Finite Group Databasebeta

← #29699756

Subgroups — #29699756

Order 15616.

934 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×#16839842C211yesmaximal, characteristic
2#21448767C211yesmaximal, characteristic, complemented
3#21448764C211yesmaximal, characteristic, complemented
4#21446684C211yesmaximal, characteristic
5#21446682C211yesmaximal, characteristic
6#21446441C211yesmaximal, characteristic, complemented
7#21446440C211yesmaximal, characteristic, complemented
8#21446438C211yesmaximal, characteristic, complemented
9#21445977C211yesmaximal, characteristic, complemented
10#21445818C211yesmaximal, characteristic, complemented
11#21445817C211yesmaximal, characteristic, complemented
12C4×#14519710C211yesmaximal, characteristic, complemented
13#21445711C211yesmaximal, characteristic, complemented
14#21445680C211yesmaximal, characteristic, complemented
15C61×#1925C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×D4×Dic61C2211yescharacteristic
18C2×#14519739C2211yescharacteristic
19C2×#14519734—21no—
20C2×#14519733—21no—
21#16839842C418yescomplemented
22C2×#14519711C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×#14519710C2211yescharacteristic
25C2×#14519710C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×C4×#92418C2211yescharacteristic
32C2×C8×Dic61C2211yescharacteristic
33C2×C8×Dic61C2211yescharacteristic
34#16839665C2211yescharacteristic
35#16839664C2211yescharacteristic
36#16839663C2211yescharacteristic
37#16839656—21no—
38#16839653—21no—
39#16839651—21no—
40#16839650—21no—
41#16839631C2211yescharacteristic
42#16839631C2211yescharacteristic
43#16839621—21no—
44#16839620—21no—
45C4⋊C4×Dic61C2211yescharacteristic
46C4⋊C4×Dic61C2211yescharacteristic
47C4×#11758196C2211yescharacteristic
48C4×C4⋊Dic61C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C61×#390C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C22×D244C2311yescharacteristic
61C23×Dic61—21no—
62C22×C4×D61—21no—
63C2×#11758199—22no—
64C2×#11758199—22no—
65C2×#11758199C2×C414yes—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68D4×Dic61—22no—
69D4×Dic61C2×C414yes—
70#14519739—22no—
71#14519739C2×C414yes—
72#14519734—44no—
73#14519733—44no—
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196D411yescharacteristic
82C2×#11758196D411yescharacteristic
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61C2311yescharacteristic
95C2×C4×Dic61C2311yescharacteristic
96#14519711—41no—
97#14519710—22no—
98#14519710—22no—
99#14519710C2×C414yes—
100#14519706—22no—
101#14519699—41no—
102#14519699C2×C414yes—
103#14519698—41no—
104#14519697—41no—
105C4×#92418—22no—
106C8×Dic61—22no—
107C8×Dic61C2×C414yes—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684D411yescharacteristic
112#14519684D411yescharacteristic
113C22×D4×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C22×C8×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C42×C61—21no—
122C2×C42×C61C2311yescharacteristic
123#107×C61—41no—
124#102×C61—41no—
125#102×C61C2×C414yes—
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—21no—
137C22×C4×C61—21no—
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2411yescharacteristic
141C22×Dic61—21no—
142C22×Dic61—24no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—42no—
146C22×Dic61—42no—
147C22×Dic61C2×D411yescharacteristic
148C22×Dic61C2×D411yescharacteristic
149C22×Dic61C2×D411yescharacteristic
150C22×Dic61C2×D411yescharacteristic
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—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61C22×C412yes—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61C22×C412yes—
172C22⋊C4×C61—42no—
173C22⋊C4×C61—81no—
174C42×C61—21no—
175C42×C61—21no—
176C42×C61—42no—
177C22⋊Dic61—24no—
178C22⋊Dic61—42no—
179C22⋊Dic61—81no—
180#11758199—28no—
181#11758198—24no—
182#11758198—42no—
183#11758198—42no—
184#11758198—81no—
185#11758198—81no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61C22×C412yes—
192#11758196—22no—
193#11758196—42no—
194#11758196—42no—
195#11758196—81no—
196#11758196—81no—
197#11758196D814yescomplemented
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—42no—
201C4×Dic61—42no—
202C4×Dic61—42no—
203C4×Dic61C22×C412yes—
204C4×Dic61#4112yes—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418C22×C412yes—
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—22no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61C2×D812yes—
245C2×C4×C61C23×C411yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C2×C4×C61H(5,𝔽2)11yescharacteristic
250C2×C4×C612−1+411yescharacteristic
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—22no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—48no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61C4×D412yes—
269C2×Dic61C4×D412yes—
270C2×Dic61C2×D812yes—
271C2×Dic61C2×D812yes—
272C2×Dic61#13512yes—
273D244—22no—
274D244—22no—
275D244—41no—
276D244—41no—
277C4×D61—48no—
278C8×C61—22no—
279C8×C61—41no—
280#92418—41no—
281#92418#11714yescomplemented
282#22807—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#54711yescharacteristic
292C22×C61#55011yescharacteristic
293C22×C61C22×D811yescharacteristic
294C22×C61C2×#13511yescharacteristic
295C22×C61#57611yescharacteristic
296C22×C61#57811yescharacteristic
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—41no—
306C4×C61—42no—
307C4×C61—81no—
308C4×C61—81no—
309C4×C61C2×#11711yescharacteristic
310C4×C61#52011yescharacteristic
311C4×C61#55511yescharacteristic
312C4×C61#55611yescharacteristic
313Dic61—22no—
314Dic61—22no—
315Dic61—41no—
316Dic61—42no—
317Dic61—81no—
318Dic61—81no—
319Dic61C4×D814yes—
320C2×C4×D8—611no—
321#2354—611no—
322#2354—611no—
323#1970—611no—
324#1970—611no—
325#1925—611no—
326#1925—611no—
327#1925—611no—
328#1925D6111yescharacteristic, complemented
329#1845—611no—
330#1802—611no—
331#1802—611no—
332C4×#107—611no—
333C4×#107—611no—
334C8×C4⋊C4—611no—
335C2×C61—82no—
336C2×C61#235411yescharacteristic
337C2×C61C2×C4×D811yescharacteristic
338C2×C61#295111yescharacteristic
339C2×C61#333411yescharacteristic
340C2×C61#334111yescharacteristic
341C2×C61#339111yescharacteristic
342C2×C61#339311yescharacteristic
343D61—82no—
344C22×D8—611no—
345C2×C4×D4—611no—
346C2×C4×D4—611no—
347C2×#117—1221no—
348C2×#117—1221no—
349C4×D8—618no—
350C2×#107—611no—
351C2×#107—611no—
352C2×#107—611no—
353C2×#107—611no—
354C2×#107C2×D6111yescharacteristic
355C2×C4⋊C8—611no—
356C2×#102—611no—
357C2×#102—611no—
358C2×#102—611no—
359C2×#102—611no—
360C2×#102C2×D6111yescharacteristic
361C2×#102C2×D6111yescharacteristic
362C2×C4×C8—611no—
363C2×C4×C8—611no—
364C2×C4×C8—611no—
365#390—611no—
366#390—611no—
367#390—611no—
368#390C2×D6111yescharacteristic
369#388—1221no—
370#388—1221no—
371#388—1221no—
372#388—1221no—
373#384—611no—
374#384—611no—
375#380—1221no—
376#380—1221no—
377C4×C4⋊C4—611no—
378C4×C4⋊C4—611no—
379C4×C4⋊C4—611no—
380C4×C4⋊C4—611no—
381C4×C4⋊C4C2×D6111yescharacteristic
382#340—611no—
383#340—611no—
384#340—611no—
385#340C2×D6111yescharacteristic
386#336—611no—
387#336C2×D6111yescharacteristic
388C61#2280711yescharacteristic, complemented, Sylow
389C22×D4—611no—
390C22×D4C22×D6111yescharacteristic
391C23×C4—1221no—
392C23×C4—1221no—
393C2×D8—614no—
394C2×D8—1222no—
395C2×D8—1222no—
396C22×C8—611no—
397C22×C8—611no—
398C22×C8C22×D6111yescharacteristic
399C22×C8C22×D6111yescharacteristic
400C4×D4—614no—
401C4×D4—614no—
402C4×D4—1222no—
403C4×D4—1222no—
404#117—2444no—
405#117—2444no—
406C2×C4⋊C4—611no—
407C2×C4⋊C4—611no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
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—21no—
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×C22⋊C4—1221no—
427C2×C22⋊C4—1221no—
428C2×C42—21no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—1221no—
432C2×C42—1221no—
433C2×C42—1221no—
434C2×C42C22×D6111yescharacteristic
435#107—41no—
436#107—614no—
437#107—1222no—
438#107—1222no—
439#107—2441no—
440C4⋊C8—1222no—
441#102—41no—
442#102—614no—
443#102—2441no—
444#102—2441no—
445#102—2441no—
446#102C4×D6114yes—
447C4×C8—614no—
448C4×C8—1222no—
449C4×C8—1222no—
450#95—21no—
451#95—611no—
452#95—611no—
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—21no—
472C22×C4—21no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—1224no—
478C22×C4—1224no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—2442no—
483C22×C4—2442no—
484C22×C4—2442no—
485C22×C4—2442no—
486C22×C4D4×D6111yescharacteristic
487C22×C4D4×D6111yescharacteristic
488C22×C4C23×D6111yescharacteristic
489D8—1228no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—612no—
496C2×C8—612no—
497C2×C8—612no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—1221no—
501C2×C8C2×C4×D6112yes—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—614no—
508C4⋊C4—612no—
509C4⋊C4—1222no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—4881no—
516C4⋊C4—4881no—
517C4⋊C4—2442no—
518C4⋊C4—2442no—
519C4⋊C4C2×C4×D6112yes—
520C22⋊C4—42no—
521C22⋊C4—81no—
522C22⋊C4—1224no—
523C22⋊C4—1224no—
524C22⋊C4—4881no—
525C22⋊C4—4881no—
526C22⋊C4—4881no—
527C22⋊C4—2442no—
528C22⋊C4—2442no—
529C22⋊C4—2442no—
530C42—21no—
531C42—21no—
532C42—42no—
533C42—612no—
534C42—612no—
535C42—1221no—
536C42—1221no—
537C42—2442no—
538C42—2442no—
539C42—2442no—
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—
554C23C2×D4×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—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—612no—
578C2×C4—612no—
579C2×C4—612no—
580C2×C4—612no—
581C2×C4—612no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1222no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—2448no—
591C2×C4—2448no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4D8×D6112yes—
601C2×C4C22×C4×D6111yescharacteristic
602C2×C4#41×D6111yescharacteristic
603C2×C4#41×D6111yescharacteristic
604C2×C4#41×D6111yescharacteristic
605C2×C4#1451982211yescharacteristic
606C2×C4#1451982411yescharacteristic
607C8—22no—
608C8—41no—
609C8—614no—
610C8—2441no—
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—
625C22C4×D4×D6111yescharacteristic
626C22#1684041011yescharacteristic
627C22#1684043011yescharacteristic
628C22C2×D8×D6111yescharacteristic
629C22#135×D6111yescharacteristic
630C22#1684056611yescharacteristic
631C22#1684057811yescharacteristic
632C4—22no—
633C4—41no—
634C4—42no—
635C4—81no—
636C4—81no—
637C4—614no—
638C4—1222no—
639C4—1222no—
640C4—4881no—
641C4—4881no—
642C4—2441no—
643C4—2442no—
644C4#117×D6111yescharacteristic
645C4#1684024111yescharacteristic
646C4#1684047411yescharacteristic
647C4#1684047911yescharacteristic
648C2—82no—
649C2—4882no—
650C2#2144876511yescharacteristic
651C2C4×D8×D6111yescharacteristic
652C2#2145469111yescharacteristic
653C2#2145816111yescharacteristic
654C2#2145823611yescharacteristic
655C2#2145879011yescharacteristic
656C2#2145880211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1925C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
cosocleC22×C4×C61C24
hypercenter#1925D61
hypocenterC61#22807
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
2. #21448767C2semidirect
3. #21448764C2semidirect
6. #21446441C2semidirect
7. #21446440C2semidirect
8. #21446438C2semidirect
9. #21445977C2semidirect
10. #21445818C2semidirect
11. #21445817C2semidirect
12. C4×#14519710C2semidirect
13. #21445711C2semidirect
14. #21445680C2semidirect
15. C61×#1925C2semidirect
21. #16839842C4semidirect
197. #11758196D8semidirect
281. #92418#117semidirect
328. #1925D61semidirect
388. C61#22807semidirect

Maximal subgroups

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

subgroupindex
C2×#168398422
#214487672
#214487642
#214466842
#214466822
#214464412
#214464402
#214464382
#214459772
#214458182
#214458172
C4×#145197102
#214457112
#214456802
C61×#19252
#2280761