Finite Group Databasebeta

← #28512223

Subgroups — #28512223

Order 15104.

1594 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×#16837293C211yesmaximal, characteristic
2C2×#16837292C211yesmaximal, characteristic
3C2×#16837291C211yesmaximal, characteristic
4C2×C4×Dic59⋊C4C211yesmaximal, characteristic, complemented
5#21422359C211yesmaximal, characteristic, complemented
6#21422357C211yesmaximal, characteristic, complemented
7#21422340C211yesmaximal, characteristic
8#21422338C211yesmaximal, characteristic
9#21422334C211yesmaximal, characteristic
10#21422334C211yesmaximal, characteristic
11#21422329C211yesmaximal, characteristic, complemented
12#21422329C211yesmaximal, characteristic, complemented
13#21422328C211yesmaximal, characteristic, complemented
14#21422321C211yesmaximal, characteristic, complemented
15C2×C4×C4⋊C4×C59C211yesmaximal, characteristic, complemented
16C22×Dic59⋊C4C2211yescharacteristic
17C22×Dic59⋊C4C2211yescharacteristic
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×(C2×D59)⋊C4C2211yescharacteristic
26C22×C4×Dic59C2211yescharacteristic
27C22×C4×Dic59C2211yescharacteristic
28#16837293—24no—
29#16837292C418yescomplemented
30#16837291—24no—
31C4×Dic59⋊C4—24no—
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
45C2×C59⋊#95C2211yescharacteristic
46C2×C59⋊#95C2211yescharacteristic
47C2×C59⋊#95C2211yescharacteristic
48C22×C4⋊C4×C59C2211yescharacteristic
49C22×C4⋊C4×C59C2211yescharacteristic
50C22×C42×C59C2211yescharacteristic
51C22×C42×C59C2211yescharacteristic
52C22×C42×C59C2211yescharacteristic
53C4×C4⋊C4×C59—24no—
54C2×#95×C59C2211yescharacteristic
55C2×#95×C59C2211yescharacteristic
56C24×D59C2311yescharacteristic
57C23×Dic59C2311yescharacteristic
58C23×Dic59C2311yescharacteristic
59C23×Dic59C2311yescharacteristic
60C23×Dic59C2311yescharacteristic
61C23×Dic59C2311yescharacteristic
62C23×Dic59C2311yescharacteristic
63C23×Dic59C2311yescharacteristic
64C2×Dic59⋊C4—22no—
65C2×Dic59⋊C4—22no—
66C2×Dic59⋊C4—22no—
67C2×Dic59⋊C4—22no—
68C2×Dic59⋊C4—22no—
69C2×Dic59⋊C4—22no—
70C2×Dic59⋊C4—22no—
71C2×Dic59⋊C4—41no—
72C2×Dic59⋊C4D414yes—
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—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—41no—
88C2×(C2×D59)⋊C4—41no—
89C2×(C2×D59)⋊C4—41no—
90C2×(C2×D59)⋊C4—41no—
91C2×(C2×D59)⋊C4C2×C414yes—
92C2×(C2×D59)⋊C4C2×C414yes—
93C2×(C2×D59)⋊C4C2×C414yes—
94C2×C4×Dic59—22no—
95C2×C4×Dic59—22no—
96C2×C4×Dic59—22no—
97C2×C4×Dic59—22no—
98C2×C4×Dic59—41no—
99C2×C4×Dic59C2×C414yes—
100C59⋊#95—22no—
101C59⋊#95—22no—
102C59⋊#95—22no—
103C59⋊#95—22no—
104C59⋊#95—22no—
105C59⋊#95—22no—
106C59⋊#95—22no—
107C59⋊#95—22no—
108C59⋊#95—22no—
109C59⋊#95—22no—
110C59⋊#95—41no—
111C59⋊#95—41no—
112C59⋊#95—41no—
113C59⋊#95—41no—
114C59⋊#95C2×C414yes—
115C59⋊#95C2×C414yes—
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—22no—
124C2×C4⋊C4×C59—22no—
125C2×C4⋊C4×C59—22no—
126C2×C4⋊C4×C59—22no—
127C2×C4⋊C4×C59—22no—
128C2×C4⋊C4×C59C2×C414yes—
129C2×C42×C59—22no—
130C2×C42×C59—22no—
131C2×C42×C59—22no—
132C2×C42×C59—22no—
133C2×C42×C59—22no—
134C2×C42×C59—22no—
135C2×C42×C59—22no—
136C2×C42×C59—41no—
137C2×C42×C59—41no—
138#95×C59—22no—
139#95×C59D414yes—
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×D59—21no—
154C23×D59—21no—
155C23×D59C22×C412yes—
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×C59C22×C412yes—
193C22×C4×C59C22×C412yes—
194C22×C4×C59C22×C412yes—
195C22×C4×C59C2×D412yes—
196C22×C4×C59C2×D412yes—
197C22×C4×C59C2×D412yes—
198C22×C4×C59C2×D412yes—
199C22×C4×C59#4112yes—
200C22×C4×C59#4112yes—
201C22×C4×C59#4112yes—
202C22×C4×C59#4112yes—
203C22×C4×C59#4112yes—
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×Dic59—21no—
243C22×Dic59—21no—
244C22×Dic59—21no—
245C22×Dic59—21no—
246C22×Dic59—21no—
247C22×Dic59C22×C412yes—
248C22×Dic59C22×C412yes—
249C22×Dic59C22×C412yes—
250C22×Dic59C2×D412yes—
251C22×Dic59C2×D412yes—
252C22×Dic59#4112yes—
253C22×Dic59#4112yes—
254C4⋊C4×C59—28no—
255C4⋊C4×C59—28no—
256C42×C59—28no—
257C42×C59—44no—
258C42×C59—44no—
259(C2×D59)⋊C4—28no—
260(C2×D59)⋊C4—28no—
261(C2×D59)⋊C4—28no—
262(C2×D59)⋊C4—44no—
263(C2×D59)⋊C4—44no—
264(C2×D59)⋊C4—44no—
265(C2×D59)⋊C4—44no—
266Dic59⋊C4—28no—
267Dic59⋊C4—28no—
268Dic59⋊C4—44no—
269C4×Dic59—28no—
270C4×Dic59—44no—
271C23×C59C23×C411yescharacteristic
272C23×C59C22×D411yescharacteristic
273C23×C59C22×D411yescharacteristic
274C23×C59C2×#4111yescharacteristic
275C23×C59C2×#4111yescharacteristic
276C23×C59C2×#4111yescharacteristic
277C23×C59C2×#4111yescharacteristic
278C23×C59C2×#4111yescharacteristic
279C23×C59C2×#4111yescharacteristic
280C23×C59C2×#4111yescharacteristic
281C23×C59C2×#4111yescharacteristic
282C23×C59H(5,𝔽2)11yescharacteristic
283C23×C59H(5,𝔽2)11yescharacteristic
284C23×C592−1+411yescharacteristic
285C23×C592−1+411yescharacteristic
286C22×D59—22no—
287C22×D59—22no—
288C22×D59—22no—
289C22×D59—22no—
290C22×D59—22no—
291C22×D59—22no—
292C22×D59—22no—
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—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—
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—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—22no—
344C2×C4×C59—22no—
345C2×C4×C59—22no—
346C2×C4×C59—22no—
347C2×C4×C59—22no—
348C2×C4×C59—22no—
349C2×C4×C59—22no—
350C2×C4×C59—22no—
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#11714yes—
368C2×C4×C59C4×D414yes—
369C2×C4×C59#12314yes—
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—22no—
381C2×Dic59—22no—
382C2×Dic59—22no—
383C2×Dic59—22no—
384C2×Dic59—22no—
385C2×Dic59—22no—
386C2×Dic59—22no—
387C2×Dic59—22no—
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—
417C2×Dic59—41no—
418C2×Dic59C4×D414yes—
419#14031—591nomaximal, Sylow
420C22×C59C2×#11711yescharacteristic
421C22×C59C2×C4×D411yescharacteristic
422C22×C59C2×C4×D411yescharacteristic
423C22×C59C4×#4111yescharacteristic
424C22×C59C4×#4111yescharacteristic
425C22×C59#52011yescharacteristic
426C22×C59#52011yescharacteristic
427C22×C59C2×#12311yescharacteristic
428C22×C59#52511yescharacteristic
429C22×C59#52511yescharacteristic
430C22×C59#52511yescharacteristic
431C22×C59#52911yescharacteristic
432C22×C59#52911yescharacteristic
433C22×C59#52911yescharacteristic
434C22×C59#52911yescharacteristic
435C22×C59#53811yescharacteristic
436C22×C59#53911yescharacteristic
437C22×C59#54111yescharacteristic
438C22×C59#54211yescharacteristic
439C22×C59D4211yescharacteristic
440C22×C59#54611yescharacteristic
441C22×C59#54711yescharacteristic
442C22×C59#54711yescharacteristic
443C22×C59#54811yescharacteristic
444C22×C59#54811yescharacteristic
445C22×C59#55011yescharacteristic
446C22×C59#55311yescharacteristic
447C22×C59#55311yescharacteristic
448C22×C59#55311yescharacteristic
449C22×C59#55511yescharacteristic
450C22×C59#55611yescharacteristic
451C22×C59#55611yescharacteristic
452C22×C59#55611yescharacteristic
453C22×C59#55611yescharacteristic
454C22×C59#55911yescharacteristic
455C2×D59—42no—
456C2×D59—42no—
457C2×D59—42no—
458C2×D59—42no—
459C2×D59—42no—
460C2×D59—42no—
461C2×D59—42no—
462C2×D59—81no—
463C2×D59—81no—
464C2×D59—81no—
465C2×D59—81no—
466C2×D59—81no—
467C2×D59—81no—
468C2×D59—81no—
469C2×D59—81no—
470C4×C59—24no—
471C4×C59—24no—
472C4×C59—24no—
473C4×C59—42no—
474C4×C59—42no—
475C4×C59—42no—
476C4×C59—42no—
477Dic59—24no—
478Dic59—42no—
479Dic59—42no—
480Dic59—42no—
481Dic59—42no—
482Dic59—81no—
483Dic59—81no—
484C2×#388—591no—
485C2×#388—591no—
486C2×#388—591no—
487C2×C4×C4⋊C4—591no—
488C2×C4×C4⋊C4D5911yescharacteristic, complemented
489#1444—591no—
490#1443—591no—
491#1439—591no—
492#1439—591no—
493#1437—591no—
494#1437—591no—
495#1436—591no—
496#1436—591no—
497#1436—591no—
498#1434—591no—
499C2×C59#229011yescharacteristic
500C2×C59C4×#12311yescharacteristic
501C2×C59#233411yescharacteristic
502C2×C59#234711yescharacteristic
503C2×C59#235411yescharacteristic
504C2×C59#236111yescharacteristic
505C2×C59#236711yescharacteristic
506C2×C59#244311yescharacteristic
507C2×C59#244811yescharacteristic
508C2×C59#245611yescharacteristic
509C2×C59#246911yescharacteristic
510C2×C59#246911yescharacteristic
511C2×C59#247411yescharacteristic
512C2×C59#259311yescharacteristic
513C2×C59#259411yescharacteristic
514D59—82no—
515C22×C4⋊C4—591no—
516C22×C4⋊C4—591no—
517C22×C4⋊C4—591no—
518C22×C4⋊C4C2×D5911yescharacteristic
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—
526C22×C22⋊C4—591no—
527C22×C42—591no—
528C22×C42—591no—
529C22×C42C2×D5911yescharacteristic
530C22×C42C2×D5911yescharacteristic
531C22×C42C2×D5911yescharacteristic
532#388—598no—
533#388—1184no—
534#388—1184no—
535C4×C4⋊C4—24no—
536C4×C4⋊C4—1184no—
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×#95—591no—
546C2×#95—591no—
547C2×#95—591no—
548C2×#95—591no—
549C2×#95—591no—
550C2×#95—591no—
551C2×#95—591no—
552C2×#95—591no—
553C2×#95C2×D5911yescharacteristic
554C2×#95C2×D5911yescharacteristic
555C59#1403111yescharacteristic, complemented, Sylow
556C25—591no—
557C23×C4—591no—
558C23×C4—591no—
559C23×C4—591no—
560C23×C4—591no—
561C23×C4—591no—
562C23×C4—591no—
563C23×C4—591no—
564C23×C4C22×D5911yescharacteristic
565C23×C4C22×D5911yescharacteristic
566C23×C4C22×D5911yescharacteristic
567C23×C4C22×D5911yescharacteristic
568C23×C4C22×D5911yescharacteristic
569C23×C4C22×D5911yescharacteristic
570C23×C4C22×D5911yescharacteristic
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—594no—
577C2×C4⋊C4—1182no—
578C2×C4⋊C4—1182no—
579C2×C4⋊C4—1182no—
580C2×C4⋊C4—1182no—
581C2×C4⋊C4—1182no—
582C2×C4⋊C4—1182no—
583C2×C4⋊C4—1182no—
584C2×C4⋊C4—2361no—
585C2×C4⋊C4C4×D5914yes—
586C2×C22⋊C4—594no—
587C2×C22⋊C4—594no—
588C2×C22⋊C4—594no—
589C2×C22⋊C4—1182no—
590C2×C22⋊C4—1182no—
591C2×C22⋊C4—1182no—
592C2×C22⋊C4—1182no—
593C2×C22⋊C4—1182no—
594C2×C22⋊C4—1182no—
595C2×C22⋊C4—1182no—
596C2×C22⋊C4—1182no—
597C2×C22⋊C4—1182no—
598C2×C22⋊C4—1182no—
599C2×C22⋊C4—1182no—
600C2×C22⋊C4—1182no—
601C2×C22⋊C4—1182no—
602C2×C22⋊C4—1182no—
603C2×C22⋊C4—2361no—
604C2×C22⋊C4—2361no—
605C2×C22⋊C4—2361no—
606C2×C22⋊C4—2361no—
607C2×C42—22no—
608C2×C42—22no—
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—22no—
612C2×C42—22no—
613C2×C42—22no—
614C2×C42—41no—
615C2×C42—41no—
616C2×C42—594no—
617C2×C42—1182no—
618C2×C42—1182no—
619C2×C42—1182no—
620C2×C42—1182no—
621C2×C42—2361no—
622#95—22no—
623#95—594no—
624#95—594no—
625#95—1182no—
626#95—1182no—
627#95—1182no—
628#95—1182no—
629#95—1182no—
630#95—1182no—
631#95—1182no—
632#95—1182no—
633#95—1182no—
634#95—1182no—
635#95—2361no—
636#95—2361no—
637#95—2361no—
638#95—2361no—
639#95C22⋊D5914yes—
640C24—592no—
641C24—1181no—
642C24—1181no—
643C24—1181no—
644C24—1181no—
645C24—1181no—
646C24—1181no—
647C24—1181no—
648C24—1181no—
649C24—1181no—
650C24—1181no—
651C24—1181no—
652C24—1181no—
653C24—1181no—
654C24—1181no—
655C24C23×D5911yescharacteristic
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—592no—
693C22×C4—592no—
694C22×C4—592no—
695C22×C4—592no—
696C22×C4—592no—
697C22×C4—592no—
698C22×C4—592no—
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—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×C4C2×C4×D5912yes—
742C22×C4C2×C4×D5912yes—
743C22×C4C2×C4×D5912yes—
744C22×C4#1174568512yes—
745C22×C4#1174568512yes—
746C22×C4#1174568512yes—
747C22×C4#1174568512yes—
748C22×C4#1174568512yes—
749C22×C4D4×D5912yes—
750C22×C4#1174568912yes—
751C22×C4C2×C22⋊D5912yes—
752C22×C4C2×C22⋊D5912yes—
753C22×C4C2×C22⋊D5912yes—
754C4⋊C4—28no—
755C4⋊C4—28no—
756C4⋊C4—1188no—
757C4⋊C4—1188no—
758C4⋊C4—2364no—
759C22⋊C4—1188no—
760C22⋊C4—1188no—
761C22⋊C4—1188no—
762C22⋊C4—2364no—
763C22⋊C4—2364no—
764C22⋊C4—2364no—
765C22⋊C4—2364no—
766C42—28no—
767C42—44no—
768C42—44no—
769C42—1188no—
770C42—2364no—
771C23—1182no—
772C23—1182no—
773C23—1182no—
774C23—1182no—
775C23—1182no—
776C23—1182no—
777C23—1182no—
778C23—2361no—
779C23—2361no—
780C23—2361no—
781C23—2361no—
782C23—2361no—
783C23—2361no—
784C23—2361no—
785C23—2361no—
786C23—2361no—
787C23—2361no—
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—
804C23—2361no—
805C23—2361no—
806C23C22×C4×D5911yescharacteristic
807C23C2×D4×D5911yescharacteristic
808C23C22×C22⋊D5911yescharacteristic
809C23#41×D5911yescharacteristic
810C23#41×D5911yescharacteristic
811C23C2×#1174568511yescharacteristic
812C23C2×#1174568511yescharacteristic
813C23C2×#1174568511yescharacteristic
814C23C2×#1174568511yescharacteristic
815C23C2×#1174568511yescharacteristic
816C23C2×#1174568911yescharacteristic
817C23#1427377211yescharacteristic
818C23#1427377311yescharacteristic
819C23#1427377411yescharacteristic
820C23#1427377511yescharacteristic
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—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—22no—
849C2×C4—22no—
850C2×C4—22no—
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—594no—
868C2×C4—1182no—
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—1182no—
882C2×C4—1182no—
883C2×C4—1182no—
884C2×C4—1182no—
885C2×C4—1182no—
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#1427368414yes—
917C2×C4C4×C22⋊D5914yes—
918C2×C4#1427371214yes—
919C22—4721no—
920C22—4721no—
921C22—4721no—
922C22—4721no—
923C22—4721no—
924C22—4721no—
925C22—4721no—
926C22—4721no—
927C22—2362no—
928C22—2362no—
929C22—2362no—
930C22—2362no—
931C22—2362no—
932C22—2362no—
933C22—2362no—
934C22C2×#1427368411yescharacteristic
935C22C4×D4×D5911yescharacteristic
936C22C2×C4×C22⋊D5911yescharacteristic
937C22C4×#1174568511yescharacteristic
938C22C4×#1174568911yescharacteristic
939C22#1683788111yescharacteristic
940C22#1683788411yescharacteristic
941C22C2×#1427371211yescharacteristic
942C22#1683791111yescharacteristic
943C22#1683791311yescharacteristic
944C22#1683791311yescharacteristic
945C22#1683793011yescharacteristic
946C22#1683793611yescharacteristic
947C22#1683793611yescharacteristic
948C22#1683793911yescharacteristic
949C22#1683798511yescharacteristic
950C22#1683799911yescharacteristic
951C22#1683801011yescharacteristic
952C22#1683802311yescharacteristic
953C22D4×C22⋊D5911yescharacteristic
954C22#1683804011yescharacteristic
955C22#1683805111yescharacteristic
956C22#1683805311yescharacteristic
957C22#1683806111yescharacteristic
958C22#1683806311yescharacteristic
959C22#1683807311yescharacteristic
960C22#1683810011yescharacteristic
961C22#1683810111yescharacteristic
962C22#1683810211yescharacteristic
963C22#1683811511yescharacteristic
964C22#1683812011yescharacteristic
965C22#1683812411yescharacteristic
966C22#1683812411yescharacteristic
967C22#1683812511yescharacteristic
968C22#1683813711yescharacteristic
969C4—24no—
970C4—24no—
971C4—24no—
972C4—42no—
973C4—42no—
974C4—42no—
975C4—42no—
976C4—1184no—
977C4—4721no—
978C4—4721no—
979C4—2362no—
980C4—2362no—
981C4—2362no—
982C4—2362no—
983C2—4722no—
984C2#2142653911yescharacteristic
985C2C4×#1427371211yescharacteristic
986C2#2142686511yescharacteristic
987C2#2142698511yescharacteristic
988C2#2142704111yescharacteristic
989C2#2142711311yescharacteristic
990C2#2142716311yescharacteristic
991C2#2142783111yescharacteristic
992C2#2142789411yescharacteristic
993C2#2142798811yescharacteristic
994C2#2142817111yescharacteristic
995C2#2142817711yescharacteristic
996C2#2142824611yescharacteristic
997C2#2142958711yescharacteristic
998C2#2142959611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C4×C4⋊C4×C59C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenterC2×C4×C4⋊C4D59
hypocenterC59#14031
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C4×Dic59⋊C4C2semidirect
5. #21422359C2semidirect
6. #21422357C2semidirect
11. #21422329C2semidirect
12. #21422329C2semidirect
13. #21422328C2semidirect
14. #21422321C2semidirect
15. C2×C4×C4⋊C4×C59C2semidirect
29. #16837292C4semidirect
488. C2×C4×C4⋊C4D59semidirect
555. C59#14031semidirect

Maximal subgroups

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

subgroupindex
C2×#168372932
C2×#168372922
C2×#168372912
C2×C4×Dic59⋊C42
#214223592
#214223572
#214223402
#214223382
#214223342
#214223292
#214223282
#214223212
C2×C4×C4⋊C4×C592
#1403159