Finite Group Databasebeta

← #28606437

Subgroups — #28606437

Order 15104.

810 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837442C211yesmaximal, characteristic
2#21426987C211yesmaximal, characteristic
3#21424831C211yesmaximal, characteristic, complemented
4#21424826C211yesmaximal, characteristic, complemented
5#21424688C211yesmaximal, characteristic, complemented
6#21424678C211yesmaximal, characteristic, complemented
7#21424671C211yesmaximal, characteristic, complemented
8#21424667C211yesmaximal, characteristic, complemented
9#21424188C211yesmaximal, characteristic
10#21424186C211yesmaximal, characteristic
11#21424127C211yesmaximal, characteristic
12#21423994C211yesmaximal, characteristic, complemented
13C4×#14273658C211yesmaximal, characteristic, complemented
14#21423880C211yesmaximal, characteristic
15C59×#2344C211yesmaximal, characteristic
16C22×#11745664C2211yescharacteristic
17C2×#14273686C2211yescharacteristic
18#16837442C418yescomplemented
19C2×#14273660C2211yescharacteristic
20C2×#14273660C2211yescharacteristic
21C2×#14273660C2211yescharacteristic
22C2×#14273658C2211yescharacteristic
23C2×#14273658C2211yescharacteristic
24C2×#14273658C2211yescharacteristic
25C2×C22⋊(C59⋊C8)C2211yescharacteristic
26C2×#14273638C2211yescharacteristic
27C2×C4×C59⋊C8C2211yescharacteristic
28#16837300C2211yescharacteristic
29#16837300C2211yescharacteristic
30#16837296—21no—
31#16837296—21no—
32#16837269—21no—
33#16837262C2211yescharacteristic
34C4×C4⋊Dic59C2211yescharacteristic
35C4×C4⋊Dic59C2211yescharacteristic
36#16837253—21no—
37#16837164C2211yescharacteristic
38#16837164C2211yescharacteristic
39#16837164C2211yescharacteristic
40#16837164C2211yescharacteristic
41#16837164C2211yescharacteristic
42#16837164C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837157C2211yescharacteristic
48#16837157C2211yescharacteristic
49C2×#117×C59—21no—
50C22×C4⋊C4×C59C2211yescharacteristic
51C59×#389C2211yescharacteristic
52C59×#389C2211yescharacteristic
53C59×#387—21no—
54C59×#387—21no—
55C59×#381—21no—
56C59×#380C2211yescharacteristic
57C4×C4⋊C4×C59C2211yescharacteristic
58C4×C4⋊C4×C59C2211yescharacteristic
59C4×C22⋊C4×C59C2211yescharacteristic
60C2×#11745664—22no—
61C2×#11745664—22no—
62C2×#11745664C2×C414yes—
63C22×C59⋊C8C2311yescharacteristic
64C22×C59⋊C8C2311yescharacteristic
65C22×C59⋊C8C2311yescharacteristic
66C22×C59⋊C8C2311yescharacteristic
67#14273686—22no—
68#14273686C2×C414yes—
69C2×C4⋊Dic59C2311yescharacteristic
70C2×C4⋊Dic59C2311yescharacteristic
71C2×C4⋊Dic59C2311yescharacteristic
72C2×C4⋊Dic59C2311yescharacteristic
73C2×Dic59⋊C4—21no—
74C2×Dic59⋊C4—21no—
75C2×C22⋊Dic59—21no—
76C2×C22⋊Dic59—21no—
77C2×C4×Dic59—21no—
78C2×C4×Dic59—21no—
79C2×C4×Dic59—21no—
80#14273660—22no—
81#14273660C2×C414yes—
82#14273660C2×C414yes—
83#14273658—22no—
84#14273658C2×C414yes—
85#14273658C2×C414yes—
86C22⋊(C59⋊C8)—22no—
87#14273638—22no—
88C4×C59⋊C8—22no—
89C59⋊#95—21no—
90C59⋊#95—21no—
91C59⋊#95—21no—
92C59⋊#95—21no—
93C59⋊#95—21no—
94C23×C4×C59—21no—
95C23×C4×C59C2311yescharacteristic
96#117×C59—44no—
97C2×C4⋊C4×C59—21no—
98C2×C4⋊C4×C59—22no—
99C2×C4⋊C4×C59—21no—
100C2×C4⋊C4×C59—21no—
101C2×C4⋊C4×C59C2×C414yes—
102C2×C4⋊C4×C59C2311yescharacteristic
103C2×C4⋊C4×C59C2311yescharacteristic
104C2×C4⋊C4×C59C2311yescharacteristic
105C2×C4⋊C4×C59C2311yescharacteristic
106C2×C22⋊C4×C59—21no—
107C2×C22⋊C4×C59D411yescharacteristic
108C2×C22⋊C4×C59D411yescharacteristic
109C2×C42×C59—21no—
110C2×C42×C59—21no—
111C2×C42×C59C2311yescharacteristic
112C2×C42×C59C2311yescharacteristic
113#95×C59—21no—
114#95×C59—21no—
115#95×C59—21no—
116#95×C59—21no—
117#95×C59—21no—
118#95×C59D411yescharacteristic
119#95×C59D411yescharacteristic
120C24×C59C2×D411yescharacteristic
121C22×C4×C59—21no—
122C22×C4×C59—21no—
123C22×C4×C59—21no—
124C22×C4×C59—21no—
125C22×C4×C59—24no—
126C22×C4×C59—21no—
127C22×C4×C59—21no—
128C22×C4×C59—21no—
129C22×C4×C59—21no—
130C22×C4×C59—42no—
131C22×C4×C59—42no—
132C22×C4×C59C22×C412yes—
133C22×C4×C59C2×D411yescharacteristic
134C22×C4×C59C2×D411yescharacteristic
135C22×C4×C59C2×D411yescharacteristic
136C22×C4×C59C2×D411yescharacteristic
137C22×C4×C59C2×D411yescharacteristic
138C22×C4×C59#4112yes—
139C22×C4×C59C2411yescharacteristic
140C22×Dic59—21no—
141C22×Dic59—21no—
142C22×Dic59—21no—
143C22×Dic59—21no—
144C4⋊C4×C59—24no—
145C4⋊C4×C59—21no—
146C4⋊C4×C59—21no—
147C4⋊C4×C59—21no—
148C4⋊C4×C59—21no—
149C4⋊C4×C59—21no—
150C4⋊C4×C59—21no—
151C4⋊C4×C59—42no—
152C4⋊C4×C59—42no—
153C4⋊C4×C59C22×C412yes—
154C4⋊C4×C59C22×C412yes—
155C22⋊C4×C59—22no—
156C22⋊C4×C59—41no—
157C22⋊C4×C59—42no—
158C42×C59—21no—
159C42×C59—21no—
160C42×C59—21no—
161C42×C59—21no—
162C42×C59—42no—
163C42×C59—42no—
164C22⋊Dic59—24no—
165C22⋊Dic59—81no—
166C4⋊Dic59—21no—
167C4⋊Dic59—21no—
168C4⋊Dic59—21no—
169C4⋊Dic59—21no—
170C4⋊Dic59—21no—
171C4⋊Dic59—21no—
172C4⋊Dic59C22×C412yes—
173C4⋊Dic59C22×C412yes—
174Dic59⋊C4—42no—
175Dic59⋊C4—42no—
176C4×Dic59—24no—
177C4×Dic59—81no—
178C4×Dic59—81no—
179#11745664—28no—
180C2×C59⋊C8—21no—
181C2×C59⋊C8—21no—
182C2×C59⋊C8—21no—
183C2×C59⋊C8—21no—
184C2×C59⋊C8—21no—
185C2×C59⋊C8—21no—
186C2×C59⋊C8—21no—
187C2×C59⋊C8—21no—
188C2×C59⋊C8C22×C412yes—
189C2×C59⋊C8C22×C412yes—
190C2×C59⋊C8#4112yes—
191C2×C59⋊C8#4112yes—
192C23×C59—21no—
193C23×C59—21no—
194C23×C59—21no—
195C23×C59—21no—
196C23×C59—21no—
197C23×C59—21no—
198C23×C59C4×D412yes—
199C23×C59C22×D411yescharacteristic
200C2×C4×C59—21no—
201C2×C4×C59—21no—
202C2×C4×C59—21no—
203C2×C4×C59—21no—
204C2×C4×C59—22no—
205C2×C4×C59—22no—
206C2×C4×C59—22no—
207C2×C4×C59—22no—
208C2×C4×C59—22no—
209C2×C4×C59—22no—
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—48no—
220C2×C4×C59—41no—
221C2×C4×C59—41no—
222C2×C4×C59—41no—
223C2×C4×C59—41no—
224C2×C4×C59—41no—
225C2×C4×C59—41no—
226C2×C4×C59—41no—
227C2×C4×C59—41no—
228C2×C4×C59—41no—
229C2×C4×C59—41no—
230C2×C4×C59C4×D412yes—
231C2×C4×C59AGL(1,ℤ/8)12yes—
232C2×C4×C59C23×C411yescharacteristic
233C2×C4×C59C2×#4111yescharacteristic
234C2×C4×C59C2×#4111yescharacteristic
235C2×C4×C59C2×#4111yescharacteristic
236C2×C4×C592−1+411yescharacteristic
237C2×C4×C592−1+411yescharacteristic
238C2×Dic59—22no—
239C2×Dic59—22no—
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—
250C59⋊C8—22no—
251C59⋊C8—41no—
252C59⋊C8—41no—
253C59⋊C8#11714yescomplemented
254#22622—591nomaximal, Sylow
255C22×C59—22no—
256C22×C59—22no—
257C22×C59—22no—
258C22×C59—41no—
259C22×C59—41no—
260C22×C59—41no—
261C22×C59—41no—
262C22×C59C2×C4×D411yescharacteristic
263C22×C59#54711yescharacteristic
264C22×C59#54711yescharacteristic
265C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C59#57511yescharacteristic
267C22×C59#57711yescharacteristic
268C22×C59#57811yescharacteristic
269C4×C59—22no—
270C4×C59—22no—
271C4×C59—41no—
272C4×C59—41no—
273C4×C59—41no—
274C4×C59—42no—
275C4×C59—42no—
276C4×C59—81no—
277C4×C59—81no—
278C4×C59C2×#11711yescharacteristic
279C4×C59#51911yescharacteristic
280C4×C59#55211yescharacteristic
281C4×C59#55211yescharacteristic
282Dic59—42no—
283Dic59—42no—
284Dic59—81no—
285Dic59—81no—
286C2×#428—591no—
287#2347—591no—
288#2344D5911yescharacteristic
289#1943—591no—
290#1942—591no—
291#1921—591no—
292#1920—591no—
293#1919—591no—
294#1918—591no—
295#1825—591no—
296#1824—591no—
297#1809—591no—
298#1776—591no—
299C4×#106—591no—
300#1753—591no—
301C2×C59—42no—
302C2×C59#234411yescharacteristic
303C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
304C2×C59#294711yescharacteristic
305C2×C59#334511yescharacteristic
306C2×C59#334911yescharacteristic
307C2×C59#335111yescharacteristic
308C2×C59#335311yescharacteristic
309C22×M16—591no—
310C2×#117—21no—
311C2×#117—591no—
312C22×C4⋊C4C2×D5911yescharacteristic
313#428—598no—
314C2×#107—591no—
315C2×#107—591no—
316C2×#107—591no—
317C2×#106—591no—
318C2×#106—591no—
319C2×#106—591no—
320C2×C22⋊C8—591no—
321C2×#97—591no—
322C2×C4×C8—591no—
323#389—591no—
324#389—591no—
325#389C2×D5911yescharacteristic
326#389C2×D5911yescharacteristic
327#388—1181no—
328#388—1181no—
329#387—21no—
330#387—21no—
331#383—1181no—
332#381—21no—
333#380—591no—
334#380C2×D5911yescharacteristic
335C4×C4⋊C4—591no—
336C4×C4⋊C4—591no—
337C4×C4⋊C4—1181no—
338C4×C4⋊C4C2×D5911yescharacteristic
339C4×C4⋊C4C2×D5911yescharacteristic
340C4×C22⋊C4C2×D5911yescharacteristic
341#340—591no—
342#340—591no—
343#340—591no—
344#340—591no—
345#340—591no—
346#340—591no—
347#340—591no—
348#340—591no—
349#340—591no—
350#340—591no—
351#336—591no—
352#336—591no—
353C59#2262211yescharacteristic, complemented, Sylow
354C23×C4—21no—
355C23×C4C22×D5911yescharacteristic
356C2×M16—594no—
357C2×M16—1182no—
358C2×M16—1182no—
359C22×C8—591no—
360C22×C8—591no—
361C22×C8—591no—
362C22×C8—591no—
363#117—44no—
364#117—594no—
365#117—1182no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—591no—
371C2×C4⋊C4—591no—
372C2×C4⋊C4—591no—
373C2×C4⋊C4—591no—
374C2×C4⋊C4—1181no—
375C2×C4⋊C4—1181no—
376C2×C4⋊C4C4×D5914yes—
377C2×C4⋊C4C22×D5911yescharacteristic
378C2×C4⋊C4C22×D5911yescharacteristic
379C2×C4⋊C4C22×D5911yescharacteristic
380C2×C4⋊C4C22×D5911yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—1181no—
383C2×C22⋊C4—1181no—
384C2×C22⋊C4C22⋊D5911yescharacteristic
385C2×C22⋊C4C22⋊D5911yescharacteristic
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—1181no—
389C2×C42—1181no—
390C2×C42—1181no—
391C2×C42C22×D5911yescharacteristic
392C2×C42C22×D5911yescharacteristic
393#107—594no—
394#107—594no—
395#107—1182no—
396#106—594no—
397#106—594no—
398#106—1182no—
399C22⋊C8—1182no—
400#97—1182no—
401C4×C8—1182no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—1181no—
408#95—1181no—
409#95—1181no—
410#95—1181no—
411#95—1181no—
412#95C22⋊D5911yescharacteristic
413#95C22⋊D5911yescharacteristic
414C24C2×C22⋊D5911yescharacteristic
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—24no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—1181no—
427C22×C4—1181no—
428C22×C4—1181no—
429C22×C4—1181no—
430C22×C4C2×C4×D5912yes—
431C22×C4#1174568512yes—
432C22×C4C2×C22⋊D5911yescharacteristic
433C22×C4C2×C22⋊D5911yescharacteristic
434C22×C4C2×C22⋊D5911yescharacteristic
435C22×C4C2×C22⋊D5911yescharacteristic
436C22×C4C2×C22⋊D5911yescharacteristic
437C22×C4C23×D5911yescharacteristic
438M16—1188no—
439C2×C8—592no—
440C2×C8—592no—
441C2×C8—592no—
442C2×C8—592no—
443C2×C8—1181no—
444C2×C8—1181no—
445C2×C8—1181no—
446C2×C8—1181no—
447C2×C8—1181no—
448C2×C8—1181no—
449C2×C8—1181no—
450C2×C8—1181no—
451C4⋊C4—24no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—592no—
461C4⋊C4—592no—
462C4⋊C4—1181no—
463C4⋊C4—1181no—
464C4⋊C4—1181no—
465C4⋊C4—1181no—
466C4⋊C4—1181no—
467C4⋊C4—1181no—
468C4⋊C4—2362no—
469C4⋊C4—2362no—
470C4⋊C4C2×C4×D5912yes—
471C4⋊C4C2×C4×D5912yes—
472C22⋊C4—22no—
473C22⋊C4—41no—
474C22⋊C4—42no—
475C22⋊C4—1184no—
476C22⋊C4—4721no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—42no—
482C42—42no—
483C42—1184no—
484C42—4721no—
485C42—4721no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23C4×C22⋊D5912yes—
493C23C22×C22⋊D5911yescharacteristic
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—48no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—1182no—
525C2×C4—1182no—
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×C4C4×C22⋊D5912yes—
537C2×C4#1427375312yes—
538C2×C4C22×C4×D5911yescharacteristic
539C2×C4#41×D5911yescharacteristic
540C2×C4#41×D5911yescharacteristic
541C2×C4C2×#1174568511yescharacteristic
542C2×C4#1427377411yescharacteristic
543C2×C4#1427377411yescharacteristic
544C8—594no—
545C8—1182no—
546C8—2361no—
547C8—2361no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22C2×C4×C22⋊D5911yescharacteristic
556C22#1683805111yescharacteristic
557C22#1683805111yescharacteristic
558C22C2×#1427375311yescharacteristic
559C22#1683820011yescharacteristic
560C22#1683821011yescharacteristic
561C22#1683821711yescharacteristic
562C4—22no—
563C4—22no—
564C4—41no—
565C4—42no—
566C4—42no—
567C4—41no—
568C4—41no—
569C4—81no—
570C4—81no—
571C4—4721no—
572C4—4721no—
573C4—2362no—
574C4—2362no—
575C4#117×D5911yescharacteristic
576C4#1683787911yescharacteristic
577C4#1683808511yescharacteristic
578C4#1683808511yescharacteristic
579C2—42no—
580C2#2142696611yescharacteristic
581C2C4×#1427375311yescharacteristic
582C2#2143293911yescharacteristic
583C2#2143656611yescharacteristic
584C2#2143662611yescharacteristic
585C2#2143665611yescharacteristic
586C2#2143668011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2344C2
socleC23×C59C22×D4
prime radicalC24×C59C2×D4
cosocleC22×C4×C59C24
hypercenter#2344D59
hypocenterC59#22622
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2344

Complements

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

NH ≅ G/Ntype
3. #21424831C2semidirect
4. #21424826C2semidirect
5. #21424688C2semidirect
6. #21424678C2semidirect
7. #21424671C2semidirect
8. #21424667C2semidirect
12. #21423994C2semidirect
13. C4×#14273658C2semidirect
18. #16837442C4semidirect
253. C59⋊C8#117semidirect
353. C59#22622semidirect

Maximal subgroups

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

subgroupindex
C2×#168374422
#214269872
#214248312
#214248262
#214246882
#214246782
#214246712
#214246672
#214241882
#214241862
#214241272
#214239942
C4×#142736582
#214238802
C59×#23442
#2262259