Finite Group Databasebeta

← #28611837

Subgroups — #28611837

Order 15104.

774 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837703C211yesmaximal, characteristic
2#21427190C211yesmaximal, characteristic, complemented
3#21427067C211yesmaximal, characteristic
4#21425061C211yesmaximal, characteristic, complemented
5#21424866C211yesmaximal, characteristic, complemented
6#21424779C211yesmaximal, characteristic
7#21424779C211yesmaximal, characteristic
8#21424724C211yesmaximal, characteristic
9#21424717C211yesmaximal, characteristic
10#21424689C211yesmaximal, characteristic, complemented
11#21424675C211yesmaximal, characteristic, complemented
12C4×#14273661C211yesmaximal, characteristic, complemented
13C4×#14273659C211yesmaximal, characteristic, complemented
14C4×#14273649C211yesmaximal, characteristic
15C8×C4⋊C4×C59C211yesmaximal, characteristic, complemented
16C2×#14273719C2211yescharacteristic
17C2×C4×D236C2211yescharacteristic
18#16837703C418yescomplemented
19C2×#14273661C2211yescharacteristic
20C2×#14273661C2211yescharacteristic
21C2×#14273659C2211yescharacteristic
22C2×#14273659C2211yescharacteristic
23C2×#14273649C2211yescharacteristic
24C2×#14273649C2211yescharacteristic
25C2×#14273649C2211yescharacteristic
26C2×#14273649C2211yescharacteristic
27#16837304C2211yescharacteristic
28#16837304C2211yescharacteristic
29#16837300C2211yescharacteristic
30#16837300C2211yescharacteristic
31#16837297—21no—
32#16837292—21no—
33#16837292—21no—
34#16837284—21no—
35#16837283—21no—
36#16837268C2211yescharacteristic
37#16837264—21no—
38C4×C4⋊Dic59C2211yescharacteristic
39C4×C4⋊Dic59C2211yescharacteristic
40C4×C4⋊Dic59C2211yescharacteristic
41C4×C4⋊Dic59C2211yescharacteristic
42C4×C4⋊Dic59C2211yescharacteristic
43#16837253—21no—
44#16837249—21no—
45#16837165C2211yescharacteristic
46#16837165C2211yescharacteristic
47#16837165C2211yescharacteristic
48#16837165C2211yescharacteristic
49#16837165C2211yescharacteristic
50#16837165C2211yescharacteristic
51#16837165C2211yescharacteristic
52#16837165C2211yescharacteristic
53C2×C4⋊C8×C59C2211yescharacteristic
54C2×C4×C8×C59C2211yescharacteristic
55C2×C4×C8×C59C2211yescharacteristic
56C2×C4×C8×C59C2211yescharacteristic
57C4×C4⋊C4×C59C2211yescharacteristic
58C59×#336C2211yescharacteristic
59C59×#336C2211yescharacteristic
60C22×D236C2311yescharacteristic
61C22×C4×D59—21no—
62#14273719—22no—
63#14273719C2×C414yes—
64C4×D236—22no—
65C4×D236C2×C414yes—
66C2×C4⋊Dic59C2311yescharacteristic
67C2×C4⋊Dic59C2311yescharacteristic
68C2×C4⋊Dic59C2311yescharacteristic
69C2×C4⋊Dic59C2311yescharacteristic
70C2×C4⋊Dic59C2311yescharacteristic
71C2×C4⋊Dic59C2311yescharacteristic
72C2×C4⋊Dic59C2311yescharacteristic
73C2×Dic59⋊C4—21no—
74C2×Dic59⋊C4—21no—
75C2×Dic59⋊C4—21no—
76C2×Dic59⋊C4—21no—
77C2×(C2×D59)⋊C4—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—
85C2×C4×Dic59—21no—
86C2×C4×Dic59—21no—
87#14273661—22no—
88#14273661C2×C414yes—
89#14273659—22no—
90#14273659C2×C414yes—
91#14273649—22no—
92#14273649—22no—
93#14273649C2×C414yes—
94#14273649C2×C414yes—
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—
104C22×C8×C59C2311yescharacteristic
105C22×C8×C59C2311yescharacteristic
106C22×C8×C59C2311yescharacteristic
107C22×C8×C59C2311yescharacteristic
108C2×C4⋊C4×C59D411yescharacteristic
109C2×C4⋊C4×C59D411yescharacteristic
110C2×C42×C59C2311yescharacteristic
111C2×C42×C59C2311yescharacteristic
112C2×C42×C59C2311yescharacteristic
113C4⋊C8×C59C2×C414yes—
114C4×C8×C59—22no—
115C4×C8×C59—22no—
116C4×C8×C59—22no—
117#95×C59D411yescharacteristic
118#95×C59D411yescharacteristic
119C23×D59—21no—
120C22×C4×C59C2×D411yescharacteristic
121C22×C4×C59C2×D411yescharacteristic
122C22×C4×C59C2×D411yescharacteristic
123C22×C4×C59C2×D411yescharacteristic
124C22×C4×C59C2×D411yescharacteristic
125C22×C4×C59C2×D411yescharacteristic
126C22×C4×C59C2411yescharacteristic
127C22×Dic59—21no—
128C22×Dic59—21no—
129C22×Dic59—21no—
130C22×Dic59—21no—
131C22×Dic59—21no—
132C22×Dic59—21no—
133C22×Dic59—21no—
134C2×D236—21no—
135C2×D236—21no—
136C2×D236—21no—
137C2×D236—21no—
138C2×D236—21no—
139C2×D236C22×C412yes—
140C2×C4×D59—24no—
141C2×C4×D59—81no—
142C2×C4×D59—81no—
143C2×C8×C59—21no—
144C2×C8×C59—21no—
145C2×C8×C59—21no—
146C2×C8×C59—21no—
147C2×C8×C59—21no—
148C2×C8×C59—21no—
149C2×C8×C59—21no—
150C2×C8×C59—21no—
151C2×C8×C59—21no—
152C2×C8×C59C22×C412yes—
153C2×C8×C59C22×C412yes—
154C2×C8×C59#4112yes—
155C4⋊C4×C59—22no—
156C4⋊C4×C59—22no—
157C42×C59—21no—
158C42×C59—21no—
159C42×C59—21no—
160C42×C59—21no—
161C42×C59C22×C412yes—
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⋊Dic59—21no—
174C4⋊Dic59—21no—
175C4⋊Dic59—21no—
176C4⋊Dic59—21no—
177C4⋊Dic59—21no—
178C4⋊Dic59C22×C412yes—
179C4⋊Dic59C22×C412yes—
180C4⋊Dic59C22×C412yes—
181C4⋊Dic59#4112yes—
182Dic59⋊C4—24no—
183Dic59⋊C4—24no—
184Dic59⋊C4—42no—
185Dic59⋊C4—81no—
186C4×Dic59—42no—
187C4×Dic59—81no—
188C4×Dic59—81no—
189C4×Dic59—81no—
190C4×Dic59—81no—
191C23×C59C22×D411yescharacteristic
192C22×D59—22no—
193C22×D59—41no—
194C22×D59—41no—
195C22×D59—41no—
196C22×D59—41no—
197C22×D59—41no—
198C22×D59—41no—
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—21no—
212C2×C4×C59—21no—
213C2×C4×C59C4×D412yes—
214C2×C4×C59C4×D412yes—
215C2×C4×C59#13512yes—
216C2×C4×C59#13512yes—
217C2×C4×C59C23×C411yescharacteristic
218C2×C4×C59C2×#4111yescharacteristic
219C2×C4×C59C2×#4111yescharacteristic
220C2×C4×C59C2×#4111yescharacteristic
221C2×C4×C592−1+411yescharacteristic
222C2×C4×C592−1+411yescharacteristic
223C2×Dic59—22no—
224C2×Dic59—22no—
225C2×Dic59—22no—
226C2×Dic59—22no—
227C2×Dic59—41no—
228C2×Dic59—41no—
229C2×Dic59—41no—
230C2×Dic59—41no—
231C2×Dic59—41no—
232C2×Dic59—41no—
233C2×Dic59—41no—
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—
244D236—22no—
245D236—22no—
246D236—41no—
247D236—41no—
248C4×D59—84no—
249C8×C59—22no—
250C8×C59—22no—
251C8×C59—22no—
252C8×C59—41no—
253#23065—591nomaximal, Sylow
254C22×C59C2×C4×D411yescharacteristic
255C22×C59#54711yescharacteristic
256C22×C59#54811yescharacteristic
257C22×C59C2×#13511yescharacteristic
258C22×C59C2×#13511yescharacteristic
259C22×C59#57611yescharacteristic
260C22×C59#57711yescharacteristic
261C2×D59—42no—
262C2×D59—42no—
263C2×D59—42no—
264C2×D59—81no—
265C2×D59—81no—
266C2×D59—81no—
267C2×D59—81no—
268C4×C59—22no—
269C4×C59—22no—
270C4×C59—22no—
271C4×C59—22no—
272C4×C59—41no—
273C4×C59—41no—
274C4×C59C4×#4111yescharacteristic
275C4×C59#51911yescharacteristic
276C4×C59#55211yescharacteristic
277C4×C59#55611yescharacteristic
278Dic59—42no—
279Dic59—42no—
280Dic59—42no—
281Dic59—42no—
282Dic59—81no—
283Dic59—81no—
284Dic59—81no—
285C2×#478—591no—
286#2370—591no—
287#2357—591no—
288#1991—591no—
289#1949—591no—
290#1934—591no—
291#1934—591no—
292#1926—591no—
293#1925—591no—
294#1921—591no—
295#1919—591no—
296C4×#107—591no—
297C4×#106—591no—
298C8×C4⋊C4D5911yescharacteristic, complemented
299C4×#102—591no—
300C2×C59#236211yescharacteristic
301C2×C59C4×#13511yescharacteristic
302C2×C59#294611yescharacteristic
303C2×C59#333711yescharacteristic
304C2×C59#333911yescharacteristic
305C2×C59#336111yescharacteristic
306C2×C59#336511yescharacteristic
307D59—82no—
308C2×#125—591no—
309C2×C4×D4—591no—
310#478—598no—
311C2×#107—591no—
312C2×#107—591no—
313C2×#106—591no—
314C2×#106—591no—
315C2×C4⋊C8C2×D5911yescharacteristic
316C2×#102—591no—
317C2×#102—591no—
318C2×#102—591no—
319C2×#102—591no—
320C2×C4×C8C2×D5911yescharacteristic
321C2×C4×C8C2×D5911yescharacteristic
322C2×C4×C8C2×D5911yescharacteristic
323#390—591no—
324#390—591no—
325#389—591no—
326#389—591no—
327#389—1181no—
328#388—1181no—
329#388—1181no—
330#387—1181no—
331#387—1181no—
332#382—591no—
333#381—1181no—
334C4×C4⋊C4—591no—
335C4×C4⋊C4—591no—
336C4×C4⋊C4—591no—
337C4×C4⋊C4—591no—
338C4×C4⋊C4—591no—
339C4×C4⋊C4—1181no—
340C4×C4⋊C4C2×D5911yescharacteristic
341C4×C22⋊C4—1181no—
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#336C2×D5911yescharacteristic
351#336C2×D5911yescharacteristic
352C59#2306511yescharacteristic, complemented, Sylow
353C22×D4—591no—
354C23×C4—1181no—
355C22×C8C22×D5911yescharacteristic
356C22×C8C22×D5911yescharacteristic
357C22×C8C22×D5911yescharacteristic
358C22×C8C22×D5911yescharacteristic
359#125—594no—
360#125—1182no—
361C4×D4—594no—
362C4×D4—1182no—
363C2×C4⋊C4—591no—
364C2×C4⋊C4—591no—
365C2×C4⋊C4—591no—
366C2×C4⋊C4—591no—
367C2×C4⋊C4—591no—
368C2×C4⋊C4—591no—
369C2×C4⋊C4—591no—
370C2×C4⋊C4—1181no—
371C2×C4⋊C4—1181no—
372C2×C4⋊C4—1181no—
373C2×C4⋊C4—1181no—
374C2×C4⋊C4D23611yescharacteristic
375C2×C4⋊C4D23611yescharacteristic
376C2×C22⋊C4—1181no—
377C2×C22⋊C4—1181no—
378C2×C22⋊C4—1181no—
379C2×C22⋊C4—1181no—
380C2×C22⋊C4—1181no—
381C2×C42—1181no—
382C2×C42—1181no—
383C2×C42—1181no—
384C2×C42—1181no—
385C2×C42—1181no—
386C2×C42C22×D5911yescharacteristic
387C2×C42C22×D5911yescharacteristic
388C2×C42C22×D5911yescharacteristic
389#107—594no—
390#107—1182no—
391#106—594no—
392#106—1182no—
393C4⋊C8C4×D5914yes—
394#102—594no—
395#102—594no—
396#102—1182no—
397#102—1182no—
398C4×C8—22no—
399C4×C8—22no—
400C4×C8—22no—
401#95—1181no—
402#95—1181no—
403#95—1181no—
404#95—1181no—
405#95—1181no—
406#95—1181no—
407#95—1181no—
408#95—1181no—
409#95—1181no—
410#95D23611yescharacteristic
411#95D23611yescharacteristic
412C24—1181no—
413C2×D4—592no—
414C2×D4—1181no—
415C2×D4—1181no—
416C2×D4—1181no—
417C2×D4—1181no—
418C2×D4—1181no—
419C22×C4—1181no—
420C22×C4—1181no—
421C22×C4—1181no—
422C22×C4—1181no—
423C22×C4—1184no—
424C22×C4—1181no—
425C22×C4—1181no—
426C22×C4—1181no—
427C22×C4—4721no—
428C22×C4—4721no—
429C22×C4C2×D23611yescharacteristic
430C22×C4C2×D23611yescharacteristic
431C22×C4C2×D23611yescharacteristic
432C22×C4C2×D23611yescharacteristic
433C22×C4C2×D23611yescharacteristic
434C22×C4C2×D23611yescharacteristic
435C22×C4C23×D5911yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8C2×C4×D5912yes—
446C2×C8C2×C4×D5912yes—
447C2×C8#1174568712yes—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—592no—
451C4⋊C4—592no—
452C4⋊C4—592no—
453C4⋊C4—592no—
454C4⋊C4—1184no—
455C4⋊C4—1184no—
456C4⋊C4—1181no—
457C4⋊C4—1181no—
458C4⋊C4—1181no—
459C4⋊C4—1181no—
460C4⋊C4—1181no—
461C4⋊C4—1181no—
462C4⋊C4—1181no—
463C4⋊C4—1181no—
464C4⋊C4—1181no—
465C4⋊C4—1181no—
466C4⋊C4—4721no—
467C4⋊C4—2362no—
468C22⋊C4—1184no—
469C22⋊C4—4721no—
470C22⋊C4—4721no—
471C22⋊C4—2362no—
472C22⋊C4—2362no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—4721no—
478C42—4721no—
479C42—4721no—
480C42—4721no—
481C42—2362no—
482C42C2×C4×D5912yes—
483C42#1174568512yes—
484C23—1182no—
485C23—2361no—
486C23—2361no—
487C23—2361no—
488C23—2361no—
489C23—2361no—
490C23—2361no—
491C23C22×D23611yescharacteristic
492D4—1182no—
493D4—1182no—
494D4—2361no—
495D4—2361no—
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—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—1182no—
511C2×C4—1182no—
512C2×C4—1182no—
513C2×C4—1182no—
514C2×C4—4724no—
515C2×C4—2361no—
516C2×C4—2361no—
517C2×C4—2361no—
518C2×C4—2361no—
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—2361no—
528C2×C4—2361no—
529C2×C4—2361no—
530C2×C4—2361no—
531C2×C4—2361no—
532C2×C4C4×D23612yes—
533C2×C4C4×D23612yes—
534C2×C4#1427374912yes—
535C2×C4#1427374912yes—
536C2×C4C22×C4×D5911yescharacteristic
537C2×C4#41×D5911yescharacteristic
538C2×C4C2×#1174568711yescharacteristic
539C2×C4C2×#1174568511yescharacteristic
540C2×C4#1427377411yescharacteristic
541C2×C4#1427377511yescharacteristic
542C8—22no—
543C8—22no—
544C8—22no—
545C8—41no—
546C22—4721no—
547C22—4721no—
548C22—4721no—
549C22—4721no—
550C22—2362no—
551C22—2362no—
552C22—2362no—
553C22C2×C4×D23611yescharacteristic
554C22#1683805611yescharacteristic
555C22#1683806411yescharacteristic
556C22C2×#1427374911yescharacteristic
557C22C2×#1427374911yescharacteristic
558C22#1683820711yescharacteristic
559C22#1683821411yescharacteristic
560C4—22no—
561C4—22no—
562C4—22no—
563C4—22no—
564C4—41no—
565C4—41no—
566C4—4721no—
567C4—4721no—
568C4—4721no—
569C4—2362no—
570C4—2362no—
571C4—2362no—
572C4—2362no—
573C4C4×#1174568711yescharacteristic
574C4#1683787811yescharacteristic
575C4#1683808711yescharacteristic
576C4#1683812011yescharacteristic
577C2—4722no—
578C2#2142712511yescharacteristic
579C2C4×#1427374911yescharacteristic
580C2#2143293011yescharacteristic
581C2#2143647711yescharacteristic
582C2#2143649911yescharacteristic
583C2#2143675811yescharacteristic
584C2#2143679411yescharacteristic
subgroupG/H
centerC23C22×D236
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC8×C4⋊C4×C59C2
socleC23×C59C22×D4
prime radicalC22×D236C23
cosocleC22×C4×C59C24
hypercenterC8×C4⋊C4D59
hypocenterC59#23065
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #21427190C2semidirect
4. #21425061C2semidirect
5. #21424866C2semidirect
10. #21424689C2semidirect
11. #21424675C2semidirect
12. C4×#14273661C2semidirect
13. C4×#14273659C2semidirect
15. C8×C4⋊C4×C59C2semidirect
18. #16837703C4semidirect
298. C8×C4⋊C4D59semidirect
352. C59#23065semidirect

Maximal subgroups

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

subgroupindex
C2×#168377032
#214271902
#214270672
#214250612
#214248662
#214247792
#214247242
#214247172
#214246892
#214246752
C4×#142736612
C4×#142736592
C4×#142736492
C8×C4⋊C4×C592
#2306559