Finite Group Databasebeta

← #28517141

Subgroups — #28517141

Order 15104.

1658 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837302C211yesmaximal, characteristic
2C2×#16837294C211yesmaximal, characteristic, complemented
3#21422344C211yesmaximal, characteristic, complemented
4#21422343C211yesmaximal, characteristic, complemented
5#21422341C211yesmaximal, characteristic, complemented
6#21422338C211yesmaximal, characteristic, complemented
7#21422335C211yesmaximal, characteristic
8#21422335C211yesmaximal, characteristic
9#21422334C211yesmaximal, characteristic, complemented
10#21422333C211yesmaximal, characteristic, complemented
11#21422329C211yesmaximal, characteristic, complemented
12#21422327C211yesmaximal, characteristic, complemented
13#21422325C211yesmaximal, characteristic, complemented
14#21422321C211yesmaximal, characteristic, complemented
15C2×C59×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×Dic59⋊C4C2211yescharacteristic
19C22×C22⋊Dic59C2211yescharacteristic
20C22×C22⋊Dic59C2211yescharacteristic
21C22×C22⋊Dic59C2211yescharacteristic
22C22×(C2×D59)⋊C4C2211yescharacteristic
23C22×(C2×D59)⋊C4C2211yescharacteristic
24C22×(C2×D59)⋊C4C2211yescharacteristic
25C22×(C2×D59)⋊C4C2211yescharacteristic
26C22×(C2×D59)⋊C4C2211yescharacteristic
27C22×(C2×D59)⋊C4C2211yescharacteristic
28C22×C4×Dic59C2211yescharacteristic
29C22×C4×Dic59C2211yescharacteristic
30#16837302C418yescomplemented
31#16837294—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
46C22×C4⋊C4×C59C2211yescharacteristic
47C22×C22⋊C4×C59C2211yescharacteristic
48C22×C22⋊C4×C59C2211yescharacteristic
49C22×C22⋊C4×C59C2211yescharacteristic
50C22×C42×C59C2211yescharacteristic
51C59×#388—24no—
52C2×#95×C59C2211yescharacteristic
53C2×#95×C59C2211yescharacteristic
54C24×D59C2311yescharacteristic
55C22×C22⋊D59—22no—
56C22×C22⋊D59—22no—
57C22×C22⋊D59—41no—
58C22×C22⋊D59—41no—
59C22×C22⋊D59—41no—
60C22×C22⋊D59—41no—
61C22×C22⋊D59C2×C414yes—
62C23×Dic59C2311yescharacteristic
63C23×Dic59C2311yescharacteristic
64C23×Dic59C2311yescharacteristic
65C23×Dic59C2311yescharacteristic
66C23×Dic59C2311yescharacteristic
67C23×Dic59C2311yescharacteristic
68C23×Dic59C2311yescharacteristic
69C2×C4⋊Dic59—22no—
70C2×C4⋊Dic59—22no—
71C2×C4⋊Dic59—41no—
72C2×Dic59⋊C4—41no—
73C2×Dic59⋊C4—41no—
74C2×Dic59⋊C4C2×C414yes—
75C2×C22⋊Dic59—22no—
76C2×C22⋊Dic59—41no—
77C2×C22⋊Dic59—41no—
78C2×C22⋊Dic59—41no—
79C2×C22⋊Dic59—41no—
80C2×C22⋊Dic59—41no—
81C2×C22⋊Dic59—41no—
82C2×C22⋊Dic59—41no—
83C2×C22⋊Dic59C2×C414yes—
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—41no—
91C2×(C2×D59)⋊C4—41no—
92C2×(C2×D59)⋊C4—41no—
93C2×(C2×D59)⋊C4—41no—
94C2×(C2×D59)⋊C4—41no—
95C2×(C2×D59)⋊C4—41no—
96C2×(C2×D59)⋊C4—41no—
97C2×(C2×D59)⋊C4—41no—
98C2×(C2×D59)⋊C4—41no—
99C2×(C2×D59)⋊C4—41no—
100C2×(C2×D59)⋊C4C2×C414yes—
101C2×(C2×D59)⋊C4C2×C414yes—
102C2×C4×Dic59—22no—
103C2×C4×Dic59—41no—
104C2×C4×Dic59—41no—
105C2×C4×Dic59—41no—
106C2×C4×Dic59—41no—
107C2×C4×Dic59C2×C414yes—
108C59⋊#95—22no—
109C59⋊#95—22no—
110C59⋊#95—22no—
111C59⋊#95—22no—
112C59⋊#95—22no—
113C59⋊#95—22no—
114C59⋊#95—41no—
115C59⋊#95—41no—
116C59⋊#95—41no—
117C59⋊#95—41no—
118C59⋊#95—41no—
119C59⋊#95—41no—
120C59⋊#95—41no—
121C59⋊#95—41no—
122C25×C59C2311yescharacteristic
123C23×C4×C59C2311yescharacteristic
124C23×C4×C59C2311yescharacteristic
125C23×C4×C59C2311yescharacteristic
126C23×C4×C59C2311yescharacteristic
127C23×C4×C59C2311yescharacteristic
128C23×C4×C59C2311yescharacteristic
129C2×C4⋊C4×C59—22no—
130C2×C4⋊C4×C59—22no—
131C2×C4⋊C4×C59—41no—
132C2×C22⋊C4×C59—22no—
133C2×C22⋊C4×C59—22no—
134C2×C22⋊C4×C59—22no—
135C2×C22⋊C4×C59—22no—
136C2×C22⋊C4×C59—22no—
137C2×C22⋊C4×C59—41no—
138C2×C22⋊C4×C59—41no—
139C2×C22⋊C4×C59—41no—
140C2×C22⋊C4×C59C2×C414yes—
141C2×C42×C59—22no—
142C2×C42×C59—41no—
143C2×C42×C59—41no—
144#95×C59—22no—
145#95×C59D414yescomplemented
146C24×C59—21no—
147C24×C59—21no—
148C24×C59—21no—
149C24×C59—21no—
150C24×C59—21no—
151C24×C59—21no—
152C24×C59—21no—
153C24×C59—21no—
154C24×C59—21no—
155C24×C59—21no—
156C24×C59—21no—
157C24×C59—21no—
158C24×C59—21no—
159C24×C59—21no—
160C24×C59C22×C412yes—
161C24×C59C2411yescharacteristic
162C23×D59—21no—
163C23×D59—21no—
164C23×D59—21no—
165C23×D59—21no—
166C23×D59—21no—
167C23×D59—21no—
168C23×D59—21no—
169C23×D59—21no—
170C23×D59—21no—
171C23×D59—21no—
172C23×D59—21no—
173C23×D59—21no—
174C23×D59—21no—
175C23×D59—21no—
176C23×D59C22×C412yes—
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×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59C22×C412yes—
213C22×C4×C59C22×C412yes—
214C22×C4×C59C2×D412yes—
215C22×C4×C59C2×D412yes—
216C22×C4×C59C2×D412yes—
217C22×C4×C59#4112yes—
218C22×C4×C59#4112yes—
219C2×C22⋊D59—28no—
220C2×C22⋊D59—44no—
221C2×C22⋊D59—44no—
222C2×C22⋊D59—44no—
223C2×C22⋊D59—44no—
224C2×C22⋊D59—44no—
225C2×C22⋊D59—44no—
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×Dic59—21no—
248C22×Dic59—21no—
249C22×Dic59—21no—
250C22×Dic59—21no—
251C22×Dic59—21no—
252C22×Dic59—21no—
253C22×Dic59—21no—
254C22×Dic59—21no—
255C22×Dic59—21no—
256C22×Dic59—21no—
257C22×Dic59—21no—
258C22×Dic59—21no—
259C22×Dic59—21no—
260C22×Dic59—21no—
261C22×Dic59—21no—
262C22×Dic59—21no—
263C22×Dic59—21no—
264C22×Dic59—21no—
265C22×Dic59—21no—
266C22×Dic59—21no—
267C22×Dic59—21no—
268C22×Dic59—21no—
269C22×Dic59C22×C412yes—
270C22×Dic59C22×C412yes—
271C22×Dic59C22×C412yes—
272C22×Dic59#4112yes—
273C22×Dic59#4112yes—
274C22×Dic59#4112yes—
275C4⋊C4×C59—44no—
276C22⋊C4×C59—28no—
277C22⋊C4×C59—44no—
278C22⋊C4×C59—44no—
279C42×C59—44no—
280C22⋊Dic59—44no—
281C22⋊Dic59—44no—
282C22⋊Dic59—44no—
283(C2×D59)⋊C4—28no—
284(C2×D59)⋊C4—44no—
285(C2×D59)⋊C4—44no—
286(C2×D59)⋊C4—44no—
287(C2×D59)⋊C4—44no—
288(C2×D59)⋊C4—44no—
289C4⋊Dic59—44no—
290Dic59⋊C4—44no—
291C4×Dic59—44no—
292C4×Dic59—44no—
293C23×C59—22no—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59—22no—
298C23×C59—22no—
299C23×C59—22no—
300C23×C59—41no—
301C23×C59—41no—
302C23×C59—41no—
303C23×C59—41no—
304C23×C59—41no—
305C23×C59—41no—
306C23×C59—41no—
307C23×C59—41no—
308C23×C59—41no—
309C23×C59—41no—
310C23×C59—41no—
311C23×C59—41no—
312C23×C59—41no—
313C23×C59—41no—
314C23×C59—41no—
315C23×C59—41no—
316C23×C59—41no—
317C23×C59—41no—
318C23×C59—41no—
319C23×C59—41no—
320C23×C59—41no—
321C23×C59—41no—
322C23×C59—41no—
323C23×C59—41no—
324C23×C59—41no—
325C23×C59—41no—
326C23×C59—41no—
327C23×C59—41no—
328C23×C59C23×C411yescharacteristic
329C23×C59C22×D411yescharacteristic
330C23×C59C2×#4111yescharacteristic
331C23×C59C2×#4111yescharacteristic
332C23×C59C2×#4111yescharacteristic
333C23×C59C2×#4111yescharacteristic
334C23×C59C2×#4111yescharacteristic
335C23×C59H(5,𝔽2)11yescharacteristic
336C23×C59H(5,𝔽2)11yescharacteristic
337C23×C59H(5,𝔽2)11yescharacteristic
338C23×C59H(5,𝔽2)11yescharacteristic
339C23×C59H(5,𝔽2)11yescharacteristic
340C23×C59H(5,𝔽2)11yescharacteristic
341C23×C59H(5,𝔽2)11yescharacteristic
342C23×C592−1+411yescharacteristic
343C22×D59—22no—
344C22×D59—22no—
345C22×D59—22no—
346C22×D59—22no—
347C22×D59—22no—
348C22×D59—22no—
349C22×D59—22no—
350C22×D59—41no—
351C22×D59—41no—
352C22×D59—41no—
353C22×D59—41no—
354C22×D59—41no—
355C22×D59—41no—
356C22×D59—41no—
357C22×D59—41no—
358C22×D59—41no—
359C22×D59—41no—
360C22×D59—41no—
361C22×D59—41no—
362C22×D59—41no—
363C22×D59—41no—
364C22×D59—41no—
365C22×D59—41no—
366C22×D59—41no—
367C22×D59—41no—
368C22×D59—41no—
369C22×D59—41no—
370C22×D59—41no—
371C22×D59—41no—
372C22×D59—41no—
373C22×D59—41no—
374C22×D59—41no—
375C22×D59—41no—
376C22×D59—41no—
377C22×D59—41no—
378C2×C4×C59—22no—
379C2×C4×C59—22no—
380C2×C4×C59—22no—
381C2×C4×C59—22no—
382C2×C4×C59—22no—
383C2×C4×C59—22no—
384C2×C4×C59—22no—
385C2×C4×C59—22no—
386C2×C4×C59—22no—
387C2×C4×C59—22no—
388C2×C4×C59—22no—
389C2×C4×C59—22no—
390C2×C4×C59—22no—
391C2×C4×C59—22no—
392C2×C4×C59—22no—
393C2×C4×C59—22no—
394C2×C4×C59—22no—
395C2×C4×C59—22no—
396C2×C4×C59—41no—
397C2×C4×C59—41no—
398C2×C4×C59—41no—
399C2×C4×C59—41no—
400C2×C4×C59—41no—
401C2×C4×C59—41no—
402C2×C4×C59—41no—
403C2×C4×C59—41no—
404C2×C4×C59—41no—
405C2×C4×C59—41no—
406C2×C4×C59—41no—
407C2×C4×C59—41no—
408C2×C4×C59—41no—
409C2×C4×C59—41no—
410C2×C4×C59—41no—
411C2×C4×C59—41no—
412C2×C4×C59—41no—
413C2×C4×C59—41no—
414C2×C4×C59—41no—
415C2×C4×C59—41no—
416C2×C4×C59—41no—
417C2×C4×C59—41no—
418C2×C4×C59—41no—
419C2×C4×C59C4×D414yes—
420C22⋊D59—416no—
421C2×Dic59—22no—
422C2×Dic59—22no—
423C2×Dic59—22no—
424C2×Dic59—22no—
425C2×Dic59—22no—
426C2×Dic59—22no—
427C2×Dic59—22no—
428C2×Dic59—22no—
429C2×Dic59—22no—
430C2×Dic59—22no—
431C2×Dic59—22no—
432C2×Dic59—22no—
433C2×Dic59—22no—
434C2×Dic59—22no—
435C2×Dic59—22no—
436C2×Dic59—41no—
437C2×Dic59—41no—
438C2×Dic59—41no—
439C2×Dic59—41no—
440C2×Dic59—41no—
441C2×Dic59—41no—
442C2×Dic59—41no—
443C2×Dic59—41no—
444C2×Dic59—41no—
445C2×Dic59—41no—
446C2×Dic59—41no—
447C2×Dic59—41no—
448C2×Dic59—41no—
449C2×Dic59—41no—
450C2×Dic59—41no—
451C2×Dic59—41no—
452C2×Dic59—41no—
453C2×Dic59—41no—
454C2×Dic59—41no—
455C2×Dic59—41no—
456C2×Dic59—41no—
457C2×Dic59—41no—
458C2×Dic59—41no—
459C2×Dic59—41no—
460C2×Dic59—41no—
461C2×Dic59—41no—
462C2×Dic59—41no—
463C2×Dic59—41no—
464C2×Dic59—41no—
465C2×Dic59—41no—
466C2×Dic59—41no—
467C2×Dic59—41no—
468C2×Dic59—41no—
469C2×Dic59#11714yes—
470#14444—591nomaximal, Sylow
471C22×C59—42no—
472C22×C59—42no—
473C22×C59—42no—
474C22×C59—42no—
475C22×C59—42no—
476C22×C59—42no—
477C22×C59—42no—
478C22×C59—81no—
479C22×C59—81no—
480C22×C59—81no—
481C22×C59—81no—
482C22×C59—81no—
483C22×C59—81no—
484C22×C59—81no—
485C22×C59—81no—
486C22×C59C2×#11711yescharacteristic
487C22×C59C2×C4×D411yescharacteristic
488C22×C59C4×#4111yescharacteristic
489C22×C59#51811yescharacteristic
490C22×C59#51811yescharacteristic
491C22×C59#51811yescharacteristic
492C22×C59#52011yescharacteristic
493C22×C59#53511yescharacteristic
494C22×C59#53511yescharacteristic
495C22×C59#53811yescharacteristic
496C22×C59#53811yescharacteristic
497C22×C59#53811yescharacteristic
498C22×C59#53811yescharacteristic
499C22×C59#53811yescharacteristic
500C22×C59#53811yescharacteristic
501C22×C59#54011yescharacteristic
502C22×C59#54011yescharacteristic
503C22×C59#54211yescharacteristic
504C22×C59#54211yescharacteristic
505C22×C59#54611yescharacteristic
506C22×C59#54611yescharacteristic
507C22×C59#54711yescharacteristic
508C22×C59#55011yescharacteristic
509C22×C59#55311yescharacteristic
510C22×C59#55311yescharacteristic
511C22×C59#55311yescharacteristic
512C22×C59#55311yescharacteristic
513C22×C59#55511yescharacteristic
514C22×C59#55611yescharacteristic
515C22×C59#55911yescharacteristic
516C22×C59#55911yescharacteristic
517C22×C59#56011yescharacteristic
518C22×C59#56011yescharacteristic
519C22×C59#56211yescharacteristic
520C22×C59#56211yescharacteristic
521C2×D59—42no—
522C2×D59—42no—
523C2×D59—42no—
524C2×D59—42no—
525C2×D59—42no—
526C2×D59—42no—
527C2×D59—42no—
528C2×D59—81no—
529C2×D59—81no—
530C2×D59—81no—
531C2×D59—81no—
532C2×D59—81no—
533C2×D59—81no—
534C2×D59—81no—
535C2×D59—81no—
536C4×C59—24no—
537C4×C59—42no—
538C4×C59—42no—
539C4×C59—42no—
540C4×C59—42no—
541C4×C59—81no—
542Dic59—24no—
543Dic59—42no—
544Dic59—42no—
545Dic59—42no—
546Dic59—81no—
547Dic59—81no—
548Dic59—81no—
549C2×#390—591no—
550C2×#388—591no—
551C2×#388D5911yescharacteristic, complemented
552#1440—591no—
553#1440—591no—
554#1439—591no—
555#1439—591no—
556#1438—591no—
557#1438—591no—
558#1437—591no—
559#1437—591no—
560#1436—591no—
561#1436—591no—
562C4⋊#95—591no—
563#1434—591no—
564C2×C59—82no—
565C2×C59#231211yescharacteristic
566C2×C59#232811yescharacteristic
567C2×C59#233711yescharacteristic
568C2×C59#235411yescharacteristic
569C2×C59#235711yescharacteristic
570C2×C59#236411yescharacteristic
571C2×C59#237711yescharacteristic
572C2×C59#271011yescharacteristic
573C2×C59#271011yescharacteristic
574C2×C59#271411yescharacteristic
575C2×C59#271411yescharacteristic
576C2×C59#280011yescharacteristic
577C2×C59#280011yescharacteristic
578C2×C59#280311yescharacteristic
579C2×C59#280311yescharacteristic
580D59—82no—
581C23×D4—591no—
582C22×C4⋊C4—591no—
583C22×C4⋊C4—591no—
584C22×C4⋊C4C2×D5911yescharacteristic
585C22×C22⋊C4—591no—
586C22×C22⋊C4—591no—
587C22×C22⋊C4—591no—
588C22×C22⋊C4—591no—
589C22×C22⋊C4—591no—
590C22×C22⋊C4—591no—
591C22×C22⋊C4—591no—
592C22×C22⋊C4—591no—
593C22×C22⋊C4—591no—
594C22×C22⋊C4C2×D5911yescharacteristic
595C22×C22⋊C4C2×D5911yescharacteristic
596C22×C22⋊C4C2×D5911yescharacteristic
597C22×C42—591no—
598C22×C42—591no—
599C22×C42C2×D5911yescharacteristic
600#390—598no—
601#388—24no—
602#388—1184no—
603C2×#95—591no—
604C2×#95—591no—
605C2×#95—591no—
606C2×#95—591no—
607C2×#95—591no—
608C2×#95—591no—
609C2×#95—591no—
610C2×#95—591no—
611C2×#95—591no—
612C2×#95—591no—
613C2×#95—591no—
614C2×#95—591no—
615C2×#95—591no—
616C2×#95—591no—
617C2×#95C2×D5911yescharacteristic
618C2×#95C2×D5911yescharacteristic
619C59#1444411yescharacteristic, complemented, Sylow
620C25—591no—
621C25C22×D5911yescharacteristic
622C22×D4—594no—
623C22×D4—1182no—
624C22×D4—1182no—
625C22×D4—2361no—
626C22×D4—2361no—
627C22×D4—2361no—
628C22×D4—2361no—
629C23×C4—591no—
630C23×C4—591no—
631C23×C4—591no—
632C23×C4—591no—
633C23×C4—591no—
634C23×C4—591no—
635C23×C4—591no—
636C23×C4C22×D5911yescharacteristic
637C23×C4C22×D5911yescharacteristic
638C23×C4C22×D5911yescharacteristic
639C23×C4C22×D5911yescharacteristic
640C23×C4C22×D5911yescharacteristic
641C23×C4C22×D5911yescharacteristic
642C2×C4⋊C4—22no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—594no—
646C2×C4⋊C4—1182no—
647C2×C4⋊C4—1182no—
648C2×C4⋊C4—2361no—
649C2×C4⋊C4—2361no—
650C2×C4⋊C4—2361no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—41no—
657C2×C22⋊C4—41no—
658C2×C22⋊C4—41no—
659C2×C22⋊C4—594no—
660C2×C22⋊C4—594no—
661C2×C22⋊C4—594no—
662C2×C22⋊C4—1182no—
663C2×C22⋊C4—1182no—
664C2×C22⋊C4—1182no—
665C2×C22⋊C4—1182no—
666C2×C22⋊C4—1182no—
667C2×C22⋊C4—1182no—
668C2×C22⋊C4—1182no—
669C2×C22⋊C4—2361no—
670C2×C22⋊C4—2361no—
671C2×C22⋊C4—2361no—
672C2×C22⋊C4—2361no—
673C2×C22⋊C4—2361no—
674C2×C22⋊C4—2361no—
675C2×C22⋊C4—2361no—
676C2×C22⋊C4—2361no—
677C2×C22⋊C4—2361no—
678C2×C22⋊C4—2361no—
679C2×C22⋊C4—2361no—
680C2×C22⋊C4—2361no—
681C2×C22⋊C4—2361no—
682C2×C22⋊C4—2361no—
683C2×C22⋊C4—2361no—
684C2×C22⋊C4—2361no—
685C2×C22⋊C4—2361no—
686C2×C22⋊C4C4×D5914yes—
687C2×C42—22no—
688C2×C42—41no—
689C2×C42—41no—
690C2×C42—594no—
691C2×C42—1182no—
692C2×C42—2361no—
693C2×C42—2361no—
694C2×C42—2361no—
695C2×C42—2361no—
696#95—22no—
697#95—1182no—
698#95—1182no—
699#95—1182no—
700#95—1182no—
701#95—1182no—
702#95—1182no—
703#95—2361no—
704#95—2361no—
705#95—2361no—
706#95—2361no—
707#95—2361no—
708#95—2361no—
709#95—2361no—
710#95—2361no—
711#95C22⋊D5914yescomplemented
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—592no—
727C24—1181no—
728C24—1181no—
729C24—1181no—
730C24—1181no—
731C24—1181no—
732C24—1181no—
733C24—1181no—
734C24—1181no—
735C24—1181no—
736C24—1181no—
737C24—1181no—
738C24—1181no—
739C24—1181no—
740C24—1181no—
741C24C2×C4×D5912yes—
742C24C23×D5911yescharacteristic
743C2×D4—1188no—
744C2×D4—2364no—
745C2×D4—2364no—
746C2×D4—2364no—
747C2×D4—2364no—
748C2×D4—2364no—
749C2×D4—2364no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—592no—
786C22×C4—592no—
787C22×C4—592no—
788C22×C4—592no—
789C22×C4—592no—
790C22×C4—592no—
791C22×C4—1181no—
792C22×C4—1181no—
793C22×C4—1181no—
794C22×C4—1181no—
795C22×C4—1181no—
796C22×C4—1181no—
797C22×C4—1181no—
798C22×C4—1181no—
799C22×C4—1181no—
800C22×C4—1181no—
801C22×C4—1181no—
802C22×C4—1181no—
803C22×C4—1181no—
804C22×C4—1181no—
805C22×C4—1181no—
806C22×C4—1181no—
807C22×C4—1181no—
808C22×C4—1181no—
809C22×C4—1181no—
810C22×C4—1181no—
811C22×C4—1181no—
812C22×C4—1181no—
813C22×C4—1181no—
814C22×C4—1181no—
815C22×C4—1181no—
816C22×C4—1181no—
817C22×C4—1181no—
818C22×C4—1181no—
819C22×C4—1181no—
820C22×C4—1181no—
821C22×C4—1181no—
822C22×C4—1181no—
823C22×C4—1181no—
824C22×C4—1181no—
825C22×C4—1181no—
826C22×C4—1181no—
827C22×C4—1181no—
828C22×C4—1181no—
829C22×C4—1181no—
830C22×C4—1181no—
831C22×C4—1181no—
832C22×C4—1181no—
833C22×C4—1181no—
834C22×C4C2×C4×D5912yes—
835C22×C4C2×C4×D5912yes—
836C22×C4#1174568512yes—
837C22×C4#1174568712yes—
838C22×C4C2×C22⋊D5912yes—
839C22×C4C2×C22⋊D5912yes—
840C22×C4C2×C22⋊D5912yes—
841C4⋊C4—44no—
842C4⋊C4—2364no—
843C4⋊C4—2364no—
844C22⋊C4—28no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—1188no—
848C22⋊C4—2364no—
849C22⋊C4—2364no—
850C22⋊C4—2364no—
851C22⋊C4—2364no—
852C22⋊C4—2364no—
853C22⋊C4—2364no—
854C22⋊C4—2364no—
855C22⋊C4—2364no—
856C42—44no—
857C42—2364no—
858C42—2364no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—1182no—
895C23—1182no—
896C23—1182no—
897C23—1182no—
898C23—1182no—
899C23—1182no—
900C23—1182no—
901C23—2361no—
902C23—2361no—
903C23—2361no—
904C23—2361no—
905C23—2361no—
906C23—2361no—
907C23—2361no—
908C23—2361no—
909C23—2361no—
910C23—2361no—
911C23—2361no—
912C23—2361no—
913C23—2361no—
914C23—2361no—
915C23—2361no—
916C23—2361no—
917C23—2361no—
918C23—2361no—
919C23—2361no—
920C23—2361no—
921C23—2361no—
922C23—2361no—
923C23—2361no—
924C23—2361no—
925C23—2361no—
926C23—2361no—
927C23—2361no—
928C23—2361no—
929C23C22×C4×D5911yescharacteristic
930C23C22×C22⋊D5911yescharacteristic
931C23#41×D5911yescharacteristic
932C23#41×D5911yescharacteristic
933C23#41×D5911yescharacteristic
934C23C2×#1174568711yescharacteristic
935C23C2×#1174568511yescharacteristic
936C23#1427377211yescharacteristic
937C23#1427377211yescharacteristic
938C23#1427377211yescharacteristic
939C23#1427377311yescharacteristic
940C23#1427377311yescharacteristic
941C23#1427377311yescharacteristic
942C23#1427377311yescharacteristic
943C23#1427377411yescharacteristic
944D4—23616no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—594no—
987C2×C4—1182no—
988C2×C4—1182no—
989C2×C4—1182no—
990C2×C4—1182no—
991C2×C4—1182no—
992C2×C4—1182no—
993C2×C4—1182no—
994C2×C4—1182no—
995C2×C4—1182no—
996C2×C4—1182no—
997C2×C4—1182no—
998C2×C4—1182no—
999C2×C4—1182no—
1000C2×C4—1182no—
1001C2×C4—1182no—
1002C2×C4—2361no—
1003C2×C4—2361no—
1004C2×C4—2361no—
1005C2×C4—2361no—
1006C2×C4—2361no—
1007C2×C4—2361no—
1008C2×C4—2361no—
1009C2×C4—2361no—
1010C2×C4—2361no—
1011C2×C4—2361no—
1012C2×C4—2361no—
1013C2×C4—2361no—
1014C2×C4—2361no—
1015C2×C4—2361no—
1016C2×C4—2361no—
1017C2×C4—2361no—
1018C2×C4—2361no—
1019C2×C4—2361no—
1020C2×C4—2361no—
1021C2×C4—2361no—
1022C2×C4—2361no—
1023C2×C4—2361no—
1024C2×C4—2361no—
1025C2×C4—2361no—
1026C2×C4—2361no—
1027C2×C4—2361no—
1028C2×C4—2361no—
1029C2×C4—2361no—
1030C2×C4—2361no—
1031C2×C4—2361no—
1032C2×C4—2361no—
1033C2×C4—2361no—
1034C2×C4—2361no—
1035C2×C4C4×C22⋊D5914yes—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—4721no—
1052C22—4721no—
1053C22—4721no—
1054C22—4721no—
1055C22—4721no—
1056C22—4721no—
1057C22—4721no—
1058C22—4721no—
1059C22—2362no—
1060C22—2362no—
1061C22—2362no—
1062C22—2362no—
1063C22—2362no—
1064C22—2362no—
1065C22—2362no—
1066C22#117×D5911yescharacteristic
1067C22C2×C4×C22⋊D5911yescharacteristic
1068C22C4×#1174568711yescharacteristic
1069C22#1683787411yescharacteristic
1070C22#1683787411yescharacteristic
1071C22#1683787411yescharacteristic
1072C22#1683788211yescharacteristic
1073C22#1683796611yescharacteristic
1074C22#1683796911yescharacteristic
1075C22#1683798411yescharacteristic
1076C22#1683798611yescharacteristic
1077C22#1683798811yescharacteristic
1078C22#1683798911yescharacteristic
1079C22#1683799111yescharacteristic
1080C22#1683799111yescharacteristic
1081C22#1683800311yescharacteristic
1082C22#1683800311yescharacteristic
1083C22#1683802011yescharacteristic
1084C22#1683802111yescharacteristic
1085C22#1683804011yescharacteristic
1086C22#1683804611yescharacteristic
1087C22#1683805111yescharacteristic
1088C22#1683807111yescharacteristic
1089C22#1683809511yescharacteristic
1090C22#1683809811yescharacteristic
1091C22#1683810111yescharacteristic
1092C22#1683810311yescharacteristic
1093C22#1683811511yescharacteristic
1094C22#1683812011yescharacteristic
1095C22#1683813411yescharacteristic
1096C22#1683813611yescharacteristic
1097C22#1683814011yescharacteristic
1098C22#1683814311yescharacteristic
1099C22#1683814611yescharacteristic
1100C22#1683814911yescharacteristic
1101C4—24no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—81no—
1107C4—1184no—
1108C4—4721no—
1109C4—4721no—
1110C4—4721no—
1111C4—2362no—
1112C4—2362no—
1113C4—2362no—
1114C2—82no—
1115C2—4722no—
1116C2#2142669011yescharacteristic
1117C2#2142681811yescharacteristic
1118C2#2142690311yescharacteristic
1119C2#2142704611yescharacteristic
1120C2#2142706611yescharacteristic
1121C2#2142714111yescharacteristic
1122C2#2142724911yescharacteristic
1123C2#2143083211yescharacteristic
1124C2#2143083411yescharacteristic
1125C2#2143088611yescharacteristic
1126C2#2143088811yescharacteristic
1127C2#2143198711yescharacteristic
1128C2#2143199211yescharacteristic
1129C2#2143202411yescharacteristic
1130C2#2143202911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C59×#388C2
socle, cosocleC24×C59C24
prime radicalC23×C22⋊D59C22
hypercenterC2×#388D59
hypocenterC59#14444
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#16837294C2semidirect
3. #21422344C2semidirect
4. #21422343C2semidirect
5. #21422341C2semidirect
6. #21422338C2semidirect
9. #21422334C2semidirect
10. #21422333C2semidirect
11. #21422329C2semidirect
12. #21422327C2semidirect
13. #21422325C2semidirect
14. #21422321C2semidirect
15. C2×C59×#388C2semidirect
30. #16837302C4semidirect
145. #95×C59D4semidirect
551. C2×#388D59semidirect
619. C59#14444semidirect
711. #95C22⋊D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168373022
C2×#168372942
#214223442
#214223432
#214223412
#214223382
#214223352
#214223342
#214223332
#214223292
#214223272
#214223252
#214223212
C2×C59×#3882
#1444459