Finite Group Databasebeta

← #28646918

Subgroups — #28646918

Order 15104.

736 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21429117C211yesmaximal, characteristic, complemented
2#21427043C211yesmaximal, characteristic
3#21425469C211yesmaximal, characteristic
4#21425469C211yesmaximal, characteristic
5#21425243C211yesmaximal, characteristic
6#21425233C211yesmaximal, characteristic
7#21425051C211yesmaximal, characteristic, complemented
8#21425047C211yesmaximal, characteristic, complemented
9#21424860C211yesmaximal, characteristic, complemented
10#21424682C211yesmaximal, characteristic, complemented
11#21424675C211yesmaximal, characteristic, complemented
12#21424230C211yesmaximal, characteristic, complemented
13#21424107C211yesmaximal, characteristic
14#21423922C211yesmaximal, characteristic
15C59×#1940C211yesmaximal, characteristic, complemented
16C2×#14273727C2211yescharacteristic
17C2×#14273719C2211yescharacteristic
18C2×C4×D236C2211yescharacteristic
19C2×#14273685—21no—
20C2×#14273659C2211yescharacteristic
21C2×#14273659C2211yescharacteristic
22C2×#14273649C2211yescharacteristic
23C2×#14273649C2211yescharacteristic
24C2×#14273649C2211yescharacteristic
25C2×#14273649C2211yescharacteristic
26#16837335—21no—
27#16837322—21no—
28#16837306—21no—
29#16837304C2211yescharacteristic
30#16837304C2211yescharacteristic
31#16837300C2211yescharacteristic
32#16837300C2211yescharacteristic
33#16837299—21no—
34#16837294—21no—
35#16837294—21no—
36#16837272C2211yescharacteristic
37#16837268C2211yescharacteristic
38#16837259—21no—
39C4×C4⋊Dic59C2211yescharacteristic
40C4×C4⋊Dic59C2211yescharacteristic
41C4×C4⋊Dic59C2211yescharacteristic
42#16837165C2211yescharacteristic
43#16837165C2211yescharacteristic
44#16837165C2211yescharacteristic
45#16837165C2211yescharacteristic
46#16837165C2211yescharacteristic
47#16837165C2211yescharacteristic
48#16837165C2211yescharacteristic
49#16837165C2211yescharacteristic
50#16837165C2211yescharacteristic
51#16837165C2211yescharacteristic
52C2×C4⋊C8×C59C2211yescharacteristic
53C2×C4⋊C8×C59C2211yescharacteristic
54C2×C4⋊C8×C59C2211yescharacteristic
55C2×#97×C59C2211yescharacteristic
56C4×C4⋊C4×C59C2211yescharacteristic
57C59×#336C2211yescharacteristic
58C59×#336C2211yescharacteristic
59C22×Dic118—21no—
60C22×D236C2311yescharacteristic
61C22×C4×D59—21no—
62#14273727—22no—
63#14273727—41no—
64#14273719—22no—
65#14273719—41no—
66C4×D236—22no—
67C4×D236Q814yescomplemented
68#14273685—44no—
69C2×C4⋊Dic59—21no—
70C2×C4⋊Dic59—21no—
71C2×C4⋊Dic59—21no—
72C2×C4⋊Dic59C2311yescharacteristic
73C2×C4⋊Dic59C2311yescharacteristic
74C2×C4⋊Dic59C2311yescharacteristic
75C2×C4⋊Dic59C2311yescharacteristic
76C2×C4⋊Dic59C2311yescharacteristic
77C2×C4⋊Dic59C2311yescharacteristic
78C2×C4⋊Dic59C2311yescharacteristic
79C2×Dic59⋊C4—21no—
80C2×Dic59⋊C4—21no—
81C2×Dic59⋊C4—21no—
82C2×Dic59⋊C4—21no—
83C2×(C2×D59)⋊C4—21no—
84C2×(C2×D59)⋊C4—21no—
85C2×(C2×D59)⋊C4—21no—
86C2×(C2×D59)⋊C4—21no—
87C2×(C2×D59)⋊C4—21no—
88C2×C4×Dic59—21no—
89C2×C4×Dic59—21no—
90C2×C4×Dic59—21no—
91#14273659—22no—
92#14273659—22no—
93#14273649—22no—
94#14273649—22no—
95#14273649—41no—
96#14273649—41no—
97C59⋊#95—21no—
98C59⋊#95—21no—
99C59⋊#95—21no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C22×C8×C59C2311yescharacteristic
105C22×C8×C59C2311yescharacteristic
106C22×C8×C59C2311yescharacteristic
107C22×C8×C59C2311yescharacteristic
108C2×C4⋊C4×C59D411yescharacteristic
109C2×C4⋊C4×C59D411yescharacteristic
110C2×C42×C59C2311yescharacteristic
111C2×C42×C59C2311yescharacteristic
112C2×C42×C59C2311yescharacteristic
113C4⋊C8×C59—22no—
114C4⋊C8×C59—41no—
115C4⋊C8×C59—41no—
116#97×C59—22no—
117#95×C59D411yescharacteristic
118#95×C59D411yescharacteristic
119C23×D59—21no—
120C22×C4×C59C2×D411yescharacteristic
121C22×C4×C59C2×D411yescharacteristic
122C22×C4×C59C2×D411yescharacteristic
123C22×C4×C59C2×D411yescharacteristic
124C22×C4×C59C2×D411yescharacteristic
125C22×C4×C59C2×D411yescharacteristic
126C22×C4×C59C2411yescharacteristic
127C22×Dic59—21no—
128C22×Dic59—21no—
129C22×Dic59—21no—
130C22×Dic59—21no—
131C22×Dic59—21no—
132C22×Dic59—21no—
133C22×Dic59—21no—
134C2×D236—21no—
135C2×D236—21no—
136C2×D236—21no—
137C2×D236—21no—
138C2×D236—21no—
139C2×D236C2×Q812yes—
140C2×C4×D59—24no—
141C2×C4×D59—42no—
142C2×C4×D59—42no—
143C2×Dic118—42no—
144C2×Dic118—42no—
145C2×Dic118—81no—
146C2×C8×C59—21no—
147C2×C8×C59—21no—
148C2×C8×C59—21no—
149C2×C8×C59—21no—
150C2×C8×C59—21no—
151C2×C8×C59—21no—
152C2×C8×C59—21no—
153C2×C8×C59—21no—
154C2×C8×C59—21no—
155C2×C8×C59—21no—
156C2×C8×C59—21no—
157C2×C8×C59—21no—
158C4⋊C4×C59—22no—
159C4⋊C4×C59—41no—
160C42×C59—21no—
161C42×C59—21no—
162C42×C59—21no—
163C42×C59—21no—
164C42×C59C2×Q812yes—
165C42×C59#4112yes—
166(C2×D59)⋊C4—24no—
167(C2×D59)⋊C4—42no—
168(C2×D59)⋊C4—42no—
169(C2×D59)⋊C4—81no—
170(C2×D59)⋊C4—81no—
171C4⋊Dic59—21no—
172C4⋊Dic59—21no—
173C4⋊Dic59—21no—
174C4⋊Dic59—21no—
175C4⋊Dic59—21no—
176C4⋊Dic59—21no—
177C4⋊Dic59—21no—
178C4⋊Dic59—21no—
179C4⋊Dic59—21no—
180C4⋊Dic59—21no—
181C4⋊Dic59—21no—
182C4⋊Dic59—42no—
183C4⋊Dic59—42no—
184C4⋊Dic59—81no—
185C4⋊Dic59C2×Q812yes—
186C4⋊Dic59#4112yes—
187C4⋊Dic59#4112yes—
188Dic59⋊C4—42no—
189Dic59⋊C4—42no—
190Dic59⋊C4—42no—
191Dic59⋊C4—81no—
192C4×Dic59—42no—
193C4×Dic59—42no—
194C4×Dic59—81no—
195C23×C59C22×D411yescharacteristic
196C22×D59—22no—
197C22×D59—41no—
198C22×D59—41no—
199C22×D59—41no—
200C22×D59—41no—
201C22×D59—41no—
202C22×D59—41no—
203C2×C4×C59—21no—
204C2×C4×C59—21no—
205C2×C4×C59—21no—
206C2×C4×C59—21no—
207C2×C4×C59—21no—
208C2×C4×C59—21no—
209C2×C4×C59—21no—
210C2×C4×C59—21no—
211C2×C4×C59—21no—
212C2×C4×C59—21no—
213C2×C4×C59—21no—
214C2×C4×C59—21no—
215C2×C4×C59—21no—
216C2×C4×C59—21no—
217C2×C4×C59—21no—
218C2×C4×C59C22⋊Q812yes—
219C2×C4×C59C22⋊Q812yes—
220C2×C4×C59AGL(1,ℤ/8)12yes—
221C2×C4×C59C22×Q811yescharacteristic
222C2×C4×C59C2×#4111yescharacteristic
223C2×C4×C59C2×#4111yescharacteristic
224C2×C4×C59C2×#4111yescharacteristic
225C2×C4×C59H(5,𝔽2)11yescharacteristic
226C2×C4×C592−1+411yescharacteristic
227C2×Dic59—22no—
228C2×Dic59—22no—
229C2×Dic59—22no—
230C2×Dic59—41no—
231C2×Dic59—41no—
232C2×Dic59—41no—
233C2×Dic59—41no—
234C2×Dic59—41no—
235C2×Dic59—41no—
236C2×Dic59—41no—
237C2×Dic59—41no—
238C2×Dic59—41no—
239C2×Dic59—41no—
240C2×Dic59—41no—
241C2×Dic59—41no—
242C2×Dic59—41no—
243C2×Dic59—41no—
244C2×Dic59—41no—
245C2×Dic59—41no—
246C2×Dic59—41no—
247C2×Dic59—41no—
248D236—22no—
249D236—22no—
250D236—41no—
251D236—41no—
252C4×D59—48no—
253Dic118—84no—
254C8×C59—41no—
255C8×C59—41no—
256C8×C59—41no—
257C8×C59—41no—
258#26032—591nomaximal, Sylow
259C22×C59C2×C22⋊Q811yescharacteristic
260C22×C59#54611yescharacteristic
261C22×C59#54811yescharacteristic
262C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
263C22×C59#57511yescharacteristic
264C22×C59#57711yescharacteristic
265C22×C59#57711yescharacteristic
266C2×D59—42no—
267C2×D59—42no—
268C2×D59—42no—
269C2×D59—81no—
270C2×D59—81no—
271C2×D59—81no—
272C2×D59—81no—
273C4×C59—22no—
274C4×C59—22no—
275C4×C59—22no—
276C4×C59—41no—
277C4×C59—41no—
278C4×C59—41no—
279C4×C59#53311yescharacteristic
280C4×C59#54411yescharacteristic
281C4×C59#55511yescharacteristic
282C4×C59#55611yescharacteristic
283Dic59—42no—
284Dic59—42no—
285Dic59—42no—
286Dic59—81no—
287Dic59—81no—
288Dic59—81no—
289Dic59—81no—
290#2550—591no—
291#2354—591no—
292#2065—591no—
293#2065—591no—
294#2025—591no—
295#2023—591no—
296#1989—591no—
297#1988—591no—
298#1948—591no—
299#1940D5911yescharacteristic, complemented
300#1920—591no—
301#1919—591no—
302#1836—591no—
303#1804—591no—
304#1762—591no—
305C2×C59#243911yescharacteristic
306C2×C59#307711yescharacteristic
307C2×C59#308411yescharacteristic
308C2×C59#330611yescharacteristic
309C2×C59#332111yescharacteristic
310C2×C59#336811yescharacteristic
311C2×C59#337611yescharacteristic
312D59—82no—
313C2×C4⋊Q8—591no—
314C2×#125—591no—
315C2×C4×D4—591no—
316C2×#117—1181no—
317C2×#106—591no—
318C2×#106—591no—
319C2×C4⋊C8C2×D5911yescharacteristic
320C2×C4⋊C8C2×D5911yescharacteristic
321C2×C4⋊C8C2×D5911yescharacteristic
322C2×#102—591no—
323C2×#102—591no—
324C2×#102—591no—
325C2×#102—591no—
326C2×#97C2×D5911yescharacteristic
327#398—1181no—
328#395—1181no—
329#391—1181no—
330#390—591no—
331#390—591no—
332#389—591no—
333#389—591no—
334#389—1181no—
335#388—1181no—
336#388—1181no—
337#384—591no—
338#382—591no—
339#380—1181no—
340C4×C4⋊C4—591no—
341C4×C4⋊C4—591no—
342C4×C4⋊C4—591no—
343C4×C4⋊C4C2×D5911yescharacteristic
344#340—591no—
345#340—591no—
346#340—591no—
347#340—591no—
348#340—591no—
349#340—591no—
350#340—591no—
351#340—591no—
352#340—591no—
353#340—591no—
354#336C2×D5911yescharacteristic
355#336C2×D5911yescharacteristic
356C59#2603211yescharacteristic, complemented, Sylow
357C22×Q8—1181no—
358C22×D4—591no—
359C23×C4—1181no—
360C22×C8C22×D5911yescharacteristic
361C22×C8C22×D5911yescharacteristic
362C22×C8C22×D5911yescharacteristic
363C22×C8C22×D5911yescharacteristic
364C4⋊Q8—1182no—
365C4⋊Q8—2361no—
366#125—1182no—
367#125—2361no—
368C4×D4—594no—
369C4×D4—1182no—
370#117—2364no—
371C2×C4⋊C4—591no—
372C2×C4⋊C4—591no—
373C2×C4⋊C4—591no—
374C2×C4⋊C4—591no—
375C2×C4⋊C4—591no—
376C2×C4⋊C4—591no—
377C2×C4⋊C4—591no—
378C2×C4⋊C4—1181no—
379C2×C4⋊C4—1181no—
380C2×C4⋊C4—1181no—
381C2×C4⋊C4—1181no—
382C2×C4⋊C4—1181no—
383C2×C4⋊C4—1181no—
384C2×C4⋊C4—1181no—
385C2×C4⋊C4D23611yescharacteristic
386C2×C4⋊C4D23611yescharacteristic
387C2×C22⋊C4—1181no—
388C2×C22⋊C4—1181no—
389C2×C22⋊C4—1181no—
390C2×C22⋊C4—1181no—
391C2×C22⋊C4—1181no—
392C2×C42—1181no—
393C2×C42—1181no—
394C2×C42—1181no—
395C2×C42C22×D5911yescharacteristic
396C2×C42C22×D5911yescharacteristic
397C2×C42C22×D5911yescharacteristic
398#106—1182no—
399#106—1182no—
400C4⋊C8—22no—
401C4⋊C8—41no—
402C4⋊C8—41no—
403#102—1182no—
404#102—1182no—
405#102—2361no—
406#102—2361no—
407#97—22no—
408#95—1181no—
409#95—1181no—
410#95—1181no—
411#95—1181no—
412#95—1181no—
413#95—1181no—
414#95—1181no—
415#95D23611yescharacteristic
416#95D23611yescharacteristic
417C24—1181no—
418C2×Q8—4721no—
419C2×Q8—2362no—
420C2×Q8—2362no—
421C2×D4—592no—
422C2×D4—1181no—
423C2×D4—1181no—
424C2×D4—1181no—
425C2×D4—1181no—
426C2×D4—1181no—
427C22×C4—1181no—
428C22×C4—1181no—
429C22×C4—1181no—
430C22×C4—1184no—
431C22×C4—1181no—
432C22×C4—1181no—
433C22×C4—1181no—
434C22×C4—1181no—
435C22×C4—2362no—
436C22×C4—2362no—
437C22×C4C2×D23611yescharacteristic
438C22×C4C2×D23611yescharacteristic
439C22×C4C2×D23611yescharacteristic
440C22×C4C2×D23611yescharacteristic
441C22×C4C2×D23611yescharacteristic
442C22×C4C2×D23611yescharacteristic
443C22×C4C23×D5911yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C4⋊C4—22no—
457C4⋊C4—41no—
458C4⋊C4—592no—
459C4⋊C4—592no—
460C4⋊C4—592no—
461C4⋊C4—1181no—
462C4⋊C4—1181no—
463C4⋊C4—1181no—
464C4⋊C4—1181no—
465C4⋊C4—1181no—
466C4⋊C4—1181no—
467C4⋊C4—1181no—
468C4⋊C4—1181no—
469C4⋊C4—1181no—
470C4⋊C4—1181no—
471C4⋊C4—1181no—
472C4⋊C4—4721no—
473C4⋊C4—4721no—
474C4⋊C4—2362no—
475C4⋊C4—2362no—
476C4⋊C4—2362no—
477C4⋊C4—2362no—
478C4⋊C4—2362no—
479C22⋊C4—1184no—
480C22⋊C4—4721no—
481C22⋊C4—4721no—
482C22⋊C4—2362no—
483C22⋊C4—2362no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—4721no—
489C42—2362no—
490C42—2362no—
491C42#1174568712yes—
492C42Q8×D5912yes—
493C23—1182no—
494C23—2361no—
495C23—2361no—
496C23—2361no—
497C23—2361no—
498C23—2361no—
499C23—2361no—
500C23C22×D23611yescharacteristic
501Q8—4724no—
502D4—1182no—
503D4—1182no—
504D4—2361no—
505D4—2361no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—1182no—
522C2×C4—1182no—
523C2×C4—1182no—
524C2×C4—2368no—
525C2×C4—2361no—
526C2×C4—2361no—
527C2×C4—2361no—
528C2×C4—2361no—
529C2×C4—2361no—
530C2×C4—2361no—
531C2×C4—2361no—
532C2×C4—2361no—
533C2×C4—2361no—
534C2×C4—2361no—
535C2×C4—2361no—
536C2×C4—2361no—
537C2×C4—2361no—
538C2×C4—2361no—
539C2×C4—2361no—
540C2×C4—2361no—
541C2×C4—2361no—
542C2×C4—2361no—
543C2×C4#1427370712yes—
544C2×C4#1427370712yes—
545C2×C4#1427375512yes—
546C2×C4C2×Q8×D5911yescharacteristic
547C2×C4#41×D5911yescharacteristic
548C2×C4#41×D5911yescharacteristic
549C2×C4C2×#1174568711yescharacteristic
550C2×C4#1427377211yescharacteristic
551C2×C4#1427377511yescharacteristic
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C22—4721no—
557C22—4721no—
558C22—4721no—
559C22—4721no—
560C22—2362no—
561C22—2362no—
562C22—2362no—
563C22C2×#1427370711yescharacteristic
564C22#1683804711yescharacteristic
565C22#1683806411yescharacteristic
566C22C2×#1427375511yescharacteristic
567C22#1683820211yescharacteristic
568C22#1683821411yescharacteristic
569C22#1683821411yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—4721no—
577C4—4721no—
578C4—4721no—
579C4—4721no—
580C4—2362no—
581C4—2362no—
582C4—2362no—
583C4#1683795811yescharacteristic
584C4#1683802911yescharacteristic
585C4#1683811611yescharacteristic
586C4#1683812311yescharacteristic
587C2—4722no—
588C2#2142778511yescharacteristic
589C2#2143389511yescharacteristic
590C2#2143396011yescharacteristic
591C2#2143605911yescharacteristic
592C2#2143628411yescharacteristic
593C2#2143682711yescharacteristic
594C2#2143692511yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#1940C2
socleC23×C59C22×D4
prime radicalC22×D236C23
hypercenter#1940D59
hypocenterC59#26032
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
1. #21429117C2semidirect
7. #21425051C2semidirect
8. #21425047C2semidirect
9. #21424860C2semidirect
10. #21424682C2semidirect
11. #21424675C2semidirect
12. #21424230C2semidirect
15. C59×#1940C2semidirect
67. C4×D236Q8semidirect
299. #1940D59semidirect
356. C59#26032semidirect

Maximal subgroups

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

subgroupindex
#214291172
#214270432
#214254692
#214252432
#214252332
#214250512
#214250472
#214248602
#214246822
#214246752
#214242302
#214241072
#214239222
C59×#19402
#2603259