Finite Group Databasebeta

← #28558783

Subgroups — #28558783

Order 15104.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21434157C211yesmaximal, characteristic
2#21433204C211yesmaximal, characteristic, complemented
3#21433171C211yesmaximal, characteristic, complemented
4#21422976C211yesmaximal, characteristic, complemented
5#21422962C211yesmaximal, characteristic, complemented
6#21422941C211yesmaximal, characteristic, complemented
7#21422927C211yesmaximal, characteristic, complemented
8#21422921C211yesmaximal, characteristic, complemented
9#21422910C211yesmaximal, characteristic, complemented
10C8×#11745660C211yesmaximal, characteristic, complemented
11C8×D472C211yesmaximal, characteristic, complemented
12#21422881C211yesmaximal, characteristic, complemented
13#21422531C211yesmaximal, characteristic, complemented
14#21422496C211yesmaximal, characteristic, complemented
15C59×#1454C211yesmaximal, characteristic, complemented
16#16837952C2211yescharacteristic
17C4×#11745685C2211yescharacteristic
18#16837727C411yescharacteristic
19#16837727C411yescharacteristic
20#16837698C411yescharacteristic
21#16837693C411yescharacteristic
22#16837603C411yescharacteristic
23#16837598C411yescharacteristic
24#16837549C411yescharacteristic
25#16837549C411yescharacteristic
26C8×Dic118C2211yescharacteristic
27C8×Dic118C2211yescharacteristic
28C4×#11745660C2211yescharacteristic
29C4×#11745660C2211yescharacteristic
30C4×D472C2211yescharacteristic
31C4×D472C2211yescharacteristic
32#16837481C2211yescharacteristic
33#16837481C2211yescharacteristic
34#16837472—21no—
35#16837472—21no—
36C8×D236C2211yescharacteristic
37C8×D236C2211yescharacteristic
38C8×D236C2211yescharacteristic
39C8×D236C2211yescharacteristic
40(C22⋊D59)⋊C8—21no—
41(C22⋊D59)⋊C8—21no—
42#16837459C2211yescharacteristic
43#16837454—21no—
44C2×C4⋊(C59⋊C8)C2211yescharacteristic
45C4⋊C8×D59—21no—
46#16837367—21no—
47#16837367—21no—
48#16837155C2211yescharacteristic
49#16837155C2211yescharacteristic
50#16837153C2211yescharacteristic
51#16837153C2211yescharacteristic
52#16837134C2211yescharacteristic
53#16837134C2211yescharacteristic
54#16837131C2211yescharacteristic
55#16837131C2211yescharacteristic
56#16837131C2211yescharacteristic
57#16837131C2211yescharacteristic
58#16837131C2211yescharacteristic
59#16837131C2211yescharacteristic
60C59×#431C2211yescharacteristic
61C59×#431C2211yescharacteristic
62C59×#431C2211yescharacteristic
63C59×#322C2211yescharacteristic
64C59×#322C2211yescharacteristic
65C59×#322C2211yescharacteristic
66C82×C59C2211yescharacteristic
67C2×#11745685—21no—
68C2×#11745685C2×C411yescharacteristic
69C2×#11745660C2×C411yescharacteristic
70C2×#11745660C2×C411yescharacteristic
71C2×D472C2×C411yescharacteristic
72C2×D472C2×C411yescharacteristic
73C2×#11745659—21no—
74C2×#11745659—21no—
75C22×C59⋊C8—21no—
76C2×C8×D59—21no—
77C2×C8×D59—21no—
78C2×C8×D59—21no—
79C2×C8×D59—21no—
80#14273727C2×C411yescharacteristic
81#14273724C2×C411yescharacteristic
82#14273715—21no—
83#14273701—21no—
84#14273701C2×C411yescharacteristic
85#14273701C2×C411yescharacteristic
86C4×Dic118C2×C411yescharacteristic
87C4×Dic118C2311yescharacteristic
88C4×D236—21no—
89C4×D236C2×C411yescharacteristic
90C4×D236C2311yescharacteristic
91C4×D236C2311yescharacteristic
92C4×D236C2311yescharacteristic
93C4×C22⋊D59—21no—
94C4×C22⋊D59—21no—
95#14273686C2×C411yescharacteristic
96#14273684—21no—
97C42×D59—21no—
98#14273661C2×C411yescharacteristic
99#14273661C2×C411yescharacteristic
100#14273659C2×C411yescharacteristic
101#14273659C2×C411yescharacteristic
102C4⋊(C59⋊C8)—21no—
103C4⋊(C59⋊C8)C2311yescharacteristic
104C4⋊(C59⋊C8)C2311yescharacteristic
105C4⋊(C59⋊C8)C2311yescharacteristic
106C4⋊(C59⋊C8)C2311yescharacteristic
107Dic59⋊C8—21no—
108Dic59⋊C8—21no—
109#14273652C2×C411yescharacteristic
110#14273652C2×C411yescharacteristic
111#14273649C2×C411yescharacteristic
112#14273649C2×C411yescharacteristic
113#14273649C2×C411yescharacteristic
114#14273649C2×C411yescharacteristic
115#14273649C2×C411yescharacteristic
116#14273649C2×C411yescharacteristic
117C22⋊(C59⋊C8)—21no—
118(C2×D59)⋊C8—21no—
119(C2×D59)⋊C8—21no—
120(C2×D59)⋊C8—21no—
121(C2×D59)⋊C8—21no—
122(C2×D59)⋊C8—21no—
123(C2×D59)⋊C8—21no—
124#14273638—21no—
125C8×Dic59—21no—
126C8×Dic59—21no—
127C2×C42×C59C2311yescharacteristic
128C4⋊C8×C59—21no—
129C4⋊C8×C59C2×C411yescharacteristic
130C4⋊C8×C59C2×C411yescharacteristic
131C4⋊C8×C59D411yescharacteristic
132C4⋊C8×C59D411yescharacteristic
133C22⋊C8×C59—21no—
134C22⋊C8×C59C2×C411yescharacteristic
135C22⋊C8×C59C2×C411yescharacteristic
136C22⋊C8×C59D411yescharacteristic
137C22⋊C8×C59D411yescharacteristic
138C4×C8×C59C2311yescharacteristic
139C4×C8×C59C2311yescharacteristic
140C4×C8×C59C2311yescharacteristic
141C4×C8×C59C2311yescharacteristic
142C4×C8×C59C2311yescharacteristic
143C4×C8×C59C2311yescharacteristic
144C22×C4×C59C22×C411yescharacteristic
145C22×C4×C59C2×D411yescharacteristic
146C22×C4×C59#4111yescharacteristic
147C2×C22⋊D59—21no—
148C2×C22⋊D59—21no—
149C2×C22⋊D59—21no—
150#11745685—22no—
151#11745685—22no—
152#11745685—81no—
153#11745685—81no—
154C2×D236—21no—
155C2×D236—21no—
156C2×D236C22×C411yescharacteristic
157C2×D236C22×C411yescharacteristic
158C2×D236C22×C411yescharacteristic
159C2×C4×D59—21no—
160C2×C4×D59—21no—
161C2×C4×D59—21no—
162C2×C4×D59—21no—
163C2×C4×D59—21no—
164C2×Dic118—21no—
165C2×Dic118C22×C411yescharacteristic
166C2×C8×C59—21no—
167C2×C8×C59—21no—
168C2×C8×C59C22×C411yescharacteristic
169C2×C8×C59C22×C411yescharacteristic
170C2×C8×C59C22×C411yescharacteristic
171C2×C8×C59C22×C411yescharacteristic
172C2×C8×C59C2×D411yescharacteristic
173C2×C8×C59C2×D411yescharacteristic
174C2×C8×C59C2×D411yescharacteristic
175C2×C8×C59C2×D411yescharacteristic
176C42×C59C22×C411yescharacteristic
177C42×C59C2×D411yescharacteristic
178C42×C59#4111yescharacteristic
179C42×C59C2411yescharacteristic
180C22⋊Dic59—21no—
181(C2×D59)⋊C4—21no—
182(C2×D59)⋊C4—21no—
183(C2×D59)⋊C4—21no—
184(C2×D59)⋊C4—21no—
185(C2×D59)⋊C4—21no—
186(C2×D59)⋊C4—21no—
187C4⋊Dic59—21no—
188C4⋊Dic59C22×C411yescharacteristic
189C4⋊Dic59C22×C411yescharacteristic
190C4⋊Dic59C22×C411yescharacteristic
191C4⋊Dic59C22×C411yescharacteristic
192Dic59⋊C4—21no—
193Dic59⋊C4—21no—
194C4×Dic59—21no—
195C4×Dic59—21no—
196C4×Dic59—21no—
197C2×C59⋊C8—21no—
198C2×C59⋊C8—21no—
199C2×C59⋊C8—21no—
200C2×C59⋊C8—21no—
201C2×C59⋊C8—81no—
202D472—22no—
203D472—22no—
204#11745660—22no—
205#11745660—22no—
206#11745659—81no—
207#11745659—81no—
208C8×D59—81no—
209C8×D59—81no—
210C8×D59—81no—
211C8×D59—81no—
212C23×C59C4×D411yescharacteristic
213C22×D59—21no—
214C22×D59—21no—
215C22×D59—21no—
216C2×C4×C59—21no—
217C2×C4×C59—21no—
218C2×C4×C59—21no—
219C2×C4×C59—21no—
220C2×C4×C59—41no—
221C2×C4×C59C4×D411yescharacteristic
222C2×C4×C59C4×D411yescharacteristic
223C2×C4×C59C4×D411yescharacteristic
224C2×C4×C59C23×C411yescharacteristic
225C2×C4×C59C22×D411yescharacteristic
226C2×C4×C59C2×#4111yescharacteristic
227C22⋊D59—24no—
228C22⋊D59—81no—
229C22⋊D59—81no—
230C2×Dic59—21no—
231C2×Dic59—21no—
232C2×Dic59—21no—
233C2×Dic59—21no—
234C2×Dic59—21no—
235D236—21no—
236D236—21no—
237D236—21no—
238D236—21no—
239D236—21no—
240D236—81no—
241D236—81no—
242D236#13112yes—
243C4×D59—24no—
244C4×D59—41no—
245C4×D59—41no—
246C4×D59—41no—
247C4×D59—41no—
248C4×D59—41no—
249C4×D59—41no—
250C4×D59—81no—
251Dic118—21no—
252Dic118—81no—
253Dic118#13112yes—
254C8×C59—21no—
255C8×C59—21no—
256C8×C59—21no—
257C8×C59—21no—
258C8×C59—21no—
259C8×C59—21no—
260C8×C59—21no—
261C8×C59—21no—
262C8×C59—41no—
263C8×C59—41no—
264C59⋊C8—41no—
265C59⋊C8—41no—
266C59⋊C8—41no—
267C59⋊C8—41no—
268#17920—591nomaximal, Sylow
269C22×C59—21no—
270C22×C59—21no—
271C22×C59—21no—
272C22×C59C2×C4×D411yescharacteristic
273C2×D59—22no—
274C2×D59—41no—
275C2×D59—41no—
276C2×D59—41no—
277C2×D59—41no—
278C2×D59—41no—
279C2×D59—41no—
280C2×D59—41no—
281C2×D59—41no—
282C4×C59—21no—
283C4×C59—21no—
284C4×C59—21no—
285C4×C59—21no—
286C4×C59C2×#13111yescharacteristic
287C4×C59C2×#13111yescharacteristic
288C4×C59#57611yescharacteristic
289C4×C59#57711yescharacteristic
290Dic59—22no—
291Dic59—41no—
292Dic59—41no—
293Dic59—41no—
294Dic59—41no—
295#3106—591no—
296#2988—591no—
297#2981—591no—
298#1588—591no—
299#1586—591no—
300#1583—591no—
301#1581—591no—
302#1580—591no—
303SD16⋊C8—591no—
304C8×SD16—591no—
305C8×D8—591no—
306#1573—591no—
307#1488—591no—
308#1480—591no—
309#1454D5911yescharacteristic, complemented
310C2×C59—41no—
311C2×C59#292911yescharacteristic
312C2×C59#294611yescharacteristic
313C2×C59#295711yescharacteristic
314D59—42no—
315D59—81no—
316D59—81no—
317#532—591no—
318C4×#41—591no—
319#482—591no—
320#482—591no—
321#477—591no—
322#476—591no—
323#460—591no—
324#459—591no—
325#449—591no—
326#449—591no—
327C8×Q8—591no—
328C8×Q8—591no—
329C4×SD16—591no—
330C4×SD16—591no—
331C4×D8—591no—
332C4×D8—591no—
333#436—591no—
334#436—591no—
335#435—1181no—
336#435—1181no—
337C8×D4—591no—
338C8×D4—591no—
339C8×D4—591no—
340C8×D4—591no—
341C8×D4—1181no—
342C8×D4—1181no—
343#432—591no—
344#431—1181no—
345#431C2×D5911yescharacteristic
346#431C2×D5911yescharacteristic
347#431C2×D5911yescharacteristic
348C2×C4⋊C8—591no—
349C2×C4⋊C8—1181no—
350#408—1181no—
351#408—1181no—
352#335—591no—
353#335—591no—
354#334—591no—
355#334—591no—
356Q8⋊C8—591no—
357Q8⋊C8—591no—
358D4⋊C8—591no—
359D4⋊C8—591no—
360D4⋊C8—591no—
361D4⋊C8—591no—
362D4⋊C8—591no—
363D4⋊C8—591no—
364#322C2×D5911yescharacteristic
365#322C2×D5911yescharacteristic
366#322C2×D5911yescharacteristic
367C82C2×D5911yescharacteristic
368C59#1792011yescharacteristic, complemented, Sylow
369C2×#41—591no—
370C2×#41—1181no—
371C2×SD16—591no—
372C2×SD16—591no—
373C2×D8—591no—
374C2×D8—591no—
375C2×M16—1181no—
376C2×M16—1181no—
377C22×C8—1181no—
378C22×C8—1181no—
379C22×C8—1181no—
380C22×C8—1181no—
381C22×C8—1181no—
382C4⋊Q8—591no—
383#127—591no—
384#124—1181no—
385#121—591no—
386#121—591no—
387#121—1181no—
388C4×Q8—591no—
389C4×Q8—591no—
390C4×D4—591no—
391C4×D4—591no—
392C4×D4—591no—
393C4×D4—591no—
394C4×D4—1181no—
395C4×D4—1181no—
396C4×D4—1181no—
397#117—591no—
398#117—1181no—
399C2×C42—1181no—
400C2×C42C22×D5911yescharacteristic
401#107—591no—
402#107—591no—
403#106—591no—
404#106—591no—
405C4⋊C8—21no—
406C4⋊C8—591no—
407C4⋊C8—591no—
408C4⋊C8—591no—
409C4⋊C8—591no—
410C4⋊C8—1181no—
411C4⋊C8—1181no—
412C4⋊C8—1181no—
413C4⋊C8C4×D5911yescharacteristic
414C4⋊C8C4×D5911yescharacteristic
415C4⋊C8D23611yescharacteristic
416C4⋊C8D23611yescharacteristic
417#103—591no—
418#103—591no—
419#102—591no—
420#102—591no—
421#102—591no—
422#102—591no—
423#102—591no—
424#102—591no—
425C22⋊C8—21no—
426C22⋊C8—1181no—
427C22⋊C8—1181no—
428C22⋊C8—1181no—
429C22⋊C8—1181no—
430C22⋊C8—1181no—
431C22⋊C8—1181no—
432C22⋊C8—1181no—
433C22⋊C8C4×D5911yescharacteristic
434C22⋊C8C4×D5911yescharacteristic
435C22⋊C8D23611yescharacteristic
436C22⋊C8D23611yescharacteristic
437#97—1181no—
438C4×C8—1181no—
439C4×C8—1181no—
440C4×C8C22×D5911yescharacteristic
441C4×C8C22×D5911yescharacteristic
442C4×C8C22×D5911yescharacteristic
443C4×C8C22×D5911yescharacteristic
444C4×C8C22×D5911yescharacteristic
445C4×C8C22×D5911yescharacteristic
446#41—1182no—
447#41—1182no—
448#41—4721no—
449#41—4721no—
450C2×Q8—591no—
451C2×Q8—1181no—
452C2×D4—591no—
453C2×D4—591no—
454C2×D4—591no—
455C2×D4—1181no—
456C2×D4—1181no—
457C2×D4—1181no—
458C2×D4—1181no—
459C2×D4—1181no—
460C22×C4—1181no—
461C22×C4—1181no—
462C22×C4—1181no—
463C22×C4—1181no—
464C22×C4—1181no—
465C22×C4C2×C4×D5911yescharacteristic
466C22×C4C2×D23611yescharacteristic
467C22×C4#1174568511yescharacteristic
468SD16—1182no—
469SD16—1182no—
470D8—1182no—
471D8—1182no—
472M16—4721no—
473M16—4721no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—1181no—
477C2×C8—1181no—
478C2×C8—1181no—
479C2×C8—1181no—
480C2×C8—4721no—
481C2×C8—4721no—
482C2×C8—4721no—
483C2×C8—4721no—
484C2×C8—4721no—
485C2×C8C2×C4×D5911yescharacteristic
486C2×C8C2×C4×D5911yescharacteristic
487C2×C8C2×C4×D5911yescharacteristic
488C2×C8C2×C4×D5911yescharacteristic
489C2×C8C2×D23611yescharacteristic
490C2×C8C2×D23611yescharacteristic
491C2×C8C2×D23611yescharacteristic
492C2×C8C2×D23611yescharacteristic
493C4⋊C4—591no—
494C4⋊C4—591no—
495C4⋊C4—591no—
496C4⋊C4—591no—
497C4⋊C4—1181no—
498C4⋊C4—1181no—
499C4⋊C4—1181no—
500C22⋊C4—1181no—
501C22⋊C4—1181no—
502C22⋊C4—1181no—
503C22⋊C4—1181no—
504C22⋊C4—1181no—
505C22⋊C4—1181no—
506C22⋊C4—1181no—
507C42—1181no—
508C42—1181no—
509C42—1181no—
510C42C2×C4×D5911yescharacteristic
511C42C2×D23611yescharacteristic
512C42#1174568511yescharacteristic
513C42C23×D5911yescharacteristic
514C23—1181no—
515C23—1181no—
516C23—1181no—
517C23C4×D23611yescharacteristic
518Q8—592no—
519Q8—1181no—
520Q8—4721no—
521D4—592no—
522D4—1184no—
523D4—1181no—
524D4—1181no—
525D4—1181no—
526D4—1181no—
527D4—1181no—
528D4—4721no—
529D4—4721no—
530D4—4721no—
531D4—4721no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—1184no—
538C2×C4—1181no—
539C2×C4—1181no—
540C2×C4—1181no—
541C2×C4—1181no—
542C2×C4—1181no—
543C2×C4—4721no—
544C2×C4—2361no—
545C2×C4—2361no—
546C2×C4—2361no—
547C2×C4—2361no—
548C2×C4—2361no—
549C2×C4—2361no—
550C2×C4C4×D23611yescharacteristic
551C2×C4C4×D23611yescharacteristic
552C2×C4C4×D23611yescharacteristic
553C2×C4C22×C4×D5911yescharacteristic
554C2×C4C22×D23611yescharacteristic
555C2×C4C2×#1174568511yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—21no—
564C8—41no—
565C8—41no—
566C8—2361no—
567C8—2361no—
568C8—2361no—
569C8—2361no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—1182no—
574C22—2361no—
575C22—2361no—
576C22—2361no—
577C22—2361no—
578C22—2361no—
579C22—2361no—
580C22—2361no—
581C22—2361no—
582C22C2×C4×D23611yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—1182no—
588C4—2361no—
589C4—2361no—
590C4—2361no—
591C4—2361no—
592C4#131×D5911yescharacteristic
593C4#131×D5911yescharacteristic
594C4#1683820711yescharacteristic
595C4#1683821411yescharacteristic
596C2—41no—
597C2—4721no—
598C2—4721no—
599C2—2362no—
600C2#2143279211yescharacteristic
601C2#2143293011yescharacteristic
602C2#2143301411yescharacteristic
subgroupG/H
centerC2×C4C22×D236
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC59×#1454C2
socleC22×C59C2×C4×D4
prime radical#21434157C2
cosocleC42×C59C24
hypercenter#1454D59
hypocenterC59#17920
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
2. #21433204C2semidirect
3. #21433171C2semidirect
4. #21422976C2semidirect
5. #21422962C2semidirect
6. #21422941C2semidirect
7. #21422927C2semidirect
8. #21422921C2semidirect
9. #21422910C2semidirect
10. C8×#11745660C2semidirect
11. C8×D472C2semidirect
12. #21422881C2semidirect
13. #21422531C2semidirect
14. #21422496C2semidirect
15. C59×#1454C2semidirect
309. #1454D59semidirect
368. C59#17920semidirect

Maximal subgroups

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

subgroupindex
#214341572
#214332042
#214331712
#214229762
#214229622
#214229412
#214229272
#214229212
#214229102
C8×#117456602
C8×D4722
#214228812
#214225312
#214224962
C59×#14542
#1792059