Finite Group Databasebeta

← #29646325

Subgroups — #29646325

Order 15616.

1022 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
1C2×#16840463C211yesmaximal, characteristic
2#21454856C211yesmaximal, characteristic, complemented
3#21454853C211yesmaximal, characteristic, complemented
4#21444188C211yesmaximal, characteristic, complemented
5#21444177C211yesmaximal, characteristic, complemented
6#21444177C211yesmaximal, characteristic, complemented
7#21444166C211yesmaximal, characteristic, complemented
8#21444166C211yesmaximal, characteristic, complemented
9#21444154C211yesmaximal, characteristic, complemented
10#21444151C211yesmaximal, characteristic, complemented
11#21444147C211yesmaximal, characteristic, complemented
12#21444134C211yesmaximal, characteristic, complemented
13#21444131C211yesmaximal, characteristic, complemented
14#324×D61C211yesmaximal, 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×#14519772C411yescharacteristic
25C2×#14519767C411yescharacteristic
26C2×#14519762C2211yescharacteristic
27C2×#14519761C411yescharacteristic
28C2×#14519752C411yescharacteristic
29C2×#14519750C411yescharacteristic
30C2×#14519750C411yescharacteristic
31C2×#14519750C2211yescharacteristic
32C2×C4×D244C2211yescharacteristic
33C2×#14519739C411yescharacteristic
34C2×#14519737C411yescharacteristic
35C2×#14519737C2211yescharacteristic
36C2×#14519734C2211yescharacteristic
37C2×C4⋊C4×D61C2211yescharacteristic
38#16839841—21no—
39#16839839—21no—
40#16839835—21no—
41#16839835—21no—
42#16839832—21no—
43#16839832—21no—
44C8×D244—21no—
45#16839827—21no—
46#16839819C2211yescharacteristic
47#16839815C2211yescharacteristic
48#16839724C2211yescharacteristic
49#16839724C2211yescharacteristic
50#16839724C2211yescharacteristic
51#16839724C2211yescharacteristic
52C22⋊C8×D61C2211yescharacteristic
53C22⋊C8×D61C2211yescharacteristic
54C22⋊C8×D61C2211yescharacteristic
55C22⋊C8×D61C2211yescharacteristic
56#16839488C2211yescharacteristic
57#16839488C2211yescharacteristic
58#16839487C2211yescharacteristic
59#16839487C2211yescharacteristic
60#16839487C2211yescharacteristic
61#16839487C2211yescharacteristic
62#16839486C2211yescharacteristic
63#16839486C2211yescharacteristic
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×D61C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C2×#11758189—21no—
88C2×#11758189—21no—
89C2×#11758189—21no—
90C2×#11758189—21no—
91C2×C8×D61—21no—
92C2×C8×D61—21no—
93C2×C8×D61—21no—
94C2×C8×D61—21no—
95#14519772—21no—
96#14519772—21no—
97#14519772—21no—
98#14519772—21no—
99#14519767—21no—
100#14519767—21no—
101#14519767—21no—
102#14519767—21no—
103#14519762—21no—
104#14519762—21no—
105#14519762—21no—
106#14519762—21no—
107#14519761—21no—
108#14519761—21no—
109#14519761—21no—
110#14519761—21no—
111#14519752—21no—
112#14519752—21no—
113#14519752—21no—
114#14519752—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—
123#14519750—21no—
124#14519750—21no—
125#14519750—21no—
126#14519750—21no—
127C4×D244D411yescharacteristic
128C4×D244D411yescharacteristic
129C4×D244D411yescharacteristic
130C4×D244D411yescharacteristic
131C4×D244D411yescharacteristic
132C4×D244D411yescharacteristic
133C4×D244D411yescharacteristic
134C4×D244D411yescharacteristic
135#14519739—21no—
136#14519739—21no—
137#14519739—21no—
138#14519739—21no—
139#14519737—21no—
140#14519737—21no—
141#14519737—21no—
142#14519737—21no—
143#14519737—21no—
144#14519737—21no—
145#14519737—21no—
146#14519737—21no—
147#14519734—21no—
148#14519734—21no—
149#14519734—21no—
150#14519734—21no—
151C2×C4⋊Dic61C2×C411yescharacteristic
152C2×C4⋊Dic61C2×C411yescharacteristic
153C2×#11758196C2×C411yescharacteristic
154C2×#11758196C2×C411yescharacteristic
155C2×#11758196C2×C411yescharacteristic
156C2×#11758196C2×C411yescharacteristic
157C2×#11758196C2311yescharacteristic
158C4⋊C4×D61—21no—
159C4⋊C4×D61—21no—
160C4⋊C4×D61—21no—
161C4⋊C4×D61—21no—
162C2×#11758198C2×C411yescharacteristic
163C2×#11758198C2×C411yescharacteristic
164C2×#11758198C2×C411yescharacteristic
165C2×#11758198C2×C411yescharacteristic
166C2×#11758198C2×C411yescharacteristic
167C2×#11758198C2×C411yescharacteristic
168C2×#11758198C2311yescharacteristic
169C2×C4×Dic61C2×C411yescharacteristic
170C2×C4×Dic61C2×C411yescharacteristic
171C4⋊#92418—21no—
172C4⋊#92418—21no—
173C22⋊#92418C2311yescharacteristic
174C22⋊#92418C2311yescharacteristic
175C22⋊#92418C2311yescharacteristic
176C22⋊#92418C2311yescharacteristic
177#14519689—21no—
178#14519689—21no—
179#14519689—21no—
180#14519689—21no—
181#14519689—21no—
182#14519689—21no—
183#14519689—21no—
184#14519689—21no—
185#14519688—21no—
186C4×#92418—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—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—22no—
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—21no—
237C2×D244—21no—
238C2×D244—42no—
239C2×D244—42no—
240C2×D244—81no—
241C2×D244C22⋊C411yescharacteristic
242C2×D244C22⋊C411yescharacteristic
243C2×D244C22⋊C411yescharacteristic
244C2×D244C22⋊C411yescharacteristic
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—22no—
250C2×C4×D61—22no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—41no—
254C2×C4×D61—41no—
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×C4×D61C2×D411yescharacteristic
263C2×C4×D61C2×D411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2×D411yescharacteristic
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C2×C8×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—21no—
276C22⋊C4×C61—21no—
277C22⋊C4×C61—21no—
278C22⋊C4×C61—21no—
279C22⋊C4×C61—21no—
280C22⋊C4×C61—21no—
281C22⋊C4×C61—21no—
282C42×C61C2×D411yescharacteristic
283C42×C61C2×D411yescharacteristic
284C42×C61C2×D411yescharacteristic
285C42×C61C2×D411yescharacteristic
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198C22⋊C411yescharacteristic
297#11758198C22⋊C411yescharacteristic
298#11758198C22⋊C411yescharacteristic
299#11758198C22⋊C411yescharacteristic
300#11758198C22⋊C411yescharacteristic
301#11758198C22⋊C411yescharacteristic
302#11758198C22⋊C411yescharacteristic
303#11758198C22⋊C411yescharacteristic
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61C22⋊C411yescharacteristic
307C4⋊Dic61C22⋊C411yescharacteristic
308C4⋊Dic61C22⋊C411yescharacteristic
309C4⋊Dic61C22⋊C411yescharacteristic
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320C4×Dic61—21no—
321C4×Dic61—21no—
322C4×Dic61—21no—
323C4×Dic61—21no—
324C2×#92418—21no—
325C2×#92418—21no—
326C2×#92418—21no—
327C2×#92418—21no—
328#11758189—81no—
329#11758189—81no—
330#11758189—81no—
331#11758189—81no—
332C8×D61—81no—
333C8×D61—81no—
334C8×D61—81no—
335C8×D61—81no—
336C23×C61—21no—
337C23×C61—21no—
338C23×C61—21no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61C23×C411yescharacteristic
342C22×D61—21no—
343C22×D61—21no—
344C22×D61—21no—
345C22×D61—21no—
346C22×D61—22no—
347C22×D61—21no—
348C22×D61—21no—
349C22×D61—21no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—41no—
355C22×D61C2×C22⋊C411yescharacteristic
356C22×D61C2×C22⋊C411yescharacteristic
357C22×D61C2×C22⋊C411yescharacteristic
358C22×D61C2×C22⋊C411yescharacteristic
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61C2×C22⋊C411yescharacteristic
371C2×C4×C61C2×C22⋊C411yescharacteristic
372C2×C4×C61C2×C22⋊C411yescharacteristic
373C2×C4×C61C2×C22⋊C411yescharacteristic
374C2×C4×C61C22×D411yescharacteristic
375C2×C4×C61C22×D411yescharacteristic
376C22⋊D61—42no—
377C22⋊D61—42no—
378C22⋊D61—42no—
379C22⋊D61—42no—
380C22⋊D61—81no—
381C22⋊D61—81no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—81no—
391C2×Dic61—81no—
392C2×Dic61C2×C22⋊C411yescharacteristic
393C2×Dic61C2×C22⋊C411yescharacteristic
394C2×Dic61C2×C22⋊C411yescharacteristic
395C2×Dic61C2×C22⋊C411yescharacteristic
396C2×Dic61#13112yes—
397D244—22no—
398D244—22no—
399D244—41no—
400D244—41no—
401D244—42no—
402D244—42no—
403D244—81no—
404D244—81no—
405C4×D61—41no—
406C4×D61—41no—
407C4×D61—41no—
408C4×D61—41no—
409C4×D61—41no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61—42no—
414C4×D61—42no—
415C4×D61—42no—
416C4×D61—42no—
417C4×D61—81no—
418C4×D61—81no—
419C8×C61—41no—
420C8×C61—41no—
421C8×C61—41no—
422C8×C61—41no—
423#92418—41no—
424#92418—41no—
425#92418—41no—
426#92418—41no—
427#17427—611nomaximal, Sylow
428C22×C61—21no—
429C22×C61—21no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—81no—
434C22×C61—81no—
435C22×C61C22×C22⋊C411yescharacteristic
436C22×C61C2×#13111yescharacteristic
437C22×C61#56811yescharacteristic
438C2×D61—21no—
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—21no—
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—21no—
448C2×D61—21no—
449C2×D61—42no—
450C2×D61—42no—
451C2×D61—41no—
452C2×D61—41no—
453C2×D61—41no—
454C2×D61—81no—
455C2×D61—81no—
456C2×D61—81no—
457C2×D61—81no—
458C2×D61#41312yes—
459C4×C61—21no—
460C4×C61—21no—
461C4×C61—21no—
462C4×C61—21no—
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—41no—
466C4×C61—41no—
467C4×C61—41no—
468Dic61—22no—
469Dic61—21no—
470Dic61—21no—
471Dic61—21no—
472Dic61—21no—
473Dic61—41no—
474Dic61—41no—
475C2×#553—611no—
476#2974—611no—
477#2974—611no—
478#1473—611no—
479#1473D6111yescharacteristic, complemented
480#1471—611no—
481#1471—611no—
482#1468—611no—
483#1468—611no—
484#1465—611no—
485#1464—611no—
486#1463—611no—
487#1459—611no—
488#1458—611no—
489C2×#324—611no—
490C2×C61—21no—
491C2×C61—21no—
492C2×C61—81no—
493C2×C61#288011yescharacteristic
494C2×C61#288311yescharacteristic
495C2×C61C2×#41311yescharacteristic
496D61—22no—
497D61—41no—
498D61—41no—
499D61—41no—
500D61—81no—
501#553—1221no—
502#553—1221no—
503#553—1221no—
504#553—1221no—
505#553—1221no—
506#553—1221no—
507#553—1221no—
508#553—1221no—
509C2×#126—611no—
510C2×#126C2×D6111yescharacteristic
511C2×#125—611no—
512C2×#123—611no—
513C2×#123—611no—
514C2×#121—611no—
515C2×#121—611no—
516C2×#121—611no—
517C2×#121—611no—
518C2×C4×D4—611no—
519C2×C4×D4—611no—
520C2×C4×D4—611no—
521C2×C4×D4—611no—
522C2×#117—611no—
523C22×C4⋊C4—611no—
524#436—1221no—
525#436—1221no—
526#435—1221no—
527#435—1221no—
528#435—1221no—
529#435—1221no—
530C8×D4—1221no—
531C8×D4—1221no—
532#432—611no—
533#432C2×D6111yescharacteristic
534#431—611no—
535#431C2×D6111yescharacteristic
536#407—611no—
537#407—611no—
538#407—611no—
539#407—611no—
540C2×C22⋊C8—611no—
541C2×C22⋊C8—611no—
542C2×C22⋊C8—611no—
543C2×C22⋊C8—611no—
544#324—611no—
545#324—611no—
546#324—611no—
547#324—611no—
548#324—611no—
549#324—611no—
550#324C2×D6111yescharacteristic
551#324C2×D6111yescharacteristic
552#323—611no—
553#323—611no—
554#323—611no—
555#323—611no—
556#323—611no—
557#323—611no—
558#323C2×D6111yescharacteristic
559#323C2×D6111yescharacteristic
560C61#1742711yescharacteristic, complemented, Sylow
561C22×D4—611no—
562C22×D4—611no—
563C22×D4—611no—
564C22×D4—611no—
565C22×D4—611no—
566C22×D4—611no—
567C23×C4—611no—
568C23×C4—611no—
569C23×C4—611no—
570C23×C4—611no—
571C23×C4—611no—
572C23×C4—611no—
573C2×M16—1221no—
574C2×M16—1221no—
575C2×M16—1221no—
576C2×M16—1221no—
577C22×C8—1221no—
578C22×C8—1221no—
579C22×C8—1221no—
580C22×C8—1221no—
581#126—21no—
582#126—21no—
583#126—21no—
584#126—21no—
585#126—1221no—
586#126—1221no—
587#126—1221no—
588#126—1221no—
589#125—1221no—
590#125—1221no—
591#125—1221no—
592#125—1221no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
598#123—1221no—
599#123—1221no—
600#123—1221no—
601#121—1221no—
602#121—1221no—
603#121—1221no—
604#121—1221no—
605#121—1221no—
606#121—1221no—
607#121—1221no—
608#121—1221no—
609#121—1221no—
610#121—1221no—
611#121—1221no—
612#121—1221no—
613#121—1221no—
614#121—1221no—
615#121—1221no—
616#121—1221no—
617C4×D4—611no—
618C4×D4—611no—
619C4×D4—611no—
620C4×D4—611no—
621C4×D4—611no—
622C4×D4—611no—
623C4×D4—611no—
624C4×D4—611no—
625C4×D4—1221no—
626C4×D4—1221no—
627C4×D4—1221no—
628C4×D4—1221no—
629C4×D4—1221no—
630C4×D4—1221no—
631C4×D4—1221no—
632C4×D4—1221no—
633C4×D4—1221no—
634C4×D4—1221no—
635C4×D4—1221no—
636C4×D4—1221no—
637#117—1221no—
638#117—1221no—
639#117—1221no—
640#117—1221no—
641C2×C4⋊C4—611no—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—611no—
644C2×C4⋊C4—611no—
645C2×C4⋊C4—611no—
646C2×C4⋊C4—611no—
647C2×C4⋊C4—611no—
648C2×C4⋊C4—1221no—
649C2×C4⋊C4—1221no—
650C2×C4⋊C4—1221no—
651C2×C4⋊C4—1221no—
652C2×C4⋊C4C4×D6111yescharacteristic
653C2×C4⋊C4C4×D6111yescharacteristic
654C2×C4⋊C4C22×D6111yescharacteristic
655C2×C22⋊C4—611no—
656C2×C22⋊C4—611no—
657C2×C22⋊C4—611no—
658C2×C22⋊C4—611no—
659C2×C22⋊C4—611no—
660C2×C22⋊C4—611no—
661C2×C22⋊C4—611no—
662C2×C22⋊C4C4×D6111yescharacteristic
663C2×C22⋊C4C4×D6111yescharacteristic
664C2×C22⋊C4C22×D6111yescharacteristic
665C2×C42—611no—
666C2×C42—611no—
667C2×C42C22×D6111yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670C4⋊C8—1221no—
671C4⋊C8—1221no—
672C22⋊C8—611no—
673C22⋊C8—611no—
674C22⋊C8—611no—
675C22⋊C8—611no—
676C22⋊C8—1221no—
677C22⋊C8—1221no—
678C22⋊C8—1221no—
679C22⋊C8—1221no—
680C22⋊C8—1221no—
681C22⋊C8—1221no—
682C22⋊C8—1221no—
683C22⋊C8—1221no—
684C22⋊C8C22×D6111yescharacteristic
685C22⋊C8C22×D6111yescharacteristic
686C22⋊C8C22×D6111yescharacteristic
687C22⋊C8C22×D6111yescharacteristic
688#97—21no—
689#97—1221no—
690C4×C8—21no—
691C4×C8—1221no—
692C24—611no—
693C24—611no—
694C24—611no—
695C24C2×C4×D6111yescharacteristic
696C2×D4—611no—
697C2×D4—611no—
698C2×D4—611no—
699C2×D4—611no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—1221no—
705C2×D4—1221no—
706C2×D4—1222no—
707C2×D4—1221no—
708C2×D4—1221no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4—4881no—
712C2×D4—4881no—
713C2×D4—2442no—
714C2×D4—2442no—
715C2×D4—2441no—
716C2×D4—2442no—
717C22×C4—611no—
718C22×C4—611no—
719C22×C4—611no—
720C22×C4—611no—
721C22×C4—611no—
722C22×C4—611no—
723C22×C4—611no—
724C22×C4—611no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—611no—
728C22×C4—611no—
729C22×C4—611no—
730C22×C4—1222no—
731C22×C4—1222no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—4881no—
741C22×C4—4881no—
742C22×C4—4881no—
743C22×C4—4881no—
744C22×C4—2441no—
745C22×C4—2441no—
746C22×C4C2×C4×D6111yescharacteristic
747C22×C4C2×C4×D6111yescharacteristic
748C22×C4C2×C4×D6111yescharacteristic
749C22×C4C2×C4×D6111yescharacteristic
750C22×C4C2×C4×D6111yescharacteristic
751C22×C4C23×D6111yescharacteristic
752M16—4881no—
753M16—4881no—
754M16—4881no—
755M16—4881no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—1221no—
761C2×C8—1221no—
762C2×C8—1221no—
763C2×C8—1221no—
764C2×C8—4881no—
765C2×C8—4881no—
766C2×C8—4881no—
767C2×C8—4881no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—611no—
775C4⋊C4—611no—
776C4⋊C4—611no—
777C4⋊C4—611no—
778C4⋊C4—1221no—
779C4⋊C4—1221no—
780C4⋊C4—1221no—
781C4⋊C4—1221no—
782C4⋊C4—1221no—
783C4⋊C4—1221no—
784C4⋊C4—1221no—
785C4⋊C4—1221no—
786C4⋊C4—1221no—
787C4⋊C4—1221no—
788C4⋊C4—1221no—
789C4⋊C4—1221no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—611no—
797C22⋊C4—611no—
798C22⋊C4—611no—
799C22⋊C4—611no—
800C22⋊C4—611no—
801C22⋊C4—611no—
802C22⋊C4—611no—
803C22⋊C4—611no—
804C22⋊C4—1221no—
805C22⋊C4—1221no—
806C22⋊C4—1221no—
807C22⋊C4—1221no—
808C22⋊C4—1221no—
809C22⋊C4—1221no—
810C22⋊C4—1221no—
811C22⋊C4—1221no—
812C22⋊C4—1221no—
813C22⋊C4—1221no—
814C42—1221no—
815C42—1221no—
816C42—1221no—
817C42—1221no—
818C42D4×D6111yescharacteristic
819C42D4×D6111yescharacteristic
820C42D4×D6111yescharacteristic
821C42D4×D6111yescharacteristic
822C23—21no—
823C23—21no—
824C23—21no—
825C23—41no—
826C23—41no—
827C23—611no—
828C23—611no—
829C23—611no—
830C23—611no—
831C23—1222no—
832C23—1221no—
833C23—1221no—
834C23—1221no—
835C23—1221no—
836C23—1221no—
837C23—1221no—
838C23—1221no—
839C23—2441no—
840C23—2441no—
841C23—2441no—
842C23—2441no—
843C23—2441no—
844C23C22×C4×D6111yescharacteristic
845D4—1222no—
846D4—1222no—
847D4—4881no—
848D4—4881no—
849D4—4881no—
850D4—4881no—
851D4—2441no—
852D4—2441no—
853D4—2442no—
854D4—2442no—
855D4—2442no—
856D4—2442no—
857D4—2442no—
858D4—2442no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—611no—
871C2×C4—611no—
872C2×C4—611no—
873C2×C4—611no—
874C2×C4—612no—
875C2×C4—1221no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—4881no—
880C2×C4—4881no—
881C2×C4—4881no—
882C2×C4—4881no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2442no—
892C2×C4—2442no—
893C2×C4—2442no—
894C2×C4—2442no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4C22⋊C4×D6111yescharacteristic
900C2×C4C22⋊C4×D6111yescharacteristic
901C2×C4C22⋊C4×D6111yescharacteristic
902C2×C4C22⋊C4×D6111yescharacteristic
903C2×C4C2×D4×D6111yescharacteristic
904C2×C4C2×D4×D6111yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C8—2441no—
910C8—2441no—
911C8—2441no—
912C8—2441no—
913C22—21no—
914C22—21no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—81no—
919C22—81no—
920C22—612no—
921C22—1221no—
922C22—1221no—
923C22—1221no—
924C22—1221no—
925C22—1221no—
926C22—1221no—
927C22—1221no—
928C22—1221no—
929C22—1221no—
930C22—1221no—
931C22—1221no—
932C22—4881no—
933C22—4881no—
934C22—4881no—
935C22—4881no—
936C22—2442no—
937C22—2442no—
938C22—2441no—
939C22—2441no—
940C22—2441no—
941C22C2×C22⋊C4×D6111yescharacteristic
942C22#131×D6111yescharacteristic
943C22#1684052711yescharacteristic
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—21no—
949C4—21no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—1222no—
954C4—1221no—
955C4—1221no—
956C4—1221no—
957C4—1221no—
958C4—2441no—
959C4—2441no—
960C2—21no—
961C2—21no—
962C2—81no—
963C2—1222no—
964C2—4881no—
965C2—2441no—
966C2—2441no—
967C2—2441no—
968C2#2145426711yescharacteristic
969C2#2145427811yescharacteristic
970C2#413×D6111yescharacteristic
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#17427
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. #21454856C2semidirect
3. #21454853C2semidirect
4. #21444188C2semidirect
5. #21444177C2semidirect
6. #21444177C2semidirect
7. #21444166C2semidirect
8. #21444166C2semidirect
9. #21444154C2semidirect
10. #21444151C2semidirect
11. #21444147C2semidirect
12. #21444134C2semidirect
13. #21444131C2semidirect
14. #324×D61C2semidirect
15. C61×#1473C2semidirect
479. #1473D61semidirect
560. C61#17427semidirect

Maximal subgroups

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

subgroupindex
C2×#168404632
#214548562
#214548532
#214441882
#214441772
#214441662
#214441542
#214441512
#214441472
#214441342
#214441312
#324×D612
C61×#14732
#1742761