Finite Group Databasebeta

← #29712896

Subgroups — #29712896

Order 15616.

1250 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455748C211yesmaximal, characteristic, complemented
2#21454338C211yesmaximal, characteristic, complemented
3#21450273C211yesmaximal, characteristic, complemented
4#21447045C211yesmaximal, characteristic, complemented
5#21447040C211yesmaximal, characteristic, complemented
6#21447033C211yesmaximal, characteristic, complemented
7#21447033C211yesmaximal, characteristic, complemented
8#21446288C211yesmaximal, characteristic, complemented
9#21446122C211yesmaximal, characteristic, complemented
10#21446052C211yesmaximal, characteristic, complemented
11#21446045C211yesmaximal, characteristic, complemented
12#21445778C211yesmaximal, characteristic, complemented
13#21445778C211yesmaximal, characteristic, complemented
14#21445763C211yesmaximal, characteristic, complemented
15C61×#3489C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C2×#14519736C2211yescharacteristic
18#16840100—21no—
19#16840100—21no—
20#16840083—21no—
21#16840083—21no—
22#16839805C2211yescharacteristic, complemented
23#16839805C2211yescharacteristic, complemented
24C2×#14519704C2211yescharacteristic
25C2×#14519704C2211yescharacteristic
26C2×#14519704C2211yescharacteristic
27C2×#14519704C2211yescharacteristic
28C2×#14519704C2211yescharacteristic, complemented
29C2×#14519704C2211yescharacteristic, complemented
30#16839771—21no—
31#16839767—21no—
32#16839763C2211yescharacteristic
33#16839763C2211yescharacteristic
34#16839763C2211yescharacteristic
35#16839763C2211yescharacteristic
36#16839763C2211yescharacteristic, complemented
37#16839763C2211yescharacteristic, complemented
38#16839758—21no—
39#16839758—21no—
40C2×#14519696C2211yescharacteristic, complemented
41C2×#14519696C2211yescharacteristic, complemented
42#16839726C2211yescharacteristic
43#16839690—22no—
44#16839669C2211yescharacteristic, complemented
45#16839669C2211yescharacteristic, complemented
46#16839643—22no—
47#16839631C2211yescharacteristic, complemented
48#16839627C2211yescharacteristic, complemented
49C4×C22⋊Dic61C2211yescharacteristic
50#16839531C2211yescharacteristic, complemented
51#16839531C2211yescharacteristic, complemented
52#16839521C2211yescharacteristic, complemented
53#16839521C2211yescharacteristic, complemented
54C2×2−1+4×C61C2211yescharacteristic
55C22×#41×C61C2211yescharacteristic
56D4×Q8×C61—21no—
57C61×#548—21no—
58C61×#547—21no—
59C61×#547—22no—
60C61×#546—21no—
61C61×#546—22no—
62C61×#537—21no—
63C61×#537C2211yescharacteristic
64C61×#536—21no—
65C61×#536C2211yescharacteristic
66C61×#525—21no—
67C61×#525C2211yescharacteristic
68C2×C22⋊Q8×C61—21no—
69C2×C22⋊Q8×C61C2211yescharacteristic
70C61×#520C2211yescharacteristic
71C2×#11758194—21no—
72C2×#11758194—41no—
73C2×#11758194—41no—
74C2×#11758194C2311yescharacteristic
75C2×#11758194C2311yescharacteristic
76C2×#11758194C2311yescharacteristic
77C2×#11758194C2311yescharacteristic
78C22×#92418—21no—
79#14519736—21no—
80#14519736—21no—
81#14519736—21no—
82#14519736—21no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×#11758196—22no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61C2311yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91#14519710—21no—
92#14519710—21no—
93#14519708—21no—
94#14519708—21no—
95#14519704—22no—
96#14519704—22no—
97#14519704—41no—
98#14519704—41no—
99#14519704—41no—
100#14519704—41no—
101#14519701—21no—
102#14519701—21no—
103#14519701—21no—
104#14519701—21no—
105#14519701—21no—
106#14519701—21no—
107#14519698—21no—
108#14519698—21no—
109#14519698—21no—
110#14519698—21no—
111#14519698—21no—
112#14519698—21no—
113#14519696—41no—
114#14519696—41no—
115C22⋊#92418—21no—
116C22⋊#92418—21no—
117#14519684—22no—
118#14519684—22no—
119#14519684—22no—
120#14519684—21no—
1212−1+4×C61—22no—
1222−1+4×C61—22no—
1232−1+4×C61—41no—
1242−1+4×C61—41no—
125C2×#41×C61—21no—
126C2×#41×C61—21no—
127C2×#41×C61—21no—
128C2×#41×C61—22no—
129C2×#41×C61—21no—
130C2×#41×C61—22no—
131C2×#41×C61—22no—
132C2×#41×C61—41no—
133C2×#41×C61—41no—
134C2×#41×C61D411yescharacteristic
135C2×#41×C61D411yescharacteristic
136C2×#41×C61C2311yescharacteristic
137C2×#41×C61C2311yescharacteristic
138C2×#41×C61C2311yescharacteristic
139C22×Q8×C61—21no—
140C22×Q8×C61—21no—
141C22×Q8×C61D411yescharacteristic
142C22×Q8×C61C2311yescharacteristic
143C22×D4×C61—21no—
144C22×D4×C61D411yescharacteristic
145C23×C4×C61—21no—
146C23×C4×C61C2311yescharacteristic
147C4⋊Q8×C61—22no—
148C4⋊Q8×C61—21no—
149#124×C61—22no—
150#124×C61—21no—
151#123×C61—22no—
152#123×C61—22no—
153#123×C61—22no—
154#123×C61—22no—
155#123×C61—21no—
156C22⋊Q8×C61—22no—
157C22⋊Q8×C61—22no—
158C22⋊Q8×C61—22no—
159C22⋊Q8×C61—21no—
160C22⋊Q8×C61—21no—
161C22⋊Q8×C61—21no—
162C22⋊Q8×C61—21no—
163C22⋊Q8×C61—21no—
164C22⋊Q8×C61—21no—
165C22⋊Q8×C61—21no—
166C22⋊Q8×C61—21no—
167C22⋊Q8×C61D411yescharacteristic
168C22⋊Q8×C61D411yescharacteristic
169#121×C61—22no—
170#121×C61—22no—
171#121×C61—22no—
172#121×C61—21no—
173#121×C61—21no—
174#121×C61—22no—
175#121×C61D411yescharacteristic
176#121×C61D411yescharacteristic
177#120×C61—22no—
178#120×C61—21no—
179C4×Q8×C61—21no—
180C4×D4×C61—22no—
181C4×D4×C61—22no—
182C4×D4×C61—21no—
183C4×D4×C61—22no—
184C4×D4×C61—21no—
185C4×D4×C61—21no—
186#117×C61—21no—
187#117×C61C2311yescharacteristic
188C2×C4⋊C4×C61—22no—
189C2×C4⋊C4×C61—21no—
190C2×C4⋊C4×C61D412yes—
191C2×C4⋊C4×C61C2311yescharacteristic
192C2×C22⋊C4×C61—22no—
193C2×C22⋊C4×C61D412yes—
194C24×C61—21no—
195C24×C61C2×D411yescharacteristic
196#41×C61—21no—
197#41×C61—21no—
198#41×C61—22no—
199#41×C61—22no—
200#41×C61—21no—
201#41×C61—21no—
202#41×C61—21no—
203#41×C61—21no—
204#41×C61—21no—
205#41×C61—21no—
206#41×C61—21no—
207#41×C61—21no—
208#41×C61—42no—
209#41×C61—42no—
210#41×C61—41no—
211#41×C61—41no—
212#41×C61—42no—
213#41×C61—42no—
214#41×C61—42no—
215#41×C61—42no—
216#41×C61—44no—
217#41×C61—44no—
218#41×C61—42no—
219#41×C61—42no—
220#41×C61#4112yes—
221#41×C61#4112yes—
222C2×Q8×C61—22no—
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—22no—
231C2×Q8×C61—41no—
232C2×Q8×C61—42no—
233C2×Q8×C61—42no—
234C2×Q8×C61—42no—
235C2×Q8×C61—42no—
236C2×Q8×C61C2×D411yescharacteristic
237C2×Q8×C61C2×D411yescharacteristic
238C2×Q8×C61C2×D411yescharacteristic
239C2×D4×C61—21no—
240C2×D4×C61—22no—
241C2×D4×C61—22no—
242C2×D4×C61—21no—
243C2×D4×C61—21no—
244C2×D4×C61—21no—
245C2×D4×C61—21no—
246C2×D4×C61—21no—
247C2×D4×C61—22no—
248C2×D4×C61—21no—
249C2×D4×C61—21no—
250C2×D4×C61—41no—
251C2×D4×C61—42no—
252C2×D4×C61—42no—
253C2×D4×C61C2×D411yescharacteristic
254C2×D4×C61C2×D411yescharacteristic
255C2×D4×C61C2×D411yescharacteristic
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61—21no—
260C22×C4×C61—21no—
261C22×C4×C61—22no—
262C22×C4×C61—22no—
263C22×C4×C61—21no—
264C22×C4×C61—22no—
265C22×C4×C61—21no—
266C22×C4×C61—21no—
267C22×C4×C61—21no—
268C22×C4×C61—21no—
269C22×C4×C61—42no—
270C22×C4×C61—42no—
271C22×C4×C61C2×D412yes—
272C22×C4×C61C2×D411yescharacteristic
273C22×C4×C61C2×D411yescharacteristic
274C22×C4×C61C2×D411yescharacteristic
275C22×C4×C61C2×D411yescharacteristic
276C22×C4×C61C2×D411yescharacteristic
277C22×C4×C61C2×D412yes—
278C22×C4×C61C2411yescharacteristic
279C22×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C4⋊C4×C61—22no—
284C4⋊C4×C61—22no—
285C4⋊C4×C61—22no—
286C4⋊C4×C61—22no—
287C4⋊C4×C61—21no—
288C4⋊C4×C61—22no—
289C4⋊C4×C61—22no—
290C4⋊C4×C61—21no—
291C4⋊C4×C61—21no—
292C4⋊C4×C61—21no—
293C4⋊C4×C61C2×D411yescharacteristic
294C4⋊C4×C61C2×D411yescharacteristic
295C22⋊C4×C61—22no—
296C22⋊C4×C61—22no—
297C22⋊C4×C61—22no—
298C22⋊C4×C61—22no—
299C22⋊C4×C61—22no—
300C22⋊C4×C61—21no—
301C22⋊C4×C61—22no—
302C22⋊C4×C61—22no—
303C22⋊C4×C61—21no—
304C22⋊C4×C61—21no—
305C22⋊C4×C61—21no—
306C22⋊C4×C61—21no—
307C42×C61—22no—
308C42×C61—21no—
309C22⋊Dic61—42no—
310C22⋊Dic61—41no—
311C22⋊Dic61—41no—
312C4⋊Dic61—21no—
313C4⋊Dic61—21no—
314C4⋊Dic61—21no—
315C4⋊Dic61—21no—
316#11758196—44no—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61—21no—
320C4×Dic61—21no—
321C4×Dic61—41no—
322C4×Dic61—41no—
323#11758194—21no—
324#11758194—21no—
325#11758194—21no—
326#11758194—21no—
327#11758194—21no—
328#11758194—21no—
329#11758194—21no—
330#11758194—21no—
331#11758194—42no—
332C2×#92418—21no—
333C2×#92418—21no—
334C2×#92418—21no—
335C2×#92418—21no—
336C2×#92418—42no—
337C23×C61—21no—
338C23×C61—21no—
339C23×C61—21no—
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—42no—
345C23×C61—42no—
346C23×C61—81no—
347C23×C61#12011yescharacteristic
348C23×C61#12011yescharacteristic
349C23×C61C22×D411yescharacteristic
350Q8×C61—21no—
351Q8×C61—21no—
352Q8×C61—21no—
353Q8×C61—21no—
354Q8×C61—21no—
355Q8×C61—42no—
356Q8×C61—44no—
357Q8×C61—41no—
358Q8×C61—41no—
359Q8×C61—41no—
360Q8×C61—41no—
361Q8×C61#12312yes—
362D4×C61—22no—
363D4×C61—22no—
364D4×C61—21no—
365D4×C61—21no—
366D4×C61—21no—
367D4×C61—21no—
368D4×C61—21no—
369D4×C61—42no—
370D4×C61—42no—
371D4×C61—42no—
372D4×C61—42no—
373D4×C61—44no—
374D4×C61—41no—
375D4×C61—41no—
376D4×C61—41no—
377D4×C61—41no—
378D4×C61—81no—
379D4×C61—82no—
380D4×C61#12312yes—
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—21no—
388C2×C4×C61—21no—
389C2×C4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—22no—
393C2×C4×C61—22no—
394C2×C4×C61—21no—
395C2×C4×C61—22no—
396C2×C4×C61—21no—
397C2×C4×C61—21no—
398C2×C4×C61—22no—
399C2×C4×C61—21no—
400C2×C4×C61—22no—
401C2×C4×C61—22no—
402C2×C4×C61—42no—
403C2×C4×C61—42no—
404C2×C4×C61—42no—
405C2×C4×C61—44no—
406C2×C4×C61—44no—
407C2×C4×C61—41no—
408C2×C4×C61—41no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—42no—
412C2×C4×C61—82no—
413C2×C4×C61#12011yescharacteristic
414C2×C4×C61#12011yescharacteristic
415C2×C4×C61C22×D411yescharacteristic
416C2×C4×C61C22×D411yescharacteristic
417C2×C4×C61C2×#4111yescharacteristic
418C2×C4×C61C2×#4111yescharacteristic
419C2×C4×C61H(5,𝔽2)11yescharacteristic
420C2×C4×C61H(5,𝔽2)11yescharacteristic
421C2×Dic61—22no—
422C2×Dic61—41no—
423C2×Dic61—41no—
424C2×Dic61—42no—
425C2×Dic61—41no—
426C2×Dic61—41no—
427C2×Dic61—42no—
428C2×Dic61—41no—
429C2×Dic61—41no—
430C2×Dic61—41no—
431#92418—41no—
432#92418—41no—
433#92418—41no—
434#92418—41no—
435#24028—611nomaximal, Sylow
436C22×C61—21no—
437C22×C61—21no—
438C22×C61—21no—
439C22×C61—21no—
440C22×C61—22no—
441C22×C61—21no—
442C22×C61—21no—
443C22×C61—21no—
444C22×C61—21no—
445C22×C61—41no—
446C22×C61—41no—
447C22×C61—41no—
448C22×C61—41no—
449C22×C61—41no—
450C22×C61—41no—
451C22×C61—41no—
452C22×C61—41no—
453C22×C61—81no—
454C22×C61—81no—
455C22×C61—84no—
456C22×C61C2×#12011yescharacteristic
457C22×C61#54611yescharacteristic
458C22×C61#54611yescharacteristic
459C4×C61—21no—
460C4×C61—21no—
461C4×C61—22no—
462C4×C61—42no—
463C4×C61—41no—
464C4×C61—41no—
465C4×C61—42no—
466C4×C61—41no—
467C4×C61—41no—
468C4×C61C2×#12311yescharacteristic
469C4×C61#53411yescharacteristic
470C4×C61#54611yescharacteristic
471C4×C61#54611yescharacteristic
472Dic61—42no—
473Dic61—81no—
474Dic61—81no—
475Dic61—81no—
476#3489D6111yescharacteristic
477#3093—611no—
478#2896—611no—
479#2499—611no—
480#2040—611no—
481#2039—611no—
482#2038—611no—
483#2038—611no—
484#1901—611no—
485#1871—611no—
486#1860—611no—
487#1859—611no—
488#1793—611no—
489#1793—611no—
490#1789—611no—
491C2×C61—21no—
492C2×C61—21no—
493C2×C61—41no—
494C2×C61—41no—
495C2×C61—42no—
496C2×C61—81no—
497C2×C61—81no—
498C2×C61#240511yescharacteristic
499C2×C61#301811yescharacteristic
500C2×C61#302011yescharacteristic
501C2×2−1+4C2×D6111yescharacteristic
502C22×#41C2×D6111yescharacteristic
503C22×M16—611no—
504D4×Q8—21no—
505#548—21no—
506#547—21no—
507#547—22no—
508#546—21no—
509#546—22no—
510#537—21no—
511#537C2×D6111yescharacteristic
512#536—21no—
513#536C2×D6111yescharacteristic
514#525—21no—
515#525C2×D6111yescharacteristic
516C2×C22⋊Q8—21no—
517C2×C22⋊Q8C2×D6111yescharacteristic
518#520C2×D6111yescharacteristic
519C2×#117—611no—
520#485—1221no—
521#485—1221no—
522#482—1221no—
523#482—1221no—
524#428—611no—
525#428—611no—
526C2×#104—611no—
527C2×#104—611no—
528C2×#104—611no—
529C2×#104—611no—
530C2×#104—611no—
531C2×#104—611no—
532#419—1221no—
533#418—1221no—
534#417—611no—
535#417—611no—
536#417—611no—
537#417—611no—
538#417—611no—
539#417—611no—
540#416—1221no—
541#416—1221no—
542C2×#101—611no—
543C2×#101—611no—
544#407—611no—
545#397—1222no—
546#391—611no—
547#391—611no—
548#387—1222no—
549#384—611no—
550#382—611no—
551C4×C22⋊C4—611no—
552#343—611no—
553#343—611no—
554#339—611no—
555#339—611no—
556C61#2402811yescharacteristic, complemented, Sylow
5572−1+4—22no—
5582−1+4—22no—
5592−1+4—41no—
5602−1+4—41no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—22no—
565C2×#41—21no—
566C2×#41—22no—
567C2×#41—22no—
568C2×#41—41no—
569C2×#41—41no—
570C2×#41C22⋊D6111yescharacteristic
571C2×#41C22⋊D6111yescharacteristic
572C2×#41C22×D6111yescharacteristic
573C2×#41C22×D6111yescharacteristic
574C2×#41C22×D6111yescharacteristic
575C22×Q8—21no—
576C22×Q8—21no—
577C22×Q8C22⋊D6111yescharacteristic
578C22×Q8C22×D6111yescharacteristic
579C22×D4—21no—
580C22×D4C22⋊D6111yescharacteristic
581C23×C4—21no—
582C23×C4C22×D6111yescharacteristic
583C2×M16—611no—
584C2×M16—611no—
585C2×M16—611no—
586C2×M16—611no—
587C2×M16—1221no—
588C2×M16—2441no—
589C2×M16—2441no—
590C22×C8—1221no—
591C4⋊Q8—22no—
592C4⋊Q8—21no—
593#124—22no—
594#124—21no—
595#123—22no—
596#123—22no—
597#123—22no—
598#123—21no—
599#123—22no—
600C22⋊Q8—22no—
601C22⋊Q8—22no—
602C22⋊Q8—22no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8C22⋊D6111yescharacteristic
612C22⋊Q8C22⋊D6111yescharacteristic
613#121—22no—
614#121—22no—
615#121—22no—
616#121—21no—
617#121—21no—
618#121—22no—
619#121C22⋊D6111yescharacteristic
620#121C22⋊D6111yescharacteristic
621#120—22no—
622#120—21no—
623C4×Q8—21no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—21no—
627C4×D4—22no—
628C4×D4—21no—
629C4×D4—21no—
630#117—21no—
631#117—1221no—
632#117—1221no—
633#117—1221no—
634#117—1221no—
635#117C22×D6111yescharacteristic
636C2×C4⋊C4—22no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—611no—
639C2×C4⋊C4—611no—
640C2×C4⋊C4—1222no—
641C2×C4⋊C4C22⋊D6112yes—
642C2×C4⋊C4C22×D6111yescharacteristic
643C2×C22⋊C4—22no—
644C2×C22⋊C4—1221no—
645C2×C22⋊C4—1221no—
646C2×C22⋊C4C22⋊D6112yes—
647C2×C42—611no—
648C2×C42—611no—
649C2×C42—1221no—
650#107—1221no—
651#107—1221no—
652#106—1221no—
653#106—1221no—
654#104—1222no—
655#104—1222no—
656#104—2441no—
657#104—2441no—
658#104—2441no—
659#104—2441no—
660#103—1221no—
661#103—1221no—
662#103—1221no—
663#103—1221no—
664#103—1221no—
665#103—1221no—
666#102—1221no—
667#102—1221no—
668#102—1221no—
669#102—1221no—
670#102—1221no—
671#102—1221no—
672#101—2441no—
673#101—2441no—
674C22⋊C8—1221no—
675C22⋊C8—1221no—
676#95—1221no—
677#95—1222no—
678#95—1222no—
679#95—1222no—
680C24—21no—
681C24C2×C22⋊D6111yescharacteristic
682#41—21no—
683#41—21no—
684#41—22no—
685#41—22no—
686#41—21no—
687#41—21no—
688#41—21no—
689#41—21no—
690#41—21no—
691#41—21no—
692#41—21no—
693#41—21no—
694#41—42no—
695#41—42no—
696#41—41no—
697#41—41no—
698#41—42no—
699#41—42no—
700#41—42no—
701#41—42no—
702#41—44no—
703#41—44no—
704#41—42no—
705#41—42no—
706#41#1175822412yes—
707#41#1175822412yes—
708C2×Q8—22no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—22no—
717C2×Q8—41no—
718C2×Q8—42no—
719C2×Q8—42no—
720C2×Q8—42no—
721C2×Q8—42no—
722C2×Q8C2×C22⋊D6111yescharacteristic
723C2×Q8C2×C22⋊D6111yescharacteristic
724C2×Q8C2×C22⋊D6111yescharacteristic
725C2×D4—21no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—41no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4C2×C22⋊D6111yescharacteristic
740C2×D4C2×C22⋊D6111yescharacteristic
741C2×D4C2×C22⋊D6111yescharacteristic
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—21no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4C2×C22⋊D6112yes—
762C22×C4C2×C22⋊D6111yescharacteristic
763C22×C4C2×C22⋊D6111yescharacteristic
764C22×C4C2×C22⋊D6111yescharacteristic
765C22×C4C2×C22⋊D6111yescharacteristic
766C22×C4C2×C22⋊D6111yescharacteristic
767C22×C4C2×C22⋊D6112yes—
768C22×C4C23×D6111yescharacteristic
769M16—1221no—
770M16—1221no—
771M16—1221no—
772M16—1221no—
773M16—1221no—
774M16—1221no—
775M16—1221no—
776M16—1221no—
777M16—2442no—
778C2×C8—1221no—
779C2×C8—1221no—
780C2×C8—1221no—
781C2×C8—1221no—
782C2×C8—2442no—
783C4⋊C4—22no—
784C4⋊C4—22no—
785C4⋊C4—22no—
786C4⋊C4—22no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—22no—
791C4⋊C4—22no—
792C4⋊C4—21no—
793C4⋊C4—1221no—
794C4⋊C4—1221no—
795C4⋊C4—1221no—
796C4⋊C4—1221no—
797C4⋊C4—2444no—
798C4⋊C4C2×C22⋊D6111yescharacteristic
799C4⋊C4C2×C22⋊D6111yescharacteristic
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—2442no—
813C22⋊C4—2441no—
814C22⋊C4—2441no—
815C42—22no—
816C42—21no—
817C42—1221no—
818C42—1221no—
819C42—1221no—
820C42—1221no—
821C42—2441no—
822C42—2441no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—41no—
829C23—41no—
830C23—42no—
831C23—42no—
832C23—81no—
833C23#1451974611yescharacteristic
834C23#1451974611yescharacteristic
835C23C22×C22⋊D6111yescharacteristic
836Q8—21no—
837Q8—21no—
838Q8—21no—
839Q8—21no—
840Q8—21no—
841Q8—42no—
842Q8—44no—
843Q8—41no—
844Q8—41no—
845Q8—41no—
846Q8—41no—
847Q8#1451975812yes—
848D4—22no—
849D4—22no—
850D4—21no—
851D4—21no—
852D4—21no—
853D4—21no—
854D4—21no—
855D4—42no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—44no—
860D4—41no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—81no—
865D4—82no—
866D4#1451975812yes—
867C2×C4—21no—
868C2×C4—21no—
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—22no—
879C2×C4—22no—
880C2×C4—21no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—44no—
892C2×C4—44no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—42no—
898C2×C4—82no—
899C2×C4—1222no—
900C2×C4—2441no—
901C2×C4—2442no—
902C2×C4—2441no—
903C2×C4—2442no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4#1451974611yescharacteristic
910C2×C4#1451974611yescharacteristic
911C2×C4C22×C22⋊D6111yescharacteristic
912C2×C4C22×C22⋊D6111yescharacteristic
913C2×C4C2×#1175822411yescharacteristic
914C2×C4C2×#1175822411yescharacteristic
915C2×C4#1451982211yescharacteristic
916C2×C4#1451982211yescharacteristic
917C8—2441no—
918C8—2441no—
919C8—2441no—
920C8—2441no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—21no—
926C22—21no—
927C22—21no—
928C22—21no—
929C22—22no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—81no—
939C22—81no—
940C22—84no—
941C22C2×#1451974611yescharacteristic
942C22#1684040611yescharacteristic
943C22#1684040611yescharacteristic
944C4—21no—
945C4—21no—
946C4—22no—
947C4—42no—
948C4—41no—
949C4—41no—
950C4—42no—
951C4—41no—
952C4—41no—
953C4—4881no—
954C4—4881no—
955C4—4881no—
956C4—2442no—
957C4C2×#1451975811yescharacteristic
958C4#1684032111yescharacteristic
959C4#1684040611yescharacteristic
960C4#1684040611yescharacteristic
961C2—21no—
962C2—21no—
963C2—41no—
964C2—41no—
965C2—42no—
966C2—81no—
967C2—81no—
968C2#2144914211yescharacteristic
969C2#2145516811yescharacteristic
970C2#2145518311yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#3489C2
socleC22×C61C2×#120
hypercenter#3489D61
hypocenterC61#24028
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. #21455748C2semidirect
2. #21454338C2semidirect
3. #21450273C2semidirect
4. #21447045C2semidirect
5. #21447040C2semidirect
6. #21447033C2semidirect
7. #21447033C2semidirect
8. #21446288C2semidirect
9. #21446122C2semidirect
10. #21446052C2semidirect
11. #21446045C2semidirect
12. #21445778C2semidirect
13. #21445778C2semidirect
14. #21445763C2semidirect
22. #16839805C22semidirect
23. #16839805C22semidirect
28. C2×#14519704C22semidirect
29. C2×#14519704C22semidirect
36. #16839763C22semidirect
37. #16839763C22semidirect
40. C2×#14519696C22semidirect
41. C2×#14519696C22semidirect
44. #16839669C22semidirect
45. #16839669C22semidirect
47. #16839631C22semidirect
48. #16839627C22semidirect
50. #16839531C22semidirect
51. #16839531C22semidirect
52. #16839521C22semidirect
53. #16839521C22semidirect
556. C61#24028semidirect

Maximal subgroups

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

subgroupindex
#214557482
#214543382
#214502732
#214470452
#214470402
#214470332
#214462882
#214461222
#214460522
#214460452
#214457782
#214457632
C61×#34892
#2402861