Finite Group Databasebeta

← #28609471

Subgroups — #28609471

Order 15104.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21433314C211yesmaximal, characteristic
2C2×#16837516C211yesmaximal, characteristic, complemented
3#21432821C211yesmaximal, characteristic, complemented
4#21432545C211yesmaximal, characteristic, complemented
5#21424986C211yesmaximal, characteristic, complemented
6#21424797C211yesmaximal, characteristic, complemented
7#21424747C211yesmaximal, characteristic, complemented
8#21424544C211yesmaximal, characteristic, complemented
9#21424421C211yesmaximal, characteristic, complemented
10#21424420C211yesmaximal, characteristic, complemented
11#21424369C211yesmaximal, characteristic, complemented
12#21424301C211yesmaximal, characteristic, complemented
13#21423941C211yesmaximal, characteristic, complemented
14#21423862C211yesmaximal, characteristic, complemented
15C2×C59×#421C211yesmaximal, characteristic, complemented
16C2×#14273747C2211yescharacteristic
17C2×#14273747C2211yescharacteristic
18C2×#14273735C2211yescharacteristic, complemented
19C2×#14273734C2211yescharacteristic
20C2×#14273734C2211yescharacteristic
21#16837913C2211yescharacteristic
22#16837564C411yescharacteristic, complemented
23#16837564C411yescharacteristic, complemented
24#16837558C411yescharacteristic, complemented
25#16837553C411yescharacteristic, complemented
26#16837547C411yescharacteristic, complemented
27#16837547C411yescharacteristic, complemented
28#16837541C411yescharacteristic, complemented
29#16837536C411yescharacteristic, complemented
30#16837516—24no—
31#16837478—21no—
32#16837473—21no—
33#16837471—21no—
34C8×C22⋊D59—21no—
35C2×#14273662C2211yescharacteristic, complemented
36C2×#14273662C2211yescharacteristic, complemented
37#16837430C2211yescharacteristic, complemented
38C2×#14273655C2211yescharacteristic, complemented
39C2×#14273655C2211yescharacteristic, complemented
40#16837398C2211yescharacteristic
41#16837398C2211yescharacteristic
42#16837370C2211yescharacteristic, complemented
43#16837369—21no—
44#16837369—21no—
45#16837369C2211yescharacteristic
46#16837369C2211yescharacteristic
47#16837366—21no—
48#16837366C2211yescharacteristic
49C2×C22⋊(C59⋊C8)—21no—
50C2×C22⋊(C59⋊C8)C2211yescharacteristic
51C2×C22⋊(C59⋊C8)C2211yescharacteristic
52#16837360C2211yescharacteristic, complemented
53C2×#14273638C2211yescharacteristic, complemented
54C2×C4×C59⋊C8C2211yescharacteristic, complemented
55#16837166C2211yescharacteristic, complemented
56#16837166C2211yescharacteristic, complemented
57#16837162C2211yescharacteristic, complemented
58#16837162C2211yescharacteristic, complemented
59#16837157C2211yescharacteristic, complemented
60#16837157C2211yescharacteristic, complemented
61C22×#41×C59C2211yescharacteristic
62C22×M16×C59C2211yescharacteristic
63C2×#117×C59C2211yescharacteristic
64C59×#421—24no—
65C2×#104×C59C2211yescharacteristic
66C2×#104×C59C2211yescharacteristic
67C2×#104×C59C2211yescharacteristic
68C2×#104×C59C2211yescharacteristic
69C2×#11745685C2311yescharacteristic
70#14273747—22no—
71#14273747—22no—
72#14273747—41no—
73#14273747—41no—
74C2×#11745672C2×C411yescharacteristic
75C2×#11745672C2×C411yescharacteristic
76C2×#11745670C2×C411yescharacteristic
77C2×#11745670C2×C411yescharacteristic
78C2×#11745671C2×C411yescharacteristic
79C2×#11745671C2×C411yescharacteristic
80C2×#11745669C2×C411yescharacteristic
81C2×#11745669C2×C411yescharacteristic
82#14273735—22no—
83#14273735—41no—
84#14273734—22no—
85#14273734—22no—
86#14273734—41no—
87#14273734—41no—
88C2×#11745664—21no—
89C2×#11745664—21no—
90C2×#11745664C2311yescharacteristic
91C2×#11745664C2311yescharacteristic
92C2×#11745659—21no—
93C22×C59⋊C8—21no—
94C22×C59⋊C8—21no—
95C22×C59⋊C8C2311yescharacteristic
96C22×C59⋊C8C2311yescharacteristic
97C22×C59⋊C8C2311yescharacteristic
98C22×C59⋊C8C2311yescharacteristic
99C2×C8×D59—21no—
100#14273710—21no—
101#14273706C2×C411yescharacteristic
102#14273706C2×C411yescharacteristic
103#14273701C2×C411yescharacteristic
104#14273701C2×C411yescharacteristic
105#14273696—21no—
106C4×C22⋊D59—21no—
107C4×C22⋊D59—21no—
108#14273686C2311yescharacteristic
109#14273662—22no—
110#14273662—41no—
111Dic59⋊C8—21no—
112Dic59⋊C8—21no—
113#14273655—22no—
114#14273655—41no—
115#14273651C2×C411yescharacteristic
116#14273651C2×C411yescharacteristic
117#14273651C2×C411yescharacteristic
118#14273651C2×C411yescharacteristic
119#14273648C2×C411yescharacteristic
120#14273648C2×C411yescharacteristic
121#14273648C2×C411yescharacteristic
122#14273648C2×C411yescharacteristic
123C22⋊(C59⋊C8)—21no—
124C22⋊(C59⋊C8)—21no—
125C22⋊(C59⋊C8)—21no—
126C22⋊(C59⋊C8)—21no—
127C22⋊(C59⋊C8)—21no—
128C22⋊(C59⋊C8)—21no—
129C22⋊(C59⋊C8)C2×C411yescharacteristic
130C22⋊(C59⋊C8)C2×C411yescharacteristic
131C22⋊(C59⋊C8)C2×C411yescharacteristic
132C22⋊(C59⋊C8)C2×C411yescharacteristic
133C22⋊(C59⋊C8)D411yescharacteristic
134C22⋊(C59⋊C8)D411yescharacteristic
135C22⋊(C59⋊C8)D411yescharacteristic
136C22⋊(C59⋊C8)D411yescharacteristic
137(C2×D59)⋊C8—21no—
138(C2×D59)⋊C8—21no—
139#14273638—41no—
140#14273637—21no—
141C4×C59⋊C8—22no—
142C8×Dic59—21no—
143C2×#41×C59—21no—
144C2×#41×C59—21no—
145C2×#41×C59—22no—
146C2×#41×C59—22no—
147C2×#41×C59—41no—
148C2×#41×C59—41no—
149C2×#41×C59C2×C411yescharacteristic
150C2×#41×C59C2×C411yescharacteristic
151C2×#41×C59C2311yescharacteristic
152C2×#41×C59C2311yescharacteristic
153C22×Q8×C59C2×C411yescharacteristic
154C22×D4×C59—21no—
155C22×D4×C59C2×C411yescharacteristic
156C23×C4×C59—21no—
157C23×C4×C59C2311yescharacteristic
158C2×M16×C59—21no—
159C2×M16×C59—22no—
160C2×M16×C59—41no—
161C2×M16×C59C2311yescharacteristic
162C2×M16×C59C2311yescharacteristic
163C22×C8×C59—21no—
164#117×C59—22no—
165#117×C59—41no—
166C2×C4⋊C4×C59—21no—
167C2×C22⋊C4×C59—21no—
168C2×C42×C59C2311yescharacteristic
169C2×C42×C59C2311yescharacteristic
170#104×C59—22no—
171#104×C59—22no—
172#104×C59—22no—
173#104×C59D414yescomplemented
174C24×C59—21no—
175C24×C59#4111yescharacteristic
176#41×C59—21no—
177#41×C59—21no—
178#41×C59—22no—
179#41×C59—22no—
180#41×C59—21no—
181#41×C59—21no—
182#41×C59—21no—
183#41×C59—21no—
184#41×C59—42no—
185#41×C59—42no—
186#41×C59—41no—
187#41×C59—41no—
188#41×C59—42no—
189#41×C59—42no—
190#41×C59C2×D412yes—
191#41×C59#4112yes—
192C2×Q8×C59—21no—
193C2×Q8×C59—22no—
194C2×Q8×C59—41no—
195C2×Q8×C59C22×C411yescharacteristic
196C2×Q8×C59C22×C411yescharacteristic
197C2×D4×C59—21no—
198C2×D4×C59—22no—
199C2×D4×C59—21no—
200C2×D4×C59—21no—
201C2×D4×C59—21no—
202C2×D4×C59—21no—
203C2×D4×C59—41no—
204C2×D4×C59—42no—
205C2×D4×C59—42no—
206C2×D4×C59C22×C411yescharacteristic
207C2×D4×C59C22×C411yescharacteristic
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—21no—
213C22×C4×C59—21no—
214C22×C4×C59—21no—
215C22×C4×C59—21no—
216C22×C4×C59—21no—
217C22×C4×C59—21no—
218C22×C4×C59—21no—
219C22×C4×C59—42no—
220C22×C4×C59—42no—
221C22×C4×C59C22×C411yescharacteristic
222C22×C4×C59C22×C411yescharacteristic
223C22×C4×C59C2×D411yescharacteristic
224C22×C4×C59C2×D411yescharacteristic
225C22×C4×C59#4111yescharacteristic
226C22×C4×C59C2411yescharacteristic
227C2×C22⋊D59—21no—
228C2×C22⋊D59—21no—
229C2×C22⋊D59—21no—
230#11745685—21no—
231#11745685—21no—
232#11745685—21no—
233#11745685—21no—
234C2×D236C22×C411yescharacteristic
235C2×C4×D59—21no—
236C2×Dic118C22×C411yescharacteristic
237M16×C59—21no—
238M16×C59—21no—
239M16×C59—21no—
240M16×C59—42no—
241M16×C59C2×D412yes—
242C2×C8×C59—21no—
243C2×C8×C59—21no—
244C2×C8×C59—42no—
245C4⋊C4×C59—42no—
246C22⋊C4×C59—42no—
247C42×C59—21no—
248C42×C59—21no—
249C42×C59—21no—
250C42×C59C2×D412yes—
251C22⋊Dic59—21no—
252C22⋊Dic59—21no—
253C22⋊Dic59—21no—
254#11745672—22no—
255#11745672—41no—
256#11745671—22no—
257#11745671—41no—
258#11745670—22no—
259#11745670—41no—
260#11745669—22no—
261#11745669—41no—
262(C2×D59)⋊C4—21no—
263(C2×D59)⋊C4—21no—
264C4⋊Dic59C22×C411yescharacteristic
265C4⋊Dic59C22×C411yescharacteristic
266Dic59⋊C4—21no—
267Dic59⋊C4—21no—
268C4×Dic59—21no—
269#11745664—21no—
270#11745664—21no—
271#11745664—21no—
272#11745664—21no—
273#11745664—42no—
274#11745664—42no—
275C2×C59⋊C8—21no—
276C2×C59⋊C8—21no—
277C2×C59⋊C8—21no—
278C2×C59⋊C8—21no—
279C2×C59⋊C8—21no—
280C2×C59⋊C8—21no—
281C2×C59⋊C8—21no—
282C2×C59⋊C8—21no—
283C2×C59⋊C8—21no—
284C2×C59⋊C8—21no—
285C2×C59⋊C8—42no—
286C2×C59⋊C8—42no—
287C2×C59⋊C8C22×C411yescharacteristic
288C2×C59⋊C8C22×C411yescharacteristic
289C2×C59⋊C8C22×C411yescharacteristic
290C2×C59⋊C8C22×C411yescharacteristic
291C2×C59⋊C8C2×D411yescharacteristic
292C2×C59⋊C8C2×D411yescharacteristic
293C2×C59⋊C8C2×D411yescharacteristic
294C2×C59⋊C8C2×D411yescharacteristic
295#11745659—42no—
296C8×D59—42no—
297C23×C59—21no—
298C23×C59—21no—
299C23×C59—21no—
300C23×C59—21no—
301C23×C59—41no—
302C23×C59—41no—
303C23×C59—42no—
304C23×C59—42no—
305C23×C59—81no—
306C23×C59C4×D411yescharacteristic
307C23×C59C4×D411yescharacteristic
308C23×C59C2×#4111yescharacteristic
309C22×D59—21no—
310Q8×C59—21no—
311Q8×C59—21no—
312Q8×C59—21no—
313Q8×C59—42no—
314Q8×C59C4×D412yes—
315D4×C59—22no—
316D4×C59—22no—
317D4×C59—21no—
318D4×C59—21no—
319D4×C59—21no—
320D4×C59—42no—
321D4×C59—42no—
322D4×C59—42no—
323D4×C59—41no—
324D4×C59—41no—
325D4×C59C4×D412yes—
326C2×C4×C59—21no—
327C2×C4×C59—21no—
328C2×C4×C59—21no—
329C2×C4×C59—21no—
330C2×C4×C59—21no—
331C2×C4×C59—21no—
332C2×C4×C59—21no—
333C2×C4×C59—22no—
334C2×C4×C59—21no—
335C2×C4×C59—21no—
336C2×C4×C59—22no—
337C2×C4×C59—21no—
338C2×C4×C59—21no—
339C2×C4×C59—21no—
340C2×C4×C59—22no—
341C2×C4×C59—42no—
342C2×C4×C59—42no—
343C2×C4×C59—42no—
344C2×C4×C59—41no—
345C2×C4×C59—41no—
346C2×C4×C59—41no—
347C2×C4×C59—41no—
348C2×C4×C59—41no—
349C2×C4×C59—41no—
350C2×C4×C59—41no—
351C2×C4×C59C4×D411yescharacteristic
352C2×C4×C59C4×D411yescharacteristic
353C2×C4×C59C23×C411yescharacteristic
354C2×C4×C59C22×D411yescharacteristic
355C2×C4×C59C22×D411yescharacteristic
356C2×C4×C59C2×#4111yescharacteristic
357C2×C4×C59H(5,𝔽2)11yescharacteristic
358C2×C4×C59H(5,𝔽2)11yescharacteristic
359C22⋊D59—42no—
360C22⋊D59—41no—
361C22⋊D59—41no—
362C22⋊D59—81no—
363C2×Dic59—21no—
364C2×Dic59—21no—
365C2×Dic59—21no—
366D236—21no—
367D236—21no—
368C4×D59—41no—
369C4×D59—41no—
370Dic118—21no—
371Dic118—21no—
372C8×C59—22no—
373C8×C59—41no—
374C59⋊C8—21no—
375C59⋊C8—21no—
376C59⋊C8—21no—
377C59⋊C8—21no—
378C59⋊C8—21no—
379C59⋊C8—21no—
380C59⋊C8—21no—
381C59⋊C8—21no—
382C59⋊C8—41no—
383C59⋊C8—41no—
384#22889—591nomaximal, Sylow
385C22×C59—21no—
386C22×C59—21no—
387C22×C59—21no—
388C22×C59—21no—
389C22×C59—22no—
390C22×C59—21no—
391C22×C59—21no—
392C22×C59—21no—
393C22×C59—21no—
394C22×C59—41no—
395C22×C59—41no—
396C22×C59—41no—
397C22×C59—41no—
398C22×C59—41no—
399C22×C59—81no—
400C22×C59—81no—
401C22×C59—84no—
402C22×C59C2×C4×D411yescharacteristic
403C22×C59#54611yescharacteristic
404C22×C59#55111yescharacteristic
405C2×D59—41no—
406C2×D59—41no—
407C2×D59—41no—
408C4×C59—21no—
409C4×C59—21no—
410C4×C59—22no—
411C4×C59—42no—
412C4×C59—41no—
413C4×C59—81no—
414C4×C59C2×C4×D411yescharacteristic
415C4×C59#51811yescharacteristic
416C4×C59D4211yescharacteristic
417C4×C59#54611yescharacteristic
418Dic59—41no—
419Dic59—41no—
420Dic59—41no—
421#3002—591no—
422C2×#443—591no—
423#2933—591no—
424C2×#421D5911yescharacteristic, complemented
425#2880—591no—
426#1975—591no—
427#1937—591no—
428#1929—591no—
429#1897—591no—
430#1876—591no—
431#1876—591no—
432#1866—591no—
433#1855—591no—
434#1765—591no—
435#1750—591no—
436C2×C59—21no—
437C2×C59—21no—
438C2×C59—41no—
439C2×C59—41no—
440C2×C59—42no—
441C2×C59—81no—
442C2×C59#235811yescharacteristic
443C2×C59#295511yescharacteristic
444C2×C59#295711yescharacteristic
445D59—81no—
446C22×#41C2×D5911yescharacteristic
447C2×#135—591no—
448C2×#135—591no—
449C2×#131—591no—
450C2×#131—591no—
451C2×#131—591no—
452C22×M16C2×D5911yescharacteristic
453#525—591no—
454C2×#117C2×D5911yescharacteristic
455#452—591no—
456#452—591no—
457#451—591no—
458#450—591no—
459#449—591no—
460#449—591no—
461#448—591no—
462#447—591no—
463#443—1184no—
464#436—1181no—
465#435—1181no—
466#435—1181no—
467C8×D4—1181no—
468C2×#108—591no—
469C2×#108—591no—
470#424—591no—
471#421—24no—
472C2×#104—591no—
473C2×#104—591no—
474C2×#104C2×D5911yescharacteristic
475C2×#104C2×D5911yescharacteristic
476C2×#104C2×D5911yescharacteristic
477C2×#104C2×D5911yescharacteristic
478#416—591no—
479#416—591no—
480#408—591no—
481#408—591no—
482#408—591no—
483#408—1181no—
484#408—1181no—
485#407—591no—
486#407—1181no—
487C2×C22⋊C8—591no—
488C2×C22⋊C8—591no—
489C2×C22⋊C8—1181no—
490#405—591no—
491C2×#97—591no—
492C2×C4×C8—591no—
493#341—591no—
494#341—591no—
495#339—591no—
496#339—591no—
497#336—591no—
498#336—591no—
499C59#2288911yescharacteristic, complemented, Sylow
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—591no—
507C2×#41C4×D5911yescharacteristic
508C2×#41C4×D5911yescharacteristic
509C2×#41C22×D5911yescharacteristic
510C2×#41C22×D5911yescharacteristic
511C22×Q8C4×D5911yescharacteristic
512C22×D4—21no—
513C22×D4C4×D5911yescharacteristic
514C23×C4—21no—
515C23×C4C22×D5911yescharacteristic
516#135—1182no—
517#135—1182no—
518#135—2361no—
519#135—2361no—
520C2×Q16—591no—
521C2×Q16—591no—
522C2×SD16—591no—
523C2×SD16—591no—
524C2×SD16—591no—
525C2×SD16—591no—
526C2×D8—591no—
527C2×D8—591no—
528#131—1182no—
529#131—1182no—
530#131—1182no—
531#131—2361no—
532#131—2361no—
533#131—2361no—
534C2×M16—21no—
535C2×M16—22no—
536C2×M16—41no—
537C2×M16—591no—
538C2×M16—591no—
539C2×M16—1181no—
540C2×M16—1181no—
541C2×M16—1181no—
542C2×M16C22×D5911yescharacteristic
543C2×M16C22×D5911yescharacteristic
544C22×C8—21no—
545C22×C8—591no—
546C22×C8—591no—
547C22×C8—591no—
548C22×C8—591no—
549C22×C8—1181no—
550C22×C8—1181no—
551C22×C8—1181no—
552#123—1181no—
553C22⋊Q8—591no—
554C22⋊Q8—591no—
555#121—591no—
556#121—591no—
557#120—1181no—
558C4×D4—1181no—
559C4×D4—1181no—
560#117—22no—
561#117—41no—
562#117—591no—
563C2×C4⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C42C22×D5911yescharacteristic
566C2×C42C22×D5911yescharacteristic
567#108—1182no—
568#108—2361no—
569C4⋊C8—1181no—
570C4⋊C8—1181no—
571#104—22no—
572#104—22no—
573#104—22no—
574#104—1182no—
575#104—2361no—
576#104C22⋊D5914yescomplemented
577#103—591no—
578#103—591no—
579#103—591no—
580#103—591no—
581#102—591no—
582#102—591no—
583#102—591no—
584#102—591no—
585C22⋊C8—591no—
586C22⋊C8—591no—
587C22⋊C8—591no—
588C22⋊C8—591no—
589C22⋊C8—591no—
590C22⋊C8—591no—
591C22⋊C8—591no—
592C22⋊C8—591no—
593C22⋊C8—1181no—
594C22⋊C8—1181no—
595C22⋊C8—1181no—
596C22⋊C8—1181no—
597C22⋊C8—1181no—
598C22⋊C8—1181no—
599C22⋊C8—1181no—
600C22⋊C8—1181no—
601#97—1181no—
602#97—2361no—
603C4×C8—1181no—
604C4×C8—1182no—
605C24—21no—
606C24#1174568711yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—42no—
616#41—42no—
617#41—41no—
618#41—41no—
619#41—42no—
620#41—42no—
621#41—1181no—
622#41—1181no—
623#41—1181no—
624#41—1181no—
625#41#1174568512yes—
626#41C2×C22⋊D5912yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8—591no—
631C2×Q8C2×C4×D5911yescharacteristic
632C2×Q8C2×C4×D5911yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—41no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—591no—
643C2×D4—1181no—
644C2×D4—1181no—
645C2×D4—1181no—
646C2×D4C2×C4×D5911yescharacteristic
647C2×D4C2×C4×D5911yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—1181no—
662C22×C4C2×C4×D5911yescharacteristic
663C22×C4C2×C4×D5911yescharacteristic
664C22×C4D4×D5911yescharacteristic
665C22×C4D4×D5911yescharacteristic
666C22×C4#1174568711yescharacteristic
667C22×C4C23×D5911yescharacteristic
668Q16—1182no—
669Q16—2361no—
670SD16—1182no—
671SD16—1182no—
672SD16—2361no—
673SD16—2361no—
674D8—1182no—
675D8—2361no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—42no—
680M16—1181no—
681M16—1181no—
682M16—1181no—
683M16—1181no—
684M16—2362no—
685M16—2362no—
686M16—2362no—
687M16C2×C22⋊D5912yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—42no—
691C2×C8—591no—
692C2×C8—591no—
693C2×C8—591no—
694C2×C8—591no—
695C2×C8—591no—
696C2×C8—591no—
697C2×C8—591no—
698C2×C8—591no—
699C2×C8—1181no—
700C2×C8—1181no—
701C2×C8—1181no—
702C2×C8—1181no—
703C2×C8—1181no—
704C2×C8—1181no—
705C2×C8—1181no—
706C2×C8—1181no—
707C2×C8—1181no—
708C2×C8—1181no—
709C2×C8—2362no—
710C2×C8—2362no—
711C2×C8—2362no—
712C4⋊C4—42no—
713C4⋊C4—591no—
714C4⋊C4—591no—
715C4⋊C4—1181no—
716C4⋊C4—1181no—
717C22⋊C4—42no—
718C22⋊C4—1181no—
719C22⋊C4—1181no—
720C22⋊C4—1181no—
721C22⋊C4—1181no—
722C22⋊C4—1181no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—1181no—
727C42C2×C22⋊D5912yes—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—41no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—81no—
737C23—1181no—
738C23(C22⋊D59)⋊C411yescharacteristic
739C23(C22⋊D59)⋊C411yescharacteristic
740C23C2×#1174568711yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—42no—
745Q8—1181no—
746Q8—1181no—
747Q8C4×C22⋊D5912yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—42no—
754D4—42no—
755D4—42no—
756D4—41no—
757D4—41no—
758D4—1181no—
759D4—1181no—
760D4—4721no—
761D4—2362no—
762D4—2361no—
763D4—2361no—
764D4C4×C22⋊D5912yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—1181no—
791C2×C4—1181no—
792C2×C4—1181no—
793C2×C4—2361no—
794C2×C4—2361no—
795C2×C4(C22⋊D59)⋊C411yescharacteristic
796C2×C4(C22⋊D59)⋊C411yescharacteristic
797C2×C4C22×C4×D5911yescharacteristic
798C2×C4C2×D4×D5911yescharacteristic
799C2×C4C22×C22⋊D5911yescharacteristic
800C2×C4C2×#1174568511yescharacteristic
801C2×C4#1427377211yescharacteristic
802C2×C4#1427377211yescharacteristic
803C8—22no—
804C8—41no—
805C8—1181no—
806C8—1181no—
807C8—1181no—
808C8—1181no—
809C8—1181no—
810C8—1181no—
811C8—1181no—
812C8—1181no—
813C8—2361no—
814C8—2361no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—81no—
830C22—81no—
831C22—84no—
832C22—2361no—
833C22—2361no—
834C22—2361no—
835C22C2×(C22⋊D59)⋊C411yescharacteristic
836C22#1683804611yescharacteristic
837C22#1683807811yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—42no—
842C4—41no—
843C4—81no—
844C4—2361no—
845C4—2361no—
846C4—2361no—
847C4C2×C4×C22⋊D5911yescharacteristic
848C4#1683787511yescharacteristic
849C4D4×C22⋊D5911yescharacteristic
850C4#1683804211yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—4721no—
858C2#2142707511yescharacteristic
859C2#2143299511yescharacteristic
860C2#2143300911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#421C2
socleC22×C59C2×C4×D4
prime radical#21433314C2
cosocleC22×C4×C59C24
hypercenterC2×#421D59
hypocenterC59#22889
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#16837516C2semidirect
3. #21432821C2semidirect
4. #21432545C2semidirect
5. #21424986C2semidirect
6. #21424797C2semidirect
7. #21424747C2semidirect
8. #21424544C2semidirect
9. #21424421C2semidirect
10. #21424420C2semidirect
11. #21424369C2semidirect
12. #21424301C2semidirect
13. #21423941C2semidirect
14. #21423862C2semidirect
15. C2×C59×#421C2semidirect
18. C2×#14273735C22semidirect
22. #16837564C4semidirect
23. #16837564C4semidirect
24. #16837558C4semidirect
25. #16837553C4semidirect
26. #16837547C4semidirect
27. #16837547C4semidirect
28. #16837541C4semidirect
29. #16837536C4semidirect
35. C2×#14273662C22semidirect
36. C2×#14273662C22semidirect
37. #16837430C22semidirect
38. C2×#14273655C22semidirect
39. C2×#14273655C22semidirect
42. #16837370C22semidirect
52. #16837360C22semidirect
53. C2×#14273638C22semidirect
54. C2×C4×C59⋊C8C22semidirect
55. #16837166C22semidirect
56. #16837166C22semidirect
57. #16837162C22semidirect
58. #16837162C22semidirect
59. #16837157C22semidirect
60. #16837157C22semidirect
173. #104×C59D4semidirect
424. C2×#421D59semidirect
499. C59#22889semidirect
576. #104C22⋊D59semidirect

Maximal subgroups

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

subgroupindex
#214333142
C2×#168375162
#214328212
#214325452
#214249862
#214247972
#214247472
#214245442
#214244212
#214244202
#214243692
#214243012
#214239412
#214238622
C2×C59×#4212
#2288959