Finite Group Databasebeta

← #28619025

Subgroups — #28619025

Order 15104.

808 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14273726C211yesmaximal, characteristic, complemented
2#21426561C211yesmaximal, characteristic
3#21425662C211yesmaximal, characteristic, complemented
4#21425627C211yesmaximal, characteristic
5#21425599C211yesmaximal, characteristic, complemented
6#21425596C211yesmaximal, characteristic, complemented
7#21425482C211yesmaximal, characteristic
8#21425480C211yesmaximal, characteristic
9#21425423C211yesmaximal, characteristic, complemented
10#21425230C211yesmaximal, characteristic
11#21423994C211yesmaximal, characteristic, complemented
12#21423993C211yesmaximal, characteristic, complemented
13#21423950C211yesmaximal, characteristic, complemented
14#21423921C211yesmaximal, characteristic
15C59×#1762C211yesmaximal, characteristic
16C2×#14273726C2211yescharacteristic
17C2×C4×Dic118—21no—
18C2×#14273686—21no—
19C2×#14273661C2211yescharacteristic
20C2×#14273660C2211yescharacteristic
21C2×#14273659C2211yescharacteristic
22C2×#14273658C2211yescharacteristic
23C2×Dic59⋊C8C2211yescharacteristic
24C2×Dic59⋊C8C2211yescharacteristic
25C2×#14273648C2211yescharacteristic
26C2×#14273648C2211yescharacteristic
27C2×#14273638C2211yescharacteristic
28#16837306—21no—
29#16837305C2211yescharacteristic
30#16837305C2211yescharacteristic
31#16837301C2211yescharacteristic
32#16837301C2211yescharacteristic
33#16837301C2211yescharacteristic
34#16837299—21no—
35#16837298C2211yescharacteristic
36#16837295—21no—
37#16837295—21no—
38#16837271C2211yescharacteristic
39C4×Dic59⋊C4—21no—
40C4×C4⋊Dic59C2211yescharacteristic
41C4×C4⋊Dic59C2211yescharacteristic
42C4×C22⋊Dic59—21no—
43C42×Dic59C2211yescharacteristic
44#16837165C2211yescharacteristic
45#16837165C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837156C2211yescharacteristic
51#16837156C2211yescharacteristic
52C2×C4×D4×C59C2211yescharacteristic
53C2×#102×C59C2211yescharacteristic
54C2×#102×C59C2211yescharacteristic
55C2×#97×C59C2211yescharacteristic
56C4×C4⋊C4×C59C2211yescharacteristic
57C59×#340C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C22×Dic118—21no—
60C22×C59⋊C8C2311yescharacteristic
61C22×C59⋊C8C2311yescharacteristic
62#14273726—22no—
63#14273726—22no—
64C4×Dic118—44no—
65#14273686—44no—
66C2×C4⋊Dic59—21no—
67C2×C4⋊Dic59—21no—
68C2×C4⋊Dic59—21no—
69C2×C4⋊Dic59C2311yescharacteristic
70C2×C4⋊Dic59C2311yescharacteristic
71C2×C4⋊Dic59C2311yescharacteristic
72C2×C4⋊Dic59C2311yescharacteristic
73C2×Dic59⋊C4—21no—
74C2×Dic59⋊C4—21no—
75C2×Dic59⋊C4—21no—
76C2×Dic59⋊C4—21no—
77C2×C22⋊Dic59—21no—
78C2×C22⋊Dic59—21no—
79C2×C22⋊Dic59—21no—
80C2×C22⋊Dic59—21no—
81C2×C4×Dic59—21no—
82C2×C4×Dic59—21no—
83C2×C4×Dic59D411yescharacteristic
84C2×C4×Dic59D411yescharacteristic
85C2×C4×Dic59D411yescharacteristic
86C2×C4×Dic59D411yescharacteristic
87C2×C4×Dic59C2311yescharacteristic
88C2×C4×Dic59C2311yescharacteristic
89#14273661—22no—
90#14273660—22no—
91#14273659—22no—
92#14273658—22no—
93Dic59⋊C8—22no—
94Dic59⋊C8—22no—
95#14273648—22no—
96#14273648—22no—
97#14273638—22no—
98C59⋊#95—21no—
99C59⋊#95—21no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C22×D4×C59C2311yescharacteristic
105C23×C4×C59—21no—
106C22×C8×C59C2311yescharacteristic
107C22×C8×C59C2311yescharacteristic
108C4×D4×C59—22no—
109C4×D4×C59Q814yescomplemented
110C2×C4⋊C4×C59C2311yescharacteristic
111C2×C4⋊C4×C59C2311yescharacteristic
112C2×C4⋊C4×C59C2311yescharacteristic
113C2×C22⋊C4×C59—21no—
114C2×C42×C59—21no—
115C2×C42×C59C2311yescharacteristic
116#102×C59—22no—
117#102×C59—22no—
118#97×C59—22no—
119#95×C59—21no—
120C24×C59—21no—
121C2×D4×C59—21no—
122C2×D4×C59—21no—
123C2×D4×C59—21no—
124C2×D4×C59—21no—
125C2×D4×C59—21no—
126C2×D4×C59C2×Q812yes—
127C22×C4×C59—21no—
128C22×C4×C59—21no—
129C22×C4×C59—24no—
130C22×C4×C59—21no—
131C22×C4×C59—42no—
132C22×C4×C59—42no—
133C22×C4×C59C2×D411yescharacteristic
134C22×C4×C59C2×D411yescharacteristic
135C22×C4×C59C2411yescharacteristic
136C22×Dic59—21no—
137C22×Dic59—21no—
138C22×Dic59—21no—
139C22×Dic59—21no—
140C22×Dic59C2×D411yescharacteristic
141C22×Dic59C2×D411yescharacteristic
142C22×Dic59C2×D411yescharacteristic
143C22×Dic59C2×D411yescharacteristic
144C2×Dic118—24no—
145C2×Dic118—42no—
146C2×Dic118—42no—
147C2×C8×C59—21no—
148C2×C8×C59—21no—
149C2×C8×C59—21no—
150C2×C8×C59—21no—
151C2×C8×C59—21no—
152C2×C8×C59#4112yes—
153C4⋊C4×C59—21no—
154C4⋊C4×C59—21no—
155C4⋊C4×C59—21no—
156C4⋊C4×C59—21no—
157C4⋊C4×C59C2×Q812yes—
158C4⋊C4×C59#4112yes—
159C22⋊C4×C59—24no—
160C42×C59—42no—
161C42×C59C2×Q812yes—
162C42×C59#4112yes—
163C22⋊Dic59—42no—
164C22⋊Dic59—42no—
165C22⋊Dic59—42no—
166C22⋊Dic59—42no—
167C4⋊Dic59—21no—
168C4⋊Dic59—21no—
169C4⋊Dic59—21no—
170C4⋊Dic59—21no—
171C4⋊Dic59—21no—
172C4⋊Dic59—21no—
173C4⋊Dic59—21no—
174C4⋊Dic59—42no—
175C4⋊Dic59—42no—
176C4⋊Dic59—42no—
177C4⋊Dic59#4112yes—
178Dic59⋊C4—24no—
179Dic59⋊C4—42no—
180Dic59⋊C4—42no—
181Dic59⋊C4—42no—
182C4×Dic59—21no—
183C4×Dic59—21no—
184C4×Dic59—21no—
185C4×Dic59—21no—
186C4×Dic59—22no—
187C4×Dic59—22no—
188C4×Dic59—22no—
189C4×Dic59—41no—
190C4×Dic59—42no—
191C4×Dic59—42no—
192C2×C59⋊C8—21no—
193C2×C59⋊C8—21no—
194C2×C59⋊C8—21no—
195C2×C59⋊C8—21no—
196C2×C59⋊C8—21no—
197C2×C59⋊C8#4112yes—
198C23×C59—22no—
199C23×C59—41no—
200C23×C59—41no—
201C23×C59—41no—
202C23×C59—41no—
203C23×C59—41no—
204C23×C59—41no—
205C23×C59C22×D411yescharacteristic
206D4×C59—22no—
207D4×C59—22no—
208D4×C59—41no—
209D4×C59—41no—
210C2×C4×C59—21no—
211C2×C4×C59—21no—
212C2×C4×C59—21no—
213C2×C4×C59—21no—
214C2×C4×C59—22no—
215C2×C4×C59—22no—
216C2×C4×C59—48no—
217C2×C4×C59—41no—
218C2×C4×C59—41no—
219C2×C4×C59—41no—
220C2×C4×C59—41no—
221C2×C4×C59—41no—
222C2×C4×C59—41no—
223C2×C4×C59—41no—
224C2×C4×C59C22⋊Q812yes—
225C2×C4×C59C22⋊Q812yes—
226C2×C4×C59C22×Q811yescharacteristic
227C2×C4×C59C2×#4111yescharacteristic
228C2×C4×C59C2×#4111yescharacteristic
229C2×C4×C59C2×#4111yescharacteristic
230C2×C4×C59C2×#4111yescharacteristic
231C2×C4×C59C2×#4111yescharacteristic
232C2×Dic59—21no—
233C2×Dic59—21no—
234C2×Dic59—21no—
235C2×Dic59—21no—
236C2×Dic59—21no—
237C2×Dic59—21no—
238C2×Dic59—22no—
239C2×Dic59—21no—
240C2×Dic59—21no—
241C2×Dic59—21no—
242C2×Dic59—41no—
243C2×Dic59—41no—
244C2×Dic59—41no—
245C2×Dic59—41no—
246C2×Dic59—41no—
247C2×Dic59—41no—
248C2×Dic59—41no—
249C2×Dic59—41no—
250C2×Dic59—41no—
251C2×Dic59—41no—
252C2×Dic59—41no—
253C2×Dic59AGL(1,ℤ/8)12yes—
254C2×Dic59AGL(1,ℤ/8)12yes—
255C2×Dic59#13712yes—
256Dic118—48no—
257C8×C59—22no—
258C8×C59—41no—
259C59⋊C8—22no—
260C59⋊C8—41no—
261#23780—591nomaximal, Sylow
262C22×C59—42no—
263C22×C59—42no—
264C22×C59—42no—
265C22×C59—81no—
266C22×C59—81no—
267C22×C59—81no—
268C22×C59—81no—
269C22×C59C2×C22⋊Q811yescharacteristic
270C22×C59#52511yescharacteristic
271C22×C59#53211yescharacteristic
272C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
273C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
274C22×C59C2×#13711yescharacteristic
275C22×C59#57511yescharacteristic
276C4×C59—22no—
277C4×C59—22no—
278C4×C59—42no—
279C4×C59—42no—
280C4×C59—81no—
281C4×C59#52911yescharacteristic
282C4×C59#52911yescharacteristic
283C4×C59#53311yescharacteristic
284C4×C59#53311yescharacteristic
285Dic59—22no—
286Dic59—22no—
287Dic59—22no—
288Dic59—42no—
289Dic59—41no—
290Dic59—81no—
291Dic59—81no—
292Dic59—81no—
293C4×C4⋊Q8—591no—
294#2293—591no—
295#2100—591no—
296#2094—591no—
297#2088—591no—
298#2088—591no—
299#2067—591no—
300#2067—591no—
301#2057—591no—
302#2023—591no—
303#1776—591no—
304#1776—591no—
305#1767—591no—
306#1762—591no—
307#1762D5911yescharacteristic
308C2×C59—82no—
309C2×C59#239611yescharacteristic
310C2×C59#307711yescharacteristic
311C2×C59#307911yescharacteristic
312C2×C59#310911yescharacteristic
313C2×C59#311711yescharacteristic
314C2×C59#318011yescharacteristic
315C2×C59#318211yescharacteristic
316C2×C4⋊Q8—591no—
317C2×C4×Q8—1181no—
318C2×C4×D4C2×D5911yescharacteristic
319C2×#117—1181no—
320C2×#107—591no—
321C2×#107—591no—
322C2×#106—591no—
323C2×#106—591no—
324C2×C4⋊C8—591no—
325C2×C4⋊C8—591no—
326C2×#102—591no—
327C2×#102—591no—
328C2×#102C2×D5911yescharacteristic
329C2×#102C2×D5911yescharacteristic
330C2×#97—591no—
331C2×#97C2×D5911yescharacteristic
332#391—1181no—
333#390—591no—
334#390—591no—
335#389—591no—
336#389—591no—
337#389—591no—
338#389—591no—
339#389—1181no—
340#388—1181no—
341#388—1181no—
342#384—591no—
343C4×C4⋊C4—591no—
344C4×C4⋊C4—591no—
345C4×C4⋊C4—1181no—
346C4×C4⋊C4C2×D5911yescharacteristic
347C4×C22⋊C4—1181no—
348C43—591no—
349#340—591no—
350#340—591no—
351#340—591no—
352#340—591no—
353#340—591no—
354#340—591no—
355#340C2×D5911yescharacteristic
356#340C2×D5911yescharacteristic
357#336—591no—
358#336—591no—
359C59#2378011yescharacteristic, complemented, Sylow
360C22×Q8—1181no—
361C22×D4C22×D5911yescharacteristic
362C23×C4—21no—
363C22×C8—591no—
364C22×C8—591no—
365C22×C8C22×D5911yescharacteristic
366C22×C8C22×D5911yescharacteristic
367C4⋊Q8—1182no—
368C4⋊Q8—1182no—
369C4×Q8—2364no—
370C4×D4—22no—
371C4×D4Dic11814yescomplemented
372#117—2364no—
373C2×C4⋊C4—591no—
374C2×C4⋊C4—591no—
375C2×C4⋊C4—591no—
376C2×C4⋊C4—591no—
377C2×C4⋊C4—1181no—
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⋊C4C22×D5911yescharacteristic
385C2×C4⋊C4C22×D5911yescharacteristic
386C2×C4⋊C4C22×D5911yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—1181no—
389C2×C22⋊C4—1181no—
390C2×C22⋊C4—1181no—
391C2×C22⋊C4—1181no—
392C2×C42—21no—
393C2×C42—591no—
394C2×C42—591no—
395C2×C42—591no—
396C2×C42—591no—
397C2×C42—591no—
398C2×C42—591no—
399C2×C42—1181no—
400C2×C42—1181no—
401C2×C42C22×D5911yescharacteristic
402#107—1182no—
403#107—1182no—
404#106—1182no—
405#106—1182no—
406C4⋊C8—1182no—
407C4⋊C8—1182no—
408#102—22no—
409#102—22no—
410#102—1182no—
411#102—1182no—
412#97—22no—
413#97—1182no—
414#95—21no—
415#95—1181no—
416#95—1181no—
417#95—1181no—
418#95—1181no—
419#95—1181no—
420#95—1181no—
421C24—21no—
422C2×Q8—1184no—
423C2×Q8—2362no—
424C2×Q8—2362no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4C2×Dic11812yes—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—24no—
434C22×C4—21no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—591no—
438C22×C4—591no—
439C22×C4—591no—
440C22×C4—591no—
441C22×C4—1181no—
442C22×C4—1181no—
443C22×C4—1181no—
444C22×C4—1181no—
445C22×C4D4×D5911yescharacteristic
446C22×C4D4×D5911yescharacteristic
447C22×C4C23×D5911yescharacteristic
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—592no—
454C2×C8—1181no—
455C2×C8—1181no—
456C2×C8—1181no—
457C2×C8—1181no—
458C2×C8—1181no—
459C2×C8#1174568512yes—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—592no—
465C4⋊C4—1184no—
466C4⋊C4—1181no—
467C4⋊C4—1181no—
468C4⋊C4—1181no—
469C4⋊C4—1181no—
470C4⋊C4—1181no—
471C4⋊C4—1181no—
472C4⋊C4—1181no—
473C4⋊C4—2362no—
474C4⋊C4—2362no—
475C4⋊C4—2362no—
476C4⋊C4—2362no—
477C4⋊C4—2362no—
478C4⋊C4—2362no—
479C4⋊C4C2×Dic11812yes—
480C4⋊C4#1174568512yes—
481C22⋊C4—24no—
482C22⋊C4—2362no—
483C22⋊C4—2362no—
484C22⋊C4—2362no—
485C22⋊C4—2362no—
486C42—42no—
487C42—1182no—
488C42—1182no—
489C42—1182no—
490C42—1181no—
491C42—1181no—
492C42—1181no—
493C42—1181no—
494C42—2361no—
495C42—2362no—
496C42—2362no—
497C42C2×Dic11812yes—
498C42#1174568712yes—
499C23—22no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23C2×D4×D5911yescharacteristic
507Q8—2368no—
508D4—22no—
509D4—22no—
510D4—41no—
511D4—41no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—48no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—592no—
527C2×C4—592no—
528C2×C4—592no—
529C2×C4—1181no—
530C2×C4—1181no—
531C2×C4—1181no—
532C2×C4—1181no—
533C2×C4—1181no—
534C2×C4—1181no—
535C2×C4—1182no—
536C2×C4—1181no—
537C2×C4—1181no—
538C2×C4—1181no—
539C2×C4—2361no—
540C2×C4—2361no—
541C2×C4—2361no—
542C2×C4—2361no—
543C2×C4—2361no—
544C2×C4—2361no—
545C2×C4—2361no—
546C2×C4—2361no—
547C2×C4—2361no—
548C2×C4—2361no—
549C2×C4—2361no—
550C2×C4#1427370412yes—
551C2×C4#1427370412yes—
552C2×C4C22×Dic11811yescharacteristic
553C2×C4#41×D5911yescharacteristic
554C2×C4#41×D5911yescharacteristic
555C2×C4C2×#1174568711yescharacteristic
556C2×C4C2×#1174568511yescharacteristic
557C2×C4C2×#1174568511yescharacteristic
558C8—22no—
559C8—41no—
560C8—1182no—
561C8—2361no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22C2×#1427370411yescharacteristic
570C22#1683791111yescharacteristic
571C22#1683794911yescharacteristic
572C22AGL(1,ℤ/8)×D5911yescharacteristic
573C22AGL(1,ℤ/8)×D5911yescharacteristic
574C22#137×D5911yescharacteristic
575C22#1683819811yescharacteristic
576C4—22no—
577C4—22no—
578C4—42no—
579C4—42no—
580C4—81no—
581C4—1182no—
582C4—1182no—
583C4—1182no—
584C4—4721no—
585C4—4721no—
586C4—4721no—
587C4—2362no—
588C4—2361no—
589C4#1683793211yescharacteristic
590C4#1683793411yescharacteristic
591C4#1683795511yescharacteristic
592C4#1683795911yescharacteristic
593C2—82no—
594C2#2142737011yescharacteristic
595C2#2143389011yescharacteristic
596C2#2143390711yescharacteristic
597C2#2143418511yescharacteristic
598C2#2143426511yescharacteristic
599C2#2143479211yescharacteristic
600C2#2143481111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#1762C2
socleC23×C59C22×D4
prime radicalC22×D4×C59C23
hypercenter#1762D59
hypocenterC59#23780
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
1. C4×#14273726C2semidirect
3. #21425662C2semidirect
5. #21425599C2semidirect
6. #21425596C2semidirect
9. #21425423C2semidirect
11. #21423994C2semidirect
12. #21423993C2semidirect
13. #21423950C2semidirect
109. C4×D4×C59Q8semidirect
359. C59#23780semidirect
371. C4×D4Dic118semidirect

Maximal subgroups

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

subgroupindex
C4×#142737262
#214265612
#214256622
#214256272
#214255992
#214255962
#214254822
#214254802
#214254232
#214252302
#214239942
#214239932
#214239502
#214239212
C59×#17622
#2378059