Finite Group Databasebeta

← C61×#9275 #29512708

Subgroups — C61×#9275 #29512708

Order 15616.

606 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3187C211yesmaximal, characteristic
2C61×#2364C211yesmaximal, characteristic
3C61×#1996C211yesmaximal, characteristic, complemented
4C61×#1519C211yesmaximal, characteristic
5C2×C61×#328C211yesmaximal, characteristic, complemented
6C61×#1294C211yesmaximal, characteristic, complemented
7C61×#1282C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C61C2211yescharacteristic
9C2×#121×C61C2211yescharacteristic
10C2×C4×D4×C61—21no—
11C61×#483—21no—
12C61×#481C412yescomplemented
13C61×#465—22no—
14C61×#450—21no—
15C61×#448C412yescomplemented
16C2×C22⋊C8×C61C2211yescharacteristic
17C2×C22⋊C8×C61C2211yescharacteristic
18C61×#388—21no—
19C61×#387—21no—
20C61×#386—21no—
21C61×#386—21no—
22C61×#380C2211yescharacteristic
23C4×C22⋊C4×C61—21no—
24C4×C22⋊C4×C61C2211yescharacteristic
25C2×#95×C61C2211yescharacteristic
26C61×#342—21no—
27C61×#342—21no—
28C61×#328—21no—
29C61×#328—21no—
30C61×#327—22no—
31C22×Q8×C61C2×C411yescharacteristic, complemented
32C22×D4×C61—21no—
33C22×D4×C61D411yescharacteristic
34C23×C4×C61—21no—
35C23×C4×C61—21no—
36C23×C4×C61C2311yescharacteristic
37C2×SD16×C61—22no—
38C22×C8×C61—21no—
39C22×C8×C61—21no—
40C22⋊Q8×C61—21no—
41C22⋊Q8×C61—21no—
42C22⋊Q8×C61—21no—
43C22⋊Q8×C61—21no—
44#121×C61—21no—
45#121×C61—21no—
46#121×C61C2×C412yes—
47#121×C61D412yes—
48C4×D4×C61—42no—
49C4×D4×C61—42no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61D411yescharacteristic
62C2×C22⋊C4×C61D411yescharacteristic
63C2×C42×C61—21no—
64C2×C42×C61—21no—
65#106×C61—22no—
66#103×C61—22no—
67#102×C61—22no—
68C22⋊C8×C61—21no—
69C22⋊C8×C61—21no—
70C22⋊C8×C61—21no—
71C22⋊C8×C61C2×C412yescomplemented
72#95×C61—21no—
73#95×C61—21no—
74#95×C61—21no—
75#95×C61—21no—
76#95×C61—21no—
77#95×C61D411yescharacteristic
78#95×C61D411yescharacteristic
79C24×C61—21no—
80C24×C61C2×D411yescharacteristic
81C2×Q8×C61—21no—
82C2×Q8×C61—21no—
83C2×Q8×C61—81no—
84C2×D4×C61—22no—
85C2×D4×C61—22no—
86C2×D4×C61—21no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—81no—
92C2×D4×C61C22⋊C412yes—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—21no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61—42no—
101C22×C4×C61—42no—
102C22×C4×C61—42no—
103C22×C4×C61—41no—
104C22×C4×C61—41no—
105C22×C4×C61—41no—
106C22×C4×C61—81no—
107C22×C4×C61—81no—
108C22×C4×C61—81no—
109C22×C4×C61C22×C411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C22×C4×C61#4111yescharacteristic
115SD16×C61—82no—
116C2×C8×C61—22no—
117C2×C8×C61—41no—
118C2×C8×C61—81no—
119C2×C8×C61—81no—
120C4⋊C4×C61—21no—
121C4⋊C4×C61—21no—
122C4⋊C4×C61—21no—
123C4⋊C4×C61—42no—
124C4⋊C4×C61—41no—
125C4⋊C4×C61—41no—
126C4⋊C4×C61—81no—
127C4⋊C4×C61C22⋊C412yes—
128C22⋊C4×C61—21no—
129C22⋊C4×C61—22no—
130C22⋊C4×C61—22no—
131C22⋊C4×C61—21no—
132C22⋊C4×C61—21no—
133C22⋊C4×C61—42no—
134C22⋊C4×C61—42no—
135C22⋊C4×C61—41no—
136C22⋊C4×C61—41no—
137C22⋊C4×C61—41no—
138C22⋊C4×C61—41no—
139C22⋊C4×C61—81no—
140C22⋊C4×C61SD1612yescomplemented
141C42×C61—42no—
142C42×C61—81no—
143C23×C61—22no—
144C23×C61—41no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61—41no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61C4×D411yescharacteristic
153C23×C61#12011yescharacteristic
154C23×C61#12111yescharacteristic
155C23×C61C2×SD1611yescharacteristic
156C23×C61#13511yescharacteristic
157C23×C61AGL(1,ℤ/8)11yescharacteristic
158C23×C61#13711yescharacteristic
159Q8×C61—42no—
160Q8×C61—81no—
161D4×C61—42no—
162D4×C61—42no—
163D4×C61—42no—
164D4×C61—42no—
165D4×C61—42no—
166D4×C61—81no—
167C2×C4×C61—22no—
168C2×C4×C61—22no—
169C2×C4×C61—22no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—84no—
191C2×C4×C61—82no—
192C2×C4×C61—82no—
193C2×C4×C61—81no—
194C2×C4×C61—81no—
195C2×C4×C61—81no—
196C2×C4×C61—81no—
197C2×C4×C61—81no—
198C2×C4×C61C2×C22⋊C411yescharacteristic
199C2×C4×C61C4×D411yescharacteristic
200C2×C4×C61#12111yescharacteristic
201C2×C4×C61#12311yescharacteristic
202C8×C61—42no—
203C8×C61—81no—
204#9275C6111yesmaximal, characteristic, direct product factor, Sylow
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—41no—
212C22×C61—41no—
213C22×C61—41no—
214C22×C61—41no—
215C22×C61—42no—
216C22×C61—42no—
217C22×C61—42no—
218C22×C61—81no—
219C22×C61—81no—
220C22×C61—81no—
221C22×C61—81no—
222C22×C61#38611yescharacteristic
223C22×C61C4×SD1611yescharacteristic
224C22×C61#44011yescharacteristic
225C22×C61#45011yescharacteristic
226C22×C61#45211yescharacteristic
227C22×C61#46111yescharacteristic
228C22×C61#46311yescharacteristic
229C4×C61—21no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—21no—
233C4×C61—42no—
234C4×C61—42no—
235C4×C61—42no—
236C4×C61—81no—
237C4×C61—81no—
238C4×C61—81no—
239C4×C61—81no—
240C4×C61—161no—
241#3187C2×C6111yescharacteristic
242#2364C2×C6111yescharacteristic
243#1996C2×C6111yescharacteristic, complemented
244#1519C2×C6111yescharacteristic
245C2×#328C2×C6111yescharacteristic, complemented
246#1294C2×C6111yescharacteristic, complemented
247#1282C2×C6111yescharacteristic, complemented
248C2×C61—21no—
249C2×C61—21no—
250C2×C61—21no—
251C2×C61—21no—
252C2×C61—21no—
253C2×C61—21no—
254C2×C61—82no—
255C2×C61#187711yescharacteristic
256C2×C61#190611yescharacteristic
257C2×C61#191311yescharacteristic
258C2×C22⋊Q8C22×C6111yescharacteristic
259C2×#121C22×C6111yescharacteristic
260C2×C4×D4—21no—
261#483—21no—
262#481C4×C6112yescomplemented
263#465—22no—
264#450—21no—
265#448C4×C6112yescomplemented
266C2×C22⋊C8C22×C6111yescharacteristic
267C2×C22⋊C8C22×C6111yescharacteristic
268#388—21no—
269#387—21no—
270#386—21no—
271#386—21no—
272#380C22×C6111yescharacteristic
273C4×C22⋊C4—21no—
274C4×C22⋊C4C22×C6111yescharacteristic
275C2×#95C22×C6111yescharacteristic
276#342—21no—
277#342—21no—
278#328—21no—
279#328—21no—
280#327—22no—
281C61#927511yescharacteristic, direct product factor, Sylow
282C22×Q8C2×C4×C6111yescharacteristic, complemented
283C22×D4—21no—
284C22×D4D4×C6111yescharacteristic
285C23×C4—21no—
286C23×C4—21no—
287C23×C4C23×C6111yescharacteristic
288C2×SD16—22no—
289C22×C8—21no—
290C22×C8—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295#121—21no—
296#121—21no—
297#121C2×C4×C6112yes—
298#121D4×C6112yes—
299C4×D4—42no—
300C4×D4—42no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4C2×C4×C6111yescharacteristic, complemented
305C2×C4⋊C4D4×C6111yescharacteristic
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4D4×C6111yescharacteristic
313C2×C22⋊C4D4×C6111yescharacteristic
314C2×C42—21no—
315C2×C42—21no—
316#106—22no—
317#103—22no—
318#102—22no—
319C22⋊C8—21no—
320C22⋊C8—21no—
321C22⋊C8—21no—
322C22⋊C8C2×C4×C6112yescomplemented
323#95—21no—
324#95—21no—
325#95—21no—
326#95—21no—
327#95—21no—
328#95D4×C6111yescharacteristic
329#95D4×C6111yescharacteristic
330C24—21no—
331C24C2×D4×C6111yescharacteristic
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—81no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—21no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—81no—
343C2×D4C22⋊C4×C6112yes—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—81no—
358C22×C4—81no—
359C22×C4—81no—
360C22×C4C22×C4×C6111yescharacteristic
361C22×C4C2×D4×C6111yescharacteristic
362C22×C4C2×D4×C6111yescharacteristic
363C22×C4C2×D4×C6111yescharacteristic
364C22×C4#41×C6111yescharacteristic
365C22×C4#41×C6111yescharacteristic
366SD16—82no—
367C2×C8—22no—
368C2×C8—41no—
369C2×C8—81no—
370C2×C8—81no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—42no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—81no—
378C4⋊C4C22⋊C4×C6112yes—
379C22⋊C4—21no—
380C22⋊C4—22no—
381C22⋊C4—22no—
382C22⋊C4—21no—
383C22⋊C4—21no—
384C22⋊C4—42no—
385C22⋊C4—42no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—81no—
391C22⋊C4SD16×C6112yescomplemented
392C42—42no—
393C42—81no—
394C23—22no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23C4×D4×C6111yescharacteristic
404C23#120×C6111yescharacteristic
405C23#121×C6111yescharacteristic
406C23C2×SD16×C6111yescharacteristic
407C23#135×C6111yescharacteristic
408C23AGL(1,ℤ/8)×C6111yescharacteristic
409C23#137×C6111yescharacteristic
410Q8—42no—
411Q8—81no—
412D4—42no—
413D4—42no—
414D4—42no—
415D4—42no—
416D4—42no—
417D4—81no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—84no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4C2×C22⋊C4×C6111yescharacteristic
450C2×C4C4×D4×C6111yescharacteristic
451C2×C4#121×C6111yescharacteristic
452C2×C4#123×C6111yescharacteristic
453C8—42no—
454C8—81no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22C61×#38611yescharacteristic
473C22C4×SD16×C6111yescharacteristic
474C22C61×#44011yescharacteristic
475C22C61×#45011yescharacteristic
476C22C61×#45211yescharacteristic
477C22C61×#46111yescharacteristic
478C22C61×#46311yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—42no—
484C4—42no—
485C4—42no—
486C4—81no—
487C4—81no—
488C4—81no—
489C4—81no—
490C4—161no—
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—21no—
497C2—82no—
498C2C61×#187711yescharacteristic
499C2C61×#190611yescharacteristic
500C2C61×#191311yescharacteristic
subgroupG/H
center, socleC22×C61#386
commutatorC22×C4C22×C4×C61
Frattini, cosocleC23×C4C23×C61
prime radicalC2×#121×C61C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
3. C61×#1996C2semidirect
5. C2×C61×#328C2semidirect
6. C61×#1294C2semidirect
7. C61×#1282C2semidirect
12. C61×#481C4semidirect
15. C61×#448C4semidirect
31. C22×Q8×C61C2×C4semidirect
53. C2×C4⋊C4×C61C2×C4semidirect
71. C22⋊C8×C61C2×C4semidirect
140. C22⋊C4×C61SD16semidirect
204. #9275C61direct (N × H)
243. #1996C2×C61semidirect
245. C2×#328C2×C61semidirect
246. #1294C2×C61semidirect
247. #1282C2×C61semidirect
262. #481C4×C61semidirect
265. #448C4×C61semidirect
281. C61#9275direct (N × H)
282. C22×Q8C2×C4×C61semidirect
304. C2×C4⋊C4C2×C4×C61semidirect
322. C22⋊C8C2×C4×C61semidirect
391. C22⋊C4SD16×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#31872
C61×#23642
C61×#19962
C61×#15192
C2×C61×#3282
C61×#12942
C61×#12822
#927561