Finite Group Databasebeta

← #28606439

Subgroups — #28606439

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×#16837443C211yesmaximal, characteristic
2#21426988C211yesmaximal, characteristic
3#21426961C211yesmaximal, characteristic
4#21424833C211yesmaximal, characteristic, complemented
5#21424826C211yesmaximal, characteristic, complemented
6#21424690C211yesmaximal, characteristic, complemented
7#21424680C211yesmaximal, characteristic, complemented
8#21424675C211yesmaximal, characteristic, complemented
9#21424190C211yesmaximal, characteristic
10#21424185C211yesmaximal, characteristic
11#21424128C211yesmaximal, characteristic
12#21423992C211yesmaximal, characteristic, complemented
13C4×#14273658C211yesmaximal, characteristic, complemented
14#21423876C211yesmaximal, characteristic
15C59×#1918C211yesmaximal, characteristic, complemented
16C22×#11745659C2211yescharacteristic
17C2×#14273685C2211yescharacteristic
18C2×#14273684—21no—
19C2×C4⋊C4×D59C2211yescharacteristic
20#16837443C418yescomplemented
21C2×#14273660C2211yescharacteristic
22C2×#14273660C2211yescharacteristic
23C2×#14273659C2211yescharacteristic
24C2×#14273658C2211yescharacteristic
25C2×#14273658C2211yescharacteristic
26C2×(C2×D59)⋊C8C2211yescharacteristic
27C2×#14273637C2211yescharacteristic
28C2×C4×C59⋊C8C2211yescharacteristic
29#16837301C2211yescharacteristic
30#16837300C2211yescharacteristic
31#16837298C2211yescharacteristic
32#16837294—21no—
33#16837292—21no—
34#16837286—21no—
35#16837284—21no—
36#16837269—21no—
37#16837264—21no—
38#16837259C2211yescharacteristic
39#16837259C2211yescharacteristic
40C4⋊C4×Dic59—21no—
41C4⋊C4×Dic59C2211yescharacteristic
42C4⋊C4×Dic59C2211yescharacteristic
43C4×C4⋊Dic59C2211yescharacteristic
44C4×(C2×D59)⋊C4C2211yescharacteristic
45#16837165C2211yescharacteristic
46#16837165C2211yescharacteristic
47#16837165C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51#16837164C2211yescharacteristic
52#16837156C2211yescharacteristic
53C2×#107×C59C2211yescharacteristic
54C59×#389C2211yescharacteristic
55C4×C4⋊C4×C59C2211yescharacteristic
56C59×#340C2211yescharacteristic
57C59×#340C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C59×#336C2211yescharacteristic
60C22×C4×D59—21no—
61C22×C4×D59C2311yescharacteristic
62C2×#11745659—22no—
63C2×#11745659—22no—
64C2×#11745659C2×C414yes—
65C22×C59⋊C8C2311yescharacteristic
66C22×C59⋊C8C2311yescharacteristic
67#14273685—22no—
68#14273685C2×C414yes—
69#14273684—44no—
70C2×C4⋊Dic59—21no—
71C2×C4⋊Dic59C2311yescharacteristic
72C2×C4⋊Dic59C2311yescharacteristic
73C2×C4⋊Dic59C2311yescharacteristic
74C2×C4⋊Dic59C2311yescharacteristic
75C2×Dic59⋊C4—21no—
76C2×Dic59⋊C4—21no—
77C2×Dic59⋊C4—21no—
78C4⋊C4×D59—22no—
79C4⋊C4×D59C2×C414yes—
80C2×(C2×D59)⋊C4—21no—
81C2×(C2×D59)⋊C4—21no—
82C2×(C2×D59)⋊C4—21no—
83C2×(C2×D59)⋊C4D411yescharacteristic
84C2×(C2×D59)⋊C4D411yescharacteristic
85C2×C4×Dic59—21no—
86C2×C4×Dic59—21no—
87C2×C4×Dic59—21no—
88C2×C4×Dic59—21no—
89C2×C4×Dic59C2311yescharacteristic
90#14273660—22no—
91#14273660C2×C414yes—
92#14273659C2×C414yes—
93#14273658—22no—
94#14273658C2×C414yes—
95(C2×D59)⋊C8—22no—
96#14273637—22no—
97C4×C59⋊C8—22no—
98C59⋊#95—21no—
99C59⋊#95—21no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C59⋊#95D411yescharacteristic
107C59⋊#95D411yescharacteristic
108C22×C8×C59C2311yescharacteristic
109C22×C8×C59C2311yescharacteristic
110C2×C4⋊C4×C59—21no—
111C2×C4⋊C4×C59C2311yescharacteristic
112C2×C4⋊C4×C59C2311yescharacteristic
113C2×C4⋊C4×C59C2311yescharacteristic
114C2×C4⋊C4×C59C2311yescharacteristic
115C2×C42×C59—21no—
116C2×C42×C59C2311yescharacteristic
117#107×C59C2×C414yes—
118#95×C59—21no—
119#95×C59—21no—
120C23×D59C2×D411yescharacteristic
121C22×C4×C59—21no—
122C22×C4×C59—21no—
123C22×C4×C59—21no—
124C22×C4×C59—21no—
125C22×C4×C59C2×D411yescharacteristic
126C22×C4×C59C2×D411yescharacteristic
127C22×C4×C59C2411yescharacteristic
128C22×Dic59—21no—
129C22×Dic59—21no—
130C22×Dic59—21no—
131C22×Dic59—21no—
132C22×Dic59C2×D411yescharacteristic
133C22×Dic59C2×D411yescharacteristic
134C22×Dic59C2×D411yescharacteristic
135C2×C4×D59—21no—
136C2×C4×D59—21no—
137C2×C4×D59—21no—
138C2×C4×D59—21no—
139C2×C4×D59—24no—
140C2×C4×D59—42no—
141C2×C4×D59—42no—
142C2×C4×D59C22×C412yes—
143C2×C4×D59#4112yes—
144C2×C8×C59—21no—
145C2×C8×C59—21no—
146C2×C8×C59—21no—
147C2×C8×C59—21no—
148C2×C8×C59—21no—
149C2×C8×C59C22×C412yes—
150C4⋊C4×C59—21no—
151C4⋊C4×C59—21no—
152C4⋊C4×C59—21no—
153C4⋊C4×C59—21no—
154C4⋊C4×C59—21no—
155C4⋊C4×C59—21no—
156C4⋊C4×C59—42no—
157C4⋊C4×C59C22×C412yes—
158C4⋊C4×C59C22×C412yes—
159C42×C59—21no—
160C42×C59—21no—
161C42×C59—42no—
162(C2×D59)⋊C4—24no—
163(C2×D59)⋊C4—22no—
164(C2×D59)⋊C4—41no—
165(C2×D59)⋊C4—42no—
166(C2×D59)⋊C4—81no—
167C4⋊Dic59—21no—
168C4⋊Dic59—21no—
169C4⋊Dic59—21no—
170C4⋊Dic59—21no—
171C4⋊Dic59—21no—
172C4⋊Dic59—21no—
173C4⋊Dic59—42no—
174C4⋊Dic59C22×C412yes—
175C4⋊Dic59C22×C412yes—
176Dic59⋊C4—24no—
177Dic59⋊C4—42no—
178Dic59⋊C4—42no—
179C4×Dic59—21no—
180C4×Dic59—21no—
181C4×Dic59—24no—
182C4×Dic59—42no—
183C4×Dic59—81no—
184C4×Dic59—81no—
185C2×C59⋊C8—21no—
186C2×C59⋊C8—21no—
187C2×C59⋊C8—21no—
188C2×C59⋊C8C22×C412yes—
189C2×C59⋊C8#4112yes—
190C2×C59⋊C8#4112yes—
191#11745659—28no—
192C23×C59C22×D411yescharacteristic
193C22×D59—21no—
194C22×D59—21no—
195C22×D59—21no—
196C22×D59—21no—
197C22×D59—21no—
198C22×D59—21no—
199C22×D59C4×D412yes—
200C2×C4×C59—21no—
201C2×C4×C59—21no—
202C2×C4×C59—22no—
203C2×C4×C59—22no—
204C2×C4×C59—21no—
205C2×C4×C59—21no—
206C2×C4×C59—21no—
207C2×C4×C59—41no—
208C2×C4×C59—41no—
209C2×C4×C59—41no—
210C2×C4×C59—41no—
211C2×C4×C59—41no—
212C2×C4×C59—41no—
213C2×C4×C59—41no—
214C2×C4×C59—41no—
215C2×C4×C59—41no—
216C2×C4×C59—41no—
217C2×C4×C59AGL(1,ℤ/8)12yes—
218C2×C4×C59C23×C411yescharacteristic
219C2×C4×C59C2×#4111yescharacteristic
220C2×C4×C59C2×#4111yescharacteristic
221C2×C4×C59C2×#4111yescharacteristic
222C2×C4×C592−1+411yescharacteristic
223C2×C4×C592−1+411yescharacteristic
224C2×Dic59—21no—
225C2×Dic59—21no—
226C2×Dic59—22no—
227C2×Dic59—22no—
228C2×Dic59—21no—
229C2×Dic59—21no—
230C2×Dic59—21no—
231C2×Dic59—21no—
232C2×Dic59—21no—
233C2×Dic59—21no—
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×Dic59C4×D412yes—
245C4×D59—22no—
246C4×D59—22no—
247C4×D59—22no—
248C4×D59—22no—
249C4×D59—48no—
250C8×C59—22no—
251C8×C59—41no—
252C59⋊C8—41no—
253C59⋊C8#11714yescomplemented
254#22622—591nomaximal, Sylow
255C22×C59C2×C4×D411yescharacteristic
256C22×C59#54711yescharacteristic
257C22×C59#54711yescharacteristic
258C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
259C22×C59#57511yescharacteristic
260C22×C59#57711yescharacteristic
261C22×C59#57811yescharacteristic
262C2×D59—22no—
263C2×D59—22no—
264C2×D59—22no—
265C2×D59—41no—
266C2×D59—41no—
267C2×D59—41no—
268C2×D59—41no—
269C4×C59—22no—
270C4×C59—41no—
271C4×C59—42no—
272C4×C59—42no—
273C4×C59—81no—
274C4×C59—81no—
275C4×C59C2×#11711yescharacteristic
276C4×C59#51911yescharacteristic
277C4×C59#55211yescharacteristic
278C4×C59#55211yescharacteristic
279Dic59—22no—
280Dic59—41no—
281Dic59—41no—
282Dic59—42no—
283Dic59—42no—
284Dic59—81no—
285Dic59—81no—
286C2×#428—591no—
287#2347—591no—
288#2344—591no—
289#1943—591no—
290#1942—591no—
291#1921—591no—
292#1920—591no—
293#1919—591no—
294#1918D5911yescharacteristic, complemented
295#1825—591no—
296#1824—591no—
297#1809—591no—
298#1776—591no—
299C4×#106—591no—
300#1753—591no—
301C2×C59#234411yescharacteristic
302C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
303C2×C59#294711yescharacteristic
304C2×C59#334511yescharacteristic
305C2×C59#334911yescharacteristic
306C2×C59#335111yescharacteristic
307C2×C59#335311yescharacteristic
308D59—42no—
309C22×M16—591no—
310C2×#117—591no—
311C2×#117—1181no—
312C22×C4⋊C4—591no—
313#428—598no—
314C2×#107—591no—
315C2×#107—591no—
316C2×#107C2×D5911yescharacteristic
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#389—591no—
326#389C2×D5911yescharacteristic
327#388—1181no—
328#388—1181no—
329#387—1181no—
330#387—1181no—
331#383—1181no—
332#381—1181no—
333#380—591no—
334#380—591no—
335C4×C4⋊C4—591no—
336C4×C4⋊C4—591no—
337C4×C4⋊C4—591no—
338C4×C4⋊C4—1181no—
339C4×C4⋊C4C2×D5911yescharacteristic
340C4×C22⋊C4—591no—
341#340—591no—
342#340—591no—
343#340—591no—
344#340—591no—
345#340—591no—
346#340—591no—
347#340—591no—
348#340C2×D5911yescharacteristic
349#340C2×D5911yescharacteristic
350#340C2×D5911yescharacteristic
351#336—591no—
352#336C2×D5911yescharacteristic
353C59#2262211yescharacteristic, complemented, Sylow
354C23×C4—591no—
355C23×C4—1181no—
356C2×M16—594no—
357C2×M16—1182no—
358C2×M16—1182no—
359C22×C8—591no—
360C22×C8—591no—
361C22×C8C22×D5911yescharacteristic
362C22×C8C22×D5911yescharacteristic
363#117—594no—
364#117—1182no—
365#117—2364no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—591no—
368C2×C4⋊C4—591no—
369C2×C4⋊C4—594no—
370C2×C4⋊C4—591no—
371C2×C4⋊C4—591no—
372C2×C4⋊C4—1182no—
373C2×C4⋊C4—1181no—
374C2×C4⋊C4—1181no—
375C2×C4⋊C4—1181no—
376C2×C4⋊C4—1181no—
377C2×C4⋊C4C22×D5911yescharacteristic
378C2×C4⋊C4C22×D5911yescharacteristic
379C2×C4⋊C4C22×D5911yescharacteristic
380C2×C4⋊C4C22×D5911yescharacteristic
381C2×C22⋊C4—591no—
382C2×C22⋊C4—591no—
383C2×C22⋊C4—1181no—
384C2×C22⋊C4—1181no—
385C2×C22⋊C4—1181no—
386C2×C42—21no—
387C2×C42—591no—
388C2×C42—1181no—
389C2×C42—1181no—
390C2×C42—1181no—
391C2×C42—1181no—
392C2×C42C22×D5911yescharacteristic
393#107—594no—
394#107—1182no—
395#107C4×D5914yes—
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—591no—
405#95—591no—
406#95—1181no—
407#95—1181no—
408#95—1181no—
409#95—1181no—
410#95—1181no—
411#95—1181no—
412#95—1181no—
413#95—1181no—
414C24—591no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—591no—
420C22×C4—592no—
421C22×C4—592no—
422C22×C4—591no—
423C22×C4—591no—
424C22×C4—1184no—
425C22×C4—1181no—
426C22×C4—1181no—
427C22×C4—1181no—
428C22×C4—1181no—
429C22×C4—1181no—
430C22×C4—1181no—
431C22×C4—1181no—
432C22×C4—1181no—
433C22×C4—2362no—
434C22×C4—2362no—
435C22×C4D4×D5911yescharacteristic
436C22×C4D4×D5911yescharacteristic
437C22×C4C23×D5911yescharacteristic
438M16—1188no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—592no—
445C2×C8—592no—
446C2×C8—592no—
447C2×C8—1181no—
448C2×C8—1181no—
449C2×C8—1181no—
450C2×C8C2×C4×D5912yes—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—42no—
458C4⋊C4—592no—
459C4⋊C4—592no—
460C4⋊C4—1184no—
461C4⋊C4—1181no—
462C4⋊C4—1181no—
463C4⋊C4—1181no—
464C4⋊C4—1181no—
465C4⋊C4—1181no—
466C4⋊C4—1181no—
467C4⋊C4—2362no—
468C4⋊C4—2362no—
469C4⋊C4—2362no—
470C4⋊C4C2×C4×D5912yes—
471C4⋊C4C2×C4×D5912yes—
472C22⋊C4—1184no—
473C22⋊C4—1182no—
474C22⋊C4—4721no—
475C22⋊C4—2361no—
476C22⋊C4—2362no—
477C42—21no—
478C42—21no—
479C42—42no—
480C42—1184no—
481C42—1181no—
482C42—1181no—
483C42—4721no—
484C42—4721no—
485C42—2362no—
486C23—592no—
487C23—1181no—
488C23—1181no—
489C23—1181no—
490C23—1181no—
491C23—1181no—
492C23—1181no—
493C23C2×D4×D5911yescharacteristic
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—592no—
512C2×C4—1181no—
513C2×C4—1181no—
514C2×C4—1182no—
515C2×C4—1182no—
516C2×C4—1182no—
517C2×C4—1182no—
518C2×C4—1181no—
519C2×C4—1181no—
520C2×C4—1181no—
521C2×C4—1181no—
522C2×C4—1181no—
523C2×C4—1181no—
524C2×C4—1182no—
525C2×C4—1182no—
526C2×C4—2368no—
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#1427375112yes—
538C2×C4C22×C4×D5911yescharacteristic
539C2×C4#41×D5911yescharacteristic
540C2×C4#41×D5911yescharacteristic
541C2×C4#41×D5911yescharacteristic
542C2×C4#1427377411yescharacteristic
543C2×C4#1427377511yescharacteristic
544C8—22no—
545C8—41no—
546C8—594no—
547C8—2361no—
548C22—1182no—
549C22—1182no—
550C22—1182no—
551C22—2361no—
552C22—2361no—
553C22—2361no—
554C22—2361no—
555C22C4×D4×D5911yescharacteristic
556C22#1683805011yescharacteristic
557C22#1683805411yescharacteristic
558C22C2×#1427375111yescharacteristic
559C22#1683819911yescharacteristic
560C22#1683821111yescharacteristic
561C22#1683821811yescharacteristic
562C4—22no—
563C4—42no—
564C4—42no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—1182no—
569C4—4721no—
570C4—4721no—
571C4—2361no—
572C4—2362no—
573C4—2362no—
574C4—2361no—
575C4#117×D5911yescharacteristic
576C4#1683787811yescharacteristic
577C4#1683808411yescharacteristic
578C4#1683808811yescharacteristic
579C2—2362no—
580C2#2142696211yescharacteristic
581C2C4×#1427375111yescharacteristic
582C2#2143293811yescharacteristic
583C2#2143657011yescharacteristic
584C2#2143663011yescharacteristic
585C2#2143665311yescharacteristic
586C2#2143667711yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1918C2
socleC23×C59C22×D4
prime radicalC23×D59C2×D4
cosocleC22×C4×C59C24
hypercenter#1918D59
hypocenterC59#22622
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
4. #21424833C2semidirect
5. #21424826C2semidirect
6. #21424690C2semidirect
7. #21424680C2semidirect
8. #21424675C2semidirect
12. #21423992C2semidirect
13. C4×#14273658C2semidirect
15. C59×#1918C2semidirect
20. #16837443C4semidirect
253. C59⋊C8#117semidirect
294. #1918D59semidirect
353. C59#22622semidirect

Maximal subgroups

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

subgroupindex
C2×#168374432
#214269882
#214269612
#214248332
#214248262
#214246902
#214246802
#214246752
#214241902
#214241852
#214241282
#214239922
C4×#142736582
#214238762
C59×#19182
#2262259