Finite Group Databasebeta

← C61×#19643 #29523076

Subgroups — C61×#19643 #29523076

Order 15616.

686 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3231C211yesmaximal, characteristic, complemented
2C61×#3228C211yesmaximal, characteristic
3C61×#3185C211yesmaximal, characteristic, complemented
4C61×#3182C211yesmaximal, characteristic
5C61×#3170C211yesmaximal, characteristic, complemented
6C61×#3131C211yesmaximal, characteristic
7C61×#1723C211yesmaximal, characteristic, complemented
8C61×#1722C211yesmaximal, characteristic, complemented
9C61×#1720C211yesmaximal, characteristic, complemented
10C61×#1718C211yesmaximal, characteristic, complemented
11C61×#1711C211yesmaximal, characteristic, complemented
12C61×#1710C211yesmaximal, characteristic, complemented
13C61×#1708C211yesmaximal, characteristic, complemented
14C61×#1707C211yesmaximal, characteristic, complemented
15C8×M16×C61C211yesmaximal, characteristic, complemented
16C61×#533C2211yescharacteristic
17C61×#533C2211yescharacteristic
18C61×#533C2211yescharacteristic
19C61×#532C2211yescharacteristic
20C61×#500C2211yescharacteristic
21C61×#500C2211yescharacteristic
22C61×#500C2211yescharacteristic
23C61×#500C2211yescharacteristic
24C61×#498C2211yescharacteristic
25C61×#498C2211yescharacteristic
26C61×#498C2211yescharacteristic
27C61×#494C2211yescharacteristic
28C61×#494C2211yescharacteristic
29C61×#492C2211yescharacteristic
30C61×#488—22no—
31C61×#487C2211yescharacteristic
32C61×#487C2211yescharacteristic
33C61×#487C2211yescharacteristic
34C61×#487C2211yescharacteristic
35C61×#487C2211yescharacteristic
36C61×#487C2211yescharacteristic
37C61×#487C2211yescharacteristic
38C61×#487C2211yescharacteristic
39C61×#487C2211yescharacteristic
40C61×#486C2211yescharacteristic
41C61×#486C2211yescharacteristic
42C61×#486C2211yescharacteristic
43C61×#486C2211yescharacteristic
44C61×#486C2211yescharacteristic
45C61×#485—22no—
46C61×#482—22no—
47C61×#479—22no—
48C61×#478—22no—
49C61×#470—22no—
50C61×#468—22no—
51C61×#467—22no—
52C61×#441—22no—
53C61×#440—22no—
54C4×Q16×C61—22no—
55C61×#431C2211yescharacteristic
56C61×#416—22no—
57C4×M16×C61C2211yescharacteristic
58C2×C4×C8×C61C2211yescharacteristic
59C61×#322C2211yescharacteristic
60C61×#322C2211yescharacteristic
61C82×C61C2211yescharacteristic
62C82×C61C2211yescharacteristic
63C2×#41×C61—21no—
64C2×Q16×C61—22no—
65C2×Q16×C61—22no—
66C2×SD16×C61—22no—
67C2×M16×C61D412yes—
68C22×C8×C61D412yes—
69C4⋊Q8×C61C2311yescharacteristic
70C4⋊Q8×C61C2311yescharacteristic
71C4⋊Q8×C61C2311yescharacteristic
72C4⋊Q8×C61C2311yescharacteristic
73C4⋊Q8×C61C2311yescharacteristic
74C4⋊Q8×C61C2311yescharacteristic
75C4⋊Q8×C61C2311yescharacteristic
76#127×C61C2311yescharacteristic
77#125×C61—21no—
78#125×C61—21no—
79#125×C61—21no—
80#124×C61—21no—
81C22⋊Q8×C61—21no—
82C22⋊Q8×C61—21no—
83C22⋊Q8×C61—21no—
84C22⋊Q8×C61—21no—
85C22⋊Q8×C61—21no—
86C22⋊Q8×C61—21no—
87#121×C61—21no—
88#121×C61—21no—
89C4×Q8×C61—21no—
90C4×Q8×C61—21no—
91C4×Q8×C61—21no—
92C4×Q8×C61—21no—
93C4×Q8×C61—21no—
94C4×Q8×C61—21no—
95C4×D4×C61—21no—
96C4×D4×C61—21no—
97#117×C61—21no—
98#117×C61—21no—
99#117×C61—21no—
100C2×C42×C61C2311yescharacteristic
101#107×C61—22no—
102#107×C61—22no—
103#107×C61—22no—
104#107×C61—22no—
105#106×C61—22no—
106#106×C61—22no—
107#106×C61—22no—
108C4⋊C8×C61D412yes—
109#103×C61—22no—
110#103×C61—22no—
111#103×C61—22no—
112#103×C61—22no—
113#103×C61—22no—
114#103×C61—22no—
115#103×C61—22no—
116#103×C61—22no—
117#103×C61—22no—
118#102×C61—22no—
119#102×C61—22no—
120#102×C61—22no—
121#102×C61—22no—
122#102×C61—22no—
123C22⋊C8×C61D412yes—
124#97×C61D412yes—
125C4×C8×C61D412yes—
126C4×C8×C61C2311yescharacteristic
127C4×C8×C61C2311yescharacteristic
128C4×C8×C61C2311yescharacteristic
129C4×C8×C61C2311yescharacteristic
130C4×C8×C61C2311yescharacteristic
131C4×C8×C61C2311yescharacteristic
132#41×C61—44no—
133C2×Q8×C61—21no—
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—41no—
144C22×C4×C61—41no—
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148Q16×C61—44no—
149Q16×C61—44no—
150SD16×C61—44no—
151M16×C61—24no—
152C2×C8×C61—42no—
153C2×C8×C61C2×D412yes—
154C2×C8×C61C2×D412yes—
155C2×C8×C61C2×D412yes—
156C2×C8×C61C2×D412yes—
157C2×C8×C61C2×D412yes—
158C2×C8×C61C2×D412yes—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—41no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61—41no—
178C4⋊C4×C61—41no—
179C22⋊C4×C61—41no—
180C22⋊C4×C61—41no—
181C22⋊C4×C61—41no—
182C22⋊C4×C61—41no—
183C22⋊C4×C61—41no—
184C42×C61—41no—
185C42×C61—41no—
186C42×C61—41no—
187C42×C61C2×D411yescharacteristic
188C42×C61C2×D411yescharacteristic
189C42×C61C2×D411yescharacteristic
190C42×C61C2411yescharacteristic
191C23×C61—41no—
192C23×C61#12711yescharacteristic
193Q8×C61—42no—
194Q8×C61—42no—
195Q8×C61—42no—
196Q8×C61—42no—
197Q8×C61—42no—
198Q8×C61—42no—
199Q8×C61—42no—
200D4×C61—42no—
201D4×C61—42no—
202D4×C61—42no—
203D4×C61—82no—
204C2×C4×C61—22no—
205C2×C4×C61—22no—
206C2×C4×C61—22no—
207C2×C4×C61—41no—
208C2×C4×C61—41no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—82no—
215C2×C4×C61#12711yescharacteristic
216C2×C4×C61#12711yescharacteristic
217C2×C4×C61#12711yescharacteristic
218C2×C4×C61C22×D411yescharacteristic
219C2×C4×C61C22×D411yescharacteristic
220C2×C4×C61C22×D411yescharacteristic
221C8×C61—22no—
222C8×C61—22no—
223C8×C61—22no—
224C8×C61—22no—
225C8×C61—22no—
226C8×C61#13514yes—
227#19643C6111yesmaximal, characteristic, direct product factor, Sylow
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—81no—
232C22×C61—81no—
233C22×C61—81no—
234C22×C61C2×#12711yescharacteristic
235C4×C61—21no—
236C4×C61—21no—
237C4×C61—21no—
238C4×C61—81no—
239C4×C61—81no—
240C4×C61—81no—
241C4×C61—81no—
242C4×C61—81no—
243C4×C61—81no—
244C4×C61—81no—
245C4×C61C2×#13512yes—
246C4×C61#57512yes—
247C4×C61#57812yes—
248#3231C2×C6111yescharacteristic, complemented
249#3228C2×C6111yescharacteristic
250#3185C2×C6111yescharacteristic, complemented
251#3182C2×C6111yescharacteristic
252#3170C2×C6111yescharacteristic, complemented
253#3131C2×C6111yescharacteristic
254#1723C2×C6111yescharacteristic, complemented
255#1722C2×C6111yescharacteristic, complemented
256#1720C2×C6111yescharacteristic, complemented
257#1718C2×C6111yescharacteristic, complemented
258#1711C2×C6111yescharacteristic, complemented
259#1710C2×C6111yescharacteristic, complemented
260#1708C2×C6111yescharacteristic, complemented
261#1707C2×C6111yescharacteristic, complemented
262C8×M16C2×C6111yescharacteristic, complemented
263C2×C61—41no—
264C2×C61—161no—
265C2×C61#314711yescharacteristic
266C2×C61#315311yescharacteristic
267C2×C61#315611yescharacteristic
268#533C22×C6111yescharacteristic
269#533C22×C6111yescharacteristic
270#533C22×C6111yescharacteristic
271#532C22×C6111yescharacteristic
272#500C22×C6111yescharacteristic
273#500C22×C6111yescharacteristic
274#500C22×C6111yescharacteristic
275#500C22×C6111yescharacteristic
276#498C22×C6111yescharacteristic
277#498C22×C6111yescharacteristic
278#498C22×C6111yescharacteristic
279#494C22×C6111yescharacteristic
280#494C22×C6111yescharacteristic
281#492C22×C6111yescharacteristic
282#488—22no—
283#487C22×C6111yescharacteristic
284#487C22×C6111yescharacteristic
285#487C22×C6111yescharacteristic
286#487C22×C6111yescharacteristic
287#487C22×C6111yescharacteristic
288#487C22×C6111yescharacteristic
289#487C22×C6111yescharacteristic
290#487C22×C6111yescharacteristic
291#487C22×C6111yescharacteristic
292#486C22×C6111yescharacteristic
293#486C22×C6111yescharacteristic
294#486C22×C6111yescharacteristic
295#486C22×C6111yescharacteristic
296#486C22×C6111yescharacteristic
297#485—22no—
298#482—22no—
299#479—22no—
300#478—22no—
301#470—22no—
302#468—22no—
303#467—22no—
304#441—22no—
305#440—22no—
306C4×Q16—22no—
307#431C22×C6111yescharacteristic
308#416—22no—
309C4×M16C22×C6111yescharacteristic
310C2×C4×C8C22×C6111yescharacteristic
311#322C22×C6111yescharacteristic
312#322C22×C6111yescharacteristic
313C82C22×C6111yescharacteristic
314C82C22×C6111yescharacteristic
315C61#1964311yescharacteristic, direct product factor, Sylow
316C2×#41—21no—
317C2×Q16—22no—
318C2×Q16—22no—
319C2×SD16—22no—
320C2×M16D4×C6112yes—
321C22×C8D4×C6112yes—
322C4⋊Q8C23×C6111yescharacteristic
323C4⋊Q8C23×C6111yescharacteristic
324C4⋊Q8C23×C6111yescharacteristic
325C4⋊Q8C23×C6111yescharacteristic
326C4⋊Q8C23×C6111yescharacteristic
327C4⋊Q8C23×C6111yescharacteristic
328C4⋊Q8C23×C6111yescharacteristic
329#127C23×C6111yescharacteristic
330#125—21no—
331#125—21no—
332#125—21no—
333#124—21no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336C22⋊Q8—21no—
337C22⋊Q8—21no—
338C22⋊Q8—21no—
339C22⋊Q8—21no—
340#121—21no—
341#121—21no—
342C4×Q8—21no—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×D4—21no—
349C4×D4—21no—
350#117—21no—
351#117—21no—
352#117—21no—
353C2×C42C23×C6111yescharacteristic
354#107—22no—
355#107—22no—
356#107—22no—
357#107—22no—
358#106—22no—
359#106—22no—
360#106—22no—
361C4⋊C8D4×C6112yes—
362#103—22no—
363#103—22no—
364#103—22no—
365#103—22no—
366#103—22no—
367#103—22no—
368#103—22no—
369#103—22no—
370#103—22no—
371#102—22no—
372#102—22no—
373#102—22no—
374#102—22no—
375#102—22no—
376C22⋊C8D4×C6112yes—
377#97D4×C6112yes—
378C4×C8D4×C6112yes—
379C4×C8C23×C6111yescharacteristic
380C4×C8C23×C6111yescharacteristic
381C4×C8C23×C6111yescharacteristic
382C4×C8C23×C6111yescharacteristic
383C4×C8C23×C6111yescharacteristic
384C4×C8C23×C6111yescharacteristic
385#41—44no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—41no—
397C22×C4—41no—
398C22×C4C2×D4×C6111yescharacteristic
399C22×C4C2×D4×C6111yescharacteristic
400C22×C4C2×D4×C6111yescharacteristic
401Q16—44no—
402Q16—44no—
403SD16—44no—
404M16—24no—
405C2×C8—42no—
406C2×C8C2×D4×C6112yes—
407C2×C8C2×D4×C6112yes—
408C2×C8C2×D4×C6112yes—
409C2×C8C2×D4×C6112yes—
410C2×C8C2×D4×C6112yes—
411C2×C8C2×D4×C6112yes—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C42—41no—
438C42—41no—
439C42—41no—
440C42C2×D4×C6111yescharacteristic
441C42C2×D4×C6111yescharacteristic
442C42C2×D4×C6111yescharacteristic
443C42C24×C6111yescharacteristic
444C23—41no—
445C23#127×C6111yescharacteristic
446Q8—42no—
447Q8—42no—
448Q8—42no—
449Q8—42no—
450Q8—42no—
451Q8—42no—
452Q8—42no—
453D4—42no—
454D4—42no—
455D4—42no—
456D4—82no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—82no—
468C2×C4#127×C6111yescharacteristic
469C2×C4#127×C6111yescharacteristic
470C2×C4#127×C6111yescharacteristic
471C2×C4C22×D4×C6111yescharacteristic
472C2×C4C22×D4×C6111yescharacteristic
473C2×C4C22×D4×C6111yescharacteristic
474C8—22no—
475C8—22no—
476C8—22no—
477C8—22no—
478C8—22no—
479C8#135×C6114yes—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22C2×#127×C6111yescharacteristic
487C4—21no—
488C4—21no—
489C4—21no—
490C4—81no—
491C4—81no—
492C4—81no—
493C4—81no—
494C4—81no—
495C4—81no—
496C4—81no—
497C4C2×#135×C6112yes—
498C4C61×#57512yes—
499C4C61×#57812yes—
500C2—41no—
501C2—161no—
502C2C61×#314711yescharacteristic
503C2C61×#315311yescharacteristic
504C2C61×#315611yescharacteristic
subgroupG/H
center, socleC22×C61C2×#127
commutator, Frattini, cosocleC42C24×C61
prime radicalC61×#532C22
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×#3231C2semidirect
3. C61×#3185C2semidirect
5. C61×#3170C2semidirect
7. C61×#1723C2semidirect
8. C61×#1722C2semidirect
9. C61×#1720C2semidirect
10. C61×#1718C2semidirect
11. C61×#1711C2semidirect
12. C61×#1710C2semidirect
13. C61×#1708C2semidirect
14. C61×#1707C2semidirect
15. C8×M16×C61C2semidirect
227. #19643C61direct (N × H)
248. #3231C2×C61semidirect
250. #3185C2×C61semidirect
252. #3170C2×C61semidirect
254. #1723C2×C61semidirect
255. #1722C2×C61semidirect
256. #1720C2×C61semidirect
257. #1718C2×C61semidirect
258. #1711C2×C61semidirect
259. #1710C2×C61semidirect
260. #1708C2×C61semidirect
261. #1707C2×C61semidirect
262. C8×M16C2×C61semidirect
315. C61#19643direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#32312
C61×#32282
C61×#31852
C61×#31822
C61×#31702
C61×#31312
C61×#17232
C61×#17222
C61×#17202
C61×#17182
C61×#17112
C61×#17102
C61×#17082
C61×#17072
C8×M16×C612
#1964361