Finite Group Databasebeta

← C61×#22392 #29525825

Subgroups — C61×#22392 #29525825

Order 15616.

732 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2398C211yesmaximal, characteristic
2C61×#1985C211yesmaximal, characteristic, complemented
3C61×#1984C211yesmaximal, characteristic, complemented
4C61×#1924C211yesmaximal, characteristic, complemented
5C61×#1923C211yesmaximal, characteristic, complemented
6C61×#1923C211yesmaximal, characteristic, complemented
7C61×#1923C211yesmaximal, characteristic, complemented
8C61×#1870C211yesmaximal, characteristic
9C61×#1869C211yesmaximal, characteristic
10C61×#1851C211yesmaximal, characteristic, complemented
11C61×#1850C211yesmaximal, characteristic, complemented
12C61×#1840C211yesmaximal, characteristic, complemented
13C61×#1768C211yesmaximal, characteristic, complemented
14C61×#1753C211yesmaximal, characteristic, complemented
15C61×#1752C211yesmaximal, characteristic, complemented
16C22×M16×C61C2211yescharacteristic
17C23×C8×C61C2211yescharacteristic
18C2×C4×Q8×C61C2211yescharacteristic
19C2×C4×D4×C61C2211yescharacteristic
20C2×C4⋊C8×C61C2211yescharacteristic
21C2×C4⋊C8×C61C2211yescharacteristic
22C2×C4⋊C8×C61C2211yescharacteristic
23C2×C4⋊C8×C61C2211yescharacteristic
24C2×C22⋊C8×C61C2211yescharacteristic
25C2×C22⋊C8×C61C2211yescharacteristic
26C2×C22⋊C8×C61C2211yescharacteristic
27C2×C22⋊C8×C61C2211yescharacteristic
28C2×C22⋊C8×C61C2211yescharacteristic
29C2×C22⋊C8×C61C2211yescharacteristic
30C2×#97×C61C2211yescharacteristic
31C2×#97×C61C2211yescharacteristic
32C2×C4×C8×C61C2211yescharacteristic
33C2×C4×C8×C61C2211yescharacteristic
34C61×#400C411yescharacteristic
35C61×#400C411yescharacteristic
36C61×#397C411yescharacteristic
37C61×#397C411yescharacteristic
38C61×#394C411yescharacteristic
39C61×#394C411yescharacteristic
40C61×#393C411yescharacteristic
41C61×#393C411yescharacteristic
42C4×C22⋊C4×C61C2211yescharacteristic
43C4×C22⋊C4×C61C2211yescharacteristic
44C4×C22⋊C4×C61C2211yescharacteristic
45C4×C22⋊C4×C61C2211yescharacteristic
46C61×#376C2211yescharacteristic
47C61×#336C2211yescharacteristic
48C61×#336C2211yescharacteristic
49C61×#336C2211yescharacteristic
50C61×#336C2211yescharacteristic
51C61×#336C2211yescharacteristic
52C61×#336C2211yescharacteristic
53C61×#336C2211yescharacteristic
54C61×#336C2211yescharacteristic
55C61×#336C2211yescharacteristic
56C61×#336C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×Q8×C61C2×C411yescharacteristic
60C22×D4×C61C2×C411yescharacteristic
61C23×C4×C61C2311yescharacteristic
62C23×C4×C61C2311yescharacteristic
63C2×M16×C61—22no—
64C2×M16×C61—41no—
65C2×M16×C61—41no—
66C22×C8×C61—22no—
67C22×C8×C61—41no—
68C22×C8×C61—41no—
69C22×C8×C61C2311yescharacteristic
70C22×C8×C61C2311yescharacteristic
71C22×C8×C61C2311yescharacteristic
72C22×C8×C61C2311yescharacteristic
73C22×C8×C61C2311yescharacteristic
74C22×C8×C61C2311yescharacteristic
75C22×C8×C61C2311yescharacteristic
76C22×C8×C61C2311yescharacteristic
77C4×Q8×C61—41no—
78C4×Q8×C61—41no—
79C4×D4×C61—41no—
80C4×D4×C61—41no—
81C2×C4⋊C4×C61C2×C411yescharacteristic
82C2×C4⋊C4×C61C2×C411yescharacteristic
83C2×C4⋊C4×C61C2×C411yescharacteristic
84C2×C4⋊C4×C61C2×C411yescharacteristic
85C2×C22⋊C4×C61C2×C411yescharacteristic
86C2×C22⋊C4×C61C2×C411yescharacteristic
87C2×C22⋊C4×C61C2×C411yescharacteristic
88C2×C22⋊C4×C61C2×C411yescharacteristic
89C2×C22⋊C4×C61C2×C411yescharacteristic
90C2×C22⋊C4×C61C2×C411yescharacteristic
91C2×C22⋊C4×C61C2×C411yescharacteristic
92C2×C22⋊C4×C61C2×C411yescharacteristic
93C2×C22⋊C4×C61C2×C411yescharacteristic
94C2×C22⋊C4×C61C2×C411yescharacteristic
95C2×C42×C61C2311yescharacteristic
96C2×C42×C61C2311yescharacteristic
97C2×C42×C61C2311yescharacteristic
98C2×C42×C61C2311yescharacteristic
99C2×C42×C61C2311yescharacteristic
100C4⋊C8×C61—22no—
101C4⋊C8×C61—22no—
102C4⋊C8×C61—41no—
103C4⋊C8×C61—41no—
104C22⋊C8×C61—22no—
105C22⋊C8×C61—22no—
106C22⋊C8×C61—41no—
107C22⋊C8×C61—41no—
108C22⋊C8×C61—41no—
109C22⋊C8×C61—41no—
110#97×C61—41no—
111#97×C61—41no—
112C4×C8×C61—41no—
113C4×C8×C61—41no—
114#95×C61C2×C411yescharacteristic
115#95×C61C2×C411yescharacteristic
116#95×C61C2×C411yescharacteristic
117#95×C61C2×C411yescharacteristic
118#95×C61C2×C411yescharacteristic
119#95×C61C2×C411yescharacteristic
120#95×C61C2×C411yescharacteristic
121#95×C61C2×C411yescharacteristic
122#95×C61C2×C411yescharacteristic
123#95×C61C2×C411yescharacteristic
124#95×C61C2×C411yescharacteristic
125#95×C61C2×C411yescharacteristic
126C24×C61C22×C411yescharacteristic
127C24×C61C22×C411yescharacteristic
128C2×Q8×C61—22no—
129C2×Q8×C61—41no—
130C2×Q8×C61—41no—
131C2×D4×C61—22no—
132C2×D4×C61—41no—
133C2×D4×C61—41no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C2411yescharacteristic
159M16×C61—44no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—44no—
183C2×C8×C61#4112yes—
184C2×C8×C61#4112yes—
185C4⋊C4×C61—41no—
186C4⋊C4×C61—41no—
187C4⋊C4×C61—41no—
188C4⋊C4×C61—41no—
189C22⋊C4×C61—22no—
190C22⋊C4×C61—22no—
191C22⋊C4×C61—22no—
192C22⋊C4×C61—22no—
193C22⋊C4×C61—41no—
194C22⋊C4×C61—41no—
195C22⋊C4×C61—41no—
196C22⋊C4×C61—41no—
197C22⋊C4×C61—41no—
198C22⋊C4×C61—41no—
199C42×C61—21no—
200C42×C61—21no—
201C42×C61—21no—
202C42×C61—21no—
203C42×C61—21no—
204C42×C61—21no—
205C42×C61—21no—
206C42×C61—21no—
207C42×C61—21no—
208C42×C61—21no—
209C23×C61—21no—
210C23×C61—21no—
211C23×C61—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61#13112yes—
223C23×C61C23×C411yescharacteristic
224Q8×C61—44no—
225D4×C61—44no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61#13112yes—
270C2×C4×C61C2×#4111yescharacteristic
271C2×C4×C61C2×#4111yescharacteristic
272C2×C4×C61H(5,𝔽2)11yescharacteristic
273C2×C4×C61H(5,𝔽2)11yescharacteristic
274C2×C4×C61H(5,𝔽2)11yescharacteristic
275C2×C4×C612−1+411yescharacteristic
276C8×C61—22no—
277C8×C61—22no—
278C8×C61—41no—
279C8×C61—41no—
280C8×C61—41no—
281C8×C61—41no—
282C8×C61—41no—
283C8×C61—41no—
284#22392C6111yesmaximal, characteristic, direct product factor, Sylow
285C22×C61—22no—
286C22×C61—22no—
287C22×C61—22no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61—41no—
297C22×C61—41no—
298C22×C61—41no—
299C22×C61C4×#4111yescharacteristic
300C22×C61#51811yescharacteristic
301C22×C61#52011yescharacteristic
302C22×C61C2×#13111yescharacteristic
303C22×C61C2×#13111yescharacteristic
304C22×C61#56811yescharacteristic
305C22×C61#56811yescharacteristic
306C4×C61—22no—
307C4×C61—41no—
308C4×C61—41no—
309C4×C61—41no—
310C4×C61—41no—
311C4×C61—41no—
312C4×C61—41no—
313C4×C61—41no—
314C4×C61—41no—
315C4×C61—41no—
316C4×C61—41no—
317C4×C61—41no—
318C4×C61#53811yescharacteristic
319C4×C61#53811yescharacteristic
320C4×C61#54211yescharacteristic
321C4×C61#54211yescharacteristic
322#2398C2×C6111yescharacteristic
323#1985C2×C6111yescharacteristic, complemented
324#1984C2×C6111yescharacteristic, complemented
325#1924C2×C6111yescharacteristic, complemented
326#1923C2×C6111yescharacteristic, complemented
327#1923C2×C6111yescharacteristic, complemented
328#1923C2×C6111yescharacteristic, complemented
329#1870C2×C6111yescharacteristic
330#1869C2×C6111yescharacteristic
331#1851C2×C6111yescharacteristic, complemented
332#1850C2×C6111yescharacteristic, complemented
333#1840C2×C6111yescharacteristic, complemented
334#1768C2×C6111yescharacteristic, complemented
335#1753C2×C6111yescharacteristic, complemented
336#1752C2×C6111yescharacteristic, complemented
337C2×C61—42no—
338C2×C61—81no—
339C2×C61#233711yescharacteristic
340C2×C61#296811yescharacteristic
341C2×C61#296911yescharacteristic
342C2×C61#297611yescharacteristic
343C2×C61#297611yescharacteristic
344C2×C61#299411yescharacteristic
345C2×C61#299511yescharacteristic
346C22×M16C22×C6111yescharacteristic
347C23×C8C22×C6111yescharacteristic
348C2×C4×Q8C22×C6111yescharacteristic
349C2×C4×D4C22×C6111yescharacteristic
350C2×C4⋊C8C22×C6111yescharacteristic
351C2×C4⋊C8C22×C6111yescharacteristic
352C2×C4⋊C8C22×C6111yescharacteristic
353C2×C4⋊C8C22×C6111yescharacteristic
354C2×C22⋊C8C22×C6111yescharacteristic
355C2×C22⋊C8C22×C6111yescharacteristic
356C2×C22⋊C8C22×C6111yescharacteristic
357C2×C22⋊C8C22×C6111yescharacteristic
358C2×C22⋊C8C22×C6111yescharacteristic
359C2×C22⋊C8C22×C6111yescharacteristic
360C2×#97C22×C6111yescharacteristic
361C2×#97C22×C6111yescharacteristic
362C2×C4×C8C22×C6111yescharacteristic
363C2×C4×C8C22×C6111yescharacteristic
364#400C4×C6111yescharacteristic
365#400C4×C6111yescharacteristic
366#397C4×C6111yescharacteristic
367#397C4×C6111yescharacteristic
368#394C4×C6111yescharacteristic
369#394C4×C6111yescharacteristic
370#393C4×C6111yescharacteristic
371#393C4×C6111yescharacteristic
372C4×C22⋊C4C22×C6111yescharacteristic
373C4×C22⋊C4C22×C6111yescharacteristic
374C4×C22⋊C4C22×C6111yescharacteristic
375C4×C22⋊C4C22×C6111yescharacteristic
376#376C22×C6111yescharacteristic
377#336C22×C6111yescharacteristic
378#336C22×C6111yescharacteristic
379#336C22×C6111yescharacteristic
380#336C22×C6111yescharacteristic
381#336C22×C6111yescharacteristic
382#336C22×C6111yescharacteristic
383#336C22×C6111yescharacteristic
384#336C22×C6111yescharacteristic
385#336C22×C6111yescharacteristic
386#336C22×C6111yescharacteristic
387#336C22×C6111yescharacteristic
388#336C22×C6111yescharacteristic
389C61#2239211yescharacteristic, direct product factor, Sylow
390C22×Q8C2×C4×C6111yescharacteristic
391C22×D4C2×C4×C6111yescharacteristic
392C23×C4C23×C6111yescharacteristic
393C23×C4C23×C6111yescharacteristic
394C2×M16—22no—
395C2×M16—41no—
396C2×M16—41no—
397C22×C8—22no—
398C22×C8—41no—
399C22×C8—41no—
400C22×C8C23×C6111yescharacteristic
401C22×C8C23×C6111yescharacteristic
402C22×C8C23×C6111yescharacteristic
403C22×C8C23×C6111yescharacteristic
404C22×C8C23×C6111yescharacteristic
405C22×C8C23×C6111yescharacteristic
406C22×C8C23×C6111yescharacteristic
407C22×C8C23×C6111yescharacteristic
408C4×Q8—41no—
409C4×Q8—41no—
410C4×D4—41no—
411C4×D4—41no—
412C2×C4⋊C4C2×C4×C6111yescharacteristic
413C2×C4⋊C4C2×C4×C6111yescharacteristic
414C2×C4⋊C4C2×C4×C6111yescharacteristic
415C2×C4⋊C4C2×C4×C6111yescharacteristic
416C2×C22⋊C4C2×C4×C6111yescharacteristic
417C2×C22⋊C4C2×C4×C6111yescharacteristic
418C2×C22⋊C4C2×C4×C6111yescharacteristic
419C2×C22⋊C4C2×C4×C6111yescharacteristic
420C2×C22⋊C4C2×C4×C6111yescharacteristic
421C2×C22⋊C4C2×C4×C6111yescharacteristic
422C2×C22⋊C4C2×C4×C6111yescharacteristic
423C2×C22⋊C4C2×C4×C6111yescharacteristic
424C2×C22⋊C4C2×C4×C6111yescharacteristic
425C2×C22⋊C4C2×C4×C6111yescharacteristic
426C2×C42C23×C6111yescharacteristic
427C2×C42C23×C6111yescharacteristic
428C2×C42C23×C6111yescharacteristic
429C2×C42C23×C6111yescharacteristic
430C2×C42C23×C6111yescharacteristic
431C4⋊C8—22no—
432C4⋊C8—22no—
433C4⋊C8—41no—
434C4⋊C8—41no—
435C22⋊C8—22no—
436C22⋊C8—22no—
437C22⋊C8—41no—
438C22⋊C8—41no—
439C22⋊C8—41no—
440C22⋊C8—41no—
441#97—41no—
442#97—41no—
443C4×C8—41no—
444C4×C8—41no—
445#95C2×C4×C6111yescharacteristic
446#95C2×C4×C6111yescharacteristic
447#95C2×C4×C6111yescharacteristic
448#95C2×C4×C6111yescharacteristic
449#95C2×C4×C6111yescharacteristic
450#95C2×C4×C6111yescharacteristic
451#95C2×C4×C6111yescharacteristic
452#95C2×C4×C6111yescharacteristic
453#95C2×C4×C6111yescharacteristic
454#95C2×C4×C6111yescharacteristic
455#95C2×C4×C6111yescharacteristic
456#95C2×C4×C6111yescharacteristic
457C24C22×C4×C6111yescharacteristic
458C24C22×C4×C6111yescharacteristic
459C2×Q8—22no—
460C2×Q8—41no—
461C2×Q8—41no—
462C2×D4—22no—
463C2×D4—41no—
464C2×D4—41no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4C22×C4×C6111yescharacteristic
478C22×C4C22×C4×C6111yescharacteristic
479C22×C4C22×C4×C6111yescharacteristic
480C22×C4C22×C4×C6111yescharacteristic
481C22×C4C22×C4×C6111yescharacteristic
482C22×C4C22×C4×C6111yescharacteristic
483C22×C4C22×C4×C6111yescharacteristic
484C22×C4C22×C4×C6111yescharacteristic
485C22×C4C22×C4×C6111yescharacteristic
486C22×C4C22×C4×C6111yescharacteristic
487C22×C4C22×C4×C6111yescharacteristic
488C22×C4C22×C4×C6111yescharacteristic
489C22×C4C24×C6111yescharacteristic
490M16—44no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—44no—
514C2×C8#41×C6112yes—
515C2×C8#41×C6112yes—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C22⋊C4—41no—
529C22⋊C4—41no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23#131×C6112yes—
554C23C23×C4×C6111yescharacteristic
555Q8—44no—
556D4—44no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4#131×C6112yes—
601C2×C4C2×#41×C6111yescharacteristic
602C2×C4C2×#41×C6111yescharacteristic
603C2×C4H(5,𝔽2)×C6111yescharacteristic
604C2×C4H(5,𝔽2)×C6111yescharacteristic
605C2×C4H(5,𝔽2)×C6111yescharacteristic
606C2×C42−1+4×C6111yescharacteristic
607C8—22no—
608C8—22no—
609C8—41no—
610C8—41no—
611C8—41no—
612C8—41no—
613C8—41no—
614C8—41no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22C4×#41×C6111yescharacteristic
630C22C61×#51811yescharacteristic
631C22C61×#52011yescharacteristic
632C22C2×#131×C6111yescharacteristic
633C22C2×#131×C6111yescharacteristic
634C22C61×#56811yescharacteristic
635C22C61×#56811yescharacteristic
636C4—22no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—41no—
643C4—41no—
644C4—41no—
645C4—41no—
646C4—41no—
647C4—41no—
648C4C61×#53811yescharacteristic
649C4C61×#53811yescharacteristic
650C4C61×#54211yescharacteristic
651C4C61×#54211yescharacteristic
652C2—42no—
653C2—81no—
654C2C61×#233711yescharacteristic
655C2C61×#296811yescharacteristic
656C2C61×#296911yescharacteristic
657C2C61×#297611yescharacteristic
658C2C61×#297611yescharacteristic
659C2C61×#299411yescharacteristic
660C2C61×#299511yescharacteristic
subgroupG/H
centerC22×C4×C61C24
commutatorC23C23×C4×C61
Frattini, cosocleC22×C4C24×C61
socleC23×C61C23×C4
prime radicalC22×D4×C61C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#1985C2semidirect
3. C61×#1984C2semidirect
4. C61×#1924C2semidirect
5. C61×#1923C2semidirect
6. C61×#1923C2semidirect
7. C61×#1923C2semidirect
10. C61×#1851C2semidirect
11. C61×#1850C2semidirect
12. C61×#1840C2semidirect
13. C61×#1768C2semidirect
14. C61×#1753C2semidirect
15. C61×#1752C2semidirect
284. #22392C61direct (N × H)
323. #1985C2×C61semidirect
324. #1984C2×C61semidirect
325. #1924C2×C61semidirect
326. #1923C2×C61semidirect
327. #1923C2×C61semidirect
328. #1923C2×C61semidirect
331. #1851C2×C61semidirect
332. #1850C2×C61semidirect
333. #1840C2×C61semidirect
334. #1768C2×C61semidirect
335. #1753C2×C61semidirect
336. #1752C2×C61semidirect
389. C61#22392direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#23982
C61×#19852
C61×#19842
C61×#19242
C61×#19232
C61×#18702
C61×#18692
C61×#18512
C61×#18502
C61×#18402
C61×#17682
C61×#17532
C61×#17522
#2239261