Finite Group Databasebeta

← C4×#16837543 #28594284

Subgroups — C4×#16837543 #28594284

Order 15104.

1532 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
1C22×C4×Dic118C211yesmaximal, characteristic, complemented
2C2×#16837543C211yesmaximal, characteristic
3C2×C4×#11745660C212yesmaximal, complemented
4C4×#14273701C211yesmaximal, characteristic
5#21424450C212yesmaximal, complemented
6#21424411C211yesmaximal, characteristic
7#21424367C212yesmaximal, complemented
8#21424291C211yesmaximal, characteristic, complemented
9#21424032C211yesmaximal, characteristic, complemented
10C4×#14273652C212yesmaximal, complemented
11C4×C22⋊C8×C59C211yesmaximal, characteristic, complemented
12C23×Dic118C2211yescharacteristic
13C22×#11745660C2212yes—
14C2×#14273701C2211yescharacteristic
15C2×C4×Dic118—28no—
16C2×C4×Dic118—21no—
17C2×C4×Dic118—21no—
18C2×C4×Dic118C2212yes—
19C2×C4×Dic118C2212yes—
20C2×C4×D236C2211yescharacteristic
21C2×C4×C22⋊D59—21no—
22C22×C4⋊Dic59C2211yescharacteristic
23C22×Dic59⋊C4—21no—
24C22×C4×Dic59—21no—
25#16837543C418yesdirect product factor
26C4×#11745660—28no—
27C2×#14273659C2212yes—
28C2×#14273652C2212yes—
29C2×#14273652C2212yes—
30C2×#14273652C2212yes—
31C2×#14273649C2212yes—
32#16837304C2211yescharacteristic
33#16837300C2211yescharacteristic
34#16837293—21no—
35#16837281—21no—
36#16837262C2211yescharacteristic
37C4×C4⋊Dic59C2211yescharacteristic
38C4×(C2×D59)⋊C4—21no—
39#16837165C2212yes—
40#16837165C2212yes—
41C22×C42×C59C2211yescharacteristic
42C2×C22⋊C8×C59C2211yescharacteristic
43C2×C22⋊C8×C59C2211yescharacteristic
44C2×C4×C8×C59C2212yes—
45C59×#336C2212yes—
46C22×Dic118—21no—
47C22×Dic118—22no—
48C22×Dic118—24no—
49C22×Dic118—24no—
50C22×Dic118C2×C414yescomplemented
51C22×Dic118C2312yes—
52C22×D236C2311yescharacteristic
53C22×C22⋊D59—21no—
54C23×Dic59—21no—
55C23×Dic59—21no—
56C22×C4×D59—21no—
57C2×#11745660—24no—
58C2×#11745660—24no—
59C2×#11745660C2×C418yescomplemented
60#14273701—22no—
61#14273701C2×C414yes—
62C4×Dic118—28no—
63C4×Dic118—28no—
64C4×Dic118—24no—
65C4×Dic118—24no—
66C4×Dic118—24no—
67C4×Dic118D418yescomplemented
68C4×D236—24no—
69C4×C22⋊D59—44no—
70C2×C4⋊Dic59—21no—
71C2×C4⋊Dic59—24no—
72C2×C4⋊Dic59C2311yescharacteristic
73C2×C4⋊Dic59C2311yescharacteristic
74C2×C4⋊Dic59C2311yescharacteristic
75C2×C4⋊Dic59C2312yes—
76C2×Dic59⋊C4—28no—
77C2×Dic59⋊C4—22no—
78C2×Dic59⋊C4—22no—
79C2×Dic59⋊C4—21no—
80C2×C22⋊Dic59—21no—
81C2×(C2×D59)⋊C4—21no—
82C2×(C2×D59)⋊C4—21no—
83C2×(C2×D59)⋊C4—21no—
84C2×(C2×D59)⋊C4—21no—
85C2×C4×Dic59—28no—
86C2×C4×Dic59—22no—
87C2×C4×Dic59—22no—
88C2×C4×Dic59—21no—
89#14273659—24no—
90#14273652—24no—
91#14273652—24no—
92#14273652C2×C418yescomplemented
93#14273649—24no—
94C59⋊#95—21no—
95C59⋊#95—21no—
96C59⋊#95—21no—
97C23×C4×C59D411yescharacteristic
98C23×C4×C59D411yescharacteristic
99C23×C4×C59C2311yescharacteristic
100C22×C8×C59C2312yes—
101C22×C8×C59C2312yes—
102C2×C42×C59—24no—
103C2×C42×C59D411yescharacteristic
104C2×C42×C59D411yescharacteristic
105C2×C42×C59C2311yescharacteristic
106C2×C42×C59C2311yescharacteristic
107C22⋊C8×C59—22no—
108C22⋊C8×C59C2×C414yescomplemented
109C4×C8×C59—24no—
110C24×C59C2×D411yescharacteristic
111C23×D59—21no—
112C22×C4×C59—22no—
113C22×C4×C59—22no—
114C22×C4×C59—22no—
115C22×C4×C59—22no—
116C22×C4×C59—22no—
117C22×C4×C59—22no—
118C22×C4×C59—41no—
119C22×C4×C59SD1614yescomplemented
120C22×C4×C59C22×C412yes—
121C22×C4×C59C2×D411yescharacteristic
122C22×C4×C59C2×D411yescharacteristic
123C22×C4×C59C2×D411yescharacteristic
124C22×C4×C59C2×D411yescharacteristic
125C22×C4×C59C2×D411yescharacteristic
126C22×C4×C59#4112yes—
127C22×C4×C59C2411yescharacteristic
128C2×C22⋊D59—24no—
129C2×C22⋊D59—42no—
130C2×C22⋊D59—42no—
131C22×Dic59—24no—
132C22×Dic59—24no—
133C22×Dic59—24no—
134C22×Dic59—22no—
135C22×Dic59—24no—
136C22×Dic59—21no—
137C22×Dic59—22no—
138C22×Dic59—21no—
139C22×Dic59—21no—
140C22×Dic59—42no—
141C22×Dic59—42no—
142C2×D236—22no—
143C2×D236—22no—
144C2×D236—21no—
145C2×D236C22×C412yes—
146C2×C4×D59—42no—
147C2×C4×D59—42no—
148C2×C4×D59—42no—
149C2×Dic118—24no—
150C2×Dic118—24no—
151C2×Dic118—216no—
152C2×Dic118—24no—
153C2×Dic118—22no—
154C2×Dic118—22no—
155C2×Dic118—22no—
156C2×Dic118—216no—
157C2×Dic118C22×C414yes—
158C2×Dic118C2×D414yes—
159C2×Dic118#4114yes—
160C2×C8×C59—22no—
161C2×C8×C59—22no—
162C2×C8×C59—22no—
163C2×C8×C59—22no—
164C2×C8×C59—22no—
165C2×C8×C59C22×C414yes—
166C42×C59—22no—
167C42×C59—22no—
168C42×C59—22no—
169C42×C59C2×D414yes—
170C22⋊Dic59—42no—
171(C2×D59)⋊C4—24no—
172(C2×D59)⋊C4—42no—
173(C2×D59)⋊C4—42no—
174(C2×D59)⋊C4—42no—
175C4⋊Dic59—24no—
176C4⋊Dic59—22no—
177C4⋊Dic59—21no—
178C4⋊Dic59—22no—
179C4⋊Dic59—22no—
180C4⋊Dic59C22×C412yes—
181C4⋊Dic59C2×D414yes—
182Dic59⋊C4—28no—
183Dic59⋊C4—28no—
184Dic59⋊C4—42no—
185C4×Dic59—28no—
186C4×Dic59—28no—
187C4×Dic59—42no—
188#11745660—216no—
189C23×C59—21no—
190C23×C59—21no—
191C23×C59—21no—
192C23×C59—21no—
193C23×C59C4×D412yes—
194C23×C59C2×SD1612yes—
195C23×C59#13512yes—
196C23×C59C22×D411yescharacteristic
197C22×D59—22no—
198C22×D59—41no—
199C22×D59—41no—
200C22×D59—41no—
201C22×D59—41no—
202C22×D59—41no—
203C22×D59—41no—
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—24no—
211C2×C4×C59—24no—
212C2×C4×C59—28no—
213C2×C4×C59—21no—
214C2×C4×C59—21no—
215C2×C4×C59—21no—
216C2×C4×C59—44no—
217C2×C4×C59C4×D412yes—
218C2×C4×C59#12012yes—
219C2×C4×C59#12012yes—
220C2×C4×C59C2×SD1612yes—
221C2×C4×C59C2×SD1612yes—
222C2×C4×C59#13712yes—
223C2×C4×C59C23×C411yescharacteristic
224C2×C4×C59C22×D412yes—
225C2×C4×C59C2×#4112yes—
226C2×C4×C59C2×#4111yescharacteristic
227C22⋊D59—48no—
228C2×Dic59—216no—
229C2×Dic59—24no—
230C2×Dic59—24no—
231C2×Dic59—24no—
232C2×Dic59—22no—
233C2×Dic59—24no—
234C2×Dic59—48no—
235C2×Dic59—41no—
236C2×Dic59—42no—
237C2×Dic59—41no—
238C2×Dic59—42no—
239C2×Dic59—41no—
240C2×Dic59—41no—
241C2×Dic59—41no—
242C2×Dic59—41no—
243C2×Dic59—41no—
244C2×Dic59—41no—
245D236—24no—
246D236—42no—
247C4×D59—84no—
248Dic118—216no—
249Dic118—24no—
250Dic118—24no—
251Dic118—24no—
252Dic118C4×D418yescomplemented
253C8×C59—24no—
254C8×C59—42no—
255C4×#448—591nomaximal, Sylow
256C22×C59—22no—
257C22×C59—22no—
258C22×C59—22no—
259C22×C59—22no—
260C22×C59—22no—
261C22×C59—22no—
262C22×C59C4×SD1614yescomplemented
263C22×C59C2×C4×D411yescharacteristic
264C22×C59C2×#12011yescharacteristic
265C22×C59#52511yescharacteristic
266C22×C59C22×SD1611yescharacteristic
267C22×C59C2×#13511yescharacteristic
268C22×C59C2×#13711yescharacteristic
269C22×C59#57511yescharacteristic
270C2×D59—42no—
271C2×D59—42no—
272C2×D59—42no—
273C2×D59—81no—
274C2×D59—81no—
275C2×D59—81no—
276C2×D59—81no—
277C4×C59—22no—
278C4×C59—22no—
279C4×C59—22no—
280C4×C59—41no—
281C4×C59#44814yescomplemented
282C4×C59C2×C4×D412yes—
283C4×C59#52512yes—
284Dic59—28no—
285Dic59—42no—
286Dic59—44no—
287Dic59—81no—
288Dic59—81no—
289C22×C4×Q8—591no—
290C2×#448—591no—
291C2×C4×SD16—592no—
292C4×#121—591no—
293#1880—592no—
294#1874—591no—
295#1865—592no—
296#1853—591no—
297#1787—591no—
298C4×#103—592no—
299C4×C22⋊C8D5911yescharacteristic, complemented
300C2×C59—24no—
301C2×C59C4×#12011yescharacteristic
302C2×C59C2×C4×SD1611yescharacteristic
303C2×C59C4×#13711yescharacteristic
304C2×C59C2×#44811yescharacteristic
305C2×C59#300211yescharacteristic
306C2×C59#310311yescharacteristic
307C2×C59#310811yescharacteristic
308D59—82no—
309C23×Q8—591no—
310C22×SD16—592no—
311C2×#121—591no—
312C2×C4×Q8—592no—
313C2×C4×Q8—592no—
314C2×C4×Q8—1188no—
315C2×C4×Q8—1181no—
316C2×C4×Q8—1181no—
317C2×C4×D4—591no—
318C2×C4×D4—1181no—
319C22×C4⋊C4—591no—
320C22×C4⋊C4—1181no—
321C22×C42—1181no—
322C22×C42C2×D5911yescharacteristic
323#448—598no—
324C4×SD16—1188no—
325C2×#106—592no—
326C2×#103—592no—
327C2×#103—592no—
328C2×#103—592no—
329C2×#102—592no—
330C2×C22⋊C8C2×D5911yescharacteristic
331C2×C22⋊C8C2×D5911yescharacteristic
332C2×C4×C8C2×D5912yes—
333#390—591no—
334#389—591no—
335#388—1181no—
336#386—1181no—
337#380—591no—
338C4×C4⋊C4—591no—
339C4×C22⋊C4—1181no—
340#340—592no—
341#340—592no—
342#336C2×D5912yes—
343C59C4×#44811yescharacteristic, complemented, Sylow
344C22×Q8—594no—
345C22×Q8—592no—
346C22×Q8—1184no—
347C22×Q8—1184no—
348C22×Q8—1181no—
349C22×Q8—1182no—
350C22×D4—591no—
351C22×D4—1181no—
352C23×C4—1181no—
353C23×C4—1181no—
354C23×C4—1181no—
355C23×C4D23611yescharacteristic
356C23×C4D23611yescharacteristic
357C23×C4C22×D5911yescharacteristic
358C2×SD16—598no—
359C2×SD16—1184no—
360C2×SD16—1184no—
361C22×C8C22×D5912yes—
362C22×C8C22×D5912yes—
363#121—594no—
364#121—1182no—
365C4×Q8—598no—
366C4×Q8—1184no—
367C4×Q8—1184no—
368C4×Q8—1188no—
369C4×Q8—1188no—
370C4×Q8—1184no—
371C4×D4—1184no—
372C4×D4—2364no—
373C2×C4⋊C4—592no—
374C2×C4⋊C4—591no—
375C2×C4⋊C4—591no—
376C2×C4⋊C4—591no—
377C2×C4⋊C4—1184no—
378C2×C4⋊C4—1188no—
379C2×C4⋊C4—1181no—
380C2×C4⋊C4—1182no—
381C2×C4⋊C4—1182no—
382C2×C4⋊C4—1181no—
383C2×C22⋊C4—1181no—
384C2×C22⋊C4—1181no—
385C2×C22⋊C4—1181no—
386C2×C22⋊C4—1181no—
387C2×C22⋊C4—1181no—
388C2×C42—24no—
389C2×C42—1188no—
390C2×C42—1182no—
391C2×C42—1182no—
392C2×C42—1181no—
393C2×C42D23611yescharacteristic
394C2×C42D23611yescharacteristic
395C2×C42C22×D5911yescharacteristic
396C2×C42C22×D5911yescharacteristic
397#106—1184no—
398#103—598no—
399#103—1184no—
400#103—1184no—
401#102—1184no—
402C22⋊C8—22no—
403C22⋊C8C4×D5914yescomplemented
404C4×C8—24no—
405#95—1181no—
406#95—1181no—
407#95—1181no—
408C24—1181no—
409C24C2×D23611yescharacteristic
410C2×Q8—594no—
411C2×Q8—594no—
412C2×Q8—594no—
413C2×Q8—11816no—
414C2×Q8—1184no—
415C2×Q8—1184no—
416C2×Q8—11816no—
417C2×Q8—1184no—
418C2×Q8—1182no—
419C2×Q8—1182no—
420C2×Q8—1182no—
421C2×D4—592no—
422C2×D4—1184no—
423C2×D4—1182no—
424C2×D4—1182no—
425C2×D4—1181no—
426C2×D4—2362no—
427C2×D4—2362no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—41no—
435C22×C4—1184no—
436C22×C4—1184no—
437C22×C4—1184no—
438C22×C4—1182no—
439C22×C4—1184no—
440C22×C4—1181no—
441C22×C4—1182no—
442C22×C4—1181no—
443C22×C4—1181no—
444C22×C4—2362no—
445C22×C4—2362no—
446C22×C4—2362no—
447C22×C4—2362no—
448C22×C4—2362no—
449C22×C4#1174566014yescomplemented
450C22×C4C2×C4×D5912yes—
451C22×C4C2×D23611yescharacteristic
452C22×C4C2×D23611yescharacteristic
453C22×C4C2×D23611yescharacteristic
454C22×C4C2×D23611yescharacteristic
455C22×C4C2×D23611yescharacteristic
456C22×C4#1174568512yes—
457C22×C4C23×D5911yescharacteristic
458SD16—11816no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8C2×C4×D5914yes—
465C4⋊C4—592no—
466C4⋊C4—594no—
467C4⋊C4—1188no—
468C4⋊C4—1184no—
469C4⋊C4—1188no—
470C4⋊C4—1182no—
471C4⋊C4—1181no—
472C4⋊C4—1182no—
473C4⋊C4—1182no—
474C4⋊C4—2362no—
475C22⋊C4—1184no—
476C22⋊C4—2362no—
477C22⋊C4—2362no—
478C22⋊C4—2362no—
479C22⋊C4—2362no—
480C42—22no—
481C42—22no—
482C42—22no—
483C42—1188no—
484C42—1188no—
485C42—2362no—
486C42D4×D5914yes—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—1182no—
492C23—2361no—
493C23—2361no—
494C23—2361no—
495C23—2361no—
496C23—2361no—
497C23—2361no—
498C23C4×D23612yes—
499C23C2×#1174566012yes—
500C23#1427374912yes—
501C23C22×D23611yescharacteristic
502Q8—598no—
503Q8—11816no—
504Q8—1184no—
505Q8—1184no—
506Q8—1184no—
507D4—1184no—
508D4—2368no—
509D4—2362no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—24no—
517C2×C4—28no—
518C2×C4—24no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—44no—
523C2×C4—11816no—
524C2×C4—1184no—
525C2×C4—1184no—
526C2×C4—1184no—
527C2×C4—1184no—
528C2×C4—1182no—
529C2×C4—4724no—
530C2×C4—2361no—
531C2×C4—2361no—
532C2×C4—2361no—
533C2×C4—2361no—
534C2×C4—2361no—
535C2×C4—2361no—
536C2×C4—2368no—
537C2×C4—2361no—
538C2×C4—2362no—
539C2×C4—2361no—
540C2×C4—2362no—
541C2×C4C4×D23612yes—
542C2×C4#1427369712yes—
543C2×C4#1427369712yes—
544C2×C4C2×#1174566012yes—
545C2×C4C2×#1174566012yes—
546C2×C4#1427376012yes—
547C2×C4C22×C4×D5911yescharacteristic
548C2×C4C2×D4×D5912yes—
549C2×C4#41×D5912yes—
550C2×C4C2×#1174568511yescharacteristic
551C8—24no—
552C8—42no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—4721no—
560C22—4721no—
561C22—4721no—
562C22—4721no—
563C22—2362no—
564C22—2362no—
565C22—2362no—
566C22C4×#1174566014yescomplemented
567C22C2×C4×D23611yescharacteristic
568C22C2×#1427369711yescharacteristic
569C22#1683791411yescharacteristic
570C22C22×#1174566011yescharacteristic
571C22C2×#1427374911yescharacteristic
572C22C2×#1427376011yescharacteristic
573C22#1683820211yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—41no—
578C4—1188no—
579C4—4721no—
580C4—4721no—
581C4—2362no—
582C4—2364no—
583C4#1683754314yesdirect product factor
584C4C4×D4×D5912yes—
585C4#1683791112yes—
586C2—24no—
587C2—4722no—
588C2C4×#1427369711yescharacteristic
589C2C2×C4×#1174566011yescharacteristic
590C2C4×#1427376011yescharacteristic
591C2C2×#1683754311yescharacteristic
592C2#2143331811yescharacteristic
593C2#2143412811yescharacteristic
594C2#2143417811yescharacteristic
subgroupG/H
centerC22×C4C2×D236
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC4×C22⋊C8×C59C2
socleC23×C59C22×D4
prime radicalC2×#14273701C22
cosocleC22×C4×C59C24
hypercenterC4×C22⋊C8D59
hypocenterC59C4×#448
LCSG ▷ C2×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
1. C22×C4×Dic118C2semidirect
3. C2×C4×#11745660C2semidirect
5. #21424450C2semidirect
7. #21424367C2semidirect
8. #21424291C2semidirect
9. #21424032C2semidirect
10. C4×#14273652C2semidirect
11. C4×C22⋊C8×C59C2semidirect
25. #16837543C4direct (N × H)
50. C22×Dic118C2×C4semidirect
59. C2×#11745660C2×C4semidirect
67. C4×Dic118D4semidirect
92. #14273652C2×C4semidirect
108. C22⋊C8×C59C2×C4semidirect
119. C22×C4×C59SD16semidirect
252. Dic118C4×D4semidirect
262. C22×C59C4×SD16semidirect
281. C4×C59#448semidirect
299. C4×C22⋊C8D59semidirect
343. C59C4×#448semidirect
403. C22⋊C8C4×D59semidirect
449. C22×C4#11745660semidirect
566. C22C4×#11745660semidirect
583. C4#16837543direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Dic1182
C2×#168375432
C2×C4×#117456602
C4×#142737012
#214244502
#214244112
#214243672
#214242912
#214240322
C4×#142736522
C4×C22⋊C8×C592
C4×#44859