Finite Group Databasebeta

← #29752676

Subgroups — #29752676

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#21448834C211yesmaximal, characteristic
3#21447226C211yesmaximal, characteristic, complemented
4#21447202C211yesmaximal, characteristic, complemented
5#21447004C211yesmaximal, characteristic
6#21447003C211yesmaximal, characteristic
7#21446574C211yesmaximal, characteristic, complemented
8#21446425C211yesmaximal, characteristic, complemented
9#21446393C211yesmaximal, characteristic, complemented
10#21446387C211yesmaximal, characteristic, complemented
11#21446065C211yesmaximal, characteristic, complemented
12#21446005C211yesmaximal, characteristic, complemented
13#21445904C211yesmaximal, characteristic, complemented
14C4×#14519699C211yesmaximal, characteristic, complemented
15C61×#1942C211yesmaximal, characteristic, complemented
16C2×#14519772—21no—
17C2×#14519752C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519739—21no—
20C2×C4⋊C4×D61C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519706C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30#16839704—21no—
31#16839691—21no—
32#16839663C2211yescharacteristic
33#16839661C2211yescharacteristic
34#16839651—21no—
35#16839643—21no—
36#16839640—21no—
37#16839633—21no—
38#16839631C2211yescharacteristic
39#16839619C2211yescharacteristic
40#16839619C2211yescharacteristic
41C4⋊C4×Dic61C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic
43C4×#11758198C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#107×C61C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C2×C4×C8×C61C2211yescharacteristic
55C61×#389C2211yescharacteristic
56C61×#389C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×D244—21no—
60C22×D244C2311yescharacteristic
61C22×C4×D61—21no—
62C22×C4×D61—21no—
63C22×C4×D61C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66#14519772—44no—
67#14519752—22no—
68#14519752—22no—
69C4×D244—22no—
70C4×D244—41no—
71#14519739—44no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C4⋊C4×D61—22no—
80C4⋊C4×D61—41no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198D411yescharacteristic
88C2×#11758198D411yescharacteristic
89C2×C4×Dic61—21no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61C2311yescharacteristic
92#14519710—22no—
93#14519710—22no—
94#14519706—22no—
95#14519699—22no—
96#14519699—22no—
97#14519697—22no—
98#14519697—41no—
99#14519689—22no—
100#14519689—41no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684D411yescharacteristic
107#14519684D411yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C42×C61C2311yescharacteristic
117#107×C61—22no—
118#107×C61—41no—
119C4×C8×C61—41no—
120#95×C61—21no—
121#95×C61—21no—
122C23×D61—21no—
123C23×D61C2×D411yescharacteristic
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2411yescharacteristic
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61C2×D411yescharacteristic
135C22×Dic61C2×D411yescharacteristic
136C22×Dic61C2×D411yescharacteristic
137C2×D244—21no—
138C2×D244—21no—
139C2×D244—21no—
140C2×D244—21no—
141C2×D244—24no—
142C2×D244—21no—
143C2×D244—42no—
144C2×D244—42no—
145C2×D244#4112yes—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61—21no—
149C2×C4×D61—21no—
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61—42no—
153C2×C4×D61—42no—
154C2×C4×D61—42no—
155C2×C4×D61—42no—
156C2×C4×D61—81no—
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#4112yes—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—42no—
172C4⋊C4×C61—42no—
173C4⋊C4×C61#4112yes—
174C42×C61—21no—
175C42×C61—21no—
176#11758198—24no—
177#11758198—41no—
178#11758198—42no—
179#11758198—42no—
180#11758198—42no—
181#11758198—42no—
182#11758198—81no—
183#11758198D814yes—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—42no—
190C4⋊Dic61#4112yes—
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—21no—
204C23×C61C22×D411yescharacteristic
205C22×D61—21no—
206C22×D61—21no—
207C22×D61—21no—
208C22×D61—21no—
209C22×D61—21no—
210C22×D61—21no—
211C22×D61—22no—
212C22×D61—41no—
213C22×D61—41no—
214C22×D61—41no—
215C22×D61—41no—
216C22×D61—41no—
217C22×D61—41no—
218C22×D61C2×D812yes—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—22no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
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×C61C2×D812yes—
237C2×C4×C61C2×#4111yescharacteristic
238C2×C4×C61C2×#4111yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×C4×C61H(5,𝔽2)11yescharacteristic
242C2×C4×C612−1+411yescharacteristic
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—22no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61C2×D812yes—
261D244—22no—
262D244—22no—
263D244—48no—
264D244—41no—
265D244—41no—
266C4×D61—41no—
267C4×D61—41no—
268C4×D61—41no—
269C4×D61—41no—
270C4×D61—84no—
271C4×D61—84no—
272C8×C61—22no—
273C8×C61—41no—
274#92418—41no—
275#92418—41no—
276#27030—611nomaximal, Sylow
277C22×C61#52511yescharacteristic
278C22×C61#54611yescharacteristic
279C22×C61#54711yescharacteristic
280C22×C61C22×D811yescharacteristic
281C22×C61#57511yescharacteristic
282C22×C61#57711yescharacteristic
283C22×C61#57811yescharacteristic
284C2×D61—22no—
285C2×D61—22no—
286C2×D61—22no—
287C2×D61—41no—
288C2×D61—41no—
289C2×D61—41no—
290C2×D61—41no—
291C2×D61—42no—
292C2×D61—42no—
293C2×D61—42no—
294C2×D61—81no—
295C2×D61—81no—
296C2×D61—81no—
297C2×D61—81no—
298C4×C61—22no—
299C4×C61—42no—
300C4×C61—41no—
301C4×C61—81no—
302C4×C61—81no—
303C4×C61—81no—
304C4×C61#52911yescharacteristic
305C4×C61#53911yescharacteristic
306C4×C61#55311yescharacteristic
307C4×C61#55611yescharacteristic
308Dic61—22no—
309Dic61—41no—
310Dic61—41no—
311Dic61—42no—
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#1942D6111yescharacteristic, complemented
322#1923—611no—
323#1918—611no—
324#1918—611no—
325#1862—611no—
326#1852—611no—
327#1823—611no—
328C4×#102—611no—
329C2×C61#246611yescharacteristic
330C2×C61#310011yescharacteristic
331C2×C61#312011yescharacteristic
332C2×C61#329411yescharacteristic
333C2×C61#331311yescharacteristic
334C2×C61#333411yescharacteristic
335C2×C61#335111yescharacteristic
336D61—42no—
337D61—82no—
338C2×#126—1221no—
339C2×#121—611no—
340C2×C4×D4—611no—
341C2×C4×D4—1221no—
342C22×C4⋊C4—611no—
343C2×#107—611no—
344C2×#107—611no—
345C2×#107C2×D6111yescharacteristic
346C2×#107C2×D6111yescharacteristic
347C2×C4⋊C8—611no—
348C2×#102—611no—
349C2×#102—611no—
350C2×#102—611no—
351C2×#102—611no—
352C2×C22⋊C8—611no—
353C2×C22⋊C8—611no—
354C2×C4×C8C2×D6111yescharacteristic
355#400—1221no—
356#397—1221no—
357#390—611no—
358#389—611no—
359#389C2×D6111yescharacteristic
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#340C2×D6111yescharacteristic
378#340C2×D6111yescharacteristic
379#336—611no—
380#336—611no—
381C61#2703011yescharacteristic, complemented, Sylow
382C22×D4—611no—
383C22×D4—1221no—
384C23×C4—611no—
385C23×C4—1221no—
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—1222no—
395C4×D4—2441no—
396C4×D4—2444no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
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—2441no—
408C2×C4⋊C4C22×D6111yescharacteristic
409C2×C4⋊C4C22×D6111yescharacteristic
410C2×C4⋊C4C22×D6111yescharacteristic
411C2×C4⋊C4C22×D6111yescharacteristic
412C2×C22⋊C4—611no—
413C2×C22⋊C4—611no—
414C2×C22⋊C4—1221no—
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—41no—
426#107—1222no—
427#107—1222no—
428C4⋊C8—1222no—
429#102—1222no—
430#102—1222no—
431#102—1222no—
432#102—2441no—
433C22⋊C8—1222no—
434C22⋊C8—2441no—
435C4×C8—41no—
436#95—21no—
437#95—21no—
438#95—611no—
439#95—611no—
440#95—1221no—
441#95—1221no—
442#95—1221no—
443#95—1221no—
444#95—1221no—
445C24—611no—
446C24—1221no—
447C2×D4—612no—
448C2×D4—1224no—
449C2×D4—1221no—
450C2×D4—1221no—
451C2×D4—1221no—
452C2×D4—1221no—
453C2×D4—1221no—
454C2×D4—2442no—
455C2×D4—2442no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—4881no—
473C22×C4—4881no—
474C22×C4—2442no—
475C22×C4—2442no—
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—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8#1175822612yes—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4—612no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—1221no—
508C4⋊C4—2442no—
509C4⋊C4—2442no—
510C4⋊C4—2442no—
511C4⋊C4—2442no—
512C4⋊C4#1175822212yes—
513C22⋊C4—614no—
514C22⋊C4—1224no—
515C22⋊C4—4881no—
516C22⋊C4—2441no—
517C22⋊C4—2442no—
518C22⋊C4—2442no—
519C22⋊C4—2442no—
520C22⋊C4—2442no—
521C42—21no—
522C42—21no—
523C42—1221no—
524C42—1221no—
525C42—2442no—
526C42—2442no—
527C23—612no—
528C23—1221no—
529C23—1221no—
530C23—1221no—
531C23—1221no—
532C23—1221no—
533C23—1221no—
534C23—1222no—
535C23—2441no—
536C23—2441no—
537C23—2441no—
538C23—2441no—
539C23—2441no—
540C23—2441no—
541C23C2×D4×D6111yescharacteristic
542D4—1222no—
543D4—1222no—
544D4—2448no—
545D4—2441no—
546D4—2441no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
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—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—612no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1222no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—4884no—
575C2×C4—4884no—
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×#1175822211yescharacteristic
592C2×C4C2×#1175822611yescharacteristic
593C2×C4#1451982211yescharacteristic
594C2×C4#1451982511yescharacteristic
595C8—22no—
596C8—41no—
597C8—2441no—
598C8—2441no—
599C22—1222no—
600C22—1222no—
601C22—1222no—
602C22—4881no—
603C22—4881no—
604C22—4881no—
605C22—4881no—
606C22—2442no—
607C22—2442no—
608C22—2442no—
609C22—2441no—
610C22—2441no—
611C22—2441no—
612C22—2441no—
613C22#1684027111yescharacteristic
614C22#1684040111yescharacteristic
615C22#1684041511yescharacteristic
616C22C2×D8×D6111yescharacteristic
617C22#1684055911yescharacteristic
618C22#1684056911yescharacteristic
619C22#1684057511yescharacteristic
620C4—22no—
621C4—42no—
622C4—41no—
623C4—81no—
624C4—81no—
625C4—81no—
626C4—1222no—
627C4—4881no—
628C4—4881no—
629C4—2441no—
630C4—2441no—
631C4—2442no—
632C4#1684029711yescharacteristic
633C4#1684035811yescharacteristic
634C4#1684046011yescharacteristic
635C4#1684048411yescharacteristic
636C2—4882no—
637C2—2442no—
638C2#2144986111yescharacteristic
639C2#2145581711yescharacteristic
640C2#2145603911yescharacteristic
641C2#2145762711yescharacteristic
642C2#2145789111yescharacteristic
643C2#2145816611yescharacteristic
644C2#2145837811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1942C2
socleC23×C61C22×D4
prime radicalC2×#14519752C22
hypercenter#1942D61
hypocenterC61#27030
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1942

Complements

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

NH ≅ G/Ntype
1. #21450242C2semidirect
3. #21447226C2semidirect
4. #21447202C2semidirect
7. #21446574C2semidirect
8. #21446425C2semidirect
9. #21446393C2semidirect
10. #21446387C2semidirect
11. #21446065C2semidirect
12. #21446005C2semidirect
13. #21445904C2semidirect
14. C4×#14519699C2semidirect
15. C61×#1942C2semidirect
321. #1942D61semidirect
381. C61#27030semidirect

Maximal subgroups

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

subgroupindex
#214502422
#214488342
#214472262
#214472022
#214470042
#214470032
#214465742
#214464252
#214463932
#214463872
#214460652
#214460052
#214459042
C4×#145196992
C61×#19422
#2703061