Finite Group Databasebeta

← #28611971

Subgroups — #28611971

Order 15104.

806 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837693C211yesmaximal, characteristic
2#21427154C211yesmaximal, characteristic, complemented
3#21427067C211yesmaximal, characteristic
4#21425069C211yesmaximal, characteristic, complemented
5#21424866C211yesmaximal, characteristic, complemented
6#21424793C211yesmaximal, characteristic
7#21424779C211yesmaximal, characteristic
8#21424724C211yesmaximal, characteristic
9#21424717C211yesmaximal, characteristic
10#21424682C211yesmaximal, characteristic, complemented
11#21424675C211yesmaximal, characteristic, complemented
12#21423993C211yesmaximal, characteristic, complemented
13C4×#14273659C211yesmaximal, characteristic, complemented
14#21423922C211yesmaximal, characteristic
15C59×#1771C211yesmaximal, characteristic, complemented
16C2×#14273727C2211yescharacteristic
17C2×#14273692—21no—
18C2×C4×D236C2211yescharacteristic
19#16837693C418yescomplemented
20C2×#14273661C2211yescharacteristic
21C2×#14273659C2211yescharacteristic
22C2×#14273659C2211yescharacteristic
23C2×#14273659C2211yescharacteristic
24C2×#14273649C2211yescharacteristic
25C2×#14273649C2211yescharacteristic
26C2×#14273649C2211yescharacteristic
27C2×#14273649C2211yescharacteristic
28#16837307—21no—
29#16837304C2211yescharacteristic
30#16837304C2211yescharacteristic
31#16837300C2211yescharacteristic
32#16837300C2211yescharacteristic
33#16837292—21no—
34#16837292—21no—
35#16837287—21no—
36#16837287—21no—
37#16837268C2211yescharacteristic
38#16837264—21no—
39C4×C4⋊Dic59C2211yescharacteristic
40C4×C4⋊Dic59C2211yescharacteristic
41C4×C4⋊Dic59C2211yescharacteristic
42C4×C4⋊Dic59C2211yescharacteristic
43C4×C4⋊Dic59C2211yescharacteristic
44#16837249—21no—
45#16837165C2211yescharacteristic
46#16837165C2211yescharacteristic
47#16837165C2211yescharacteristic
48#16837165C2211yescharacteristic
49#16837165C2211yescharacteristic
50#16837165C2211yescharacteristic
51#16837165C2211yescharacteristic
52#16837165C2211yescharacteristic
53C2×C4⋊C8×C59C2211yescharacteristic
54C2×#97×C59C2211yescharacteristic
55C2×#97×C59C2211yescharacteristic
56C2×C4×C8×C59C2211yescharacteristic
57C4×C4⋊C4×C59C2211yescharacteristic
58C59×#336C2211yescharacteristic
59C59×#336C2211yescharacteristic
60C22×Dic118—21no—
61C22×D236C2311yescharacteristic
62C22×C4×D59—21no—
63#14273727—22no—
64#14273727C2×C414yes—
65#14273692—44no—
66C4×D236—22no—
67C4×D236C2×C414yes—
68C2×C4⋊Dic59—21no—
69C2×C4⋊Dic59C2311yescharacteristic
70C2×C4⋊Dic59C2311yescharacteristic
71C2×C4⋊Dic59C2311yescharacteristic
72C2×C4⋊Dic59C2311yescharacteristic
73C2×C4⋊Dic59C2311yescharacteristic
74C2×C4⋊Dic59C2311yescharacteristic
75C2×C4⋊Dic59C2311yescharacteristic
76C2×Dic59⋊C4—21no—
77C2×Dic59⋊C4—21no—
78C2×(C2×D59)⋊C4—21no—
79C2×(C2×D59)⋊C4—21no—
80C2×(C2×D59)⋊C4—21no—
81C2×(C2×D59)⋊C4—21no—
82C2×(C2×D59)⋊C4—21no—
83C2×C4×Dic59—21no—
84C2×C4×Dic59—21no—
85C2×C4×Dic59—21no—
86C2×C4×Dic59—21no—
87C2×C4×Dic59—21no—
88#14273661—22no—
89#14273659—22no—
90#14273659C2×C414yes—
91#14273659C2×C414yes—
92#14273649—22no—
93#14273649—22no—
94#14273649C2×C414yes—
95#14273649C2×C414yes—
96C59⋊#95—21no—
97C59⋊#95—21no—
98C59⋊#95—21no—
99C59⋊#95—21no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C22×C8×C59C2311yescharacteristic
106C22×C8×C59C2311yescharacteristic
107C22×C8×C59C2311yescharacteristic
108C22×C8×C59C2311yescharacteristic
109C2×C4⋊C4×C59D411yescharacteristic
110C2×C4⋊C4×C59D411yescharacteristic
111C2×C42×C59C2311yescharacteristic
112C2×C42×C59C2311yescharacteristic
113C2×C42×C59C2311yescharacteristic
114C4⋊C8×C59C2×C414yes—
115#97×C59—22no—
116#97×C59—22no—
117C4×C8×C59—22no—
118#95×C59D411yescharacteristic
119#95×C59D411yescharacteristic
120C23×D59—21no—
121C22×C4×C59C2×D411yescharacteristic
122C22×C4×C59C2×D411yescharacteristic
123C22×C4×C59C2×D411yescharacteristic
124C22×C4×C59C2×D411yescharacteristic
125C22×C4×C59C2×D411yescharacteristic
126C22×C4×C59C2×D411yescharacteristic
127C22×C4×C59C2411yescharacteristic
128C22×Dic59—21no—
129C22×Dic59—21no—
130C22×Dic59—21no—
131C22×Dic59—21no—
132C22×Dic59—21no—
133C22×Dic59—21no—
134C22×Dic59—21no—
135C2×D236—21no—
136C2×D236—21no—
137C2×D236—21no—
138C2×D236—21no—
139C2×D236—21no—
140C2×D236C22×C412yes—
141C2×C4×D59—24no—
142C2×C4×D59—81no—
143C2×C4×D59—81no—
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—21no—
153C2×C8×C59—21no—
154C2×C8×C59—21no—
155C2×C8×C59—21no—
156C2×C8×C59C22×C412yes—
157C2×C8×C59C22×C412yes—
158C2×C8×C59#4112yes—
159C4⋊C4×C59—22no—
160C4⋊C4×C59—41no—
161C42×C59—21no—
162C42×C59—21no—
163C42×C59—21no—
164C42×C59—21no—
165C42×C59C22×C412yes—
166C42×C59#4112yes—
167(C2×D59)⋊C4—24no—
168(C2×D59)⋊C4—42no—
169(C2×D59)⋊C4—42no—
170(C2×D59)⋊C4—81no—
171(C2×D59)⋊C4—81no—
172C4⋊Dic59—24no—
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—21no—
183C4⋊Dic59C22×C412yes—
184C4⋊Dic59C22×C412yes—
185C4⋊Dic59C22×C412yes—
186C4⋊Dic59#4112yes—
187Dic59⋊C4—42no—
188Dic59⋊C4—42no—
189C4×Dic59—42no—
190C4×Dic59—42no—
191C4×Dic59—42no—
192C4×Dic59—81no—
193C4×Dic59—81no—
194C23×C59C22×D411yescharacteristic
195C22×D59—22no—
196C22×D59—41no—
197C22×D59—41no—
198C22×D59—41no—
199C22×D59—41no—
200C22×D59—41no—
201C22×D59—41no—
202C2×C4×C59—21no—
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×C59C4×D412yes—
218C2×C4×C59C4×D412yes—
219C2×C4×C59AGL(1,ℤ/8)12yes—
220C2×C4×C59C23×C411yescharacteristic
221C2×C4×C59C2×#4111yescharacteristic
222C2×C4×C59C2×#4111yescharacteristic
223C2×C4×C59C2×#4111yescharacteristic
224C2×C4×C592−1+411yescharacteristic
225C2×C4×C592−1+411yescharacteristic
226C2×Dic59—22no—
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—
247D236—22no—
248D236—22no—
249D236—41no—
250D236—41no—
251C4×D59—84no—
252Dic118—48no—
253C8×C59—22no—
254C8×C59—22no—
255C8×C59—22no—
256C8×C59—41no—
257#23075—591nomaximal, Sylow
258C22×C59C2×C4×D411yescharacteristic
259C22×C59#54711yescharacteristic
260C22×C59#54811yescharacteristic
261C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
262C22×C59#57511yescharacteristic
263C22×C59#57711yescharacteristic
264C22×C59#57711yescharacteristic
265C2×D59—42no—
266C2×D59—42no—
267C2×D59—42no—
268C2×D59—81no—
269C2×D59—81no—
270C2×D59—81no—
271C2×D59—81no—
272C4×C59—22no—
273C4×C59—22no—
274C4×C59—22no—
275C4×C59—41no—
276C4×C59—41no—
277C4×C59—41no—
278C4×C59C4×#4111yescharacteristic
279C4×C59#51911yescharacteristic
280C4×C59#55211yescharacteristic
281C4×C59#55611yescharacteristic
282Dic59—42no—
283Dic59—42no—
284Dic59—42no—
285Dic59—42no—
286Dic59—81no—
287Dic59—81no—
288Dic59—81no—
289C2×#476—591no—
290#2365—591no—
291#2357—591no—
292#1993—591no—
293#1949—591no—
294#1936—591no—
295#1934—591no—
296#1926—591no—
297#1925—591no—
298#1920—591no—
299#1919—591no—
300#1776—591no—
301C4×#106—591no—
302#1771D5911yescharacteristic, complemented
303#1762—591no—
304C2×C59#236211yescharacteristic
305C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
306C2×C59#294911yescharacteristic
307C2×C59#334511yescharacteristic
308C2×C59#335011yescharacteristic
309C2×C59#337111yescharacteristic
310C2×C59#337311yescharacteristic
311D59—82no—
312C2×C4⋊Q8—591no—
313C2×C4×Q8—1181no—
314C2×C4×D4—591no—
315#476—598no—
316C2×#107—591no—
317C2×#106—591no—
318C2×#106—591no—
319C2×#106—591no—
320C2×C4⋊C8C2×D5911yescharacteristic
321C2×#102—591no—
322C2×#102—591no—
323C2×#102—591no—
324C2×#102—591no—
325C2×#97C2×D5911yescharacteristic
326C2×#97C2×D5911yescharacteristic
327C2×C4×C8C2×D5911yescharacteristic
328#391—1181no—
329#390—591no—
330#390—591no—
331#389—591no—
332#389—591no—
333#388—1181no—
334#388—1181no—
335#387—1181no—
336#387—1181no—
337#382—591no—
338#381—1181no—
339C4×C4⋊C4—591no—
340C4×C4⋊C4—591no—
341C4×C4⋊C4—591no—
342C4×C4⋊C4—591no—
343C4×C4⋊C4—591no—
344C4×C4⋊C4C2×D5911yescharacteristic
345C4×C22⋊C4—1181no—
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#2307511yescharacteristic, 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—594no—
365C4⋊Q8—1182no—
366C4×Q8—2364no—
367C4×D4—594no—
368C4×D4—1182no—
369C2×C4⋊C4—591no—
370C2×C4⋊C4—591no—
371C2×C4⋊C4—591no—
372C2×C4⋊C4—591no—
373C2×C4⋊C4—591no—
374C2×C4⋊C4—591no—
375C2×C4⋊C4—591no—
376C2×C4⋊C4—1181no—
377C2×C4⋊C4—1181no—
378C2×C4⋊C4—1181no—
379C2×C4⋊C4D23611yescharacteristic
380C2×C4⋊C4D23611yescharacteristic
381C2×C22⋊C4—1181no—
382C2×C22⋊C4—1181no—
383C2×C22⋊C4—1181no—
384C2×C22⋊C4—1181no—
385C2×C22⋊C4—1181no—
386C2×C42—1181no—
387C2×C42—1181no—
388C2×C42—1181no—
389C2×C42—1181no—
390C2×C42—1181no—
391C2×C42C22×D5911yescharacteristic
392C2×C42C22×D5911yescharacteristic
393C2×C42C22×D5911yescharacteristic
394#107—1182no—
395#106—594no—
396#106—594no—
397#106—1182no—
398C4⋊C8C4×D5914yes—
399#102—594no—
400#102—594no—
401#102—1182no—
402#102—1182no—
403#97—22no—
404#97—22no—
405C4×C8—22no—
406#95—1181no—
407#95—1181no—
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—1184no—
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—1181no—
431C22×C4—1184no—
432C22×C4—1181no—
433C22×C4—1181no—
434C22×C4—1181no—
435C22×C4—4721no—
436C22×C4—4721no—
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×C8C2×C4×D5912yes—
454C2×C8C2×C4×D5912yes—
455C2×C8#1174568712yes—
456C4⋊C4—22no—
457C4⋊C4—41no—
458C4⋊C4—592no—
459C4⋊C4—592no—
460C4⋊C4—592no—
461C4⋊C4—592no—
462C4⋊C4—1184no—
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—1181no—
473C4⋊C4—2362no—
474C4⋊C4—2362no—
475C22⋊C4—1184no—
476C22⋊C4—4721no—
477C22⋊C4—4721no—
478C22⋊C4—2362no—
479C22⋊C4—2362no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—4721no—
485C42—4721no—
486C42—2362no—
487C42—2362no—
488C42—2362no—
489C42C2×C4×D5912yes—
490C42#1174568512yes—
491C23—1182no—
492C23—2361no—
493C23—2361no—
494C23—2361no—
495C23—2361no—
496C23—2361no—
497C23—2361no—
498C23C22×D23611yescharacteristic
499Q8—2368no—
500D4—1182no—
501D4—1182no—
502D4—2361no—
503D4—2361no—
504C2×C4—21no—
505C2×C4—21no—
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—1182no—
520C2×C4—1182no—
521C2×C4—1182no—
522C2×C4—1182no—
523C2×C4—4724no—
524C2×C4—2361no—
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×C4C4×D23612yes—
542C2×C4C4×D23612yes—
543C2×C4#1427375512yes—
544C2×C4C22×C4×D5911yescharacteristic
545C2×C4#41×D5911yescharacteristic
546C2×C4C2×#1174568711yescharacteristic
547C2×C4C2×#1174568511yescharacteristic
548C2×C4#1427377411yescharacteristic
549C2×C4#1427377511yescharacteristic
550C8—22no—
551C8—22no—
552C8—22no—
553C8—41no—
554C22—4721no—
555C22—4721no—
556C22—4721no—
557C22—4721no—
558C22—2362no—
559C22—2362no—
560C22—2362no—
561C22C2×C4×D23611yescharacteristic
562C22#1683805611yescharacteristic
563C22#1683806411yescharacteristic
564C22C2×#1427375511yescharacteristic
565C22#1683820211yescharacteristic
566C22#1683821411yescharacteristic
567C22#1683821411yescharacteristic
568C4—22no—
569C4—22no—
570C4—22no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—4721no—
575C4—4721no—
576C4—4721no—
577C4—2362no—
578C4—2362no—
579C4—2362no—
580C4—2362no—
581C4C4×#1174568711yescharacteristic
582C4#1683787811yescharacteristic
583C4#1683808711yescharacteristic
584C4#1683812011yescharacteristic
585C2—4722no—
586C2#2142712511yescharacteristic
587C2C4×#1427375511yescharacteristic
588C2#2143295711yescharacteristic
589C2#2143656811yescharacteristic
590C2#2143664311yescharacteristic
591C2#2143686611yescharacteristic
592C2#2143689011yescharacteristic
subgroupG/H
centerC23C22×D236
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1771C2
socleC23×C59C22×D4
prime radicalC22×D236C23
cosocleC22×C4×C59C24
hypercenter#1771D59
hypocenterC59#23075
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
2. #21427154C2semidirect
4. #21425069C2semidirect
5. #21424866C2semidirect
10. #21424682C2semidirect
11. #21424675C2semidirect
12. #21423993C2semidirect
13. C4×#14273659C2semidirect
15. C59×#1771C2semidirect
19. #16837693C4semidirect
302. #1771D59semidirect
356. C59#23075semidirect

Maximal subgroups

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

subgroupindex
C2×#168376932
#214271542
#214270672
#214250692
#214248662
#214247932
#214247792
#214247242
#214247172
#214246822
#214246752
#214239932
C4×#142736592
#214239222
C59×#17712
#2307559