Finite Group Databasebeta

← C61×#24562 #29527995

Subgroups — C61×#24562 #29527995

Order 15616.

1040 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#480C211yesmaximal, characteristic, complemented
2C2×C61×#408C211yesmaximal, characteristic, complemented
3C61×#2615C211yesmaximal, characteristic
4C61×#2311C211yesmaximal, characteristic, complemented
5C61×#2076C211yesmaximal, characteristic, complemented
6C61×#2075C211yesmaximal, characteristic, complemented
7C61×#2034C211yesmaximal, characteristic, complemented
8C61×#2033C211yesmaximal, characteristic, complemented
9C61×#1895C211yesmaximal, characteristic, complemented
10C61×#1893C211yesmaximal, characteristic, complemented
11C61×#1875C211yesmaximal, characteristic, complemented
12C61×#1854C211yesmaximal, characteristic, complemented
13C61×#1824C211yesmaximal, characteristic, complemented
14C61×#1809C211yesmaximal, characteristic, complemented
15C61×#1808C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×M16×C61C2211yescharacteristic
18C23×C8×C61C2211yescharacteristic
19C2×#121×C61C2211yescharacteristic
20C2×#121×C61C2211yescharacteristic
21C2×#121×C61C2211yescharacteristic
22C2×#117×C61C2211yescharacteristic
23C22×C4⋊C4×C61C2211yescharacteristic
24C61×#480—24no—
25C2×#107×C61C2211yescharacteristic
26C2×#107×C61C2211yescharacteristic
27C2×#107×C61C2211yescharacteristic
28C2×#106×C61C2211yescharacteristic
29C2×#102×C61C2211yescharacteristic
30C2×#102×C61C2211yescharacteristic
31C2×#102×C61C2211yescharacteristic
32C2×#102×C61C2211yescharacteristic
33C61×#408—24no—
34C2×C22⋊C8×C61C2211yescharacteristic
35C2×C22⋊C8×C61C2211yescharacteristic
36C2×C22⋊C8×C61C2211yescharacteristic
37C2×C22⋊C8×C61C2211yescharacteristic
38C61×#393—21no—
39C61×#392—21no—
40C61×#392—21no—
41C61×#392—21no—
42C61×#391—21no—
43C61×#390—21no—
44C61×#386—21no—
45C61×#386—21no—
46C61×#380C2211yescharacteristic
47C61×#380C2211yescharacteristic
48C61×#380C2211yescharacteristic
49C61×#380C2211yescharacteristic
50C61×#380C2211yescharacteristic
51C61×#380C2211yescharacteristic
52C61×#380C2211yescharacteristic
53C61×#340C2211yescharacteristic
54C61×#340C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C2×#41×C61—22no—
62C2×#41×C61—22no—
63C2×#41×C61—22no—
64C2×#41×C61—22no—
65C2×#41×C61—41no—
66C2×#41×C61—41no—
67C22×Q8×C61D411yescharacteristic
68C22×D4×C61—21no—
69C22×D4×C61—21no—
70C22×D4×C61—21no—
71C22×D4×C61D411yescharacteristic
72C22×D4×C61D411yescharacteristic
73C22×D4×C61D411yescharacteristic
74C22×D4×C61C2311yescharacteristic
75C23×C4×C61—21no—
76C23×C4×C61C2311yescharacteristic
77C23×C4×C61C2311yescharacteristic
78C23×C4×C61C2311yescharacteristic
79C2×M16×C61—22no—
80C2×M16×C61—22no—
81C2×M16×C61—41no—
82C22×C8×C61—22no—
83C22×C8×C61—22no—
84C22×C8×C61—41no—
85C22×C8×C61C2311yescharacteristic
86C22×C8×C61C2311yescharacteristic
87C22×C8×C61C2311yescharacteristic
88C22×C8×C61C2311yescharacteristic
89#121×C61—22no—
90#121×C61—22no—
91#121×C61—22no—
92#121×C61—22no—
93#121×C61—41no—
94#121×C61—41no—
95#117×C61—41no—
96#117×C61—41no—
97C2×C4⋊C4×C61—22no—
98C2×C4⋊C4×C61—22no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61C2311yescharacteristic
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C4⋊C4×C61C2311yescharacteristic
104C2×C4⋊C4×C61C2311yescharacteristic
105C2×C4⋊C4×C61C2311yescharacteristic
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C22⋊C4×C61—21no—
108C2×C22⋊C4×C61—21no—
109C2×C22⋊C4×C61—21no—
110C2×C22⋊C4×C61—21no—
111C2×C22⋊C4×C61—21no—
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118C2×C42×C61—21no—
119#107×C61—22no—
120#107×C61—22no—
121#107×C61—41no—
122#106×C61—41no—
123#102×C61—22no—
124#102×C61—22no—
125#102×C61—41no—
126#102×C61—41no—
127C22⋊C8×C61—22no—
128C22⋊C8×C61—22no—
129C22⋊C8×C61—22no—
130C22⋊C8×C61D414yescomplemented
131#95×C61—21no—
132#95×C61—21no—
133#95×C61—21no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61—21no—
137#95×C61—21no—
138C24×C61—21no—
139C24×C61C2×D411yescharacteristic
140C24×C61C2×D411yescharacteristic
141C24×C61C2×D411yescharacteristic
142#41×C61—44no—
143#41×C61—44no—
144#41×C61—44no—
145#41×C61—44no—
146C2×Q8×C61—22no—
147C2×Q8×C61—22no—
148C2×Q8×C61—41no—
149C2×D4×C61—22no—
150C2×D4×C61—22no—
151C2×D4×C61—22no—
152C2×D4×C61—22no—
153C2×D4×C61—22no—
154C2×D4×C61—22no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—41no—
162C2×D4×C61—41no—
163C2×D4×C61—41no—
164C2×D4×C61—42no—
165C2×D4×C61—42no—
166C2×D4×C61—42no—
167C2×D4×C61—81no—
168C2×D4×C61—81no—
169C2×D4×C61—81no—
170C2×D4×C61—81no—
171C2×D4×C61—81no—
172C2×D4×C61—81no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—42no—
195C22×C4×C61—81no—
196C22×C4×C61—81no—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D412yes—
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61#4112yes—
202C22×C4×C61#4112yes—
203C22×C4×C61#4112yes—
204C22×C4×C61C2411yescharacteristic
205M16×C61—44no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—44no—
217C2×C8×C61C2×D412yes—
218C2×C8×C61C2×D412yes—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—42no—
234C22⋊C4×C61—42no—
235C22⋊C4×C61—42no—
236C22⋊C4×C61—42no—
237C22⋊C4×C61—42no—
238C22⋊C4×C61—81no—
239C22⋊C4×C61—81no—
240C22⋊C4×C61—81no—
241C22⋊C4×C61—81no—
242C22⋊C4×C61—81no—
243C22⋊C4×C61—81no—
244C22⋊C4×C61—81no—
245C42×C61—42no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61#12112yes—
273C23×C61#12312yes—
274C23×C61C22×D411yescharacteristic
275Q8×C61—44no—
276D4×C61—44no—
277D4×C61—44no—
278D4×C61—44no—
279D4×C61—41no—
280D4×C61—41no—
281D4×C61—41no—
282D4×C61—41no—
283D4×C61—84no—
284D4×C61—84no—
285D4×C61—84no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—84no—
327C2×C4×C61#12112yes—
328C2×C4×C61#12312yes—
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C2×#4111yescharacteristic
331C2×C4×C61C2×#4111yescharacteristic
332C2×C4×C61C2×#4111yescharacteristic
333C2×C4×C61H(5,𝔽2)11yescharacteristic
334C2×C4×C61H(5,𝔽2)11yescharacteristic
335C8×C61—22no—
336C8×C61—22no—
337C8×C61—41no—
338C8×C61—41no—
339#24562C6111yesmaximal, characteristic, direct product factor, Sylow
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—81no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61C2×#12111yescharacteristic
369C22×C61C2×#12311yescharacteristic
370C22×C61#53411yescharacteristic
371C22×C61#57611yescharacteristic
372C22×C61#57611yescharacteristic
373C22×C61#57711yescharacteristic
374C22×C61#57811yescharacteristic
375C4×C61—22no—
376C4×C61—22no—
377C4×C61—41no—
378C4×C61—81no—
379C4×C61—81no—
380C4×C61—81no—
381C4×C61—81no—
382C4×C61—81no—
383C4×C61—81no—
384C4×C61—81no—
385C4×C61#54611yescharacteristic
386C4×C61#54611yescharacteristic
387C4×C61#55111yescharacteristic
388C4×C61#55111yescharacteristic
389C2×#480C2×C6111yescharacteristic, complemented
390C2×#408C2×C6111yescharacteristic, complemented
391#2615C2×C6111yescharacteristic
392#2311C2×C6111yescharacteristic, complemented
393#2076C2×C6111yescharacteristic, complemented
394#2075C2×C6111yescharacteristic, complemented
395#2034C2×C6111yescharacteristic, complemented
396#2033C2×C6111yescharacteristic, complemented
397#1895C2×C6111yescharacteristic, complemented
398#1893C2×C6111yescharacteristic, complemented
399#1875C2×C6111yescharacteristic, complemented
400#1854C2×C6111yescharacteristic, complemented
401#1824C2×C6111yescharacteristic, complemented
402#1809C2×C6111yescharacteristic, complemented
403#1808C2×C6111yescharacteristic, complemented
404C2×C61—42no—
405C2×C61—42no—
406C2×C61—81no—
407C2×C61—161no—
408C2×C61#241211yescharacteristic
409C2×C61#305811yescharacteristic
410C2×C61#306311yescharacteristic
411C2×C61#309611yescharacteristic
412C2×C61#309811yescharacteristic
413C2×C61#319811yescharacteristic
414C2×C61#320311yescharacteristic
415C22×#41C22×C6111yescharacteristic
416C22×M16C22×C6111yescharacteristic
417C23×C8C22×C6111yescharacteristic
418C2×#121C22×C6111yescharacteristic
419C2×#121C22×C6111yescharacteristic
420C2×#121C22×C6111yescharacteristic
421C2×#117C22×C6111yescharacteristic
422C22×C4⋊C4C22×C6111yescharacteristic
423#480—24no—
424C2×#107C22×C6111yescharacteristic
425C2×#107C22×C6111yescharacteristic
426C2×#107C22×C6111yescharacteristic
427C2×#106C22×C6111yescharacteristic
428C2×#102C22×C6111yescharacteristic
429C2×#102C22×C6111yescharacteristic
430C2×#102C22×C6111yescharacteristic
431C2×#102C22×C6111yescharacteristic
432#408—24no—
433C2×C22⋊C8C22×C6111yescharacteristic
434C2×C22⋊C8C22×C6111yescharacteristic
435C2×C22⋊C8C22×C6111yescharacteristic
436C2×C22⋊C8C22×C6111yescharacteristic
437#393—21no—
438#392—21no—
439#392—21no—
440#392—21no—
441#391—21no—
442#390—21no—
443#386—21no—
444#386—21no—
445#380C22×C6111yescharacteristic
446#380C22×C6111yescharacteristic
447#380C22×C6111yescharacteristic
448#380C22×C6111yescharacteristic
449#380C22×C6111yescharacteristic
450#380C22×C6111yescharacteristic
451#380C22×C6111yescharacteristic
452#340C22×C6111yescharacteristic
453#340C22×C6111yescharacteristic
454#340C22×C6111yescharacteristic
455#340C22×C6111yescharacteristic
456#340C22×C6111yescharacteristic
457#340C22×C6111yescharacteristic
458#340C22×C6111yescharacteristic
459#340C22×C6111yescharacteristic
460C61#2456211yescharacteristic, direct product factor, Sylow
461C2×#41—22no—
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—22no—
465C2×#41—41no—
466C2×#41—41no—
467C22×Q8D4×C6111yescharacteristic
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4D4×C6111yescharacteristic
472C22×D4D4×C6111yescharacteristic
473C22×D4D4×C6111yescharacteristic
474C22×D4C23×C6111yescharacteristic
475C23×C4—21no—
476C23×C4C23×C6111yescharacteristic
477C23×C4C23×C6111yescharacteristic
478C23×C4C23×C6111yescharacteristic
479C2×M16—22no—
480C2×M16—22no—
481C2×M16—41no—
482C22×C8—22no—
483C22×C8—22no—
484C22×C8—41no—
485C22×C8C23×C6111yescharacteristic
486C22×C8C23×C6111yescharacteristic
487C22×C8C23×C6111yescharacteristic
488C22×C8C23×C6111yescharacteristic
489#121—22no—
490#121—22no—
491#121—22no—
492#121—22no—
493#121—41no—
494#121—41no—
495#117—41no—
496#117—41no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4C23×C6111yescharacteristic
501C2×C4⋊C4C23×C6111yescharacteristic
502C2×C4⋊C4C23×C6111yescharacteristic
503C2×C4⋊C4C23×C6111yescharacteristic
504C2×C4⋊C4C23×C6111yescharacteristic
505C2×C4⋊C4C23×C6111yescharacteristic
506C2×C4⋊C4C23×C6111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C42—21no—
519#107—22no—
520#107—22no—
521#107—41no—
522#106—41no—
523#102—22no—
524#102—22no—
525#102—41no—
526#102—41no—
527C22⋊C8—22no—
528C22⋊C8—22no—
529C22⋊C8—22no—
530C22⋊C8D4×C6114yescomplemented
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538C24—21no—
539C24C2×D4×C6111yescharacteristic
540C24C2×D4×C6111yescharacteristic
541C24C2×D4×C6111yescharacteristic
542#41—44no—
543#41—44no—
544#41—44no—
545#41—44no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—41no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—81no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—42no—
595C22×C4—81no—
596C22×C4—81no—
597C22×C4C2×D4×C6111yescharacteristic
598C22×C4C2×D4×C6111yescharacteristic
599C22×C4C2×D4×C6112yes—
600C22×C4C2×D4×C6111yescharacteristic
601C22×C4#41×C6112yes—
602C22×C4#41×C6112yes—
603C22×C4#41×C6112yes—
604C22×C4C24×C6111yescharacteristic
605M16—44no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—44no—
617C2×C8C2×D4×C6112yes—
618C2×C8C2×D4×C6112yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4—81no—
643C22⋊C4—81no—
644C22⋊C4—81no—
645C42—42no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23#121×C6112yes—
673C23#123×C6112yes—
674C23C22×D4×C6111yescharacteristic
675Q8—44no—
676D4—44no—
677D4—44no—
678D4—44no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—84no—
684D4—84no—
685D4—84no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—84no—
727C2×C4#121×C6112yes—
728C2×C4#123×C6112yes—
729C2×C4C22×D4×C6111yescharacteristic
730C2×C4C2×#41×C6111yescharacteristic
731C2×C4C2×#41×C6111yescharacteristic
732C2×C4C2×#41×C6111yescharacteristic
733C2×C4H(5,𝔽2)×C6111yescharacteristic
734C2×C4H(5,𝔽2)×C6111yescharacteristic
735C8—22no—
736C8—22no—
737C8—41no—
738C8—41no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×#121×C6111yescharacteristic
768C22C2×#123×C6111yescharacteristic
769C22C61×#53411yescharacteristic
770C22C61×#57611yescharacteristic
771C22C61×#57611yescharacteristic
772C22C61×#57711yescharacteristic
773C22C61×#57811yescharacteristic
774C4—22no—
775C4—22no—
776C4—41no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4C61×#54611yescharacteristic
785C4C61×#54611yescharacteristic
786C4C61×#55111yescharacteristic
787C4C61×#55111yescharacteristic
788C2—42no—
789C2—42no—
790C2—81no—
791C2—161no—
792C2C61×#241211yescharacteristic
793C2C61×#305811yescharacteristic
794C2C61×#306311yescharacteristic
795C2C61×#309611yescharacteristic
796C2C61×#309811yescharacteristic
797C2C61×#319811yescharacteristic
798C2C61×#320311yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#2615C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C22×#41×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#480C2semidirect
2. C2×C61×#408C2semidirect
4. C61×#2311C2semidirect
5. C61×#2076C2semidirect
6. C61×#2075C2semidirect
7. C61×#2034C2semidirect
8. C61×#2033C2semidirect
9. C61×#1895C2semidirect
10. C61×#1893C2semidirect
11. C61×#1875C2semidirect
12. C61×#1854C2semidirect
13. C61×#1824C2semidirect
14. C61×#1809C2semidirect
15. C61×#1808C2semidirect
130. C22⋊C8×C61D4semidirect
339. #24562C61direct (N × H)
389. C2×#480C2×C61semidirect
390. C2×#408C2×C61semidirect
392. #2311C2×C61semidirect
393. #2076C2×C61semidirect
394. #2075C2×C61semidirect
395. #2034C2×C61semidirect
396. #2033C2×C61semidirect
397. #1895C2×C61semidirect
398. #1893C2×C61semidirect
399. #1875C2×C61semidirect
400. #1854C2×C61semidirect
401. #1824C2×C61semidirect
402. #1809C2×C61semidirect
403. #1808C2×C61semidirect
460. C61#24562direct (N × H)
530. C22⋊C8D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4802
C2×C61×#4082
C61×#26152
C61×#23112
C61×#20762
C61×#20752
C61×#20342
C61×#20332
C61×#18952
C61×#18932
C61×#18752
C61×#18542
C61×#18242
C61×#18092
C61×#18082
#2456261