Finite Group Databasebeta

← C2×C61×#2009 #29526844

Subgroups — C2×C61×#2009 #29526844

Order 15616.

1926 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
1C2×C61×#575C211yesmaximal, characteristic
2C22×#137×C61C211yesmaximal, characteristic, complemented
3C2×C61×#536C211yesmaximal, characteristic, complemented
4C2×C61×#421C211yesmaximal, characteristic, complemented
5C2×C61×#419C211yesmaximal, characteristic, complemented
6C2×C61×#410C211yesmaximal, characteristic, complemented
7C61×#2009C218yesmaximal, direct product factor
8C2×C61×#344C211yesmaximal, characteristic, complemented
9C22×#41×C61C2211yescharacteristic
10C22×#41×C61C2211yescharacteristic
11C23×Q8×C61C2211yescharacteristic
12C61×#575—22no—
13C61×#575—22no—
14C61×#575—22no—
15C61×#575C2214yes—
16C2×#137×C61—22no—
17C2×#137×C61—22no—
18C2×#137×C61—22no—
19C2×#137×C61—21no—
20C2×#137×C61—21no—
21C2×#137×C61—22no—
22C2×#137×C61—22no—
23C2×#137×C61C2214yescomplemented
24C2×AGL(1,ℤ/8)×C61—21no—
25C2×AGL(1,ℤ/8)×C61—21no—
26C2×#135×C61—22no—
27C22×Q16×C61—21no—
28C22×SD16×C61—21no—
29C22×M16×C61C2211yescharacteristic
30C22×M16×C61C2211yescharacteristic
31C61×#536—22no—
32C61×#536—22no—
33C61×#536—22no—
34C61×#536C2214yescomplemented
35C2×C4⋊Q8×C61—21no—
36C2×#124×C61—21no—
37C2×#123×C61—22no—
38C2×C22⋊Q8×C61—22no—
39C2×#117×C61C2211yescharacteristic
40C2×#117×C61C2211yescharacteristic
41C61×#421—22no—
42C61×#421C2214yescomplemented
43C2×#104×C61—22no—
44C61×#419—22no—
45C61×#419C2214yescomplemented
46C2×#103×C61—22no—
47C61×#410—22no—
48C61×#410C2214yescomplemented
49C2×#99×C61—22no—
50C61×#344C2214yescomplemented
51C2×#41×C61—21no—
52C2×#41×C61—21no—
53C2×#41×C61—21no—
54C2×#41×C61—21no—
55C2×#41×C61—21no—
56C2×#41×C61—21no—
57C2×#41×C61—21no—
58C2×#41×C61—21no—
59C2×#41×C61—21no—
60C2×#41×C61—21no—
61C2×#41×C61—21no—
62C2×#41×C61—21no—
63C2×#41×C61—21no—
64C2×#41×C61—21no—
65C2×#41×C61—21no—
66C2×#41×C61—21no—
67C2×#41×C61—21no—
68C2×#41×C61—21no—
69C2×#41×C61—21no—
70C2×#41×C61—21no—
71C2×#41×C61D412yes—
72C2×#41×C61D412yes—
73C2×#41×C61C2312yes—
74C2×#41×C61C2312yes—
75C22×Q8×C61—21no—
76C22×Q8×C61—21no—
77C22×Q8×C61—21no—
78C22×Q8×C61—21no—
79C22×Q8×C61—21no—
80C22×Q8×C61—21no—
81C22×Q8×C61—21no—
82C22×Q8×C61—21no—
83C22×Q8×C61—21no—
84C22×Q8×C61—21no—
85C22×Q8×C61—21no—
86C22×Q8×C61D411yescharacteristic
87C22×Q8×C61D412yes—
88C22×Q8×C61D411yescharacteristic
89C22×Q8×C61D412yes—
90C22×Q8×C61C2312yes—
91C22×D4×C61—21no—
92C22×D4×C61—21no—
93C22×D4×C61D411yescharacteristic
94C22×D4×C61D411yescharacteristic
95C23×C4×C61—21no—
96C23×C4×C61—21no—
97C23×C4×C61—21no—
98C23×C4×C61C2311yescharacteristic
99#137×C61—28no—
100#137×C61—28no—
101#137×C61—24no—
102#137×C61—24no—
103#137×C61—28no—
104#137×C61—24no—
105#137×C61—24no—
106#137×C61—28no—
107AGL(1,ℤ/8)×C61—24no—
108AGL(1,ℤ/8)×C61—24no—
109AGL(1,ℤ/8)×C61—24no—
110AGL(1,ℤ/8)×C61—24no—
111#135×C61—28no—
112#135×C61—28no—
113C2×Q16×C61—24no—
114C2×Q16×C61—24no—
115C2×Q16×C61—22no—
116C2×Q16×C61—24no—
117C2×SD16×C61—24no—
118C2×SD16×C61—24no—
119C2×SD16×C61—22no—
120C2×SD16×C61—22no—
121C2×SD16×C61—24no—
122C2×D8×C61—22no—
123C2×M16×C61—21no—
124C2×M16×C61—21no—
125C2×M16×C61—21no—
126C2×M16×C61—21no—
127C2×M16×C61—21no—
128C2×M16×C61—21no—
129C2×M16×C61—21no—
130C2×M16×C61D412yes—
131C2×M16×C61D412yes—
132C2×M16×C61D412yes—
133C2×M16×C61C2312yes—
134C2×M16×C61C2312yes—
135C22×C8×C61—21no—
136C22×C8×C61D412yes—
137C4⋊Q8×C61—24no—
138C4⋊Q8×C61—24no—
139#124×C61—24no—
140#124×C61—24no—
141#123×C61—28no—
142#123×C61—28no—
143C22⋊Q8×C61—28no—
144C22⋊Q8×C61—28no—
145#117×C61—21no—
146#117×C61—21no—
147#117×C61—21no—
148#117×C61—21no—
149#117×C61—21no—
150#117×C61D412yes—
151#117×C61C2312yes—
152#117×C61C2312yes—
153C2×C4⋊C4×C61—24no—
154C2×C4⋊C4×C61—21no—
155C2×C4⋊C4×C61—21no—
156C2×C22⋊C4×C61—24no—
157C2×C22⋊C4×C61—21no—
158C2×C22⋊C4×C61D412yes—
159C2×C42×C61—21no—
160C2×C42×C61—21no—
161#104×C61—28no—
162#103×C61—28no—
163#99×C61—28no—
164C24×C61—21no—
165C24×C61—21no—
166C24×C61C2×D411yescharacteristic
167#41×C61—22no—
168#41×C61—22no—
169#41×C61—22no—
170#41×C61—22no—
171#41×C61—22no—
172#41×C61—22no—
173#41×C61—22no—
174#41×C61—22no—
175#41×C61—22no—
176#41×C61—22no—
177#41×C61—22no—
178#41×C61—22no—
179#41×C61—22no—
180#41×C61—22no—
181#41×C61—22no—
182#41×C61—22no—
183#41×C61—41no—
184#41×C61—41no—
185#41×C61—41no—
186#41×C61—41no—
187#41×C61—41no—
188#41×C61—41no—
189#41×C61—41no—
190#41×C61—41no—
191#41×C61—41no—
192#41×C61—41no—
193#41×C61—41no—
194#41×C61—41no—
195#41×C61—41no—
196#41×C61—41no—
197#41×C61—41no—
198#41×C61—41no—
199C2×Q8×C61—22no—
200C2×Q8×C61—22no—
201C2×Q8×C61—21no—
202C2×Q8×C61—21no—
203C2×Q8×C61—22no—
204C2×Q8×C61—22no—
205C2×Q8×C61—22no—
206C2×Q8×C61—21no—
207C2×Q8×C61—21no—
208C2×Q8×C61—21no—
209C2×Q8×C61—21no—
210C2×Q8×C61—22no—
211C2×Q8×C61—22no—
212C2×Q8×C61—21no—
213C2×Q8×C61—21no—
214C2×Q8×C61—22no—
215C2×Q8×C61—22no—
216C2×Q8×C61—22no—
217C2×Q8×C61—22no—
218C2×Q8×C61—21no—
219C2×Q8×C61—21no—
220C2×Q8×C61—22no—
221C2×Q8×C61—22no—
222C2×Q8×C61—22no—
223C2×Q8×C61—22no—
224C2×Q8×C61—41no—
225C2×Q8×C61—41no—
226C2×Q8×C61—41no—
227C2×Q8×C61—41no—
228C2×Q8×C61—41no—
229C2×Q8×C61—41no—
230C2×Q8×C61—41no—
231C2×Q8×C61—41no—
232C2×Q8×C61—41no—
233C2×Q8×C61—41no—
234C2×Q8×C61—41no—
235C2×Q8×C61—41no—
236C2×Q8×C61C2×D414yes—
237C2×Q8×C61C2×D412yes—
238C2×Q8×C61C2×D412yes—
239C2×D4×C61—22no—
240C2×D4×C61—22no—
241C2×D4×C61—22no—
242C2×D4×C61—22no—
243C2×D4×C61—21no—
244C2×D4×C61—21no—
245C2×D4×C61—21no—
246C2×D4×C61—21no—
247C2×D4×C61—21no—
248C2×D4×C61—21no—
249C2×D4×C61—21no—
250C2×D4×C61—21no—
251C2×D4×C61—21no—
252C2×D4×C61—21no—
253C2×D4×C61—41no—
254C2×D4×C61—41no—
255C2×D4×C61—41no—
256C2×D4×C61—41no—
257C2×D4×C61—41no—
258C2×D4×C61—41no—
259C2×D4×C61—41no—
260C2×D4×C61—41no—
261C2×D4×C61C2×D412yes—
262C2×D4×C61C2×D412yes—
263C22×C4×C61—22no—
264C22×C4×C61—22no—
265C22×C4×C61—21no—
266C22×C4×C61—22no—
267C22×C4×C61—21no—
268C22×C4×C61—22no—
269C22×C4×C61—22no—
270C22×C4×C61—22no—
271C22×C4×C61—22no—
272C22×C4×C61—22no—
273C22×C4×C61—41no—
274C22×C4×C61—41no—
275C22×C4×C61—41no—
276C22×C4×C61—41no—
277C22×C4×C61—41no—
278C22×C4×C61—41no—
279C22×C4×C61—41no—
280C22×C4×C61—41no—
281C22×C4×C61—41no—
282C22×C4×C61—41no—
283C22×C4×C61—41no—
284C22×C4×C61—41no—
285C22×C4×C61—41no—
286C22×C4×C61C2×D411yescharacteristic
287C22×C4×C61C2×D411yescharacteristic
288C22×C4×C61C2×D411yescharacteristic
289C22×C4×C61C2×D411yescharacteristic
290C22×C4×C61C2×D411yescharacteristic
291C22×C4×C61C2×D411yescharacteristic
292C22×C4×C61C2×D411yescharacteristic
293C22×C4×C61C2×D411yescharacteristic
294C22×C4×C61C2×D411yescharacteristic
295C22×C4×C61C2×D411yescharacteristic
296C22×C4×C61C2×D411yescharacteristic
297C22×C4×C61#4111yescharacteristic
298C22×C4×C61#4111yescharacteristic
299C22×C4×C61C2411yescharacteristic
300Q16×C61—216no—
301Q16×C61—28no—
302SD16×C61—216no—
303SD16×C61—28no—
304SD16×C61—28no—
305D8×C61—28no—
306M16×C61—22no—
307M16×C61—22no—
308M16×C61—22no—
309M16×C61—22no—
310M16×C61—22no—
311M16×C61—22no—
312M16×C61—22no—
313M16×C61C2×D414yes—
314C2×C8×C61—22no—
315C2×C8×C61—22no—
316C2×C8×C61—22no—
317C2×C8×C61—22no—
318C2×C8×C61—22no—
319C2×C8×C61C2×D414yes—
320C4⋊C4×C61—216no—
321C4⋊C4×C61—22no—
322C4⋊C4×C61—22no—
323C4⋊C4×C61—22no—
324C4⋊C4×C61—41no—
325C22⋊C4×C61—216no—
326C22⋊C4×C61—22no—
327C22⋊C4×C61—22no—
328C22⋊C4×C61—41no—
329C22⋊C4×C61C2×D414yes—
330C42×C61—22no—
331C42×C61—22no—
332C42×C61—22no—
333C42×C61—41no—
334C23×C61—22no—
335C23×C61—22no—
336C23×C61—42no—
337C23×C61—44no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61—82no—
343C23×C61#12011yescharacteristic
344C23×C61#12011yescharacteristic
345C23×C61#12111yescharacteristic
346C23×C61#12111yescharacteristic
347C23×C61#12711yescharacteristic
348C23×C61#12711yescharacteristic
349C23×C61C22×D411yescharacteristic
350Q8×C61—24no—
351Q8×C61—22no—
352Q8×C61—22no—
353Q8×C61—22no—
354Q8×C61—24no—
355Q8×C61—22no—
356Q8×C61—42no—
357Q8×C61—42no—
358Q8×C61—42no—
359Q8×C61—42no—
360Q8×C61—42no—
361Q8×C61—42no—
362Q8×C61—41no—
363Q8×C61—41no—
364Q8×C61—41no—
365Q8×C61—41no—
366D4×C61—22no—
367D4×C61—22no—
368D4×C61—22no—
369D4×C61—22no—
370D4×C61—42no—
371D4×C61—42no—
372D4×C61—42no—
373D4×C61—42no—
374D4×C61—42no—
375D4×C61—42no—
376D4×C61—42no—
377D4×C61—42no—
378D4×C61—41no—
379D4×C61—41no—
380D4×C61—41no—
381D4×C61—41no—
382C2×C4×C61—24no—
383C2×C4×C61—24no—
384C2×C4×C61—22no—
385C2×C4×C61—22no—
386C2×C4×C61—44no—
387C2×C4×C61—42no—
388C2×C4×C61—42no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—42no—
392C2×C4×C61—42no—
393C2×C4×C61—42no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—42no—
397C2×C4×C61—42no—
398C2×C4×C61—42no—
399C2×C4×C61—42no—
400C2×C4×C61—42no—
401C2×C4×C61—42no—
402C2×C4×C61—42no—
403C2×C4×C61—42no—
404C2×C4×C61—42no—
405C2×C4×C61—42no—
406C2×C4×C61—82no—
407C2×C4×C61#12011yescharacteristic
408C2×C4×C61#12011yescharacteristic
409C2×C4×C61#12011yescharacteristic
410C2×C4×C61#12011yescharacteristic
411C2×C4×C61#12011yescharacteristic
412C2×C4×C61#12011yescharacteristic
413C2×C4×C61#12011yescharacteristic
414C2×C4×C61#12011yescharacteristic
415C2×C4×C61#12011yescharacteristic
416C2×C4×C61#12011yescharacteristic
417C2×C4×C61#12111yescharacteristic
418C2×C4×C61#12111yescharacteristic
419C2×C4×C61#12111yescharacteristic
420C2×C4×C61#12111yescharacteristic
421C2×C4×C61#12111yescharacteristic
422C2×C4×C61#12111yescharacteristic
423C2×C4×C61#12111yescharacteristic
424C2×C4×C61#12111yescharacteristic
425C2×C4×C61#12111yescharacteristic
426C2×C4×C61#12111yescharacteristic
427C2×C4×C61#12711yescharacteristic
428C2×C4×C61#12711yescharacteristic
429C2×C4×C61C22×D411yescharacteristic
430C2×C4×C61C22×D411yescharacteristic
431C2×C4×C61C22×D411yescharacteristic
432C2×C4×C61C22×D411yescharacteristic
433C2×C4×C61C22×D411yescharacteristic
434C2×C4×C61C2×#4111yescharacteristic
435C8×C61—24no—
436C8×C61—24no—
437C2×#2009C6111yesmaximal, characteristic, direct product factor, Sylow
438C22×C61—22no—
439C22×C61—22no—
440C22×C61—22no—
441C22×C61—41no—
442C22×C61—41no—
443C22×C61—41no—
444C22×C61—41no—
445C22×C61—44no—
446C22×C61—42no—
447C22×C61—42no—
448C22×C61—82no—
449C22×C61—82no—
450C22×C61—82no—
451C22×C61—82no—
452C22×C61—82no—
453C22×C61#39211yescharacteristic
454C22×C61#39211yescharacteristic
455C22×C61#39211yescharacteristic
456C22×C61#39211yescharacteristic
457C22×C61C2×#12011yescharacteristic
458C22×C61C2×#12111yescharacteristic
459C22×C61C2×#12711yescharacteristic
460C4×C61—44no—
461C4×C61—42no—
462C4×C61—42no—
463C4×C61—44no—
464C4×C61—82no—
465C4×C61#39211yescharacteristic
466C4×C61#39211yescharacteristic
467C4×C61#39211yescharacteristic
468C4×C61#39211yescharacteristic
469C4×C61C2×#12011yescharacteristic
470C4×C61C2×#12011yescharacteristic
471C4×C61C2×#12111yescharacteristic
472C4×C61C2×#12111yescharacteristic
473C2×#575C2×C6111yescharacteristic
474C22×#137C2×C6111yescharacteristic, complemented
475C2×#536C2×C6111yescharacteristic, complemented
476C2×#421C2×C6111yescharacteristic, complemented
477C2×#419C2×C6111yescharacteristic, complemented
478C2×#410C2×C6111yescharacteristic, complemented
479#2009C2×C6118yesdirect product factor
480C2×#344C2×C6111yescharacteristic, complemented
481C2×C61—21no—
482C2×C61—21no—
483C2×C61—21no—
484C2×C61—21no—
485C2×C61—21no—
486C2×C61—21no—
487C2×C61—82no—
488C2×C61—82no—
489C2×C61#200912yesdirect product factor
490C2×C61C2×#39211yescharacteristic
491C22×#41C22×C6111yescharacteristic
492C22×#41C22×C6111yescharacteristic
493C23×Q8C22×C6111yescharacteristic
494#575—22no—
495#575—22no—
496#575—22no—
497#575C22×C6114yes—
498C2×#137—22no—
499C2×#137—22no—
500C2×#137—22no—
501C2×#137—21no—
502C2×#137—21no—
503C2×#137—22no—
504C2×#137—22no—
505C2×#137C22×C6114yescomplemented
506C2×AGL(1,ℤ/8)—21no—
507C2×AGL(1,ℤ/8)—21no—
508C2×#135—22no—
509C22×Q16—21no—
510C22×SD16—21no—
511C22×M16C22×C6111yescharacteristic
512C22×M16C22×C6111yescharacteristic
513#536—22no—
514#536—22no—
515#536—22no—
516#536C22×C6114yescomplemented
517C2×C4⋊Q8—21no—
518C2×#124—21no—
519C2×#123—22no—
520C2×C22⋊Q8—22no—
521C2×#117C22×C6111yescharacteristic
522C2×#117C22×C6111yescharacteristic
523#421—22no—
524#421C22×C6114yescomplemented
525C2×#104—22no—
526#419—22no—
527#419C22×C6114yescomplemented
528C2×#103—22no—
529#410—22no—
530#410C22×C6114yescomplemented
531C2×#99—22no—
532#344C22×C6114yescomplemented
533C61C2×#200911yescharacteristic, direct product factor, Sylow
534C2×#41—21no—
535C2×#41—21no—
536C2×#41—21no—
537C2×#41—21no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—21no—
545C2×#41—21no—
546C2×#41—21no—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—21no—
550C2×#41—21no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41D4×C6112yes—
555C2×#41D4×C6112yes—
556C2×#41C23×C6112yes—
557C2×#41C23×C6112yes—
558C22×Q8—21no—
559C22×Q8—21no—
560C22×Q8—21no—
561C22×Q8—21no—
562C22×Q8—21no—
563C22×Q8—21no—
564C22×Q8—21no—
565C22×Q8—21no—
566C22×Q8—21no—
567C22×Q8—21no—
568C22×Q8—21no—
569C22×Q8D4×C6112yes—
570C22×Q8D4×C6111yescharacteristic
571C22×Q8D4×C6112yes—
572C22×Q8D4×C6111yescharacteristic
573C22×Q8C23×C6112yes—
574C22×D4—21no—
575C22×D4—21no—
576C22×D4D4×C6111yescharacteristic
577C22×D4D4×C6111yescharacteristic
578C23×C4—21no—
579C23×C4—21no—
580C23×C4—21no—
581C23×C4C23×C6111yescharacteristic
582#137—28no—
583#137—28no—
584#137—24no—
585#137—24no—
586#137—28no—
587#137—24no—
588#137—24no—
589#137—28no—
590AGL(1,ℤ/8)—24no—
591AGL(1,ℤ/8)—24no—
592AGL(1,ℤ/8)—24no—
593AGL(1,ℤ/8)—24no—
594#135—28no—
595#135—28no—
596C2×Q16—24no—
597C2×Q16—24no—
598C2×Q16—22no—
599C2×Q16—24no—
600C2×SD16—24no—
601C2×SD16—24no—
602C2×SD16—22no—
603C2×SD16—22no—
604C2×SD16—24no—
605C2×D8—22no—
606C2×M16—21no—
607C2×M16—21no—
608C2×M16—21no—
609C2×M16—21no—
610C2×M16—21no—
611C2×M16—21no—
612C2×M16—21no—
613C2×M16D4×C6112yes—
614C2×M16D4×C6112yes—
615C2×M16D4×C6112yes—
616C2×M16C23×C6112yes—
617C2×M16C23×C6112yes—
618C22×C8—21no—
619C22×C8D4×C6112yes—
620C4⋊Q8—24no—
621C4⋊Q8—24no—
622#124—24no—
623#124—24no—
624#123—28no—
625#123—28no—
626C22⋊Q8—28no—
627C22⋊Q8—28no—
628#117—21no—
629#117—21no—
630#117—21no—
631#117—21no—
632#117—21no—
633#117D4×C6112yes—
634#117C23×C6112yes—
635#117C23×C6112yes—
636C2×C4⋊C4—24no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C22⋊C4—24no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4D4×C6112yes—
642C2×C42—21no—
643C2×C42—21no—
644#104—28no—
645#103—28no—
646#99—28no—
647C24—21no—
648C24—21no—
649C24C2×D4×C6111yescharacteristic
650#41—22no—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—22no—
659#41—22no—
660#41—22no—
661#41—22no—
662#41—22no—
663#41—22no—
664#41—22no—
665#41—22no—
666#41—41no—
667#41—41no—
668#41—41no—
669#41—41no—
670#41—41no—
671#41—41no—
672#41—41no—
673#41—41no—
674#41—41no—
675#41—41no—
676#41—41no—
677#41—41no—
678#41—41no—
679#41—41no—
680#41—41no—
681#41—41no—
682C2×Q8—22no—
683C2×Q8—22no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—22no—
687C2×Q8—22no—
688C2×Q8—22no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—22no—
694C2×Q8—22no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—22no—
698C2×Q8—22no—
699C2×Q8—22no—
700C2×Q8—22no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—22no—
704C2×Q8—22no—
705C2×Q8—22no—
706C2×Q8—22no—
707C2×Q8—41no—
708C2×Q8—41no—
709C2×Q8—41no—
710C2×Q8—41no—
711C2×Q8—41no—
712C2×Q8—41no—
713C2×Q8—41no—
714C2×Q8—41no—
715C2×Q8—41no—
716C2×Q8—41no—
717C2×Q8—41no—
718C2×Q8—41no—
719C2×Q8C2×D4×C6114yes—
720C2×Q8C2×D4×C6112yes—
721C2×Q8C2×D4×C6112yes—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—41no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—41no—
744C2×D4C2×D4×C6112yes—
745C2×D4C2×D4×C6112yes—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—22no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—41no—
757C22×C4—41no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4—41no—
761C22×C4—41no—
762C22×C4—41no—
763C22×C4—41no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—41no—
768C22×C4—41no—
769C22×C4C2×D4×C6111yescharacteristic
770C22×C4C2×D4×C6111yescharacteristic
771C22×C4C2×D4×C6111yescharacteristic
772C22×C4C2×D4×C6111yescharacteristic
773C22×C4C2×D4×C6111yescharacteristic
774C22×C4C2×D4×C6111yescharacteristic
775C22×C4C2×D4×C6111yescharacteristic
776C22×C4C2×D4×C6111yescharacteristic
777C22×C4C2×D4×C6111yescharacteristic
778C22×C4C2×D4×C6111yescharacteristic
779C22×C4C2×D4×C6111yescharacteristic
780C22×C4#41×C6111yescharacteristic
781C22×C4#41×C6111yescharacteristic
782C22×C4C24×C6111yescharacteristic
783Q16—216no—
784Q16—28no—
785SD16—216no—
786SD16—28no—
787SD16—28no—
788D8—28no—
789M16—22no—
790M16—22no—
791M16—22no—
792M16—22no—
793M16—22no—
794M16—22no—
795M16—22no—
796M16C2×D4×C6114yes—
797C2×C8—22no—
798C2×C8—22no—
799C2×C8—22no—
800C2×C8—22no—
801C2×C8—22no—
802C2×C8C2×D4×C6114yes—
803C4⋊C4—216no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—22no—
807C4⋊C4—41no—
808C22⋊C4—216no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—41no—
812C22⋊C4C2×D4×C6114yes—
813C42—22no—
814C42—22no—
815C42—22no—
816C42—41no—
817C23—22no—
818C23—22no—
819C23—42no—
820C23—44no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—82no—
826C23#120×C6111yescharacteristic
827C23#120×C6111yescharacteristic
828C23#121×C6111yescharacteristic
829C23#121×C6111yescharacteristic
830C23#127×C6111yescharacteristic
831C23#127×C6111yescharacteristic
832C23C22×D4×C6111yescharacteristic
833Q8—24no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—24no—
838Q8—22no—
839Q8—42no—
840Q8—42no—
841Q8—42no—
842Q8—42no—
843Q8—41no—
844Q8—41no—
845Q8—41no—
846Q8—41no—
847Q8—42no—
848Q8—42no—
849D4—22no—
850D4—22no—
851D4—22no—
852D4—22no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—42no—
860D4—42no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—41no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—44no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—82no—
890C2×C4#120×C6111yescharacteristic
891C2×C4#120×C6111yescharacteristic
892C2×C4#120×C6111yescharacteristic
893C2×C4#120×C6111yescharacteristic
894C2×C4#120×C6111yescharacteristic
895C2×C4#120×C6111yescharacteristic
896C2×C4#120×C6111yescharacteristic
897C2×C4#120×C6111yescharacteristic
898C2×C4#120×C6111yescharacteristic
899C2×C4#120×C6111yescharacteristic
900C2×C4#121×C6111yescharacteristic
901C2×C4#121×C6111yescharacteristic
902C2×C4#121×C6111yescharacteristic
903C2×C4#121×C6111yescharacteristic
904C2×C4#121×C6111yescharacteristic
905C2×C4#121×C6111yescharacteristic
906C2×C4#121×C6111yescharacteristic
907C2×C4#121×C6111yescharacteristic
908C2×C4#121×C6111yescharacteristic
909C2×C4#121×C6111yescharacteristic
910C2×C4#127×C6111yescharacteristic
911C2×C4#127×C6111yescharacteristic
912C2×C4C22×D4×C6111yescharacteristic
913C2×C4C22×D4×C6111yescharacteristic
914C2×C4C22×D4×C6111yescharacteristic
915C2×C4C22×D4×C6111yescharacteristic
916C2×C4C22×D4×C6111yescharacteristic
917C2×C4C2×#41×C6111yescharacteristic
918C8—24no—
919C8—24no—
920C22—22no—
921C22—22no—
922C22—22no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—44no—
928C22—42no—
929C22—42no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22C61×#39211yescharacteristic
936C22C61×#39211yescharacteristic
937C22C61×#39211yescharacteristic
938C22C61×#39211yescharacteristic
939C22C2×#120×C6111yescharacteristic
940C22C2×#121×C6111yescharacteristic
941C22C2×#127×C6111yescharacteristic
942C4—44no—
943C4—42no—
944C4—42no—
945C4—44no—
946C4—82no—
947C4C61×#39211yescharacteristic
948C4C61×#39211yescharacteristic
949C4C61×#39211yescharacteristic
950C4C61×#39211yescharacteristic
951C4C2×#120×C6111yescharacteristic
952C4C2×#120×C6111yescharacteristic
953C4C2×#121×C6111yescharacteristic
954C4C2×#121×C6111yescharacteristic
955C2—21no—
956C2—21no—
957C2—21no—
958C2—21no—
959C2—21no—
960C2—21no—
961C2—82no—
962C2—82no—
963C2C61×#200912yesdirect product factor
964C2C2×C61×#39211yescharacteristic
subgroupG/H
center, socleC22×C61#392
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×C61×#575C2
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. C22×#137×C61C2semidirect
3. C2×C61×#536C2semidirect
4. C2×C61×#421C2semidirect
5. C2×C61×#419C2semidirect
6. C2×C61×#410C2semidirect
7. C61×#2009C2direct (N × H)
8. C2×C61×#344C2semidirect
23. C2×#137×C61C22semidirect
34. C61×#536C22semidirect
42. C61×#421C22semidirect
45. C61×#419C22semidirect
48. C61×#410C22semidirect
50. C61×#344C22semidirect
437. C2×#2009C61direct (N × H)
474. C22×#137C2×C61semidirect
475. C2×#536C2×C61semidirect
476. C2×#421C2×C61semidirect
477. C2×#419C2×C61semidirect
478. C2×#410C2×C61semidirect
479. #2009C2×C61direct (N × H)
480. C2×#344C2×C61semidirect
489. C2×C61#2009direct (N × H)
505. C2×#137C22×C61semidirect
516. #536C22×C61semidirect
524. #421C22×C61semidirect
527. #419C22×C61semidirect
530. #410C22×C61semidirect
532. #344C22×C61semidirect
533. C61C2×#2009direct (N × H)
963. C2C61×#2009direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#5752
C22×#137×C612
C2×C61×#5362
C2×C61×#4212
C2×C61×#4192
C2×C61×#4102
C61×#20092
C2×C61×#3442
C2×#200961