Finite Group Databasebeta

← C61×#9264 #29512697

Subgroups — C61×#9264 #29512697

Order 15616.

504 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3188C211yesmaximal, characteristic
2C61×#2977C211yesmaximal, characteristic, complemented
3C61×#1504C211yesmaximal, characteristic, complemented
4C2×C61×#327C211yesmaximal, characteristic, complemented
5C61×#1471C211yesmaximal, characteristic, complemented
6C61×#1298C211yesmaximal, characteristic, complemented
7C61×#1280C211yesmaximal, characteristic, complemented
8C61×#525C2211yescharacteristic
9C2×#121×C61C2211yescharacteristic
10C61×#484C411yescharacteristic, complemented
11C61×#482—21no—
12C61×#481C411yescharacteristic, complemented
13C61×#466—21no—
14C61×#465—21no—
15C61×#450C411yescharacteristic, complemented
16C61×#449—21no—
17C61×#447C411yescharacteristic, complemented
18C61×#435—21no—
19C61×#435—21no—
20C8×D4×C61—21no—
21C8×D4×C61—21no—
22C61×#433—21no—
23C61×#408—21no—
24C61×#407C2211yescharacteristic
25C2×C22⋊C8×C61C2211yescharacteristic
26C2×C22⋊C8×C61C2211yescharacteristic
27C2×C22⋊C8×C61C2211yescharacteristic
28C2×#95×C61C2211yescharacteristic
29C61×#328—21no—
30C61×#327—21no—
31C61×#327—21no—
32C61×#327—21no—
33C61×#323—21no—
34C61×#323—21no—
35C2×#41×C61D411yescharacteristic
36C22×D4×C61—21no—
37C22×D4×C61C2×C411yescharacteristic
38C23×C4×C61—21no—
39C23×C4×C61C2311yescharacteristic
40C2×SD16×C61—21no—
41C2×D8×C61—21no—
42C2×M16×C61—21no—
43C2×M16×C61—21no—
44C22×C8×C61—21no—
45C22×C8×C61—21no—
46C22×C8×C61—21no—
47C22×C8×C61—21no—
48#123×C61—21no—
49C22⋊Q8×C61C2×C411yescharacteristic
50C22⋊Q8×C61D411yescharacteristic
51#121×C61—21no—
52#121×C61—21no—
53#121×C61—21no—
54#121×C61—21no—
55#121×C61C2×C411yescharacteristic
56#121×C61D411yescharacteristic
57#120×C61—21no—
58C4×D4×C61—21no—
59C4×D4×C61—21no—
60#117×C61D411yescharacteristic
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C22⋊C4×C61—21no—
63#107×C61—21no—
64#106×C61—21no—
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67#103×C61—21no—
68#102×C61—21no—
69#102×C61—21no—
70#102×C61—21no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61—21no—
75C22⋊C8×C61—21no—
76C22⋊C8×C61—21no—
77C22⋊C8×C61—21no—
78C22⋊C8×C61C2×C411yescharacteristic
79C22⋊C8×C61C2×C411yescharacteristic
80C22⋊C8×C61D411yescharacteristic
81C22⋊C8×C61D411yescharacteristic
82C22⋊C8×C61D411yescharacteristic
83C22⋊C8×C61D411yescharacteristic
84#97×C61—21no—
85C4×C8×C61—21no—
86#95×C61—21no—
87#95×C61—21no—
88C24×C61—21no—
89C24×C61#4111yescharacteristic
90#41×C61—81no—
91C2×Q8×C61C22⋊C411yescharacteristic
92C2×D4×C61—21no—
93C2×D4×C61—21no—
94C2×D4×C61—21no—
95C2×D4×C61—21no—
96C2×D4×C61—21no—
97C2×D4×C61—41no—
98C2×D4×C61—41no—
99C2×D4×C61—81no—
100C2×D4×C61—81no—
101C2×D4×C61—81no—
102C2×D4×C61C22⋊C411yescharacteristic
103C22×C4×C61—21no—
104C22×C4×C61—22no—
105C22×C4×C61—21no—
106C22×C4×C61—41no—
107C22×C4×C61—41no—
108C22×C4×C61—81no—
109C22×C4×C61—81no—
110C22×C4×C61—81no—
111C22×C4×C61C22×C411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61#4111yescharacteristic
117SD16×C61—81no—
118D8×C61—81no—
119M16×C61—81no—
120M16×C61—81no—
121C2×C8×C61—21no—
122C2×C8×C61—21no—
123C2×C8×C61—21no—
124C2×C8×C61—21no—
125C2×C8×C61—21no—
126C2×C8×C61—21no—
127C2×C8×C61—41no—
128C2×C8×C61—81no—
129C2×C8×C61—81no—
130C2×C8×C61—81no—
131C2×C8×C61—81no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—21no—
136C4⋊C4×C61C22⋊C411yescharacteristic
137C4⋊C4×C61C22⋊C411yescharacteristic
138C22⋊C4×C61—21no—
139C22⋊C4×C61—21no—
140C22⋊C4×C61—21no—
141C22⋊C4×C61—21no—
142C22⋊C4×C61—21no—
143C22⋊C4×C61—41no—
144C22⋊C4×C61—41no—
145C42×C61—21no—
146C23×C61—21no—
147C23×C61—21no—
148C23×C61—21no—
149C23×C61—21no—
150C23×C61—21no—
151C23×C61—41no—
152C23×C61—41no—
153C23×C61—41no—
154C23×C61—41no—
155C23×C61—81no—
156C23×C61—81no—
157C23×C61C4×D411yescharacteristic
158C23×C61#12111yescharacteristic
159C23×C61#12311yescharacteristic
160Q8×C61—41no—
161D4×C61—41no—
162D4×C61—41no—
163D4×C61—41no—
164D4×C61—41no—
165D4×C61—41no—
166D4×C61—41no—
167D4×C61—41no—
168D4×C61—81no—
169D4×C61—81no—
170D4×C61—82no—
171D4×C61—81no—
172D4×C61—81no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
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—42no—
185C2×C4×C61—41no—
186C2×C4×C61—81no—
187C2×C4×C61—82no—
188C2×C4×C61—81no—
189C2×C4×C61—81no—
190C2×C4×C61—82no—
191C2×C4×C61C2×C22⋊C411yescharacteristic
192C2×C4×C61C4×D411yescharacteristic
193C2×C4×C61#12011yescharacteristic
194C2×C4×C61#12111yescharacteristic
195C8×C61—41no—
196C8×C61—41no—
197C8×C61—41no—
198C8×C61—41no—
199C8×C61—41no—
200C8×C61—41no—
201C8×C61—81no—
202#9264C6111yesmaximal, characteristic, direct product factor, Sylow
203C22×C61—21no—
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—41no—
211C22×C61—41no—
212C22×C61—41no—
213C22×C61—41no—
214C22×C61—41no—
215C22×C61—41no—
216C22×C61—41no—
217C22×C61—81no—
218C22×C61—81no—
219C22×C61—81no—
220C22×C61—161no—
221C22×C61—161no—
222C22×C61#38611yescharacteristic
223C22×C61#44311yescharacteristic
224C22×C61#44411yescharacteristic
225C22×C61#47111yescharacteristic
226C22×C61#47211yescharacteristic
227C4×C61—21no—
228C4×C61—21no—
229C4×C61—21no—
230C4×C61—21no—
231C4×C61—41no—
232C4×C61—41no—
233C4×C61—41no—
234C4×C61—82no—
235C4×C61—81no—
236#3188C2×C6111yescharacteristic
237#2977C2×C6111yescharacteristic, complemented
238#1504C2×C6111yescharacteristic, complemented
239C2×#327C2×C6111yescharacteristic, complemented
240#1471C2×C6111yescharacteristic, complemented
241#1298C2×C6111yescharacteristic, complemented
242#1280C2×C6111yescharacteristic, complemented
243C2×C61—21no—
244C2×C61—21no—
245C2×C61—21no—
246C2×C61—21no—
247C2×C61—41no—
248C2×C61—81no—
249C2×C61—161no—
250C2×C61#187611yescharacteristic
251C2×C61#190711yescharacteristic
252C2×C61#191311yescharacteristic
253#525C22×C6111yescharacteristic
254C2×#121C22×C6111yescharacteristic
255#484C4×C6111yescharacteristic, complemented
256#482—21no—
257#481C4×C6111yescharacteristic, complemented
258#466—21no—
259#465—21no—
260#450C4×C6111yescharacteristic, complemented
261#449—21no—
262#447C4×C6111yescharacteristic, complemented
263#435—21no—
264#435—21no—
265C8×D4—21no—
266C8×D4—21no—
267#433—21no—
268#408—21no—
269#407C22×C6111yescharacteristic
270C2×C22⋊C8C22×C6111yescharacteristic
271C2×C22⋊C8C22×C6111yescharacteristic
272C2×C22⋊C8C22×C6111yescharacteristic
273C2×#95C22×C6111yescharacteristic
274#328—21no—
275#327—21no—
276#327—21no—
277#327—21no—
278#323—21no—
279#323—21no—
280C61#926411yescharacteristic, direct product factor, Sylow
281C2×#41D4×C6111yescharacteristic
282C22×D4—21no—
283C22×D4C2×C4×C6111yescharacteristic
284C23×C4—21no—
285C23×C4C23×C6111yescharacteristic
286C2×SD16—21no—
287C2×D8—21no—
288C2×M16—21no—
289C2×M16—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294#123—21no—
295C22⋊Q8C2×C4×C6111yescharacteristic
296C22⋊Q8D4×C6111yescharacteristic
297#121—21no—
298#121—21no—
299#121—21no—
300#121—21no—
301#121C2×C4×C6111yescharacteristic
302#121D4×C6111yescharacteristic
303#120—21no—
304C4×D4—21no—
305C4×D4—21no—
306#117D4×C6111yescharacteristic
307C2×C4⋊C4C2×C4×C6111yescharacteristic
308C2×C22⋊C4—21no—
309#107—21no—
310#106—21no—
311C4⋊C8—21no—
312C4⋊C8—21no—
313#103—21no—
314#102—21no—
315#102—21no—
316#102—21no—
317C22⋊C8—21no—
318C22⋊C8—21no—
319C22⋊C8—21no—
320C22⋊C8—21no—
321C22⋊C8—21no—
322C22⋊C8—21no—
323C22⋊C8—21no—
324C22⋊C8C2×C4×C6111yescharacteristic
325C22⋊C8C2×C4×C6111yescharacteristic
326C22⋊C8D4×C6111yescharacteristic
327C22⋊C8D4×C6111yescharacteristic
328C22⋊C8D4×C6111yescharacteristic
329C22⋊C8D4×C6111yescharacteristic
330#97—21no—
331C4×C8—21no—
332#95—21no—
333#95—21no—
334C24—21no—
335C24#41×C6111yescharacteristic
336#41—81no—
337C2×Q8C22⋊C4×C6111yescharacteristic
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—81no—
346C2×D4—81no—
347C2×D4—81no—
348C2×D4C22⋊C4×C6111yescharacteristic
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—81no—
355C22×C4—81no—
356C22×C4—81no—
357C22×C4C22×C4×C6111yescharacteristic
358C22×C4C2×D4×C6111yescharacteristic
359C22×C4C2×D4×C6111yescharacteristic
360C22×C4C2×D4×C6111yescharacteristic
361C22×C4C2×D4×C6111yescharacteristic
362C22×C4#41×C6111yescharacteristic
363SD16—81no—
364D8—81no—
365M16—81no—
366M16—81no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—41no—
374C2×C8—81no—
375C2×C8—81no—
376C2×C8—81no—
377C2×C8—81no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4C22⋊C4×C6111yescharacteristic
383C4⋊C4C22⋊C4×C6111yescharacteristic
384C22⋊C4—21no—
385C22⋊C4—21no—
386C22⋊C4—21no—
387C22⋊C4—21no—
388C22⋊C4—21no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C42—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—81no—
402C23—81no—
403C23C4×D4×C6111yescharacteristic
404C23#121×C6111yescharacteristic
405C23#123×C6111yescharacteristic
406Q8—41no—
407D4—41no—
408D4—41no—
409D4—41no—
410D4—41no—
411D4—41no—
412D4—41no—
413D4—41no—
414D4—81no—
415D4—81no—
416D4—82no—
417D4—81no—
418D4—81no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
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—42no—
431C2×C4—41no—
432C2×C4—81no—
433C2×C4—82no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—82no—
437C2×C4C2×C22⋊C4×C6111yescharacteristic
438C2×C4C4×D4×C6111yescharacteristic
439C2×C4#120×C6111yescharacteristic
440C2×C4#121×C6111yescharacteristic
441C8—41no—
442C8—41no—
443C8—41no—
444C8—41no—
445C8—41no—
446C8—41no—
447C8—81no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—161no—
466C22—161no—
467C22C61×#38611yescharacteristic
468C22C61×#44311yescharacteristic
469C22C61×#44411yescharacteristic
470C22C61×#47111yescharacteristic
471C22C61×#47211yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—41no—
477C4—41no—
478C4—41no—
479C4—82no—
480C4—81no—
481C2—21no—
482C2—21no—
483C2—21no—
484C2—21no—
485C2—41no—
486C2—81no—
487C2—161no—
488C2C61×#187611yescharacteristic
489C2C61×#190711yescharacteristic
490C2C61×#191311yescharacteristic
subgroupG/H
center, socleC22×C61#386
commutatorC22×C4C22×C4×C61
Frattini, cosocleC23×C4C23×C61
prime radicalC61×#3188C2
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
2. C61×#2977C2semidirect
3. C61×#1504C2semidirect
4. C2×C61×#327C2semidirect
5. C61×#1471C2semidirect
6. C61×#1298C2semidirect
7. C61×#1280C2semidirect
10. C61×#484C4semidirect
12. C61×#481C4semidirect
15. C61×#450C4semidirect
17. C61×#447C4semidirect
202. #9264C61direct (N × H)
237. #2977C2×C61semidirect
238. #1504C2×C61semidirect
239. C2×#327C2×C61semidirect
240. #1471C2×C61semidirect
241. #1298C2×C61semidirect
242. #1280C2×C61semidirect
255. #484C4×C61semidirect
257. #481C4×C61semidirect
260. #450C4×C61semidirect
262. #447C4×C61semidirect
280. C61#9264direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#31882
C61×#29772
C61×#15042
C2×C61×#3272
C61×#14712
C61×#12982
C61×#12802
#926461