Finite Group Databasebeta

← #28640571

Subgroups — #28640571

Order 15104.

774 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837703C211yesmaximal, characteristic
2#21429484C211yesmaximal, characteristic, complemented
3#21429454C211yesmaximal, characteristic
4#21425594C211yesmaximal, characteristic, complemented
5#21425589C211yesmaximal, characteristic, complemented
6#21425483C211yesmaximal, characteristic
7#21425469C211yesmaximal, characteristic
8#21425061C211yesmaximal, characteristic, complemented
9#21424866C211yesmaximal, characteristic, complemented
10#21424829C211yesmaximal, characteristic, complemented
11#21424824C211yesmaximal, characteristic, complemented
12#21424779C211yesmaximal, characteristic
13#21424779C211yesmaximal, characteristic
14C4×#14273649C211yesmaximal, characteristic
15C2×C8×Q8×C59C211yesmaximal, characteristic, complemented
16C2×#14273719C2211yescharacteristic
17C2×C4×D236C2211yescharacteristic
18#16837703—24no—
19C2×#14273661C2211yescharacteristic
20C2×#14273661C2211yescharacteristic
21C2×#14273659C2211yescharacteristic
22C2×#14273659C2211yescharacteristic
23C2×#14273649C2211yescharacteristic
24C2×#14273649C2211yescharacteristic
25C2×#14273649C2211yescharacteristic
26C2×#14273649C2211yescharacteristic
27#16837337—21no—
28#16837333—21no—
29#16837321—21no—
30#16837313—21no—
31#16837304C2211yescharacteristic
32#16837304C2211yescharacteristic
33#16837300C2211yescharacteristic
34#16837300C2211yescharacteristic
35#16837300C2211yescharacteristic
36#16837300C2211yescharacteristic
37#16837300C2211yescharacteristic
38#16837300C2211yescharacteristic
39#16837297—21no—
40#16837297—21no—
41#16837273—21no—
42#16837273—21no—
43#16837268C2211yescharacteristic
44C4×C4⋊Dic59C2211yescharacteristic
45#16837165C2211yescharacteristic
46#16837165C2211yescharacteristic
47#16837165C2211yescharacteristic
48#16837165C2211yescharacteristic
49#16837165C2211yescharacteristic
50#16837165C2211yescharacteristic
51#16837165C2211yescharacteristic
52#16837165C2211yescharacteristic
53C2×C4×Q8×C59C2211yescharacteristic
54C8×Q8×C59—24no—
55C2×C4⋊C8×C59C2211yescharacteristic
56C2×C4⋊C8×C59C2211yescharacteristic
57C2×C4⋊C8×C59C2211yescharacteristic
58C2×C4×C8×C59C2211yescharacteristic
59C2×C4×C8×C59C2211yescharacteristic
60C2×C4×C8×C59C2211yescharacteristic
61C22×D236C2311yescharacteristic
62C22×C4×D59—21no—
63#14273719—22no—
64#14273719—22no—
65C4×D236—22no—
66C4×D236—22no—
67C2×C4⋊Dic59C2311yescharacteristic
68C2×C4⋊Dic59C2311yescharacteristic
69C2×C4⋊Dic59C2311yescharacteristic
70C2×C4⋊Dic59C2311yescharacteristic
71C2×C4⋊Dic59C2311yescharacteristic
72C2×C4⋊Dic59C2311yescharacteristic
73C2×C4⋊Dic59C2311yescharacteristic
74C2×Dic59⋊C4—21no—
75C2×Dic59⋊C4—21no—
76C2×Dic59⋊C4—21no—
77C2×Dic59⋊C4—21no—
78C2×Dic59⋊C4—21no—
79C2×Dic59⋊C4—21no—
80C2×Dic59⋊C4—21no—
81C2×Dic59⋊C4—21no—
82C2×(C2×D59)⋊C4—21no—
83C2×(C2×D59)⋊C4—21no—
84C2×(C2×D59)⋊C4—21no—
85C2×(C2×D59)⋊C4—21no—
86C2×(C2×D59)⋊C4—21no—
87C2×C4×Dic59—21no—
88#14273661—22no—
89#14273661—22no—
90#14273659—22no—
91#14273659—22no—
92#14273649—22no—
93#14273649—22no—
94#14273649—22no—
95#14273649Q814yescomplemented
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×Q8×C59D411yescharacteristic
106C22×C8×C59C2311yescharacteristic
107C22×C8×C59C2311yescharacteristic
108C22×C8×C59C2311yescharacteristic
109C22×C8×C59C2311yescharacteristic
110C4×Q8×C59—22no—
111C4×Q8×C59—22no—
112C2×C4⋊C4×C59D411yescharacteristic
113C2×C4⋊C4×C59D411yescharacteristic
114C2×C4⋊C4×C59D411yescharacteristic
115C2×C42×C59C2311yescharacteristic
116C2×C42×C59C2311yescharacteristic
117C2×C42×C59C2311yescharacteristic
118C4⋊C8×C59—22no—
119C4⋊C8×C59—22no—
120C4⋊C8×C59D414yes—
121C4×C8×C59—22no—
122C4×C8×C59—22no—
123C4×C8×C59—22no—
124C23×D59—21no—
125C2×Q8×C59—22no—
126C2×Q8×C59—22no—
127C2×Q8×C59—22no—
128C22×C4×C59C2×D411yescharacteristic
129C22×C4×C59C2×D411yescharacteristic
130C22×C4×C59C2×D411yescharacteristic
131C22×C4×C59C2×D411yescharacteristic
132C22×C4×C59C2×D411yescharacteristic
133C22×C4×C59C2×D411yescharacteristic
134C22×C4×C59C2411yescharacteristic
135C22×Dic59—21no—
136C22×Dic59—21no—
137C22×Dic59—21no—
138C22×Dic59—21no—
139C22×Dic59—21no—
140C22×Dic59—21no—
141C22×Dic59—21no—
142C2×D236—21no—
143C2×D236—21no—
144C2×D236—21no—
145C2×D236—21no—
146C2×D236—21no—
147C2×D236C2×Q812yes—
148C2×C4×D59—42no—
149C2×C4×D59—81no—
150C2×C4×D59—81no—
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—
158C2×C8×C59—21no—
159C2×C8×C59—21no—
160C2×C8×C59C2×D412yes—
161C2×C8×C59C2×D412yes—
162C2×C8×C59C2×Q812yes—
163C4⋊C4×C59—22no—
164C4⋊C4×C59—22no—
165C4⋊C4×C59—22no—
166C42×C59—21no—
167C42×C59—21no—
168C42×C59—21no—
169C42×C59—21no—
170C42×C59C2×D412yes—
171C42×C59#4112yes—
172(C2×D59)⋊C4—42no—
173(C2×D59)⋊C4—42no—
174(C2×D59)⋊C4—42no—
175(C2×D59)⋊C4—81no—
176(C2×D59)⋊C4—81no—
177C4⋊Dic59—21no—
178C4⋊Dic59—21no—
179C4⋊Dic59—21no—
180C4⋊Dic59—21no—
181C4⋊Dic59—21no—
182C4⋊Dic59—21no—
183C4⋊Dic59—21no—
184C4⋊Dic59—21no—
185C4⋊Dic59—21no—
186C4⋊Dic59—21no—
187C4⋊Dic59—21no—
188C4⋊Dic59—21no—
189C4⋊Dic59C2×Q812yes—
190C4⋊Dic59#4112yes—
191Dic59⋊C4—42no—
192Dic59⋊C4—42no—
193Dic59⋊C4—42no—
194Dic59⋊C4—42no—
195Dic59⋊C4—81no—
196Dic59⋊C4—81no—
197Dic59⋊C4—81no—
198Dic59⋊C4—81no—
199C4×Dic59—81no—
200C23×C59C22×D411yescharacteristic
201C22×D59—22no—
202C22×D59—41no—
203C22×D59—41no—
204C22×D59—41no—
205C22×D59—41no—
206C22×D59—41no—
207C22×D59—41no—
208Q8×C59—28no—
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×C59—21no—
219C2×C4×C59—21no—
220C2×C4×C59—21no—
221C2×C4×C59—21no—
222C2×C4×C59—21no—
223C2×C4×C59#12112yes—
224C2×C4×C59#12112yes—
225C2×C4×C59#13512yes—
226C2×C4×C59#13512yes—
227C2×C4×C59C22×D411yescharacteristic
228C2×C4×C59C22×Q811yescharacteristic
229C2×C4×C59C2×#4111yescharacteristic
230C2×C4×C59C2×#4111yescharacteristic
231C2×C4×C592−1+411yescharacteristic
232C2×C4×C592−1+411yescharacteristic
233C2×Dic59—22no—
234C2×Dic59—22no—
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—
248C2×Dic59—41no—
249C2×Dic59—41no—
250C2×Dic59—41no—
251C2×Dic59—41no—
252C2×Dic59—41no—
253C2×Dic59—41no—
254D236—22no—
255D236—22no—
256D236—41no—
257D236—41no—
258C4×D59—84no—
259C8×C59—22no—
260C8×C59—22no—
261C8×C59—22no—
262C8×C59—41no—
263#25473—591nomaximal, Sylow
264C22×C59C2×#12111yescharacteristic
265C22×C59#54811yescharacteristic
266C22×C59D4×Q811yescharacteristic
267C22×C59C2×#13511yescharacteristic
268C22×C59C2×#13511yescharacteristic
269C22×C59#57611yescharacteristic
270C22×C59#57711yescharacteristic
271C2×D59—42no—
272C2×D59—42no—
273C2×D59—42no—
274C2×D59—81no—
275C2×D59—81no—
276C2×D59—81no—
277C2×D59—81no—
278C4×C59—22no—
279C4×C59—22no—
280C4×C59—22no—
281C4×C59—22no—
282C4×C59—41no—
283C4×C59—41no—
284C4×C59#53311yescharacteristic
285C4×C59#54111yescharacteristic
286C4×C59#54711yescharacteristic
287C4×C59D4×Q811yescharacteristic
288Dic59—42no—
289Dic59—42no—
290Dic59—81no—
291Dic59—81no—
292Dic59—81no—
293Dic59—81no—
294Dic59—81no—
295C2×#478—591no—
296C2×C8×Q8D5911yescharacteristic, complemented
297#2584—591no—
298#2580—591no—
299#2088—591no—
300#2087—591no—
301#2067—591no—
302#2065—591no—
303#1991—591no—
304#1949—591no—
305#1942—591no—
306#1941—591no—
307#1934—591no—
308#1934—591no—
309C4×#102—591no—
310C2×C59#242911yescharacteristic
311C2×C59#305011yescharacteristic
312C2×C59#306211yescharacteristic
313C2×C59#336111yescharacteristic
314C2×C59#336511yescharacteristic
315C2×C59#338011yescharacteristic
316C2×C59#338111yescharacteristic
317D59—82no—
318C2×#125—591no—
319C2×C4×Q8C2×D5911yescharacteristic
320C2×C4×D4—591no—
321#478—1184no—
322C8×Q8—24no—
323C2×#107—591no—
324C2×#107—591no—
325C2×#106—591no—
326C2×#106—591no—
327C2×C4⋊C8C2×D5911yescharacteristic
328C2×C4⋊C8C2×D5911yescharacteristic
329C2×C4⋊C8C2×D5911yescharacteristic
330C2×#102—591no—
331C2×#102—591no—
332C2×#102—591no—
333C2×#102—591no—
334C2×C4×C8C2×D5911yescharacteristic
335C2×C4×C8C2×D5911yescharacteristic
336C2×C4×C8C2×D5911yescharacteristic
337#399—1181no—
338#398—1181no—
339#395—1181no—
340#393—1181no—
341#390—591no—
342#390—591no—
343#389—591no—
344#389—591no—
345#389—591no—
346#389—591no—
347#389—591no—
348#389—591no—
349#389—1181no—
350#389—1181no—
351#385—1181no—
352#385—1181no—
353#382—591no—
354C4×C4⋊C4—591no—
355#340—591no—
356#340—591no—
357#340—591no—
358#340—591no—
359#340—591no—
360#340—591no—
361#340—591no—
362#340—591no—
363C59#2547311yescharacteristic, complemented, Sylow
364C22×Q8D23611yescharacteristic
365C22×D4—591no—
366C23×C4—1181no—
367C22×C8C22×D5911yescharacteristic
368C22×C8C22×D5911yescharacteristic
369C22×C8C22×D5911yescharacteristic
370C22×C8C22×D5911yescharacteristic
371#125—1182no—
372#125—1182no—
373C4×Q8—22no—
374C4×Q8—22no—
375C4×D4—1182no—
376C4×D4—1182no—
377C2×C4⋊C4—591no—
378C2×C4⋊C4—591no—
379C2×C4⋊C4—591no—
380C2×C4⋊C4—591no—
381C2×C4⋊C4—591no—
382C2×C4⋊C4—591no—
383C2×C4⋊C4—591no—
384C2×C4⋊C4—1181no—
385C2×C4⋊C4—1181no—
386C2×C4⋊C4—1181no—
387C2×C4⋊C4—1181no—
388C2×C4⋊C4—1181no—
389C2×C4⋊C4—1181no—
390C2×C4⋊C4—1181no—
391C2×C4⋊C4—1181no—
392C2×C4⋊C4D23611yescharacteristic
393C2×C4⋊C4D23611yescharacteristic
394C2×C4⋊C4D23611yescharacteristic
395C2×C22⋊C4—1181no—
396C2×C22⋊C4—1181no—
397C2×C22⋊C4—1181no—
398C2×C22⋊C4—1181no—
399C2×C22⋊C4—1181no—
400C2×C42—1181no—
401C2×C42C22×D5911yescharacteristic
402C2×C42C22×D5911yescharacteristic
403C2×C42C22×D5911yescharacteristic
404#107—1182no—
405#107—1182no—
406#106—1182no—
407#106—1182no—
408C4⋊C8—22no—
409C4⋊C8—22no—
410C4⋊C8C22⋊D5914yes—
411#102—594no—
412#102—1182no—
413#102—1182no—
414#102—1182no—
415C4×C8—22no—
416C4×C8—22no—
417C4×C8—22no—
418#95—1181no—
419#95—1181no—
420#95—1181no—
421#95—1181no—
422#95—1181no—
423#95—1181no—
424#95—1181no—
425#95—1181no—
426#95—1181no—
427C24—1181no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×D4—592no—
432C2×D4—1181no—
433C2×D4—1181no—
434C2×D4—1181no—
435C2×D4—1181no—
436C2×D4—1181no—
437C22×C4—1181no—
438C22×C4—1181no—
439C22×C4—1181no—
440C22×C4—1181no—
441C22×C4—1181no—
442C22×C4—1181no—
443C22×C4—1181no—
444C22×C4—4721no—
445C22×C4—4721no—
446C22×C4—2362no—
447C22×C4C2×D23611yescharacteristic
448C22×C4C2×D23611yescharacteristic
449C22×C4C2×D23611yescharacteristic
450C22×C4C2×D23611yescharacteristic
451C22×C4C2×D23611yescharacteristic
452C22×C4C2×D23611yescharacteristic
453C22×C4C23×D5911yescharacteristic
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8Q8×D5912yes—
464C2×C8C2×C22⋊D5912yes—
465C2×C8C2×C22⋊D5912yes—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—592no—
470C4⋊C4—592no—
471C4⋊C4—1181no—
472C4⋊C4—1181no—
473C4⋊C4—1181no—
474C4⋊C4—1181no—
475C4⋊C4—1181no—
476C4⋊C4—1181no—
477C4⋊C4—1181no—
478C4⋊C4—1181no—
479C4⋊C4—1181no—
480C4⋊C4—1181no—
481C4⋊C4—1181no—
482C4⋊C4—1181no—
483C4⋊C4—4721no—
484C4⋊C4—4721no—
485C4⋊C4—4721no—
486C4⋊C4—4721no—
487C4⋊C4—2362no—
488C4⋊C4—2362no—
489C4⋊C4—2362no—
490C4⋊C4—2362no—
491C22⋊C4—4721no—
492C22⋊C4—4721no—
493C22⋊C4—2362no—
494C22⋊C4—2362no—
495C22⋊C4—2362no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—4721no—
501C42#1174568512yes—
502C42C2×C22⋊D5912yes—
503C23—1182no—
504C23—2361no—
505C23—2361no—
506C23—2361no—
507C23—2361no—
508C23—2361no—
509C23—2361no—
510C23C22×D23611yescharacteristic
511Q8—28no—
512D4—1182no—
513D4—1182no—
514D4—2361no—
515D4—2361no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—1182no—
531C2×C4—1182no—
532C2×C4—4724no—
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—2361no—
544C2×C4—2361no—
545C2×C4—2361no—
546C2×C4—2361no—
547C2×C4—2361no—
548C2×C4—2361no—
549C2×C4—2361no—
550C2×C4—2361no—
551C2×C4—2361no—
552C2×C4#1427370112yes—
553C2×C4#1427370112yes—
554C2×C4#1427374912yes—
555C2×C4#1427374912yes—
556C2×C4C22×C22⋊D5911yescharacteristic
557C2×C4C2×Q8×D5911yescharacteristic
558C2×C4#41×D5911yescharacteristic
559C2×C4C2×#1174568511yescharacteristic
560C2×C4#1427377411yescharacteristic
561C2×C4#1427377511yescharacteristic
562C8—22no—
563C8—22no—
564C8—22no—
565C8—41no—
566C22—4721no—
567C22—4721no—
568C22—4721no—
569C22—4721no—
570C22—2362no—
571C22—2362no—
572C22—2362no—
573C22C2×#1427370111yescharacteristic
574C22#1683806411yescharacteristic
575C22Q8×D23611yescharacteristic
576C22C2×#1427374911yescharacteristic
577C22C2×#1427374911yescharacteristic
578C22#1683820711yescharacteristic
579C22#1683821411yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—41no—
586C4—4721no—
587C4—4721no—
588C4—4721no—
589C4—4721no—
590C4—4721no—
591C4—2362no—
592C4—2362no—
593C4#1683795611yescharacteristic
594C4#1683801011yescharacteristic
595C4#1683805111yescharacteristic
596C4Q8×C22⋊D5911yescharacteristic
597C2—4722no—
598C2#2142768911yescharacteristic
599C2#2143367711yescharacteristic
600C2#2143377611yescharacteristic
601C2#2143675811yescharacteristic
602C2#2143679411yescharacteristic
603C2#2143696411yescharacteristic
604C2#2143697311yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C8×Q8×C59C2
socleC23×C59C22×D4
prime radicalC22×D236C23
hypercenterC2×C8×Q8D59
hypocenterC59#25473
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
2. #21429484C2semidirect
4. #21425594C2semidirect
5. #21425589C2semidirect
8. #21425061C2semidirect
9. #21424866C2semidirect
10. #21424829C2semidirect
11. #21424824C2semidirect
15. C2×C8×Q8×C59C2semidirect
95. #14273649Q8semidirect
296. C2×C8×Q8D59semidirect
363. C59#25473semidirect

Maximal subgroups

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

subgroupindex
C2×#168377032
#214294842
#214294542
#214255942
#214255892
#214254832
#214254692
#214250612
#214248662
#214248292
#214248242
#214247792
C4×#142736492
C2×C8×Q8×C592
#2547359