Finite Group Databasebeta

← C61×#19362 #29522795

Subgroups — C61×#19362 #29522795

Order 15616.

648 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3238C211yesmaximal, characteristic, complemented
2C61×#3217C211yesmaximal, characteristic
3C2×C61×#486C211yesmaximal, characteristic, complemented
4C61×#2966C211yesmaximal, characteristic, complemented
5C61×#1698C212yesmaximal, complemented
6C61×#1697C212yesmaximal, complemented
7C61×#1678C212yesmaximal, complemented
8C61×#1677C212yesmaximal, complemented
9C61×#1568C211yesmaximal, characteristic, complemented
10C61×#1558C211yesmaximal, characteristic, complemented
11C61×#1555C211yesmaximal, characteristic, complemented
12C2×C4⋊Q8×C61C2211yescharacteristic
13C2×#127×C61C2211yescharacteristic
14C61×#529C2211yescharacteristic
15C61×#501—21no—
16C61×#496—21no—
17C61×#490—21no—
18C61×#489—21no—
19C61×#486—21no—
20C61×#486—21no—
21C61×#486C2212yes—
22C61×#486C2212yes—
23C61×#483—21no—
24C61×#480—21no—
25C61×#477C2212yescomplemented
26C61×#476C2212yescomplemented
27C61×#460C2212yes—
28C61×#459C2212yes—
29C61×#450—21no—
30C61×#447—21no—
31C61×#446C2211yescharacteristic, complemented
32C8×Q8×C61C2211yescharacteristic, complemented
33C61×#436C2211yescharacteristic, complemented
34C61×#435—21no—
35C8×D4×C61—21no—
36C8×D4×C61C2211yescharacteristic, complemented
37C61×#433—21no—
38C61×#432C2211yescharacteristic
39C61×#432C2211yescharacteristic
40C61×#432C2211yescharacteristic
41C2×#102×C61—21no—
42C2×#102×C61—21no—
43C61×#405—21no—
44C2×C4×C8×C61C2211yescharacteristic
45C61×#335C2212yescomplemented
46C61×#334C2212yescomplemented
47C61×#333C2212yescomplemented
48C61×#333C2212yescomplemented
49C61×#331C2212yes—
50C61×#331C2212yes—
51C22×Q8×C61—21no—
52C22×D4×C61—21no—
53C22×D4×C61—21no—
54C22×D4×C61—21no—
55C2×SD16×C61—22no—
56C2×D8×C61—22no—
57C2×M16×C61—21no—
58C22×C8×C61—21no—
59C22×C8×C61D411yescharacteristic
60C22×C8×C61D411yescharacteristic
61C4⋊Q8×C61—21no—
62C4⋊Q8×C61—21no—
63C4⋊Q8×C61—21no—
64C4⋊Q8×C61C2312yes—
65#127×C61—21no—
66#127×C61—21no—
67#127×C61—21no—
68#127×C61C2312yes—
69#126×C61—21no—
70#125×C61D411yescharacteristic
71#124×C61D411yescharacteristic
72#123×C61—21no—
73C22⋊Q8×C61D411yescharacteristic
74#121×C61D411yescharacteristic
75C4×Q8×C61C2311yescharacteristic
76C4×D4×C61—21no—
77C4×D4×C61C2311yescharacteristic
78#117×C61—21no—
79C2×C4⋊C4×C61—21no—
80C2×C4⋊C4×C61—21no—
81C2×C42×C61C2311yescharacteristic
82#107×C61—22no—
83#106×C61—22no—
84C4⋊C8×C61—21no—
85C4⋊C8×C61—21no—
86C4⋊C8×C61C2311yescharacteristic
87C4⋊C8×C61C2311yescharacteristic
88C4⋊C8×C61C2312yes—
89C4⋊C8×C61C2312yes—
90#103×C61—22no—
91#102×C61—22no—
92#102×C61—22no—
93#102×C61—22no—
94#102×C61—22no—
95#102×C61—22no—
96#102×C61—22no—
97#102×C61—22no—
98C22⋊C8×C61—21no—
99C22⋊C8×C61—21no—
100C22⋊C8×C61—21no—
101C22⋊C8×C61—21no—
102C22⋊C8×C61—21no—
103#97×C61—21no—
104#97×C61—21no—
105#97×C61—21no—
106#97×C61—21no—
107C4×C8×C61—21no—
108C4×C8×C61D411yescharacteristic
109C4×C8×C61D411yescharacteristic
110C4×C8×C61C2311yescharacteristic
111C4×C8×C61C2311yescharacteristic
112C24×C61—41no—
113C2×Q8×C61—22no—
114C2×Q8×C61—41no—
115C2×Q8×C61—82no—
116C2×Q8×C61C2×D411yescharacteristic
117C2×D4×C61—21no—
118C2×D4×C61—22no—
119C2×D4×C61—22no—
120C2×D4×C61—22no—
121C2×D4×C61—42no—
122C2×D4×C61—42no—
123C2×D4×C61—41no—
124C2×D4×C61—41no—
125C2×D4×C61—41no—
126C2×D4×C61—82no—
127C2×D4×C61—82no—
128C2×D4×C61C2×D411yescharacteristic
129C22×C4×C61—21no—
130C22×C4×C61—41no—
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61#4111yescharacteristic
134SD16×C61—82no—
135D8×C61—82no—
136M16×C61—42no—
137C2×C8×C61—21no—
138C2×C8×C61—21no—
139C2×C8×C61—22no—
140C2×C8×C61—22no—
141C2×C8×C61—41no—
142C2×C8×C61—41no—
143C2×C8×C61—42no—
144C2×C8×C61C2×D411yescharacteristic
145C2×C8×C61C2×D411yescharacteristic
146C2×C8×C61C2×D411yescharacteristic
147C2×C8×C61C2×D411yescharacteristic
148C4⋊C4×C61—21no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—22no—
153C4⋊C4×C61—22no—
154C4⋊C4×C61—41no—
155C4⋊C4×C61—41no—
156C4⋊C4×C61C2×D411yescharacteristic
157C4⋊C4×C61C2×D411yescharacteristic
158C22⋊C4×C61—21no—
159C22⋊C4×C61—21no—
160C22⋊C4×C61—21no—
161C22⋊C4×C61—21no—
162C22⋊C4×C61—21no—
163C42×C61—21no—
164C42×C61C2×D411yescharacteristic
165C42×C61C2×D411yescharacteristic
166C42×C61#4111yescharacteristic
167C42×C61C2411yescharacteristic
168C23×C61—21no—
169C23×C61—42no—
170C23×C61—82no—
171C23×C61—82no—
172C23×C61—82no—
173C23×C61#12111yescharacteristic
174Q8×C61—22no—
175Q8×C61—82no—
176Q8×C61—82no—
177D4×C61—22no—
178D4×C61—42no—
179D4×C61—42no—
180D4×C61—42no—
181D4×C61—42no—
182D4×C61—42no—
183D4×C61—82no—
184D4×C61—82no—
185D4×C61—82no—
186D4×C61—82no—
187C2×C4×C61—22no—
188C2×C4×C61—21no—
189C2×C4×C61—21no—
190C2×C4×C61—22no—
191C2×C4×C61—21no—
192C2×C4×C61—21no—
193C2×C4×C61—21no—
194C2×C4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61—42no—
197C2×C4×C61—82no—
198C2×C4×C61#12111yescharacteristic
199C2×C4×C61#12111yescharacteristic
200C2×C4×C61#12111yescharacteristic
201C2×C4×C61C22×D411yescharacteristic
202C2×C4×C61C22×D411yescharacteristic
203C2×C4×C61C2×#4111yescharacteristic
204C8×C61—21no—
205C8×C61—21no—
206C8×C61—21no—
207C8×C61—21no—
208C8×C61—41no—
209C8×C61—41no—
210C8×C61—42no—
211C8×C61—42no—
212#19362C6111yesmaximal, characteristic, direct product factor, Sylow
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—41no—
216C22×C61—41no—
217C22×C61—41no—
218C22×C61—82no—
219C22×C61—82no—
220C22×C61—82no—
221C22×C61—164no—
222C22×C61#47212yes—
223C22×C61C2×#12111yescharacteristic
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—21no—
227C4×C61—21no—
228C4×C61—41no—
229C4×C61—41no—
230C4×C61—41no—
231C4×C61—82no—
232C4×C61#57511yescharacteristic
233C4×C61#57511yescharacteristic
234C4×C61#57712yes—
235#3238C2×C6111yescharacteristic, complemented
236#3217C2×C6111yescharacteristic
237C2×#486C2×C6111yescharacteristic, complemented
238#2966C2×C6111yescharacteristic, complemented
239#1698C2×C6112yescomplemented
240#1697C2×C6112yescomplemented
241#1678C2×C6112yescomplemented
242#1677C2×C6112yescomplemented
243#1568C2×C6111yescharacteristic, complemented
244#1558C2×C6111yescharacteristic, complemented
245#1555C2×C6111yescharacteristic, complemented
246C2×C61—22no—
247C2×C61—81no—
248C2×C61—162no—
249C2×C61#304011yescharacteristic
250C2×C61#305711yescharacteristic
251C2×C61C2×#47211yescharacteristic
252C2×C4⋊Q8C22×C6111yescharacteristic
253C2×#127C22×C6111yescharacteristic
254#529C22×C6111yescharacteristic
255#501—21no—
256#496—21no—
257#490—21no—
258#489—21no—
259#486—21no—
260#486—21no—
261#486C22×C6112yes—
262#486C22×C6112yes—
263#483—21no—
264#480—21no—
265#477C22×C6112yescomplemented
266#476C22×C6112yescomplemented
267#460C22×C6112yes—
268#459C22×C6112yes—
269#450—21no—
270#447—21no—
271#446C22×C6111yescharacteristic, complemented
272C8×Q8C22×C6111yescharacteristic, complemented
273#436C22×C6111yescharacteristic, complemented
274#435—21no—
275C8×D4—21no—
276C8×D4C22×C6111yescharacteristic, complemented
277#433—21no—
278#432C22×C6111yescharacteristic
279#432C22×C6111yescharacteristic
280#432C22×C6111yescharacteristic
281C2×#102—21no—
282C2×#102—21no—
283#405—21no—
284C2×C4×C8C22×C6111yescharacteristic
285#335C22×C6112yescomplemented
286#334C22×C6112yescomplemented
287#333C22×C6112yescomplemented
288#333C22×C6112yescomplemented
289#331C22×C6112yes—
290#331C22×C6112yes—
291C61#1936211yescharacteristic, direct product factor, Sylow
292C22×Q8—21no—
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—21no—
296C2×SD16—22no—
297C2×D8—22no—
298C2×M16—21no—
299C22×C8—21no—
300C22×C8D4×C6111yescharacteristic
301C22×C8D4×C6111yescharacteristic
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8C23×C6112yes—
306#127—21no—
307#127—21no—
308#127—21no—
309#127C23×C6112yes—
310#126—21no—
311#125D4×C6111yescharacteristic
312#124D4×C6111yescharacteristic
313#123—21no—
314C22⋊Q8D4×C6111yescharacteristic
315#121D4×C6111yescharacteristic
316C4×Q8C23×C6111yescharacteristic
317C4×D4—21no—
318C4×D4C23×C6111yescharacteristic
319#117—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C42C23×C6111yescharacteristic
323#107—22no—
324#106—22no—
325C4⋊C8—21no—
326C4⋊C8—21no—
327C4⋊C8C23×C6111yescharacteristic
328C4⋊C8C23×C6111yescharacteristic
329C4⋊C8C23×C6112yes—
330C4⋊C8C23×C6112yes—
331#103—22no—
332#102—22no—
333#102—22no—
334#102—22no—
335#102—22no—
336#102—22no—
337#102—22no—
338#102—22no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C22⋊C8—21no—
344#97—21no—
345#97—21no—
346#97—21no—
347#97—21no—
348C4×C8—21no—
349C4×C8D4×C6111yescharacteristic
350C4×C8D4×C6111yescharacteristic
351C4×C8C23×C6111yescharacteristic
352C4×C8C23×C6111yescharacteristic
353C24—41no—
354C2×Q8—22no—
355C2×Q8—41no—
356C2×Q8—82no—
357C2×Q8C2×D4×C6111yescharacteristic
358C2×D4—21no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—42no—
363C2×D4—42no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—82no—
368C2×D4—82no—
369C2×D4C2×D4×C6111yescharacteristic
370C22×C4—21no—
371C22×C4—41no—
372C22×C4C2×D4×C6111yescharacteristic
373C22×C4C2×D4×C6111yescharacteristic
374C22×C4#41×C6111yescharacteristic
375SD16—82no—
376D8—82no—
377M16—42no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—41no—
383C2×C8—41no—
384C2×C8—42no—
385C2×C8C2×D4×C6111yescharacteristic
386C2×C8C2×D4×C6111yescharacteristic
387C2×C8C2×D4×C6111yescharacteristic
388C2×C8C2×D4×C6111yescharacteristic
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4C2×D4×C6111yescharacteristic
398C4⋊C4C2×D4×C6111yescharacteristic
399C22⋊C4—21no—
400C22⋊C4—21no—
401C22⋊C4—21no—
402C22⋊C4—21no—
403C22⋊C4—21no—
404C42—21no—
405C42C2×D4×C6111yescharacteristic
406C42C2×D4×C6111yescharacteristic
407C42#41×C6111yescharacteristic
408C42C24×C6111yescharacteristic
409C23—21no—
410C23—42no—
411C23—82no—
412C23—82no—
413C23—82no—
414C23#121×C6111yescharacteristic
415Q8—22no—
416Q8—82no—
417Q8—82no—
418D4—22no—
419D4—42no—
420D4—42no—
421D4—42no—
422D4—42no—
423D4—42no—
424D4—82no—
425D4—82no—
426D4—82no—
427D4—82no—
428C2×C4—22no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—82no—
439C2×C4#121×C6111yescharacteristic
440C2×C4#121×C6111yescharacteristic
441C2×C4#121×C6111yescharacteristic
442C2×C4C22×D4×C6111yescharacteristic
443C2×C4C22×D4×C6111yescharacteristic
444C2×C4C2×#41×C6111yescharacteristic
445C8—21no—
446C8—21no—
447C8—21no—
448C8—21no—
449C8—41no—
450C8—41no—
451C8—42no—
452C8—42no—
453C22—21no—
454C22—21no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—82no—
459C22—82no—
460C22—82no—
461C22—164no—
462C22C61×#47212yes—
463C22C2×#121×C6111yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—82no—
472C4C61×#57511yescharacteristic
473C4C61×#57511yescharacteristic
474C4C61×#57712yes—
475C2—22no—
476C2—81no—
477C2—162no—
478C2C61×#304011yescharacteristic
479C2C61×#305711yescharacteristic
480C2C2×C61×#47211yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
commutator, Frattini, cosocleC42C24×C61
prime radicalC61×#3217C2
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×#3238C2semidirect
3. C2×C61×#486C2semidirect
4. C61×#2966C2semidirect
5. C61×#1698C2semidirect
6. C61×#1697C2semidirect
7. C61×#1678C2semidirect
8. C61×#1677C2semidirect
9. C61×#1568C2semidirect
10. C61×#1558C2semidirect
11. C61×#1555C2semidirect
25. C61×#477C22semidirect
26. C61×#476C22semidirect
31. C61×#446C22semidirect
32. C8×Q8×C61C22semidirect
33. C61×#436C22semidirect
36. C8×D4×C61C22semidirect
45. C61×#335C22semidirect
46. C61×#334C22semidirect
47. C61×#333C22semidirect
48. C61×#333C22semidirect
212. #19362C61direct (N × H)
235. #3238C2×C61semidirect
237. C2×#486C2×C61semidirect
238. #2966C2×C61semidirect
239. #1698C2×C61semidirect
240. #1697C2×C61semidirect
241. #1678C2×C61semidirect
242. #1677C2×C61semidirect
243. #1568C2×C61semidirect
244. #1558C2×C61semidirect
245. #1555C2×C61semidirect
265. #477C22×C61semidirect
266. #476C22×C61semidirect
271. #446C22×C61semidirect
272. C8×Q8C22×C61semidirect
273. #436C22×C61semidirect
276. C8×D4C22×C61semidirect
285. #335C22×C61semidirect
286. #334C22×C61semidirect
287. #333C22×C61semidirect
288. #333C22×C61semidirect
291. C61#19362direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#32382
C61×#32172
C2×C61×#4862
C61×#29662
C61×#16982
C61×#16972
C61×#16782
C61×#16772
C61×#15682
C61×#15582
C61×#15552
#1936261