Finite Group Databasebeta

← #29646228

Subgroups — #29646228

Order 15616.

1008 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840463C211yesmaximal, characteristic
2#21454478C211yesmaximal, characteristic, complemented
3#21454472C211yesmaximal, characteristic, complemented
4#21444188C211yesmaximal, characteristic, complemented
5#21444187C211yesmaximal, characteristic, complemented
6#21444187C211yesmaximal, characteristic, complemented
7#21444177C211yesmaximal, characteristic, complemented
8#21444177C211yesmaximal, characteristic, complemented
9#21444159C211yesmaximal, characteristic, complemented
10#21444158C211yesmaximal, characteristic, complemented
11#21444156C211yesmaximal, characteristic, complemented
12#21444139C211yesmaximal, characteristic, complemented
13#21444138C211yesmaximal, characteristic, complemented
14#21444136C211yesmaximal, characteristic, complemented
15C61×#1473C211yesmaximal, characteristic, complemented
16#16840463—21no—
17#16840463—21no—
18#16840463—21no—
19#16840463—21no—
20#16840463—21no—
21#16840463—21no—
22#16840463—21no—
23#16840463—21no—
24C2×#14519772C2211yescharacteristic
25C2×#14519767C411yescharacteristic
26C2×#14519762C411yescharacteristic
27C2×#14519761C411yescharacteristic
28C2×#14519752C411yescharacteristic
29C2×#14519750C411yescharacteristic
30C2×#14519750C411yescharacteristic
31C2×#14519750C2211yescharacteristic
32C2×C4×D244C2211yescharacteristic
33C2×#14519739C2211yescharacteristic
34C2×#14519737C411yescharacteristic
35C2×#14519737C2211yescharacteristic
36C2×#14519734C2211yescharacteristic
37C2×C4⋊C4×D61C411yescharacteristic
38#16839824—21no—
39#16839822—21no—
40#16839822—21no—
41#16839821—21no—
42#16839819C2211yescharacteristic
43#16839816C2211yescharacteristic
44#16839816C2211yescharacteristic
45#16839815C2211yescharacteristic
46#16839812C2211yescharacteristic
47#16839812C2211yescharacteristic
48#16839787—21no—
49#16839787—21no—
50#16839724C2211yescharacteristic
51#16839724C2211yescharacteristic
52C22⋊C8×D61C2211yescharacteristic
53C22⋊C8×D61C2211yescharacteristic
54#16839719—21no—
55#16839716—21no—
56#16839488C2211yescharacteristic
57#16839488C2211yescharacteristic
58#16839486C2211yescharacteristic
59#16839486C2211yescharacteristic
60#16839485C2211yescharacteristic
61#16839485C2211yescharacteristic
62#16839485C2211yescharacteristic
63#16839485C2211yescharacteristic
64#16839485C2211yescharacteristic
65#16839485C2211yescharacteristic
66#16839485C2211yescharacteristic
67#16839485C2211yescharacteristic
68C2×#126×C61C2211yescharacteristic
69C61×#432C2211yescharacteristic
70C61×#431C2211yescharacteristic
71C61×#324C2211yescharacteristic
72C61×#324C2211yescharacteristic
73C61×#323C2211yescharacteristic
74C61×#323C2211yescharacteristic
75C22×D244C2×C411yescharacteristic
76C22×D244C2×C411yescharacteristic
77C22×D244C2×C411yescharacteristic
78C22×C22⋊D61C2×C411yescharacteristic
79C22×C22⋊D61C2×C411yescharacteristic
80C22×C22⋊D61C2×C411yescharacteristic
81C23×Dic61C2×C411yescharacteristic
82C22×C4×D61C2×C411yescharacteristic
83C22×C4×D61C2×C411yescharacteristic
84C22×C4×D61C2×C411yescharacteristic
85C22×C4×D61C2×C411yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C2×#11758189—21no—
88C2×#11758189—21no—
89C2×C8×D61—21no—
90C2×C8×D61—21no—
91#14519772—21no—
92#14519772—21no—
93#14519772—21no—
94#14519772—21no—
95#14519767—21no—
96#14519767—21no—
97#14519767—21no—
98#14519767—21no—
99#14519762—21no—
100#14519762—21no—
101#14519762—21no—
102#14519762—21no—
103#14519761—21no—
104#14519761—21no—
105#14519761—21no—
106#14519761—21no—
107#14519752—21no—
108#14519752—21no—
109#14519752—21no—
110#14519752—21no—
111#14519750—21no—
112#14519750—21no—
113#14519750—21no—
114#14519750—21no—
115#14519750—21no—
116#14519750—21no—
117#14519750—21no—
118#14519750—21no—
119#14519750—21no—
120#14519750—21no—
121#14519750—21no—
122#14519750—21no—
123C4×D244—21no—
124C4×D244—21no—
125C4×D244—21no—
126C4×D244—21no—
127#14519739—21no—
128#14519739—21no—
129#14519739—21no—
130#14519739—21no—
131#14519737—21no—
132#14519737—21no—
133#14519737—21no—
134#14519737—21no—
135#14519737—21no—
136#14519737—21no—
137#14519737—21no—
138#14519737—21no—
139#14519734D411yescharacteristic
140#14519734D411yescharacteristic
141#14519734D411yescharacteristic
142#14519734D411yescharacteristic
143#14519734D411yescharacteristic
144#14519734D411yescharacteristic
145#14519734D411yescharacteristic
146#14519734D411yescharacteristic
147C2×C4⋊Dic61C2×C411yescharacteristic
148C2×C4⋊Dic61C2×C411yescharacteristic
149C2×#11758196C2×C411yescharacteristic
150C2×#11758196C2×C411yescharacteristic
151C2×#11758196C2×C411yescharacteristic
152C2×#11758196C2×C411yescharacteristic
153C2×#11758196C2×C411yescharacteristic
154C4⋊C4×D61—21no—
155C4⋊C4×D61—21no—
156C4⋊C4×D61—21no—
157C4⋊C4×D61—21no—
158C2×#11758198C2×C411yescharacteristic
159C2×#11758198C2×C411yescharacteristic
160C2×#11758198C2×C411yescharacteristic
161C2×#11758198C2×C411yescharacteristic
162C2×#11758198C2×C411yescharacteristic
163C2×#11758198C2311yescharacteristic
164C2×#11758198C2311yescharacteristic
165C2×C4×Dic61C2×C411yescharacteristic
166C2×C4×Dic61C2311yescharacteristic
167C4⋊#92418—21no—
168C4⋊#92418—21no—
169#14519706—21no—
170#14519706—21no—
171#14519706—21no—
172#14519706—21no—
173C22⋊#92418C2311yescharacteristic
174C22⋊#92418C2311yescharacteristic
175C22⋊#92418C2311yescharacteristic
176C22⋊#92418C2311yescharacteristic
177#14519689—21no—
178#14519689—21no—
179#14519689—21no—
180#14519689—21no—
181#14519688—21no—
182#14519687—21no—
183#14519687—21no—
184C4×#92418—21no—
185C8×Dic61—21no—
186C8×Dic61—21no—
187#126×C61—21no—
188#126×C61—21no—
189#126×C61—21no—
190#126×C61—21no—
191C2×C4⋊C4×C61C2×C411yescharacteristic
192C2×C4⋊C4×C61C2×C411yescharacteristic
193C2×C4⋊C4×C61C2311yescharacteristic
194C2×C22⋊C4×C61C2×C411yescharacteristic
195C2×C22⋊C4×C61C2×C411yescharacteristic
196C2×C22⋊C4×C61C2311yescharacteristic
197C2×C42×C61C2311yescharacteristic
198C4⋊C8×C61—21no—
199C4⋊C8×C61—21no—
200C22⋊C8×C61C2311yescharacteristic
201C22⋊C8×C61C2311yescharacteristic
202C22⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61C2311yescharacteristic
204#97×C61—21no—
205C4×C8×C61—21no—
206C24×C61C22×C411yescharacteristic
207C23×D61C22×C411yescharacteristic
208C23×D61C22×C411yescharacteristic
209C23×D61C22×C411yescharacteristic
210C22×C4×C61C22×C411yescharacteristic
211C22×C4×C61C22×C411yescharacteristic
212C22×C4×C61C22×C411yescharacteristic
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C22×C411yescharacteristic
215C22×C4×C61C2411yescharacteristic
216C2×C22⋊D61—22no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—41no—
224C2×C22⋊D61—42no—
225C2×C22⋊D61—81no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—81no—
229C22×Dic61C22×C411yescharacteristic
230C22×Dic61C22×C411yescharacteristic
231C22×Dic61C22×C411yescharacteristic
232C22×Dic61C22×C411yescharacteristic
233C22×Dic61C22×C411yescharacteristic
234C2×D244—21no—
235C2×D244—21no—
236C2×D244—22no—
237C2×D244—22no—
238C2×D244—21no—
239C2×D244—21no—
240C2×D244—21no—
241C2×D244—21no—
242C2×D244—41no—
243C2×D244—41no—
244C2×D244—81no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—42no—
254C2×C4×D61—42no—
255C2×C4×D61—81no—
256C2×C4×D61—81no—
257C2×C4×D61—81no—
258C2×C4×D61C2×D411yescharacteristic
259C2×C4×D61C2×D411yescharacteristic
260C2×C4×D61C2×D411yescharacteristic
261C2×C4×D61C2×D411yescharacteristic
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C22⋊C4×C61—21no—
277C22⋊C4×C61—21no—
278C42×C61C2×D411yescharacteristic
279C42×C61C2×D411yescharacteristic
280C42×C61C2×D411yescharacteristic
281C42×C61C2×D411yescharacteristic
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198C22⋊C411yescharacteristic
293#11758198C22⋊C411yescharacteristic
294#11758198C22⋊C411yescharacteristic
295#11758198C22⋊C411yescharacteristic
296#11758198C22⋊C411yescharacteristic
297#11758198C22⋊C411yescharacteristic
298#11758198C22⋊C411yescharacteristic
299#11758198C22⋊C411yescharacteristic
300C4⋊Dic61—21no—
301C4⋊Dic61—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196C22⋊C411yescharacteristic
311#11758196C22⋊C411yescharacteristic
312#11758196C22⋊C411yescharacteristic
313#11758196C22⋊C411yescharacteristic
314#11758196C22⋊C411yescharacteristic
315#11758196C22⋊C411yescharacteristic
316#11758196C22⋊C411yescharacteristic
317#11758196C22⋊C411yescharacteristic
318C4×Dic61—21no—
319C4×Dic61—21no—
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C2×#92418—21no—
325C2×#92418—21no—
326C2×#92418—21no—
327C2×#92418—21no—
328#11758189—42no—
329#11758189—42no—
330C8×D61—42no—
331C8×D61—42no—
332C23×C61—21no—
333C23×C61—21no—
334C23×C61—21no—
335C23×C61—41no—
336C23×C61—41no—
337C23×C61C23×C411yescharacteristic
338C22×D61—21no—
339C22×D61—21no—
340C22×D61—21no—
341C22×D61—21no—
342C22×D61—21no—
343C22×D61—21no—
344C22×D61—21no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61C2×C22⋊C411yescharacteristic
352C22×D61C2×C22⋊C411yescharacteristic
353C22×D61#13112yes—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61C2×C22⋊C411yescharacteristic
366C2×C4×C61C2×C22⋊C411yescharacteristic
367C2×C4×C61C2×C22⋊C411yescharacteristic
368C2×C4×C61C2×C22⋊C411yescharacteristic
369C2×C4×C61C22×D411yescharacteristic
370C2×C4×C61C22×D411yescharacteristic
371C22⋊D61—42no—
372C22⋊D61—42no—
373C22⋊D61—42no—
374C22⋊D61—42no—
375C22⋊D61—81no—
376C22⋊D61—81no—
377C2×Dic61—21no—
378C2×Dic61—21no—
379C2×Dic61—22no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—81no—
386C2×Dic61—81no—
387C2×Dic61C2×C22⋊C411yescharacteristic
388C2×Dic61C2×C22⋊C411yescharacteristic
389C2×Dic61C2×C22⋊C411yescharacteristic
390C2×Dic61C2×C22⋊C411yescharacteristic
391C2×Dic61C2×C22⋊C411yescharacteristic
392C2×Dic61C2×C22⋊C411yescharacteristic
393D244—42no—
394D244—42no—
395D244—42no—
396D244—42no—
397D244—81no—
398D244—81no—
399C4×D61—22no—
400C4×D61—22no—
401C4×D61—41no—
402C4×D61—41no—
403C4×D61—42no—
404C4×D61—42no—
405C4×D61—81no—
406C4×D61—81no—
407C4×D61—81no—
408C4×D61—81no—
409C4×D61—81no—
410C4×D61—81no—
411C8×C61—41no—
412C8×C61—41no—
413C8×C61—41no—
414C8×C61—41no—
415#92418—41no—
416#92418—41no—
417#92418—41no—
418#92418—41no—
419#17415—611nomaximal, Sylow
420C22×C61—21no—
421C22×C61—21no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—81no—
426C22×C61—81no—
427C22×C61C22×C22⋊C411yescharacteristic
428C22×C61C2×#13111yescharacteristic
429C22×C61#56811yescharacteristic
430C2×D61—22no—
431C2×D61—21no—
432C2×D61—21no—
433C2×D61—21no—
434C2×D61—21no—
435C2×D61—21no—
436C2×D61—21no—
437C2×D61—42no—
438C2×D61—41no—
439C2×D61—41no—
440C2×D61—42no—
441C2×D61—41no—
442C2×D61—41no—
443C2×D61—41no—
444C2×D61—81no—
445C2×D61—81no—
446C2×D61—81no—
447C2×D61—81no—
448C4×C61—21no—
449C4×C61—21no—
450C4×C61—21no—
451C4×C61—21no—
452C4×C61—21no—
453C4×C61—21no—
454C4×C61—41no—
455C4×C61—41no—
456C4×C61—41no—
457Dic61—21no—
458Dic61—21no—
459Dic61—21no—
460Dic61—21no—
461Dic61—21no—
462Dic61—41no—
463Dic61—41no—
464Dic61#41012yes—
465C2×#553—611no—
466#2924—611no—
467#2924—611no—
468#1473—611no—
469#1473—611no—
470#1473—611no—
471#1473D6111yescharacteristic, complemented
472#1471—611no—
473#1471—611no—
474#1466—611no—
475#1466—611no—
476#1465—611no—
477#1460—611no—
478#1460—611no—
479#1459—611no—
480C2×C61—21no—
481C2×C61—21no—
482C2×C61—81no—
483C2×C61#288011yescharacteristic
484C2×C61C2×#41011yescharacteristic
485C2×C61#288811yescharacteristic
486D61—41no—
487D61—41no—
488D61—42no—
489D61—81no—
490#553—1221no—
491#553—1221no—
492#553—1221no—
493#553—1221no—
494#553—1221no—
495#553—1221no—
496#553—1221no—
497#553—1221no—
498C2×#126—611no—
499C2×#126C2×D6111yescharacteristic
500C2×#125—611no—
501C2×#123—611no—
502C2×#123—611no—
503C2×#121—611no—
504C2×#121—611no—
505C2×#121—611no—
506C2×#121—611no—
507C2×C4×D4—611no—
508C2×C4×D4—611no—
509C2×C4×D4—611no—
510C2×C4×D4—611no—
511C2×#117—611no—
512C22×C4⋊C4—611no—
513#433—1221no—
514#433—1221no—
515#433—1221no—
516#433—1221no—
517#432—611no—
518#432—611no—
519#432—611no—
520#432C2×D6111yescharacteristic
521#431—611no—
522#431—611no—
523#431—611no—
524#431C2×D6111yescharacteristic
525#424—1221no—
526#424—1221no—
527#407—611no—
528#407—611no—
529C2×C22⋊C8—611no—
530C2×C22⋊C8—611no—
531#405—1221no—
532#405—1221no—
533#324—611no—
534#324—611no—
535#324C2×D6111yescharacteristic
536#324C2×D6111yescharacteristic
537#323—611no—
538#323—611no—
539#323—611no—
540#323—611no—
541#323—611no—
542#323—611no—
543#323—611no—
544#323—611no—
545#323—611no—
546#323—611no—
547#323C2×D6111yescharacteristic
548#323C2×D6111yescharacteristic
549C61#1741511yescharacteristic, complemented, Sylow
550C22×D4—611no—
551C22×D4—611no—
552C22×D4—611no—
553C22×D4—611no—
554C22×D4—611no—
555C22×D4—611no—
556C23×C4—611no—
557C23×C4—611no—
558C23×C4—611no—
559C23×C4—611no—
560C23×C4—611no—
561C23×C4—611no—
562C2×M16—1221no—
563C2×M16—1221no—
564C22×C8—1221no—
565C22×C8—1221no—
566#126—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—1221no—
571#126—1221no—
572#126—1221no—
573#126—1221no—
574#125—1221no—
575#125—1221no—
576#125—1221no—
577#125—1221no—
578#123—1221no—
579#123—1221no—
580#123—1221no—
581#123—1221no—
582#123—1221no—
583#123—1221no—
584#123—1221no—
585#123—1221no—
586#121—1221no—
587#121—1221no—
588#121—1221no—
589#121—1221no—
590#121—1221no—
591#121—1221no—
592#121—1221no—
593#121—1221no—
594#121—1221no—
595#121—1221no—
596#121—1221no—
597#121—1221no—
598#121—1221no—
599#121—1221no—
600#121—1221no—
601#121—1221no—
602C4×D4—1221no—
603C4×D4—1221no—
604C4×D4—1221no—
605C4×D4—1221no—
606C4×D4—1221no—
607C4×D4—1221no—
608C4×D4—1221no—
609C4×D4—1221no—
610C4×D4—1221no—
611C4×D4—1221no—
612C4×D4—1221no—
613C4×D4—1221no—
614C4×D4—1221no—
615C4×D4—1221no—
616C4×D4—1221no—
617C4×D4—1221no—
618#117—611no—
619#117—611no—
620#117—611no—
621#117—611no—
622#117—611no—
623#117—611no—
624#117—611no—
625#117—611no—
626C2×C4⋊C4—611no—
627C2×C4⋊C4—611no—
628C2×C4⋊C4—611no—
629C2×C4⋊C4—611no—
630C2×C4⋊C4—611no—
631C2×C4⋊C4—611no—
632C2×C4⋊C4—611no—
633C2×C4⋊C4—1221no—
634C2×C4⋊C4—1221no—
635C2×C4⋊C4—1221no—
636C2×C4⋊C4—1221no—
637C2×C4⋊C4C4×D6111yescharacteristic
638C2×C4⋊C4C4×D6111yescharacteristic
639C2×C4⋊C4C22×D6111yescharacteristic
640C2×C22⋊C4—611no—
641C2×C22⋊C4—611no—
642C2×C22⋊C4—611no—
643C2×C22⋊C4—611no—
644C2×C22⋊C4—611no—
645C2×C22⋊C4—611no—
646C2×C22⋊C4—611no—
647C2×C22⋊C4C4×D6111yescharacteristic
648C2×C22⋊C4C4×D6111yescharacteristic
649C2×C22⋊C4C22×D6111yescharacteristic
650C2×C42—611no—
651C2×C42—611no—
652C2×C42C22×D6111yescharacteristic
653C4⋊C8—21no—
654C4⋊C8—21no—
655C4⋊C8—1221no—
656C4⋊C8—1221no—
657C4⋊C8—1221no—
658C4⋊C8—1221no—
659C4⋊C8—1221no—
660C4⋊C8—1221no—
661C22⋊C8—611no—
662C22⋊C8—611no—
663C22⋊C8—611no—
664C22⋊C8—611no—
665C22⋊C8—1221no—
666C22⋊C8—1221no—
667C22⋊C8—1221no—
668C22⋊C8—1221no—
669C22⋊C8C22×D6111yescharacteristic
670C22⋊C8C22×D6111yescharacteristic
671C22⋊C8C22×D6111yescharacteristic
672C22⋊C8C22×D6111yescharacteristic
673#97—21no—
674#97—1221no—
675#97—1221no—
676#97—1221no—
677C4×C8—21no—
678C4×C8—1221no—
679C4×C8—1221no—
680C4×C8—1221no—
681C24—611no—
682C24—611no—
683C24—611no—
684C24C2×C4×D6111yescharacteristic
685C2×D4—1221no—
686C2×D4—1221no—
687C2×D4—1221no—
688C2×D4—1221no—
689C2×D4—1222no—
690C2×D4—1222no—
691C2×D4—1221no—
692C2×D4—1221no—
693C2×D4—1221no—
694C2×D4—1221no—
695C2×D4—1221no—
696C2×D4—1221no—
697C2×D4—1222no—
698C2×D4—1221no—
699C2×D4—1221no—
700C2×D4—4881no—
701C2×D4—4881no—
702C2×D4—2441no—
703C2×D4—2441no—
704C2×D4—2441no—
705C2×D4—2442no—
706C22×C4—611no—
707C22×C4—611no—
708C22×C4—611no—
709C22×C4—611no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—4881no—
726C22×C4—4881no—
727C22×C4—4881no—
728C22×C4—4881no—
729C22×C4—2442no—
730C22×C4—2442no—
731C22×C4C2×C4×D6111yescharacteristic
732C22×C4C2×C4×D6111yescharacteristic
733C22×C4C2×C4×D6111yescharacteristic
734C22×C4C2×C4×D6111yescharacteristic
735C22×C4C2×C4×D6111yescharacteristic
736C22×C4C23×D6111yescharacteristic
737M16—2442no—
738M16—2442no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—1221no—
744C2×C8—1221no—
745C2×C8—1221no—
746C2×C8—1221no—
747C2×C8—2442no—
748C2×C8—2442no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—611no—
756C4⋊C4—611no—
757C4⋊C4—611no—
758C4⋊C4—611no—
759C4⋊C4—611no—
760C4⋊C4—611no—
761C4⋊C4—611no—
762C4⋊C4—611no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
766C4⋊C4—1221no—
767C4⋊C4—1221no—
768C4⋊C4—1221no—
769C4⋊C4—1221no—
770C4⋊C4—1221no—
771C4⋊C4—1221no—
772C4⋊C4—1221no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—611no—
780C22⋊C4—611no—
781C22⋊C4—611no—
782C22⋊C4—611no—
783C22⋊C4—611no—
784C22⋊C4—611no—
785C22⋊C4—611no—
786C22⋊C4—611no—
787C22⋊C4—1221no—
788C22⋊C4—1221no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C22⋊C4—1221no—
793C22⋊C4—1221no—
794C22⋊C4—1221no—
795C22⋊C4—1221no—
796C22⋊C4—1221no—
797C42—611no—
798C42—611no—
799C42—611no—
800C42—611no—
801C42—1221no—
802C42—1221no—
803C42D4×D6111yescharacteristic
804C42D4×D6111yescharacteristic
805C42D4×D6111yescharacteristic
806C42D4×D6111yescharacteristic
807C23—21no—
808C23—21no—
809C23—21no—
810C23—41no—
811C23—41no—
812C23—611no—
813C23—611no—
814C23—612no—
815C23—1221no—
816C23—1221no—
817C23—1221no—
818C23—1221no—
819C23—1221no—
820C23—1221no—
821C23—1221no—
822C23—2441no—
823C23—2441no—
824C23—2441no—
825C23—2441no—
826C23—2441no—
827C23—2441no—
828C23C22×C4×D6111yescharacteristic
829D4—4881no—
830D4—4881no—
831D4—4881no—
832D4—4881no—
833D4—2442no—
834D4—2442no—
835D4—2442no—
836D4—2442no—
837D4—2442no—
838D4—2442no—
839D4—2442no—
840D4—2442no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—611no—
853C2×C4—611no—
854C2×C4—611no—
855C2×C4—611no—
856C2×C4—611no—
857C2×C4—611no—
858C2×C4—1222no—
859C2×C4—1222no—
860C2×C4—1222no—
861C2×C4—1221no—
862C2×C4—1221no—
863C2×C4—1221no—
864C2×C4—1221no—
865C2×C4—4881no—
866C2×C4—4881no—
867C2×C4—4881no—
868C2×C4—4881no—
869C2×C4—4881no—
870C2×C4—4881no—
871C2×C4—4881no—
872C2×C4—4881no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2442no—
876C2×C4—2442no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4C22⋊C4×D6111yescharacteristic
881C2×C4C22⋊C4×D6111yescharacteristic
882C2×C4C22⋊C4×D6111yescharacteristic
883C2×C4C22⋊C4×D6111yescharacteristic
884C2×C4C2×D4×D6111yescharacteristic
885C2×C4C2×D4×D6111yescharacteristic
886C8—41no—
887C8—41no—
888C8—41no—
889C8—41no—
890C8—2441no—
891C8—2441no—
892C8—2441no—
893C8—2441no—
894C22—21no—
895C22—21no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—81no—
900C22—81no—
901C22—1222no—
902C22—1221no—
903C22—1221no—
904C22—1221no—
905C22—1221no—
906C22—1221no—
907C22—1221no—
908C22—4881no—
909C22—4881no—
910C22—4881no—
911C22—4881no—
912C22—2442no—
913C22—2442no—
914C22—2441no—
915C22—2441no—
916C22—2441no—
917C22—2441no—
918C22—2441no—
919C22C2×C22⋊C4×D6111yescharacteristic
920C22#131×D6111yescharacteristic
921C22#1684052711yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—612no—
932C4—1221no—
933C4—1221no—
934C4—1221no—
935C4—1221no—
936C4—1221no—
937C4—2441no—
938C4—2441no—
939C2—21no—
940C2—21no—
941C2—81no—
942C2—4881no—
943C2—2441no—
944C2—2441no—
945C2—2442no—
946C2#2145426711yescharacteristic
947C2#410×D6111yescharacteristic
948C2#2145429611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1473C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840463C2
cosocleC22×C4×C61C24
hypercenter#1473D61
hypocenterC61#17415
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1473

Complements

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

NH ≅ G/Ntype
2. #21454478C2semidirect
3. #21454472C2semidirect
4. #21444188C2semidirect
5. #21444187C2semidirect
6. #21444187C2semidirect
7. #21444177C2semidirect
8. #21444177C2semidirect
9. #21444159C2semidirect
10. #21444158C2semidirect
11. #21444156C2semidirect
12. #21444139C2semidirect
13. #21444138C2semidirect
14. #21444136C2semidirect
15. C61×#1473C2semidirect
471. #1473D61semidirect
549. C61#17415semidirect

Maximal subgroups

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

subgroupindex
C2×#168404632
#214544782
#214544722
#214441882
#214441872
#214441772
#214441592
#214441582
#214441562
#214441392
#214441382
#214441362
C61×#14732
#1741561