Finite Group Databasebeta

← #28517565

Subgroups — #28517565

Order 15104.

1406 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837291C211yesmaximal, characteristic
2#21422362C211yesmaximal, characteristic, complemented
3#21422357C211yesmaximal, characteristic, complemented
4#21422353C211yesmaximal, characteristic, complemented
5#21422352C211yesmaximal, characteristic, complemented
6#21422344C211yesmaximal, characteristic
7#21422342C211yesmaximal, characteristic
8#21422334C211yesmaximal, characteristic
9#21422329C211yesmaximal, characteristic, complemented
10#21422322C211yesmaximal, characteristic, complemented
11#21422320C211yesmaximal, characteristic, complemented
12(C2×D59)⋊#95C211yesmaximal, characteristic
13(C2×D59)⋊#95C211yesmaximal, characteristic
14(C2×D59)⋊#95C211yesmaximal, characteristic
15C59×#1434C211yesmaximal, characteristic, complemented
16C23×C4×D59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×Dic59⋊C4C2211yescharacteristic
19C22×(C2×D59)⋊C4C2211yescharacteristic
20C22×(C2×D59)⋊C4C2211yescharacteristic
21C22×(C2×D59)⋊C4C2211yescharacteristic
22C22×(C2×D59)⋊C4C2211yescharacteristic
23C22×(C2×D59)⋊C4C2211yescharacteristic
24C22×(C2×D59)⋊C4C2211yescharacteristic
25C22×C4×Dic59C2211yescharacteristic
26#16837291C418yescomplemented
27C2×C59⋊#95C2211yescharacteristic
28C2×C59⋊#95C2211yescharacteristic
29C2×C59⋊#95C2211yescharacteristic
30C2×C59⋊#95C2211yescharacteristic
31C2×C59⋊#95C2211yescharacteristic
32C2×C59⋊#95C2211yescharacteristic
33C2×C59⋊#95C2211yescharacteristic
34C2×C59⋊#95C2211yescharacteristic
35C2×C59⋊#95C2211yescharacteristic
36C2×C59⋊#95C2211yescharacteristic
37C2×C59⋊#95C2211yescharacteristic
38C2×C59⋊#95C2211yescharacteristic
39C2×C59⋊#95C2211yescharacteristic
40C2×C59⋊#95C2211yescharacteristic
41C2×C59⋊#95C2211yescharacteristic
42C2×C59⋊#95C2211yescharacteristic
43C2×C59⋊#95C2211yescharacteristic
44C2×C59⋊#95C2211yescharacteristic
45C22×C42×C59C2211yescharacteristic
46C2×#95×C59C2211yescharacteristic
47C2×#95×C59C2211yescharacteristic
48C2×#95×C59C2211yescharacteristic
49C2×#95×C59C2211yescharacteristic
50C2×#95×C59C2211yescharacteristic
51C2×#95×C59C2211yescharacteristic
52C24×D59C2311yescharacteristic
53C23×Dic59C2311yescharacteristic
54C23×Dic59C2311yescharacteristic
55C23×Dic59C2311yescharacteristic
56C23×Dic59C2311yescharacteristic
57C23×Dic59C2311yescharacteristic
58C23×Dic59C2311yescharacteristic
59C23×Dic59C2311yescharacteristic
60C22×C4×D59—22no—
61C22×C4×D59—22no—
62C22×C4×D59—22no—
63C22×C4×D59—41no—
64C22×C4×D59—41no—
65C22×C4×D59—41no—
66C22×C4×D59—41no—
67C2×C4⋊Dic59—41no—
68C2×C4⋊Dic59—41no—
69C2×C4⋊Dic59—41no—
70C2×Dic59⋊C4—41no—
71C2×Dic59⋊C4—41no—
72C2×Dic59⋊C4C2×C414yescomplemented
73C2×(C2×D59)⋊C4—22no—
74C2×(C2×D59)⋊C4—22no—
75C2×(C2×D59)⋊C4—22no—
76C2×(C2×D59)⋊C4—22no—
77C2×(C2×D59)⋊C4—22no—
78C2×(C2×D59)⋊C4—22no—
79C2×(C2×D59)⋊C4—22no—
80C2×(C2×D59)⋊C4—41no—
81C2×(C2×D59)⋊C4—41no—
82C2×(C2×D59)⋊C4—41no—
83C2×(C2×D59)⋊C4—41no—
84C2×(C2×D59)⋊C4—41no—
85C2×(C2×D59)⋊C4—41no—
86C2×(C2×D59)⋊C4—41no—
87C2×(C2×D59)⋊C4—41no—
88C2×(C2×D59)⋊C4C2×C414yes—
89C2×(C2×D59)⋊C4C2×C414yes—
90C2×(C2×D59)⋊C4C2×C414yes—
91C2×C4×Dic59—41no—
92C2×C4×Dic59—41no—
93C2×C4×Dic59C2×C414yescomplemented
94C59⋊#95—22no—
95C59⋊#95—22no—
96C59⋊#95—22no—
97C59⋊#95—22no—
98C59⋊#95—22no—
99C59⋊#95—22no—
100C59⋊#95—41no—
101C59⋊#95—41no—
102C59⋊#95—41no—
103C59⋊#95—41no—
104C59⋊#95—41no—
105C59⋊#95—41no—
106C59⋊#95—41no—
107C59⋊#95—41no—
108C59⋊#95—41no—
109C59⋊#95—41no—
110C59⋊#95—41no—
111C59⋊#95C2×C414yescomplemented
112C23×C4×C59C2311yescharacteristic
113C23×C4×C59C2311yescharacteristic
114C23×C4×C59C2311yescharacteristic
115C23×C4×C59C2311yescharacteristic
116C23×C4×C59C2311yescharacteristic
117C23×C4×C59C2311yescharacteristic
118C23×C4×C59C2311yescharacteristic
119C2×C42×C59—22no—
120C2×C42×C59—41no—
121C2×C42×C59—41no—
122#95×C59—22no—
123#95×C59—41no—
124#95×C59—41no—
125#95×C59—41no—
126#95×C59—41no—
127#95×C59C2×C414yescomplemented
128C24×C59C2411yescharacteristic
129C23×D59—21no—
130C23×D59—21no—
131C23×D59—21no—
132C23×D59—21no—
133C23×D59—21no—
134C23×D59—21no—
135C23×D59—21no—
136C23×D59—21no—
137C23×D59—21no—
138C23×D59—21no—
139C23×D59—21no—
140C23×D59—21no—
141C23×D59C22×C412yes—
142C23×D59#4112yes—
143C23×D59#4112yes—
144C22×C4×C59—21no—
145C22×C4×C59—21no—
146C22×C4×C59—21no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59C22×C412yes—
188C22×C4×C59C22×C412yes—
189C22×C4×C59C22×C412yes—
190C22×C4×C59#4112yes—
191C22×C4×C59#4112yes—
192C22×C4×C59#4112yes—
193C22×Dic59—21no—
194C22×Dic59—21no—
195C22×Dic59—21no—
196C22×Dic59—21no—
197C22×Dic59—21no—
198C22×Dic59—21no—
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C22×Dic59—21no—
217C22×Dic59—21no—
218C22×Dic59—21no—
219C22×Dic59—21no—
220C22×Dic59—21no—
221C22×Dic59—21no—
222C22×Dic59—21no—
223C22×Dic59—21no—
224C22×Dic59—21no—
225C22×Dic59—21no—
226C22×Dic59—21no—
227C22×Dic59—21no—
228C22×Dic59—21no—
229C22×Dic59—21no—
230C22×Dic59—21no—
231C22×Dic59—21no—
232C22×Dic59—21no—
233C22×Dic59—21no—
234C22×Dic59—21no—
235C22×Dic59—21no—
236C22×Dic59—21no—
237C22×Dic59—21no—
238C22×Dic59C22×C412yes—
239C22×Dic59C22×C412yes—
240C22×Dic59C22×C412yes—
241C22×Dic59#4112yes—
242C2×C4×D59—44no—
243C2×C4×D59—44no—
244C2×C4×D59—44no—
245C2×C4×D59—44no—
246C2×C4×D59—44no—
247C2×C4×D59—44no—
248C2×C4×D59—44no—
249C42×C59—44no—
250(C2×D59)⋊C4—28no—
251(C2×D59)⋊C4—44no—
252(C2×D59)⋊C4—44no—
253(C2×D59)⋊C4—44no—
254(C2×D59)⋊C4—44no—
255(C2×D59)⋊C4—44no—
256C4⋊Dic59—44no—
257Dic59⋊C4—44no—
258C4×Dic59—44no—
259C23×C59C23×C411yescharacteristic
260C23×C59C2×#4111yescharacteristic
261C23×C59C2×#4111yescharacteristic
262C23×C59C2×#4111yescharacteristic
263C23×C59C2×#4111yescharacteristic
264C23×C59C2×#4111yescharacteristic
265C23×C59C2×#4111yescharacteristic
266C23×C59H(5,𝔽2)11yescharacteristic
267C23×C59H(5,𝔽2)11yescharacteristic
268C23×C59H(5,𝔽2)11yescharacteristic
269C23×C59H(5,𝔽2)11yescharacteristic
270C23×C59H(5,𝔽2)11yescharacteristic
271C23×C59H(5,𝔽2)11yescharacteristic
272C23×C592−1+411yescharacteristic
273C23×C592−1+411yescharacteristic
274C22×D59—22no—
275C22×D59—22no—
276C22×D59—22no—
277C22×D59—22no—
278C22×D59—22no—
279C22×D59—22no—
280C22×D59—22no—
281C22×D59—22no—
282C22×D59—22no—
283C22×D59—22no—
284C22×D59—22no—
285C22×D59—22no—
286C22×D59—22no—
287C22×D59—22no—
288C22×D59—22no—
289C22×D59—22no—
290C22×D59—22no—
291C22×D59—22no—
292C22×D59—41no—
293C22×D59—41no—
294C22×D59—41no—
295C22×D59—41no—
296C22×D59—41no—
297C22×D59—41no—
298C22×D59—41no—
299C22×D59—41no—
300C22×D59—41no—
301C22×D59—41no—
302C22×D59—41no—
303C22×D59—41no—
304C22×D59—41no—
305C22×D59—41no—
306C22×D59—41no—
307C22×D59—41no—
308C22×D59#11714yes—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—22no—
318C2×C4×C59—22no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
323C2×C4×C59—22no—
324C2×C4×C59—22no—
325C2×C4×C59—22no—
326C2×C4×C59—22no—
327C2×C4×C59—41no—
328C2×C4×C59—41no—
329C2×C4×C59—41no—
330C2×C4×C59—41no—
331C2×C4×C59—41no—
332C2×C4×C59—41no—
333C2×C4×C59—41no—
334C2×C4×C59—41no—
335C2×C4×C59—41no—
336C2×C4×C59—41no—
337C2×C4×C59—41no—
338C2×C4×C59—41no—
339C2×C4×C59—41no—
340C2×C4×C59—41no—
341C2×C4×C59—41no—
342C2×C4×C59—41no—
343C2×C4×C59—41no—
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×C59—41no—
352C2×C4×C59—41no—
353C2×C4×C59—41no—
354C2×C4×C59—41no—
355C2×C4×C59—41no—
356C2×C4×C59—41no—
357C2×C4×C59—41no—
358C2×Dic59—22no—
359C2×Dic59—22no—
360C2×Dic59—22no—
361C2×Dic59—22no—
362C2×Dic59—22no—
363C2×Dic59—22no—
364C2×Dic59—22no—
365C2×Dic59—22no—
366C2×Dic59—22no—
367C2×Dic59—22no—
368C2×Dic59—22no—
369C2×Dic59—22no—
370C2×Dic59—41no—
371C2×Dic59—41no—
372C2×Dic59—41no—
373C2×Dic59—41no—
374C2×Dic59—41no—
375C2×Dic59—41no—
376C2×Dic59—41no—
377C2×Dic59—41no—
378C2×Dic59—41no—
379C2×Dic59—41no—
380C2×Dic59—41no—
381C2×Dic59—41no—
382C2×Dic59—41no—
383C2×Dic59—41no—
384C2×Dic59—41no—
385C2×Dic59—41no—
386C2×Dic59—41no—
387C2×Dic59—41no—
388C2×Dic59—41no—
389C2×Dic59—41no—
390C2×Dic59—41no—
391C2×Dic59—41no—
392C2×Dic59—41no—
393C2×Dic59—41no—
394C2×Dic59—41no—
395C2×Dic59—41no—
396C2×Dic59—41no—
397C2×Dic59—41no—
398C2×Dic59—41no—
399C2×Dic59—41no—
400C2×Dic59—41no—
401C2×Dic59—41no—
402C2×Dic59—41no—
403C2×Dic59—41no—
404C2×Dic59—41no—
405C2×Dic59—41no—
406C2×Dic59—41no—
407C4×D59—416no—
408#14481—591nomaximal, Sylow
409C22×C59C2×#11711yescharacteristic
410C22×C59C4×#4111yescharacteristic
411C22×C59C4×#4111yescharacteristic
412C22×C59#51811yescharacteristic
413C22×C59#51811yescharacteristic
414C22×C59#52011yescharacteristic
415C22×C59#52011yescharacteristic
416C22×C59#53811yescharacteristic
417C22×C59#53811yescharacteristic
418C22×C59#53811yescharacteristic
419C22×C59#53811yescharacteristic
420C22×C59#53811yescharacteristic
421C22×C59#53911yescharacteristic
422C22×C59#53911yescharacteristic
423C22×C59#53911yescharacteristic
424C22×C59#54011yescharacteristic
425C22×C59#54011yescharacteristic
426C22×C59#54011yescharacteristic
427C22×C59#54211yescharacteristic
428C22×C59#55111yescharacteristic
429C22×C59#55111yescharacteristic
430C22×C59#55111yescharacteristic
431C22×C59#55111yescharacteristic
432C22×C59#55111yescharacteristic
433C22×C59#55211yescharacteristic
434C22×C59#55211yescharacteristic
435C22×C59#55211yescharacteristic
436C22×C59#55311yescharacteristic
437C22×C59#55311yescharacteristic
438C22×C59#55311yescharacteristic
439C22×C59#55611yescharacteristic
440C22×C59H(3,𝔽4)11yescharacteristic
441C22×C59#56211yescharacteristic
442C22×C59#56211yescharacteristic
443C22×C59#56311yescharacteristic
444C2×D59—24no—
445C2×D59—24no—
446C2×D59—24no—
447C2×D59—42no—
448C2×D59—42no—
449C2×D59—42no—
450C2×D59—42no—
451C2×D59—42no—
452C2×D59—42no—
453C2×D59—42no—
454C2×D59—42no—
455C2×D59—42no—
456C2×D59—42no—
457C2×D59—42no—
458C2×D59—42no—
459C4×C59—42no—
460C4×C59—42no—
461C4×C59—42no—
462C4×C59—42no—
463C4×C59—42no—
464C4×C59—42no—
465C4×C59—81no—
466Dic59—42no—
467Dic59—42no—
468Dic59—42no—
469Dic59—42no—
470Dic59—81no—
471Dic59—81no—
472Dic59—81no—
473C2×#388—591no—
474#1445—591no—
475#1443—591no—
476#1442—591no—
477#1442—591no—
478#1440—591no—
479#1439—591no—
480#1437—591no—
481#1436—591no—
482#1434—591no—
483#1434—591no—
484#1434D5911yescharacteristic, complemented
485C22⋊#95—591no—
486C22⋊#95—591no—
487C22⋊#95—591no—
488C2×C59#231811yescharacteristic
489C2×C59#233311yescharacteristic
490C2×C59#233511yescharacteristic
491C2×C59#234311yescharacteristic
492C2×C59#235311yescharacteristic
493C2×C59#237311yescharacteristic
494C2×C59#237911yescharacteristic
495C2×C59#273611yescharacteristic
496C2×C59#273811yescharacteristic
497C2×C59#274011yescharacteristic
498C2×C59#274111yescharacteristic
499C2×C59#275011yescharacteristic
500C2×C59#275011yescharacteristic
501C2×C59#275311yescharacteristic
502C2×C59#278711yescharacteristic
503D59—44no—
504C24×C4—591no—
505C22×C4⋊C4—591no—
506C22×C4⋊C4—591no—
507C22×C22⋊C4—591no—
508C22×C22⋊C4—591no—
509C22×C22⋊C4—591no—
510C22×C22⋊C4—591no—
511C22×C22⋊C4—591no—
512C22×C22⋊C4—591no—
513C22×C42—591no—
514C22×C42C2×D5911yescharacteristic
515#388—598no—
516C2×#95—591no—
517C2×#95—591no—
518C2×#95—591no—
519C2×#95—591no—
520C2×#95—591no—
521C2×#95—591no—
522C2×#95—591no—
523C2×#95—591no—
524C2×#95—591no—
525C2×#95—591no—
526C2×#95—591no—
527C2×#95—591no—
528C2×#95—591no—
529C2×#95—591no—
530C2×#95—591no—
531C2×#95—591no—
532C2×#95—591no—
533C2×#95—591no—
534C2×#95C2×D5911yescharacteristic
535C2×#95C2×D5911yescharacteristic
536C2×#95C2×D5911yescharacteristic
537C2×#95C2×D5911yescharacteristic
538C2×#95C2×D5911yescharacteristic
539C2×#95C2×D5911yescharacteristic
540C59#1448111yescharacteristic, complemented, Sylow
541C25—591no—
542C23×C4—591no—
543C23×C4—591no—
544C23×C4—591no—
545C23×C4—591no—
546C23×C4—591no—
547C23×C4—591no—
548C23×C4—591no—
549C23×C4—1182no—
550C23×C4—1182no—
551C23×C4—1182no—
552C23×C4—2361no—
553C23×C4—2361no—
554C23×C4—2361no—
555C23×C4—2361no—
556C23×C4C22×D5911yescharacteristic
557C23×C4C22×D5911yescharacteristic
558C23×C4C22×D5911yescharacteristic
559C23×C4C22×D5911yescharacteristic
560C23×C4C22×D5911yescharacteristic
561C23×C4C22×D5911yescharacteristic
562C23×C4C22×D5911yescharacteristic
563C2×C4⋊C4—594no—
564C2×C4⋊C4—2361no—
565C2×C4⋊C4—2361no—
566C2×C4⋊C4—2361no—
567C2×C4⋊C4—2361no—
568C2×C4⋊C4—2361no—
569C2×C22⋊C4—594no—
570C2×C22⋊C4—594no—
571C2×C22⋊C4—594no—
572C2×C22⋊C4—1182no—
573C2×C22⋊C4—1182no—
574C2×C22⋊C4—1182no—
575C2×C22⋊C4—1182no—
576C2×C22⋊C4—1182no—
577C2×C22⋊C4—1182no—
578C2×C22⋊C4—1182no—
579C2×C22⋊C4—2361no—
580C2×C22⋊C4—2361no—
581C2×C22⋊C4—2361no—
582C2×C22⋊C4—2361no—
583C2×C22⋊C4—2361no—
584C2×C22⋊C4—2361no—
585C2×C22⋊C4—2361no—
586C2×C22⋊C4—2361no—
587C2×C42—22no—
588C2×C42—41no—
589C2×C42—41no—
590C2×C42—594no—
591C2×C42—2361no—
592C2×C42—2361no—
593#95—22no—
594#95—41no—
595#95—41no—
596#95—41no—
597#95—41no—
598#95—594no—
599#95—1182no—
600#95—1182no—
601#95—1182no—
602#95—1182no—
603#95—1182no—
604#95—1182no—
605#95—2361no—
606#95—2361no—
607#95—2361no—
608#95—2361no—
609#95—2361no—
610#95—2361no—
611#95—2361no—
612#95—2361no—
613#95—2361no—
614#95—2361no—
615#95—2361no—
616#95C4×D5914yescomplemented
617C24—592no—
618C24—592no—
619C24—592no—
620C24—1181no—
621C24—1181no—
622C24—1181no—
623C24—1181no—
624C24—1181no—
625C24—1181no—
626C24—1181no—
627C24—1181no—
628C24—1181no—
629C24—1181no—
630C24—1181no—
631C24—1181no—
632C24C23×D5911yescharacteristic
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
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—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—592no—
677C22×C4—592no—
678C22×C4—592no—
679C22×C4—592no—
680C22×C4—1181no—
681C22×C4—1181no—
682C22×C4—1181no—
683C22×C4—1181no—
684C22×C4—1181no—
685C22×C4—1181no—
686C22×C4—1181no—
687C22×C4—1181no—
688C22×C4—1181no—
689C22×C4—1181no—
690C22×C4—1181no—
691C22×C4—1181no—
692C22×C4—1181no—
693C22×C4—1181no—
694C22×C4—1181no—
695C22×C4—1181no—
696C22×C4—1181no—
697C22×C4—1181no—
698C22×C4—1181no—
699C22×C4—1181no—
700C22×C4—1181no—
701C22×C4—1181no—
702C22×C4—1181no—
703C22×C4—1181no—
704C22×C4—1181no—
705C22×C4—1181no—
706C22×C4—1181no—
707C22×C4—1181no—
708C22×C4—1181no—
709C22×C4—1181no—
710C22×C4—1181no—
711C22×C4—1181no—
712C22×C4—1181no—
713C22×C4—1181no—
714C22×C4—1181no—
715C22×C4—1181no—
716C22×C4—1181no—
717C22×C4—1181no—
718C22×C4—1181no—
719C22×C4—1181no—
720C22×C4—1181no—
721C22×C4—1181no—
722C22×C4—1181no—
723C22×C4—1181no—
724C22×C4—1181no—
725C22×C4—2364no—
726C22×C4—2364no—
727C22×C4—2364no—
728C22×C4—2364no—
729C22×C4—2364no—
730C22×C4—2364no—
731C22×C4—2364no—
732C22×C4C2×C4×D5912yes—
733C22×C4C2×C4×D5912yes—
734C22×C4C2×C4×D5912yes—
735C22×C4#1174568512yes—
736C22×C4#1174568512yes—
737C22×C4#1174568912yes—
738C4⋊C4—2364no—
739C4⋊C4—2364no—
740C22⋊C4—1188no—
741C22⋊C4—2364no—
742C22⋊C4—2364no—
743C22⋊C4—2364no—
744C22⋊C4—2364no—
745C22⋊C4—2364no—
746C42—44no—
747C42—2364no—
748C23—594no—
749C23—1182no—
750C23—1182no—
751C23—1182no—
752C23—1182no—
753C23—1182no—
754C23—1182no—
755C23—1182no—
756C23—1182no—
757C23—1182no—
758C23—1182no—
759C23—1182no—
760C23—1182no—
761C23—1182no—
762C23—1182no—
763C23—1182no—
764C23—1182no—
765C23—1182no—
766C23—1182no—
767C23—2361no—
768C23—2361no—
769C23—2361no—
770C23—2361no—
771C23—2361no—
772C23—2361no—
773C23—2361no—
774C23—2361no—
775C23—2361no—
776C23—2361no—
777C23—2361no—
778C23—2361no—
779C23—2361no—
780C23—2361no—
781C23—2361no—
782C23—2361no—
783C23C22×C4×D5911yescharacteristic
784C23#41×D5911yescharacteristic
785C23#41×D5911yescharacteristic
786C23#41×D5911yescharacteristic
787C23C2×#1174568511yescharacteristic
788C23C2×#1174568511yescharacteristic
789C23C2×#1174568911yescharacteristic
790C23#1427377211yescharacteristic
791C23#1427377211yescharacteristic
792C23#1427377211yescharacteristic
793C23#1427377311yescharacteristic
794C23#1427377311yescharacteristic
795C23#1427377311yescharacteristic
796C23#1427377411yescharacteristic
797C23#1427377411yescharacteristic
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—1182no—
848C2×C4—1182no—
849C2×C4—1182no—
850C2×C4—1182no—
851C2×C4—1182no—
852C2×C4—1182no—
853C2×C4—1182no—
854C2×C4—1182no—
855C2×C4—1182no—
856C2×C4—1182no—
857C2×C4—1182no—
858C2×C4—1182no—
859C2×C4—23616no—
860C2×C4—2361no—
861C2×C4—2361no—
862C2×C4—2361no—
863C2×C4—2361no—
864C2×C4—2361no—
865C2×C4—2361no—
866C2×C4—2361no—
867C2×C4—2361no—
868C2×C4—2361no—
869C2×C4—2361no—
870C2×C4—2361no—
871C2×C4—2361no—
872C2×C4—2361no—
873C2×C4—2361no—
874C2×C4—2361no—
875C2×C4—2361no—
876C2×C4—2361no—
877C2×C4—2361no—
878C2×C4—2361no—
879C2×C4—2361no—
880C2×C4—2361no—
881C2×C4—2361no—
882C2×C4—2361no—
883C2×C4—2361no—
884C2×C4—2361no—
885C2×C4—2361no—
886C2×C4—2361no—
887C2×C4—2361no—
888C2×C4—2361no—
889C2×C4—2361no—
890C2×C4—2361no—
891C2×C4—2361no—
892C2×C4—2361no—
893C2×C4—2361no—
894C2×C4—2361no—
895C2×C4—2361no—
896C2×C4—2361no—
897C22—1184no—
898C22—1184no—
899C22—1184no—
900C22—2362no—
901C22—2362no—
902C22—2362no—
903C22—2362no—
904C22—2362no—
905C22—2362no—
906C22—2362no—
907C22—2362no—
908C22—2362no—
909C22—2362no—
910C22—2362no—
911C22—2362no—
912C22#117×D5911yescharacteristic
913C22C4×#1174568511yescharacteristic
914C22C4×#1174568911yescharacteristic
915C22#1683787411yescharacteristic
916C22#1683787411yescharacteristic
917C22#1683788111yescharacteristic
918C22#1683788211yescharacteristic
919C22#1683798411yescharacteristic
920C22#1683798511yescharacteristic
921C22#1683798611yescharacteristic
922C22#1683798811yescharacteristic
923C22#1683799011yescharacteristic
924C22#1683799311yescharacteristic
925C22#1683799511yescharacteristic
926C22#1683800111yescharacteristic
927C22#1683800311yescharacteristic
928C22#1683800711yescharacteristic
929C22#1683800811yescharacteristic
930C22#1683801811yescharacteristic
931C22#1683807611yescharacteristic
932C22#1683807611yescharacteristic
933C22#1683807711yescharacteristic
934C22#1683807911yescharacteristic
935C22#1683808111yescharacteristic
936C22#1683808511yescharacteristic
937C22#1683809111yescharacteristic
938C22#1683809111yescharacteristic
939C22#1683809711yescharacteristic
940C22#1683810011yescharacteristic
941C22#1683810511yescharacteristic
942C22#1683812511yescharacteristic
943C22#1683814411yescharacteristic
944C22#1683814711yescharacteristic
945C22#1683814911yescharacteristic
946C22#1683815411yescharacteristic
947C4—42no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—42no—
953C4—81no—
954C4—4721no—
955C4—4721no—
956C4—4721no—
957C4—2362no—
958C4—2362no—
959C4—2362no—
960C4—2362no—
961C2—2364no—
962C2#2142672611yescharacteristic
963C2#2142685611yescharacteristic
964C2#2142688511yescharacteristic
965C2#2142695711yescharacteristic
966C2#2142703511yescharacteristic
967C2#2142721011yescharacteristic
968C2#2142726511yescharacteristic
969C2#2143114111yescharacteristic
970C2#2143116711yescharacteristic
971C2#2143119111yescharacteristic
972C2#2143121411yescharacteristic
973C2#2143133011yescharacteristic
974C2#2143133511yescharacteristic
975C2#2143136911yescharacteristic
976C2#2143182511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×#1434C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenter#1434D59
hypocenterC59#14481
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. #21422362C2semidirect
3. #21422357C2semidirect
4. #21422353C2semidirect
5. #21422352C2semidirect
9. #21422329C2semidirect
10. #21422322C2semidirect
11. #21422320C2semidirect
15. C59×#1434C2semidirect
26. #16837291C4semidirect
72. C2×Dic59⋊C4C2×C4semidirect
93. C2×C4×Dic59C2×C4semidirect
111. C59⋊#95C2×C4semidirect
127. #95×C59C2×C4semidirect
484. #1434D59semidirect
540. C59#14481semidirect
616. #95C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168372912
#214223622
#214223572
#214223532
#214223522
#214223442
#214223422
#214223342
#214223292
#214223222
#214223202
(C2×D59)⋊#952
C59×#14342
#1448159