Finite Group Databasebeta

← #29752672

Subgroups — #29752672

Order 15616.

812 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450242C211yesmaximal, characteristic, complemented
2#21448831C211yesmaximal, characteristic
3#21447225C211yesmaximal, characteristic, complemented
4#21447203C211yesmaximal, characteristic, complemented
5#21447000C211yesmaximal, characteristic
6#21446999C211yesmaximal, characteristic
7#21446576C211yesmaximal, characteristic, complemented
8#21446549C211yesmaximal, characteristic, complemented
9#21446423C211yesmaximal, characteristic, complemented
10#21446392C211yesmaximal, characteristic, complemented
11#21446391C211yesmaximal, characteristic, complemented
12#21446005C211yesmaximal, characteristic, complemented
13#21445904C211yesmaximal, characteristic, complemented
14C4×#14519698C211yesmaximal, characteristic, complemented
15C61×#1862C211yesmaximal, characteristic, complemented
16C2×#14519772—21no—
17C2×#14519748C2211yescharacteristic
18C2×C4×C22⋊D61—21no—
19C2×C4⋊C4×D61C2211yescharacteristic
20C2×#14519711C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519706C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519689C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28C2×C4×#92418C2211yescharacteristic
29#16839704—21no—
30#16839691—21no—
31#16839665C2211yescharacteristic
32#16839661C2211yescharacteristic
33#16839660C2211yescharacteristic
34#16839656—21no—
35#16839643—21no—
36#16839638—21no—
37#16839635—21no—
38#16839631C2211yescharacteristic
39#16839619C2211yescharacteristic
40#16839619C2211yescharacteristic
41C4⋊C4×Dic61C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic
43C4×#11758198C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C61×#389C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×C22⋊D61—21no—
60C22×C4×D61—21no—
61C22×C4×D61C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64#14519772—44no—
65#14519748—22no—
66#14519748—22no—
67C4×C22⋊D61—44no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C4⋊C4×D61—22no—
78C4⋊C4×D61—41no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198D411yescharacteristic
85C2×#11758198D411yescharacteristic
86C2×C4×Dic61—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61C2311yescharacteristic
89#14519711—22no—
90#14519710—22no—
91#14519710—41no—
92#14519706—22no—
93#14519698—22no—
94#14519698—22no—
95#14519689—22no—
96#14519689—41no—
97C4×#92418—41no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684D411yescharacteristic
105#14519684D411yescharacteristic
106C22×D4×C61C2311yescharacteristic
107C23×C4×C61—21no—
108C22×C8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C4×D4×C61—22no—
111C4×D4×C61—41no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C22⋊C4×C61—21no—
117C2×C42×C61C2311yescharacteristic
118#107×C61—22no—
119#102×C61—22no—
120#102×C61—41no—
121#95×C61—21no—
122C24×C61—21no—
123C23×D61C2×D411yescharacteristic
124C2×D4×C61—21no—
125C2×D4×C61—21no—
126C2×D4×C61—21no—
127C2×D4×C61—21no—
128C2×D4×C61—21no—
129C2×D4×C61#4112yes—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—42no—
134C22×C4×C61—42no—
135C22×C4×C61—81no—
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2411yescharacteristic
139C2×C22⋊D61—24no—
140C2×C22⋊D61—42no—
141C2×C22⋊D61—42no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61C2×D411yescharacteristic
147C22×Dic61C2×D411yescharacteristic
148C22×Dic61C2×D411yescharacteristic
149C2×C4×D61—21no—
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—42no—
156C2×C4×D61—42no—
157C2×C4×D61—81no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—42no—
170C4⋊C4×C61#4112yes—
171C22⋊C4×C61—42no—
172C42×C61—21no—
173C42×C61—21no—
174C22⋊Dic61—24no—
175C22⋊Dic61—42no—
176C22⋊Dic61—81no—
177#11758198—41no—
178#11758198—42no—
179#11758198—42no—
180#11758198D814yes—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—42no—
189C4⋊Dic61#4112yes—
190#11758196—42no—
191#11758196—42no—
192#11758196—42no—
193#11758196—42no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—42no—
197C4×Dic61—42no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418#4112yes—
204C23×C61—22no—
205C23×C61—41no—
206C23×C61—41no—
207C23×C61—41no—
208C23×C61—41no—
209C23×C61—41no—
210C23×C61—41no—
211C23×C61C22×D411yescharacteristic
212C22×D61—21no—
213C22×D61—21no—
214C22×D61—21no—
215C22×D61—21no—
216C22×D61—21no—
217C22×D61—21no—
218C22×D61C2×D812yes—
219D4×C61—22no—
220D4×C61—22no—
221D4×C61—41no—
222D4×C61—41no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—22no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—84no—
238C2×C4×C61C2×D812yes—
239C2×C4×C61C2×#4111yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61H(5,𝔽2)11yescharacteristic
244C2×C4×C612−1+411yescharacteristic
245C22⋊D61—48no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—22no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61C2×D812yes—
267C4×D61—41no—
268C4×D61—41no—
269C4×D61—41no—
270C4×D61—41no—
271C4×D61—84no—
272C8×C61—41no—
273C8×C61—41no—
274#92418—22no—
275#92418—41no—
276#27030—611nomaximal, Sylow
277C22×C61—42no—
278C22×C61—42no—
279C22×C61—42no—
280C22×C61—81no—
281C22×C61—81no—
282C22×C61—81no—
283C22×C61—81no—
284C22×C61#52511yescharacteristic
285C22×C61#54611yescharacteristic
286C22×C61#54711yescharacteristic
287C22×C61C22×D811yescharacteristic
288C22×C61#57511yescharacteristic
289C22×C61#57711yescharacteristic
290C22×C61#57811yescharacteristic
291C2×D61—22no—
292C2×D61—22no—
293C2×D61—22no—
294C2×D61—41no—
295C2×D61—41no—
296C2×D61—41no—
297C2×D61—41no—
298C4×C61—22no—
299C4×C61—42no—
300C4×C61—41no—
301C4×C61—81no—
302C4×C61—81no—
303C4×C61#52911yescharacteristic
304C4×C61#53911yescharacteristic
305C4×C61#55311yescharacteristic
306C4×C61#55611yescharacteristic
307Dic61—22no—
308Dic61—41no—
309Dic61—42no—
310Dic61—41no—
311Dic61—81no—
312Dic61—81no—
313Dic61—81no—
314#2496—611no—
315#2361—611no—
316#2071—611no—
317#2067—611no—
318#2033—611no—
319#2033—611no—
320#1947—611no—
321#1942—611no—
322#1923—611no—
323#1918—611no—
324#1918—611no—
325#1862D6111yescharacteristic, complemented
326#1852—611no—
327#1823—611no—
328C4×#102—611no—
329C2×C61—82no—
330C2×C61#246611yescharacteristic
331C2×C61#310011yescharacteristic
332C2×C61#312011yescharacteristic
333C2×C61#329411yescharacteristic
334C2×C61#331311yescharacteristic
335C2×C61#333411yescharacteristic
336C2×C61#335111yescharacteristic
337D61—42no—
338C2×#126—1221no—
339C2×#121—611no—
340C2×C4×D4—1221no—
341C2×C4×D4C2×D6111yescharacteristic
342C22×C4⋊C4—611no—
343C2×#107—611no—
344C2×#107—611no—
345C2×#107—611no—
346C2×#107C2×D6111yescharacteristic
347C2×C4⋊C8—611no—
348C2×#102—611no—
349C2×#102—611no—
350C2×#102C2×D6111yescharacteristic
351C2×#102C2×D6111yescharacteristic
352C2×C22⋊C8—611no—
353C2×C22⋊C8—611no—
354C2×C4×C8—611no—
355#400—1221no—
356#397—1221no—
357#390—611no—
358#389—611no—
359#389—611no—
360#389C2×D6111yescharacteristic
361#388—1221no—
362#387—1221no—
363#386—1221no—
364#385—1221no—
365#384—611no—
366#380—611no—
367#380—611no—
368C4×C4⋊C4—611no—
369C4×C4⋊C4—611no—
370C4×C22⋊C4—611no—
371#340—611no—
372#340—611no—
373#340—611no—
374#340—611no—
375#340—611no—
376#340—611no—
377#340—611no—
378#340C2×D6111yescharacteristic
379#336—611no—
380#336C2×D6111yescharacteristic
381C61#2703011yescharacteristic, complemented, Sylow
382C22×D4—1221no—
383C22×D4C22×D6111yescharacteristic
384C23×C4—21no—
385C23×C4—611no—
386C23×C4—1221no—
387C22×C8—611no—
388C22×C8—611no—
389C22×C8C22×D6111yescharacteristic
390C22×C8C22×D6111yescharacteristic
391#126—2444no—
392#121—1222no—
393#121—1222no—
394C4×D4—22no—
395C4×D4—41no—
396C4×D4—2444no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—1222no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4—1221no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—2441no—
409C2×C4⋊C4C22×D6111yescharacteristic
410C2×C4⋊C4C22×D6111yescharacteristic
411C2×C4⋊C4C22×D6111yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—611no—
414C2×C22⋊C4—611no—
415C2×C22⋊C4—1221no—
416C2×C22⋊C4—1221no—
417C2×C22⋊C4—1221no—
418C2×C22⋊C4—1221no—
419C2×C22⋊C4—1221no—
420C2×C42—611no—
421C2×C42—1221no—
422C2×C42—1221no—
423C2×C42C22×D6111yescharacteristic
424#107—22no—
425#107—1222no—
426#107—1222no—
427#107—2441no—
428C4⋊C8—1222no—
429#102—22no—
430#102—41no—
431#102—1222no—
432#102—1222no—
433C22⋊C8—1222no—
434C22⋊C8—2441no—
435C4×C8—2441no—
436#95—21no—
437#95—611no—
438#95—611no—
439#95—1221no—
440#95—1221no—
441#95—1221no—
442#95—1221no—
443#95—1221no—
444#95—1221no—
445C24—21no—
446C24—611no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—1224no—
453C2×D4—2442no—
454C2×D4—2442no—
455C2×D4#1175822212yes—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—81no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—4881no—
476C22×C4—2442no—
477C22×C4—2442no—
478C22×C4D4×D6111yescharacteristic
479C22×C4D4×D6111yescharacteristic
480C22×C4C23×D6111yescharacteristic
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—612no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—42no—
499C4⋊C4—612no—
500C4⋊C4—1221no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—2442no—
508C4⋊C4—2442no—
509C4⋊C4—2442no—
510C4⋊C4—2442no—
511C4⋊C4—2442no—
512C4⋊C4#1175822412yes—
513C22⋊C4—42no—
514C22⋊C4—614no—
515C22⋊C4—1224no—
516C22⋊C4—4881no—
517C22⋊C4—2441no—
518C22⋊C4—2442no—
519C22⋊C4—2442no—
520C22⋊C4—2442no—
521C42—21no—
522C42—21no—
523C42—1221no—
524C42—1221no—
525C42—2442no—
526C42—2442no—
527C23—22no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—612no—
535C23—1221no—
536C23—1221no—
537C23—1221no—
538C23—1221no—
539C23—1221no—
540C23—1221no—
541C23C2×D4×D6111yescharacteristic
542D4—22no—
543D4—22no—
544D4—41no—
545D4—41no—
546D4—2448no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—84no—
562C2×C4—612no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—1222no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—4884no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4D8×D6112yes—
589C2×C4#41×D6111yescharacteristic
590C2×C4#41×D6111yescharacteristic
591C2×C4C2×#1175822411yescharacteristic
592C2×C4C2×#1175822211yescharacteristic
593C2×C4#1451982211yescharacteristic
594C2×C4#1451982511yescharacteristic
595C8—41no—
596C8—41no—
597C8—1222no—
598C8—2441no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—1222no—
607C22—1222no—
608C22—1222no—
609C22—2441no—
610C22—2441no—
611C22—2441no—
612C22—2441no—
613C22#1684027111yescharacteristic
614C22#1684039911yescharacteristic
615C22#1684041411yescharacteristic
616C22C2×D8×D6111yescharacteristic
617C22#1684055911yescharacteristic
618C22#1684057211yescharacteristic
619C22#1684057811yescharacteristic
620C4—22no—
621C4—42no—
622C4—41no—
623C4—81no—
624C4—81no—
625C4—1222no—
626C4—4881no—
627C4—4881no—
628C4—4881no—
629C4—2441no—
630C4—2442no—
631C4—2441no—
632C4#1684029211yescharacteristic
633C4#1684035911yescharacteristic
634C4#1684045711yescharacteristic
635C4#1684048311yescharacteristic
636C2—82no—
637C2—2442no—
638C2#2144985711yescharacteristic
639C2#2145581711yescharacteristic
640C2#2145603711yescharacteristic
641C2#2145762511yescharacteristic
642C2#2145788911yescharacteristic
643C2#2145816511yescharacteristic
644C2#2145838611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1862C2
socleC23×C61C22×D4
prime radicalC2×#14519748C22
hypercenter#1862D61
hypocenterC61#27030
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
1. #21450242C2semidirect
3. #21447225C2semidirect
4. #21447203C2semidirect
7. #21446576C2semidirect
8. #21446549C2semidirect
9. #21446423C2semidirect
10. #21446392C2semidirect
11. #21446391C2semidirect
12. #21446005C2semidirect
13. #21445904C2semidirect
14. C4×#14519698C2semidirect
15. C61×#1862C2semidirect
325. #1862D61semidirect
381. C61#27030semidirect

Maximal subgroups

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

subgroupindex
#214502422
#214488312
#214472252
#214472032
#214470002
#214469992
#214465762
#214465492
#214464232
#214463922
#214463912
#214460052
#214459042
C4×#145196982
C61×#18622
#2703061