Finite Group Databasebeta

← #29683100

Subgroups — #29683100

Order 15616.

938 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839872C211yesmaximal, characteristic
2#21448457C211yesmaximal, characteristic, complemented
3#21448180C211yesmaximal, characteristic, complemented
4#21446444C211yesmaximal, characteristic, complemented
5#21446437C211yesmaximal, characteristic, complemented
6#21446402C211yesmaximal, characteristic, complemented
7#21446395C211yesmaximal, characteristic, complemented
8#21446165C211yesmaximal, characteristic
9#21446165C211yesmaximal, characteristic
10#21446078C211yesmaximal, characteristic, complemented
11#21446064C211yesmaximal, characteristic, complemented
12#21445717C211yesmaximal, characteristic, complemented
13C4×#14519699C211yesmaximal, characteristic, complemented
14#21445570C211yesmaximal, characteristic, complemented
15C4×#102×C61C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18C2×D4×Dic61C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20#16839872C418yescomplemented
21C2×#14519710C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519688C2211yescharacteristic
29#16839663C2211yescharacteristic
30#16839663C2211yescharacteristic
31#16839658C2211yescharacteristic
32#16839658C2211yescharacteristic
33#16839653—21no—
34#16839653—21no—
35#16839624—21no—
36#16839621—21no—
37C4⋊C4×Dic61C2211yescharacteristic
38C4⋊C4×Dic61C2211yescharacteristic
39C4×C4⋊Dic61C2211yescharacteristic
40C22⋊C4×Dic61—21no—
41C22⋊C4×Dic61—21no—
42C4×C22⋊Dic61—21no—
43#16839608C2211yescharacteristic
44C2×#14519684—21no—
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C2×C4×C8×C61C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C22×D244C2311yescharacteristic
61C23×Dic61—21no—
62C23×Dic61—21no—
63C22×C4×D61—21no—
64C2×#11758199—22no—
65C2×#11758199—22no—
66C2×#11758199C2×C414yes—
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C4×D244—22no—
70C4×D244C2×C414yescomplemented
71D4×Dic61—22no—
72D4×Dic61—22no—
73D4×Dic61—22no—
74D4×Dic61—22no—
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61C2311yescharacteristic
91C2×C4×Dic61C2311yescharacteristic
92#14519710—22no—
93#14519708—22no—
94#14519708C2×C414yescomplemented
95#14519699—22no—
96#14519699—22no—
97#14519698C2×C414yes—
98#14519697C2×C414yescomplemented
99#14519688C2×C414yescomplemented
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684D411yescharacteristic
106#14519684D411yescharacteristic
107#14519684D411yescharacteristic
108#14519684D411yescharacteristic
109C22×D4×C61C2311yescharacteristic
110C23×C4×C61—21no—
111C22×C8×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C4×D4×C61—22no—
114C4×D4×C61C2×C414yes—
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C22⋊C4×C61—21no—
119C2×C42×C61—21no—
120C2×C42×C61C2311yescharacteristic
121#102×C61—22no—
122#102×C61—22no—
123C4×C8×C61—22no—
124#95×C61—21no—
125C24×C61—21no—
126C23×D61—21no—
127C2×D4×C61—21no—
128C2×D4×C61—21no—
129C2×D4×C61—21no—
130C2×D4×C61C22×C412yes—
131C2×D4×C61#4112yes—
132C2×D4×C61#4112yes—
133C22×C4×C61—21no—
134C22×C4×C61—24no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—81no—
138C22×C4×C61—81no—
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2411yescharacteristic
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—24no—
146C22×Dic61—24no—
147C22×Dic61—81no—
148C22×Dic61—81no—
149C22×Dic61—81no—
150C22×Dic61—81no—
151C22×Dic61C2×D411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153C22×Dic61C2×D411yescharacteristic
154C22×Dic61C2×D411yescharacteristic
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—21no—
158C2×D244—21no—
159C2×D244—21no—
160C2×D244C22×C412yes—
161C2×C4×D61—24no—
162C2×C4×D61—81no—
163C2×C4×D61—81no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61C22×C412yes—
176C22⋊C4×C61—24no—
177C42×C61—81no—
178C42×C61C22×C412yes—
179C42×C61#4112yes—
180C22⋊Dic61—24no—
181C22⋊Dic61—24no—
182#11758199—28no—
183#11758198—24no—
184#11758198—81no—
185#11758198—81no—
186#11758198—81no—
187#11758198—81no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61C22×C412yes—
192C4⋊Dic61#4112yes—
193C4⋊Dic61#4112yes—
194#11758196—81no—
195#11758196—81no—
196C4×Dic61—21no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—81no—
201C4×Dic61—81no—
202C4×Dic61—81no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418C22×C412yes—
208C2×#92418C22×C412yes—
209C23×C61—22no—
210C23×C61—22no—
211C23×C61—22no—
212C23×C61—41no—
213C23×C61—41no—
214C23×C61—41no—
215C23×C61—41no—
216C23×C61C22×D411yescharacteristic
217C22×D61—22no—
218C22×D61—41no—
219C22×D61—41no—
220C22×D61—41no—
221C22×D61—41no—
222C22×D61—41no—
223C22×D61—41no—
224D4×C61—22no—
225D4×C61—22no—
226D4×C61—22no—
227D4×C61#11714yes—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—22no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—84no—
242C2×C4×C61C4×D412yes—
243C2×C4×C61C4×D412yes—
244C2×C4×C61C23×C411yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C2×C4×C61C2×#4111yescharacteristic
250C2×Dic61—22no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—84no—
272C2×Dic61—84no—
273D244—22no—
274D244—22no—
275D244—41no—
276D244—41no—
277C4×D61—84no—
278C8×C61—41no—
279C8×C61—41no—
280#92418—22no—
281#92418—22no—
282#21126—611nomaximal, Sylow
283C22×C61—24no—
284C22×C61—42no—
285C22×C61—42no—
286C22×C61—42no—
287C22×C61—42no—
288C22×C61—42no—
289C22×C61—42no—
290C22×C61C2×C4×D411yescharacteristic
291C22×C61#52511yescharacteristic
292C22×C61#52511yescharacteristic
293C22×C61#57611yescharacteristic
294C22×C61#57611yescharacteristic
295C22×C61#57711yescharacteristic
296C22×C61#57711yescharacteristic
297C2×D61—42no—
298C2×D61—42no—
299C2×D61—42no—
300C2×D61—81no—
301C2×D61—81no—
302C2×D61—81no—
303C2×D61—81no—
304C4×C61—22no—
305C4×C61—22no—
306C4×C61—42no—
307C4×C61—81no—
308C4×C61—81no—
309C4×C61C2×#11711yescharacteristic
310C4×C61C4×#4111yescharacteristic
311C4×C61#52911yescharacteristic
312C4×C61#52911yescharacteristic
313Dic61—41no—
314Dic61—42no—
315Dic61—41no—
316Dic61—41no—
317Dic61—42no—
318Dic61—41no—
319Dic61—42no—
320C2×#442—611no—
321#2319—611no—
322#2275—611no—
323#1926—611no—
324#1925—611no—
325#1920—611no—
326#1919—611no—
327#1879—611no—
328#1879—611no—
329#1864—611no—
330#1862—611no—
331#1776—611no—
332C4×#102—611no—
333C4×#102D6111yescharacteristic, complemented
334#1746—611no—
335C2×C61—44no—
336C2×C61#229011yescharacteristic
337C2×C61#294611yescharacteristic
338C2×C61#294611yescharacteristic
339C2×C61#311811yescharacteristic
340C2×C61#311911yescharacteristic
341C2×C61#312211yescharacteristic
342C2×C61#312511yescharacteristic
343D61—82no—
344C22×D8—611no—
345C2×C4×D4—611no—
346C2×C4×D4—611no—
347C2×C4×D4—611no—
348C2×C4×D4C2×D6111yescharacteristic
349#442—618no—
350C2×#107—611no—
351C2×#106—611no—
352C2×#106—611no—
353C2×#102—611no—
354C2×#102—611no—
355C2×#102—611no—
356C2×#102—611no—
357C2×#102C2×D6111yescharacteristic
358C2×#102C2×D6111yescharacteristic
359C2×#97—611no—
360C2×C4×C8C2×D6111yescharacteristic
361#390—611no—
362#390—611no—
363#389—611no—
364#389—611no—
365#388—1221no—
366#388—1221no—
367#381—1221no—
368#380—1221no—
369C4×C4⋊C4—611no—
370C4×C4⋊C4—611no—
371C4×C4⋊C4—611no—
372C4×C4⋊C4C2×D6111yescharacteristic
373C4×C22⋊C4—1221no—
374C4×C22⋊C4—1221no—
375C4×C22⋊C4—1221no—
376#376—611no—
377C2×#95—1221no—
378#340—611no—
379#340—611no—
380#340—611no—
381#340—611no—
382#340C2×D6111yescharacteristic
383#340C2×D6111yescharacteristic
384#336—611no—
385#336—611no—
386#336—611no—
387#336—611no—
388C61#2112611yescharacteristic, complemented, Sylow
389C22×D4—611no—
390C22×D4C22×D6111yescharacteristic
391C23×C4—21no—
392C23×C4—1221no—
393C23×C4—1221no—
394C23×C4—1221no—
395C2×D8—614no—
396C2×D8—1222no—
397C2×D8—1222no—
398C22×C8—611no—
399C22×C8—611no—
400C22×C8C22×D6111yescharacteristic
401C22×C8C22×D6111yescharacteristic
402C4×D4—22no—
403C4×D4—614no—
404C4×D4—1222no—
405C4×D4—1222no—
406C4×D4—1222no—
407C4×D4—1222no—
408C4×D4—1222no—
409C4×D4C4×D6114yes—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4C22×D6111yescharacteristic
416C2×C4⋊C4C22×D6111yescharacteristic
417C2×C4⋊C4C22×D6111yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—1221no—
420C2×C22⋊C4—1221no—
421C2×C22⋊C4—1221no—
422C2×C22⋊C4—1221no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1221no—
425C2×C22⋊C4—1221no—
426C2×C42—21no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—1221no—
430C2×C42—1221no—
431C2×C42—1221no—
432C2×C42C22×D6111yescharacteristic
433#107—1222no—
434#106—614no—
435#106—1222no—
436#102—22no—
437#102—22no—
438#102—614no—
439#102—614no—
440#102—1222no—
441#102—1222no—
442#97—614no—
443C4×C8—22no—
444#95—21no—
445#95—611no—
446#95—611no—
447#95—611no—
448#95—611no—
449#95—1221no—
450#95—1221no—
451#95—1221no—
452#95—1221no—
453#95—1221no—
454C24—21no—
455C24—1221no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—612no—
460C2×D4—1221no—
461C2×D4—1221no—
462C2×D4—1221no—
463C2×D4—1221no—
464C2×D4—1221no—
465C2×D4C2×C4×D6112yes—
466C2×D4#1175822212yes—
467C2×D4#1175822212yes—
468C22×C4—21no—
469C22×C4—24no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—81no—
473C22×C4—81no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—1224no—
479C22×C4—1224no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1224no—
484C22×C4—4881no—
485C22×C4—4881no—
486C22×C4—4881no—
487C22×C4—4881no—
488C22×C4—4881no—
489C22×C4—4881no—
490C22×C4D4×D6111yescharacteristic
491C22×C4D4×D6111yescharacteristic
492C22×C4C23×D6111yescharacteristic
493D8—1228no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—612no—
501C2×C8—612no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1221no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—612no—
512C4⋊C4—612no—
513C4⋊C4—612no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—1221no—
517C4⋊C4—4881no—
518C4⋊C4—4881no—
519C4⋊C4C2×C4×D6112yes—
520C22⋊C4—24no—
521C22⋊C4—1224no—
522C22⋊C4—1224no—
523C22⋊C4—1224no—
524C22⋊C4—4881no—
525C22⋊C4—4881no—
526C22⋊C4—4881no—
527C22⋊C4—4881no—
528C42—81no—
529C42—1221no—
530C42—1221no—
531C42—1221no—
532C42—1221no—
533C42—4881no—
534C42—4881no—
535C42—4881no—
536C42C2×C4×D6112yes—
537C42#1175822412yes—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—1222no—
546C23—2441no—
547C23—2441no—
548C23—2441no—
549C23—2441no—
550C23—2441no—
551C23—2441no—
552C23C2×D4×D6111yescharacteristic
553D4—22no—
554D4—22no—
555D4—22no—
556D4—1222no—
557D4—1222no—
558D4—2441no—
559D4—2441no—
560D4#1451973414yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—84no—
575C2×C4—1222no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1222no—
581C2×C4—1222no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—4884no—
591C2×C4—4884no—
592C2×C4—4884no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4#1451973712yes—
600C2×C4#1451973712yes—
601C2×C4C22×C4×D6111yescharacteristic
602C2×C4#41×D6111yescharacteristic
603C2×C4#41×D6111yescharacteristic
604C2×C4C2×#1175822411yescharacteristic
605C2×C4C2×#1175822211yescharacteristic
606C2×C4C2×#1175822211yescharacteristic
607C8—41no—
608C8—41no—
609C8—1222no—
610C8—1222no—
611C22—24no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—4881no—
619C22—4881no—
620C22—4881no—
621C22—4881no—
622C22—2442no—
623C22—2442no—
624C22—2442no—
625C22C2×#1451973711yescharacteristic
626C22#1684027111yescharacteristic
627C22#1684027111yescharacteristic
628C22#1684056311yescharacteristic
629C22#1684056411yescharacteristic
630C22#1684056811yescharacteristic
631C22#1684056911yescharacteristic
632C4—22no—
633C4—22no—
634C4—42no—
635C4—81no—
636C4—81no—
637C4—2442no—
638C4—2441no—
639C4—2442no—
640C4—2441no—
641C4—2441no—
642C4—2442no—
643C4—2441no—
644C4C2×#1451973411yescharacteristic
645C4#1684023011yescharacteristic
646C4#1684029211yescharacteristic
647C4#1684029211yescharacteristic
648C2—44no—
649C2—4882no—
650C2#2144825811yescharacteristic
651C2#2145464511yescharacteristic
652C2#2145465411yescharacteristic
653C2#2145600911yescharacteristic
654C2#2145601411yescharacteristic
655C2#2145605911yescharacteristic
656C2#2145609211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#102×C61C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
cosocleC22×C4×C61C24
hypercenterC4×#102D61
hypocenterC61#21126
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. #21448457C2semidirect
3. #21448180C2semidirect
4. #21446444C2semidirect
5. #21446437C2semidirect
6. #21446402C2semidirect
7. #21446395C2semidirect
10. #21446078C2semidirect
11. #21446064C2semidirect
12. #21445717C2semidirect
13. C4×#14519699C2semidirect
14. #21445570C2semidirect
15. C4×#102×C61C2semidirect
20. #16839872C4semidirect
70. C4×D244C2×C4semidirect
94. #14519708C2×C4semidirect
98. #14519697C2×C4semidirect
99. #14519688C2×C4semidirect
333. C4×#102D61semidirect
388. C61#21126semidirect

Maximal subgroups

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

subgroupindex
C2×#168398722
#214484572
#214481802
#214464442
#214464372
#214464022
#214463952
#214461652
#214460782
#214460642
#214457172
C4×#145196992
#214455702
C4×#102×C612
#2112661