Finite Group Databasebeta

← C61×#33552 #29536985

Subgroups — C61×#33552 #29536985

Order 15616.

1156 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3533C211yesmaximal, characteristic, complemented
2C61×#3026C211yesmaximal, characteristic, complemented
3C2×C61×#458C211yesmaximal, characteristic, complemented
4C61×#3019C211yesmaximal, characteristic, complemented
5C61×#2201C212yesmaximal, complemented
6C61×#2200C212yesmaximal, complemented
7C61×#2198C212yesmaximal, complemented
8C61×#2197C212yesmaximal, complemented
9C61×#2127C211yesmaximal, characteristic, complemented
10C61×#2121C211yesmaximal, characteristic, complemented
11C2×C61×#352C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C61C2211yescharacteristic
13C61×#575—21no—
14C61×#563C2211yescharacteristic, complemented
15C61×#562—21no—
16C61×#560C2211yescharacteristic, complemented
17C61×#559C2211yescharacteristic, complemented
18C61×#553—21no—
19C61×#552—21no—
20C61×#551—21no—
21C61×#551C2211yescharacteristic, complemented
22C61×#547—21no—
23C61×#546—21no—
24C61×#542—21no—
25C61×#540—21no—
26C61×#539—21no—
27C61×#538—21no—
28C61×#538—21no—
29C61×#535C2211yescharacteristic
30C61×#534—21no—
31C61×#534C2211yescharacteristic
32C61×#525—21no—
33C2×#123×C61—21no—
34C2×#123×C61C2211yescharacteristic
35C61×#458—21no—
36C61×#458—21no—
37C61×#458—21no—
38C61×#458C2212yes—
39C61×#458C2212yes—
40C61×#458C2212yes—
41C61×B(4,𝔽2)—21no—
42C61×B(4,𝔽2)C2212yes—
43C61×#455—21no—
44C61×#455C2212yes—
45C61×#453—21no—
46C61×#453C2212yes—
47C61×#421—21no—
48C2×#100×C61C2211yescharacteristic
49C2×#99×C61—21no—
50C2×#99×C61—21no—
51C2×#99×C61C2211yescharacteristic
52C2×#99×C61C2211yescharacteristic
53C61×#354C2212yescomplemented
54C61×#353C2212yescomplemented
55C61×#352C2212yescomplemented
56C61×#352C2212yescomplemented
57C61×#352C2212yescomplemented
58C61×AΣL(1,𝔽16)C2212yescomplemented
59H(5,𝔽2)×C61—21no—
60H(5,𝔽2)×C61—21no—
61H(5,𝔽2)×C61—21no—
62H(5,𝔽2)×C61—42no—
63H(5,𝔽2)×C61C2312yes—
64C2×#41×C61—21no—
65C2×#41×C61—21no—
66C2×#41×C61—41no—
67C2×#41×C61D411yescharacteristic, complemented
68C22×D4×C61—21no—
69C22×D4×C61—21no—
70C22×D4×C61—41no—
71C22×D4×C61D411yescharacteristic
72C22×D4×C61C2311yescharacteristic
73C23×C4×C61D411yescharacteristic, complemented
74#137×C61—22no—
75#137×C61—41no—
76AGL(1,ℤ/8)×C61—22no—
77AGL(1,ℤ/8)×C61—41no—
78#135×C61—42no—
79C2×M16×C61—21no—
80C4⋊Q8×C61—21no—
81#127×C61D411yescharacteristic, complemented
82#127×C61C2311yescharacteristic
83#126×C61—21no—
84#126×C61—21no—
85#126×C61—21no—
86#126×C61—21no—
87#126×C61—21no—
88#126×C61—21no—
89#125×C61—21no—
90#125×C61—21no—
91#125×C61—21no—
92#124×C61—21no—
93#124×C61—21no—
94#124×C61—21no—
95#124×C61—21no—
96#124×C61D411yescharacteristic, complemented
97#124×C61C2311yescharacteristic
98#123×C61—21no—
99#123×C61—21no—
100#123×C61—21no—
101#123×C61—21no—
102#123×C61—21no—
103#123×C61—21no—
104#123×C61—21no—
105#123×C61—21no—
106#123×C61—21no—
107#123×C61—21no—
108#123×C61—21no—
109#123×C61—21no—
110#123×C61—22no—
111#123×C61—22no—
112#123×C61—22no—
113#123×C61—41no—
114#123×C61—42no—
115#123×C61D411yescharacteristic
116#123×C61D411yescharacteristic, complemented
117#123×C61D411yescharacteristic, complemented
118#123×C61C2311yescharacteristic
119#123×C61C2311yescharacteristic
120#123×C61C2311yescharacteristic
121C22⋊Q8×C61—21no—
122C22⋊Q8×C61—21no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—21no—
126C22⋊Q8×C61—21no—
127C22⋊Q8×C61—21no—
128C22⋊Q8×C61—21no—
129#121×C61—21no—
130#121×C61—21no—
131#121×C61—21no—
132#121×C61—21no—
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—42no—
142#120×C61—21no—
143#120×C61—21no—
144#120×C61—21no—
145#120×C61—21no—
146#120×C61—22no—
147#120×C61—41no—
148#120×C61D411yescharacteristic
149#120×C61C2311yescharacteristic
150C4×Q8×C61—21no—
151C4×D4×C61—21no—
152C4×D4×C61—21no—
153C4×D4×C61—21no—
154C4×D4×C61—21no—
155C4×D4×C61—21no—
156C4×D4×C61—21no—
157C4×D4×C61—21no—
158C4×D4×C61—21no—
159C4×D4×C61—21no—
160#117×C61—21no—
161#117×C61—21no—
162#117×C61—21no—
163#117×C61D411yescharacteristic, complemented
164C2×C4⋊C4×C61—21no—
165C2×C4⋊C4×C61—21no—
166C2×C4⋊C4×C61—41no—
167C2×C22⋊C4×C61—21no—
168C2×C22⋊C4×C61—21no—
169C2×C22⋊C4×C61—21no—
170C2×C22⋊C4×C61—21no—
171C2×C22⋊C4×C61—41no—
172C2×C22⋊C4×C61D411yescharacteristic
173C2×C22⋊C4×C61D411yescharacteristic, complemented
174#104×C61—22no—
175#104×C61—22no—
176#100×C61—21no—
177#100×C61C2312yes—
178#99×C61—21no—
179#99×C61—21no—
180#99×C61—22no—
181#99×C61—22no—
182#99×C61—22no—
183#99×C61—22no—
184#99×C61C2312yes—
185#99×C61C2312yes—
186C24×C61—21no—
187C24×C61—21no—
188C24×C61C2×D411yescharacteristic
189C24×C61C2×D411yescharacteristic
190C24×C61C2×D411yescharacteristic
191#41×C61—22no—
192#41×C61—22no—
193#41×C61—42no—
194#41×C61—41no—
195#41×C61—42no—
196#41×C61—42no—
197#41×C61—41no—
198#41×C61—41no—
199#41×C61—42no—
200#41×C61—41no—
201#41×C61—81no—
202#41×C61—81no—
203C2×Q8×C61—21no—
204C2×Q8×C61—21no—
205C2×Q8×C61—21no—
206C2×Q8×C61C2×D411yescharacteristic
207C2×D4×C61—21no—
208C2×D4×C61—22no—
209C2×D4×C61—22no—
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61—22no—
213C2×D4×C61—22no—
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—41no—
224C2×D4×C61—41no—
225C2×D4×C61—42no—
226C2×D4×C61—42no—
227C2×D4×C61—41no—
228C2×D4×C61—41no—
229C2×D4×C61—41no—
230C2×D4×C61—41no—
231C2×D4×C61—42no—
232C2×D4×C61—42no—
233C2×D4×C61—41no—
234C2×D4×C61—41no—
235C2×D4×C61—41no—
236C2×D4×C61—41no—
237C2×D4×C61—41no—
238C2×D4×C61—42no—
239C2×D4×C61C2×D411yescharacteristic
240C2×D4×C61C2×D411yescharacteristic
241C2×D4×C61C2×D411yescharacteristic
242C2×D4×C61C2×D411yescharacteristic
243C2×D4×C61C2411yescharacteristic
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×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—41no—
256C22×C4×C61—41no—
257C22×C4×C61—41no—
258C22×C4×C61—41no—
259C22×C4×C61—41no—
260C22×C4×C61C2×D411yescharacteristic
261C22×C4×C61C2×D411yescharacteristic
262C22×C4×C61C2×D411yescharacteristic
263C22×C4×C61C2×D411yescharacteristic
264Q16×C61—42no—
265SD16×C61—42no—
266SD16×C61—42no—
267D8×C61—42no—
268M16×C61—22no—
269M16×C61—41no—
270C2×C8×C61—41no—
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—21no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61—42no—
291C4⋊C4×C61—42no—
292C4⋊C4×C61—42no—
293C22⋊C4×C61—21no—
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—22no—
317C22⋊C4×C61—22no—
318C22⋊C4×C61—42no—
319C22⋊C4×C61—41no—
320C22⋊C4×C61—41no—
321C22⋊C4×C61—42no—
322C22⋊C4×C61—42no—
323C22⋊C4×C61—42no—
324C22⋊C4×C61C2×D411yescharacteristic
325C22⋊C4×C61C2×D411yescharacteristic
326C22⋊C4×C61C2×D411yescharacteristic
327C22⋊C4×C61C2×D411yescharacteristic
328C42×C61—21no—
329C42×C61—21no—
330C42×C61—21no—
331C42×C61—21no—
332C42×C61C2×D411yescharacteristic
333C42×C61C2×D411yescharacteristic
334C23×C61—21no—
335C23×C61—21no—
336C23×C61—21no—
337C23×C61—21no—
338C23×C61—22no—
339C23×C61—22no—
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—81no—
347C23×C61—81no—
348C23×C61—81no—
349C23×C61—82no—
350C23×C61—161no—
351C23×C61#12011yescharacteristic
352C23×C61#12011yescharacteristic
353C23×C61#12011yescharacteristic
354C23×C61C22×D411yescharacteristic
355C23×C61C22×D411yescharacteristic
356Q8×C61—22no—
357Q8×C61—41no—
358Q8×C61—41no—
359Q8×C61—81no—
360Q8×C61—81no—
361D4×C61—22no—
362D4×C61—41no—
363D4×C61—41no—
364D4×C61—41no—
365D4×C61—41no—
366D4×C61—41no—
367D4×C61—41no—
368D4×C61—42no—
369D4×C61—42no—
370D4×C61—42no—
371D4×C61—42no—
372D4×C61—42no—
373D4×C61—42no—
374D4×C61—41no—
375D4×C61—41no—
376D4×C61—41no—
377D4×C61—41no—
378D4×C61—81no—
379D4×C61—81no—
380D4×C61—81no—
381D4×C61—81no—
382D4×C61—81no—
383D4×C61—81no—
384D4×C61—81no—
385D4×C61—81no—
386D4×C61—81no—
387D4×C61—162no—
388C2×C4×C61—21no—
389C2×C4×C61—21no—
390C2×C4×C61—22no—
391C2×C4×C61—22no—
392C2×C4×C61—21no—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—21no—
396C2×C4×C61—21no—
397C2×C4×C61—21no—
398C2×C4×C61—21no—
399C2×C4×C61—21no—
400C2×C4×C61—21no—
401C2×C4×C61—21no—
402C2×C4×C61—42no—
403C2×C4×C61—42no—
404C2×C4×C61—41no—
405C2×C4×C61—41no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61—41no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—41no—
412C2×C4×C61—42no—
413C2×C4×C61—42no—
414C2×C4×C61—81no—
415C2×C4×C61—81no—
416C2×C4×C61—81no—
417C2×C4×C61—81no—
418C2×C4×C61—81no—
419C2×C4×C61—81no—
420C2×C4×C61—81no—
421C2×C4×C61—81no—
422C2×C4×C61—82no—
423C2×C4×C61—161no—
424C2×C4×C61#12011yescharacteristic
425C2×C4×C61C22×D411yescharacteristic
426C8×C61—42no—
427#33552C6111yesmaximal, characteristic, direct product factor, Sylow
428C22×C61—21no—
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61—42no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61—41no—
441C22×C61—41no—
442C22×C61—42no—
443C22×C61—41no—
444C22×C61—41no—
445C22×C61—81no—
446C22×C61—81no—
447C22×C61—81no—
448C22×C61—82no—
449C22×C61—82no—
450C22×C61—82no—
451C22×C61—82no—
452C22×C61—161no—
453C22×C61—161no—
454C22×C61B(4,𝔽2)11yescharacteristic
455C22×C61B(4,𝔽2)11yescharacteristic
456C22×C61C2×#12011yescharacteristic
457C4×C61—21no—
458C4×C61—21no—
459C4×C61—41no—
460C4×C61—41no—
461C4×C61—41no—
462C4×C61—41no—
463C4×C61—41no—
464C4×C61—41no—
465C4×C61—42no—
466C4×C61—41no—
467C4×C61—41no—
468C4×C61—41no—
469C4×C61—41no—
470C4×C61—82no—
471C4×C61—82no—
472#3533C2×C6111yescharacteristic, complemented
473#3026C2×C6111yescharacteristic, complemented
474C2×#458C2×C6111yescharacteristic, complemented
475#3019C2×C6111yescharacteristic, complemented
476#2201C2×C6112yescomplemented
477#2200C2×C6112yescomplemented
478#2198C2×C6112yescomplemented
479#2197C2×C6112yescomplemented
480#2127C2×C6111yescharacteristic, complemented
481#2121C2×C6111yescharacteristic, complemented
482C2×#352C2×C6111yescharacteristic, complemented
483C2×C61—21no—
484C2×C61—21no—
485C2×C61—21no—
486C2×C61—41no—
487C2×C61—41no—
488C2×C61—41no—
489C2×C61—41no—
490C2×C61—81no—
491C2×C61—81no—
492C2×C61—82no—
493C2×C61C2×B(4,𝔽2)11yescharacteristic
494C2×H(5,𝔽2)C22×C6111yescharacteristic
495#575—21no—
496#563C22×C6111yescharacteristic, complemented
497#562—21no—
498#560C22×C6111yescharacteristic, complemented
499#559C22×C6111yescharacteristic, complemented
500#553—21no—
501#552—21no—
502#551—21no—
503#551C22×C6111yescharacteristic, complemented
504#547—21no—
505#546—21no—
506#542—21no—
507#540—21no—
508#539—21no—
509#538—21no—
510#538—21no—
511#535C22×C6111yescharacteristic
512#534—21no—
513#534C22×C6111yescharacteristic
514#525—21no—
515C2×#123—21no—
516C2×#123C22×C6111yescharacteristic
517#458—21no—
518#458—21no—
519#458—21no—
520#458C22×C6112yes—
521#458C22×C6112yes—
522#458C22×C6112yes—
523B(4,𝔽2)—21no—
524B(4,𝔽2)C22×C6112yes—
525#455—21no—
526#455C22×C6112yes—
527#453—21no—
528#453C22×C6112yes—
529#421—21no—
530C2×#100C22×C6111yescharacteristic
531C2×#99—21no—
532C2×#99—21no—
533C2×#99C22×C6111yescharacteristic
534C2×#99C22×C6111yescharacteristic
535#354C22×C6112yescomplemented
536#353C22×C6112yescomplemented
537#352C22×C6112yescomplemented
538#352C22×C6112yescomplemented
539#352C22×C6112yescomplemented
540AΣL(1,𝔽16)C22×C6112yescomplemented
541C61#3355211yescharacteristic, direct product factor, Sylow
542H(5,𝔽2)—21no—
543H(5,𝔽2)—21no—
544H(5,𝔽2)—21no—
545H(5,𝔽2)—42no—
546H(5,𝔽2)C23×C6112yes—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—41no—
550C2×#41D4×C6111yescharacteristic, complemented
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—41no—
554C22×D4D4×C6111yescharacteristic
555C22×D4C23×C6111yescharacteristic
556C23×C4D4×C6111yescharacteristic, complemented
557#137—22no—
558#137—41no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—41no—
561#135—42no—
562C2×M16—21no—
563C4⋊Q8—21no—
564#127D4×C6111yescharacteristic, complemented
565#127C23×C6111yescharacteristic
566#126—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#125—21no—
573#125—21no—
574#125—21no—
575#124—21no—
576#124—21no—
577#124—21no—
578#124—21no—
579#124D4×C6111yescharacteristic, complemented
580#124C23×C6111yescharacteristic
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—22no—
594#123—22no—
595#123—22no—
596#123—41no—
597#123—42no—
598#123D4×C6111yescharacteristic
599#123D4×C6111yescharacteristic, complemented
600#123D4×C6111yescharacteristic, complemented
601#123C23×C6111yescharacteristic
602#123C23×C6111yescharacteristic
603#123C23×C6111yescharacteristic
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612#121—21no—
613#121—21no—
614#121—21no—
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—42no—
625#120—21no—
626#120—21no—
627#120—21no—
628#120—21no—
629#120—22no—
630#120—41no—
631#120D4×C6111yescharacteristic
632#120C23×C6111yescharacteristic
633C4×Q8—21no—
634C4×D4—21no—
635C4×D4—21no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643#117—21no—
644#117—21no—
645#117—21no—
646#117D4×C6111yescharacteristic, complemented
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—41no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4D4×C6111yescharacteristic
656C2×C22⋊C4D4×C6111yescharacteristic, complemented
657#104—22no—
658#104—22no—
659#100—21no—
660#100C23×C6112yes—
661#99—21no—
662#99—21no—
663#99—22no—
664#99—22no—
665#99—22no—
666#99—22no—
667#99C23×C6112yes—
668#99C23×C6112yes—
669C24—21no—
670C24—21no—
671C24C2×D4×C6111yescharacteristic
672C24C2×D4×C6111yescharacteristic
673C24C2×D4×C6111yescharacteristic
674#41—22no—
675#41—22no—
676#41—42no—
677#41—41no—
678#41—42no—
679#41—42no—
680#41—41no—
681#41—41no—
682#41—42no—
683#41—41no—
684#41—81no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8C2×D4×C6111yescharacteristic
690C2×D4—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—41no—
713C2×D4—41no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—41no—
717C2×D4—41no—
718C2×D4—41no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—42no—
722C2×D4C2×D4×C6111yescharacteristic
723C2×D4C2×D4×C6111yescharacteristic
724C2×D4C2×D4×C6111yescharacteristic
725C2×D4C2×D4×C6111yescharacteristic
726C2×D4C24×C6111yescharacteristic
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×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4C2×D4×C6111yescharacteristic
744C22×C4C2×D4×C6111yescharacteristic
745C22×C4C2×D4×C6111yescharacteristic
746C22×C4C2×D4×C6111yescharacteristic
747Q16—42no—
748SD16—42no—
749SD16—42no—
750D8—42no—
751M16—22no—
752M16—41no—
753C2×C8—41no—
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—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—42no—
774C4⋊C4—42no—
775C4⋊C4—42no—
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—22no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—42no—
807C22⋊C4C2×D4×C6111yescharacteristic
808C22⋊C4C2×D4×C6111yescharacteristic
809C22⋊C4C2×D4×C6111yescharacteristic
810C22⋊C4C2×D4×C6111yescharacteristic
811C42—21no—
812C42—21no—
813C42—21no—
814C42—21no—
815C42C2×D4×C6111yescharacteristic
816C42C2×D4×C6111yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—22no—
822C23—22no—
823C23—21no—
824C23—21no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—81no—
830C23—81no—
831C23—81no—
832C23—82no—
833C23—161no—
834C23#120×C6111yescharacteristic
835C23#120×C6111yescharacteristic
836C23#120×C6111yescharacteristic
837C23C22×D4×C6111yescharacteristic
838C23C22×D4×C6111yescharacteristic
839Q8—22no—
840Q8—41no—
841Q8—41no—
842Q8—81no—
843Q8—81no—
844D4—22no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—42no—
852D4—42no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—41no—
857D4—41no—
858D4—41no—
859D4—41no—
860D4—42no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868D4—81no—
869D4—81no—
870D4—162no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—82no—
906C2×C4—161no—
907C2×C4#120×C6111yescharacteristic
908C2×C4C22×D4×C6111yescharacteristic
909C8—42no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—41no—
926C22—41no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—161no—
935C22—161no—
936C22C61×B(4,𝔽2)11yescharacteristic
937C22C61×B(4,𝔽2)11yescharacteristic
938C22C2×#120×C6111yescharacteristic
939C4—21no—
940C4—21no—
941C4—41no—
942C4—41no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—42no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—82no—
953C4—82no—
954C2—21no—
955C2—21no—
956C2—21no—
957C2—41no—
958C2—41no—
959C2—41no—
960C2—41no—
961C2—81no—
962C2—81no—
963C2—82no—
964C2C2×C61×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C61C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C61
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C61 ◁ C23×C61 ◁ C22×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3533C2semidirect
2. C61×#3026C2semidirect
3. C2×C61×#458C2semidirect
4. C61×#3019C2semidirect
5. C61×#2201C2semidirect
6. C61×#2200C2semidirect
7. C61×#2198C2semidirect
8. C61×#2197C2semidirect
9. C61×#2127C2semidirect
10. C61×#2121C2semidirect
11. C2×C61×#352C2semidirect
14. C61×#563C22semidirect
16. C61×#560C22semidirect
17. C61×#559C22semidirect
21. C61×#551C22semidirect
53. C61×#354C22semidirect
54. C61×#353C22semidirect
55. C61×#352C22semidirect
56. C61×#352C22semidirect
57. C61×#352C22semidirect
58. C61×AΣL(1,𝔽16)C22semidirect
67. C2×#41×C61D4semidirect
73. C23×C4×C61D4semidirect
81. #127×C61D4semidirect
96. #124×C61D4semidirect
116. #123×C61D4semidirect
117. #123×C61D4semidirect
163. #117×C61D4semidirect
173. C2×C22⋊C4×C61D4semidirect
427. #33552C61direct (N × H)
472. #3533C2×C61semidirect
473. #3026C2×C61semidirect
474. C2×#458C2×C61semidirect
475. #3019C2×C61semidirect
476. #2201C2×C61semidirect
477. #2200C2×C61semidirect
478. #2198C2×C61semidirect
479. #2197C2×C61semidirect
480. #2127C2×C61semidirect
481. #2121C2×C61semidirect
482. C2×#352C2×C61semidirect
496. #563C22×C61semidirect
498. #560C22×C61semidirect
499. #559C22×C61semidirect
503. #551C22×C61semidirect
535. #354C22×C61semidirect
536. #353C22×C61semidirect
537. #352C22×C61semidirect
538. #352C22×C61semidirect
539. #352C22×C61semidirect
540. AΣL(1,𝔽16)C22×C61semidirect
541. C61#33552direct (N × H)
550. C2×#41D4×C61semidirect
556. C23×C4D4×C61semidirect
564. #127D4×C61semidirect
579. #124D4×C61semidirect
599. #123D4×C61semidirect
600. #123D4×C61semidirect
646. #117D4×C61semidirect
656. C2×C22⋊C4D4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#35332
C61×#30262
C2×C61×#4582
C61×#30192
C61×#22012
C61×#22002
C61×#21982
C61×#21972
C61×#21272
C61×#21212
C2×C61×#3522
#3355261