Finite Group Databasebeta

← #29684324

Subgroups — #29684324

Order 15616.

950 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#21448283C211yesmaximal, characteristic, complemented
3#21446694C211yesmaximal, characteristic
4#21446684C211yesmaximal, characteristic
5#21446559C211yesmaximal, characteristic, complemented
6#21446544C211yesmaximal, characteristic, complemented
7#21446519C211yesmaximal, characteristic, complemented
8#21446515C211yesmaximal, characteristic, complemented
9#21446505C211yesmaximal, characteristic, complemented
10#21446501C211yesmaximal, characteristic, complemented
11#21445717C211yesmaximal, characteristic, complemented
12#21445647C211yesmaximal, characteristic, complemented
13#21445644C211yesmaximal, characteristic, complemented
14C4×#14519688C211yesmaximal, characteristic, complemented
15C61×#2293C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18C2×#14519734—21no—
19#16839872C418yescomplemented
20C2×#14519710C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519688C2211yescharacteristic
30C2×#14519688C2211yescharacteristic
31C2×#14519688C2211yescharacteristic
32C2×#14519688C2211yescharacteristic
33C2×C4×#92418C2211yescharacteristic
34C2×C4×#92418C2211yescharacteristic
35#16839664C2211yescharacteristic
36#16839664C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839660C2211yescharacteristic
39#16839653—21no—
40#16839653—21no—
41C4×C4⋊Dic61C2211yescharacteristic
42C4×#11758198—21no—
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49C2×C4×D4×C61C2211yescharacteristic
50C2×#117×C61—21no—
51C61×#390C2211yescharacteristic
52C61×#390C2211yescharacteristic
53C61×#389C2211yescharacteristic
54C61×#389C2211yescharacteristic
55C61×#388—21no—
56C61×#388—21no—
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C22⋊C4×C61—21no—
59C43×C61C2211yescharacteristic
60C22×D244C2311yescharacteristic
61C22×C4×D61—21no—
62C2×#11758199—22no—
63C2×#11758199—22no—
64C2×#11758199C2×C414yes—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C4×D244—22no—
70C4×D244C2×C414yes—
71#14519734—44no—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×C4×Dic61—21no—
83#14519710—22no—
84#14519708—22no—
85#14519708C2×C414yes—
86#14519698—22no—
87#14519698—22no—
88#14519698C2×C414yes—
89#14519697—22no—
90#14519697—22no—
91#14519697C2×C414yes—
92#14519688—22no—
93#14519688—22no—
94#14519688—22no—
95#14519688C2×C414yes—
96C4×#92418—22no—
97C4×#92418—22no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101C22×D4×C61C2311yescharacteristic
102C23×C4×C61—21no—
103C4×D4×C61—22no—
104C4×D4×C61C2×C414yes—
105#117×C61—44no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C22⋊C4×C61—21no—
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C42×C61—21no—
117C2×C42×C61D411yescharacteristic
118C2×C42×C61D411yescharacteristic
119C2×C42×C61D411yescharacteristic
120C2×C42×C61D411yescharacteristic
121C2×C42×C61C2311yescharacteristic
122C2×C42×C61C2311yescharacteristic
123C2×C42×C61C2311yescharacteristic
124#95×C61—21no—
125#95×C61—21no—
126#95×C61—21no—
127C24×C61—21no—
128C23×D61—21no—
129C2×D4×C61—21no—
130C2×D4×C61—21no—
131C2×D4×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61C22×C412yes—
135C22×C4×C61—21no—
136C22×C4×C61—24no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—42no—
140C22×C4×C61—42no—
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2411yescharacteristic
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244—21no—
156C2×D244C22×C412yes—
157C2×C4×D61—24no—
158C2×C4×D61—42no—
159C2×C4×D61—42no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—42no—
166C4⋊C4×C61—42no—
167C4⋊C4×C61C22×C412yes—
168C22⋊C4×C61—24no—
169C22⋊C4×C61—42no—
170C22⋊C4×C61—42no—
171C22⋊C4×C61—42no—
172C22⋊C4×C61—42no—
173C42×C61—22no—
174C42×C61—22no—
175C42×C61—21no—
176C42×C61—21no—
177C42×C61—21no—
178C42×C61—21no—
179C42×C61—41no—
180C42×C61—41no—
181C42×C61—42no—
182C42×C61C22×C412yes—
183C42×C61#4112yes—
184#11758199—28no—
185#11758198—24no—
186#11758198—42no—
187#11758198—42no—
188#11758198—42no—
189#11758198—42no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61C22×C412yes—
196#11758196—42no—
197#11758196—42no—
198C4×Dic61—42no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418C22×C412yes—
206C2×#92418C22×C412yes—
207C2×#92418#4112yes—
208C2×#92418#4112yes—
209C2×#92418#4112yes—
210C2×#92418#4112yes—
211C23×C61—22no—
212C23×C61—41no—
213C23×C61—41no—
214C23×C61—41no—
215C23×C61—41no—
216C23×C61—41no—
217C23×C61—41no—
218C23×C61C22×D411yescharacteristic
219C22×D61—22no—
220C22×D61—41no—
221C22×D61—41no—
222C22×D61—41no—
223C22×D61—41no—
224C22×D61—41no—
225C22×D61—41no—
226D4×C61—22no—
227D4×C61—22no—
228D4×C61—41no—
229D4×C61—41no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—22no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—48no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61C4×D412yes—
255C2×C4×C61C4×D412yes—
256C2×C4×C61AGL(1,ℤ/8)12yes—
257C2×C4×C61AGL(1,ℤ/8)12yes—
258C2×C4×C61C23×C411yescharacteristic
259C2×C4×C61C2×#4111yescharacteristic
260C2×C4×C61C2×#4111yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C2×C4×C61C2×#4111yescharacteristic
264C2×Dic61—22no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273D244—22no—
274D244—22no—
275D244—41no—
276D244—41no—
277C4×D61—48no—
278#92418—22no—
279#92418—22no—
280#92418—22no—
281#92418#11714yescomplemented
282#21286—611nomaximal, Sylow
283C22×C61—42no—
284C22×C61—42no—
285C22×C61—42no—
286C22×C61—81no—
287C22×C61—81no—
288C22×C61—81no—
289C22×C61—81no—
290C22×C61C2×C4×D411yescharacteristic
291C22×C61#53211yescharacteristic
292C22×C61#53211yescharacteristic
293C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
294C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
295C22×C61#57511yescharacteristic
296C22×C61#57511yescharacteristic
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—22no—
307C4×C61—22no—
308C4×C61—41no—
309C4×C61—41no—
310C4×C61—42no—
311C4×C61—81no—
312C4×C61—81no—
313C4×C61C2×#11711yescharacteristic
314C4×C61C4×#4111yescharacteristic
315C4×C61#52911yescharacteristic
316C4×C61#52911yescharacteristic
317Dic61—42no—
318Dic61—81no—
319Dic61—81no—
320C2×#442—611no—
321#2293—611no—
322#2293D6111yescharacteristic, complemented
323#1972—611no—
324#1970—611no—
325#1944—611no—
326#1941—611no—
327#1936—611no—
328#1936—611no—
329#1934—611no—
330#1934—611no—
331#1776—611no—
332#1762—611no—
333#1762—611no—
334C4×#97—611no—
335C2×C61—82no—
336C2×C61#229311yescharacteristic
337C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
338C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
339C2×C61#318011yescharacteristic
340C2×C61#318011yescharacteristic
341C2×C61#318311yescharacteristic
342C2×C61#318411yescharacteristic
343D61—82no—
344C22×D8—611no—
345C2×C4×D4—611no—
346C2×C4×D4C2×D6111yescharacteristic
347C2×#117—21no—
348C2×#117—1221no—
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×#102—611no—
358C2×#102—611no—
359C2×#97—611no—
360C2×#97—611no—
361C2×#97—611no—
362C2×#97—611no—
363C2×C4×C8—611no—
364C2×C4×C8—611no—
365#390—611no—
366#390—611no—
367#390C2×D6111yescharacteristic
368#390C2×D6111yescharacteristic
369#389—611no—
370#389—611no—
371#389C2×D6111yescharacteristic
372#389C2×D6111yescharacteristic
373#388—21no—
374#388—21no—
375#388—1221no—
376#388—1221no—
377C4×C4⋊C4—611no—
378C4×C4⋊C4C2×D6111yescharacteristic
379C4×C22⋊C4—21no—
380C4×C22⋊C4—1221no—
381C43C2×D6111yescharacteristic
382#340—611no—
383#340—611no—
384#340—611no—
385#340—611no—
386#340—611no—
387#340—611no—
388C61#2128611yescharacteristic, complemented, Sylow
389C22×D4—611no—
390C22×D4C22×D6111yescharacteristic
391C23×C4—21no—
392C23×C4—1221no—
393C2×D8—614no—
394C2×D8—1222no—
395C2×D8—1222no—
396C22×C8—611no—
397C22×C8—611no—
398C22×C8—611no—
399C22×C8—611no—
400C4×D4—22no—
401C4×D4—614no—
402C4×D4—1222no—
403C4×D4C4×D6114yes—
404#117—44no—
405#117—2444no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4C22×D6111yescharacteristic
414C2×C4⋊C4C22×D6111yescharacteristic
415C2×C4⋊C4C22×D6111yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
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—1221no—
428C2×C42C22⋊D6111yescharacteristic
429C2×C42C22⋊D6111yescharacteristic
430C2×C42C22⋊D6111yescharacteristic
431C2×C42C22⋊D6111yescharacteristic
432C2×C42C22×D6111yescharacteristic
433C2×C42C22×D6111yescharacteristic
434C2×C42C22×D6111yescharacteristic
435#107—1222no—
436#106—614no—
437#106—1222no—
438#102—614no—
439#102—614no—
440#102—1222no—
441#102—1222no—
442#102—1222no—
443#102—1222no—
444#97—614no—
445#97—1222no—
446#97—1222no—
447#97—1222no—
448C4×C8—1222no—
449C4×C8—1222no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—1221no—
454#95—1221no—
455#95—1221no—
456C24—21no—
457C24—1221no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—612no—
464C2×D4—1221no—
465C2×D4—1221no—
466C2×D4—1221no—
467C2×D4—1221no—
468C2×D4—1221no—
469C2×D4C2×C4×D6112yes—
470C22×C4—21no—
471C22×C4—24no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—1221no—
477C22×C4—1224no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—2442no—
481C22×C4—2442no—
482C22×C4C2×C22⋊D6111yescharacteristic
483C22×C4C2×C22⋊D6111yescharacteristic
484C22×C4C2×C22⋊D6111yescharacteristic
485C22×C4C2×C22⋊D6111yescharacteristic
486C22×C4C2×C22⋊D6111yescharacteristic
487C22×C4C2×C22⋊D6111yescharacteristic
488C22×C4C23×D6111yescharacteristic
489D8—1228no—
490C2×C8—612no—
491C2×C8—612no—
492C2×C8—612no—
493C2×C8—612no—
494C2×C8—612no—
495C2×C8—612no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—1221no—
501C2×C8—1221no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—612no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—2442no—
516C4⋊C4—2442no—
517C4⋊C4C2×C4×D6112yes—
518C22⋊C4—24no—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—1224no—
524C22⋊C4—2442no—
525C22⋊C4—2442no—
526C22⋊C4—2442no—
527C22⋊C4—2442no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—22no—
533C42—22no—
534C42—41no—
535C42—41no—
536C42—42no—
537C42—2442no—
538C42C2×C4×D6112yes—
539C42#1175822212yes—
540C23—22no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—1222no—
548C23—2441no—
549C23—2441no—
550C23—2441no—
551C23—2441no—
552C23—2441no—
553C23—2441no—
554C23C22×C22⋊D6111yescharacteristic
555D4—22no—
556D4—22no—
557D4—41no—
558D4—41no—
559D4—1222no—
560D4—1222no—
561D4—2441no—
562D4—2441no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—48no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—1222no—
588C2×C4—2448no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4C4×C22⋊D6112yes—
598C2×C4C4×C22⋊D6112yes—
599C2×C4#1451980212yes—
600C2×C4#1451980312yes—
601C2×C4C22×C4×D6111yescharacteristic
602C2×C4#41×D6111yescharacteristic
603C2×C4#41×D6111yescharacteristic
604C2×C4#41×D6111yescharacteristic
605C2×C4#41×D6111yescharacteristic
606C2×C4C2×#1175822211yescharacteristic
607C8—614no—
608C8—1222no—
609C8—1222no—
610C8—1222no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—4881no—
619C22—4881no—
620C22—4881no—
621C22—4881no—
622C22—2442no—
623C22—2442no—
624C22—2442no—
625C22C2×C4×C22⋊D6111yescharacteristic
626C22#1684030811yescharacteristic
627C22#1684030811yescharacteristic
628C22C2×#1451980211yescharacteristic
629C22C2×#1451980311yescharacteristic
630C22#1684056011yescharacteristic
631C22#1684056011yescharacteristic
632C4—22no—
633C4—22no—
634C4—22no—
635C4—22no—
636C4—42no—
637C4—41no—
638C4—41no—
639C4—81no—
640C4—81no—
641C4—4881no—
642C4—4881no—
643C4—2442no—
644C4#117×D6111yescharacteristic
645C4#1684023011yescharacteristic
646C4#1684029011yescharacteristic
647C4#1684029011yescharacteristic
648C2—82no—
649C2—4882no—
650C2#2144827811yescharacteristic
651C2C4×#1451980211yescharacteristic
652C2C4×#1451980311yescharacteristic
653C2#2145651111yescharacteristic
654C2#2145651811yescharacteristic
655C2#2145654211yescharacteristic
656C2#2145655311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2293C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
cosocleC22×C4×C61C24
hypercenter#2293D61
hypocenterC61#21286
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C43 ◁ #2293

Complements

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

NH ≅ G/Ntype
2. #21448283C2semidirect
5. #21446559C2semidirect
6. #21446544C2semidirect
7. #21446519C2semidirect
8. #21446515C2semidirect
9. #21446505C2semidirect
10. #21446501C2semidirect
11. #21445717C2semidirect
12. #21445647C2semidirect
13. #21445644C2semidirect
14. C4×#14519688C2semidirect
15. C61×#2293C2semidirect
19. #16839872C4semidirect
281. #92418#117semidirect
322. #2293D61semidirect
388. C61#21286semidirect

Maximal subgroups

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

subgroupindex
C2×#168398722
#214482832
#214466942
#214466842
#214465592
#214465442
#214465192
#214465152
#214465052
#214465012
#214457172
#214456472
#214456442
C4×#145196882
C61×#22932
#2128661