61C22×D411yescharacteristic
207C2×C4×C61C2×#4111yescharacteristic
208C8×C61—22no—
209C8×C61—22no—
210C8×C61—42no—
211C8×C61—41no—
212C8×C61—42no—
213C8×C61—41no—
214#19316C6111yesmaximal, characteristic, direct product factor, Sylow
215C22×C61—21no—
216C22×C61—21no—
217C22×C61—22no—
218C22×C61—21no—
219C22×C61—41no—
220C22×C61—41no—
221C22×C61—82no—
222C22×C61—82no—
223C22×C61—82no—
224C22×C61—164no—
225C22×C61C2×#12111yescharacteristic
226C4×C61—21no—
227C4×C61—21no—
228C4×C61—21no—
229C4×C61—21no—
230C4×C61—41no—
231C4×C61—41no—
232C4×C61—41no—
233C4×C61—81no—
234C4×C61—81no—
235C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
236C4×C61#57512yes—
237C4×C61#57511yescharacteristic
238#3138C2×C6111yescharacteristic, complemented
239#3116C2×C6111yescharacteristic, complemented
240#3038C2×C6111yescharacteristic
241#2970C2×C6111yescharacteristic, complemented
242#1702C2×C6112yescomplemented
243#1698C2×C6112yescomplemented
244#1681C2×C6112yescomplemented
245#1677C2×C6112yescomplemented
246#1569C2×C6111yescharacteristic, complemented
247#1559C2×C6111yescharacteristic, complemented
248#1555C2×C6111yescharacteristic, complemented
249C2×C61—41no—
250C2×C61—42no—
251C2×C61—162no—
252C2×C61#304011yescharacteristic
253C2×C61#305511yescharacteristic
254C2×C61#306811yescharacteristic
255C2×AGL(1,ℤ/8)—21no—
256#533C22×C6111yescharacteristic
257C2×#127C22×C6111yescharacteristic
258C4×#41C22×C6111yescharacteristic
259#490—21no—
260#490—21no—
261#486C22×C6112yes—
262#486C22×C6112yes—
263#485—21no—
264#477C22×C6111yescharacteristic, complemented
265#476C22×C6111yescharacteristic, complemented
266#462C22×C6111yescharacteristic, complemented
267#461C22×C6111yescharacteristic, complemented
268#460—21no—
269#460C22×C6112yes—
270#459—21no—
271#459C22×C6112yes—
272#452—21no—
273#446C22×C6112yescomplemented
274#441—21no—
275#440—21no—
276#435—22no—
277C8×D4C22×C6112yescomplemented
278#432—21no—
279#432C22×C6111yescharacteristic
280#432C22×C6111yescharacteristic
281#423C22×C6111yescharacteristic
282#418—22no—
283#418—21no—
284C4×M16C22×C6111yescharacteristic
285C2×#97—21no—
286#335C22×C6112yescomplemented
287#334C22×C6112yescomplemented
288#333C22×C6112yescomplemented
289#332C22×C6112yescomplemented
290#331C22×C6112yes—
291#331C22×C6112yes—
292C61#1931611yescharacteristic, direct product factor, Sylow
293C2×#41D4×C6111yescharacteristic
294C22×D4—21no—
295C22×D4—21no—
296C22×D4—21no—
297AGL(1,ℤ/8)—44no—
298C2×Q16—21no—
299C2×SD16—22no—
300C2×SD16—21no—
301C2×D8—22no—
302C2×M16—21no—
303C2×M16D4×C6112yes—
304C22×C8—22no—
305C4⋊Q8C23×C6111yescharacteristic
306C4⋊Q8C23×C6111yescharacteristic
307#127—21no—
308#127—21no—
309#127—21no—
310#127C23×C6112yes—
311#125—21no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8D4×C6111yescharacteristic
317C4×Q8C23×C6111yescharacteristic
318C4×D4—21no—
319C4×D4—21no—
320C4×D4D4×C6111yescharacteristic
321C4×D4C23×C6111yescharacteristic
322#117—21no—
323#117—21no—
324#117D4×C6111yescharacteristic
325C2×C42—21no—
326C2×C42C23×C6111yescharacteristic
327#107—21no—
328#106—21no—
329C4⋊C8—22no—
330C4⋊C8—21no—
331C4⋊C8C23×C6112yes—
332C4⋊C8C23×C6111yescharacteristic
333C4⋊C8C23×C6111yescharacteristic
334C4⋊C8C23×C6112yes—
335#103—21no—
336#103—21no—
337#103—21no—
338#102—21no—
339#102—22no—
340#102—22no—
341#102—22no—
342#102—22no—
343#102—22no—
344#102—22no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347C22⋊C8—22no—
348#97—22no—
349#97—21no—
350#97—21no—
351#97D4×C6111yescharacteristic
352#97D4×C6111yescharacteristic
353C4×C8C23×C6112yes—
354C24—41no—
355#41—22no—
356#41—41no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8C2×D4×C6111yescharacteristic
360C2×D4—21no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—42no—
365C2×D4—44no—
366C2×D4—42no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—82no—
371C2×D4C2×D4×C6111yescharacteristic
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4C2×D4×C6111yescharacteristic
376C22×C4C2×D4×C6111yescharacteristic
377C22×C4#41×C6111yescharacteristic
378Q16—42no—
379SD16—44no—
380SD16—42no—
381D8—44no—
382M16—42no—
383M16—42no—
384C2×C8—22no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—22no—
388C2×C8—44no—
389C2×C8C2×D4×C6112yes—
390C2×C8C2×D4×C6112yes—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4C2×D4×C6111yescharacteristic
400C4⋊C4C2×D4×C6111yescharacteristic
401C22⋊C4—21no—
402C22⋊C4—21no—
403C22⋊C4—21no—
404C22⋊C4—41no—
405C42—21no—
406C42—21no—
407C42—21no—
408C42—41no—
409C42C2×D4×C6111yescharacteristic
410C42C2×D4×C6111yescharacteristic
411C42#41×C6111yescharacteristic
412C42C24×C6111yescharacteristic
413C23—21no—
414C23—42no—
415C23—82no—
416C23—82no—
417C23—82no—
418C23#121×C6111yescharacteristic
419Q8—21no—
420Q8—21no—
421Q8—41no—
422Q8—41no—
423Q8—81no—
424D4—21no—
425D4—42no—
426D4—42no—
427D4—44no—
428D4—42no—
429D4—82no—
430D4—82no—
431D4—82no—
432D4—82no—
433D4AGL(1,ℤ/8)×C6112yes—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—81no—
446C2×C4#121×C6111yescharacteristic
447C2×C4#121×C6111yescharacteristic
448C2×C4#121×C6111yescharacteristic
449C2×C4C22×D4×C6111yescharacteristic
450C2×C4C22×D4×C6111yescharacteristic
451C2×C4C2×#41×C6111yescharacteristic
452C8—22no—
453C8—22no—
454C8—42no—
455C8—41no—
456C8—42no—
457C8—41no—
458C22—21no—
459C22—21no—
460C22—22no—
461C22—21no—
462C22—41no—
463C22—41no—
464C22—82no—
465C22—82no—
466C22—82no—
467C22—164no—
468C22C2×#121×C6111yescharacteristic
469C4—21no—
470C4—21no—
471C4—21no—
472C4—21no—
473C4—41no—
474C4—41no—
475C4—41no—
476C4—81no—
477C4—81no—
478C4C2×AGL(1,ℤ/8)×C6111yescharacteristic
479C4C61×#57512yes—
480C4C61×#57511yescharacteristic
481C2—41no—
482C2—42no—
483C2—162no—
484C2C61×#304011yescharacteristic
485C2C61×#305511yescharacteristic
486C2C61×#306811yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
commutator, Frattini, cosocleC42C24×C61
prime radicalC61×#3038C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3138C2semidirect
2. C61×#3116C2semidirect
4. C61×#2970C2semidirect
5. C61×#1702C2semidirect
6. C61×#1698C2semidirect
7. C61×#1681C2semidirect
8. C61×#1677C2semidirect
9. C61×#1569C2semidirect
10. C61×#1559C2semidirect
11. C61×#1555C2semidirect
21. C61×#477C22semidirect
22. C61×#476C22semidirect
23. C61×#462C22semidirect
24. C61×#461C22semidirect
30. C61×#446C22semidirect
34. C8×D4×C61C22semidirect
43. C61×#335C22semidirect
44. C61×#334C22semidirect
45. C61×#333C22semidirect
46. C61×#332C22semidirect
214. #19316C61direct (N × H)
238. #3138C2×C61semidirect
239. #3116C2×C61semidirect
241. #2970C2×C61semidirect
242. #1702C2×C61semidirect
243. #1698C2×C61semidirect
244. #1681C2×C61semidirect
245. #1677C2×C61semidirect
246. #1569C2×C61semidirect
247. #1559C2×C61semidirect
248. #1555C2×C61semidirect
264. #477C22×C61semidirect
265. #476C22×C61semidirect
266. #462C22×C61semidirect
267. #461C22×C61semidirect
273. #446C22×C61semidirect
277. C8×D4C22×C61semidirect
286. #335C22×C61semidirect
287. #334C22×C61semidirect
288. #333C22×C61semidirect
289. #332C22×C61semidirect
292. C61#19316direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#31382
C61×#31162
C61×#30382
C61×#29702
C61×#17022
C61×#16982
C61×#16812
C61×#16772
C61×#15692
C61×#15592
C61×#15552
#1931661