Finite Group Databasebeta

← #28647734

Subgroups — #28647734

Order 15104.

678 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21427067C211yesmaximal, characteristic
2#21425625C211yesmaximal, characteristic
3#21425620C211yesmaximal, characteristic
4#21425467C211yesmaximal, characteristic
5#21425467C211yesmaximal, characteristic
6#21424864C211yesmaximal, characteristic, complemented
7#21424862C211yesmaximal, characteristic, complemented
8#21424857C211yesmaximal, characteristic, complemented
9#21424815C211yesmaximal, characteristic, complemented
10#21424685C211yesmaximal, characteristic, complemented
11#21424664C211yesmaximal, characteristic, complemented
12#21424258C211yesmaximal, characteristic, complemented
13#21424103C211yesmaximal, characteristic
14C4×#14273647C211yesmaximal, characteristic
15C59×#2570C211yesmaximal, characteristic, complemented
16C2×C4×D236C2211yescharacteristic
17C2×#14273660C2211yescharacteristic
18C2×#14273660C2211yescharacteristic
19C2×#14273660C2211yescharacteristic
20C2×#14273658C2211yescharacteristic
21C2×#14273658C2211yescharacteristic
22C2×#14273658C2211yescharacteristic
23C2×C4⋊(C59⋊C8)C2211yescharacteristic
24C2×C4⋊(C59⋊C8)C2211yescharacteristic
25C2×C4⋊(C59⋊C8)C2211yescharacteristic
26C2×#14273647C2211yescharacteristic
27C2×#14273647C2211yescharacteristic
28C2×#14273647C2211yescharacteristic
29C2×#14273647C2211yescharacteristic
30C2×C4×C59⋊C8C2211yescharacteristic
31#16837304C2211yescharacteristic
32#16837304C2211yescharacteristic
33#16837292—21no—
34#16837292—21no—
35#16837268C2211yescharacteristic
36#16837264—21no—
37C4×C4⋊Dic59C2211yescharacteristic
38C4×C4⋊Dic59C2211yescharacteristic
39#16837249—21no—
40#16837164C2211yescharacteristic
41#16837164C2211yescharacteristic
42#16837164C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837157C2211yescharacteristic
47#16837157C2211yescharacteristic
48C59×#400—21no—
49C59×#398—21no—
50C59×#389C2211yescharacteristic
51C59×#389C2211yescharacteristic
52C59×#387—21no—
53C59×#387—21no—
54C59×#384C2211yescharacteristic
55C59×#382C2211yescharacteristic
56C59×#382C2211yescharacteristic
57C4×C4⋊C4×C59C2211yescharacteristic
58C4×C4⋊C4×C59C2211yescharacteristic
59C22×D236C2311yescharacteristic
60C22×C4×D59—21no—
61C22×C59⋊C8C2311yescharacteristic
62C22×C59⋊C8C2311yescharacteristic
63C22×C59⋊C8C2311yescharacteristic
64C22×C59⋊C8C2311yescharacteristic
65C4×D236—22no—
66C4×D236Q814yes—
67C2×C4⋊Dic59C2311yescharacteristic
68C2×C4⋊Dic59C2311yescharacteristic
69C2×C4⋊Dic59C2311yescharacteristic
70C2×(C2×D59)⋊C4—21no—
71C2×(C2×D59)⋊C4—21no—
72C2×(C2×D59)⋊C4—21no—
73C2×(C2×D59)⋊C4—21no—
74C2×(C2×D59)⋊C4—21no—
75C2×C4×Dic59—21no—
76C2×C4×Dic59—21no—
77#14273660—22no—
78#14273660—22no—
79#14273660—41no—
80#14273658—41no—
81#14273658—41no—
82#14273658—41no—
83C4⋊(C59⋊C8)—22no—
84C4⋊(C59⋊C8)—22no—
85C4⋊(C59⋊C8)—22no—
86#14273647—22no—
87#14273647—22no—
88#14273647—41no—
89#14273647—41no—
90C4×C59⋊C8—22no—
91C59⋊#95—21no—
92C59⋊#95—21no—
93C59⋊#95—21no—
94C59⋊#95—21no—
95C2×C4⋊C4×C59—21no—
96C2×C4⋊C4×C59—21no—
97C2×C4⋊C4×C59—21no—
98C2×C4⋊C4×C59—21no—
99C2×C4⋊C4×C59D411yescharacteristic
100C2×C4⋊C4×C59D411yescharacteristic
101C2×C4⋊C4×C59C2311yescharacteristic
102C2×C4⋊C4×C59C2311yescharacteristic
103C2×C4⋊C4×C59C2311yescharacteristic
104C2×C4⋊C4×C59C2311yescharacteristic
105C2×C42×C59—21no—
106C2×C42×C59C2311yescharacteristic
107C2×C42×C59C2311yescharacteristic
108C2×C42×C59C2311yescharacteristic
109#95×C59—21no—
110#95×C59—21no—
111#95×C59—21no—
112#95×C59—21no—
113#95×C59—21no—
114#95×C59—21no—
115#95×C59—21no—
116#95×C59D411yescharacteristic
117#95×C59D411yescharacteristic
118C23×D59—21no—
119C22×C4×C59—21no—
120C22×C4×C59—21no—
121C22×C4×C59—21no—
122C22×C4×C59—21no—
123C22×C4×C59C2×D411yescharacteristic
124C22×C4×C59C2×D411yescharacteristic
125C22×C4×C59C2×D411yescharacteristic
126C22×C4×C59C2×D411yescharacteristic
127C22×C4×C59C2×D411yescharacteristic
128C22×C4×C59C2×D411yescharacteristic
129C22×C4×C59C2411yescharacteristic
130C22×Dic59—21no—
131C22×Dic59—21no—
132C22×Dic59—21no—
133C2×D236—21no—
134C2×D236—21no—
135C2×D236—21no—
136C2×D236—21no—
137C2×D236—21no—
138C2×D236C2×Q812yes—
139C2×C4×D59—24no—
140C2×C4×D59—81no—
141C2×C4×D59—81no—
142C4⋊C4×C59—22no—
143C4⋊C4×C59—21no—
144C4⋊C4×C59—21no—
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—41no—
152C4⋊C4×C59—42no—
153C4⋊C4×C59—42no—
154C4⋊C4×C59—81no—
155C4⋊C4×C59—81no—
156C42×C59—21no—
157C42×C59—21no—
158C42×C59—21no—
159C42×C59—21no—
160C42×C59—81no—
161C42×C59C2×Q812yes—
162C42×C59#4112yes—
163(C2×D59)⋊C4—24no—
164(C2×D59)⋊C4—42no—
165(C2×D59)⋊C4—42no—
166(C2×D59)⋊C4—81no—
167(C2×D59)⋊C4—81no—
168C4⋊Dic59—21no—
169C4⋊Dic59—21no—
170C4⋊Dic59—21no—
171C4⋊Dic59—21no—
172C4⋊Dic59—21no—
173C4⋊Dic59C2×Q812yes—
174C4×Dic59—81no—
175C4×Dic59—81no—
176C2×C59⋊C8—21no—
177C2×C59⋊C8—21no—
178C2×C59⋊C8—21no—
179C2×C59⋊C8—21no—
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#4112yes—
187C2×C59⋊C8#4112yes—
188C23×C59C22×D411yescharacteristic
189C22×D59—22no—
190C22×D59—41no—
191C22×D59—41no—
192C22×D59—41no—
193C22×D59—41no—
194C22×D59—41no—
195C22×D59—41no—
196C2×C4×C59—21no—
197C2×C4×C59—21no—
198C2×C4×C59—21no—
199C2×C4×C59—21no—
200C2×C4×C59—21no—
201C2×C4×C59—21no—
202C2×C4×C59—21no—
203C2×C4×C59—21no—
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—21no—
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×C59—41no—
218C2×C4×C59—41no—
219C2×C4×C59—41no—
220C2×C4×C59—41no—
221C2×C4×C59—41no—
222C2×C4×C59—41no—
223C2×C4×C59C22⋊Q812yes—
224C2×C4×C59C22⋊Q812yes—
225C2×C4×C59#13512yes—
226C2×C4×C59C22×Q811yescharacteristic
227C2×C4×C59C2×#4111yescharacteristic
228C2×C4×C59C2×#4111yescharacteristic
229C2×C4×C59C2×#4111yescharacteristic
230C2×C4×C59H(5,𝔽2)11yescharacteristic
231C2×C4×C592−1+411yescharacteristic
232C2×Dic59—22no—
233C2×Dic59—41no—
234C2×Dic59—41no—
235C2×Dic59—41no—
236C2×Dic59—41no—
237C2×Dic59—41no—
238C2×Dic59—41no—
239C2×Dic59—41no—
240C2×Dic59—41no—
241D236—22no—
242D236—22no—
243D236—41no—
244D236—41no—
245C4×D59—84no—
246C59⋊C8—22no—
247C59⋊C8—22no—
248C59⋊C8—41no—
249C59⋊C8—41no—
250#26094—591nomaximal, Sylow
251C22×C59C2×C22⋊Q811yescharacteristic
252C22×C59#54711yescharacteristic
253C22×C59#55011yescharacteristic
254C22×C59C2×#13511yescharacteristic
255C22×C59#57511yescharacteristic
256C22×C59#57611yescharacteristic
257C22×C59#57711yescharacteristic
258C2×D59—42no—
259C2×D59—42no—
260C2×D59—42no—
261C2×D59—81no—
262C2×D59—81no—
263C2×D59—81no—
264C2×D59—81no—
265C4×C59—22no—
266C4×C59—22no—
267C4×C59—22no—
268C4×C59—41no—
269C4×C59—41no—
270C4×C59—41no—
271C4×C59—81no—
272C4×C59—81no—
273C4×C59—81no—
274C4×C59—81no—
275C4×C59#53311yescharacteristic
276C4×C59#54411yescharacteristic
277C4×C59#55211yescharacteristic
278C4×C59#55311yescharacteristic
279Dic59—42no—
280Dic59—81no—
281Dic59—81no—
282#2570D5911yescharacteristic, complemented
283#2357—591no—
284#2093—591no—
285#2092—591no—
286#2065—591no—
287#2065—591no—
288#1949—591no—
289#1949—591no—
290#1948—591no—
291#1939—591no—
292#1921—591no—
293#1918—591no—
294#1846—591no—
295#1804—591no—
296C4×#102—591no—
297C2×C59#244111yescharacteristic
298C2×C59#307611yescharacteristic
299C2×C59#308111yescharacteristic
300C2×C59#333711yescharacteristic
301C2×C59#335511yescharacteristic
302C2×C59#339611yescharacteristic
303C2×C59#340111yescharacteristic
304D59—82no—
305C2×C4×D4—591no—
306C2×#107—591no—
307C2×#107—591no—
308C2×#107—591no—
309C2×#106—591no—
310C2×#106—591no—
311C2×#106—591no—
312C2×C4⋊C8—591no—
313C2×C4⋊C8—591no—
314C2×C4⋊C8—591no—
315C2×#102—591no—
316C2×#102—591no—
317C2×#102—591no—
318C2×#102—591no—
319C2×C4×C8—591no—
320#400—21no—
321#398—21no—
322#390—591no—
323#390—591no—
324#389C2×D5911yescharacteristic
325#389C2×D5911yescharacteristic
326#388—1181no—
327#388—1181no—
328#387—21no—
329#387—21no—
330#384C2×D5911yescharacteristic
331#382—591no—
332#382C2×D5911yescharacteristic
333#382C2×D5911yescharacteristic
334#381—1181no—
335C4×C4⋊C4—591no—
336C4×C4⋊C4—591no—
337C4×C4⋊C4C2×D5911yescharacteristic
338C4×C4⋊C4C2×D5911yescharacteristic
339C4×C22⋊C4—1181no—
340#340—591no—
341#340—591no—
342#340—591no—
343#340—591no—
344#340—591no—
345#340—591no—
346#336—591no—
347#336—591no—
348C59#2609411yescharacteristic, complemented, Sylow
349C22×D4—591no—
350C23×C4—1181no—
351C22×C8—591no—
352C22×C8—591no—
353C22×C8—591no—
354C22×C8—591no—
355C4×D4—594no—
356C4×D4—1182no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—591no—
362C2×C4⋊C4—591no—
363C2×C4⋊C4—591no—
364C2×C4⋊C4C22⋊D5911yescharacteristic
365C2×C4⋊C4C22⋊D5911yescharacteristic
366C2×C4⋊C4C22×D5911yescharacteristic
367C2×C4⋊C4C22×D5911yescharacteristic
368C2×C4⋊C4C22×D5911yescharacteristic
369C2×C4⋊C4C22×D5911yescharacteristic
370C2×C22⋊C4—1181no—
371C2×C22⋊C4—1181no—
372C2×C22⋊C4—1181no—
373C2×C22⋊C4—1181no—
374C2×C22⋊C4—1181no—
375C2×C42—21no—
376C2×C42—1181no—
377C2×C42—1181no—
378C2×C42C22×D5911yescharacteristic
379C2×C42C22×D5911yescharacteristic
380C2×C42C22×D5911yescharacteristic
381#107—1182no—
382#107—1182no—
383#107—2361no—
384#106—2361no—
385#106—2361no—
386#106—2361no—
387C4⋊C8—1182no—
388C4⋊C8—1182no—
389C4⋊C8—1182no—
390#102—1182no—
391#102—1182no—
392#102—2361no—
393#102—2361no—
394C4×C8—1182no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—1181no—
403#95—1181no—
404#95—1181no—
405#95—1181no—
406#95C22⋊D5911yescharacteristic
407#95C22⋊D5911yescharacteristic
408C24—1181no—
409C2×D4—592no—
410C2×D4—1181no—
411C2×D4—1181no—
412C2×D4—1181no—
413C2×D4—1181no—
414C2×D4—1181no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—1181no—
420C22×C4—1184no—
421C22×C4—1181no—
422C22×C4—1181no—
423C22×C4—4721no—
424C22×C4—4721no—
425C22×C4C2×C22⋊D5911yescharacteristic
426C22×C4C2×C22⋊D5911yescharacteristic
427C22×C4C2×C22⋊D5911yescharacteristic
428C22×C4C2×C22⋊D5911yescharacteristic
429C22×C4C2×C22⋊D5911yescharacteristic
430C22×C4C2×C22⋊D5911yescharacteristic
431C22×C4C23×D5911yescharacteristic
432C2×C8—592no—
433C2×C8—592no—
434C2×C8—1181no—
435C2×C8—1181no—
436C2×C8—1181no—
437C2×C8—1181no—
438C2×C8—1181no—
439C2×C8—1181no—
440C2×C8—1181no—
441C2×C8—1181no—
442C2×C8—1181no—
443C2×C8—1181no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—41no—
454C4⋊C4—42no—
455C4⋊C4—42no—
456C4⋊C4—81no—
457C4⋊C4—81no—
458C4⋊C4—592no—
459C4⋊C4—1181no—
460C4⋊C4—1181no—
461C4⋊C4—1181no—
462C4⋊C4—1181no—
463C4⋊C4—1181no—
464C22⋊C4—1184no—
465C22⋊C4—4721no—
466C22⋊C4—4721no—
467C22⋊C4—2362no—
468C22⋊C4—2362no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—81no—
474C42—4721no—
475C42—4721no—
476C42Q8×D5912yes—
477C42#1174568912yes—
478C23—1182no—
479C23—2361no—
480C23—2361no—
481C23—2361no—
482C23—2361no—
483C23—2361no—
484C23—2361no—
485C23C22×C22⋊D5911yescharacteristic
486D4—1182no—
487D4—1182no—
488D4—2361no—
489D4—2361no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—1182no—
518C2×C4—4724no—
519C2×C4—2361no—
520C2×C4—2361no—
521C2×C4—2361no—
522C2×C4—2361no—
523C2×C4—2361no—
524C2×C4—2361no—
525C2×C4—2361no—
526C2×C4—2361no—
527C2×C4#1427370312yes—
528C2×C4#1427370312yes—
529C2×C4#1427374712yes—
530C2×C4C2×Q8×D5911yescharacteristic
531C2×C4#41×D5911yescharacteristic
532C2×C4#41×D5911yescharacteristic
533C2×C4C2×#1174568911yescharacteristic
534C2×C4#1427377311yescharacteristic
535C2×C4#1427377411yescharacteristic
536C8—1182no—
537C8—1182no—
538C8—2361no—
539C8—2361no—
540C22—4721no—
541C22—4721no—
542C22—4721no—
543C22—4721no—
544C22—2362no—
545C22—2362no—
546C22—2362no—
547C22C2×#1427370311yescharacteristic
548C22#1683805111yescharacteristic
549C22#1683807111yescharacteristic
550C22C2×#1427374711yescharacteristic
551C22#1683820011yescharacteristic
552C22#1683820511yescharacteristic
553C22#1683821011yescharacteristic
554C4—22no—
555C4—22no—
556C4—22no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4—4721no—
565C4—4721no—
566C4—2362no—
567C4#1683795811yescharacteristic
568C4#1683803211yescharacteristic
569C4#1683809011yescharacteristic
570C4#1683810511yescharacteristic
571C2—4722no—
572C2#2142780511yescharacteristic
573C2#2143387811yescharacteristic
574C2#2143392111yescharacteristic
575C2#2143647511yescharacteristic
576C2#2143669611yescharacteristic
577C2#2143710411yescharacteristic
578C2#2143716211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2570C2
socleC23×C59C22×D4
prime radicalC22×D236C23
hypercenter#2570D59
hypocenterC59#26094
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2570

Complements

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

NH ≅ G/Ntype
6. #21424864C2semidirect
7. #21424862C2semidirect
8. #21424857C2semidirect
9. #21424815C2semidirect
10. #21424685C2semidirect
11. #21424664C2semidirect
12. #21424258C2semidirect
15. C59×#2570C2semidirect
282. #2570D59semidirect
348. C59#26094semidirect

Maximal subgroups

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

subgroupindex
#214270672
#214256252
#214256202
#214254672
#214248642
#214248622
#214248572
#214248152
#214246852
#214246642
#214242582
#214241032
C4×#142736472
C59×#25702
#2609459