Finite Group Databasebeta

← C61×#18434 #29521867

Subgroups — C61×#18434 #29521867

Order 15616.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3560C211yesmaximal, characteristic, complemented
2C61×#3213C211yesmaximal, characteristic, complemented
3C61×#3211C211yesmaximal, characteristic, complemented
4C61×#2662C211yesmaximal, characteristic, complemented
5C61×#1606C211yesmaximal, characteristic, complemented
6C61×#1604C211yesmaximal, characteristic, complemented
7C61×#1603C211yesmaximal, characteristic, complemented
8C61×#1601C211yesmaximal, characteristic, complemented
9C61×#1600C211yesmaximal, characteristic, complemented
10C61×#1598C211yesmaximal, characteristic, complemented
11C61×#1597C211yesmaximal, characteristic, complemented
12C61×#1595C211yesmaximal, characteristic, complemented
13C61×#1509C211yesmaximal, characteristic, complemented
14C61×#1502C211yesmaximal, characteristic, complemented
15C61×#1473C211yesmaximal, characteristic, complemented
16C61×#563—21no—
17C61×#560—21no—
18C61×#553—21no—
19C61×#553—21no—
20C61×#551—21no—
21C61×#547—21no—
22C61×#546—21no—
23C61×#546—21no—
24C61×#542—21no—
25C61×#539—21no—
26C61×#539C2211yescharacteristic
27C61×#538—21no—
28C61×#538—21no—
29C61×#538C2211yescharacteristic
30C61×#537C2211yescharacteristic
31C61×#534C2211yescharacteristic
32C61×#532C2211yescharacteristic
33C61×#529C2211yescharacteristic
34C2×#126×C61C2211yescharacteristic
35C2×#124×C61C2211yescharacteristic, complemented
36C61×#496—21no—
37C61×#495—21no—
38C61×#489—21no—
39C61×#488—21no—
40C61×#464—21no—
41C61×#463—21no—
42C61×#463—21no—
43C61×#463—21no—
44C61×#451C2211yescharacteristic, complemented
45C61×#450C2211yescharacteristic, complemented
46C61×#448C2211yescharacteristic
47C61×#448C2211yescharacteristic
48C61×#448C2211yescharacteristic, complemented
49C61×#447C2211yescharacteristic
50C61×#447C2211yescharacteristic
51C61×#447C2211yescharacteristic, complemented
52C61×#432C2211yescharacteristic, complemented
53C61×#431C2211yescharacteristic, complemented
54C61×#396—21no—
55C61×#395C2211yescharacteristic, complemented
56C61×#394—21no—
57C61×#394C2211yescharacteristic, complemented
58C61×#393C2211yescharacteristic
59C61×#392C2211yescharacteristic
60C61×#390—21no—
61C61×#388—21no—
62C4×C4⋊C4×C61C2211yescharacteristic, complemented
63C61×#328C2211yescharacteristic, complemented
64C61×#328C2211yescharacteristic, complemented
65C61×#327C2211yescharacteristic
66C61×#327C2211yescharacteristic
67C61×#327C2211yescharacteristic
68C61×#327C2211yescharacteristic
69C61×#327C2211yescharacteristic, complemented
70C61×#327C2211yescharacteristic, complemented
71C61×#324C2211yescharacteristic, complemented
72C61×#324C2211yescharacteristic, complemented
73C61×#323C2211yescharacteristic
74C61×#323C2211yescharacteristic
75C2×#41×C61—21no—
76C2×#41×C61—21no—
77C22×Q8×C61C2311yescharacteristic
78C22×D4×C61—21no—
79C22×D4×C61—21no—
80C22×D4×C61C2311yescharacteristic
81C2×Q16×C61—21no—
82C2×SD16×C61—21no—
83C2×SD16×C61—21no—
84C2×SD16×C61—21no—
85C2×SD16×C61—21no—
86C2×D8×C61—21no—
87C2×D8×C61—21no—
88C2×D8×C61—21no—
89C4⋊Q8×C61—21no—
90C4⋊Q8×C61D411yescharacteristic, complemented
91#127×C61D411yescharacteristic, complemented
92#126×C61—21no—
93#126×C61—21no—
94#126×C61—21no—
95#126×C61—21no—
96#126×C61—21no—
97#126×C61—21no—
98#126×C61—21no—
99#126×C61—21no—
100#126×C61—21no—
101#125×C61—21no—
102#125×C61—21no—
103#125×C61D411yescharacteristic, complemented
104#124×C61—21no—
105#124×C61—21no—
106#124×C61—21no—
107#124×C61—21no—
108#124×C61—21no—
109#124×C61—21no—
110#124×C61—21no—
111#124×C61—21no—
112#124×C61D411yescharacteristic, complemented
113#123×C61—21no—
114#123×C61—21no—
115#123×C61—21no—
116#123×C61—21no—
117#123×C61—21no—
118#123×C61—21no—
119#123×C61—21no—
120#123×C61—21no—
121#123×C61—21no—
122#123×C61—21no—
123#123×C61—21no—
124#123×C61—21no—
125C22⋊Q8×C61—21no—
126C22⋊Q8×C61—21no—
127C22⋊Q8×C61—21no—
128C22⋊Q8×C61—21no—
129C22⋊Q8×C61—21no—
130C22⋊Q8×C61—21no—
131C22⋊Q8×C61—21no—
132C22⋊Q8×C61C2311yescharacteristic
133#121×C61—21no—
134#121×C61—21no—
135#121×C61—21no—
136#121×C61—21no—
137#121×C61—21no—
138#121×C61—21no—
139#121×C61—21no—
140#121×C61—21no—
141#121×C61—21no—
142#121×C61—21no—
143#121×C61—21no—
144#121×C61—21no—
145#121×C61C2311yescharacteristic
146#121×C61C2311yescharacteristic
147#121×C61C2311yescharacteristic
148#120×C61—21no—
149#120×C61—21no—
150#120×C61—21no—
151#120×C61—21no—
152#120×C61—21no—
153C4×Q8×C61D411yescharacteristic, complemented
154C4×D4×C61—21no—
155C4×D4×C61—21no—
156C4×D4×C61—21no—
157C4×D4×C61—21no—
158C4×D4×C61—21no—
159C4×D4×C61—21no—
160C4×D4×C61—21no—
161C4×D4×C61—21no—
162C4×D4×C61D411yescharacteristic, complemented
163C4×D4×C61D411yescharacteristic, complemented
164C4×D4×C61D411yescharacteristic, complemented
165#117×C61—21no—
166#117×C61—21no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61D411yescharacteristic
171C2×C4⋊C4×C61D411yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C22⋊C4×C61—21no—
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61D411yescharacteristic
182C2×C22⋊C4×C61D411yescharacteristic
183C2×C22⋊C4×C61C2311yescharacteristic
184C2×C42×C61—21no—
185C2×C42×C61C2311yescharacteristic
186C4⋊C8×C61—21no—
187C4⋊C8×C61—21no—
188#103×C61—21no—
189#103×C61—21no—
190#103×C61—21no—
191#103×C61—21no—
192#102×C61—21no—
193#102×C61—21no—
194#102×C61—21no—
195#102×C61—21no—
196C22⋊C8×C61C2311yescharacteristic
197C22⋊C8×C61C2311yescharacteristic
198C22⋊C8×C61C2311yescharacteristic
199C22⋊C8×C61C2311yescharacteristic
200#97×C61—21no—
201C4×C8×C61—21no—
202#95×C61—21no—
203#95×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C24×C61—21no—
207C24×C61—21no—
208C24×C61C2×D411yescharacteristic
209#41×C61—81no—
210#41×C61—81no—
211#41×C61—81no—
212#41×C61—81no—
213C2×Q8×C61—21no—
214C2×Q8×C61—21no—
215C2×Q8×C61—21no—
216C2×Q8×C61—21no—
217C2×Q8×C61—81no—
218C2×Q8×C61C2×D411yescharacteristic
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61—21no—
225C2×D4×C61—21no—
226C2×D4×C61—21no—
227C2×D4×C61—21no—
228C2×D4×C61—21no—
229C2×D4×C61—21no—
230C2×D4×C61—21no—
231C2×D4×C61—21no—
232C2×D4×C61—21no—
233C2×D4×C61—42no—
234C2×D4×C61—81no—
235C2×D4×C61—81no—
236C2×D4×C61—81no—
237C2×D4×C61—81no—
238C2×D4×C61—81no—
239C2×D4×C61C2×D411yescharacteristic
240C2×D4×C61C2×D411yescharacteristic
241C2×D4×C61C2×D411yescharacteristic
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61C2×D411yescharacteristic
254C22×C4×C61C2×D411yescharacteristic
255C22×C4×C61C2×D411yescharacteristic
256C22×C4×C61C2×D411yescharacteristic
257C22×C4×C61C2×D411yescharacteristic
258C22×C4×C61C2411yescharacteristic
259Q16×C61—81no—
260SD16×C61—81no—
261SD16×C61—81no—
262SD16×C61—81no—
263SD16×C61—81no—
264D8×C61—81no—
265D8×C61—81no—
266D8×C61—81no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C2×C8×C61—21no—
270C2×C8×C61—21no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61—21no—
285C4⋊C4×C61—21no—
286C4⋊C4×C61—21no—
287C4⋊C4×C61—21no—
288C4⋊C4×C61—42no—
289C4⋊C4×C61—81no—
290C4⋊C4×C61C2×D411yescharacteristic
291C4⋊C4×C61C2×D411yescharacteristic
292C4⋊C4×C61C2×D411yescharacteristic
293C4⋊C4×C61C2×D411yescharacteristic
294C22⋊C4×C61—21no—
295C22⋊C4×C61—21no—
296C22⋊C4×C61—21no—
297C22⋊C4×C61—21no—
298C22⋊C4×C61—21no—
299C22⋊C4×C61—21no—
300C22⋊C4×C61—21no—
301C22⋊C4×C61—21no—
302C22⋊C4×C61—21no—
303C22⋊C4×C61—21no—
304C22⋊C4×C61—21no—
305C22⋊C4×C61—21no—
306C22⋊C4×C61—21no—
307C22⋊C4×C61—21no—
308C22⋊C4×C61—21no—
309C22⋊C4×C61—21no—
310C22⋊C4×C61—21no—
311C22⋊C4×C61—21no—
312C22⋊C4×C61—21no—
313C22⋊C4×C61—21no—
314C22⋊C4×C61—21no—
315C22⋊C4×C61—21no—
316C22⋊C4×C61—21no—
317C22⋊C4×C61—21no—
318C22⋊C4×C61—21no—
319C22⋊C4×C61—42no—
320C22⋊C4×C61—41no—
321C22⋊C4×C61—41no—
322C22⋊C4×C61—41no—
323C22⋊C4×C61—41no—
324C22⋊C4×C61—81no—
325C22⋊C4×C61—81no—
326C22⋊C4×C61—81no—
327C42×C61—21no—
328C42×C61—21no—
329C42×C61—21no—
330C42×C61—81no—
331C42×C61C2×D411yescharacteristic
332C42×C61C2×D411yescharacteristic
333C42×C61C2×D411yescharacteristic
334C42×C61C2×D411yescharacteristic
335C23×C61—21no—
336C23×C61—21no—
337C23×C61—21no—
338C23×C61—21no—
339C23×C61—21no—
340C23×C61—21no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61—81no—
351C23×C61—81no—
352C23×C61—81no—
353C23×C61C22×D411yescharacteristic
354Q8×C61—41no—
355Q8×C61—41no—
356Q8×C61—41no—
357Q8×C61—41no—
358Q8×C61—41no—
359Q8×C61—81no—
360Q8×C61—81no—
361D4×C61—41no—
362D4×C61—41no—
363D4×C61—41no—
364D4×C61—41no—
365D4×C61—41no—
366D4×C61—41no—
367D4×C61—41no—
368D4×C61—41no—
369D4×C61—41no—
370D4×C61—41no—
371D4×C61—41no—
372D4×C61—41no—
373D4×C61—41no—
374D4×C61—81no—
375D4×C61—81no—
376D4×C61—81no—
377D4×C61—81no—
378D4×C61—81no—
379D4×C61—81no—
380D4×C61—81no—
381D4×C61—81no—
382D4×C61—81no—
383D4×C61—84no—
384C2×C4×C61—21no—
385C2×C4×C61—21no—
386C2×C4×C61—22no—
387C2×C4×C61—21no—
388C2×C4×C61—21no—
389C2×C4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—21no—
396C2×C4×C61—21no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61—41no—
401C2×C4×C61—41no—
402C2×C4×C61—41no—
403C2×C4×C61—41no—
404C2×C4×C61—41no—
405C2×C4×C61—41no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61—41no—
409C2×C4×C61—81no—
410C2×C4×C61—81no—
411C2×C4×C61—81no—
412C2×C4×C61—81no—
413C2×C4×C61—81no—
414C2×C4×C61—81no—
415C2×C4×C61—81no—
416C2×C4×C61—81no—
417C2×C4×C61#12011yescharacteristic
418C2×C4×C61#12011yescharacteristic
419C2×C4×C61#12011yescharacteristic
420C2×C4×C61#12011yescharacteristic
421C2×C4×C61C22×D411yescharacteristic
422C2×C4×C61C22×D411yescharacteristic
423C8×C61—41no—
424C8×C61—41no—
425C8×C61—41no—
426C8×C61—41no—
427#18434C6111yesmaximal, characteristic, direct product factor, Sylow
428C22×C61—21no—
429C22×C61—21no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61—41no—
441C22×C61—41no—
442C22×C61—81no—
443C22×C61—81no—
444C22×C61—81no—
445C22×C61—81no—
446C22×C61—81no—
447C22×C61—81no—
448C22×C61—81no—
449C22×C61—81no—
450C22×C61—81no—
451C22×C61—162no—
452C22×C61C2×#12011yescharacteristic
453C22×C61#57611yescharacteristic
454C22×C61#57711yescharacteristic
455C4×C61—21no—
456C4×C61—21no—
457C4×C61—21no—
458C4×C61—21no—
459C4×C61—21no—
460C4×C61—21no—
461C4×C61—42no—
462C4×C61—41no—
463C4×C61—41no—
464C4×C61—41no—
465C4×C61—41no—
466C4×C61—41no—
467C4×C61—41no—
468C4×C61—41no—
469C4×C61—41no—
470C4×C61—81no—
471C4×C61—81no—
472#3560C2×C6111yescharacteristic, complemented
473#3213C2×C6111yescharacteristic, complemented
474#3211C2×C6111yescharacteristic, complemented
475#2662C2×C6111yescharacteristic, complemented
476#1606C2×C6111yescharacteristic, complemented
477#1604C2×C6111yescharacteristic, complemented
478#1603C2×C6111yescharacteristic, complemented
479#1601C2×C6111yescharacteristic, complemented
480#1600C2×C6111yescharacteristic, complemented
481#1598C2×C6111yescharacteristic, complemented
482#1597C2×C6111yescharacteristic, complemented
483#1595C2×C6111yescharacteristic, complemented
484#1509C2×C6111yescharacteristic, complemented
485#1502C2×C6111yescharacteristic, complemented
486#1473C2×C6111yescharacteristic, complemented
487C2×C61—21no—
488C2×C61—21no—
489C2×C61—81no—
490C2×C61—81no—
491C2×C61—81no—
492C2×C61—81no—
493C2×C61—161no—
494C2×C61#301211yescharacteristic
495C2×C61#301811yescharacteristic
496C2×C61#302711yescharacteristic
497#563—21no—
498#560—21no—
499#553—21no—
500#553—21no—
501#551—21no—
502#547—21no—
503#546—21no—
504#546—21no—
505#542—21no—
506#539—21no—
507#539C22×C6111yescharacteristic
508#538—21no—
509#538—21no—
510#538C22×C6111yescharacteristic
511#537C22×C6111yescharacteristic
512#534C22×C6111yescharacteristic
513#532C22×C6111yescharacteristic
514#529C22×C6111yescharacteristic
515C2×#126C22×C6111yescharacteristic
516C2×#124C22×C6111yescharacteristic, complemented
517#496—21no—
518#495—21no—
519#489—21no—
520#488—21no—
521#464—21no—
522#463—21no—
523#463—21no—
524#463—21no—
525#451C22×C6111yescharacteristic, complemented
526#450C22×C6111yescharacteristic, complemented
527#448C22×C6111yescharacteristic
528#448C22×C6111yescharacteristic
529#448C22×C6111yescharacteristic, complemented
530#447C22×C6111yescharacteristic
531#447C22×C6111yescharacteristic
532#447C22×C6111yescharacteristic, complemented
533#432C22×C6111yescharacteristic, complemented
534#431C22×C6111yescharacteristic, complemented
535#396—21no—
536#395C22×C6111yescharacteristic, complemented
537#394—21no—
538#394C22×C6111yescharacteristic, complemented
539#393C22×C6111yescharacteristic
540#392C22×C6111yescharacteristic
541#390—21no—
542#388—21no—
543C4×C4⋊C4C22×C6111yescharacteristic, complemented
544#328C22×C6111yescharacteristic, complemented
545#328C22×C6111yescharacteristic, complemented
546#327C22×C6111yescharacteristic
547#327C22×C6111yescharacteristic
548#327C22×C6111yescharacteristic
549#327C22×C6111yescharacteristic
550#327C22×C6111yescharacteristic, complemented
551#327C22×C6111yescharacteristic, complemented
552#324C22×C6111yescharacteristic, complemented
553#324C22×C6111yescharacteristic, complemented
554#323C22×C6111yescharacteristic
555#323C22×C6111yescharacteristic
556C61#1843411yescharacteristic, direct product factor, Sylow
557C2×#41—21no—
558C2×#41—21no—
559C22×Q8C23×C6111yescharacteristic
560C22×D4—21no—
561C22×D4—21no—
562C22×D4C23×C6111yescharacteristic
563C2×Q16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×D8—21no—
569C2×D8—21no—
570C2×D8—21no—
571C4⋊Q8—21no—
572C4⋊Q8D4×C6111yescharacteristic, complemented
573#127D4×C6111yescharacteristic, complemented
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#126—21no—
583#125—21no—
584#125—21no—
585#125D4×C6111yescharacteristic, complemented
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124—21no—
594#124D4×C6111yescharacteristic, complemented
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606#123—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8C23×C6111yescharacteristic
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121C23×C6111yescharacteristic
628#121C23×C6111yescharacteristic
629#121C23×C6111yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635C4×Q8D4×C6111yescharacteristic, complemented
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4D4×C6111yescharacteristic, complemented
645C4×D4D4×C6111yescharacteristic, complemented
646C4×D4D4×C6111yescharacteristic, complemented
647#117—21no—
648#117—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C6111yescharacteristic
653C2×C4⋊C4D4×C6111yescharacteristic
654C2×C4⋊C4C23×C6111yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C6111yescharacteristic
664C2×C22⋊C4D4×C6111yescharacteristic
665C2×C22⋊C4C23×C6111yescharacteristic
666C2×C42—21no—
667C2×C42C23×C6111yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8C23×C6111yescharacteristic
679C22⋊C8C23×C6111yescharacteristic
680C22⋊C8C23×C6111yescharacteristic
681C22⋊C8C23×C6111yescharacteristic
682#97—21no—
683C4×C8—21no—
684#95—21no—
685#95—21no—
686#95C23×C6111yescharacteristic
687#95C23×C6111yescharacteristic
688C24—21no—
689C24—21no—
690C24C2×D4×C6111yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C6111yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C6111yescharacteristic
722C2×D4C2×D4×C6111yescharacteristic
723C2×D4C2×D4×C6111yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4C2×D4×C6111yescharacteristic
736C22×C4C2×D4×C6111yescharacteristic
737C22×C4C2×D4×C6111yescharacteristic
738C22×C4C2×D4×C6111yescharacteristic
739C22×C4C2×D4×C6111yescharacteristic
740C22×C4C24×C6111yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C6111yescharacteristic
773C4⋊C4C2×D4×C6111yescharacteristic
774C4⋊C4C2×D4×C6111yescharacteristic
775C4⋊C4C2×D4×C6111yescharacteristic
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C6111yescharacteristic
814C42C2×D4×C6111yescharacteristic
815C42C2×D4×C6111yescharacteristic
816C42C2×D4×C6111yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C6111yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4#120×C6111yescharacteristic
900C2×C4#120×C6111yescharacteristic
901C2×C4#120×C6111yescharacteristic
902C2×C4#120×C6111yescharacteristic
903C2×C4C22×D4×C6111yescharacteristic
904C2×C4C22×D4×C6111yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×#120×C6111yescharacteristic
934C22C61×#57611yescharacteristic
935C22C61×#57711yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2C61×#301211yescharacteristic
961C2C61×#301811yescharacteristic
962C2C61×#302711yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3560C2semidirect
2. C61×#3213C2semidirect
3. C61×#3211C2semidirect
4. C61×#2662C2semidirect
5. C61×#1606C2semidirect
6. C61×#1604C2semidirect
7. C61×#1603C2semidirect
8. C61×#1601C2semidirect
9. C61×#1600C2semidirect
10. C61×#1598C2semidirect
11. C61×#1597C2semidirect
12. C61×#1595C2semidirect
13. C61×#1509C2semidirect
14. C61×#1502C2semidirect
15. C61×#1473C2semidirect
35. C2×#124×C61C22semidirect
44. C61×#451C22semidirect
45. C61×#450C22semidirect
48. C61×#448C22semidirect
51. C61×#447C22semidirect
52. C61×#432C22semidirect
53. C61×#431C22semidirect
55. C61×#395C22semidirect
57. C61×#394C22semidirect
62. C4×C4⋊C4×C61C22semidirect
63. C61×#328C22semidirect
64. C61×#328C22semidirect
69. C61×#327C22semidirect
70. C61×#327C22semidirect
71. C61×#324C22semidirect
72. C61×#324C22semidirect
90. C4⋊Q8×C61D4semidirect
91. #127×C61D4semidirect
103. #125×C61D4semidirect
112. #124×C61D4semidirect
153. C4×Q8×C61D4semidirect
162. C4×D4×C61D4semidirect
163. C4×D4×C61D4semidirect
164. C4×D4×C61D4semidirect
427. #18434C61direct (N × H)
472. #3560C2×C61semidirect
473. #3213C2×C61semidirect
474. #3211C2×C61semidirect
475. #2662C2×C61semidirect
476. #1606C2×C61semidirect
477. #1604C2×C61semidirect
478. #1603C2×C61semidirect
479. #1601C2×C61semidirect
480. #1600C2×C61semidirect
481. #1598C2×C61semidirect
482. #1597C2×C61semidirect
483. #1595C2×C61semidirect
484. #1509C2×C61semidirect
485. #1502C2×C61semidirect
486. #1473C2×C61semidirect
516. C2×#124C22×C61semidirect
525. #451C22×C61semidirect
526. #450C22×C61semidirect
529. #448C22×C61semidirect
532. #447C22×C61semidirect
533. #432C22×C61semidirect
534. #431C22×C61semidirect
536. #395C22×C61semidirect
538. #394C22×C61semidirect
543. C4×C4⋊C4C22×C61semidirect
544. #328C22×C61semidirect
545. #328C22×C61semidirect
550. #327C22×C61semidirect
551. #327C22×C61semidirect
552. #324C22×C61semidirect
553. #324C22×C61semidirect
556. C61#18434direct (N × H)
572. C4⋊Q8D4×C61semidirect
573. #127D4×C61semidirect
585. #125D4×C61semidirect
594. #124D4×C61semidirect
635. C4×Q8D4×C61semidirect
644. C4×D4D4×C61semidirect
645. C4×D4D4×C61semidirect
646. C4×D4D4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#35602
C61×#32132
C61×#32112
C61×#26622
C61×#16062
C61×#16042
C61×#16032
C61×#16012
C61×#16002
C61×#15982
C61×#15972
C61×#15952
C61×#15092
C61×#15022
C61×#14732
#1843461