Finite Group Databasebeta

← C61×#25288 #29528721

Subgroups — C61×#25288 #29528721

Order 15616.

964 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#490C211yesmaximal, characteristic, complemented
2C2×C61×#478C211yesmaximal, characteristic, complemented
3C61×#2541C211yesmaximal, characteristic
4C61×#2370C211yesmaximal, characteristic, complemented
5C61×#2067C211yesmaximal, characteristic, complemented
6C61×#2065C211yesmaximal, characteristic, complemented
7C61×#2041C211yesmaximal, characteristic, complemented
8C61×#2041C211yesmaximal, characteristic, complemented
9C61×#1982C211yesmaximal, characteristic, complemented
10C61×#1982C211yesmaximal, characteristic, complemented
11C61×#1982C211yesmaximal, characteristic, complemented
12C61×#1940C211yesmaximal, characteristic, complemented
13C61×#1926C211yesmaximal, characteristic, complemented
14C61×#1925C211yesmaximal, characteristic, complemented
15C61×#1762C211yesmaximal, characteristic, complemented
16C2×#127×C61C2211yescharacteristic
17C2×#127×C61C2211yescharacteristic
18C2×#127×C61C2211yescharacteristic
19C2×#125×C61C2211yescharacteristic
20C2×#121×C61—21no—
21C2×#121×C61—21no—
22C2×C4×D4×C61C2211yescharacteristic
23C61×#490—24no—
24C61×#478—24no—
25C2×#107×C61C2211yescharacteristic
26C2×#106×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×C4⋊C8×C61C2211yescharacteristic
30C2×#102×C61C2211yescharacteristic
31C2×#102×C61C2211yescharacteristic
32C2×#102×C61C2211yescharacteristic
33C2×#102×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic
35C2×#102×C61C2211yescharacteristic
36C2×#102×C61C2211yescharacteristic
37C2×#102×C61C2211yescharacteristic
38C2×#102×C61C2211yescharacteristic
39C2×#102×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic
42C2×#97×C61C2211yescharacteristic
43C61×#392—21no—
44C61×#392—21no—
45C61×#390C2211yescharacteristic
46C61×#390C2211yescharacteristic
47C61×#389—21no—
48C61×#389C2211yescharacteristic
49C61×#389C2211yescharacteristic
50C61×#387—21no—
51C61×#387—21no—
52C4×C4⋊C4×C61—21no—
53C4×C4⋊C4×C61C2211yescharacteristic
54C4×C4⋊C4×C61C2211yescharacteristic
55C4×C4⋊C4×C61C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×D4×C61—21no—
62C22×D4×C61—21no—
63C22×D4×C61—21no—
64C22×D4×C61—21no—
65C22×D4×C61—21no—
66C22×D4×C61—21no—
67C22×D4×C61C2311yescharacteristic
68C22×D4×C61C2311yescharacteristic
69C22×D4×C61C2311yescharacteristic
70C23×C4×C61—21no—
71C22×C8×C61C2311yescharacteristic
72C22×C8×C61C2311yescharacteristic
73C22×C8×C61C2311yescharacteristic
74C22×C8×C61C2311yescharacteristic
75#127×C61—22no—
76#127×C61—22no—
77#127×C61—22no—
78#127×C61—22no—
79#127×C61—41no—
80#127×C61—41no—
81#125×C61—22no—
82#125×C61D414yescomplemented
83#121×C61—44no—
84#121×C61—44no—
85C4×D4×C61—22no—
86C4×D4×C61—22no—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61D411yescharacteristic
92C2×C4⋊C4×C61D411yescharacteristic
93C2×C4⋊C4×C61C2311yescharacteristic
94C2×C4⋊C4×C61C2311yescharacteristic
95C2×C4⋊C4×C61C2311yescharacteristic
96C2×C4⋊C4×C61C2311yescharacteristic
97C2×C4⋊C4×C61C2311yescharacteristic
98C2×C22⋊C4×C61—21no—
99C2×C22⋊C4×C61—21no—
100C2×C22⋊C4×C61—21no—
101C2×C22⋊C4×C61—21no—
102C2×C22⋊C4×C61—21no—
103C2×C42×C61—21no—
104C2×C42×C61—21no—
105C2×C42×C61—21no—
106C2×C42×C61C2311yescharacteristic
107C2×C42×C61C2311yescharacteristic
108C2×C42×C61C2311yescharacteristic
109#107×C61—22no—
110#106×C61—22no—
111C4⋊C8×C61—22no—
112C4⋊C8×C61—41no—
113C4⋊C8×C61—41no—
114#102×C61—22no—
115#102×C61—22no—
116#102×C61—22no—
117#102×C61—22no—
118#102×C61—22no—
119#102×C61—22no—
120#102×C61—22no—
121#102×C61—22no—
122#102×C61—22no—
123#102×C61—22no—
124#102×C61—41no—
125#102×C61—41no—
126#97×C61—22no—
127#95×C61—21no—
128#95×C61—21no—
129#95×C61—21no—
130#95×C61—21no—
131#95×C61—21no—
132#95×C61D411yescharacteristic
133#95×C61D411yescharacteristic
134C24×C61—21no—
135C24×C61—21no—
136C24×C61—21no—
137C2×D4×C61—21no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—42no—
155C2×D4×C61—42no—
156C2×D4×C61—42no—
157C2×D4×C61—42no—
158C2×D4×C61—42no—
159C2×D4×C61—42no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61—42no—
163C2×D4×C61—42no—
164C2×D4×C61—42no—
165C2×D4×C61—42no—
166C2×D4×C61—81no—
167C2×D4×C61—81no—
168C2×D4×C61—81no—
169C2×D4×C61—81no—
170C2×D4×C61—81no—
171C2×D4×C61—81no—
172C2×D4×C61#4112yes—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—42no—
179C22×C4×C61—42no—
180C22×C4×C61—42no—
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2411yescharacteristic
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C4⋊C4×C61—24no—
201C4⋊C4×C61—24no—
202C4⋊C4×C61—22no—
203C4⋊C4×C61—22no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—42no—
212C4⋊C4×C61—81no—
213C4⋊C4×C61C2×D412yes—
214C4⋊C4×C61C2×D412yes—
215C4⋊C4×C61#4112yes—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—42no—
218C22⋊C4×C61—42no—
219C22⋊C4×C61—42no—
220C22⋊C4×C61—42no—
221C42×C61—21no—
222C42×C61—21no—
223C42×C61—21no—
224C42×C61—21no—
225C42×C61—42no—
226C42×C61—81no—
227C42×C61—81no—
228C42×C61C2×D412yes—
229C42×C61#4112yes—
230C23×C61—22no—
231C23×C61—41no—
232C23×C61—41no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61C22×D411yescharacteristic
252D4×C61—22no—
253D4×C61—22no—
254D4×C61—41no—
255D4×C61—41no—
256D4×C61—41no—
257D4×C61—41no—
258D4×C61—41no—
259D4×C61—41no—
260D4×C61—41no—
261D4×C61—41no—
262D4×C61—41no—
263D4×C61—41no—
264D4×C61—84no—
265D4×C61—84no—
266D4×C61—84no—
267D4×C61—84no—
268D4×C61—84no—
269D4×C61—84no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—22no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—84no—
300C2×C4×C61#12112yes—
301C2×C4×C61#12112yes—
302C2×C4×C61AGL(1,ℤ/8)12yes—
303C2×C4×C61AGL(1,ℤ/8)12yes—
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C61H(5,𝔽2)11yescharacteristic
309C2×C4×C612−1+411yescharacteristic
310C8×C61—41no—
311C8×C61—41no—
312C8×C61—41no—
313C8×C61—41no—
314#25288C6111yesmaximal, characteristic, direct product factor, Sylow
315C22×C61—42no—
316C22×C61—42no—
317C22×C61—42no—
318C22×C61—81no—
319C22×C61—81no—
320C22×C61—81no—
321C22×C61—81no—
322C22×C61—81no—
323C22×C61—81no—
324C22×C61—81no—
325C22×C61—81no—
326C22×C61—81no—
327C22×C61—81no—
328C22×C61—81no—
329C22×C61—81no—
330C22×C61—81no—
331C22×C61—81no—
332C22×C61—81no—
333C22×C61—81no—
334C22×C61—81no—
335C22×C61—81no—
336C22×C61C2×#12111yescharacteristic
337C22×C61#54611yescharacteristic
338C22×C61#54811yescharacteristic
339C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
340C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
341C22×C61#57611yescharacteristic
342C22×C61#57711yescharacteristic
343C4×C61—22no—
344C4×C61—22no—
345C4×C61—22no—
346C4×C61—22no—
347C4×C61—42no—
348C4×C61—42no—
349C4×C61—42no—
350C4×C61—41no—
351C4×C61—41no—
352C4×C61—81no—
353C4×C61—81no—
354C4×C61#52911yescharacteristic
355C4×C61#54211yescharacteristic
356C4×C61#54811yescharacteristic
357C4×C61#55011yescharacteristic
358C2×#490C2×C6111yescharacteristic, complemented
359C2×#478C2×C6111yescharacteristic, complemented
360#2541C2×C6111yescharacteristic
361#2370C2×C6111yescharacteristic, complemented
362#2067C2×C6111yescharacteristic, complemented
363#2065C2×C6111yescharacteristic, complemented
364#2041C2×C6111yescharacteristic, complemented
365#2041C2×C6111yescharacteristic, complemented
366#1982C2×C6111yescharacteristic, complemented
367#1982C2×C6111yescharacteristic, complemented
368#1982C2×C6111yescharacteristic, complemented
369#1940C2×C6111yescharacteristic, complemented
370#1926C2×C6111yescharacteristic, complemented
371#1925C2×C6111yescharacteristic, complemented
372#1762C2×C6111yescharacteristic, complemented
373C2×C61—82no—
374C2×C61—161no—
375C2×C61—161no—
376C2×C61#242611yescharacteristic
377C2×C61#303811yescharacteristic
378C2×C61#304511yescharacteristic
379C2×C61#331011yescharacteristic
380C2×C61#331811yescharacteristic
381C2×C61#336611yescharacteristic
382C2×C61#336811yescharacteristic
383C2×#127C22×C6111yescharacteristic
384C2×#127C22×C6111yescharacteristic
385C2×#127C22×C6111yescharacteristic
386C2×#125C22×C6111yescharacteristic
387C2×#121—21no—
388C2×#121—21no—
389C2×C4×D4C22×C6111yescharacteristic
390#490—24no—
391#478—24no—
392C2×#107C22×C6111yescharacteristic
393C2×#106C22×C6111yescharacteristic
394C2×C4⋊C8C22×C6111yescharacteristic
395C2×C4⋊C8C22×C6111yescharacteristic
396C2×C4⋊C8C22×C6111yescharacteristic
397C2×#102C22×C6111yescharacteristic
398C2×#102C22×C6111yescharacteristic
399C2×#102C22×C6111yescharacteristic
400C2×#102C22×C6111yescharacteristic
401C2×#102C22×C6111yescharacteristic
402C2×#102C22×C6111yescharacteristic
403C2×#102C22×C6111yescharacteristic
404C2×#102C22×C6111yescharacteristic
405C2×#102C22×C6111yescharacteristic
406C2×#102C22×C6111yescharacteristic
407C2×#102C22×C6111yescharacteristic
408C2×#102C22×C6111yescharacteristic
409C2×#97C22×C6111yescharacteristic
410#392—21no—
411#392—21no—
412#390C22×C6111yescharacteristic
413#390C22×C6111yescharacteristic
414#389—21no—
415#389C22×C6111yescharacteristic
416#389C22×C6111yescharacteristic
417#387—21no—
418#387—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4C22×C6111yescharacteristic
421C4×C4⋊C4C22×C6111yescharacteristic
422C4×C4⋊C4C22×C6111yescharacteristic
423C4×C4⋊C4C22×C6111yescharacteristic
424#340C22×C6111yescharacteristic
425#340C22×C6111yescharacteristic
426#336C22×C6111yescharacteristic
427#336C22×C6111yescharacteristic
428C61#2528811yescharacteristic, direct product factor, Sylow
429C22×D4—21no—
430C22×D4—21no—
431C22×D4—21no—
432C22×D4—21no—
433C22×D4—21no—
434C22×D4—21no—
435C22×D4C23×C6111yescharacteristic
436C22×D4C23×C6111yescharacteristic
437C22×D4C23×C6111yescharacteristic
438C23×C4—21no—
439C22×C8C23×C6111yescharacteristic
440C22×C8C23×C6111yescharacteristic
441C22×C8C23×C6111yescharacteristic
442C22×C8C23×C6111yescharacteristic
443#127—22no—
444#127—22no—
445#127—22no—
446#127—22no—
447#127—41no—
448#127—41no—
449#125—22no—
450#125D4×C6114yescomplemented
451#121—44no—
452#121—44no—
453C4×D4—22no—
454C4×D4—22no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4D4×C6111yescharacteristic
460C2×C4⋊C4D4×C6111yescharacteristic
461C2×C4⋊C4C23×C6111yescharacteristic
462C2×C4⋊C4C23×C6111yescharacteristic
463C2×C4⋊C4C23×C6111yescharacteristic
464C2×C4⋊C4C23×C6111yescharacteristic
465C2×C4⋊C4C23×C6111yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42C23×C6111yescharacteristic
475C2×C42C23×C6111yescharacteristic
476C2×C42C23×C6111yescharacteristic
477#107—22no—
478#106—22no—
479C4⋊C8—22no—
480C4⋊C8—41no—
481C4⋊C8—41no—
482#102—22no—
483#102—22no—
484#102—22no—
485#102—22no—
486#102—22no—
487#102—22no—
488#102—22no—
489#102—22no—
490#102—22no—
491#102—22no—
492#102—41no—
493#102—41no—
494#97—22no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95D4×C6111yescharacteristic
501#95D4×C6111yescharacteristic
502C24—21no—
503C24—21no—
504C24—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—81no—
535C2×D4—81no—
536C2×D4—81no—
537C2×D4—81no—
538C2×D4—81no—
539C2×D4—81no—
540C2×D4#41×C6112yes—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4C2×D4×C6111yescharacteristic
550C22×C4C2×D4×C6111yescharacteristic
551C22×C4C2×D4×C6111yescharacteristic
552C22×C4C2×D4×C6111yescharacteristic
553C22×C4C2×D4×C6111yescharacteristic
554C22×C4C2×D4×C6111yescharacteristic
555C22×C4C24×C6111yescharacteristic
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—42no—
580C4⋊C4—81no—
581C4⋊C4C2×D4×C6112yes—
582C4⋊C4C2×D4×C6112yes—
583C4⋊C4#41×C6112yes—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—42no—
594C42—81no—
595C42—81no—
596C42C2×D4×C6112yes—
597C42#41×C6112yes—
598C23—22no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23C22×D4×C6111yescharacteristic
620D4—22no—
621D4—22no—
622D4—41no—
623D4—41no—
624D4—41no—
625D4—41no—
626D4—41no—
627D4—41no—
628D4—41no—
629D4—41no—
630D4—41no—
631D4—41no—
632D4—84no—
633D4—84no—
634D4—84no—
635D4—84no—
636D4—84no—
637D4—84no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4#121×C6112yes—
669C2×C4#121×C6112yes—
670C2×C4AGL(1,ℤ/8)×C6112yes—
671C2×C4AGL(1,ℤ/8)×C6112yes—
672C2×C4C22×D4×C6111yescharacteristic
673C2×C4C2×#41×C6111yescharacteristic
674C2×C4C2×#41×C6111yescharacteristic
675C2×C4C2×#41×C6111yescharacteristic
676C2×C4H(5,𝔽2)×C6111yescharacteristic
677C2×C42−1+4×C6111yescharacteristic
678C8—41no—
679C8—41no—
680C8—41no—
681C8—41no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22C2×#121×C6111yescharacteristic
704C22C61×#54611yescharacteristic
705C22C61×#54811yescharacteristic
706C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
707C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
708C22C61×#57611yescharacteristic
709C22C61×#57711yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—42no—
715C4—42no—
716C4—41no—
717C4—41no—
718C4—42no—
719C4—81no—
720C4—81no—
721C4C61×#52911yescharacteristic
722C4C61×#54211yescharacteristic
723C4C61×#54811yescharacteristic
724C4C61×#55011yescharacteristic
725C2—82no—
726C2—161no—
727C2—161no—
728C2C61×#242611yescharacteristic
729C2C61×#303811yescharacteristic
730C2C61×#304511yescharacteristic
731C2C61×#331011yescharacteristic
732C2C61×#331811yescharacteristic
733C2C61×#336611yescharacteristic
734C2C61×#336811yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#2541C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C4×C4⋊C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#490C2semidirect
2. C2×C61×#478C2semidirect
4. C61×#2370C2semidirect
5. C61×#2067C2semidirect
6. C61×#2065C2semidirect
7. C61×#2041C2semidirect
8. C61×#2041C2semidirect
9. C61×#1982C2semidirect
10. C61×#1982C2semidirect
11. C61×#1982C2semidirect
12. C61×#1940C2semidirect
13. C61×#1926C2semidirect
14. C61×#1925C2semidirect
15. C61×#1762C2semidirect
82. #125×C61D4semidirect
314. #25288C61direct (N × H)
358. C2×#490C2×C61semidirect
359. C2×#478C2×C61semidirect
361. #2370C2×C61semidirect
362. #2067C2×C61semidirect
363. #2065C2×C61semidirect
364. #2041C2×C61semidirect
365. #2041C2×C61semidirect
366. #1982C2×C61semidirect
367. #1982C2×C61semidirect
368. #1982C2×C61semidirect
369. #1940C2×C61semidirect
370. #1926C2×C61semidirect
371. #1925C2×C61semidirect
372. #1762C2×C61semidirect
428. C61#25288direct (N × H)
450. #125D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4902
C2×C61×#4782
C61×#25412
C61×#23702
C61×#20672
C61×#20652
C61×#20412
C61×#19822
C61×#19402
C61×#19262
C61×#19252
C61×#17622
#2528861