Finite Group Databasebeta

← C61×#24028 #29527461

Subgroups — C61×#24028 #29527461

Order 15616.

1250 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3489C211yesmaximal, characteristic
2C61×#3093C211yesmaximal, characteristic, complemented
3C61×#2896C211yesmaximal, characteristic, complemented
4C61×#2499C211yesmaximal, characteristic, complemented
5C61×#2040C211yesmaximal, characteristic, complemented
6C61×#2039C211yesmaximal, characteristic, complemented
7C61×#2038C211yesmaximal, characteristic, complemented
8C61×#2038C211yesmaximal, characteristic, complemented
9C61×#1901C211yesmaximal, characteristic, complemented
10C61×#1871C211yesmaximal, characteristic, complemented
11C61×#1860C211yesmaximal, characteristic, complemented
12C61×#1859C211yesmaximal, characteristic, complemented
13C61×#1793C211yesmaximal, characteristic, complemented
14C61×#1793C211yesmaximal, characteristic, complemented
15C61×#1789C211yesmaximal, characteristic, complemented
16C2×2−1+4×C61C2211yescharacteristic
17C22×#41×C61C2211yescharacteristic
18C22×M16×C61C2211yescharacteristic
19D4×Q8×C61—21no—
20C61×#548—21no—
21C61×#547—21no—
22C61×#547—22no—
23C61×#546—21no—
24C61×#546—22no—
25C61×#537—21no—
26C61×#537C2211yescharacteristic
27C61×#536—21no—
28C61×#536C2211yescharacteristic
29C61×#525—21no—
30C61×#525C2211yescharacteristic
31C2×C22⋊Q8×C61—21no—
32C2×C22⋊Q8×C61C2211yescharacteristic
33C61×#520C2211yescharacteristic
34C2×#117×C61C2211yescharacteristic
35C61×#485—21no—
36C61×#485—21no—
37C61×#482—21no—
38C61×#482—21no—
39C61×#428C2211yescharacteristic, complemented
40C61×#428C2211yescharacteristic, complemented
41C2×#104×C61C2211yescharacteristic
42C2×#104×C61C2211yescharacteristic
43C2×#104×C61C2211yescharacteristic
44C2×#104×C61C2211yescharacteristic
45C2×#104×C61C2211yescharacteristic, complemented
46C2×#104×C61C2211yescharacteristic, complemented
47C61×#419—21no—
48C61×#418—21no—
49C61×#417C2211yescharacteristic
50C61×#417C2211yescharacteristic
51C61×#417C2211yescharacteristic
52C61×#417C2211yescharacteristic
53C61×#417C2211yescharacteristic, complemented
54C61×#417C2211yescharacteristic, complemented
55C61×#416—21no—
56C61×#416—21no—
57C2×#101×C61C2211yescharacteristic, complemented
58C2×#101×C61C2211yescharacteristic, complemented
59C61×#407C2211yescharacteristic
60C61×#397—22no—
61C61×#391C2211yescharacteristic, complemented
62C61×#391C2211yescharacteristic, complemented
63C61×#387—22no—
64C61×#384C2211yescharacteristic, complemented
65C61×#382C2211yescharacteristic, complemented
66C4×C22⋊C4×C61C2211yescharacteristic
67C61×#343C2211yescharacteristic, complemented
68C61×#343C2211yescharacteristic, complemented
69C61×#339C2211yescharacteristic, complemented
70C61×#339C2211yescharacteristic, complemented
712−1+4×C61—22no—
722−1+4×C61—22no—
732−1+4×C61—41no—
742−1+4×C61—41no—
75C2×#41×C61—21no—
76C2×#41×C61—21no—
77C2×#41×C61—21no—
78C2×#41×C61—22no—
79C2×#41×C61—21no—
80C2×#41×C61—22no—
81C2×#41×C61—22no—
82C2×#41×C61—41no—
83C2×#41×C61—41no—
84C2×#41×C61D411yescharacteristic
85C2×#41×C61D411yescharacteristic
86C2×#41×C61C2311yescharacteristic
87C2×#41×C61C2311yescharacteristic
88C2×#41×C61C2311yescharacteristic
89C22×Q8×C61—21no—
90C22×Q8×C61—21no—
91C22×Q8×C61D411yescharacteristic
92C22×Q8×C61C2311yescharacteristic
93C22×D4×C61—21no—
94C22×D4×C61D411yescharacteristic
95C23×C4×C61—21no—
96C23×C4×C61C2311yescharacteristic
97C2×M16×C61—21no—
98C2×M16×C61—41no—
99C2×M16×C61—41no—
100C2×M16×C61C2311yescharacteristic
101C2×M16×C61C2311yescharacteristic
102C2×M16×C61C2311yescharacteristic
103C2×M16×C61C2311yescharacteristic
104C22×C8×C61—21no—
105C4⋊Q8×C61—22no—
106C4⋊Q8×C61—21no—
107#124×C61—22no—
108#124×C61—21no—
109#123×C61—22no—
110#123×C61—22no—
111#123×C61—22no—
112#123×C61—22no—
113#123×C61—21no—
114C22⋊Q8×C61—22no—
115C22⋊Q8×C61—22no—
116C22⋊Q8×C61—22no—
117C22⋊Q8×C61—21no—
118C22⋊Q8×C61—21no—
119C22⋊Q8×C61—21no—
120C22⋊Q8×C61—21no—
121C22⋊Q8×C61—21no—
122C22⋊Q8×C61—21no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61D411yescharacteristic
126C22⋊Q8×C61D411yescharacteristic
127#121×C61—22no—
128#121×C61—22no—
129#121×C61—22no—
130#121×C61—21no—
131#121×C61—21no—
132#121×C61—22no—
133#121×C61D411yescharacteristic
134#121×C61D411yescharacteristic
135#120×C61—22no—
136#120×C61—21no—
137C4×Q8×C61—21no—
138C4×D4×C61—22no—
139C4×D4×C61—22no—
140C4×D4×C61—21no—
141C4×D4×C61—22no—
142C4×D4×C61—21no—
143C4×D4×C61—21no—
144#117×C61—21no—
145#117×C61—21no—
146#117×C61—21no—
147#117×C61—21no—
148#117×C61—21no—
149#117×C61C2311yescharacteristic
150C2×C4⋊C4×C61—22no—
151C2×C4⋊C4×C61—21no—
152C2×C4⋊C4×C61—22no—
153C2×C4⋊C4×C61D412yes—
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C4⋊C4×C61C2311yescharacteristic
156C2×C4⋊C4×C61C2311yescharacteristic
157C2×C22⋊C4×C61—22no—
158C2×C22⋊C4×C61—21no—
159C2×C22⋊C4×C61—21no—
160C2×C22⋊C4×C61D412yes—
161C2×C42×C61—21no—
162C2×C42×C61C2311yescharacteristic
163C2×C42×C61C2311yescharacteristic
164#107×C61—21no—
165#107×C61—21no—
166#106×C61—21no—
167#106×C61—21no—
168#104×C61—22no—
169#104×C61—22no—
170#104×C61—41no—
171#104×C61—41no—
172#104×C61—41no—
173#104×C61—41no—
174#103×C61—21no—
175#103×C61—21no—
176#103×C61—21no—
177#103×C61—21no—
178#103×C61—21no—
179#103×C61—21no—
180#102×C61—21no—
181#102×C61—21no—
182#102×C61—21no—
183#102×C61—21no—
184#102×C61—21no—
185#102×C61—21no—
186#101×C61—41no—
187#101×C61—41no—
188C22⋊C8×C61—21no—
189C22⋊C8×C61—21no—
190#95×C61—21no—
191#95×C61—22no—
192#95×C61—22no—
193#95×C61—22no—
194C24×C61—21no—
195C24×C61C2×D411yescharacteristic
196#41×C61—21no—
197#41×C61—21no—
198#41×C61—22no—
199#41×C61—22no—
200#41×C61—21no—
201#41×C61—21no—
202#41×C61—21no—
203#41×C61—21no—
204#41×C61—21no—
205#41×C61—21no—
206#41×C61—21no—
207#41×C61—21no—
208#41×C61—42no—
209#41×C61—42no—
210#41×C61—41no—
211#41×C61—41no—
212#41×C61—42no—
213#41×C61—42no—
214#41×C61—42no—
215#41×C61—42no—
216#41×C61—44no—
217#41×C61—44no—
218#41×C61—42no—
219#41×C61—42no—
220#41×C61#4112yes—
221#41×C61#4112yes—
222C2×Q8×C61—22no—
223C2×Q8×C61—21no—
224C2×Q8×C61—21no—
225C2×Q8×C61—21no—
226C2×Q8×C61—21no—
227C2×Q8×C61—21no—
228C2×Q8×C61—21no—
229C2×Q8×C61—21no—
230C2×Q8×C61—22no—
231C2×Q8×C61—41no—
232C2×Q8×C61—42no—
233C2×Q8×C61—42no—
234C2×Q8×C61—42no—
235C2×Q8×C61—42no—
236C2×Q8×C61C2×D411yescharacteristic
237C2×Q8×C61C2×D411yescharacteristic
238C2×Q8×C61C2×D411yescharacteristic
239C2×D4×C61—21no—
240C2×D4×C61—22no—
241C2×D4×C61—22no—
242C2×D4×C61—21no—
243C2×D4×C61—21no—
244C2×D4×C61—21no—
245C2×D4×C61—21no—
246C2×D4×C61—21no—
247C2×D4×C61—22no—
248C2×D4×C61—21no—
249C2×D4×C61—21no—
250C2×D4×C61—41no—
251C2×D4×C61—42no—
252C2×D4×C61—42no—
253C2×D4×C61C2×D411yescharacteristic
254C2×D4×C61C2×D411yescharacteristic
255C2×D4×C61C2×D411yescharacteristic
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61—21no—
260C22×C4×C61—21no—
261C22×C4×C61—22no—
262C22×C4×C61—22no—
263C22×C4×C61—21no—
264C22×C4×C61—21no—
265C22×C4×C61—22no—
266C22×C4×C61—21no—
267C22×C4×C61—21no—
268C22×C4×C61—21no—
269C22×C4×C61—21no—
270C22×C4×C61—21no—
271C22×C4×C61—21no—
272C22×C4×C61—21no—
273C22×C4×C61—42no—
274C22×C4×C61—42no—
275C22×C4×C61C2×D412yes—
276C22×C4×C61C2×D411yescharacteristic
277C22×C4×C61C2×D411yescharacteristic
278C22×C4×C61C2×D411yescharacteristic
279C22×C4×C61C2×D411yescharacteristic
280C22×C4×C61C2×D411yescharacteristic
281C22×C4×C61C2×D412yes—
282C22×C4×C61C2411yescharacteristic
283M16×C61—21no—
284M16×C61—21no—
285M16×C61—21no—
286M16×C61—21no—
287M16×C61—21no—
288M16×C61—21no—
289M16×C61—21no—
290M16×C61—21no—
291M16×C61—42no—
292C2×C8×C61—21no—
293C2×C8×C61—21no—
294C2×C8×C61—21no—
295C2×C8×C61—21no—
296C2×C8×C61—42no—
297C4⋊C4×C61—22no—
298C4⋊C4×C61—22no—
299C4⋊C4×C61—22no—
300C4⋊C4×C61—22no—
301C4⋊C4×C61—21no—
302C4⋊C4×C61—22no—
303C4⋊C4×C61—22no—
304C4⋊C4×C61—21no—
305C4⋊C4×C61—21no—
306C4⋊C4×C61—21no—
307C4⋊C4×C61—21no—
308C4⋊C4×C61—21no—
309C4⋊C4×C61—21no—
310C4⋊C4×C61—21no—
311C4⋊C4×C61—44no—
312C4⋊C4×C61C2×D411yescharacteristic
313C4⋊C4×C61C2×D411yescharacteristic
314C22⋊C4×C61—22no—
315C22⋊C4×C61—22no—
316C22⋊C4×C61—22no—
317C22⋊C4×C61—22no—
318C22⋊C4×C61—22no—
319C22⋊C4×C61—21no—
320C22⋊C4×C61—22no—
321C22⋊C4×C61—22no—
322C22⋊C4×C61—21no—
323C22⋊C4×C61—21no—
324C22⋊C4×C61—21no—
325C22⋊C4×C61—21no—
326C22⋊C4×C61—42no—
327C22⋊C4×C61—41no—
328C22⋊C4×C61—41no—
329C42×C61—22no—
330C42×C61—21no—
331C42×C61—21no—
332C42×C61—21no—
333C42×C61—21no—
334C42×C61—21no—
335C42×C61—41no—
336C42×C61—41no—
337C23×C61—21no—
338C23×C61—21no—
339C23×C61—21no—
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—42no—
345C23×C61—42no—
346C23×C61—81no—
347C23×C61#12011yescharacteristic
348C23×C61#12011yescharacteristic
349C23×C61C22×D411yescharacteristic
350Q8×C61—21no—
351Q8×C61—21no—
352Q8×C61—21no—
353Q8×C61—21no—
354Q8×C61—21no—
355Q8×C61—42no—
356Q8×C61—44no—
357Q8×C61—41no—
358Q8×C61—41no—
359Q8×C61—41no—
360Q8×C61—41no—
361Q8×C61#12312yes—
362D4×C61—22no—
363D4×C61—22no—
364D4×C61—21no—
365D4×C61—21no—
366D4×C61—21no—
367D4×C61—21no—
368D4×C61—21no—
369D4×C61—42no—
370D4×C61—42no—
371D4×C61—42no—
372D4×C61—42no—
373D4×C61—44no—
374D4×C61—41no—
375D4×C61—41no—
376D4×C61—41no—
377D4×C61—41no—
378D4×C61—81no—
379D4×C61—82no—
380D4×C61#12312yes—
381C2×C4×C61—21no—
382C2×C4×C61—21no—
383C2×C4×C61—21no—
384C2×C4×C61—21no—
385C2×C4×C61—21no—
386C2×C4×C61—21no—
387C2×C4×C61—21no—
388C2×C4×C61—21no—
389C2×C4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—22no—
393C2×C4×C61—22no—
394C2×C4×C61—22no—
395C2×C4×C61—21no—
396C2×C4×C61—22no—
397C2×C4×C61—21no—
398C2×C4×C61—21no—
399C2×C4×C61—22no—
400C2×C4×C61—21no—
401C2×C4×C61—22no—
402C2×C4×C61—22no—
403C2×C4×C61—42no—
404C2×C4×C61—42no—
405C2×C4×C61—42no—
406C2×C4×C61—44no—
407C2×C4×C61—41no—
408C2×C4×C61—44no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61—41no—
414C2×C4×C61—42no—
415C2×C4×C61—41no—
416C2×C4×C61—42no—
417C2×C4×C61—41no—
418C2×C4×C61—42no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61—41no—
422C2×C4×C61—82no—
423C2×C4×C61#12011yescharacteristic
424C2×C4×C61#12011yescharacteristic
425C2×C4×C61C22×D411yescharacteristic
426C2×C4×C61C22×D411yescharacteristic
427C2×C4×C61C2×#4111yescharacteristic
428C2×C4×C61C2×#4111yescharacteristic
429C2×C4×C61H(5,𝔽2)11yescharacteristic
430C2×C4×C61H(5,𝔽2)11yescharacteristic
431C8×C61—41no—
432C8×C61—41no—
433C8×C61—41no—
434C8×C61—41no—
435#24028C6111yesmaximal, characteristic, direct product factor, Sylow
436C22×C61—21no—
437C22×C61—21no—
438C22×C61—21no—
439C22×C61—21no—
440C22×C61—22no—
441C22×C61—21no—
442C22×C61—21no—
443C22×C61—21no—
444C22×C61—21no—
445C22×C61—41no—
446C22×C61—41no—
447C22×C61—41no—
448C22×C61—41no—
449C22×C61—41no—
450C22×C61—41no—
451C22×C61—41no—
452C22×C61—41no—
453C22×C61—81no—
454C22×C61—81no—
455C22×C61—84no—
456C22×C61C2×#12011yescharacteristic
457C22×C61#54611yescharacteristic
458C22×C61#54611yescharacteristic
459C4×C61—21no—
460C4×C61—21no—
461C4×C61—22no—
462C4×C61—42no—
463C4×C61—42no—
464C4×C61—41no—
465C4×C61—41no—
466C4×C61—42no—
467C4×C61—41no—
468C4×C61—41no—
469C4×C61—81no—
470C4×C61—81no—
471C4×C61—81no—
472C4×C61C2×#12311yescharacteristic
473C4×C61#53411yescharacteristic
474C4×C61#54611yescharacteristic
475C4×C61#54611yescharacteristic
476#3489C2×C6111yescharacteristic
477#3093C2×C6111yescharacteristic, complemented
478#2896C2×C6111yescharacteristic, complemented
479#2499C2×C6111yescharacteristic, complemented
480#2040C2×C6111yescharacteristic, complemented
481#2039C2×C6111yescharacteristic, complemented
482#2038C2×C6111yescharacteristic, complemented
483#2038C2×C6111yescharacteristic, complemented
484#1901C2×C6111yescharacteristic, complemented
485#1871C2×C6111yescharacteristic, complemented
486#1860C2×C6111yescharacteristic, complemented
487#1859C2×C6111yescharacteristic, complemented
488#1793C2×C6111yescharacteristic, complemented
489#1793C2×C6111yescharacteristic, complemented
490#1789C2×C6111yescharacteristic, complemented
491C2×C61—21no—
492C2×C61—21no—
493C2×C61—41no—
494C2×C61—41no—
495C2×C61—42no—
496C2×C61—81no—
497C2×C61—81no—
498C2×C61#240511yescharacteristic
499C2×C61#301811yescharacteristic
500C2×C61#302011yescharacteristic
501C2×2−1+4C22×C6111yescharacteristic
502C22×#41C22×C6111yescharacteristic
503C22×M16C22×C6111yescharacteristic
504D4×Q8—21no—
505#548—21no—
506#547—21no—
507#547—22no—
508#546—21no—
509#546—22no—
510#537—21no—
511#537C22×C6111yescharacteristic
512#536—21no—
513#536C22×C6111yescharacteristic
514#525—21no—
515#525C22×C6111yescharacteristic
516C2×C22⋊Q8—21no—
517C2×C22⋊Q8C22×C6111yescharacteristic
518#520C22×C6111yescharacteristic
519C2×#117C22×C6111yescharacteristic
520#485—21no—
521#485—21no—
522#482—21no—
523#482—21no—
524#428C22×C6111yescharacteristic, complemented
525#428C22×C6111yescharacteristic, complemented
526C2×#104C22×C6111yescharacteristic
527C2×#104C22×C6111yescharacteristic
528C2×#104C22×C6111yescharacteristic
529C2×#104C22×C6111yescharacteristic
530C2×#104C22×C6111yescharacteristic, complemented
531C2×#104C22×C6111yescharacteristic, complemented
532#419—21no—
533#418—21no—
534#417C22×C6111yescharacteristic
535#417C22×C6111yescharacteristic
536#417C22×C6111yescharacteristic
537#417C22×C6111yescharacteristic
538#417C22×C6111yescharacteristic, complemented
539#417C22×C6111yescharacteristic, complemented
540#416—21no—
541#416—21no—
542C2×#101C22×C6111yescharacteristic, complemented
543C2×#101C22×C6111yescharacteristic, complemented
544#407C22×C6111yescharacteristic
545#397—22no—
546#391C22×C6111yescharacteristic, complemented
547#391C22×C6111yescharacteristic, complemented
548#387—22no—
549#384C22×C6111yescharacteristic, complemented
550#382C22×C6111yescharacteristic, complemented
551C4×C22⋊C4C22×C6111yescharacteristic
552#343C22×C6111yescharacteristic, complemented
553#343C22×C6111yescharacteristic, complemented
554#339C22×C6111yescharacteristic, complemented
555#339C22×C6111yescharacteristic, complemented
556C61#2402811yescharacteristic, direct product factor, Sylow
5572−1+4—22no—
5582−1+4—22no—
5592−1+4—41no—
5602−1+4—41no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—22no—
565C2×#41—21no—
566C2×#41—22no—
567C2×#41—22no—
568C2×#41—41no—
569C2×#41—41no—
570C2×#41D4×C6111yescharacteristic
571C2×#41D4×C6111yescharacteristic
572C2×#41C23×C6111yescharacteristic
573C2×#41C23×C6111yescharacteristic
574C2×#41C23×C6111yescharacteristic
575C22×Q8—21no—
576C22×Q8—21no—
577C22×Q8D4×C6111yescharacteristic
578C22×Q8C23×C6111yescharacteristic
579C22×D4—21no—
580C22×D4D4×C6111yescharacteristic
581C23×C4—21no—
582C23×C4C23×C6111yescharacteristic
583C2×M16—21no—
584C2×M16—41no—
585C2×M16—41no—
586C2×M16C23×C6111yescharacteristic
587C2×M16C23×C6111yescharacteristic
588C2×M16C23×C6111yescharacteristic
589C2×M16C23×C6111yescharacteristic
590C22×C8—21no—
591C4⋊Q8—22no—
592C4⋊Q8—21no—
593#124—22no—
594#124—21no—
595#123—22no—
596#123—22no—
597#123—22no—
598#123—21no—
599#123—22no—
600C22⋊Q8—22no—
601C22⋊Q8—22no—
602C22⋊Q8—22no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8D4×C6111yescharacteristic
612C22⋊Q8D4×C6111yescharacteristic
613#121—22no—
614#121—22no—
615#121—22no—
616#121—21no—
617#121—21no—
618#121—22no—
619#121D4×C6111yescharacteristic
620#121D4×C6111yescharacteristic
621#120—22no—
622#120—21no—
623C4×Q8—21no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—21no—
627C4×D4—22no—
628C4×D4—21no—
629C4×D4—21no—
630#117—21no—
631#117—21no—
632#117—21no—
633#117—21no—
634#117—21no—
635#117C23×C6111yescharacteristic
636C2×C4⋊C4—22no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—22no—
639C2×C4⋊C4D4×C6112yes—
640C2×C4⋊C4C23×C6111yescharacteristic
641C2×C4⋊C4C23×C6111yescharacteristic
642C2×C4⋊C4C23×C6111yescharacteristic
643C2×C22⋊C4—22no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4D4×C6112yes—
647C2×C42—21no—
648C2×C42C23×C6111yescharacteristic
649C2×C42C23×C6111yescharacteristic
650#107—21no—
651#107—21no—
652#106—21no—
653#106—21no—
654#104—22no—
655#104—22no—
656#104—41no—
657#104—41no—
658#104—41no—
659#104—41no—
660#103—21no—
661#103—21no—
662#103—21no—
663#103—21no—
664#103—21no—
665#103—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671#102—21no—
672#101—41no—
673#101—41no—
674C22⋊C8—21no—
675C22⋊C8—21no—
676#95—21no—
677#95—22no—
678#95—22no—
679#95—22no—
680C24—21no—
681C24C2×D4×C6111yescharacteristic
682#41—21no—
683#41—21no—
684#41—22no—
685#41—22no—
686#41—21no—
687#41—21no—
688#41—21no—
689#41—21no—
690#41—21no—
691#41—21no—
692#41—21no—
693#41—21no—
694#41—42no—
695#41—42no—
696#41—41no—
697#41—41no—
698#41—42no—
699#41—42no—
700#41—42no—
701#41—42no—
702#41—44no—
703#41—44no—
704#41—42no—
705#41—42no—
706#41#41×C6112yes—
707#41#41×C6112yes—
708C2×Q8—22no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—22no—
717C2×Q8—41no—
718C2×Q8—42no—
719C2×Q8—42no—
720C2×Q8—42no—
721C2×Q8—42no—
722C2×Q8C2×D4×C6111yescharacteristic
723C2×Q8C2×D4×C6111yescharacteristic
724C2×Q8C2×D4×C6111yescharacteristic
725C2×D4—21no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—41no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4C2×D4×C6111yescharacteristic
740C2×D4C2×D4×C6111yescharacteristic
741C2×D4C2×D4×C6111yescharacteristic
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4C2×D4×C6112yes—
762C22×C4C2×D4×C6111yescharacteristic
763C22×C4C2×D4×C6111yescharacteristic
764C22×C4C2×D4×C6111yescharacteristic
765C22×C4C2×D4×C6111yescharacteristic
766C22×C4C2×D4×C6111yescharacteristic
767C22×C4C2×D4×C6112yes—
768C22×C4C24×C6111yescharacteristic
769M16—21no—
770M16—21no—
771M16—21no—
772M16—21no—
773M16—21no—
774M16—21no—
775M16—21no—
776M16—21no—
777M16—42no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—42no—
783C4⋊C4—22no—
784C4⋊C4—22no—
785C4⋊C4—22no—
786C4⋊C4—22no—
787C4⋊C4—21no—
788C4⋊C4—22no—
789C4⋊C4—22no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—44no—
798C4⋊C4C2×D4×C6111yescharacteristic
799C4⋊C4C2×D4×C6111yescharacteristic
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—21no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—42no—
813C22⋊C4—41no—
814C22⋊C4—41no—
815C42—22no—
816C42—21no—
817C42—21no—
818C42—21no—
819C42—21no—
820C42—21no—
821C42—41no—
822C42—41no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—41no—
829C23—41no—
830C23—42no—
831C23—42no—
832C23—81no—
833C23#120×C6111yescharacteristic
834C23#120×C6111yescharacteristic
835C23C22×D4×C6111yescharacteristic
836Q8—21no—
837Q8—21no—
838Q8—21no—
839Q8—21no—
840Q8—21no—
841Q8—42no—
842Q8—44no—
843Q8—41no—
844Q8—41no—
845Q8—41no—
846Q8—41no—
847Q8#123×C6112yes—
848D4—22no—
849D4—22no—
850D4—21no—
851D4—21no—
852D4—21no—
853D4—21no—
854D4—21no—
855D4—42no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—44no—
860D4—41no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—81no—
865D4—82no—
866D4#123×C6112yes—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—22no—
888C2×C4—21no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—44no—
893C2×C4—41no—
894C2×C4—44no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—42no—
901C2×C4—41no—
902C2×C4—42no—
903C2×C4—41no—
904C2×C4—42no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—82no—
909C2×C4#120×C6111yescharacteristic
910C2×C4#120×C6111yescharacteristic
911C2×C4C22×D4×C6111yescharacteristic
912C2×C4C22×D4×C6111yescharacteristic
913C2×C4C2×#41×C6111yescharacteristic
914C2×C4C2×#41×C6111yescharacteristic
915C2×C4H(5,𝔽2)×C6111yescharacteristic
916C2×C4H(5,𝔽2)×C6111yescharacteristic
917C8—41no—
918C8—41no—
919C8—41no—
920C8—41no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—22no—
926C22—21no—
927C22—21no—
928C22—21no—
929C22—21no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—81no—
939C22—81no—
940C22—84no—
941C22C2×#120×C6111yescharacteristic
942C22C61×#54611yescharacteristic
943C22C61×#54611yescharacteristic
944C4—21no—
945C4—21no—
946C4—22no—
947C4—42no—
948C4—42no—
949C4—41no—
950C4—41no—
951C4—42no—
952C4—41no—
953C4—41no—
954C4—81no—
955C4—81no—
956C4—81no—
957C4C2×#123×C6111yescharacteristic
958C4C61×#53411yescharacteristic
959C4C61×#54611yescharacteristic
960C4C61×#54611yescharacteristic
961C2—21no—
962C2—21no—
963C2—41no—
964C2—41no—
965C2—42no—
966C2—81no—
967C2—81no—
968C2C61×#240511yescharacteristic
969C2C61×#301811yescharacteristic
970C2C61×#302011yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#3489C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#3093C2semidirect
3. C61×#2896C2semidirect
4. C61×#2499C2semidirect
5. C61×#2040C2semidirect
6. C61×#2039C2semidirect
7. C61×#2038C2semidirect
8. C61×#2038C2semidirect
9. C61×#1901C2semidirect
10. C61×#1871C2semidirect
11. C61×#1860C2semidirect
12. C61×#1859C2semidirect
13. C61×#1793C2semidirect
14. C61×#1793C2semidirect
15. C61×#1789C2semidirect
39. C61×#428C22semidirect
40. C61×#428C22semidirect
45. C2×#104×C61C22semidirect
46. C2×#104×C61C22semidirect
53. C61×#417C22semidirect
54. C61×#417C22semidirect
57. C2×#101×C61C22semidirect
58. C2×#101×C61C22semidirect
61. C61×#391C22semidirect
62. C61×#391C22semidirect
64. C61×#384C22semidirect
65. C61×#382C22semidirect
67. C61×#343C22semidirect
68. C61×#343C22semidirect
69. C61×#339C22semidirect
70. C61×#339C22semidirect
435. #24028C61direct (N × H)
477. #3093C2×C61semidirect
478. #2896C2×C61semidirect
479. #2499C2×C61semidirect
480. #2040C2×C61semidirect
481. #2039C2×C61semidirect
482. #2038C2×C61semidirect
483. #2038C2×C61semidirect
484. #1901C2×C61semidirect
485. #1871C2×C61semidirect
486. #1860C2×C61semidirect
487. #1859C2×C61semidirect
488. #1793C2×C61semidirect
489. #1793C2×C61semidirect
490. #1789C2×C61semidirect
524. #428C22×C61semidirect
525. #428C22×C61semidirect
530. C2×#104C22×C61semidirect
531. C2×#104C22×C61semidirect
538. #417C22×C61semidirect
539. #417C22×C61semidirect
542. C2×#101C22×C61semidirect
543. C2×#101C22×C61semidirect
546. #391C22×C61semidirect
547. #391C22×C61semidirect
549. #384C22×C61semidirect
550. #382C22×C61semidirect
552. #343C22×C61semidirect
553. #343C22×C61semidirect
554. #339C22×C61semidirect
555. #339C22×C61semidirect
556. C61#24028direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#34892
C61×#30932
C61×#28962
C61×#24992
C61×#20402
C61×#20392
C61×#20382
C61×#19012
C61×#18712
C61×#18602
C61×#18592
C61×#17932
C61×#17892
#2402861