Finite Group Databasebeta

← C61×#23876 #29527309

Subgroups — C61×#23876 #29527309

Order 15616.

2012 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic, complemented
2C61×#3488C211yesmaximal, characteristic, complemented
3C2×C61×#453C212yesmaximal, complemented
4C61×#3003C211yesmaximal, characteristic, complemented
5C61×#2433C211yesmaximal, characteristic, complemented
6C61×#2006C212yesmaximal, complemented
7C61×#2002C212yesmaximal, complemented
8C61×#1900C211yesmaximal, characteristic, complemented
9C61×#1883C212yesmaximal, complemented
10C61×#1871C211yesmaximal, characteristic, complemented
11C61×#1789C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C61C2211yescharacteristic, complemented
13C22×#41×C61C2211yescharacteristic
14C23×D4×C61C2211yescharacteristic, complemented
15C2×AGL(1,ℤ/8)×C61—21no—
16C2×AGL(1,ℤ/8)×C61—21no—
17C2×AGL(1,ℤ/8)×C61—28no—
18C2×AGL(1,ℤ/8)×C61C2212yes—
19C2×AGL(1,ℤ/8)×C61C2212yescomplemented
20C2×AGL(1,ℤ/8)×C61C2212yescomplemented
21C22×SD16×C61—21no—
22C22×D8×C61—21no—
23C22×M16×C61C2211yescharacteristic, complemented
24C61×#550—21no—
25C61×#548—21no—
26C61×#546—21no—
27C61×#546—22no—
28D42×C61—22no—
29D42×C61—21no—
30C61×#537—21no—
31C61×#537C2211yescharacteristic, complemented
32C61×#535—21no—
33C61×#535C2211yescharacteristic, complemented
34C2×#127×C61C2212yescomplemented
35C61×#525—21no—
36C61×#525C2211yescharacteristic
37C2×#121×C61—21no—
38C2×#121×C61C2211yescharacteristic
39C2×#120×C61—22no—
40C61×#520C2211yescharacteristic, complemented
41C61×#453—28no—
42C61×#450—21no—
43C61×#450—21no—
44C61×#447—21no—
45C61×#447—21no—
46C2×#104×C61C2212yescomplemented
47C2×#104×C61C2212yescomplemented
48C2×#104×C61C2212yescomplemented
49C61×#418C2212yescomplemented
50C2×#100×C61C2212yescomplemented
51C61×#407C2211yescharacteristic, complemented
52C61×#392—22no—
53C61×#390C2212yescomplemented
54C4×C22⋊C4×C61C2211yescharacteristic, complemented
55C61×#343C2212yescomplemented
56C61×#339C2212yescomplemented
57C25×C61—21no—
58H(5,𝔽2)×C61—24no—
59H(5,𝔽2)×C61—42no—
60C2×#41×C61—21no—
61C2×#41×C61—21no—
62C2×#41×C61—21no—
63C2×#41×C61—21no—
64C2×#41×C61—24no—
65C2×#41×C61—42no—
66C2×#41×C61D411yescharacteristic, complemented
67C2×#41×C61D411yescharacteristic, complemented
68C2×#41×C61C2311yescharacteristic
69C2×#41×C61C2311yescharacteristic
70C2×#41×C61C2311yescharacteristic
71C22×Q8×C61D411yescharacteristic, complemented
72C22×D4×C61—24no—
73C22×D4×C61—21no—
74C22×D4×C61—22no—
75C22×D4×C61—22no—
76C22×D4×C61—21no—
77C22×D4×C61—21no—
78C22×D4×C61—24no—
79C22×D4×C61—21no—
80C22×D4×C61—21no—
81C22×D4×C61—21no—
82C22×D4×C61—21no—
83C22×D4×C61—21no—
84C22×D4×C61—42no—
85C22×D4×C61D412yes—
86C22×D4×C61D411yescharacteristic, complemented
87C22×D4×C61C2311yescharacteristic
88C22×D4×C61C2312yes—
89C23×C4×C61—21no—
90C23×C4×C61C2311yescharacteristic
91AGL(1,ℤ/8)×C61—28no—
92AGL(1,ℤ/8)×C61—28no—
93AGL(1,ℤ/8)×C61—24no—
94AGL(1,ℤ/8)×C61—24no—
95AGL(1,ℤ/8)×C61—24no—
96AGL(1,ℤ/8)×C61—24no—
97AGL(1,ℤ/8)×C61—42no—
98AGL(1,ℤ/8)×C61D418yescomplemented
99C2×SD16×C61—28no—
100C2×SD16×C61—22no—
101C2×SD16×C61—22no—
102C2×SD16×C61—22no—
103C2×D8×C61—28no—
104C2×D8×C61—22no—
105C2×D8×C61—22no—
106C2×D8×C61—22no—
107C2×M16×C61—21no—
108C2×M16×C61—24no—
109C2×M16×C61C2312yes—
110C2×M16×C61C2312yes—
111C22×C8×C61—21no—
112#127×C61—22no—
113#127×C61—21no—
114#127×C61—24no—
115#127×C61—42no—
116#124×C61—22no—
117#124×C61—21no—
118#123×C61—22no—
119#123×C61—21no—
120C22⋊Q8×C61—22no—
121C22⋊Q8×C61—21no—
122C22⋊Q8×C61—21no—
123C22⋊Q8×C61D411yescharacteristic, complemented
124C22⋊Q8×C61D411yescharacteristic, complemented
125#121×C61—22no—
126#121×C61—22no—
127#121×C61—22no—
128#121×C61—22no—
129#121×C61—22no—
130#121×C61—21no—
131#121×C61—21no—
132#121×C61—21no—
133#121×C61—22no—
134#121×C61—21no—
135#121×C61—21no—
136#121×C61—21no—
137#121×C61—21no—
138#121×C61—21no—
139#121×C61D411yescharacteristic, complemented
140#121×C61D411yescharacteristic, complemented
141#120×C61—22no—
142#120×C61—22no—
143#120×C61—22no—
144#120×C61—22no—
145#120×C61—21no—
146#120×C61—48no—
147C4×Q8×C61—21no—
148C4×D4×C61—22no—
149C4×D4×C61—22no—
150C4×D4×C61—21no—
151C4×D4×C61—22no—
152C4×D4×C61—21no—
153C4×D4×C61—21no—
154#117×C61—21no—
155#117×C61C2311yescharacteristic
156C2×C4⋊C4×C61—21no—
157C2×C4⋊C4×C61C2311yescharacteristic
158C2×C22⋊C4×C61—22no—
159C2×C22⋊C4×C61—21no—
160C2×C22⋊C4×C61—24no—
161C2×C22⋊C4×C61D412yes—
162C2×C42×C61C2312yes—
163#104×C61—24no—
164#104×C61—24no—
165#104×C61—42no—
166#102×C61—22no—
167#102×C61—22no—
168#100×C61—24no—
169C22⋊C8×C61—21no—
170C22⋊C8×C61—21no—
171#95×C61—21no—
172C24×C61—22no—
173C24×C61—22no—
174C24×C61—21no—
175C24×C61—44no—
176C24×C61—44no—
177C24×C61—41no—
178C24×C61—41no—
179C24×C61—82no—
180C24×C61C2×D411yescharacteristic
181C24×C61C2×D412yes—
182#41×C61—22no—
183#41×C61—22no—
184#41×C61—22no—
185#41×C61—22no—
186#41×C61—22no—
187#41×C61—22no—
188#41×C61—22no—
189#41×C61—44no—
190#41×C61—41no—
191#41×C61—41no—
192#41×C61—44no—
193#41×C61—44no—
194#41×C61—42no—
195#41×C61—42no—
196#41×C61C2×D414yes—
197C2×Q8×C61—21no—
198C2×Q8×C61—22no—
199C2×Q8×C61—41no—
200C2×Q8×C61C2×D411yescharacteristic
201C2×Q8×C61C2×D411yescharacteristic
202C2×Q8×C61C2×D411yescharacteristic
203C2×D4×C61—21no—
204C2×D4×C61—24no—
205C2×D4×C61—24no—
206C2×D4×C61—22no—
207C2×D4×C61—22no—
208C2×D4×C61—22no—
209C2×D4×C61—22no—
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—22no—
216C2×D4×C61—22no—
217C2×D4×C61—22no—
218C2×D4×C61—21no—
219C2×D4×C61—22no—
220C2×D4×C61—21no—
221C2×D4×C61—22no—
222C2×D4×C61—22no—
223C2×D4×C61—22no—
224C2×D4×C61—22no—
225C2×D4×C61—21no—
226C2×D4×C61—21no—
227C2×D4×C61—22no—
228C2×D4×C61—22no—
229C2×D4×C61—22no—
230C2×D4×C61—41no—
231C2×D4×C61—44no—
232C2×D4×C61—44no—
233C2×D4×C61—44no—
234C2×D4×C61—44no—
235C2×D4×C61—42no—
236C2×D4×C61—42no—
237C2×D4×C61—48no—
238C2×D4×C61—44no—
239C2×D4×C61—48no—
240C2×D4×C61—42no—
241C2×D4×C61—42no—
242C2×D4×C61—44no—
243C2×D4×C61—48no—
244C2×D4×C61—41no—
245C2×D4×C61—41no—
246C2×D4×C61—84no—
247C2×D4×C61—84no—
248C2×D4×C61C2×D411yescharacteristic
249C2×D4×C61C2×D411yescharacteristic
250C2×D4×C61C2×D411yescharacteristic
251C2×D4×C61C2×D414yescomplemented
252C22×C4×C61—21no—
253C22×C4×C61—22no—
254C22×C4×C61—22no—
255C22×C4×C61—22no—
256C22×C4×C61—21no—
257C22×C4×C61—22no—
258C22×C4×C61—22no—
259C22×C4×C61—21no—
260C22×C4×C61—21no—
261C22×C4×C61—21no—
262C22×C4×C61—21no—
263C22×C4×C61—44no—
264C22×C4×C61C2×D411yescharacteristic
265C22×C4×C61C2×D411yescharacteristic
266C22×C4×C61C2×D411yescharacteristic
267C22×C4×C61C2×D411yescharacteristic
268C22×C4×C61C2×D411yescharacteristic
269C22×C4×C61C2×D412yes—
270C22×C4×C61C2411yescharacteristic
271SD16×C61—28no—
272SD16×C61—28no—
273SD16×C61—44no—
274D8×C61—28no—
275D8×C61—28no—
276D8×C61—44no—
277M16×C61—24no—
278M16×C61—22no—
279M16×C61—22no—
280M16×C61—22no—
281M16×C61C2×D414yescomplemented
282C2×C8×C61—24no—
283C2×C8×C61—22no—
284C2×C8×C61—22no—
285C4⋊C4×C61—22no—
286C4⋊C4×C61—22no—
287C4⋊C4×C61—21no—
288C4⋊C4×C61—21no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61—21no—
291C4⋊C4×C61C2×D411yescharacteristic
292C4⋊C4×C61C2×D411yescharacteristic
293C22⋊C4×C61—22no—
294C22⋊C4×C61—22no—
295C22⋊C4×C61—24no—
296C22⋊C4×C61—22no—
297C22⋊C4×C61—22no—
298C22⋊C4×C61—22no—
299C22⋊C4×C61—21no—
300C22⋊C4×C61—21no—
301C22⋊C4×C61—21no—
302C22⋊C4×C61—21no—
303C22⋊C4×C61—22no—
304C22⋊C4×C61—22no—
305C22⋊C4×C61—21no—
306C22⋊C4×C61—48no—
307C42×C61—22no—
308C42×C61—21no—
309C42×C61—22no—
310C42×C61—22no—
311C23×C61—21no—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61—22no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—24no—
318C23×C61—24no—
319C23×C61—41no—
320C23×C61—42no—
321C23×C61—44no—
322C23×C61—44no—
323C23×C61—44no—
324C23×C61—44no—
325C23×C61—44no—
326C23×C61—42no—
327C23×C61—42no—
328C23×C61—42no—
329C23×C61—42no—
330C23×C61—42no—
331C23×C61—81no—
332C23×C61—82no—
333C23×C61—82no—
334C23×C61—82no—
335C23×C61—82no—
336C23×C61—82no—
337C23×C61—816no—
338C23×C61—82no—
339C23×C61#12011yescharacteristic
340C23×C61#12011yescharacteristic
341C23×C61C22×D411yescharacteristic
342Q8×C61—21no—
343Q8×C61—21no—
344Q8×C61—21no—
345Q8×C61—22no—
346Q8×C61—42no—
347Q8×C61#12012yescomplemented
348D4×C61—24no—
349D4×C61—21no—
350D4×C61—24no—
351D4×C61—21no—
352D4×C61—21no—
353D4×C61—22no—
354D4×C61—24no—
355D4×C61—42no—
356D4×C61—42no—
357D4×C61—44no—
358D4×C61—44no—
359D4×C61—44no—
360D4×C61—42no—
361D4×C61—44no—
362D4×C61—42no—
363D4×C61—42no—
364D4×C61—44no—
365D4×C61—42no—
366D4×C61—41no—
367D4×C61—42no—
368D4×C61—41no—
369D4×C61—42no—
370D4×C61—42no—
371D4×C61—81no—
372D4×C61—82no—
373D4×C61—82no—
374D4×C61—82no—
375D4×C61—82no—
376D4×C61—816no—
377D4×C61#12012yescomplemented
378C2×C4×C61—21no—
379C2×C4×C61—22no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61—21no—
383C2×C4×C61—21no—
384C2×C4×C61—22no—
385C2×C4×C61—22no—
386C2×C4×C61—24no—
387C2×C4×C61—24no—
388C2×C4×C61—21no—
389C2×C4×C61—22no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61—42no—
394C2×C4×C61—42no—
395C2×C4×C61—42no—
396C2×C4×C61—44no—
397C2×C4×C61—42no—
398C2×C4×C61—42no—
399C2×C4×C61—41no—
400C2×C4×C61—41no—
401C2×C4×C61—42no—
402C2×C4×C61—42no—
403C2×C4×C61—82no—
404C2×C4×C61#12011yescharacteristic
405C2×C4×C61#12011yescharacteristic
406C2×C4×C61C22×D411yescharacteristic
407C2×C4×C61C22×D412yes—
408C2×C4×C61C22×D411yescharacteristic
409C2×C4×C61H(5,𝔽2)12yes—
410C8×C61—24no—
411C8×C61—42no—
412#23876C6111yesmaximal, characteristic, direct product factor, Sylow
413C22×C61—21no—
414C22×C61—21no—
415C22×C61—21no—
416C22×C61—21no—
417C22×C61—21no—
418C22×C61—22no—
419C22×C61—21no—
420C22×C61—21no—
421C22×C61—44no—
422C22×C61—48no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—41no—
427C22×C61—42no—
428C22×C61—44no—
429C22×C61—42no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—42no—
434C22×C61—41no—
435C22×C61—84no—
436C22×C61—84no—
437C22×C61—84no—
438C22×C61—88no—
439C22×C61—88no—
440C22×C61—82no—
441C22×C61—82no—
442C22×C61—164no—
443C22×C61#45312yescomplemented
444C22×C61C2×#12011yescharacteristic
445C22×C61D4212yes—
446C4×C61—21no—
447C4×C61—21no—
448C4×C61—22no—
449C4×C61—44no—
450C4×C61—41no—
451C4×C61—41no—
452C4×C61—42no—
453C4×C61—41no—
454C4×C61—41no—
455C4×C61C2×#12011yescharacteristic
456C4×C61#53411yescharacteristic
457C4×C61D4212yes—
458C22×AGL(1,ℤ/8)C2×C6111yescharacteristic, complemented
459#3488C2×C6111yescharacteristic, complemented
460C2×#453C2×C6112yescomplemented
461#3003C2×C6111yescharacteristic, complemented
462#2433C2×C6111yescharacteristic, complemented
463#2006C2×C6112yescomplemented
464#2002C2×C6112yescomplemented
465#1900C2×C6111yescharacteristic, complemented
466#1883C2×C6112yescomplemented
467#1871C2×C6111yescharacteristic, complemented
468#1789C2×C6111yescharacteristic, complemented
469C2×C61—22no—
470C2×C61—22no—
471C2×C61—41no—
472C2×C61—42no—
473C2×C61—81no—
474C2×C61—84no—
475C2×C61—82no—
476C2×C61—81no—
477C2×C61#240311yescharacteristic
478C2×C61C2×#45311yescharacteristic
479C2×C61#302111yescharacteristic
480C2×H(5,𝔽2)C22×C6111yescharacteristic, complemented
481C22×#41C22×C6111yescharacteristic
482C23×D4C22×C6111yescharacteristic, complemented
483C2×AGL(1,ℤ/8)—21no—
484C2×AGL(1,ℤ/8)—21no—
485C2×AGL(1,ℤ/8)—28no—
486C2×AGL(1,ℤ/8)C22×C6112yes—
487C2×AGL(1,ℤ/8)C22×C6112yescomplemented
488C2×AGL(1,ℤ/8)C22×C6112yescomplemented
489C22×SD16—21no—
490C22×D8—21no—
491C22×M16C22×C6111yescharacteristic, complemented
492#550—21no—
493#548—21no—
494#546—21no—
495#546—22no—
496D42—22no—
497D42—21no—
498#537—21no—
499#537C22×C6111yescharacteristic, complemented
500#535—21no—
501#535C22×C6111yescharacteristic, complemented
502C2×#127C22×C6112yescomplemented
503#525—21no—
504#525C22×C6111yescharacteristic
505C2×#121—21no—
506C2×#121C22×C6111yescharacteristic
507C2×#120—22no—
508#520C22×C6111yescharacteristic, complemented
509#453—28no—
510#450—21no—
511#450—21no—
512#447—21no—
513#447—21no—
514C2×#104C22×C6112yescomplemented
515C2×#104C22×C6112yescomplemented
516C2×#104C22×C6112yescomplemented
517#418C22×C6112yescomplemented
518C2×#100C22×C6112yescomplemented
519#407C22×C6111yescharacteristic, complemented
520#392—22no—
521#390C22×C6112yescomplemented
522C4×C22⋊C4C22×C6111yescharacteristic, complemented
523#343C22×C6112yescomplemented
524#339C22×C6112yescomplemented
525C61#2387611yescharacteristic, direct product factor, Sylow
526C25—21no—
527H(5,𝔽2)—24no—
528H(5,𝔽2)—42no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—21no—
532C2×#41—21no—
533C2×#41—24no—
534C2×#41—42no—
535C2×#41D4×C6111yescharacteristic, complemented
536C2×#41D4×C6111yescharacteristic, complemented
537C2×#41C23×C6111yescharacteristic
538C2×#41C23×C6111yescharacteristic
539C2×#41C23×C6111yescharacteristic
540C22×Q8D4×C6111yescharacteristic, complemented
541C22×D4—24no—
542C22×D4—21no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—24no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—42no—
554C22×D4D4×C6112yes—
555C22×D4D4×C6111yescharacteristic, complemented
556C22×D4C23×C6111yescharacteristic
557C22×D4C23×C6112yes—
558C23×C4—21no—
559C23×C4C23×C6111yescharacteristic
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—28no—
562AGL(1,ℤ/8)—24no—
563AGL(1,ℤ/8)—24no—
564AGL(1,ℤ/8)—24no—
565AGL(1,ℤ/8)—24no—
566AGL(1,ℤ/8)—42no—
567AGL(1,ℤ/8)D4×C6118yescomplemented
568C2×SD16—28no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×D8—28no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—22no—
576C2×M16—21no—
577C2×M16—24no—
578C2×M16C23×C6112yes—
579C2×M16C23×C6112yes—
580C22×C8—21no—
581#127—22no—
582#127—21no—
583#127—24no—
584#127—42no—
585#124—22no—
586#124—21no—
587#123—22no—
588#123—21no—
589C22⋊Q8—22no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8D4×C6111yescharacteristic, complemented
593C22⋊Q8D4×C6111yescharacteristic, complemented
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—22no—
606#121—21no—
607#121—21no—
608#121D4×C6111yescharacteristic, complemented
609#121D4×C6111yescharacteristic, complemented
610#120—22no—
611#120—22no—
612#120—22no—
613#120—21no—
614#120—22no—
615#120—48no—
616C4×Q8—21no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—21no—
620C4×D4—22no—
621C4×D4—21no—
622C4×D4—21no—
623#117—21no—
624#117C23×C6111yescharacteristic
625C2×C4⋊C4—21no—
626C2×C4⋊C4C23×C6111yescharacteristic
627C2×C22⋊C4—22no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4D4×C6112yes—
631C2×C42C23×C6112yes—
632#104—24no—
633#104—24no—
634#104—42no—
635#102—22no—
636#102—22no—
637#100—24no—
638C22⋊C8—21no—
639C22⋊C8—21no—
640#95—21no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—44no—
645C24—44no—
646C24—41no—
647C24—41no—
648C24—82no—
649C24C2×D4×C6111yescharacteristic
650C24C2×D4×C6112yes—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—44no—
659#41—41no—
660#41—41no—
661#41—44no—
662#41—44no—
663#41—42no—
664#41—42no—
665#41C2×D4×C6114yes—
666C2×Q8—21no—
667C2×Q8—22no—
668C2×Q8—41no—
669C2×Q8C2×D4×C6111yescharacteristic
670C2×Q8C2×D4×C6111yescharacteristic
671C2×Q8C2×D4×C6111yescharacteristic
672C2×D4—21no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—21no—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—41no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—48no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—44no—
712C2×D4—48no—
713C2×D4—41no—
714C2×D4—41no—
715C2×D4—84no—
716C2×D4—84no—
717C2×D4C2×D4×C6111yescharacteristic
718C2×D4C2×D4×C6111yescharacteristic
719C2×D4C2×D4×C6111yescharacteristic
720C2×D4C2×D4×C6114yescomplemented
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—21no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—44no—
733C22×C4C2×D4×C6111yescharacteristic
734C22×C4C2×D4×C6111yescharacteristic
735C22×C4C2×D4×C6111yescharacteristic
736C22×C4C2×D4×C6111yescharacteristic
737C22×C4C2×D4×C6111yescharacteristic
738C22×C4C2×D4×C6112yes—
739C22×C4C24×C6111yescharacteristic
740SD16—28no—
741SD16—28no—
742SD16—44no—
743D8—28no—
744D8—28no—
745D8—44no—
746M16—24no—
747M16—22no—
748M16—22no—
749M16—22no—
750M16C2×D4×C6114yescomplemented
751C2×C8—24no—
752C2×C8—22no—
753C2×C8—22no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4C2×D4×C6111yescharacteristic
761C4⋊C4C2×D4×C6111yescharacteristic
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—24no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—21no—
775C22⋊C4—48no—
776C42—22no—
777C42—21no—
778C42—22no—
779C42—22no—
780C23—22no—
781C23—22no—
782C23—21no—
783C23—24no—
784C23—22no—
785C23—21no—
786C23—21no—
787C23—24no—
788C23—41no—
789C23—42no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—81no—
801C23—82no—
802C23—82no—
803C23—82no—
804C23—82no—
805C23—82no—
806C23—816no—
807C23—82no—
808C23#120×C6111yescharacteristic
809C23#120×C6111yescharacteristic
810C23C22×D4×C6111yescharacteristic
811Q8—21no—
812Q8—21no—
813Q8—22no—
814Q8—21no—
815Q8—42no—
816Q8#120×C6112yescomplemented
817D4—24no—
818D4—21no—
819D4—21no—
820D4—22no—
821D4—24no—
822D4—21no—
823D4—24no—
824D4—42no—
825D4—42no—
826D4—44no—
827D4—44no—
828D4—44no—
829D4—42no—
830D4—44no—
831D4—42no—
832D4—42no—
833D4—44no—
834D4—42no—
835D4—42no—
836D4—41no—
837D4—42no—
838D4—42no—
839D4—41no—
840D4—81no—
841D4—82no—
842D4—82no—
843D4—82no—
844D4—82no—
845D4—816no—
846D4#120×C6112yescomplemented
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—24no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—24no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—44no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—41no—
871C2×C4—42no—
872C2×C4—82no—
873C2×C4#120×C6111yescharacteristic
874C2×C4#120×C6111yescharacteristic
875C2×C4C22×D4×C6111yescharacteristic
876C2×C4C22×D4×C6111yescharacteristic
877C2×C4C22×D4×C6112yes—
878C2×C4H(5,𝔽2)×C6112yes—
879C8—24no—
880C8—42no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—22no—
887C22—21no—
888C22—21no—
889C22—44no—
890C22—48no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—42no—
896C22—44no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—84no—
904C22—84no—
905C22—84no—
906C22—88no—
907C22—88no—
908C22—82no—
909C22—82no—
910C22—164no—
911C22C61×#45312yescomplemented
912C22C2×#120×C6111yescharacteristic
913C22D42×C6112yes—
914C4—21no—
915C4—21no—
916C4—22no—
917C4—44no—
918C4—41no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—41no—
923C4C2×#120×C6111yescharacteristic
924C4C61×#53411yescharacteristic
925C4D42×C6112yes—
926C2—22no—
927C2—22no—
928C2—41no—
929C2—42no—
930C2—84no—
931C2—81no—
932C2—82no—
933C2—81no—
934C2C61×#240311yescharacteristic
935C2C2×C61×#45311yescharacteristic
936C2C61×#302111yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
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
1. C22×AGL(1,ℤ/8)×C61C2semidirect
2. C61×#3488C2semidirect
3. C2×C61×#453C2semidirect
4. C61×#3003C2semidirect
5. C61×#2433C2semidirect
6. C61×#2006C2semidirect
7. C61×#2002C2semidirect
8. C61×#1900C2semidirect
9. C61×#1883C2semidirect
10. C61×#1871C2semidirect
11. C61×#1789C2semidirect
12. C2×H(5,𝔽2)×C61C22semidirect
14. C23×D4×C61C22semidirect
19. C2×AGL(1,ℤ/8)×C61C22semidirect
20. C2×AGL(1,ℤ/8)×C61C22semidirect
23. C22×M16×C61C22semidirect
31. C61×#537C22semidirect
33. C61×#535C22semidirect
34. C2×#127×C61C22semidirect
40. C61×#520C22semidirect
46. C2×#104×C61C22semidirect
47. C2×#104×C61C22semidirect
48. C2×#104×C61C22semidirect
49. C61×#418C22semidirect
50. C2×#100×C61C22semidirect
51. C61×#407C22semidirect
53. C61×#390C22semidirect
54. C4×C22⋊C4×C61C22semidirect
55. C61×#343C22semidirect
56. C61×#339C22semidirect
66. C2×#41×C61D4semidirect
67. C2×#41×C61D4semidirect
71. C22×Q8×C61D4semidirect
86. C22×D4×C61D4semidirect
98. AGL(1,ℤ/8)×C61D4semidirect
123. C22⋊Q8×C61D4semidirect
124. C22⋊Q8×C61D4semidirect
139. #121×C61D4semidirect
140. #121×C61D4semidirect
251. C2×D4×C61C2×D4semidirect
281. M16×C61C2×D4semidirect
347. Q8×C61#120semidirect
377. D4×C61#120semidirect
412. #23876C61direct (N × H)
443. C22×C61#453semidirect
458. C22×AGL(1,ℤ/8)C2×C61semidirect
459. #3488C2×C61semidirect
460. C2×#453C2×C61semidirect
461. #3003C2×C61semidirect
462. #2433C2×C61semidirect
463. #2006C2×C61semidirect
464. #2002C2×C61semidirect
465. #1900C2×C61semidirect
466. #1883C2×C61semidirect
467. #1871C2×C61semidirect
468. #1789C2×C61semidirect
480. C2×H(5,𝔽2)C22×C61semidirect
482. C23×D4C22×C61semidirect
487. C2×AGL(1,ℤ/8)C22×C61semidirect
488. C2×AGL(1,ℤ/8)C22×C61semidirect
491. C22×M16C22×C61semidirect
499. #537C22×C61semidirect
501. #535C22×C61semidirect
502. C2×#127C22×C61semidirect
508. #520C22×C61semidirect
514. C2×#104C22×C61semidirect
515. C2×#104C22×C61semidirect
516. C2×#104C22×C61semidirect
517. #418C22×C61semidirect
518. C2×#100C22×C61semidirect
519. #407C22×C61semidirect
521. #390C22×C61semidirect
522. C4×C22⋊C4C22×C61semidirect
523. #343C22×C61semidirect
524. #339C22×C61semidirect
525. C61#23876direct (N × H)
535. C2×#41D4×C61semidirect
536. C2×#41D4×C61semidirect
540. C22×Q8D4×C61semidirect
555. C22×D4D4×C61semidirect
567. AGL(1,ℤ/8)D4×C61semidirect
592. C22⋊Q8D4×C61semidirect
593. C22⋊Q8D4×C61semidirect
608. #121D4×C61semidirect
609. #121D4×C61semidirect
720. C2×D4C2×D4×C61semidirect
750. M16C2×D4×C61semidirect
816. Q8#120×C61semidirect
846. D4#120×C61semidirect
911. C22C61×#453semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C612
C61×#34882
C2×C61×#4532
C61×#30032
C61×#24332
C61×#20062
C61×#20022
C61×#19002
C61×#18832
C61×#18712
C61×#17892
#2387661