Finite Group Databasebeta

← C61×#19319 #29522752

Subgroups — C61×#19319 #29522752

Order 15616.

652 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3141C211yesmaximal, characteristic, complemented
2C61×#3115C211yesmaximal, characteristic
3C61×#3039C211yesmaximal, characteristic, complemented
4C61×#2970C211yesmaximal, characteristic, complemented
5C61×#1702C212yesmaximal, complemented
6C61×#1700C212yesmaximal, complemented
7C61×#1681C212yesmaximal, complemented
8C61×#1679C212yesmaximal, complemented
9C61×#1569C211yesmaximal, characteristic, complemented
10C61×#1557C211yesmaximal, characteristic, complemented
11C61×#1556C211yesmaximal, characteristic, complemented
12C2×#137×C61—21no—
13C61×#532C2211yescharacteristic
14C2×C4⋊Q8×C61C2211yescharacteristic
15C4×#41×C61C2211yescharacteristic
16C61×#489—21no—
17C61×#489—21no—
18C61×#487C2212yes—
19C61×#486C2212yes—
20C61×#482—21no—
21C61×#475C2211yescharacteristic
22C61×#474C2211yescharacteristic
23C61×#462—21no—
24C61×#462C2212yes—
25C61×#461—21no—
26C61×#461C2212yes—
27C61×#460C2211yescharacteristic
28C61×#459C2211yescharacteristic
29C61×#449—21no—
30C61×#446C2212yes—
31C61×#442—21no—
32C61×#440—21no—
33C61×#435—22no—
34C8×D4×C61C2212yes—
35C61×#432—21no—
36C61×#432C2211yescharacteristic
37C61×#432C2211yescharacteristic
38C61×#423C2211yescharacteristic
39C61×#419—21no—
40C61×#417—22no—
41C4×M16×C61C2211yescharacteristic
42C2×#97×C61—21no—
43C61×#335C2212yes—
44C61×#334C2212yes—
45C61×#332C2212yes—
46C61×#332C2212yes—
47C61×#332C2212yes—
48C61×#331C2212yes—
49C2×#41×C61—21no—
50C2×#41×C61D411yescharacteristic
51C22×Q8×C61—21no—
52#137×C61—44no—
53C2×Q16×C61—22no—
54C2×SD16×C61—21no—
55C2×SD16×C61—22no—
56C2×D8×C61—21no—
57C2×M16×C61—21no—
58C2×M16×C61D412yes—
59C22×C8×C61—22no—
60C4⋊Q8×C61—21no—
61C4⋊Q8×C61—21no—
62C4⋊Q8×C61—21no—
63C4⋊Q8×C61C2312yes—
64C4⋊Q8×C61C2311yescharacteristic
65#127×C61C2311yescharacteristic
66#124×C61—21no—
67#121×C61—21no—
68#121×C61—21no—
69C4×Q8×C61D411yescharacteristic
70C4×Q8×C61C2311yescharacteristic
71C4×D4×C61—21no—
72C4×D4×C61—21no—
73C4×D4×C61—21no—
74C4×D4×C61—21no—
75C4×D4×C61D411yescharacteristic
76C4×D4×C61C2311yescharacteristic
77#117×C61—21no—
78#117×C61D411yescharacteristic
79C2×C4⋊C4×C61—21no—
80C2×C4⋊C4×C61—21no—
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×C61C2312yes—
89C4⋊C8×C61C2311yescharacteristic
90C4⋊C8×C61C2311yescharacteristic
91#103×C61—21no—
92#103×C61—22no—
93#103×C61—22no—
94#103×C61—22no—
95#103×C61—22no—
96#102×C61—21no—
97#102×C61—22no—
98#102×C61—22no—
99#102×C61—21no—
100#102×C61—21no—
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—
110#41×C61—22no—
111#41×C61—41no—
112#41×C61—44no—
113C2×Q8×C61—21no—
114C2×Q8×C61—22no—
115C2×Q8×C61—42no—
116C2×Q8×C61—42no—
117C2×Q8×C61—41no—
118C2×Q8×C61C2×D411yescharacteristic
119C2×D4×C61—21no—
120C2×D4×C61—21no—
121C2×D4×C61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—41no—
124C2×D4×C61C2×D411yescharacteristic
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—41no—
129C22×C4×C61—41no—
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61#4111yescharacteristic
133Q16×C61—44no—
134SD16×C61—42no—
135SD16×C61—44no—
136D8×C61—42no—
137M16×C61—42no—
138M16×C61—42no—
139C2×C8×C61—22no—
140C2×C8×C61—21no—
141C2×C8×C61—21no—
142C2×C8×C61—22no—
143C2×C8×C61—44no—
144C2×C8×C61C2×D412yes—
145C2×C8×C61C2×D412yes—
146C4⋊C4×C61—21no—
147C4⋊C4×C61—21no—
148C4⋊C4×C61—22no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—22no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—41no—
153C4⋊C4×C61—41no—
154C4⋊C4×C61C2×D411yescharacteristic
155C4⋊C4×C61C2×D411yescharacteristic
156C22⋊C4×C61—21no—
157C22⋊C4×C61—21no—
158C22⋊C4×C61—21no—
159C22⋊C4×C61—41no—
160C22⋊C4×C61—41no—
161C42×C61—21no—
162C42×C61—21no—
163C42×C61—21no—
164C42×C61C2×D411yescharacteristic
165C42×C61C2×D411yescharacteristic
166C42×C61#4111yescharacteristic
167C42×C61C2411yescharacteristic
168C23×C61—21no—
169C23×C61—41no—
170C23×C61#12111yescharacteristic
171Q8×C61—21no—
172Q8×C61—21no—
173Q8×C61—42no—
174Q8×C61—42no—
175Q8×C61—42no—
176Q8×C61—82no—
177D4×C61—21no—
178D4×C61—42no—
179D4×C61—41no—
180D4×C61—41no—
181D4×C61—42no—
182D4×C61—81no—
183D4×C61—82no—
184D4×C61AGL(1,ℤ/8)12yes—
185C2×C4×C61—21no—
186C2×C4×C61—22no—
187C2×C4×C61—21no—
188C2×C4×C61—21no—
189C2×C4×C61—21no—
190C2×C4×C61—21no—
191C2×C4×C61—41no—
192C2×C4×C61—42no—
193C2×C4×C61—42no—
194C2×C4×C61—41no—
195C2×C4×C61—42no—
196C2×C4×C61—81no—
197C2×C4×C61—82no—
198C2×C4×C61—82no—
199C2×C4×C61#12111yescharacteristic
200C2×C4×C61#12111yescharacteristic
201C2×C4×C61#12111yescharacteristic
202C2×C4×C61C22×D411yescharacteristic
203C2×C4×C61C22×D411yescharacteristic
204C2×C4×C61C2×#4111yescharacteristic
205C8×C61—22no—
206C8×C61—22no—
207C8×C61—42no—
208C8×C61—41no—
209C8×C61—42no—
210C8×C61—41no—
211#19319C6111yesmaximal, characteristic, direct product factor, Sylow
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—22no—
215C22×C61—21no—
216C22×C61—41no—
217C22×C61—41no—
218C22×C61—81no—
219C22×C61—81no—
220C22×C61—81no—
221C22×C61C2×#12111yescharacteristic
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—41no—
227C4×C61—41no—
228C4×C61—41no—
229C4×C61—81no—
230C4×C61—82no—
231C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
232C4×C61#57512yes—
233C4×C61#57511yescharacteristic
234#3141C2×C6111yescharacteristic, complemented
235#3115C2×C6111yescharacteristic
236#3039C2×C6111yescharacteristic, complemented
237#2970C2×C6111yescharacteristic, complemented
238#1702C2×C6112yescomplemented
239#1700C2×C6112yescomplemented
240#1681C2×C6112yescomplemented
241#1679C2×C6112yescomplemented
242#1569C2×C6111yescharacteristic, complemented
243#1557C2×C6111yescharacteristic, complemented
244#1556C2×C6111yescharacteristic, complemented
245C2×C61—41no—
246C2×C61—42no—
247C2×C61—161no—
248C2×C61#304011yescharacteristic
249C2×C61#305511yescharacteristic
250C2×C61#306911yescharacteristic
251C2×#137—21no—
252#532C22×C6111yescharacteristic
253C2×C4⋊Q8C22×C6111yescharacteristic
254C4×#41C22×C6111yescharacteristic
255#489—21no—
256#489—21no—
257#487C22×C6112yes—
258#486C22×C6112yes—
259#482—21no—
260#475C22×C6111yescharacteristic
261#474C22×C6111yescharacteristic
262#462—21no—
263#462C22×C6112yes—
264#461—21no—
265#461C22×C6112yes—
266#460C22×C6111yescharacteristic
267#459C22×C6111yescharacteristic
268#449—21no—
269#446C22×C6112yes—
270#442—21no—
271#440—21no—
272#435—22no—
273C8×D4C22×C6112yes—
274#432—21no—
275#432C22×C6111yescharacteristic
276#432C22×C6111yescharacteristic
277#423C22×C6111yescharacteristic
278#419—21no—
279#417—22no—
280C4×M16C22×C6111yescharacteristic
281C2×#97—21no—
282#335C22×C6112yes—
283#334C22×C6112yes—
284#332C22×C6112yes—
285#332C22×C6112yes—
286#332C22×C6112yes—
287#331C22×C6112yes—
288C61#1931911yescharacteristic, direct product factor, Sylow
289C2×#41—21no—
290C2×#41D4×C6111yescharacteristic
291C22×Q8—21no—
292#137—44no—
293C2×Q16—22no—
294C2×SD16—21no—
295C2×SD16—22no—
296C2×D8—21no—
297C2×M16—21no—
298C2×M16D4×C6112yes—
299C22×C8—22no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8C23×C6112yes—
304C4⋊Q8C23×C6111yescharacteristic
305#127C23×C6111yescharacteristic
306#124—21no—
307#121—21no—
308#121—21no—
309C4×Q8D4×C6111yescharacteristic
310C4×Q8C23×C6111yescharacteristic
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4D4×C6111yescharacteristic
316C4×D4C23×C6111yescharacteristic
317#117—21no—
318#117D4×C6111yescharacteristic
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C42—21no—
322C2×C42C23×C6111yescharacteristic
323#107—21no—
324#106—21no—
325C4⋊C8—22no—
326C4⋊C8—21no—
327C4⋊C8C23×C6112yes—
328C4⋊C8C23×C6112yes—
329C4⋊C8C23×C6111yescharacteristic
330C4⋊C8C23×C6111yescharacteristic
331#103—21no—
332#103—22no—
333#103—22no—
334#103—22no—
335#103—22no—
336#102—21no—
337#102—22no—
338#102—22no—
339#102—21no—
340#102—21no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C22⋊C8—22no—
344#97—22no—
345#97—21no—
346#97—21no—
347#97D4×C6111yescharacteristic
348#97D4×C6111yescharacteristic
349C4×C8C23×C6112yes—
350#41—22no—
351#41—41no—
352#41—44no—
353C2×Q8—21no—
354C2×Q8—22no—
355C2×Q8—42no—
356C2×Q8—42no—
357C2×Q8—41no—
358C2×Q8C2×D4×C6111yescharacteristic
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—41no—
364C2×D4C2×D4×C6111yescharacteristic
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4C2×D4×C6111yescharacteristic
371C22×C4C2×D4×C6111yescharacteristic
372C22×C4#41×C6111yescharacteristic
373Q16—44no—
374SD16—42no—
375SD16—44no—
376D8—42no—
377M16—42no—
378M16—42no—
379C2×C8—22no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—22no—
383C2×C8—44no—
384C2×C8C2×D4×C6112yes—
385C2×C8C2×D4×C6112yes—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4C2×D4×C6111yescharacteristic
395C4⋊C4C2×D4×C6111yescharacteristic
396C22⋊C4—21no—
397C22⋊C4—21no—
398C22⋊C4—21no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C42—21no—
402C42—21no—
403C42—21no—
404C42C2×D4×C6111yescharacteristic
405C42C2×D4×C6111yescharacteristic
406C42#41×C6111yescharacteristic
407C42C24×C6111yescharacteristic
408C23—21no—
409C23—41no—
410C23#121×C6111yescharacteristic
411Q8—21no—
412Q8—21no—
413Q8—42no—
414Q8—42no—
415Q8—42no—
416Q8—82no—
417D4—21no—
418D4—42no—
419D4—41no—
420D4—41no—
421D4—42no—
422D4—81no—
423D4—82no—
424D4AGL(1,ℤ/8)×C6112yes—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—81no—
437C2×C4—82no—
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—22no—
446C8—22no—
447C8—42no—
448C8—41no—
449C8—42no—
450C8—41no—
451C22—21no—
452C22—21no—
453C22—22no—
454C22—21no—
455C22—41no—
456C22—41no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22C2×#121×C6111yescharacteristic
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—41no—
466C4—41no—
467C4—41no—
468C4—81no—
469C4—82no—
470C4C2×AGL(1,ℤ/8)×C6111yescharacteristic
471C4C61×#57512yes—
472C4C61×#57511yescharacteristic
473C2—41no—
474C2—42no—
475C2—161no—
476C2C61×#304011yescharacteristic
477C2C61×#305511yescharacteristic
478C2C61×#306911yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
commutator, Frattini, cosocleC42C24×C61
prime radicalC61×#3115C2
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×#3141C2semidirect
3. C61×#3039C2semidirect
4. C61×#2970C2semidirect
5. C61×#1702C2semidirect
6. C61×#1700C2semidirect
7. C61×#1681C2semidirect
8. C61×#1679C2semidirect
9. C61×#1569C2semidirect
10. C61×#1557C2semidirect
11. C61×#1556C2semidirect
211. #19319C61direct (N × H)
234. #3141C2×C61semidirect
236. #3039C2×C61semidirect
237. #2970C2×C61semidirect
238. #1702C2×C61semidirect
239. #1700C2×C61semidirect
240. #1681C2×C61semidirect
241. #1679C2×C61semidirect
242. #1569C2×C61semidirect
243. #1557C2×C61semidirect
244. #1556C2×C61semidirect
288. C61#19319direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#31412
C61×#31152
C61×#30392
C61×#29702
C61×#17022
C61×#17002
C61×#16812
C61×#16792
C61×#15692
C61×#15572
C61×#15562
#1931961