Finite Group Databasebeta

← #29646285

Subgroups — #29646285

Order 15616.

1060 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840437C211yesmaximal, characteristic
2#21454856C211yesmaximal, characteristic, complemented
3#21454853C211yesmaximal, characteristic, complemented
4#21444188C211yesmaximal, characteristic, complemented
5#21444181C211yesmaximal, characteristic, complemented
6#21444181C211yesmaximal, characteristic, complemented
7#21444164C211yesmaximal, characteristic, complemented
8#21444164C211yesmaximal, characteristic, complemented
9#21444156C211yesmaximal, characteristic, complemented
10#21444151C211yesmaximal, characteristic, complemented
11#21444144C211yesmaximal, characteristic, complemented
12#21444136C211yesmaximal, characteristic, complemented
13#21444131C211yesmaximal, characteristic, complemented
14#323×D61C211yesmaximal, characteristic, complemented
15C61×#1473C211yesmaximal, characteristic, complemented
16#16840437—21no—
17#16840437—21no—
18#16840437—21no—
19#16840437—21no—
20#16840437—21no—
21#16840437—21no—
22#16840437—21no—
23#16840437—21no—
24C2×#14519770C411yescharacteristic
25C2×#14519763C411yescharacteristic
26C2×#14519762C411yescharacteristic
27C2×#14519762C411yescharacteristic
28C2×#14519759C2211yescharacteristic
29C2×#14519757C411yescharacteristic
30C2×#14519755C2211yescharacteristic
31C2×#14519747C411yescharacteristic
32C2×C4×D244C2211yescharacteristic
33C2×#14519739C2211yescharacteristic
34C2×#14519735C411yescharacteristic
35C2×#14519734C2211yescharacteristic
36C2×C22⋊C4×D61C411yescharacteristic
37C2×C22⋊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, complemented
47#16839815C2211yescharacteristic, complemented
48#16839724C2211yescharacteristic
49#16839724C2211yescharacteristic
50#16839724C2211yescharacteristic, complemented
51#16839724C2211yescharacteristic, complemented
52C22⋊C8×D61C2211yescharacteristic
53C22⋊C8×D61C2211yescharacteristic
54C22⋊C8×D61C2211yescharacteristic, complemented
55C22⋊C8×D61C2211yescharacteristic, complemented
56#16839488C2211yescharacteristic, complemented
57#16839488C2211yescharacteristic, complemented
58#16839487C2211yescharacteristic, complemented
59#16839487C2211yescharacteristic, complemented
60#16839487C2211yescharacteristic, complemented
61#16839487C2211yescharacteristic, complemented
62#16839486C2211yescharacteristic
63#16839486C2211yescharacteristic
64#16839485C2211yescharacteristic
65#16839485C2211yescharacteristic
66#16839485C2211yescharacteristic
67#16839485C2211yescharacteristic
68C2×#126×C61C2211yescharacteristic
69C61×#432C2211yescharacteristic, complemented
70C61×#431C2211yescharacteristic, complemented
71C61×#324C2211yescharacteristic, complemented
72C61×#324C2211yescharacteristic, complemented
73C61×#323C2211yescharacteristic
74C61×#323C2211yescharacteristic
75C24×D61C2×C411yescharacteristic
76C22×Dic122C2×C411yescharacteristic
77C22×D244C2×C411yescharacteristic
78C22×D244C2×C411yescharacteristic
79C22×C22⋊D61C2×C411yescharacteristic
80C22×C4×D61C2×C411yescharacteristic
81C22×C4×D61C2×C411yescharacteristic
82C22×C4×D61C2×C411yescharacteristic
83C22×C4×D61C2311yescharacteristic
84C22×C4×D61C2311yescharacteristic
85C2×#11758189—21no—
86C2×#11758189—21no—
87C2×#11758189—21no—
88C2×#11758189—21no—
89C2×C8×D61—21no—
90C2×C8×D61—21no—
91C2×C8×D61—21no—
92C2×C8×D61—21no—
93#14519770—21no—
94#14519770—21no—
95#14519770—21no—
96#14519770—21no—
97#14519763—21no—
98#14519763—21no—
99#14519763—21no—
100#14519763—21no—
101#14519762—21no—
102#14519762—21no—
103#14519762—21no—
104#14519762—21no—
105#14519762—21no—
106#14519762—21no—
107#14519762—21no—
108#14519762—21no—
109#14519759—21no—
110#14519759—21no—
111#14519759—21no—
112#14519759—21no—
113#14519757—21no—
114#14519757—21no—
115#14519757—21no—
116#14519757—21no—
117#14519755—21no—
118#14519755—21no—
119#14519755—21no—
120#14519755—21no—
121#14519747—21no—
122#14519747—21no—
123#14519747—21no—
124#14519747—21no—
125C4×D244D411yescharacteristic
126C4×D244D411yescharacteristic
127C4×D244D411yescharacteristic
128C4×D244D411yescharacteristic
129C4×D244D411yescharacteristic
130C4×D244D411yescharacteristic
131C4×D244D411yescharacteristic
132C4×D244D411yescharacteristic
133#14519739—21no—
134#14519739—21no—
135#14519739—21no—
136#14519739—21no—
137#14519735—21no—
138#14519735—21no—
139#14519735—21no—
140#14519735—21no—
141#14519734—21no—
142#14519734—21no—
143#14519734—21no—
144#14519734—21no—
145C2×C4⋊Dic61C2×C411yescharacteristic
146C2×C4⋊Dic61C2×C411yescharacteristic
147C2×#11758196C2×C411yescharacteristic
148C2×#11758196C2×C411yescharacteristic
149C2×#11758196C2311yescharacteristic
150C2×C22⋊Dic61C2×C411yescharacteristic
151C2×C22⋊Dic61C2×C411yescharacteristic
152C2×#11758198C2×C411yescharacteristic
153C2×#11758198C2×C411yescharacteristic
154C2×#11758198C2×C411yescharacteristic
155C2×#11758198C2×C411yescharacteristic
156C2×#11758198C2×C411yescharacteristic
157C2×#11758198C2×C411yescharacteristic
158C2×#11758198C2×C411yescharacteristic
159C2×#11758198C2×C411yescharacteristic
160C2×#11758198C2311yescharacteristic
161C22⋊C4×D61—21no—
162C22⋊C4×D61—21no—
163C22⋊C4×D61—21no—
164C22⋊C4×D61—21no—
165C22⋊C4×D61—21no—
166C22⋊C4×D61—21no—
167C22⋊C4×D61—21no—
168C22⋊C4×D61—21no—
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×D61—21no—
208C23×D61—21no—
209C23×D61—22no—
210C23×D61—41no—
211C23×D61—42no—
212C23×D61—81no—
213C23×D61C22×C411yescharacteristic
214C23×D61C22×C411yescharacteristic
215C23×D61C22×C411yescharacteristic
216C22×C4×C61C22×C411yescharacteristic
217C22×C4×C61C22×C411yescharacteristic
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C2411yescharacteristic
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—81no—
225C22×Dic61C22×C411yescharacteristic
226C22×Dic61C22×C411yescharacteristic
227C22×Dic61C22×C411yescharacteristic
228C22×Dic61C22×C411yescharacteristic
229C22×Dic61C22×C411yescharacteristic
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—22no—
233C2×D244—42no—
234C2×D244—41no—
235C2×D244C22⋊C411yescharacteristic
236C2×D244C22⋊C411yescharacteristic
237C2×D244C22⋊C411yescharacteristic
238C2×D244C22⋊C411yescharacteristic
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—22no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—41no—
247C2×C4×D61—42no—
248C2×C4×D61—81no—
249C2×C4×D61—81no—
250C2×C4×D61—81no—
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×C4×D61C2×D411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×Dic122—21no—
260C2×Dic122—21no—
261C2×Dic122—81no—
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
282C22⋊Dic61—21no—
283C22⋊Dic61—21no—
284C22⋊Dic61—21no—
285C22⋊Dic61—21no—
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#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198C22⋊C411yescharacteristic
301#11758198C22⋊C411yescharacteristic
302#11758198C22⋊C411yescharacteristic
303#11758198C22⋊C411yescharacteristic
304#11758198C22⋊C411yescharacteristic
305#11758198C22⋊C411yescharacteristic
306#11758198C22⋊C411yescharacteristic
307#11758198C22⋊C411yescharacteristic
308C4⋊Dic61—21no—
309C4⋊Dic61—21no—
310C4⋊Dic61C22⋊C411yescharacteristic
311C4⋊Dic61C22⋊C411yescharacteristic
312C4⋊Dic61C22⋊C411yescharacteristic
313C4⋊Dic61C22⋊C411yescharacteristic
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—21no—
347C22×D61—21no—
348C22×D61—22no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—42no—
353C22×D61—42no—
354C22×D61—42no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—42no—
358C22×D61—81no—
359C22×D61—81no—
360C22×D61—84no—
361C22×D61—84no—
362C22×D61C2×C22⋊C411yescharacteristic
363C22×D61C2×C22⋊C411yescharacteristic
364C22×D61C2×C22⋊C411yescharacteristic
365C22×D61C2×C22⋊C411yescharacteristic
366C22×D61#13112yes—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61C2×C22⋊C411yescharacteristic
379C2×C4×C61C2×C22⋊C411yescharacteristic
380C2×C4×C61C2×C22⋊C411yescharacteristic
381C2×C4×C61C2×C22⋊C411yescharacteristic
382C2×C4×C61C22×D411yescharacteristic
383C2×C4×C61C22×D411yescharacteristic
384C22⋊D61—81no—
385C22⋊D61—81no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61C2×C22⋊C411yescharacteristic
396C2×Dic61C2×C22⋊C411yescharacteristic
397C2×Dic61C2×C22⋊C411yescharacteristic
398C2×Dic61C2×C22⋊C411yescharacteristic
399D244—22no—
400D244—22no—
401D244—41no—
402D244—41no—
403D244—42no—
404D244—42no—
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—
419Dic122—81no—
420Dic122—81no—
421C8×C61—41no—
422C8×C61—41no—
423C8×C61—41no—
424C8×C61—41no—
425#92418—41no—
426#92418—41no—
427#92418—41no—
428#92418—41no—
429#17422—611nomaximal, Sylow
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—81no—
436C22×C61—81no—
437C22×C61C22×C22⋊C411yescharacteristic
438C22×C61C2×#13111yescharacteristic
439C22×C61#56811yescharacteristic
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—22no—
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—21no—
448C2×D61—21no—
449C2×D61—21no—
450C2×D61—21no—
451C2×D61—21no—
452C2×D61—42no—
453C2×D61—42no—
454C2×D61—42no—
455C2×D61—41no—
456C2×D61—41no—
457C2×D61—42no—
458C2×D61—84no—
459C2×D61—81no—
460C2×D61—81no—
461C2×D61—84no—
462C2×D61#41312yes—
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—21no—
466C4×C61—21no—
467C4×C61—21no—
468C4×C61—21no—
469C4×C61—41no—
470C4×C61—41no—
471C4×C61—41no—
472Dic61—21no—
473Dic61—21no—
474Dic61—21no—
475Dic61—21no—
476Dic61—41no—
477Dic61—41no—
478Dic61—41no—
479C2×#551—611no—
480#2974—611no—
481#2974—611no—
482#1473—611no—
483#1473D6111yescharacteristic, complemented
484#1472—611no—
485#1472—611no—
486#1468—611no—
487#1468—611no—
488#1465—611no—
489#1464—611no—
490#1462—611no—
491#1459—611no—
492#1458—611no—
493C2×#323—611no—
494C2×C61—21no—
495C2×C61—21no—
496C2×C61—81no—
497C2×C61#288011yescharacteristic
498C2×C61#288311yescharacteristic
499C2×C61C2×#41311yescharacteristic
500D61—22no—
501D61—41no—
502D61—41no—
503D61—41no—
504D61—42no—
505#551—1221no—
506#551—1221no—
507#551—1221no—
508#551—1221no—
509#551—1221no—
510#551—1221no—
511#551—1221no—
512#551—1221no—
513C2×#126—611no—
514C2×#126C2×D6111yescharacteristic
515C2×#124—611no—
516C2×#123—611no—
517C2×#123—611no—
518C2×#123—611no—
519C2×C22⋊Q8—611no—
520C2×C22⋊Q8—611no—
521C2×#120—611no—
522C2×C4×D4—611no—
523C2×C4×D4—611no—
524C2×#117—611no—
525C2×#117—611no—
526C22×C22⋊C4—611no—
527C22×C22⋊C4—611no—
528#436—1221no—
529#436—1221no—
530#435—1221no—
531#435—1221no—
532#435—1221no—
533#435—1221no—
534C8×D4—1221no—
535C8×D4—1221no—
536#432—611no—
537#432C2×D6111yescharacteristic, complemented
538#431—611no—
539#431C2×D6111yescharacteristic, complemented
540#407—611no—
541#407—611no—
542#407—611no—
543#407—611no—
544C2×C22⋊C8—611no—
545C2×C22⋊C8—611no—
546C2×C22⋊C8—611no—
547C2×C22⋊C8—611no—
548#324—611no—
549#324—611no—
550#324—611no—
551#324—611no—
552#324—611no—
553#324—611no—
554#324C2×D6111yescharacteristic, complemented
555#324C2×D6111yescharacteristic, complemented
556#323—611no—
557#323—611no—
558#323—611no—
559#323—611no—
560#323—611no—
561#323—611no—
562#323C2×D6111yescharacteristic
563#323C2×D6111yescharacteristic
564C61#1742211yescharacteristic, complemented, Sylow
565C25—611no—
566C22×Q8—611no—
567C22×D4—611no—
568C22×D4—611no—
569C22×D4—611no—
570C23×C4—611no—
571C23×C4—611no—
572C23×C4—611no—
573C23×C4—611no—
574C23×C4—611no—
575C2×M16—1221no—
576C2×M16—1221no—
577C2×M16—1221no—
578C2×M16—1221no—
579C22×C8—1221no—
580C22×C8—1221no—
581C22×C8—1221no—
582C22×C8—1221no—
583#126—21no—
584#126—21no—
585#126—21no—
586#126—21no—
587#126—1221no—
588#126—1221no—
589#126—1221no—
590#126—1221no—
591#124—1221no—
592#124—1221no—
593#124—1221no—
594#124—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
598#123—1221no—
599#123—1221no—
600#123—1221no—
601#123—1221no—
602#123—1221no—
603#123—1221no—
604#123—1221no—
605#123—1221no—
606#123—1221no—
607C22⋊Q8—1221no—
608C22⋊Q8—1221no—
609C22⋊Q8—1221no—
610C22⋊Q8—1221no—
611C22⋊Q8—1221no—
612C22⋊Q8—1221no—
613C22⋊Q8—1221no—
614C22⋊Q8—1221no—
615#120—1221no—
616#120—1221no—
617#120—1221no—
618#120—1221no—
619C4×D4—611no—
620C4×D4—611no—
621C4×D4—611no—
622C4×D4—611no—
623C4×D4—611no—
624C4×D4—611no—
625C4×D4—611no—
626C4×D4—611no—
627C4×D4—1221no—
628C4×D4—1221no—
629C4×D4—1221no—
630C4×D4—1221no—
631#117—1221no—
632#117—1221no—
633#117—1221no—
634#117—1221no—
635#117—1221no—
636#117—1221no—
637#117—1221no—
638#117—1221no—
639C2×C4⋊C4—611no—
640C2×C4⋊C4—611no—
641C2×C4⋊C4—611no—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—611no—
644C2×C4⋊C4C4×D6111yescharacteristic
645C2×C4⋊C4C4×D6111yescharacteristic
646C2×C4⋊C4C22×D6111yescharacteristic
647C2×C22⋊C4—611no—
648C2×C22⋊C4—611no—
649C2×C22⋊C4—611no—
650C2×C22⋊C4—611no—
651C2×C22⋊C4—611no—
652C2×C22⋊C4—611no—
653C2×C22⋊C4—611no—
654C2×C22⋊C4—611no—
655C2×C22⋊C4—611no—
656C2×C22⋊C4—611no—
657C2×C22⋊C4—611no—
658C2×C22⋊C4—1221no—
659C2×C22⋊C4—1221no—
660C2×C22⋊C4—1221no—
661C2×C22⋊C4—1221no—
662C2×C22⋊C4—1221no—
663C2×C22⋊C4—1221no—
664C2×C22⋊C4—1221no—
665C2×C22⋊C4—1221no—
666C2×C22⋊C4C4×D6111yescharacteristic
667C2×C22⋊C4C4×D6111yescharacteristic
668C2×C22⋊C4C22×D6111yescharacteristic
669C2×C42—611no—
670C2×C42—611no—
671C2×C42C22×D6111yescharacteristic
672C4⋊C8—21no—
673C4⋊C8—21no—
674C4⋊C8—1221no—
675C4⋊C8—1221no—
676C22⋊C8—611no—
677C22⋊C8—611no—
678C22⋊C8—611no—
679C22⋊C8—611no—
680C22⋊C8—1221no—
681C22⋊C8—1221no—
682C22⋊C8—1221no—
683C22⋊C8—1221no—
684C22⋊C8—1221no—
685C22⋊C8—1221no—
686C22⋊C8—1221no—
687C22⋊C8—1221no—
688C22⋊C8C22×D6111yescharacteristic
689C22⋊C8C22×D6111yescharacteristic
690C22⋊C8C22×D6111yescharacteristic
691C22⋊C8C22×D6111yescharacteristic
692#97—21no—
693#97—1221no—
694C4×C8—21no—
695C4×C8—1221no—
696C24—611no—
697C24—611no—
698C24—611no—
699C24—1222no—
700C24—1221no—
701C24—1221no—
702C24—4881no—
703C24—2441no—
704C24—2442no—
705C24C2×C4×D6111yescharacteristic
706C2×Q8—1221no—
707C2×Q8—1221no—
708C2×Q8—4881no—
709C2×D4—611no—
710C2×D4—611no—
711C2×D4—611no—
712C2×D4—611no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1222no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4—4881no—
719C2×D4—2441no—
720C2×D4—2442no—
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—611no—
731C22×C4—611no—
732C22×C4—611no—
733C22×C4—611no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1222no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—4881no—
742C22×C4—4881no—
743C22×C4—4881no—
744C22×C4—2441no—
745C22×C4—2442no—
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—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—611no—
793C22⋊C4—611no—
794C22⋊C4—611no—
795C22⋊C4—611no—
796C22⋊C4—611no—
797C22⋊C4—611no—
798C22⋊C4—611no—
799C22⋊C4—611no—
800C22⋊C4—1221no—
801C22⋊C4—1221no—
802C22⋊C4—1221no—
803C22⋊C4—1221no—
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—
814C22⋊C4—1221no—
815C22⋊C4—1221no—
816C22⋊C4—1221no—
817C22⋊C4—1221no—
818C42—1221no—
819C42—1221no—
820C42—1221no—
821C42—1221no—
822C42D4×D6111yescharacteristic
823C42D4×D6111yescharacteristic
824C42D4×D6111yescharacteristic
825C42D4×D6111yescharacteristic
826C23—21no—
827C23—21no—
828C23—21no—
829C23—41no—
830C23—41no—
831C23—611no—
832C23—611no—
833C23—611no—
834C23—611no—
835C23—612no—
836C23—1222no—
837C23—1221no—
838C23—1221no—
839C23—1221no—
840C23—1221no—
841C23—1221no—
842C23—1221no—
843C23—4881no—
844C23—4881no—
845C23—4884no—
846C23—4884no—
847C23—2441no—
848C23—2441no—
849C23—2441no—
850C23—2441no—
851C23—2441no—
852C23—2442no—
853C23—2442no—
854C23—2442no—
855C23—2442no—
856C23C22×C4×D6111yescharacteristic
857Q8—4881no—
858Q8—4881no—
859D4—1222no—
860D4—1222no—
861D4—4881no—
862D4—4881no—
863D4—2441no—
864D4—2441no—
865D4—2442no—
866D4—2442no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—611no—
879C2×C4—611no—
880C2×C4—611no—
881C2×C4—611no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—4881no—
888C2×C4—4881no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2442no—
898C2×C4—2442no—
899C2×C4—2442no—
900C2×C4—2442no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4C22⋊C4×D6111yescharacteristic
906C2×C4C22⋊C4×D6111yescharacteristic
907C2×C4C22⋊C4×D6111yescharacteristic
908C2×C4C22⋊C4×D6111yescharacteristic
909C2×C4C2×D4×D6111yescharacteristic
910C2×C4C2×D4×D6111yescharacteristic
911C8—41no—
912C8—41no—
913C8—41no—
914C8—41no—
915C8—2441no—
916C8—2441no—
917C8—2441no—
918C8—2441no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—81no—
925C22—81no—
926C22—612no—
927C22—1221no—
928C22—1221no—
929C22—1222no—
930C22—1221no—
931C22—1221no—
932C22—1221no—
933C22—1221no—
934C22—1221no—
935C22—1221no—
936C22—1221no—
937C22—1221no—
938C22—1221no—
939C22—4881no—
940C22—4881no—
941C22—4884no—
942C22—4884no—
943C22—2442no—
944C22—2442no—
945C22—2442no—
946C22—2442no—
947C22—2441no—
948C22—2441no—
949C22C2×C22⋊C4×D6111yescharacteristic
950C22#131×D6111yescharacteristic
951C22#1684052711yescharacteristic
952C4—21no—
953C4—21no—
954C4—21no—
955C4—21no—
956C4—21no—
957C4—21no—
958C4—41no—
959C4—41no—
960C4—41no—
961C4—1221no—
962C4—1221no—
963C4—1221no—
964C4—1221no—
965C4—2441no—
966C4—2441no—
967C4—2441no—
968C2—21no—
969C2—21no—
970C2—81no—
971C2—1222no—
972C2—2441no—
973C2—2441no—
974C2—2441no—
975C2—2442no—
976C2#2145426711yescharacteristic
977C2#2145427811yescharacteristic
978C2#413×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1473C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519747C4
cosocleC22×C4×C61C24
hypercenter#1473D61
hypocenterC61#17422
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. #21444181C2semidirect
6. #21444181C2semidirect
7. #21444164C2semidirect
8. #21444164C2semidirect
9. #21444156C2semidirect
10. #21444151C2semidirect
11. #21444144C2semidirect
12. #21444136C2semidirect
13. #21444131C2semidirect
14. #323×D61C2semidirect
15. C61×#1473C2semidirect
46. #16839819C22semidirect
47. #16839815C22semidirect
50. #16839724C22semidirect
51. #16839724C22semidirect
54. C22⋊C8×D61C22semidirect
55. C22⋊C8×D61C22semidirect
56. #16839488C22semidirect
57. #16839488C22semidirect
58. #16839487C22semidirect
59. #16839487C22semidirect
60. #16839487C22semidirect
61. #16839487C22semidirect
69. C61×#432C22semidirect
70. C61×#431C22semidirect
71. C61×#324C22semidirect
72. C61×#324C22semidirect
483. #1473D61semidirect
537. #432C2×D61semidirect
539. #431C2×D61semidirect
554. #324C2×D61semidirect
555. #324C2×D61semidirect
564. C61#17422semidirect

Maximal subgroups

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

subgroupindex
C2×#168404372
#214548562
#214548532
#214441882
#214441812
#214441642
#214441562
#214441512
#214441442
#214441362
#214441312
#323×D612
C61×#14732
#1742261