Finite Group Databasebeta

← C61×#24403 #29527836

Subgroups — C61×#24403 #29527836

Order 15616.

1332 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#575C211yesmaximal, characteristic
2C2×C61×#473C211yesmaximal, characteristic, complemented
3C2×C61×#471C211yesmaximal, characteristic, complemented
4C61×#3007C211yesmaximal, characteristic, complemented
5C2×C61×#452C211yesmaximal, characteristic, complemented
6C61×#2880C211yesmaximal, characteristic, complemented
7C61×#2052C211yesmaximal, characteristic, complemented
8C61×#2051C211yesmaximal, characteristic, complemented
9C61×#2020C211yesmaximal, characteristic, complemented
10C61×#2019C211yesmaximal, characteristic, complemented
11C61×#1908C211yesmaximal, characteristic, complemented
12C61×#1907C211yesmaximal, characteristic, complemented
13C61×#1901C211yesmaximal, characteristic, complemented
14C61×#1855C211yesmaximal, characteristic, complemented
15C61×#1785C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×#41×C61C2211yescharacteristic
18C61×#575—24no—
19C61×#575—24no—
20C2×#137×C61—21no—
21C2×#137×C61C2211yescharacteristic
22C2×#137×C61C2211yescharacteristic
23C2×#137×C61C2211yescharacteristic
24C2×#137×C61C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C61—21no—
26C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
28C2×#135×C61—21no—
29C2×#135×C61—21no—
30C22×Q16×C61C2211yescharacteristic, complemented
31C22×SD16×C61C2211yescharacteristic, complemented
32C2×#131×C61C2211yescharacteristic
33C2×#131×C61C2211yescharacteristic
34C22×M16×C61C2211yescharacteristic
35C2×C22⋊Q8×C61C2211yescharacteristic
36C61×#473—24no—
37C61×#471—24no—
38C61×#452—21no—
39C61×#452—21no—
40C61×#452—21no—
41C61×#452—21no—
42C61×#452—21no—
43C61×#452—21no—
44C61×#451—21no—
45C61×#450—21no—
46C2×#108×C61C2211yescharacteristic, complemented
47C2×#108×C61C2211yescharacteristic, complemented
48C61×#417C2211yescharacteristic
49C61×#417C2211yescharacteristic
50C2×#103×C61C2211yescharacteristic, complemented
51C2×#102×C61C2211yescharacteristic, complemented
52C2×#101×C61C2211yescharacteristic, complemented
53C2×#101×C61C2211yescharacteristic, complemented
54C2×#101×C61C2211yescharacteristic, complemented
55C2×#101×C61C2211yescharacteristic, complemented
56C2×#100×C61C2211yescharacteristic, complemented
57C2×#100×C61C2211yescharacteristic, complemented
58C61×#408—21no—
59C61×#408—21no—
60C61×#408C2211yescharacteristic
61C61×#408C2211yescharacteristic
62C61×#407—21no—
63C61×#407C2211yescharacteristic
64C61×#407C2211yescharacteristic
65C2×C22⋊C8×C61—21no—
66C2×C22⋊C8×C61C2211yescharacteristic
67C61×#343C2211yescharacteristic, complemented
68C61×#343C2211yescharacteristic, complemented
69C61×#341C2211yescharacteristic, complemented
70C61×#341C2211yescharacteristic, complemented
71C2×#41×C61—21no—
72C2×#41×C61—21no—
73C2×#41×C61—22no—
74C2×#41×C61—22no—
75C2×#41×C61—22no—
76C2×#41×C61—22no—
77C2×#41×C61—21no—
78C2×#41×C61—21no—
79C2×#41×C61—21no—
80C2×#41×C61—21no—
81C2×#41×C61—41no—
82C2×#41×C61—41no—
83C2×#41×C61—41no—
84C2×#41×C61—41no—
85C2×#41×C61D411yescharacteristic
86C2×#41×C61D411yescharacteristic
87C2×#41×C61C2311yescharacteristic
88C2×#41×C61C2311yescharacteristic
89C22×Q8×C61D411yescharacteristic
90C22×Q8×C61C2311yescharacteristic
91C22×Q8×C61C2311yescharacteristic
92C22×D4×C61—21no—
93C22×D4×C61—21no—
94C22×D4×C61D411yescharacteristic
95C22×D4×C61C2311yescharacteristic
96C23×C4×C61—21no—
97C23×C4×C61—21no—
98C23×C4×C61C2311yescharacteristic
99#137×C61—28no—
100#137×C61—22no—
101#137×C61—22no—
102#137×C61—22no—
103#137×C61—22no—
104#137×C61—22no—
105#137×C61—41no—
106#137×C61—41no—
107#137×C61D414yes—
108AGL(1,ℤ/8)×C61—28no—
109AGL(1,ℤ/8)×C61—22no—
110AGL(1,ℤ/8)×C61—22no—
111AGL(1,ℤ/8)×C61—22no—
112AGL(1,ℤ/8)×C61D414yes—
113#135×C61—28no—
114#135×C61—28no—
115C2×Q16×C61—21no—
116C2×Q16×C61—21no—
117C2×Q16×C61—22no—
118C2×Q16×C61—21no—
119C2×Q16×C61—21no—
120C2×Q16×C61—21no—
121C2×Q16×C61—21no—
122C2×Q16×C61—41no—
123C2×SD16×C61—21no—
124C2×SD16×C61—21no—
125C2×SD16×C61—21no—
126C2×SD16×C61—21no—
127C2×SD16×C61—22no—
128C2×SD16×C61—21no—
129C2×SD16×C61—21no—
130C2×SD16×C61—21no—
131C2×SD16×C61—21no—
132C2×SD16×C61—41no—
133C2×D8×C61—21no—
134C2×D8×C61—21no—
135#131×C61—22no—
136#131×C61—22no—
137#131×C61—41no—
138#131×C61—41no—
139C2×M16×C61—21no—
140C2×M16×C61—22no—
141C2×M16×C61—22no—
142C2×M16×C61—21no—
143C2×M16×C61—21no—
144C2×M16×C61C2311yescharacteristic
145C2×M16×C61C2311yescharacteristic
146C2×M16×C61C2311yescharacteristic
147C2×M16×C61C2311yescharacteristic
148C2×M16×C61C2311yescharacteristic
149C2×M16×C61C2311yescharacteristic
150C22×C8×C61—21no—
151C22×C8×C61—21no—
152C22×C8×C61—21no—
153C22×C8×C61C2311yescharacteristic
154C22×C8×C61C2311yescharacteristic
155C22⋊Q8×C61—21no—
156C22⋊Q8×C61—21no—
157C22⋊Q8×C61—21no—
158C22⋊Q8×C61—21no—
159C2×C4⋊C4×C61—21no—
160C2×C4⋊C4×C61C2311yescharacteristic
161C2×C22⋊C4×C61—21no—
162#108×C61—22no—
163#108×C61—22no—
164#103×C61—21no—
165#103×C61—21no—
166#103×C61—21no—
167#103×C61—21no—
168#102×C61—21no—
169#102×C61—21no—
170#102×C61—21no—
171#102×C61—21no—
172#101×C61—22no—
173#101×C61—22no—
174#101×C61—22no—
175#101×C61—41no—
176#100×C61—22no—
177#100×C61—41no—
178C22⋊C8×C61—21no—
179C22⋊C8×C61—21no—
180C22⋊C8×C61—21no—
181C22⋊C8×C61—21no—
182C22⋊C8×C61—21no—
183C22⋊C8×C61—21no—
184C22⋊C8×C61—21no—
185C22⋊C8×C61—21no—
186C22⋊C8×C61D411yescharacteristic
187C22⋊C8×C61D411yescharacteristic
188C22⋊C8×C61D411yescharacteristic
189C22⋊C8×C61D411yescharacteristic
190C24×C61—21no—
191C24×C61—21no—
192C24×C61#4111yescharacteristic
193#41×C61—21no—
194#41×C61—21no—
195#41×C61—24no—
196#41×C61—24no—
197#41×C61—22no—
198#41×C61—22no—
199#41×C61—21no—
200#41×C61—21no—
201#41×C61—21no—
202#41×C61—21no—
203#41×C61—42no—
204#41×C61—42no—
205#41×C61—41no—
206#41×C61—41no—
207#41×C61—42no—
208#41×C61—42no—
209#41×C61—42no—
210#41×C61—42no—
211#41×C61—42no—
212#41×C61—42no—
213#41×C61—42no—
214#41×C61—42no—
215#41×C61C2×D412yes—
216#41×C61C2×D412yes—
217C2×Q8×C61—21no—
218C2×Q8×C61—21no—
219C2×Q8×C61—22no—
220C2×Q8×C61—21no—
221C2×Q8×C61—21no—
222C2×Q8×C61—21no—
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—41no—
231C2×Q8×C61C2×D412yes—
232C2×Q8×C61C2×D411yescharacteristic
233C2×Q8×C61C2×D411yescharacteristic
234C2×D4×C61—21no—
235C2×D4×C61—22no—
236C2×D4×C61—21no—
237C2×D4×C61—21no—
238C2×D4×C61—21no—
239C2×D4×C61—21no—
240C2×D4×C61—21no—
241C2×D4×C61—21no—
242C2×D4×C61—21no—
243C2×D4×C61—21no—
244C2×D4×C61—21no—
245C2×D4×C61—41no—
246C2×D4×C61—42no—
247C2×D4×C61—42no—
248C2×D4×C61—42no—
249C2×D4×C61—42no—
250C2×D4×C61—41no—
251C2×D4×C61—41no—
252C2×D4×C61C2×D412yes—
253C2×D4×C61C2×D411yescharacteristic
254C2×D4×C61C2×D411yescharacteristic
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61—21no—
260C22×C4×C61—21no—
261C22×C4×C61—21no—
262C22×C4×C61—21no—
263C22×C4×C61—21no—
264C22×C4×C61—21no—
265C22×C4×C61—21no—
266C22×C4×C61—21no—
267C22×C4×C61—42no—
268C22×C4×C61—42no—
269C22×C4×C61—42no—
270C22×C4×C61—42no—
271C22×C4×C61—41no—
272C22×C4×C61—41no—
273C22×C4×C61C2×D411yescharacteristic
274C22×C4×C61C2×D411yescharacteristic
275C22×C4×C61C2×D411yescharacteristic
276C22×C4×C61C2×D411yescharacteristic
277C22×C4×C61#4111yescharacteristic
278C22×C4×C61C2411yescharacteristic
279Q16×C61—24no—
280Q16×C61—24no—
281Q16×C61—42no—
282Q16×C61—42no—
283Q16×C61—42no—
284Q16×C61—42no—
285SD16×C61—24no—
286SD16×C61—24no—
287SD16×C61—24no—
288SD16×C61—24no—
289SD16×C61—42no—
290SD16×C61—42no—
291SD16×C61—42no—
292SD16×C61—42no—
293D8×C61—24no—
294D8×C61—24no—
295M16×C61—24no—
296M16×C61—21no—
297M16×C61—21no—
298M16×C61—21no—
299M16×C61—21no—
300M16×C61—21no—
301M16×C61—21no—
302M16×C61—21no—
303M16×C61—21no—
304M16×C61—21no—
305M16×C61—21no—
306M16×C61—42no—
307M16×C61—42no—
308M16×C61C2×D412yes—
309M16×C61C2×D412yes—
310C2×C8×C61—24no—
311C2×C8×C61—21no—
312C2×C8×C61—21no—
313C2×C8×C61—21no—
314C2×C8×C61—21no—
315C2×C8×C61—21no—
316C2×C8×C61—21no—
317C2×C8×C61—21no—
318C2×C8×C61—21no—
319C2×C8×C61—21no—
320C2×C8×C61—21no—
321C2×C8×C61—42no—
322C2×C8×C61—42no—
323C2×C8×C61C2×D411yescharacteristic
324C2×C8×C61C2×D411yescharacteristic
325C2×C8×C61C2×D411yescharacteristic
326C2×C8×C61C2×D411yescharacteristic
327C4⋊C4×C61—21no—
328C4⋊C4×C61—21no—
329C4⋊C4×C61—41no—
330C4⋊C4×C61—41no—
331C22⋊C4×C61—41no—
332C22⋊C4×C61—41no—
333C23×C61—21no—
334C23×C61—21no—
335C23×C61—21no—
336C23×C61—21no—
337C23×C61—22no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—42no—
341C23×C61—42no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—81no—
345C23×C61—81no—
346C23×C61—81no—
347C23×C61#12111yescharacteristic
348C23×C61#12111yescharacteristic
349C23×C61C2×#4111yescharacteristic
350Q8×C61—21no—
351Q8×C61—21no—
352Q8×C61—22no—
353Q8×C61—21no—
354Q8×C61—22no—
355Q8×C61—42no—
356Q8×C61—41no—
357Q8×C61—41no—
358Q8×C61—41no—
359Q8×C61—41no—
360Q8×C61—41no—
361Q8×C61—41no—
362Q8×C61#12012yes—
363D4×C61—22no—
364D4×C61—22no—
365D4×C61—21no—
366D4×C61—22no—
367D4×C61—21no—
368D4×C61—21no—
369D4×C61—22no—
370D4×C61—42no—
371D4×C61—42no—
372D4×C61—42no—
373D4×C61—44no—
374D4×C61—44no—
375D4×C61—41no—
376D4×C61—41no—
377D4×C61—41no—
378D4×C61—41no—
379D4×C61#12012yes—
380C2×C4×C61—21no—
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—22no—
388C2×C4×C61—22no—
389C2×C4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61—21no—
394C2×C4×C61—22no—
395C2×C4×C61—42no—
396C2×C4×C61—42no—
397C2×C4×C61—42no—
398C2×C4×C61—44no—
399C2×C4×C61—44no—
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—81no—
409C2×C4×C61#12111yescharacteristic
410C2×C4×C61#12111yescharacteristic
411C2×C4×C61C22×D411yescharacteristic
412C2×C4×C61C22×D411yescharacteristic
413C2×C4×C61C22×D411yescharacteristic
414C2×C4×C61C22×D411yescharacteristic
415C2×C4×C61H(5,𝔽2)11yescharacteristic
416C2×C4×C61H(5,𝔽2)11yescharacteristic
417C8×C61—22no—
418C8×C61—22no—
419C8×C61—21no—
420C8×C61—21no—
421C8×C61—21no—
422C8×C61—21no—
423C8×C61—41no—
424C8×C61—41no—
425C8×C61—41no—
426C8×C61—41no—
427#24403C6111yesmaximal, characteristic, direct product factor, Sylow
428C22×C61—21no—
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—22no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61—42no—
441C22×C61—41no—
442C22×C61—41no—
443C22×C61—81no—
444C22×C61—81no—
445C22×C61—82no—
446C22×C61—82no—
447C22×C61—84no—
448C22×C61—81no—
449C22×C61—81no—
450C22×C61C2×#12111yescharacteristic
451C22×C61#54611yescharacteristic
452C22×C61#54611yescharacteristic
453C4×C61—21no—
454C4×C61—21no—
455C4×C61—22no—
456C4×C61—41no—
457C4×C61—42no—
458C4×C61—81no—
459C4×C61—81no—
460C4×C61C2×#12011yescharacteristic
461C4×C61#53411yescharacteristic
462C4×C61D4211yescharacteristic
463C4×C61D4211yescharacteristic
464C2×#575C2×C6111yescharacteristic
465C2×#473C2×C6111yescharacteristic, complemented
466C2×#471C2×C6111yescharacteristic, complemented
467#3007C2×C6111yescharacteristic, complemented
468C2×#452C2×C6111yescharacteristic, complemented
469#2880C2×C6111yescharacteristic, complemented
470#2052C2×C6111yescharacteristic, complemented
471#2051C2×C6111yescharacteristic, complemented
472#2020C2×C6111yescharacteristic, complemented
473#2019C2×C6111yescharacteristic, complemented
474#1908C2×C6111yescharacteristic, complemented
475#1907C2×C6111yescharacteristic, complemented
476#1901C2×C6111yescharacteristic, complemented
477#1855C2×C6111yescharacteristic, complemented
478#1785C2×C6111yescharacteristic, complemented
479C2×C61—21no—
480C2×C61—21no—
481C2×C61—41no—
482C2×C61—41no—
483C2×C61—42no—
484C2×C61—81no—
485C2×C61—82no—
486C2×C61#241011yescharacteristic
487C2×C61#306711yescharacteristic
488C2×C61#306911yescharacteristic
489C22×#41C22×C6111yescharacteristic
490C22×#41C22×C6111yescharacteristic
491#575—24no—
492#575—24no—
493C2×#137—21no—
494C2×#137C22×C6111yescharacteristic
495C2×#137C22×C6111yescharacteristic
496C2×#137C22×C6111yescharacteristic
497C2×#137C22×C6111yescharacteristic
498C2×AGL(1,ℤ/8)—21no—
499C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
500C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
501C2×#135—21no—
502C2×#135—21no—
503C22×Q16C22×C6111yescharacteristic, complemented
504C22×SD16C22×C6111yescharacteristic, complemented
505C2×#131C22×C6111yescharacteristic
506C2×#131C22×C6111yescharacteristic
507C22×M16C22×C6111yescharacteristic
508C2×C22⋊Q8C22×C6111yescharacteristic
509#473—24no—
510#471—24no—
511#452—21no—
512#452—21no—
513#452—21no—
514#452—21no—
515#452—21no—
516#452—21no—
517#451—21no—
518#450—21no—
519C2×#108C22×C6111yescharacteristic, complemented
520C2×#108C22×C6111yescharacteristic, complemented
521#417C22×C6111yescharacteristic
522#417C22×C6111yescharacteristic
523C2×#103C22×C6111yescharacteristic, complemented
524C2×#102C22×C6111yescharacteristic, complemented
525C2×#101C22×C6111yescharacteristic, complemented
526C2×#101C22×C6111yescharacteristic, complemented
527C2×#101C22×C6111yescharacteristic, complemented
528C2×#101C22×C6111yescharacteristic, complemented
529C2×#100C22×C6111yescharacteristic, complemented
530C2×#100C22×C6111yescharacteristic, complemented
531#408—21no—
532#408—21no—
533#408C22×C6111yescharacteristic
534#408C22×C6111yescharacteristic
535#407—21no—
536#407C22×C6111yescharacteristic
537#407C22×C6111yescharacteristic
538C2×C22⋊C8—21no—
539C2×C22⋊C8C22×C6111yescharacteristic
540#343C22×C6111yescharacteristic, complemented
541#343C22×C6111yescharacteristic, complemented
542#341C22×C6111yescharacteristic, complemented
543#341C22×C6111yescharacteristic, complemented
544C61#2440311yescharacteristic, direct product factor, Sylow
545C2×#41—21no—
546C2×#41—21no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41—21no—
555C2×#41—41no—
556C2×#41—41no—
557C2×#41—41no—
558C2×#41—41no—
559C2×#41D4×C6111yescharacteristic
560C2×#41D4×C6111yescharacteristic
561C2×#41C23×C6111yescharacteristic
562C2×#41C23×C6111yescharacteristic
563C22×Q8D4×C6111yescharacteristic
564C22×Q8C23×C6111yescharacteristic
565C22×Q8C23×C6111yescharacteristic
566C22×D4—21no—
567C22×D4—21no—
568C22×D4D4×C6111yescharacteristic
569C22×D4C23×C6111yescharacteristic
570C23×C4—21no—
571C23×C4—21no—
572C23×C4C23×C6111yescharacteristic
573#137—28no—
574#137—22no—
575#137—22no—
576#137—22no—
577#137—22no—
578#137—22no—
579#137—41no—
580#137—41no—
581#137D4×C6114yes—
582AGL(1,ℤ/8)—28no—
583AGL(1,ℤ/8)—22no—
584AGL(1,ℤ/8)—22no—
585AGL(1,ℤ/8)—22no—
586AGL(1,ℤ/8)D4×C6114yes—
587#135—28no—
588#135—28no—
589C2×Q16—21no—
590C2×Q16—21no—
591C2×Q16—22no—
592C2×Q16—21no—
593C2×Q16—21no—
594C2×Q16—21no—
595C2×Q16—21no—
596C2×Q16—41no—
597C2×SD16—21no—
598C2×SD16—21no—
599C2×SD16—21no—
600C2×SD16—21no—
601C2×SD16—22no—
602C2×SD16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×SD16—21no—
606C2×SD16—41no—
607C2×D8—21no—
608C2×D8—21no—
609#131—22no—
610#131—22no—
611#131—41no—
612#131—41no—
613C2×M16—21no—
614C2×M16—22no—
615C2×M16—22no—
616C2×M16—21no—
617C2×M16—21no—
618C2×M16C23×C6111yescharacteristic
619C2×M16C23×C6111yescharacteristic
620C2×M16C23×C6111yescharacteristic
621C2×M16C23×C6111yescharacteristic
622C2×M16C23×C6111yescharacteristic
623C2×M16C23×C6111yescharacteristic
624C22×C8—21no—
625C22×C8—21no—
626C22×C8—21no—
627C22×C8C23×C6111yescharacteristic
628C22×C8C23×C6111yescharacteristic
629C22⋊Q8—21no—
630C22⋊Q8—21no—
631C22⋊Q8—21no—
632C22⋊Q8—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4C23×C6111yescharacteristic
635C2×C22⋊C4—21no—
636#108—22no—
637#108—22no—
638#103—21no—
639#103—21no—
640#103—21no—
641#103—21no—
642#102—21no—
643#102—21no—
644#102—21no—
645#102—21no—
646#101—22no—
647#101—22no—
648#101—22no—
649#101—41no—
650#100—22no—
651#100—41no—
652C22⋊C8—21no—
653C22⋊C8—21no—
654C22⋊C8—21no—
655C22⋊C8—21no—
656C22⋊C8—21no—
657C22⋊C8—21no—
658C22⋊C8—21no—
659C22⋊C8—21no—
660C22⋊C8D4×C6111yescharacteristic
661C22⋊C8D4×C6111yescharacteristic
662C22⋊C8D4×C6111yescharacteristic
663C22⋊C8D4×C6111yescharacteristic
664C24—21no—
665C24—21no—
666C24#41×C6111yescharacteristic
667#41—21no—
668#41—21no—
669#41—24no—
670#41—24no—
671#41—22no—
672#41—22no—
673#41—21no—
674#41—21no—
675#41—21no—
676#41—21no—
677#41—42no—
678#41—42no—
679#41—41no—
680#41—41no—
681#41—42no—
682#41—42no—
683#41—42no—
684#41—42no—
685#41—42no—
686#41—42no—
687#41—42no—
688#41—42no—
689#41C2×D4×C6112yes—
690#41C2×D4×C6112yes—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—22no—
694C2×Q8—21no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—41no—
705C2×Q8C2×D4×C6112yes—
706C2×Q8C2×D4×C6111yescharacteristic
707C2×Q8C2×D4×C6111yescharacteristic
708C2×D4—21no—
709C2×D4—22no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—41no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—41no—
725C2×D4—41no—
726C2×D4C2×D4×C6112yes—
727C2×D4C2×D4×C6111yescharacteristic
728C2×D4C2×D4×C6111yescharacteristic
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—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—41no—
746C22×C4—41no—
747C22×C4C2×D4×C6111yescharacteristic
748C22×C4C2×D4×C6111yescharacteristic
749C22×C4C2×D4×C6111yescharacteristic
750C22×C4C2×D4×C6111yescharacteristic
751C22×C4#41×C6111yescharacteristic
752C22×C4C24×C6111yescharacteristic
753Q16—24no—
754Q16—24no—
755Q16—42no—
756Q16—42no—
757Q16—42no—
758Q16—42no—
759SD16—24no—
760SD16—24no—
761SD16—24no—
762SD16—24no—
763SD16—42no—
764SD16—42no—
765SD16—42no—
766SD16—42no—
767D8—24no—
768D8—24no—
769M16—24no—
770M16—21no—
771M16—21no—
772M16—21no—
773M16—21no—
774M16—21no—
775M16—21no—
776M16—21no—
777M16—21no—
778M16—21no—
779M16—21no—
780M16—42no—
781M16—42no—
782M16C2×D4×C6112yes—
783M16C2×D4×C6112yes—
784C2×C8—24no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—42no—
796C2×C8—42no—
797C2×C8C2×D4×C6111yescharacteristic
798C2×C8C2×D4×C6111yescharacteristic
799C2×C8C2×D4×C6111yescharacteristic
800C2×C8C2×D4×C6111yescharacteristic
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—41no—
804C4⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—41no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—41no—
813C23—41no—
814C23—42no—
815C23—42no—
816C23—41no—
817C23—41no—
818C23—81no—
819C23—81no—
820C23—81no—
821C23#121×C6111yescharacteristic
822C23#121×C6111yescharacteristic
823C23C2×#41×C6111yescharacteristic
824Q8—21no—
825Q8—21no—
826Q8—22no—
827Q8—21no—
828Q8—22no—
829Q8—42no—
830Q8—41no—
831Q8—41no—
832Q8—41no—
833Q8—41no—
834Q8—41no—
835Q8—41no—
836Q8#120×C6112yes—
837D4—22no—
838D4—22no—
839D4—21no—
840D4—21no—
841D4—22no—
842D4—21no—
843D4—22no—
844D4—42no—
845D4—42no—
846D4—42no—
847D4—44no—
848D4—44no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4#120×C6112yes—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—22no—
868C2×C4—21no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—81no—
883C2×C4#121×C6111yescharacteristic
884C2×C4#121×C6111yescharacteristic
885C2×C4C22×D4×C6111yescharacteristic
886C2×C4C22×D4×C6111yescharacteristic
887C2×C4C22×D4×C6111yescharacteristic
888C2×C4C22×D4×C6111yescharacteristic
889C2×C4H(5,𝔽2)×C6111yescharacteristic
890C2×C4H(5,𝔽2)×C6111yescharacteristic
891C8—21no—
892C8—21no—
893C8—21no—
894C8—21no—
895C8—22no—
896C8—22no—
897C8—41no—
898C8—41no—
899C8—41no—
900C8—41no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—22no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—42no—
916C22—81no—
917C22—81no—
918C22—82no—
919C22—82no—
920C22—84no—
921C22—81no—
922C22—81no—
923C22C2×#121×C6111yescharacteristic
924C22C61×#54611yescharacteristic
925C22C61×#54611yescharacteristic
926C4—21no—
927C4—21no—
928C4—22no—
929C4—42no—
930C4—41no—
931C4—81no—
932C4—81no—
933C4C2×#120×C6111yescharacteristic
934C4C61×#53411yescharacteristic
935C4D42×C6111yescharacteristic
936C4D42×C6111yescharacteristic
937C2—21no—
938C2—21no—
939C2—41no—
940C2—41no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C61×#241011yescharacteristic
945C2C61×#306711yescharacteristic
946C2C61×#306911yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
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. C2×C61×#473C2semidirect
3. C2×C61×#471C2semidirect
4. C61×#3007C2semidirect
5. C2×C61×#452C2semidirect
6. C61×#2880C2semidirect
7. C61×#2052C2semidirect
8. C61×#2051C2semidirect
9. C61×#2020C2semidirect
10. C61×#2019C2semidirect
11. C61×#1908C2semidirect
12. C61×#1907C2semidirect
13. C61×#1901C2semidirect
14. C61×#1855C2semidirect
15. C61×#1785C2semidirect
30. C22×Q16×C61C22semidirect
31. C22×SD16×C61C22semidirect
46. C2×#108×C61C22semidirect
47. C2×#108×C61C22semidirect
50. C2×#103×C61C22semidirect
51. C2×#102×C61C22semidirect
52. C2×#101×C61C22semidirect
53. C2×#101×C61C22semidirect
54. C2×#101×C61C22semidirect
55. C2×#101×C61C22semidirect
56. C2×#100×C61C22semidirect
57. C2×#100×C61C22semidirect
67. C61×#343C22semidirect
68. C61×#343C22semidirect
69. C61×#341C22semidirect
70. C61×#341C22semidirect
427. #24403C61direct (N × H)
465. C2×#473C2×C61semidirect
466. C2×#471C2×C61semidirect
467. #3007C2×C61semidirect
468. C2×#452C2×C61semidirect
469. #2880C2×C61semidirect
470. #2052C2×C61semidirect
471. #2051C2×C61semidirect
472. #2020C2×C61semidirect
473. #2019C2×C61semidirect
474. #1908C2×C61semidirect
475. #1907C2×C61semidirect
476. #1901C2×C61semidirect
477. #1855C2×C61semidirect
478. #1785C2×C61semidirect
503. C22×Q16C22×C61semidirect
504. C22×SD16C22×C61semidirect
519. C2×#108C22×C61semidirect
520. C2×#108C22×C61semidirect
523. C2×#103C22×C61semidirect
524. C2×#102C22×C61semidirect
525. C2×#101C22×C61semidirect
526. C2×#101C22×C61semidirect
527. C2×#101C22×C61semidirect
528. C2×#101C22×C61semidirect
529. C2×#100C22×C61semidirect
530. C2×#100C22×C61semidirect
540. #343C22×C61semidirect
541. #343C22×C61semidirect
542. #341C22×C61semidirect
543. #341C22×C61semidirect
544. C61#24403direct (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
C2×C61×#4732
C2×C61×#4712
C61×#30072
C2×C61×#4522
C61×#28802
C61×#20522
C61×#20512
C61×#20202
C61×#20192
C61×#19082
C61×#19072
C61×#19012
C61×#18552
C61×#17852
#2440361