Finite Group Databasebeta

← #29655297

Subgroups — #29655297

Order 15616.

1032 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456616C211yesmaximal, characteristic, complemented
2#21456580C211yesmaximal, characteristic, complemented
3#21453821C211yesmaximal, characteristic, complemented
4#21444867C211yesmaximal, characteristic, complemented
5#21444856C211yesmaximal, characteristic, complemented
6#21444850C211yesmaximal, characteristic, complemented
7#21444839C211yesmaximal, characteristic, complemented
8#21444765C211yesmaximal, characteristic, complemented
9#21444754C211yesmaximal, characteristic, complemented
10#21444748C211yesmaximal, characteristic, complemented
11#21444737C211yesmaximal, characteristic, complemented
12#21444387C211yesmaximal, characteristic, complemented
13#21444362C211yesmaximal, characteristic, complemented
14#21444167C211yesmaximal, characteristic, complemented
15C61×#3534C211yesmaximal, characteristic, complemented
16C2×#14519751C2211yescharacteristic, complemented
17#16840095C2211yescharacteristic, complemented
18#16840086—21no—
19#16840080—21no—
20#16840078C2211yescharacteristic
21#16840078C2211yescharacteristic, complemented
22#16840078C2211yescharacteristic, complemented
23#16840013—21no—
24#16840013—21no—
25#16839996—21no—
26#16839993—21no—
27#16839912C2211yescharacteristic, complemented
28#16839907—21no—
29#16839896—21no—
30#16839895C2211yescharacteristic
31#16839895C2211yescharacteristic, complemented
32#16839895C2211yescharacteristic, complemented
33#16839726C2211yescharacteristic, complemented
34C2×C22⋊#92418C2211yescharacteristic, complemented
35#16839701C2211yescharacteristic, complemented
36#16839698C2211yescharacteristic, complemented
37#16839684—21no—
38#16839679C2211yescharacteristic, complemented
39#16839678—21no—
40#16839677—21no—
41#16839671C2211yescharacteristic, complemented
42#16839670—21no—
43#16839622C2211yescharacteristic, complemented
44#16839499C2211yescharacteristic, complemented
45#16839499C2211yescharacteristic, complemented
46#16839496C2211yescharacteristic
47#16839496C2211yescharacteristic
48#16839496C2211yescharacteristic, complemented
49#16839496C2211yescharacteristic, complemented
50#16839496C2211yescharacteristic, complemented
51#16839496C2211yescharacteristic, complemented
52#16839488C2211yescharacteristic, complemented
53#16839488C2211yescharacteristic, complemented
54#16839486C2211yescharacteristic, complemented
55#16839486C2211yescharacteristic, complemented
56C61×#562—21no—
57C61×#560—21no—
58C61×#553—21no—
59C61×#551—21no—
60C61×#546—21no—
61C61×#546—21no—
62C61×#546—21no—
63D42×C61—21no—
64C61×#540—21no—
65C61×#539—21no—
66C61×#539C2211yescharacteristic
67C61×#538—21no—
68C61×#538C2211yescharacteristic
69C61×#537C2211yescharacteristic
70C61×#534—21no—
71C61×#534C2211yescharacteristic
72C61×#525C2211yescharacteristic
73C2×#123×C61C2211yescharacteristic
74C2×#121×C61C2211yescharacteristic
75C22×D244C2311yescharacteristic
76C22×C22⋊D61—21no—
77C22×C22⋊D61—21no—
78C2×#11758201—21no—
79C2×#11758199—21no—
80C2×#11758199—21no—
81C2×#11758199—21no—
82C2×#11758194—21no—
83C22×#92418—21no—
84#14519751—21no—
85#14519751—21no—
86#14519751—21no—
87#14519751—21no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61C2311yescharacteristic
90C2×#11758196—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97#14519710—21no—
98#14519708—21no—
99#14519708—21no—
100#14519708—21no—
101#14519701—21no—
102#14519698—21no—
103#14519698—21no—
104#14519698—21no—
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109C22⋊#92418—21no—
110C22⋊#92418—21no—
111C22⋊#92418C2311yescharacteristic
112C22⋊#92418C2311yescharacteristic
113C22⋊#92418C2311yescharacteristic
114C22⋊#92418C2311yescharacteristic
115#14519684—21no—
116#14519684—21no—
117#14519684C2311yescharacteristic
118#14519684C2311yescharacteristic
119C2×#41×C61—21no—
120C2×#41×C61D411yescharacteristic, complemented
121C22×D4×C61—21no—
122C22×D4×C61—21no—
123C22×D4×C61—21no—
124C22×D4×C61D411yescharacteristic
125C22×D4×C61D411yescharacteristic, complemented
126C23×C4×C61C2311yescharacteristic
127#127×C61—21no—
128#126×C61—21no—
129#126×C61—21no—
130#126×C61—21no—
131#126×C61—21no—
132#125×C61—21no—
133#125×C61—21no—
134#124×C61—21no—
135#124×C61—21no—
136#124×C61—21no—
137#123×C61—21no—
138#123×C61—21no—
139#123×C61—21no—
140#123×C61—21no—
141#123×C61—21no—
142#123×C61—21no—
143#123×C61—21no—
144#123×C61—21no—
145#123×C61—21no—
146#123×C61—21no—
147#123×C61—21no—
148#123×C61—21no—
149#123×C61—21no—
150#123×C61—21no—
151C22⋊Q8×C61—21no—
152C22⋊Q8×C61—21no—
153C22⋊Q8×C61—21no—
154C22⋊Q8×C61—21no—
155C22⋊Q8×C61—21no—
156C22⋊Q8×C61D411yescharacteristic, complemented
157C22⋊Q8×C61C2311yescharacteristic
158#121×C61—21no—
159#121×C61—21no—
160#121×C61—21no—
161#121×C61—21no—
162#121×C61—21no—
163#121×C61—21no—
164#121×C61—21no—
165#121×C61—21no—
166#121×C61—21no—
167#121×C61—21no—
168#121×C61—21no—
169#121×C61—21no—
170#121×C61—21no—
171#121×C61—21no—
172#121×C61—21no—
173#121×C61D411yescharacteristic, complemented
174#121×C61D411yescharacteristic, complemented
175#121×C61D411yescharacteristic, complemented
176#121×C61C2311yescharacteristic
177#121×C61C2311yescharacteristic
178#121×C61C2311yescharacteristic
179#120×C61—21no—
180#120×C61—21no—
181#120×C61—21no—
182#120×C61—21no—
183#120×C61—21no—
184#120×C61—21no—
185#120×C61—21no—
186#120×C61—21no—
187C4×D4×C61—21no—
188C4×D4×C61—21no—
189C4×D4×C61—21no—
190C4×D4×C61—21no—
191C4×D4×C61—21no—
192C4×D4×C61—21no—
193C4×D4×C61—21no—
194C4×D4×C61—21no—
195#117×C61—21no—
196#117×C61D411yescharacteristic, complemented
197C2×C4⋊C4×C61D411yescharacteristic
198C2×C4⋊C4×C61D411yescharacteristic, complemented
199C2×C4⋊C4×C61C2311yescharacteristic
200C2×C22⋊C4×C61—21no—
201C2×C22⋊C4×C61—21no—
202C2×C22⋊C4×C61—21no—
203C2×C22⋊C4×C61D411yescharacteristic
204C2×C22⋊C4×C61D411yescharacteristic
205C2×C22⋊C4×C61C2311yescharacteristic
206C24×C61—21no—
207C24×C61—21no—
208C24×C61C2×D411yescharacteristic
209C24×C61C2×D411yescharacteristic
210C23×D61—21no—
211#41×C61—81no—
212#41×C61—81no—
213#41×C61—81no—
214C2×Q8×C61—21no—
215C2×Q8×C61C2×D411yescharacteristic
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—21no—
224C2×D4×C61—21no—
225C2×D4×C61—21no—
226C2×D4×C61—21no—
227C2×D4×C61—21no—
228C2×D4×C61—21no—
229C2×D4×C61—21no—
230C2×D4×C61—21no—
231C2×D4×C61—21no—
232C2×D4×C61—21no—
233C2×D4×C61—81no—
234C2×D4×C61—81no—
235C2×D4×C61—81no—
236C2×D4×C61—81no—
237C2×D4×C61—81no—
238C2×D4×C61—81no—
239C2×D4×C61—82no—
240C2×D4×C61C2×D411yescharacteristic
241C2×D4×C61C2×D411yescharacteristic
242C2×D4×C61C2×D411yescharacteristic
243C22×C4×C61—21no—
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—81no—
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D411yescharacteristic
253C22×C4×C61C2×D411yescharacteristic
254C22×C4×C61C2×D411yescharacteristic
255C22×C4×C61C2×D411yescharacteristic
256C22×C4×C61C2×D411yescharacteristic
257C22×C4×C61C2×D411yescharacteristic
258C22×C4×C61C2×D411yescharacteristic
259C22×C4×C61C2411yescharacteristic
260C2×C22⋊D61—41no—
261C2×C22⋊D61—41no—
262C2×C22⋊D61—81no—
263C2×C22⋊D61—81no—
264C2×C22⋊D61—81no—
265C2×C22⋊D61—81no—
266C2×C22⋊D61—81no—
267C22×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61—21no—
270C2×D244—21no—
271C2×D244—21no—
272C2×D244—81no—
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×C61C2×D411yescharacteristic
287C4⋊C4×C61C2×D411yescharacteristic
288C4⋊C4×C61C2×D411yescharacteristic
289C4⋊C4×C61C2×D411yescharacteristic
290C22⋊C4×C61—21no—
291C22⋊C4×C61—21no—
292C22⋊C4×C61—21no—
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—
315C42×C61—21no—
316C42×C61—21no—
317C42×C61—21no—
318C22⋊Dic61—81no—
319C22⋊Dic61—81no—
320#11758201—81no—
321#11758199—81no—
322#11758199—81no—
323#11758199—81no—
324#11758198—41no—
325#11758198—41no—
326#11758198—81no—
327#11758198—81no—
328#11758198—81no—
329C4⋊Dic61—21no—
330C4⋊Dic61—21no—
331C4⋊Dic61—81no—
332#11758196—81no—
333#11758194—81no—
334C2×#92418—21no—
335C2×#92418—21no—
336C2×#92418—21no—
337C2×#92418—21no—
338C2×#92418—81no—
339C23×C61—21no—
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—21no—
343C23×C61—21no—
344C23×C61—21no—
345C23×C61—21no—
346C23×C61—21no—
347C23×C61—41no—
348C23×C61—41no—
349C23×C61—42no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61—81no—
353C23×C61—81no—
354C23×C61—81no—
355C23×C61—81no—
356C23×C61—81no—
357C23×C61#12011yescharacteristic
358C23×C61#12011yescharacteristic
359C23×C61C22×D411yescharacteristic
360C22×D61—41no—
361C22×D61—41no—
362C22×D61—41no—
363C22×D61—41no—
364C22×D61—41no—
365C22×D61—41no—
366C22×D61—41no—
367Q8×C61—41no—
368Q8×C61—81no—
369D4×C61—41no—
370D4×C61—41no—
371D4×C61—41no—
372D4×C61—42no—
373D4×C61—42no—
374D4×C61—41no—
375D4×C61—41no—
376D4×C61—41no—
377D4×C61—41no—
378D4×C61—41no—
379D4×C61—41no—
380D4×C61—81no—
381D4×C61—81no—
382D4×C61—81no—
383D4×C61—81no—
384D4×C61—81no—
385D4×C61—81no—
386D4×C61—81no—
387D4×C61—81no—
388D4×C61—81no—
389D4×C61—81no—
390D4×C61—81no—
391D4×C61—81no—
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—41no—
403C2×C4×C61—41no—
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—81no—
411C2×C4×C61—81no—
412C2×C4×C61—81no—
413C2×C4×C61—81no—
414C2×C4×C61—81no—
415C2×C4×C61—81no—
416C2×C4×C61—81no—
417C2×C4×C61#12011yescharacteristic
418C2×C4×C61#12011yescharacteristic
419C2×C4×C61C22×D411yescharacteristic
420C2×C4×C61C22×D411yescharacteristic
421C22⋊D61—82no—
422C22⋊D61—82no—
423C22⋊D61—84no—
424C2×Dic61—41no—
425C2×Dic61—41no—
426C2×Dic61—41no—
427C2×Dic61—41no—
428C2×Dic61—41no—
429C2×Dic61—41no—
430C2×Dic61—41no—
431C2×Dic61—41no—
432C2×Dic61—41no—
433D244—41no—
434D244—41no—
435D244—41no—
436D244—41no—
437#92418—41no—
438#92418—41no—
439#92418—41no—
440#92418—41no—
441#18446—611nomaximal, Sylow
442C22×C61—21no—
443C22×C61—21no—
444C22×C61—21no—
445C22×C61—21no—
446C22×C61—21no—
447C22×C61—21no—
448C22×C61—21no—
449C22×C61—21no—
450C22×C61—41no—
451C22×C61—41no—
452C22×C61—41no—
453C22×C61—41no—
454C22×C61—41no—
455C22×C61—41no—
456C22×C61—41no—
457C22×C61—41no—
458C22×C61—41no—
459C22×C61—41no—
460C22×C61—41no—
461C22×C61—41no—
462C22×C61—81no—
463C22×C61—81no—
464C22×C61—81no—
465C22×C61—81no—
466C22×C61—162no—
467C22×C61—162no—
468C22×C61C2×#12011yescharacteristic
469C22×C61#57611yescharacteristic
470C22×C61#57711yescharacteristic
471C2×D61—81no—
472C2×D61—81no—
473C2×D61—81no—
474C2×D61—81no—
475C2×D61—81no—
476C2×D61—81no—
477C2×D61—81no—
478C4×C61—21no—
479C4×C61—21no—
480C4×C61—21no—
481C4×C61—21no—
482C4×C61—41no—
483C4×C61—41no—
484C4×C61—41no—
485C4×C61—41no—
486C4×C61—41no—
487C4×C61—41no—
488C4×C61—41no—
489C4×C61—41no—
490Dic61—81no—
491Dic61—81no—
492Dic61—81no—
493#3534D6111yescharacteristic, complemented
494#3192—611no—
495#3188—611no—
496#2813—611no—
497#1618—611no—
498#1616—611no—
499#1615—611no—
500#1613—611no—
501#1600—611no—
502#1598—611no—
503#1597—611no—
504#1595—611no—
505#1519—611no—
506#1513—611no—
507#1468—611no—
508C2×C61—21no—
509C2×C61—21no—
510C2×C61—41no—
511C2×C61—41no—
512C2×C61—81no—
513C2×C61—81no—
514C2×C61—81no—
515C2×C61—81no—
516C2×C61#301211yescharacteristic
517C2×C61#302111yescharacteristic
518C2×C61#302611yescharacteristic
519D61—161no—
520#562—21no—
521#560—21no—
522#553—21no—
523#551—21no—
524#546—21no—
525#546—21no—
526#546—21no—
527D42—21no—
528#540—21no—
529#539—21no—
530#539C2×D6111yescharacteristic
531#538—21no—
532#538C2×D6111yescharacteristic
533#537C2×D6111yescharacteristic
534#534—21no—
535#534C2×D6111yescharacteristic
536#525C2×D6111yescharacteristic
537C2×#123C2×D6111yescharacteristic
538C2×#121—611no—
539C2×#121C2×D6111yescharacteristic
540#484—611no—
541#482—1221no—
542#481—611no—
543#481—611no—
544#481—611no—
545#481—1221no—
546#469—1221no—
547#469—1221no—
548#466—1221no—
549#465—1221no—
550#450—611no—
551#449—1221no—
552#447—611no—
553#447—611no—
554#447—611no—
555#447—1221no—
556#407—611no—
557C2×C22⋊C8—611no—
558#400—611no—
559#399—611no—
560#396—1221no—
561#394—611no—
562#394—1221no—
563#394—1221no—
564#392—611no—
565#392—1221no—
566#380—611no—
567#328—611no—
568#328—611no—
569#327—611no—
570#327—611no—
571#327—611no—
572#327—611no—
573#327—611no—
574#327—611no—
575#324—611no—
576#324—611no—
577#323—611no—
578#323—611no—
579C61#1844611yescharacteristic, complemented, Sylow
580C2×#41—21no—
581C2×#41C22⋊D6111yescharacteristic, complemented
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—611no—
586C22×D4—1221no—
587C22×D4—1221no—
588C22×D4C22⋊D6111yescharacteristic
589C22×D4C22⋊D6111yescharacteristic, complemented
590C23×C4C22×D6111yescharacteristic
591C2×SD16—1221no—
592C2×D8—1221no—
593C2×D8—1221no—
594C2×D8—1221no—
595C2×M16—1221no—
596C22×C8—1221no—
597#127—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#123—21no—
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620#123—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8C22⋊D6111yescharacteristic, complemented
627C22⋊Q8C22×D6111yescharacteristic
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—1221no—
644#121—1221no—
645#121—1221no—
646#121—1221no—
647#121C22⋊D6111yescharacteristic, complemented
648#121C22⋊D6111yescharacteristic, complemented
649#121C22⋊D6111yescharacteristic, complemented
650#121C22×D6111yescharacteristic
651#121C22×D6111yescharacteristic
652#121C22×D6111yescharacteristic
653#120—21no—
654#120—21no—
655#120—21no—
656#120—21no—
657#120—21no—
658#120—21no—
659#120—21no—
660#120—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669#117—21no—
670#117C22⋊D6111yescharacteristic, complemented
671C2×C4⋊C4—611no—
672C2×C4⋊C4—1221no—
673C2×C4⋊C4—1221no—
674C2×C4⋊C4C22⋊D6111yescharacteristic
675C2×C4⋊C4C22⋊D6111yescharacteristic, complemented
676C2×C4⋊C4C22×D6111yescharacteristic
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—1221no—
681C2×C22⋊C4—1221no—
682C2×C22⋊C4—1221no—
683C2×C22⋊C4—1221no—
684C2×C22⋊C4—1221no—
685C2×C22⋊C4—1221no—
686C2×C22⋊C4C22⋊D6111yescharacteristic
687C2×C22⋊C4C22⋊D6111yescharacteristic
688C2×C22⋊C4C22×D6111yescharacteristic
689#107—1221no—
690#106—1221no—
691#106—1221no—
692#106—1221no—
693#103—1221no—
694#102—1221no—
695#102—1221no—
696#102—1221no—
697#102—1221no—
698#102—1221no—
699#102—1221no—
700#102—1221no—
701C22⋊C8—611no—
702C22⋊C8—611no—
703C22⋊C8—611no—
704C22⋊C8—611no—
705C22⋊C8—1221no—
706C22⋊C8—1221no—
707#95—611no—
708#95—611no—
709#95—1221no—
710#95—1221no—
711C24—21no—
712C24—21no—
713C24—1221no—
714C24C2×C22⋊D6111yescharacteristic
715C24C2×C22⋊D6111yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C2×C22⋊D6111yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
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—21no—
737C2×D4—21no—
738C2×D4—81no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4—81no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—82no—
745C2×D4—1221no—
746C2×D4—1221no—
747C2×D4—4881no—
748C2×D4—4881no—
749C2×D4—4881no—
750C2×D4—4881no—
751C2×D4—4881no—
752C2×D4—4881no—
753C2×D4—2441no—
754C2×D4—2441no—
755C2×D4C2×C22⋊D6111yescharacteristic
756C2×D4C2×C22⋊D6111yescharacteristic
757C2×D4C2×C22⋊D6111yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—81no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4C2×C22⋊D6111yescharacteristic
770C22×C4C2×C22⋊D6111yescharacteristic
771C22×C4C2×C22⋊D6111yescharacteristic
772C22×C4C2×C22⋊D6111yescharacteristic
773C22×C4C2×C22⋊D6111yescharacteristic
774C22×C4C2×C22⋊D6111yescharacteristic
775C22×C4C2×C22⋊D6111yescharacteristic
776C22×C4C2×C22⋊D6111yescharacteristic
777C22×C4C23×D6111yescharacteristic
778SD16—4881no—
779D8—4881no—
780D8—4881no—
781D8—4881no—
782M16—4881no—
783C2×C8—1221no—
784C2×C8—1221no—
785C2×C8—1221no—
786C2×C8—1221no—
787C2×C8—4881no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—1221no—
802C4⋊C4—1221no—
803C4⋊C4—4881no—
804C4⋊C4—4881no—
805C4⋊C4C2×C22⋊D6111yescharacteristic
806C4⋊C4C2×C22⋊D6111yescharacteristic
807C4⋊C4C2×C22⋊D6111yescharacteristic
808C4⋊C4C2×C22⋊D6111yescharacteristic
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—4881no—
835C22⋊C4—4881no—
836C22⋊C4—4881no—
837C22⋊C4—4881no—
838C22⋊C4—4881no—
839C22⋊C4—2441no—
840C22⋊C4—2441no—
841C42—21no—
842C42—21no—
843C42—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—81no—
858C23—81no—
859C23—81no—
860C23—81no—
861C23—81no—
862C23—2441no—
863C23—2441no—
864C23—2441no—
865C23—2441no—
866C23—2441no—
867C23—2441no—
868C23—2441no—
869C23#1451974611yescharacteristic
870C23#1451974611yescharacteristic
871C23C22×C22⋊D6111yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—42no—
878D4—42no—
879D4—41no—
880D4—41no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—81no—
886D4—81no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—4882no—
898D4—4882no—
899D4—4884no—
900D4—2441no—
901D4—2441no—
902D4—2441no—
903D4—2441no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—81no—
923C2×C4—81no—
924C2×C4—81no—
925C2×C4—81no—
926C2×C4—81no—
927C2×C4—81no—
928C2×C4—81no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4#1451974611yescharacteristic
939C2×C4#1451974611yescharacteristic
940C2×C4C22×C22⋊D6111yescharacteristic
941C2×C4C22×C22⋊D6111yescharacteristic
942C8—2441no—
943C8—2441no—
944C8—2441no—
945C8—2441no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—162no—
971C22—162no—
972C22—4881no—
973C22—4881no—
974C22—4881no—
975C22—4881no—
976C22—4881no—
977C22—4881no—
978C22—4881no—
979C22C2×#1451974611yescharacteristic
980C22#1684056511yescharacteristic
981C22#1684057311yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—41no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—4881no—
995C4—4881no—
996C4—4881no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—9761no—
1006C2#2145512311yescharacteristic
1007C2#2145519111yescharacteristic
1008C2#2145521611yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#3534C2
socleC22×C61C2×#120
hypercenter#3534D61
hypocenterC61#18446
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3534

Complements

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

NH ≅ G/Ntype
1. #21456616C2semidirect
2. #21456580C2semidirect
3. #21453821C2semidirect
4. #21444867C2semidirect
5. #21444856C2semidirect
6. #21444850C2semidirect
7. #21444839C2semidirect
8. #21444765C2semidirect
9. #21444754C2semidirect
10. #21444748C2semidirect
11. #21444737C2semidirect
12. #21444387C2semidirect
13. #21444362C2semidirect
14. #21444167C2semidirect
15. C61×#3534C2semidirect
16. C2×#14519751C22semidirect
17. #16840095C22semidirect
21. #16840078C22semidirect
22. #16840078C22semidirect
27. #16839912C22semidirect
31. #16839895C22semidirect
32. #16839895C22semidirect
33. #16839726C22semidirect
34. C2×C22⋊#92418C22semidirect
35. #16839701C22semidirect
36. #16839698C22semidirect
38. #16839679C22semidirect
41. #16839671C22semidirect
43. #16839622C22semidirect
44. #16839499C22semidirect
45. #16839499C22semidirect
48. #16839496C22semidirect
49. #16839496C22semidirect
50. #16839496C22semidirect
51. #16839496C22semidirect
52. #16839488C22semidirect
53. #16839488C22semidirect
54. #16839486C22semidirect
55. #16839486C22semidirect
120. C2×#41×C61D4semidirect
125. C22×D4×C61D4semidirect
156. C22⋊Q8×C61D4semidirect
173. #121×C61D4semidirect
174. #121×C61D4semidirect
175. #121×C61D4semidirect
196. #117×C61D4semidirect
198. C2×C4⋊C4×C61D4semidirect
493. #3534D61semidirect
579. C61#18446semidirect
581. C2×#41C22⋊D61semidirect
589. C22×D4C22⋊D61semidirect
626. C22⋊Q8C22⋊D61semidirect
647. #121C22⋊D61semidirect
648. #121C22⋊D61semidirect
649. #121C22⋊D61semidirect
670. #117C22⋊D61semidirect
675. C2×C4⋊C4C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214566162
#214565802
#214538212
#214448672
#214448562
#214448502
#214448392
#214447652
#214447542
#214447482
#214447372
#214443872
#214443622
#214441672
C61×#35342
#1844661