Finite Group Databasebeta

← #28519478

Subgroups — #28519478

Order 15104.

1442 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837315C211yesmaximal, characteristic
2#21422366C211yesmaximal, characteristic, complemented
3#21422366C211yesmaximal, characteristic, complemented
4#21422355C211yesmaximal, characteristic, complemented
5#21422354C211yesmaximal, characteristic, complemented
6#21422353C211yesmaximal, characteristic, complemented
7#21422352C211yesmaximal, characteristic, complemented
8#21422351C211yesmaximal, characteristic, complemented
9#21422342C211yesmaximal, characteristic
10#21422340C211yesmaximal, characteristic
11#21422338C211yesmaximal, characteristic
12(C2×D59)⋊#95C211yesmaximal, characteristic
13(C2×D59)⋊#95C211yesmaximal, characteristic
14(C2×D59)⋊#95C211yesmaximal, characteristic
15C59×#1442C211yesmaximal, characteristic, complemented
16C23×Dic118C2211yescharacteristic
17C23×C4×D59C2211yescharacteristic
18C22×C4⋊Dic59C2211yescharacteristic
19C22×Dic59⋊C4C2211yescharacteristic
20C22×(C2×D59)⋊C4C2211yescharacteristic
21C22×(C2×D59)⋊C4C2211yescharacteristic
22C22×(C2×D59)⋊C4C2211yescharacteristic
23C22×(C2×D59)⋊C4C2211yescharacteristic
24C22×(C2×D59)⋊C4C2211yescharacteristic
25C22×(C2×D59)⋊C4C2211yescharacteristic
26#16837315C418yescomplemented
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×C4⋊C4×C59C2211yescharacteristic
46C2×#95×C59C2211yescharacteristic
47C2×#95×C59C2211yescharacteristic
48C2×#95×C59C2211yescharacteristic
49C2×#95×C59C2211yescharacteristic
50C2×#95×C59C2211yescharacteristic
51C2×#95×C59C2211yescharacteristic
52C24×D59C2311yescharacteristic
53C22×Dic118—41no—
54C22×Dic118—41no—
55C22×Dic118—41no—
56C22×Dic118—41no—
57C22×Dic118—41no—
58C22×Dic118—41no—
59C22×Dic118C2×C414yescomplemented
60C23×Dic59C2311yescharacteristic
61C23×Dic59C2311yescharacteristic
62C23×Dic59C2311yescharacteristic
63C23×Dic59C2311yescharacteristic
64C23×Dic59C2311yescharacteristic
65C23×Dic59C2311yescharacteristic
66C23×Dic59C2311yescharacteristic
67C22×C4×D59—41no—
68C22×C4×D59—41no—
69C22×C4×D59—41no—
70C22×C4×D59—41no—
71C22×C4×D59—41no—
72C22×C4×D59—41no—
73C22×C4×D59Q814yescomplemented
74C2×C4⋊Dic59—41no—
75C2×C4⋊Dic59—41no—
76C2×C4⋊Dic59—41no—
77C2×Dic59⋊C4—41no—
78C2×Dic59⋊C4—41no—
79C2×Dic59⋊C4—41no—
80C2×(C2×D59)⋊C4—22no—
81C2×(C2×D59)⋊C4—22no—
82C2×(C2×D59)⋊C4—22no—
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)⋊C4—41no—
89C2×(C2×D59)⋊C4—41no—
90C2×(C2×D59)⋊C4—41no—
91C2×(C2×D59)⋊C4—41no—
92C2×(C2×D59)⋊C4—41no—
93C2×(C2×D59)⋊C4—41no—
94C2×(C2×D59)⋊C4—41no—
95C2×(C2×D59)⋊C4C2×C414yes—
96C2×(C2×D59)⋊C4C2×C414yes—
97C2×(C2×D59)⋊C4C2×C414yes—
98C59⋊#95—41no—
99C59⋊#95—41no—
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⋊#95—41no—
112C59⋊#95—41no—
113C59⋊#95—41no—
114C59⋊#95C2×C414yescomplemented
115C59⋊#95C2×C414yescomplemented
116C23×C4×C59C2311yescharacteristic
117C23×C4×C59C2311yescharacteristic
118C23×C4×C59C2311yescharacteristic
119C23×C4×C59C2311yescharacteristic
120C23×C4×C59C2311yescharacteristic
121C23×C4×C59C2311yescharacteristic
122C23×C4×C59C2311yescharacteristic
123C2×C4⋊C4×C59—41no—
124C2×C4⋊C4×C59—41no—
125C2×C4⋊C4×C59—41no—
126#95×C59—41no—
127#95×C59—41no—
128#95×C59—41no—
129#95×C59—41no—
130#95×C59—41no—
131#95×C59C2×C414yescomplemented
132C24×C59C2411yescharacteristic
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×D59—21no—
142C23×D59—21no—
143C23×D59—21no—
144C23×D59—21no—
145C23×D59C22×C412yes—
146C23×D59C2×Q812yes—
147C23×D59#4112yes—
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×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59C22×C412yes—
194C22×C4×C59C22×C412yes—
195C22×C4×C59C22×C412yes—
196C22×C4×C59C2×Q812yes—
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×Dic59—21no—
239C22×Dic59—21no—
240C22×Dic59—21no—
241C22×Dic59—21no—
242C22×Dic59C22×C412yes—
243C22×Dic59C22×C412yes—
244C22×Dic59C22×C412yes—
245C22×Dic59C2×Q812yes—
246C2×C4×D59—44no—
247C2×C4×D59—44no—
248C2×C4×D59—44no—
249C2×C4×D59—44no—
250C2×C4×D59—44no—
251C2×C4×D59—44no—
252C2×C4×D59—44no—
253C2×Dic118—44no—
254C2×Dic118—44no—
255C2×Dic118—44no—
256C2×Dic118—44no—
257C2×Dic118—44no—
258C2×Dic118—44no—
259C2×Dic118—44no—
260C4⋊C4×C59—44no—
261(C2×D59)⋊C4—44no—
262(C2×D59)⋊C4—44no—
263(C2×D59)⋊C4—44no—
264(C2×D59)⋊C4—44no—
265(C2×D59)⋊C4—44no—
266(C2×D59)⋊C4—44no—
267C4⋊Dic59—44no—
268Dic59⋊C4—44no—
269C23×C59C23×C411yescharacteristic
270C23×C59C22×Q811yescharacteristic
271C23×C59C2×#4111yescharacteristic
272C23×C59H(5,𝔽2)11yescharacteristic
273C23×C59H(5,𝔽2)11yescharacteristic
274C23×C59H(5,𝔽2)11yescharacteristic
275C23×C59H(5,𝔽2)11yescharacteristic
276C23×C59H(5,𝔽2)11yescharacteristic
277C23×C59H(5,𝔽2)11yescharacteristic
278C23×C59H(5,𝔽2)11yescharacteristic
279C23×C59H(5,𝔽2)11yescharacteristic
280C23×C59H(5,𝔽2)11yescharacteristic
281C23×C592−1+411yescharacteristic
282C23×C592−1+411yescharacteristic
283C23×C592−1+411yescharacteristic
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—22no—
293C22×D59—22no—
294C22×D59—22no—
295C22×D59—22no—
296C22×D59—22no—
297C22×D59—22no—
298C22×D59—22no—
299C22×D59—22no—
300C22×D59—22no—
301C22×D59—22no—
302C22×D59—41no—
303C22×D59—41no—
304C22×D59—41no—
305C22×D59—41no—
306C22×D59—41no—
307C22×D59—41no—
308C22×D59—41no—
309C22×D59—41no—
310C22×D59—41no—
311C22×D59—41no—
312C22×D59—41no—
313C22×D59—41no—
314C22×D59—41no—
315C22×D59—41no—
316C22×D59—41no—
317C22×D59—41no—
318C22×D59C4×Q814yes—
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—22no—
328C2×C4×C59—22no—
329C2×C4×C59—22no—
330C2×C4×C59—22no—
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×C4×C59—41no—
359C2×C4×C59—41no—
360C2×C4×C59—41no—
361C2×C4×C59—41no—
362C2×C4×C59—41no—
363C2×C4×C59—41no—
364C2×C4×C59—41no—
365C2×C4×C59—41no—
366C2×C4×C59—41no—
367C2×C4×C59—41no—
368C2×Dic59—22no—
369C2×Dic59—22no—
370C2×Dic59—22no—
371C2×Dic59—22no—
372C2×Dic59—22no—
373C2×Dic59—22no—
374C2×Dic59—22no—
375C2×Dic59—22no—
376C2×Dic59—22no—
377C2×Dic59—22no—
378C2×Dic59—22no—
379C2×Dic59—22no—
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—
407C2×Dic59—41no—
408C2×Dic59—41no—
409C2×Dic59—41no—
410C2×Dic59—41no—
411C2×Dic59—41no—
412C2×Dic59—41no—
413C2×Dic59—41no—
414C2×Dic59—41no—
415C2×Dic59—41no—
416C2×Dic59—41no—
417C4×D59—416no—
418Dic118—416no—
419#14635—591nomaximal, Sylow
420C22×C59C2×C4×Q811yescharacteristic
421C22×C59#51811yescharacteristic
422C22×C59#51811yescharacteristic
423C22×C59#51811yescharacteristic
424C22×C59#52011yescharacteristic
425C22×C59#52011yescharacteristic
426C22×C59#52011yescharacteristic
427C22×C59#53811yescharacteristic
428C22×C59#53811yescharacteristic
429C22×C59#53811yescharacteristic
430C22×C59#53911yescharacteristic
431C22×C59#53911yescharacteristic
432C22×C59#53911yescharacteristic
433C22×C59#54311yescharacteristic
434C22×C59#54311yescharacteristic
435C22×C59#54311yescharacteristic
436C22×C59#54411yescharacteristic
437C22×C59#54411yescharacteristic
438C22×C59#54411yescharacteristic
439C22×C59#56011yescharacteristic
440C22×C59#56011yescharacteristic
441C22×C59#56011yescharacteristic
442C22×C59H(3,𝔽4)11yescharacteristic
443C22×C59H(3,𝔽4)11yescharacteristic
444C22×C59H(3,𝔽4)11yescharacteristic
445C22×C59H(3,𝔽4)11yescharacteristic
446C22×C59#56211yescharacteristic
447C22×C59#56211yescharacteristic
448C22×C59#56211yescharacteristic
449C22×C59#56211yescharacteristic
450C22×C59#56211yescharacteristic
451C22×C59#56211yescharacteristic
452C22×C59#56311yescharacteristic
453C22×C59#56311yescharacteristic
454C22×C59#56311yescharacteristic
455C2×D59—24no—
456C2×D59—24no—
457C2×D59—24no—
458C2×D59—42no—
459C2×D59—42no—
460C2×D59—42no—
461C2×D59—42no—
462C2×D59—42no—
463C2×D59—42no—
464C2×D59—42no—
465C2×D59—42no—
466C2×D59—42no—
467C2×D59—42no—
468C2×D59—42no—
469C2×D59—42no—
470C4×C59—42no—
471C4×C59—42no—
472C4×C59—42no—
473C4×C59—42no—
474C4×C59—81no—
475C4×C59—81no—
476C4×C59—81no—
477Dic59—42no—
478Dic59—42no—
479Dic59—42no—
480Dic59—42no—
481Dic59—81no—
482Dic59—81no—
483Dic59—81no—
484C2×#393—591no—
485#1446—591no—
486#1446—591no—
487#1442—591no—
488#1442—591no—
489#1442—591no—
490#1442—591no—
491#1442—591no—
492#1442D5911yescharacteristic, complemented
493#1439—591no—
494#1439—591no—
495#1439—591no—
496C22⋊#95—591no—
497C22⋊#95—591no—
498C22⋊#95—591no—
499C2×C59#232911yescharacteristic
500C2×C59#232911yescharacteristic
501C2×C59#232911yescharacteristic
502C2×C59#237511yescharacteristic
503C2×C59#237911yescharacteristic
504C2×C59#237911yescharacteristic
505C2×C59#237911yescharacteristic
506C2×C59#282411yescharacteristic
507C2×C59#282411yescharacteristic
508C2×C59#282411yescharacteristic
509C2×C59#283511yescharacteristic
510C2×C59#284011yescharacteristic
511C2×C59#284111yescharacteristic
512C2×C59#284111yescharacteristic
513C2×C59#284111yescharacteristic
514D59—44no—
515C23×Q8—591no—
516C24×C4—591no—
517C22×C4⋊C4—591no—
518C22×C4⋊C4—591no—
519C22×C4⋊C4C2×D5911yescharacteristic
520C22×C22⋊C4—591no—
521C22×C22⋊C4—591no—
522C22×C22⋊C4—591no—
523C22×C22⋊C4—591no—
524C22×C22⋊C4—591no—
525C22×C22⋊C4—591no—
526#393—598no—
527C2×#95—591no—
528C2×#95—591no—
529C2×#95—591no—
530C2×#95—591no—
531C2×#95—591no—
532C2×#95—591no—
533C2×#95—591no—
534C2×#95—591no—
535C2×#95—591no—
536C2×#95—591no—
537C2×#95—591no—
538C2×#95—591no—
539C2×#95—591no—
540C2×#95—591no—
541C2×#95—591no—
542C2×#95—591no—
543C2×#95—591no—
544C2×#95—591no—
545C2×#95C2×D5911yescharacteristic
546C2×#95C2×D5911yescharacteristic
547C2×#95C2×D5911yescharacteristic
548C2×#95C2×D5911yescharacteristic
549C2×#95C2×D5911yescharacteristic
550C2×#95C2×D5911yescharacteristic
551C59#1463511yescharacteristic, complemented, Sylow
552C25—591no—
553C22×Q8—594no—
554C22×Q8—2361no—
555C22×Q8—2361no—
556C22×Q8—2361no—
557C22×Q8—2361no—
558C22×Q8—2361no—
559C22×Q8—2361no—
560C23×C4—591no—
561C23×C4—591no—
562C23×C4—591no—
563C23×C4—591no—
564C23×C4—594no—
565C23×C4—591no—
566C23×C4—591no—
567C23×C4—591no—
568C23×C4—2361no—
569C23×C4—2361no—
570C23×C4—2361no—
571C23×C4—2361no—
572C23×C4—2361no—
573C23×C4—2361no—
574C23×C4C22×D5911yescharacteristic
575C23×C4C22×D5911yescharacteristic
576C23×C4C22×D5911yescharacteristic
577C23×C4C22×D5911yescharacteristic
578C23×C4C22×D5911yescharacteristic
579C23×C4C22×D5911yescharacteristic
580C23×C4C22×D5911yescharacteristic
581C2×C4⋊C4—41no—
582C2×C4⋊C4—41no—
583C2×C4⋊C4—41no—
584C2×C4⋊C4—2361no—
585C2×C4⋊C4—2361no—
586C2×C4⋊C4—2361no—
587C2×C4⋊C4—2361no—
588C2×C4⋊C4—2361no—
589C2×C4⋊C4—2361no—
590C2×C22⋊C4—594no—
591C2×C22⋊C4—594no—
592C2×C22⋊C4—594no—
593C2×C22⋊C4—1182no—
594C2×C22⋊C4—1182no—
595C2×C22⋊C4—1182no—
596C2×C22⋊C4—2361no—
597C2×C22⋊C4—2361no—
598C2×C22⋊C4—2361no—
599C2×C22⋊C4—2361no—
600C2×C22⋊C4—2361no—
601C2×C22⋊C4—2361no—
602C2×C22⋊C4—2361no—
603C2×C22⋊C4—2361no—
604C2×C22⋊C4—2361no—
605C2×C22⋊C4—2361no—
606C2×C22⋊C4—2361no—
607C2×C22⋊C4—2361no—
608#95—41no—
609#95—41no—
610#95—41no—
611#95—41no—
612#95—41no—
613#95—594no—
614#95—594no—
615#95—2361no—
616#95—2361no—
617#95—2361no—
618#95—2361no—
619#95—2361no—
620#95—2361no—
621#95—2361no—
622#95—2361no—
623#95—2361no—
624#95—2361no—
625#95—2361no—
626#95—2361no—
627#95—2361no—
628#95—2361no—
629#95—2361no—
630#95—2361no—
631#95C4×D5914yescomplemented
632C24—592no—
633C24—592no—
634C24—592no—
635C24—1181no—
636C24—1181no—
637C24—1181no—
638C24—1181no—
639C24—1181no—
640C24—1181no—
641C24—1181no—
642C24—1181no—
643C24—1181no—
644C24—1181no—
645C24—1181no—
646C24—1181no—
647C24C23×D5911yescharacteristic
648C2×Q8—2364no—
649C2×Q8—2364no—
650C2×Q8—2364no—
651C2×Q8—2364no—
652C2×Q8—2364no—
653C2×Q8—2364no—
654C2×Q8—2364no—
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—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—592no—
701C22×C4—592no—
702C22×C4—592no—
703C22×C4—592no—
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—1181no—
726C22×C4—1181no—
727C22×C4—1181no—
728C22×C4—1181no—
729C22×C4—1181no—
730C22×C4—1181no—
731C22×C4—1181no—
732C22×C4—1181no—
733C22×C4—1181no—
734C22×C4—1181no—
735C22×C4—1181no—
736C22×C4—1181no—
737C22×C4—1181no—
738C22×C4—1181no—
739C22×C4—1181no—
740C22×C4—1181no—
741C22×C4—1181no—
742C22×C4—1181no—
743C22×C4—1181no—
744C22×C4—1181no—
745C22×C4—1181no—
746C22×C4—1181no—
747C22×C4—1181no—
748C22×C4—1181no—
749C22×C4—2364no—
750C22×C4—2364no—
751C22×C4—2364no—
752C22×C4—2364no—
753C22×C4—2364no—
754C22×C4—2364no—
755C22×C4—2364no—
756C22×C4C2×C4×D5912yes—
757C22×C4C2×C4×D5912yes—
758C22×C4C2×C4×D5912yes—
759C22×C4Q8×D5912yes—
760C4⋊C4—44no—
761C4⋊C4—2364no—
762C4⋊C4—2364no—
763C22⋊C4—2364no—
764C22⋊C4—2364no—
765C22⋊C4—2364no—
766C22⋊C4—2364no—
767C22⋊C4—2364no—
768C22⋊C4—2364no—
769C23—594no—
770C23—1182no—
771C23—1182no—
772C23—1182no—
773C23—1182no—
774C23—1182no—
775C23—1182no—
776C23—1182no—
777C23—1182no—
778C23—1182no—
779C23—1182no—
780C23—1182no—
781C23—1182no—
782C23—1182no—
783C23—1182no—
784C23—1182no—
785C23—1182no—
786C23—1182no—
787C23—1182no—
788C23—2361no—
789C23—2361no—
790C23—2361no—
791C23—2361no—
792C23—2361no—
793C23—2361no—
794C23—2361no—
795C23—2361no—
796C23—2361no—
797C23—2361no—
798C23—2361no—
799C23—2361no—
800C23—2361no—
801C23—2361no—
802C23—2361no—
803C23—2361no—
804C23C22×C4×D5911yescharacteristic
805C23C2×Q8×D5911yescharacteristic
806C23#41×D5911yescharacteristic
807C23#1427377211yescharacteristic
808C23#1427377211yescharacteristic
809C23#1427377211yescharacteristic
810C23#1427377211yescharacteristic
811C23#1427377311yescharacteristic
812C23#1427377311yescharacteristic
813C23#1427377311yescharacteristic
814C23#1427377311yescharacteristic
815C23#1427377311yescharacteristic
816C23#1427377411yescharacteristic
817C23#1427377411yescharacteristic
818C23#1427377511yescharacteristic
819Q8—23616no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
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—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—1182no—
870C2×C4—1182no—
871C2×C4—1182no—
872C2×C4—1182no—
873C2×C4—1182no—
874C2×C4—1182no—
875C2×C4—1182no—
876C2×C4—1182no—
877C2×C4—1182no—
878C2×C4—1182no—
879C2×C4—1182no—
880C2×C4—1182no—
881C2×C4—23616no—
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—
897C2×C4—2361no—
898C2×C4—2361no—
899C2×C4—2361no—
900C2×C4—2361no—
901C2×C4—2361no—
902C2×C4—2361no—
903C2×C4—2361no—
904C2×C4—2361no—
905C2×C4—2361no—
906C2×C4—2361no—
907C2×C4—2361no—
908C2×C4—2361no—
909C2×C4—2361no—
910C2×C4—2361no—
911C2×C4—2361no—
912C2×C4—2361no—
913C2×C4—2361no—
914C2×C4—2361no—
915C2×C4—2361no—
916C2×C4—2361no—
917C2×C4—2361no—
918C2×C4—2361no—
919C22—1184no—
920C22—1184no—
921C22—1184no—
922C22—2362no—
923C22—2362no—
924C22—2362no—
925C22—2362no—
926C22—2362no—
927C22—2362no—
928C22—2362no—
929C22—2362no—
930C22—2362no—
931C22—2362no—
932C22—2362no—
933C22—2362no—
934C22C4×Q8×D5911yescharacteristic
935C22#1683787411yescharacteristic
936C22#1683787411yescharacteristic
937C22#1683787611yescharacteristic
938C22#1683788111yescharacteristic
939C22#1683788211yescharacteristic
940C22#1683788311yescharacteristic
941C22#1683798411yescharacteristic
942C22#1683798811yescharacteristic
943C22#1683799111yescharacteristic
944C22#1683799311yescharacteristic
945C22#1683799511yescharacteristic
946C22#1683800011yescharacteristic
947C22#1683802711yescharacteristic
948C22#1683802711yescharacteristic
949C22#1683802711yescharacteristic
950C22#1683802911yescharacteristic
951C22#1683803211yescharacteristic
952C22#1683803211yescharacteristic
953C22#1683814011yescharacteristic
954C22#1683814211yescharacteristic
955C22#1683814311yescharacteristic
956C22#1683814411yescharacteristic
957C22#1683814411yescharacteristic
958C22#1683814411yescharacteristic
959C22#1683814511yescharacteristic
960C22#1683814611yescharacteristic
961C22#1683814711yescharacteristic
962C22#1683814811yescharacteristic
963C22#1683814911yescharacteristic
964C22#1683814911yescharacteristic
965C22#1683815011yescharacteristic
966C22#1683815311yescharacteristic
967C22#1683815411yescharacteristic
968C22#1683815611yescharacteristic
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—81no—
974C4—81no—
975C4—81no—
976C4—4721no—
977C4—4721no—
978C4—4721no—
979C4—2362no—
980C4—2362no—
981C4—2362no—
982C4—2362no—
983C2—2364no—
984C2#2142682311yescharacteristic
985C2#2142682511yescharacteristic
986C2#2142683011yescharacteristic
987C2#2142723611yescharacteristic
988C2#2142726511yescharacteristic
989C2#2142726711yescharacteristic
990C2#2142726911yescharacteristic
991C2#2143217211yescharacteristic
992C2#2143217411yescharacteristic
993C2#2143217711yescharacteristic
994C2#2143228311yescharacteristic
995C2#2143234811yescharacteristic
996C2#2143235211yescharacteristic
997C2#2143235411yescharacteristic
998C2#2143235511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×#1442C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenter#1442D59
hypocenterC59#14635
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. #21422366C2semidirect
3. #21422366C2semidirect
4. #21422355C2semidirect
5. #21422354C2semidirect
6. #21422353C2semidirect
7. #21422352C2semidirect
8. #21422351C2semidirect
15. C59×#1442C2semidirect
26. #16837315C4semidirect
59. C22×Dic118C2×C4semidirect
73. C22×C4×D59Q8semidirect
114. C59⋊#95C2×C4semidirect
115. C59⋊#95C2×C4semidirect
131. #95×C59C2×C4semidirect
492. #1442D59semidirect
551. C59#14635semidirect
631. #95C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168373152
#214223662
#214223552
#214223542
#214223532
#214223522
#214223512
#214223422
#214223402
#214223382
(C2×D59)⋊#952
C59×#14422
#1463559