Finite Group Databasebeta

← #28512247

Subgroups — #28512247

Order 15104.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837291C211yesmaximal, characteristic
2C2×#16837283C211yesmaximal, characteristic, complemented
3C2×#16837273C211yesmaximal, characteristic
4C2×#16837253C211yesmaximal, characteristic, complemented
5C2×#16837249C211yesmaximal, characteristic
6#21422351C211yesmaximal, characteristic, complemented
7#21422344C211yesmaximal, characteristic
8#21422340C211yesmaximal, characteristic
9#21422332C211yesmaximal, characteristic
10#21422327C211yesmaximal, characteristic, complemented
11#21422327C211yesmaximal, characteristic, complemented
12#21422322C211yesmaximal, characteristic, complemented
13#21422321C211yesmaximal, characteristic, complemented
14(C2×D59)⋊#95C211yesmaximal, characteristic
15C59×#1442C211yesmaximal, characteristic, complemented
16C23×C4×D59C2211yescharacteristic
17C22×Dic59⋊C4C2211yescharacteristic
18C22×Dic59⋊C4C2211yescharacteristic
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
26C22×C4×Dic59C2211yescharacteristic
27C22×C4×Dic59C2211yescharacteristic
28C22×C4×Dic59C2211yescharacteristic
29C22×C4×Dic59C2211yescharacteristic
30#16837291C418yescomplemented
31#16837283—24no—
32#16837273—24no—
33#16837253—24no—
34#16837249—24no—
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
45C2×C59⋊#95C2211yescharacteristic
46C2×C59⋊#95C2211yescharacteristic
47C2×C59⋊#95C2211yescharacteristic
48C2×C59⋊#95C2211yescharacteristic
49C22×C4⋊C4×C59C2211yescharacteristic
50C2×#95×C59C2211yescharacteristic
51C2×#95×C59C2211yescharacteristic
52C2×#95×C59C2211yescharacteristic
53C2×#95×C59C2211yescharacteristic
54C2×#95×C59C2211yescharacteristic
55C2×#95×C59C2211yescharacteristic
56C24×D59C2311yescharacteristic
57C23×Dic59C2311yescharacteristic
58C23×Dic59C2311yescharacteristic
59C23×Dic59C2311yescharacteristic
60C23×Dic59C2311yescharacteristic
61C23×Dic59C2311yescharacteristic
62C23×Dic59C2311yescharacteristic
63C23×Dic59C2311yescharacteristic
64C22×C4×D59—22no—
65C22×C4×D59—22no—
66C22×C4×D59—22no—
67C22×C4×D59—22no—
68C22×C4×D59—22no—
69C22×C4×D59—41no—
70C22×C4×D59—41no—
71C2×Dic59⋊C4—22no—
72C2×Dic59⋊C4—22no—
73C2×Dic59⋊C4—22no—
74C2×Dic59⋊C4—22no—
75C2×Dic59⋊C4—22no—
76C2×Dic59⋊C4—22no—
77C2×Dic59⋊C4—22no—
78C2×Dic59⋊C4C2×C414yescomplemented
79C2×Dic59⋊C4D414yes—
80C2×(C2×D59)⋊C4—22no—
81C2×(C2×D59)⋊C4—22no—
82C2×(C2×D59)⋊C4—22no—
83C2×(C2×D59)⋊C4—22no—
84C2×(C2×D59)⋊C4—22no—
85C2×(C2×D59)⋊C4—22no—
86C2×(C2×D59)⋊C4—22no—
87C2×(C2×D59)⋊C4—22no—
88C2×(C2×D59)⋊C4—22no—
89C2×(C2×D59)⋊C4—22no—
90C2×(C2×D59)⋊C4—22no—
91C2×(C2×D59)⋊C4—22no—
92C2×(C2×D59)⋊C4—22no—
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—
98C2×C4×Dic59—22no—
99C2×C4×Dic59—22no—
100C2×C4×Dic59—22no—
101C2×C4×Dic59—22no—
102C2×C4×Dic59—22no—
103C2×C4×Dic59—22no—
104C2×C4×Dic59—22no—
105C2×C4×Dic59—22no—
106C2×C4×Dic59—41no—
107C2×C4×Dic59—41no—
108C2×C4×Dic59—41no—
109C2×C4×Dic59C2×C414yescomplemented
110C59⋊#95—22no—
111C59⋊#95—22no—
112C59⋊#95—22no—
113C59⋊#95—22no—
114C59⋊#95—22no—
115C59⋊#95—22no—
116C59⋊#95—22no—
117C59⋊#95—22no—
118C59⋊#95—22no—
119C59⋊#95—22no—
120C59⋊#95—22no—
121C59⋊#95—41no—
122C59⋊#95C2×C414yescomplemented
123C59⋊#95D414yes—
124C23×C4×C59C2311yescharacteristic
125C23×C4×C59C2311yescharacteristic
126C23×C4×C59C2311yescharacteristic
127C23×C4×C59C2311yescharacteristic
128C23×C4×C59C2311yescharacteristic
129C23×C4×C59C2311yescharacteristic
130C23×C4×C59C2311yescharacteristic
131C2×C4⋊C4×C59—22no—
132C2×C4⋊C4×C59—22no—
133C2×C4⋊C4×C59—41no—
134#95×C59—22no—
135#95×C59—22no—
136#95×C59—41no—
137#95×C59—41no—
138#95×C59—41no—
139#95×C59C2×C414yescomplemented
140C24×C59C2411yescharacteristic
141C23×D59—21no—
142C23×D59—21no—
143C23×D59—21no—
144C23×D59—21no—
145C23×D59—21no—
146C23×D59—21no—
147C23×D59—21no—
148C23×D59—21no—
149C23×D59—21no—
150C23×D59—21no—
151C23×D59—21no—
152C23×D59—21no—
153C23×D59C22×C412yes—
154C23×D59#4112yes—
155C23×D59#4112yes—
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×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59C22×C412yes—
200C22×C4×C59C22×C412yes—
201C22×C4×C59C22×C412yes—
202C22×C4×C59C2×D412yes—
203C22×C4×C59C2×D412yes—
204C22×C4×C59#4112yes—
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×D412yes—
246C22×Dic59C2×D412yes—
247C22×Dic59C2×D412yes—
248C22×Dic59C2×D412yes—
249C22×Dic59#4112yes—
250C22×Dic59#4112yes—
251C22×Dic59#4112yes—
252C22×Dic59#4112yes—
253C22×Dic59#4112yes—
254C2×C4×D59—28no—
255C2×C4×D59—44no—
256C2×C4×D59—44no—
257C2×C4×D59—44no—
258C2×C4×D59—44no—
259C2×C4×D59—44no—
260C2×C4×D59—44no—
261C4⋊C4×C59—44no—
262(C2×D59)⋊C4—28no—
263(C2×D59)⋊C4—28no—
264(C2×D59)⋊C4—28no—
265(C2×D59)⋊C4—28no—
266(C2×D59)⋊C4—44no—
267(C2×D59)⋊C4—44no—
268Dic59⋊C4—28no—
269Dic59⋊C4—28no—
270Dic59⋊C4—28no—
271C4×Dic59—28no—
272C4×Dic59—44no—
273C4×Dic59—44no—
274C4×Dic59—44no—
275C23×C59C23×C411yescharacteristic
276C23×C59C22×D411yescharacteristic
277C23×C59C22×D411yescharacteristic
278C23×C59C2×#4111yescharacteristic
279C23×C59C2×#4111yescharacteristic
280C23×C59C2×#4111yescharacteristic
281C23×C59C2×#4111yescharacteristic
282C23×C59C2×#4111yescharacteristic
283C23×C59C2×#4111yescharacteristic
284C23×C59C2×#4111yescharacteristic
285C23×C59C2×#4111yescharacteristic
286C23×C59H(5,𝔽2)11yescharacteristic
287C23×C59H(5,𝔽2)11yescharacteristic
288C23×C592−1+411yescharacteristic
289C23×C592−1+411yescharacteristic
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—22no—
303C22×D59—22no—
304C22×D59—22no—
305C22×D59—22no—
306C22×D59—22no—
307C22×D59—22no—
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×D59—41no—
319C22×D59—41no—
320C22×D59—41no—
321C22×D59—41no—
322C22×D59—41no—
323C22×D59—41no—
324C22×D59#11714yes—
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—22no—
332C2×C4×C59—22no—
333C2×C4×C59—22no—
334C2×C4×C59—22no—
335C2×C4×C59—22no—
336C2×C4×C59—22no—
337C2×C4×C59—22no—
338C2×C4×C59—22no—
339C2×C4×C59—22no—
340C2×C4×C59—22no—
341C2×C4×C59—22no—
342C2×C4×C59—22no—
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×C4×C59—41no—
369C2×C4×C59—41no—
370C2×C4×C59—41no—
371C2×C4×C59—41no—
372C2×C4×C59—41no—
373C2×C4×C59—41no—
374C2×Dic59—22no—
375C2×Dic59—22no—
376C2×Dic59—22no—
377C2×Dic59—22no—
378C2×Dic59—22no—
379C2×Dic59—22no—
380C2×Dic59—22no—
381C2×Dic59—22no—
382C2×Dic59—22no—
383C2×Dic59—22no—
384C2×Dic59—22no—
385C2×Dic59—22no—
386C2×Dic59—22no—
387C2×Dic59—22no—
388C2×Dic59—22no—
389C2×Dic59—22no—
390C2×Dic59—22no—
391C2×Dic59—22no—
392C2×Dic59—22no—
393C2×Dic59—22no—
394C2×Dic59—22no—
395C2×Dic59—22no—
396C2×Dic59—22no—
397C2×Dic59—22no—
398C2×Dic59—22no—
399C2×Dic59—22no—
400C2×Dic59—22no—
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—
417C2×Dic59—41no—
418C2×Dic59—41no—
419C2×Dic59—41no—
420C2×Dic59C4×D414yes—
421C2×Dic59C4×D414yes—
422C2×Dic59#12314yes—
423C4×D59—416no—
424#14032—591nomaximal, Sylow
425C22×C59C2×#11711yescharacteristic
426C22×C59C2×C4×D411yescharacteristic
427C22×C59C2×C4×D411yescharacteristic
428C22×C59C4×#4111yescharacteristic
429C22×C59C4×#4111yescharacteristic
430C22×C59#52011yescharacteristic
431C22×C59#52011yescharacteristic
432C22×C59C2×#12311yescharacteristic
433C22×C59#52511yescharacteristic
434C22×C59#52511yescharacteristic
435C22×C59#52511yescharacteristic
436C22×C59#52911yescharacteristic
437C22×C59#52911yescharacteristic
438C22×C59#52911yescharacteristic
439C22×C59#52911yescharacteristic
440C22×C59#53811yescharacteristic
441C22×C59#53911yescharacteristic
442C22×C59#54111yescharacteristic
443C22×C59#54211yescharacteristic
444C22×C59D4211yescharacteristic
445C22×C59#54611yescharacteristic
446C22×C59#54611yescharacteristic
447C22×C59#54711yescharacteristic
448C22×C59#54811yescharacteristic
449C22×C59#54811yescharacteristic
450C22×C59#54811yescharacteristic
451C22×C59#55111yescharacteristic
452C22×C59#55111yescharacteristic
453C22×C59#55211yescharacteristic
454C22×C59#55211yescharacteristic
455C22×C59#55211yescharacteristic
456C22×C59#55311yescharacteristic
457C22×C59#55311yescharacteristic
458C22×C59#55611yescharacteristic
459C22×C59#55911yescharacteristic
460C2×D59—24no—
461C2×D59—24no—
462C2×D59—24no—
463C2×D59—42no—
464C2×D59—42no—
465C2×D59—42no—
466C2×D59—42no—
467C2×D59—42no—
468C2×D59—42no—
469C2×D59—42no—
470C2×D59—42no—
471C2×D59—42no—
472C2×D59—42no—
473C2×D59—42no—
474C2×D59—42no—
475C4×C59—42no—
476C4×C59—42no—
477C4×C59—42no—
478C4×C59—42no—
479C4×C59—42no—
480C4×C59—42no—
481C4×C59—81no—
482Dic59—24no—
483Dic59—24no—
484Dic59—24no—
485Dic59—42no—
486Dic59—42no—
487Dic59—42no—
488Dic59—81no—
489C2×#388—591no—
490C2×#387—591no—
491C2×#385—591no—
492C2×C4×C4⋊C4—591no—
493C2×C4×C22⋊C4—591no—
494#1442—591no—
495#1442D5911yescharacteristic, complemented
496#1440—591no—
497#1439—591no—
498#1437—591no—
499#1436—591no—
500#1436—591no—
501#1434—591no—
502#1434—591no—
503C22⋊#95—591no—
504C2×C59#229011yescharacteristic
505C2×C59C4×#12311yescharacteristic
506C2×C59#233411yescharacteristic
507C2×C59#234311yescharacteristic
508C2×C59#235211yescharacteristic
509C2×C59#236111yescharacteristic
510C2×C59#236711yescharacteristic
511C2×C59#241811yescharacteristic
512C2×C59#242111yescharacteristic
513C2×C59#245811yescharacteristic
514C2×C59#246311yescharacteristic
515C2×C59#246811yescharacteristic
516C2×C59#247511yescharacteristic
517C2×C59#257311yescharacteristic
518C2×C59#259511yescharacteristic
519D59—44no—
520C24×C4—591no—
521C22×C4⋊C4—591no—
522C22×C4⋊C4—591no—
523C22×C4⋊C4—591no—
524C22×C4⋊C4C2×D5911yescharacteristic
525C22×C22⋊C4—591no—
526C22×C22⋊C4—591no—
527C22×C22⋊C4—591no—
528C22×C22⋊C4—591no—
529C22×C22⋊C4—591no—
530C22×C22⋊C4—591no—
531C22×C42—591no—
532C22×C42—591no—
533C22×C42—591no—
534C22×C42—591no—
535#388—598no—
536#387—1184no—
537#385—1184no—
538C4×C4⋊C4—1184no—
539C4×C22⋊C4—1184no—
540C2×#95—591no—
541C2×#95—591no—
542C2×#95—591no—
543C2×#95—591no—
544C2×#95—591no—
545C2×#95—591no—
546C2×#95—591no—
547C2×#95—591no—
548C2×#95—591no—
549C2×#95—591no—
550C2×#95—591no—
551C2×#95—591no—
552C2×#95—591no—
553C2×#95—591no—
554C2×#95C2×D5911yescharacteristic
555C2×#95C2×D5911yescharacteristic
556C2×#95C2×D5911yescharacteristic
557C2×#95C2×D5911yescharacteristic
558C2×#95C2×D5911yescharacteristic
559C2×#95C2×D5911yescharacteristic
560C59#1403211yescharacteristic, complemented, Sylow
561C25—591no—
562C23×C4—591no—
563C23×C4—591no—
564C23×C4—591no—
565C23×C4—591no—
566C23×C4—591no—
567C23×C4—591no—
568C23×C4—591no—
569C23×C4—1182no—
570C23×C4—1182no—
571C23×C4—1182no—
572C23×C4—1182no—
573C23×C4—1182no—
574C23×C4—2361no—
575C23×C4—2361no—
576C23×C4C22×D5911yescharacteristic
577C23×C4C22×D5911yescharacteristic
578C23×C4C22×D5911yescharacteristic
579C23×C4C22×D5911yescharacteristic
580C23×C4C22×D5911yescharacteristic
581C23×C4C22×D5911yescharacteristic
582C23×C4C22×D5911yescharacteristic
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—594no—
587C2×C4⋊C4—594no—
588C2×C4⋊C4—1182no—
589C2×C4⋊C4—1182no—
590C2×C4⋊C4—1182no—
591C2×C4⋊C4—1182no—
592C2×C4⋊C4—1182no—
593C2×C4⋊C4—1182no—
594C2×C4⋊C4—1182no—
595C2×C22⋊C4—594no—
596C2×C22⋊C4—594no—
597C2×C22⋊C4—594no—
598C2×C22⋊C4—1182no—
599C2×C22⋊C4—1182no—
600C2×C22⋊C4—1182no—
601C2×C22⋊C4—1182no—
602C2×C22⋊C4—1182no—
603C2×C22⋊C4—1182no—
604C2×C22⋊C4—1182no—
605C2×C22⋊C4—1182no—
606C2×C22⋊C4—1182no—
607C2×C22⋊C4—1182no—
608C2×C22⋊C4—1182no—
609C2×C22⋊C4—1182no—
610C2×C22⋊C4—1182no—
611C2×C22⋊C4—2361no—
612C2×C22⋊C4—2361no—
613C2×C42—594no—
614C2×C42—1182no—
615C2×C42—1182no—
616C2×C42—1182no—
617C2×C42—1182no—
618C2×C42—1182no—
619C2×C42—1182no—
620C2×C42—1182no—
621C2×C42—1182no—
622C2×C42—2361no—
623C2×C42—2361no—
624C2×C42—2361no—
625#95—22no—
626#95—22no—
627#95—41no—
628#95—41no—
629#95—41no—
630#95—594no—
631#95—594no—
632#95—1182no—
633#95—1182no—
634#95—1182no—
635#95—1182no—
636#95—1182no—
637#95—1182no—
638#95—1182no—
639#95—1182no—
640#95—1182no—
641#95—1182no—
642#95—1182no—
643#95—2361no—
644#95C4×D5914yescomplemented
645C24—592no—
646C24—592no—
647C24—592no—
648C24—1181no—
649C24—1181no—
650C24—1181no—
651C24—1181no—
652C24—1181no—
653C24—1181no—
654C24—1181no—
655C24—1181no—
656C24—1181no—
657C24—1181no—
658C24—1181no—
659C24—1181no—
660C24C23×D5911yescharacteristic
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—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—592no—
705C22×C4—592no—
706C22×C4—592no—
707C22×C4—592no—
708C22×C4—592no—
709C22×C4—592no—
710C22×C4—592no—
711C22×C4—592no—
712C22×C4—592no—
713C22×C4—592no—
714C22×C4—592no—
715C22×C4—592no—
716C22×C4—1188no—
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—1181no—
750C22×C4—1181no—
751C22×C4—1181no—
752C22×C4—1181no—
753C22×C4—1181no—
754C22×C4—2364no—
755C22×C4—2364no—
756C22×C4—2364no—
757C22×C4—2364no—
758C22×C4—2364no—
759C22×C4—2364no—
760C22×C4C2×C4×D5912yes—
761C22×C4C2×C4×D5912yes—
762C22×C4C2×C4×D5912yes—
763C22×C4D4×D5912yes—
764C22×C4D4×D5912yes—
765C22×C4#1174568912yes—
766C4⋊C4—44no—
767C4⋊C4—1188no—
768C4⋊C4—1188no—
769C4⋊C4—1188no—
770C22⋊C4—1188no—
771C22⋊C4—1188no—
772C22⋊C4—1188no—
773C22⋊C4—1188no—
774C22⋊C4—2364no—
775C22⋊C4—2364no—
776C42—1188no—
777C42—2364no—
778C42—2364no—
779C42—2364no—
780C23—594no—
781C23—1182no—
782C23—1182no—
783C23—1182no—
784C23—1182no—
785C23—1182no—
786C23—1182no—
787C23—1182no—
788C23—1182no—
789C23—1182no—
790C23—1182no—
791C23—1182no—
792C23—1182no—
793C23—1182no—
794C23—1182no—
795C23—1182no—
796C23—1182no—
797C23—1182no—
798C23—1182no—
799C23—2361no—
800C23—2361no—
801C23—2361no—
802C23—2361no—
803C23—2361no—
804C23—2361no—
805C23—2361no—
806C23—2361no—
807C23—2361no—
808C23—2361no—
809C23—2361no—
810C23—2361no—
811C23—2361no—
812C23—2361no—
813C23—2361no—
814C23—2361no—
815C23C22×C4×D5911yescharacteristic
816C23C2×D4×D5911yescharacteristic
817C23C2×D4×D5911yescharacteristic
818C23#41×D5911yescharacteristic
819C23#41×D5911yescharacteristic
820C23#41×D5911yescharacteristic
821C23#41×D5911yescharacteristic
822C23#41×D5911yescharacteristic
823C23#41×D5911yescharacteristic
824C23#41×D5911yescharacteristic
825C23C2×#1174568911yescharacteristic
826C23#1427377211yescharacteristic
827C23#1427377211yescharacteristic
828C23#1427377411yescharacteristic
829C23#1427377511yescharacteristic
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
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—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—594no—
880C2×C4—594no—
881C2×C4—594no—
882C2×C4—1182no—
883C2×C4—1182no—
884C2×C4—1182no—
885C2×C4—1182no—
886C2×C4—1182no—
887C2×C4—1182no—
888C2×C4—1182no—
889C2×C4—1182no—
890C2×C4—1182no—
891C2×C4—1182no—
892C2×C4—1182no—
893C2×C4—1182no—
894C2×C4—1182no—
895C2×C4—1182no—
896C2×C4—1182no—
897C2×C4—1182no—
898C2×C4—1182no—
899C2×C4—1182no—
900C2×C4—1182no—
901C2×C4—1182no—
902C2×C4—1182no—
903C2×C4—1182no—
904C2×C4—1182no—
905C2×C4—1182no—
906C2×C4—1182no—
907C2×C4—1182no—
908C2×C4—1182no—
909C2×C4—23616no—
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—
919C2×C4—2361no—
920C2×C4—2361no—
921C2×C4—2361no—
922C2×C4—2361no—
923C2×C4—2361no—
924C2×C4—2361no—
925C2×C4—2361no—
926C2×C4—2361no—
927C2×C4—2361no—
928C2×C4—2361no—
929C22—1184no—
930C22—1184no—
931C22—1184no—
932C22—2362no—
933C22—2362no—
934C22—2362no—
935C22—2362no—
936C22—2362no—
937C22—2362no—
938C22—2362no—
939C22—2362no—
940C22—2362no—
941C22—2362no—
942C22—2362no—
943C22—2362no—
944C22#117×D5911yescharacteristic
945C22C4×D4×D5911yescharacteristic
946C22C4×D4×D5911yescharacteristic
947C22#1683787011yescharacteristic
948C22C4×#1174568911yescharacteristic
949C22#1683788111yescharacteristic
950C22#1683788311yescharacteristic
951C22#123×D5911yescharacteristic
952C22#1683791011yescharacteristic
953C22#1683791511yescharacteristic
954C22#1683791511yescharacteristic
955C22#1683793511yescharacteristic
956C22#1683793511yescharacteristic
957C22#1683793711yescharacteristic
958C22#1683793711yescharacteristic
959C22#1683798411yescharacteristic
960C22#1683800111yescharacteristic
961C22#1683801111yescharacteristic
962C22#1683802611yescharacteristic
963C22#1683803411yescharacteristic
964C22#1683804111yescharacteristic
965C22#1683804111yescharacteristic
966C22#1683805411yescharacteristic
967C22#1683806011yescharacteristic
968C22#1683806011yescharacteristic
969C22#1683806211yescharacteristic
970C22#1683808211yescharacteristic
971C22#1683808211yescharacteristic
972C22#1683808411yescharacteristic
973C22#1683808411yescharacteristic
974C22#1683808811yescharacteristic
975C22#1683809711yescharacteristic
976C22#1683809711yescharacteristic
977C22#1683811911yescharacteristic
978C22#1683813611yescharacteristic
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—81no—
986C4—1184no—
987C4—1184no—
988C4—1184no—
989C4—4721no—
990C4—2362no—
991C4—2362no—
992C4—2362no—
993C2—2364no—
994C2#2142653411yescharacteristic
995C2#2142661711yescharacteristic
996C2#2142687011yescharacteristic
997C2#2142694911yescharacteristic
998C2#2142702411yescharacteristic
999C2#2142711511yescharacteristic
1000C2#2142716211yescharacteristic
1001C2#2142755111yescharacteristic
1002C2#2142759411yescharacteristic
1003C2#2142802111yescharacteristic
1004C2#2142809311yescharacteristic
1005C2#2142816511yescharacteristic
1006C2#2142826011yescharacteristic
1007C2#2142935811yescharacteristic
1008C2#2142961211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×#1442C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenter#1442D59
hypocenterC59#14032
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. C2×#16837283C2semidirect
4. C2×#16837253C2semidirect
6. #21422351C2semidirect
10. #21422327C2semidirect
11. #21422327C2semidirect
12. #21422322C2semidirect
13. #21422321C2semidirect
15. C59×#1442C2semidirect
30. #16837291C4semidirect
78. C2×Dic59⋊C4C2×C4semidirect
109. C2×C4×Dic59C2×C4semidirect
122. C59⋊#95C2×C4semidirect
139. #95×C59C2×C4semidirect
495. #1442D59semidirect
560. C59#14032semidirect
644. #95C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168372912
C2×#168372832
C2×#168372732
C2×#168372532
C2×#168372492
#214223512
#214223442
#214223402
#214223322
#214223272
#214223222
#214223212
(C2×D59)⋊#952
C59×#14422
#1403259