Finite Group Databasebeta

← #28618725

Subgroups — #28618725

Order 15104.

836 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
1C4×#14273701C211yesmaximal, characteristic
2#21426494C211yesmaximal, characteristic, complemented
3#21425665C211yesmaximal, characteristic, complemented
4#21425616C211yesmaximal, characteristic, complemented
5#21425579C211yesmaximal, characteristic, complemented
6#21425529C211yesmaximal, characteristic, complemented
7#21425524C211yesmaximal, characteristic, complemented
8#21425511C211yesmaximal, characteristic, complemented
9#21425286C211yesmaximal, characteristic
10#21425279C211yesmaximal, characteristic
11C4×#14273661C211yesmaximal, characteristic, complemented
12C4×#14273659C211yesmaximal, characteristic, complemented
13C4×#14273649C211yesmaximal, characteristic, complemented
14C4×#14273649C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C59C211yesmaximal, characteristic, complemented
16C2×#14273701C2211yescharacteristic
17C2×C4×D236C2211yescharacteristic
18C2×C4×C22⋊D59—21no—
19C2×#14273661C2211yescharacteristic
20C2×#14273661C2211yescharacteristic
21C2×#14273659C2211yescharacteristic
22C2×#14273659C2211yescharacteristic
23C2×#14273649C2211yescharacteristic
24C2×#14273649C2211yescharacteristic
25C2×#14273649C2211yescharacteristic
26C2×#14273649C2211yescharacteristic
27#16837304C2211yescharacteristic
28#16837300C2211yescharacteristic
29#16837293—21no—
30#16837281—21no—
31#16837270—21no—
32#16837268C2211yescharacteristic
33#16837268C2211yescharacteristic
34#16837265—21no—
35#16837262C2211yescharacteristic
36#16837262C2211yescharacteristic
37#16837262C2211yescharacteristic
38C4×C4⋊Dic59C2211yescharacteristic
39C4×C4⋊Dic59C2211yescharacteristic
40C4×C4⋊Dic59C2211yescharacteristic
41C4×(C2×D59)⋊C4—21no—
42C4×C22⋊Dic59—21no—
43#16837248—21no—
44#16837165C2211yescharacteristic
45#16837165C2211yescharacteristic
46#16837165C2211yescharacteristic
47#16837165C2211yescharacteristic
48#16837165C2211yescharacteristic
49#16837165C2211yescharacteristic
50#16837165C2211yescharacteristic
51#16837165C2211yescharacteristic
52C22×C42×C59C2211yescharacteristic
53C2×C22⋊C8×C59C2211yescharacteristic
54C2×C22⋊C8×C59C2211yescharacteristic
55C2×C4×C8×C59C2211yescharacteristic
56C2×C4×C8×C59C2211yescharacteristic
57C59×#336C2211yescharacteristic
58C59×#336C2211yescharacteristic
59C22×D236C2311yescharacteristic
60C22×C22⋊D59—21no—
61C22×C4×D59—21no—
62#14273701—22no—
63#14273701—22no—
64C4×D236—22no—
65C4×D236—22no—
66C4×C22⋊D59—44no—
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×C22⋊Dic59—21no—
76C2×C22⋊Dic59—21no—
77C2×C22⋊Dic59—21no—
78C2×(C2×D59)⋊C4—21no—
79C2×(C2×D59)⋊C4—21no—
80C2×(C2×D59)⋊C4—21no—
81C2×(C2×D59)⋊C4—21no—
82C2×C4×Dic59—21no—
83C2×C4×Dic59—21no—
84C2×C4×Dic59—21no—
85#14273661—22no—
86#14273661—22no—
87#14273659—22no—
88#14273659—22no—
89#14273649—22no—
90#14273649—22no—
91#14273649—22no—
92#14273649—22no—
93C59⋊#95—21no—
94C59⋊#95—21no—
95C59⋊#95—21no—
96C59⋊#95—21no—
97C59⋊#95—21no—
98C59⋊#95—21no—
99C59⋊#95—21no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C23×C4×C59D411yescharacteristic
105C23×C4×C59D411yescharacteristic
106C23×C4×C59C2311yescharacteristic
107C22×C8×C59C2311yescharacteristic
108C22×C8×C59C2311yescharacteristic
109C22×C8×C59C2311yescharacteristic
110C22×C8×C59C2311yescharacteristic
111C2×C42×C59—22no—
112C2×C42×C59—22no—
113C2×C42×C59D411yescharacteristic
114C2×C42×C59D411yescharacteristic
115C2×C42×C59C2311yescharacteristic
116C2×C42×C59C2311yescharacteristic
117C22⋊C8×C59—22no—
118C22⋊C8×C59—22no—
119C4×C8×C59—22no—
120C4×C8×C59—22no—
121C24×C59C2×D411yescharacteristic
122C23×D59—21no—
123C22×C4×C59—22no—
124C22×C4×C59—22no—
125C22×C4×C59—22no—
126C22×C4×C59—22no—
127C22×C4×C59—22no—
128C22×C4×C59—21no—
129C22×C4×C59—21no—
130C22×C4×C59—21no—
131C22×C4×C59—21no—
132C22×C4×C59—21no—
133C22×C4×C59—21no—
134C22×C4×C59—41no—
135C22×C4×C59C2×D411yescharacteristic
136C22×C4×C59C2×D411yescharacteristic
137C22×C4×C59C2×D411yescharacteristic
138C22×C4×C59C2×D411yescharacteristic
139C22×C4×C59C2×D411yescharacteristic
140C22×C4×C59C2411yescharacteristic
141C2×C22⋊D59—24no—
142C2×C22⋊D59—42no—
143C2×C22⋊D59—42no—
144C22×Dic59—21no—
145C22×Dic59—21no—
146C22×Dic59—21no—
147C22×Dic59—21no—
148C22×Dic59—21no—
149C22×Dic59—21no—
150C22×Dic59—21no—
151C2×D236—21no—
152C2×D236—21no—
153C2×D236—21no—
154C2×D236—21no—
155C2×D236—21no—
156C2×D236#4112yes—
157C2×C4×D59—42no—
158C2×C4×D59—42no—
159C2×C4×D59—42no—
160C2×C8×C59—21no—
161C2×C8×C59—21no—
162C2×C8×C59—21no—
163C2×C8×C59—21no—
164C2×C8×C59—21no—
165C2×C8×C59—21no—
166C2×C8×C59—21no—
167C2×C8×C59—21no—
168C2×C8×C59—21no—
169C2×C8×C59—21no—
170C2×C8×C59#4112yes—
171C2×C8×C59#4112yes—
172C42×C59—22no—
173C42×C59—22no—
174C42×C59—21no—
175C42×C59—21no—
176C42×C59#4112yes—
177C42×C59#4112yes—
178C22⋊Dic59—42no—
179C22⋊Dic59—42no—
180C22⋊Dic59—42no—
181(C2×D59)⋊C4—24no—
182(C2×D59)⋊C4—42no—
183(C2×D59)⋊C4—42no—
184(C2×D59)⋊C4—42no—
185C4⋊Dic59—21no—
186C4⋊Dic59—21no—
187C4⋊Dic59—21no—
188C4⋊Dic59—21no—
189C4⋊Dic59—21no—
190C4⋊Dic59—21no—
191C4⋊Dic59—21no—
192C4⋊Dic59—21no—
193C4⋊Dic59—21no—
194C4⋊Dic59—21no—
195C4⋊Dic59—21no—
196C4⋊Dic59—21no—
197C4⋊Dic59—21no—
198C4⋊Dic59#4112yes—
199Dic59⋊C4—42no—
200C4×Dic59—42no—
201C4×Dic59—42no—
202C4×Dic59—42no—
203C23×C59—21no—
204C23×C59—21no—
205C23×C59—21no—
206C23×C59—21no—
207C23×C59—21no—
208C23×C59—21no—
209C23×C59#13512yes—
210C23×C59C22×D411yescharacteristic
211C22×D59—22no—
212C22×D59—41no—
213C22×D59—41no—
214C22×D59—41no—
215C22×D59—41no—
216C22×D59—41no—
217C22×D59—41no—
218C2×C4×C59—21no—
219C2×C4×C59—21no—
220C2×C4×C59—21no—
221C2×C4×C59—21no—
222C2×C4×C59—21no—
223C2×C4×C59—21no—
224C2×C4×C59—21no—
225C2×C4×C59—21no—
226C2×C4×C59—21no—
227C2×C4×C59—21no—
228C2×C4×C59—21no—
229C2×C4×C59—44no—
230C2×C4×C59—41no—
231C2×C4×C59—41no—
232C2×C4×C59—41no—
233C2×C4×C59—41no—
234C2×C4×C59—44no—
235C2×C4×C59#12312yes—
236C2×C4×C59#12312yes—
237C2×C4×C59#13512yes—
238C2×C4×C59AGL(1,ℤ/8)12yes—
239C2×C4×C59C2×#4111yescharacteristic
240C2×C4×C59C2×#4111yescharacteristic
241C2×C4×C59C2×#4111yescharacteristic
242C2×C4×C59C2×#4111yescharacteristic
243C2×C4×C59C2×#4111yescharacteristic
244C2×C4×C59C2×#4111yescharacteristic
245C22⋊D59—48no—
246C2×Dic59—22no—
247C2×Dic59—41no—
248C2×Dic59—41no—
249C2×Dic59—41no—
250C2×Dic59—41no—
251C2×Dic59—41no—
252C2×Dic59—41no—
253C2×Dic59—41no—
254C2×Dic59—41no—
255C2×Dic59—41no—
256C2×Dic59—41no—
257C2×Dic59—41no—
258C2×Dic59—41no—
259C2×Dic59—41no—
260C2×Dic59—41no—
261C2×Dic59—41no—
262C2×Dic59—41no—
263C2×Dic59—41no—
264C2×Dic59—41no—
265C2×Dic59—41no—
266C2×Dic59—41no—
267D236—22no—
268D236—22no—
269D236—41no—
270D236—41no—
271C4×D59—84no—
272C8×C59—22no—
273C8×C59—22no—
274C8×C59—41no—
275C8×C59—41no—
276#23758—591nomaximal, Sylow
277C22×C59—22no—
278C22×C59—22no—
279C22×C59—22no—
280C22×C59—41no—
281C22×C59—41no—
282C22×C59—41no—
283C22×C59—41no—
284C22×C59C2×#12311yescharacteristic
285C22×C59#52511yescharacteristic
286C22×C59#53211yescharacteristic
287C22×C59C2×#13511yescharacteristic
288C22×C59C2×#13511yescharacteristic
289C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C59#57511yescharacteristic
291C2×D59—42no—
292C2×D59—42no—
293C2×D59—42no—
294C2×D59—81no—
295C2×D59—81no—
296C2×D59—81no—
297C2×D59—81no—
298C4×C59—22no—
299C4×C59—41no—
300C4×C59—41no—
301C4×C59—41no—
302C4×C59#48214yes—
303C4×C59#52911yescharacteristic
304C4×C59#52911yescharacteristic
305C4×C59#52911yescharacteristic
306C4×C59#52911yescharacteristic
307Dic59—42no—
308Dic59—81no—
309Dic59—81no—
310Dic59—81no—
311Dic59—81no—
312Dic59—81no—
313Dic59—81no—
314C4×#121—591no—
315#2283—591no—
316#2101—591no—
317#2092—591no—
318#2085—591no—
319#2077—591no—
320#2076—591no—
321#2073—591no—
322#2034—591no—
323#2033—591no—
324C4×#107—591no—
325C4×#106—591no—
326C4×#102—591no—
327C4×#102—591no—
328C4×C22⋊C8D5911yescharacteristic, complemented
329C2×C59—42no—
330C2×C59#239511yescharacteristic
331C2×C59C2×#48211yescharacteristic
332C2×C59#309111yescharacteristic
333C2×C59#310211yescharacteristic
334C2×C59#310511yescharacteristic
335C2×C59#316811yescharacteristic
336C2×C59#317111yescharacteristic
337D59—82no—
338C2×#121—591no—
339C2×C4×D4—591no—
340C2×C4×D4—1181no—
341C22×C42C2×D5911yescharacteristic
342C2×#107—591no—
343C2×#107—591no—
344C2×#106—591no—
345C2×#106—591no—
346C2×#102—591no—
347C2×#102—591no—
348C2×#102—591no—
349C2×#102—591no—
350C2×C22⋊C8C2×D5911yescharacteristic
351C2×C22⋊C8C2×D5911yescharacteristic
352C2×C4×C8C2×D5911yescharacteristic
353C2×C4×C8C2×D5911yescharacteristic
354#390—591no—
355#389—591no—
356#388—1181no—
357#386—1181no—
358#383—1181no—
359#382—591no—
360#382—591no—
361#381—1181no—
362#380—591no—
363#380—591no—
364#380—591no—
365C4×C4⋊C4—591no—
366C4×C4⋊C4—591no—
367C4×C4⋊C4—591no—
368C4×C22⋊C4—1181no—
369C4×C22⋊C4—1181no—
370#376—1181no—
371#340—591no—
372#340—591no—
373#340—591no—
374#340—591no—
375#340—591no—
376#340—591no—
377#340—591no—
378#340—591no—
379#336C2×D5911yescharacteristic
380#336C2×D5911yescharacteristic
381C59#2375811yescharacteristic, complemented, Sylow
382C22×D4—591no—
383C22×D4—1181no—
384C23×C4—1181no—
385C23×C4D23611yescharacteristic
386C23×C4D23611yescharacteristic
387C23×C4C22×D5911yescharacteristic
388C22×C8C22×D5911yescharacteristic
389C22×C8C22×D5911yescharacteristic
390C22×C8C22×D5911yescharacteristic
391C22×C8C22×D5911yescharacteristic
392#121—1182no—
393#121—1182no—
394C4×D4—1182no—
395C4×D4—1182no—
396C4×D4—2364no—
397C2×C4⋊C4—591no—
398C2×C4⋊C4—591no—
399C2×C4⋊C4—591no—
400C2×C4⋊C4—591no—
401C2×C4⋊C4—591no—
402C2×C4⋊C4—591no—
403C2×C4⋊C4—591no—
404C2×C4⋊C4—1181no—
405C2×C22⋊C4—1181no—
406C2×C22⋊C4—1181no—
407C2×C22⋊C4—1181no—
408C2×C22⋊C4—1181no—
409C2×C22⋊C4—1181no—
410C2×C22⋊C4—1181no—
411C2×C22⋊C4—1181no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—1181no—
415C2×C42—1181no—
416C2×C42—1181no—
417C2×C42D23611yescharacteristic
418C2×C42D23611yescharacteristic
419C2×C42C22×D5911yescharacteristic
420C2×C42C22×D5911yescharacteristic
421#107—1182no—
422#107—1182no—
423#106—1182no—
424#106—1182no—
425#102—1182no—
426#102—1182no—
427#102—1182no—
428#102—1182no—
429C22⋊C8—22no—
430C22⋊C8—22no—
431C4×C8—22no—
432C4×C8—22no—
433#95—1181no—
434#95—1181no—
435#95—1181no—
436#95—1181no—
437#95—1181no—
438#95—1181no—
439#95—1181no—
440#95—1181no—
441#95—1181no—
442#95—1181no—
443#95—1181no—
444C24—1181no—
445C24C2×D23611yescharacteristic
446C2×D4—592no—
447C2×D4—1184no—
448C2×D4—1181no—
449C2×D4—1181no—
450C2×D4—1181no—
451C2×D4—1181no—
452C2×D4—1181no—
453C2×D4—2362no—
454C2×D4—2362no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—41no—
467C22×C4—1181no—
468C22×C4—1181no—
469C22×C4—1181no—
470C22×C4—1181no—
471C22×C4—1181no—
472C22×C4—1181no—
473C22×C4—1181no—
474C22×C4—2362no—
475C22×C4—2362no—
476C22×C4—2362no—
477C22×C4C2×D23611yescharacteristic
478C22×C4C2×D23611yescharacteristic
479C22×C4C2×D23611yescharacteristic
480C22×C4C2×D23611yescharacteristic
481C22×C4C2×D23611yescharacteristic
482C22×C4C23×D5911yescharacteristic
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8#1174568512yes—
494C2×C8#1174568512yes—
495C4⋊C4—592no—
496C4⋊C4—1181no—
497C4⋊C4—1181no—
498C4⋊C4—1181no—
499C4⋊C4—1181no—
500C4⋊C4—1181no—
501C4⋊C4—1181no—
502C4⋊C4—1181no—
503C4⋊C4—1181no—
504C4⋊C4—1181no—
505C4⋊C4—1181no—
506C4⋊C4—1181no—
507C4⋊C4—1181no—
508C4⋊C4—1181no—
509C4⋊C4—2362no—
510C22⋊C4—1184no—
511C22⋊C4—2362no—
512C22⋊C4—2362no—
513C22⋊C4—2362no—
514C22⋊C4—2362no—
515C22⋊C4—2362no—
516C22⋊C4—2362no—
517C42—22no—
518C42—22no—
519C42—21no—
520C42—21no—
521C42—2362no—
522C42—2362no—
523C42—2362no—
524C42#1174568712yes—
525C42#1174568712yes—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—1182no—
533C23—2361no—
534C23—2361no—
535C23—2361no—
536C23—2361no—
537C23—2361no—
538C23—2361no—
539C23#1427374912yes—
540C23C22×D23611yescharacteristic
541D4—1182no—
542D4—1182no—
543D4—2368no—
544D4—2361no—
545D4—2361no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—44no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—44no—
563C2×C4—1182no—
564C2×C4—4724no—
565C2×C4—2361no—
566C2×C4—2361no—
567C2×C4—2361no—
568C2×C4—2361no—
569C2×C4—2361no—
570C2×C4—2361no—
571C2×C4—2361no—
572C2×C4—2361no—
573C2×C4—2361no—
574C2×C4—2361no—
575C2×C4—2361no—
576C2×C4—2361no—
577C2×C4—2361no—
578C2×C4—2361no—
579C2×C4—2361no—
580C2×C4—2361no—
581C2×C4—2361no—
582C2×C4—2361no—
583C2×C4—2361no—
584C2×C4—2361no—
585C2×C4#1427371112yes—
586C2×C4#1427371112yes—
587C2×C4#1427374912yes—
588C2×C4#1427375512yes—
589C2×C4#41×D5911yescharacteristic
590C2×C4#41×D5911yescharacteristic
591C2×C4C2×#1174568711yescharacteristic
592C2×C4C2×#1174568711yescharacteristic
593C2×C4C2×#1174568511yescharacteristic
594C2×C4C2×#1174568511yescharacteristic
595C8—22no—
596C8—22no—
597C8—41no—
598C8—41no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—4721no—
607C22—4721no—
608C22—4721no—
609C22—4721no—
610C22—2362no—
611C22—2362no—
612C22—2362no—
613C22C2×#1427371111yescharacteristic
614C22#1683791411yescharacteristic
615C22#1683795211yescharacteristic
616C22C2×#1427374911yescharacteristic
617C22C2×#1427374911yescharacteristic
618C22C2×#1427375511yescharacteristic
619C22#1683820211yescharacteristic
620C4—22no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—4721no—
625C4—4721no—
626C4—4721no—
627C4—4721no—
628C4—4721no—
629C4—4721no—
630C4—2362no—
631C4#1683772714yes—
632C4#1683793211yescharacteristic
633C4#1683793211yescharacteristic
634C4#1683793411yescharacteristic
635C4#1683793411yescharacteristic
636C2—42no—
637C2—4722no—
638C2#2142735611yescharacteristic
639C2C2×#1683772711yescharacteristic
640C2#2143401111yescharacteristic
641C2#2143411611yescharacteristic
642C2#2143414511yescharacteristic
643C2#2143466611yescharacteristic
644C2#2143469111yescharacteristic
subgroupG/H
centerC22×C4C2×D236
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC4×C22⋊C8×C59C2
socleC23×C59C22×D4
prime radicalC2×#14273701C22
hypercenterC4×C22⋊C8D59
hypocenterC59#23758
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #21426494C2semidirect
3. #21425665C2semidirect
4. #21425616C2semidirect
5. #21425579C2semidirect
6. #21425529C2semidirect
7. #21425524C2semidirect
8. #21425511C2semidirect
11. C4×#14273661C2semidirect
12. C4×#14273659C2semidirect
13. C4×#14273649C2semidirect
14. C4×#14273649C2semidirect
15. C4×C22⋊C8×C59C2semidirect
328. C4×C22⋊C8D59semidirect
381. C59#23758semidirect

Maximal subgroups

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

subgroupindex
C4×#142737012
#214264942
#214256652
#214256162
#214255792
#214255292
#214255242
#214255112
#214252862
#214252792
C4×#142736612
C4×#142736592
C4×#142736492
C4×C22⋊C8×C592
#2375859