Finite Group Databasebeta

← #28510330

Subgroups — #28510330

Order 15104.

1998 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837302C211yesmaximal, characteristic
2C2×#16837281C211yesmaximal, characteristic
3C2×#16837278C211yesmaximal, characteristic
4#21422333C211yesmaximal, characteristic, complemented
5#21422333C211yesmaximal, characteristic, complemented
6#21422332C211yesmaximal, characteristic, complemented
7#21422332C211yesmaximal, characteristic, complemented
8#21422331C211yesmaximal, characteristic, complemented
9#21422327C211yesmaximal, characteristic, complemented
10#21422322C211yesmaximal, characteristic, complemented
11#21422320C211yesmaximal, characteristic, complemented
12#21422319C211yesmaximal, characteristic, complemented
13(C2×D59)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D59)⋊#95C211yesmaximal, characteristic, complemented
15C59×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C22⋊D59C2211yescharacteristic
17C23×C4×D59C2211yescharacteristic
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×C4×Dic59C2211yescharacteristic
28C22×C4×Dic59C2211yescharacteristic
29C22×C4×Dic59C2211yescharacteristic
30#16837302C418yescomplemented
31#16837281C418yescomplemented
32#16837278C418yescomplemented
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
47C24×C4×C59C2211yescharacteristic
48C22×C22⋊C4×C59C2211yescharacteristic
49C22×C22⋊C4×C59C2211yescharacteristic
50C2×#95×C59C2211yescharacteristic
51C2×#95×C59C2211yescharacteristic
52C2×#95×C59C2211yescharacteristic
53C2×#95×C59C2211yescharacteristic
54C24×D59C2311yescharacteristic
55C22×C22⋊D59—41no—
56C22×C22⋊D59—41no—
57C22×C22⋊D59—41no—
58C22×C22⋊D59—41no—
59C22×C22⋊D59C2×C414yes—
60C22×C22⋊D59C2×C414yes—
61C22×C22⋊D59C2×C414yes—
62C23×Dic59C2311yescharacteristic
63C23×Dic59C2311yescharacteristic
64C23×Dic59C2311yescharacteristic
65C23×Dic59C2311yescharacteristic
66C23×Dic59C2311yescharacteristic
67C23×Dic59C2311yescharacteristic
68C23×Dic59C2311yescharacteristic
69C22×C4×D59—41no—
70C22×C4×D59—41no—
71C22×C4×D59—41no—
72C22×C4×D59—41no—
73C22×C4×D59—41no—
74C22×C4×D59—41no—
75C22×C4×D59C2×C414yescomplemented
76C2×Dic59⋊C4—41no—
77C2×Dic59⋊C4—41no—
78C2×Dic59⋊C4C2×C414yescomplemented
79C2×C22⋊Dic59—41no—
80C2×C22⋊Dic59—41no—
81C2×C22⋊Dic59—41no—
82C2×C22⋊Dic59—41no—
83C2×C22⋊Dic59—41no—
84C2×C22⋊Dic59—41no—
85C2×C22⋊Dic59C2×C414yes—
86C2×C22⋊Dic59C2×C414yescomplemented
87C2×C22⋊Dic59C2×C414yescomplemented
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)⋊C4—41no—
96C2×(C2×D59)⋊C4—41no—
97C2×(C2×D59)⋊C4—41no—
98C2×(C2×D59)⋊C4C2×C414yes—
99C2×(C2×D59)⋊C4C2×C414yes—
100C2×(C2×D59)⋊C4C2×C414yescomplemented
101C2×(C2×D59)⋊C4C2×C414yescomplemented
102C2×(C2×D59)⋊C4C2×C414yescomplemented
103C2×C4×Dic59—41no—
104C2×C4×Dic59—41no—
105C2×C4×Dic59—41no—
106C2×C4×Dic59—41no—
107C2×C4×Dic59—41no—
108C2×C4×Dic59—41no—
109C2×C4×Dic59—41no—
110C2×C4×Dic59—41no—
111C2×C4×Dic59C2×C414yescomplemented
112C59⋊#95—41no—
113C59⋊#95—41no—
114C59⋊#95—41no—
115C59⋊#95—41no—
116C59⋊#95—41no—
117C59⋊#95—41no—
118C59⋊#95—41no—
119C59⋊#95—41no—
120C59⋊#95—41no—
121C59⋊#95—41no—
122C59⋊#95C2×C414yescomplemented
123C59⋊#95C2×C414yescomplemented
124C59⋊#95C2×C414yescomplemented
125C59⋊#95C2×C414yescomplemented
126C25×C59C2311yescharacteristic
127C23×C4×C59—41no—
128C23×C4×C59—41no—
129C23×C4×C59—41no—
130C23×C4×C59—41no—
131C23×C4×C59—41no—
132C23×C4×C59—41no—
133C23×C4×C59C2×C414yescomplemented
134C23×C4×C59C2311yescharacteristic
135C23×C4×C59C2311yescharacteristic
136C23×C4×C59C2311yescharacteristic
137C23×C4×C59C2311yescharacteristic
138C23×C4×C59C2311yescharacteristic
139C23×C4×C59C2311yescharacteristic
140C2×C22⋊C4×C59—41no—
141C2×C22⋊C4×C59—41no—
142C2×C22⋊C4×C59—41no—
143C2×C22⋊C4×C59—41no—
144C2×C22⋊C4×C59C2×C414yes—
145C2×C22⋊C4×C59C2×C414yescomplemented
146#95×C59—41no—
147#95×C59—41no—
148#95×C59—41no—
149#95×C59—41no—
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×C59—21no—
161C24×C59—21no—
162C24×C59C22×C412yes—
163C24×C59C22×C412yes—
164C24×C59C22×C412yes—
165C24×C59C2411yescharacteristic
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×D59—21no—
177C23×D59—21no—
178C23×D59C22×C412yes—
179C23×D59C22×C412yes—
180C23×D59C22×C412yes—
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×C59—21no—
213C22×C4×C59—21no—
214C22×C4×C59—21no—
215C22×C4×C59—21no—
216C22×C4×C59—21no—
217C22×C4×C59—44no—
218C22×C4×C59—44no—
219C22×C4×C59—44no—
220C22×C4×C59—44no—
221C22×C4×C59—44no—
222C22×C4×C59—44no—
223C22×C4×C59—44no—
224C22×C4×C59C22×C412yes—
225C22×C4×C59C22×C412yes—
226C22×C4×C59C22×C412yes—
227C22×C4×C59C22×C412yes—
228C22×C4×C59C22×C412yes—
229C22×C4×C59C22×C412yes—
230C2×C22⋊D59—44no—
231C2×C22⋊D59—44no—
232C2×C22⋊D59—44no—
233C2×C22⋊D59—44no—
234C2×C22⋊D59—44no—
235C2×C22⋊D59—44no—
236C2×C22⋊D59C42116yescomplemented
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×Dic59—21no—
270C22×Dic59—21no—
271C22×Dic59—21no—
272C22×Dic59—21no—
273C22×Dic59—21no—
274C22×Dic59—21no—
275C22×Dic59—21no—
276C22×Dic59—21no—
277C22×Dic59C22×C412yes—
278C22×Dic59C22×C412yes—
279C22×Dic59C22×C412yes—
280C22×Dic59C22×C412yes—
281C22×Dic59C22×C412yes—
282C22×Dic59C22×C412yes—
283C22×Dic59C22×C412yes—
284C22×Dic59C22×C412yes—
285C22×Dic59C22×C412yes—
286C2×C4×D59—44no—
287C2×C4×D59—44no—
288C2×C4×D59—44no—
289C2×C4×D59—44no—
290C2×C4×D59—44no—
291C2×C4×D59—44no—
292C2×C4×D59—44no—
293C22⋊C4×C59—44no—
294C22⋊C4×C59—44no—
295C22⋊Dic59—44no—
296C22⋊Dic59—44no—
297C22⋊Dic59—44no—
298(C2×D59)⋊C4—44no—
299(C2×D59)⋊C4—44no—
300(C2×D59)⋊C4—44no—
301(C2×D59)⋊C4—44no—
302(C2×D59)⋊C4—44no—
303Dic59⋊C4—44no—
304C4×Dic59—44no—
305C4×Dic59—44no—
306C4×Dic59—44no—
307C23×C59—22no—
308C23×C59—22no—
309C23×C59—22no—
310C23×C59—22no—
311C23×C59—22no—
312C23×C59—22no—
313C23×C59—22no—
314C23×C59—22no—
315C23×C59—22no—
316C23×C59—22no—
317C23×C59—22no—
318C23×C59—22no—
319C23×C59—22no—
320C23×C59—22no—
321C23×C59—22no—
322C23×C59—22no—
323C23×C59—22no—
324C23×C59—22no—
325C23×C59—41no—
326C23×C59—41no—
327C23×C59—41no—
328C23×C59—41no—
329C23×C59—41no—
330C23×C59—41no—
331C23×C59—41no—
332C23×C59—41no—
333C23×C59—41no—
334C23×C59—41no—
335C23×C59—41no—
336C23×C59—41no—
337C23×C59—41no—
338C23×C59—41no—
339C23×C59—41no—
340C23×C59—41no—
341C23×C59C2×C4214yes—
342C23×C59C23×C411yescharacteristic
343C23×C59C23×C411yescharacteristic
344C23×C59C23×C411yescharacteristic
345C23×C59H(5,𝔽2)11yescharacteristic
346C23×C59H(5,𝔽2)11yescharacteristic
347C23×C59H(5,𝔽2)11yescharacteristic
348C23×C59H(5,𝔽2)11yescharacteristic
349C23×C59H(5,𝔽2)11yescharacteristic
350C23×C59H(5,𝔽2)11yescharacteristic
351C23×C59H(5,𝔽2)11yescharacteristic
352C23×C59H(5,𝔽2)11yescharacteristic
353C23×C59H(5,𝔽2)11yescharacteristic
354C23×C59H(5,𝔽2)11yescharacteristic
355C23×C592−1+411yescharacteristic
356C23×C592−1+411yescharacteristic
357C22×D59—22no—
358C22×D59—22no—
359C22×D59—22no—
360C22×D59—22no—
361C22×D59—22no—
362C22×D59—22no—
363C22×D59—22no—
364C22×D59—22no—
365C22×D59—22no—
366C22×D59—22no—
367C22×D59—22no—
368C22×D59—22no—
369C22×D59—22no—
370C22×D59—22no—
371C22×D59—22no—
372C22×D59—22no—
373C22×D59—22no—
374C22×D59—22no—
375C22×D59—41no—
376C22×D59—41no—
377C22×D59—41no—
378C22×D59—41no—
379C22×D59—41no—
380C22×D59—41no—
381C22×D59—41no—
382C22×D59—41no—
383C22×D59—41no—
384C22×D59—41no—
385C22×D59—41no—
386C22×D59—41no—
387C22×D59—41no—
388C22×D59—41no—
389C22×D59—41no—
390C22×D59—41no—
391C22×D59C2×C4214yes—
392C2×C4×C59—22no—
393C2×C4×C59—22no—
394C2×C4×C59—22no—
395C2×C4×C59—22no—
396C2×C4×C59—22no—
397C2×C4×C59—22no—
398C2×C4×C59—22no—
399C2×C4×C59—22no—
400C2×C4×C59—22no—
401C2×C4×C59—22no—
402C2×C4×C59—22no—
403C2×C4×C59—22no—
404C2×C4×C59—22no—
405C2×C4×C59—22no—
406C2×C4×C59—22no—
407C2×C4×C59—22no—
408C2×C4×C59—22no—
409C2×C4×C59—22no—
410C2×C4×C59—416no—
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×C59—41no—
420C2×C4×C59—41no—
421C2×C4×C59—41no—
422C2×C4×C59—41no—
423C2×C4×C59—41no—
424C2×C4×C59—41no—
425C2×C4×C59—41no—
426C2×C4×C59—41no—
427C2×C4×C59—41no—
428C2×C4×C59—41no—
429C2×C4×C59—41no—
430C2×C4×C59—41no—
431C2×C4×C59—41no—
432C2×C4×C59—41no—
433C2×C4×C59—41no—
434C2×C4×C59—41no—
435C22⋊D59—416no—
436C2×Dic59—22no—
437C2×Dic59—22no—
438C2×Dic59—22no—
439C2×Dic59—22no—
440C2×Dic59—22no—
441C2×Dic59—22no—
442C2×Dic59—22no—
443C2×Dic59—22no—
444C2×Dic59—22no—
445C2×Dic59—22no—
446C2×Dic59—22no—
447C2×Dic59—22no—
448C2×Dic59—22no—
449C2×Dic59—22no—
450C2×Dic59—22no—
451C2×Dic59—22no—
452C2×Dic59—22no—
453C2×Dic59—22no—
454C2×Dic59—22no—
455C2×Dic59—22no—
456C2×Dic59—22no—
457C2×Dic59—22no—
458C2×Dic59—22no—
459C2×Dic59—22no—
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—41no—
470C2×Dic59—41no—
471C2×Dic59—41no—
472C2×Dic59—41no—
473C2×Dic59—41no—
474C2×Dic59—41no—
475C2×Dic59—41no—
476C2×Dic59—41no—
477C2×Dic59—41no—
478C2×Dic59—41no—
479C2×Dic59—41no—
480C2×Dic59—41no—
481C2×Dic59—41no—
482C2×Dic59—41no—
483C2×Dic59—41no—
484C2×Dic59C2×C4214yes—
485C4×D59—416no—
486#13832—591nomaximal, Sylow
487C22×C59—24no—
488C22×C59—24no—
489C22×C59—24no—
490C22×C59—42no—
491C22×C59—42no—
492C22×C59—42no—
493C22×C59—42no—
494C22×C59—42no—
495C22×C59—42no—
496C22×C59—42no—
497C22×C59—42no—
498C22×C59—42no—
499C22×C59—42no—
500C22×C59—42no—
501C22×C59—42no—
502C22×C59C22×C4211yescharacteristic
503C22×C59#51811yescharacteristic
504C22×C59#51811yescharacteristic
505C22×C59#51811yescharacteristic
506C22×C59#51811yescharacteristic
507C22×C59#51811yescharacteristic
508C22×C59#51811yescharacteristic
509C22×C59#51811yescharacteristic
510C22×C59#51811yescharacteristic
511C22×C59#51811yescharacteristic
512C22×C59#51811yescharacteristic
513C22×C59#51811yescharacteristic
514C22×C59#51811yescharacteristic
515C22×C59#52011yescharacteristic
516C22×C59#52011yescharacteristic
517C22×C59#52011yescharacteristic
518C22×C59#52011yescharacteristic
519C22×C59#52011yescharacteristic
520C22×C59#52011yescharacteristic
521C22×C59#56011yescharacteristic
522C22×C59#56011yescharacteristic
523C22×C59#56011yescharacteristic
524C22×C59#56011yescharacteristic
525C22×C59#56011yescharacteristic
526C22×C59#56011yescharacteristic
527C22×C59#56011yescharacteristic
528C22×C59#56011yescharacteristic
529C22×C59H(3,𝔽4)11yescharacteristic
530C22×C59#56211yescharacteristic
531C22×C59#56211yescharacteristic
532C22×C59#56211yescharacteristic
533C22×C59#56211yescharacteristic
534C22×C59#56211yescharacteristic
535C22×C59#56211yescharacteristic
536C22×C59#56311yescharacteristic
537C2×D59—24no—
538C2×D59—24no—
539C2×D59—24no—
540C2×D59—42no—
541C2×D59—42no—
542C2×D59—42no—
543C2×D59—42no—
544C2×D59—42no—
545C2×D59—42no—
546C2×D59—42no—
547C2×D59—42no—
548C2×D59—42no—
549C2×D59—42no—
550C2×D59—42no—
551C2×D59—42no—
552C4×C59—42no—
553C4×C59—42no—
554C4×C59—42no—
555C4×C59—42no—
556C4×C59—42no—
557C4×C59—42no—
558Dic59—24no—
559Dic59—42no—
560Dic59—42no—
561Dic59—42no—
562Dic59—42no—
563Dic59—42no—
564Dic59—42no—
565C2×#390—591no—
566C2×#386—591no—
567C2×#386—591no—
568#1437—591no—
569#1437—591no—
570#1437—591no—
571#1437—591no—
572#1436—591no—
573#1436—591no—
574#1434—591no—
575#1434—591no—
576C22⋊#95—591no—
577C22⋊#95—591no—
578C22⋊#95—591no—
579C22⋊#95D5911yescharacteristic, complemented
580C2×C59—44no—
581C2×C59#227311yescharacteristic
582C2×C59#227511yescharacteristic
583C2×C59#227511yescharacteristic
584C2×C59#237511yescharacteristic
585C2×C59#237511yescharacteristic
586C2×C59#237611yescharacteristic
587C2×C59#237611yescharacteristic
588C2×C59#237711yescharacteristic
589C2×C59#237711yescharacteristic
590C2×C59#237711yescharacteristic
591C2×C59#237711yescharacteristic
592C2×C59#237711yescharacteristic
593C2×C59#237711yescharacteristic
594C2×C59#237911yescharacteristic
595C2×C59#238011yescharacteristic
596D59—44no—
597C23×D4—591no—
598C24×C4—591no—
599C24×C4C2×D5911yescharacteristic
600C22×C4⋊C4—591no—
601C22×C22⋊C4—591no—
602C22×C22⋊C4—591no—
603C22×C22⋊C4—591no—
604C22×C22⋊C4—591no—
605C22×C22⋊C4—591no—
606C22×C22⋊C4—591no—
607C22×C22⋊C4—591no—
608C22×C22⋊C4—591no—
609C22×C22⋊C4C2×D5911yescharacteristic
610C22×C22⋊C4C2×D5911yescharacteristic
611C22×C42—591no—
612C22×C42—591no—
613C22×C42—591no—
614#390—598no—
615#386—598no—
616#386—598no—
617C2×#95—591no—
618C2×#95—591no—
619C2×#95—591no—
620C2×#95—591no—
621C2×#95—591no—
622C2×#95—591no—
623C2×#95—591no—
624C2×#95—591no—
625C2×#95—591no—
626C2×#95—591no—
627C2×#95—591no—
628C2×#95—591no—
629C2×#95—591no—
630C2×#95—591no—
631C2×#95C2×D5911yescharacteristic
632C2×#95C2×D5911yescharacteristic
633C2×#95C2×D5911yescharacteristic
634C2×#95C2×D5911yescharacteristic
635C59#1383211yescharacteristic, complemented, Sylow
636C25—591no—
637C25C22×D5911yescharacteristic
638C22×D4—594no—
639C22×D4—594no—
640C22×D4—594no—
641C22×D4—2361no—
642C22×D4—2361no—
643C22×D4—2361no—
644C22×D4—2361no—
645C23×C4—41no—
646C23×C4—41no—
647C23×C4—41no—
648C23×C4—41no—
649C23×C4—41no—
650C23×C4—41no—
651C23×C4—591no—
652C23×C4—591no—
653C23×C4—591no—
654C23×C4—591no—
655C23×C4—591no—
656C23×C4—591no—
657C23×C4—591no—
658C23×C4—594no—
659C23×C4—2361no—
660C23×C4—2361no—
661C23×C4—2361no—
662C23×C4—2361no—
663C23×C4—2361no—
664C23×C4—2361no—
665C23×C4C4×D5914yescomplemented
666C23×C4C22×D5911yescharacteristic
667C23×C4C22×D5911yescharacteristic
668C23×C4C22×D5911yescharacteristic
669C23×C4C22×D5911yescharacteristic
670C23×C4C22×D5911yescharacteristic
671C23×C4C22×D5911yescharacteristic
672C2×C4⋊C4—594no—
673C2×C4⋊C4—2361no—
674C2×C4⋊C4—2361no—
675C2×C22⋊C4—41no—
676C2×C22⋊C4—41no—
677C2×C22⋊C4—41no—
678C2×C22⋊C4—41no—
679C2×C22⋊C4—594no—
680C2×C22⋊C4—594no—
681C2×C22⋊C4—594no—
682C2×C22⋊C4—594no—
683C2×C22⋊C4—594no—
684C2×C22⋊C4—594no—
685C2×C22⋊C4—594no—
686C2×C22⋊C4—594no—
687C2×C22⋊C4—2361no—
688C2×C22⋊C4—2361no—
689C2×C22⋊C4—2361no—
690C2×C22⋊C4—2361no—
691C2×C22⋊C4—2361no—
692C2×C22⋊C4—2361no—
693C2×C22⋊C4—2361no—
694C2×C22⋊C4—2361no—
695C2×C22⋊C4—2361no—
696C2×C22⋊C4—2361no—
697C2×C22⋊C4—2361no—
698C2×C22⋊C4—2361no—
699C2×C22⋊C4—2361no—
700C2×C22⋊C4—2361no—
701C2×C22⋊C4—2361no—
702C2×C22⋊C4—2361no—
703C2×C22⋊C4C4×D5914yes—
704C2×C22⋊C4C4×D5914yescomplemented
705C2×C42—594no—
706C2×C42—2361no—
707C2×C42—2361no—
708C2×C42—2361no—
709C2×C42—2361no—
710C2×C42—2361no—
711C2×C42—2361no—
712C2×C42—2361no—
713C2×C42—2361no—
714#95—41no—
715#95—41no—
716#95—41no—
717#95—41no—
718#95—594no—
719#95—594no—
720#95—594no—
721#95—594no—
722#95—2361no—
723#95—2361no—
724#95—2361no—
725#95—2361no—
726#95—2361no—
727#95—2361no—
728#95—2361no—
729#95—2361no—
730#95—2361no—
731#95—2361no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—592no—
745C24—592no—
746C24—592no—
747C24—1181no—
748C24—1181no—
749C24—1181no—
750C24—1181no—
751C24—1181no—
752C24—1181no—
753C24—1181no—
754C24—1181no—
755C24—1181no—
756C24—1181no—
757C24—1181no—
758C24—1181no—
759C24C2×C4×D5912yes—
760C24C2×C4×D5912yes—
761C24C2×C4×D5912yes—
762C24C23×D5911yescharacteristic
763C2×D4—5916no—
764C2×D4—2364no—
765C2×D4—2364no—
766C2×D4—2364no—
767C2×D4—2364no—
768C2×D4—2364no—
769C2×D4—2364no—
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—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—592no—
814C22×C4—592no—
815C22×C4—592no—
816C22×C4—592no—
817C22×C4—592no—
818C22×C4—592no—
819C22×C4—592no—
820C22×C4—592no—
821C22×C4—592no—
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×C4—1181no—
835C22×C4—1181no—
836C22×C4—1181no—
837C22×C4—1181no—
838C22×C4—1181no—
839C22×C4—1181no—
840C22×C4—1181no—
841C22×C4—1181no—
842C22×C4—1181no—
843C22×C4—1181no—
844C22×C4—1181no—
845C22×C4—1181no—
846C22×C4—1181no—
847C22×C4—1181no—
848C22×C4—1181no—
849C22×C4—1181no—
850C22×C4—1181no—
851C22×C4—1181no—
852C22×C4—1181no—
853C22×C4—1181no—
854C22×C4—1181no—
855C22×C4—1181no—
856C22×C4—1181no—
857C22×C4—1181no—
858C22×C4—1181no—
859C22×C4—1181no—
860C22×C4—1181no—
861C22×C4—1181no—
862C22×C4—2364no—
863C22×C4—2364no—
864C22×C4—2364no—
865C22×C4—2364no—
866C22×C4—2364no—
867C22×C4—2364no—
868C22×C4—2364no—
869C22×C4C2×C4×D5912yes—
870C22×C4C2×C4×D5912yes—
871C22×C4C2×C4×D5912yes—
872C22×C4C2×C4×D5912yes—
873C22×C4C2×C4×D5912yes—
874C22×C4C2×C4×D5912yes—
875C4⋊C4—2364no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—2364no—
879C22⋊C4—2364no—
880C22⋊C4—2364no—
881C22⋊C4—2364no—
882C22⋊C4—2364no—
883C22⋊C4—2364no—
884C22⋊C4—2364no—
885C22⋊C4—2364no—
886C42—2364no—
887C42—2364no—
888C42—2364no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—594no—
924C23—1182no—
925C23—1182no—
926C23—1182no—
927C23—1182no—
928C23—1182no—
929C23—1182no—
930C23—1182no—
931C23—1182no—
932C23—1182no—
933C23—1182no—
934C23—1182no—
935C23—1182no—
936C23—1182no—
937C23—1182no—
938C23—1182no—
939C23—1182no—
940C23—1182no—
941C23—1182no—
942C23—2361no—
943C23—2361no—
944C23—2361no—
945C23—2361no—
946C23—2361no—
947C23—2361no—
948C23—2361no—
949C23—2361no—
950C23—2361no—
951C23—2361no—
952C23—2361no—
953C23—2361no—
954C23—2361no—
955C23—2361no—
956C23—2361no—
957C23—2361no—
958C23C42×D5914yes—
959C23C22×C4×D5911yescharacteristic
960C23C22×C4×D5911yescharacteristic
961C23C22×C4×D5911yescharacteristic
962C23#1427377211yescharacteristic
963C23#1427377211yescharacteristic
964C23#1427377211yescharacteristic
965C23#1427377211yescharacteristic
966C23#1427377211yescharacteristic
967C23#1427377211yescharacteristic
968C23#1427377211yescharacteristic
969C23#1427377311yescharacteristic
970C23#1427377311yescharacteristic
971C23#1427377311yescharacteristic
972C23#1427377411yescharacteristic
973C23#1427377511yescharacteristic
974D4—23616no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—416no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—594no—
1019C2×C4—1182no—
1020C2×C4—1182no—
1021C2×C4—1182no—
1022C2×C4—1182no—
1023C2×C4—1182no—
1024C2×C4—1182no—
1025C2×C4—1182no—
1026C2×C4—1182no—
1027C2×C4—1182no—
1028C2×C4—1182no—
1029C2×C4—1182no—
1030C2×C4—1182no—
1031C2×C4—1182no—
1032C2×C4—1182no—
1033C2×C4—1182no—
1034C2×C4—1182no—
1035C2×C4—1182no—
1036C2×C4—1182no—
1037C2×C4—1182no—
1038C2×C4—1182no—
1039C2×C4—1182no—
1040C2×C4—1182no—
1041C2×C4—1182no—
1042C2×C4—1182no—
1043C2×C4—23616no—
1044C2×C4—2361no—
1045C2×C4—2361no—
1046C2×C4—2361no—
1047C2×C4—2361no—
1048C2×C4—2361no—
1049C2×C4—2361no—
1050C2×C4—2361no—
1051C2×C4—2361no—
1052C2×C4—2361no—
1053C2×C4—2361no—
1054C2×C4—2361no—
1055C2×C4—2361no—
1056C2×C4—2361no—
1057C2×C4—2361no—
1058C2×C4—2361no—
1059C2×C4—2361no—
1060C2×C4—2361no—
1061C2×C4—2361no—
1062C2×C4—2361no—
1063C2×C4—2361no—
1064C2×C4—2361no—
1065C2×C4—2361no—
1066C2×C4—2361no—
1067C2×C4—2361no—
1068C22—24no—
1069C22—24no—
1070C22—24no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—1184no—
1084C22—1184no—
1085C22—1184no—
1086C22—2362no—
1087C22—2362no—
1088C22—2362no—
1089C22—2362no—
1090C22—2362no—
1091C22—2362no—
1092C22—2362no—
1093C22—2362no—
1094C22—2362no—
1095C22—2362no—
1096C22—2362no—
1097C22—2362no—
1098C22C2×C42×D5911yescharacteristic
1099C22#1683787411yescharacteristic
1100C22#1683787411yescharacteristic
1101C22#1683787411yescharacteristic
1102C22#1683787411yescharacteristic
1103C22#1683787411yescharacteristic
1104C22#1683787411yescharacteristic
1105C22#1683787511yescharacteristic
1106C22#1683787511yescharacteristic
1107C22#1683787511yescharacteristic
1108C22#1683787511yescharacteristic
1109C22#1683787511yescharacteristic
1110C22#1683787611yescharacteristic
1111C22#1683788111yescharacteristic
1112C22#1683788111yescharacteristic
1113C22#1683788211yescharacteristic
1114C22#1683788311yescharacteristic
1115C22#1683788311yescharacteristic
1116C22#1683788311yescharacteristic
1117C22#1683814011yescharacteristic
1118C22#1683814011yescharacteristic
1119C22#1683814011yescharacteristic
1120C22#1683814111yescharacteristic
1121C22#1683814111yescharacteristic
1122C22#1683814111yescharacteristic
1123C22#1683814211yescharacteristic
1124C22#1683814211yescharacteristic
1125C22#1683814511yescharacteristic
1126C22#1683814711yescharacteristic
1127C22#1683814811yescharacteristic
1128C22#1683814811yescharacteristic
1129C22#1683814811yescharacteristic
1130C22#1683814911yescharacteristic
1131C22#1683814911yescharacteristic
1132C22#1683815311yescharacteristic
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—42no—
1139C4—1184no—
1140C4—2362no—
1141C4—2362no—
1142C4—2362no—
1143C4—2362no—
1144C4—2362no—
1145C4—2362no—
1146C2—44no—
1147C2—2364no—
1148C2#2142644811yescharacteristic
1149C2#2142645411yescharacteristic
1150C2#2142645511yescharacteristic
1151C2#2142723411yescharacteristic
1152C2#2142723511yescharacteristic
1153C2#2142724011yescharacteristic
1154C2#2142724511yescharacteristic
1155C2#2142724811yescharacteristic
1156C2#2142725011yescharacteristic
1157C2#2142725211yescharacteristic
1158C2#2142725211yescharacteristic
1159C2#2142725411yescharacteristic
1160C2#2142725511yescharacteristic
1161C2#2142726911yescharacteristic
1162C2#2142727111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC22×C59C22×C42
FittingC59×C22⋊#95C2
socle, cosocleC24×C59C24
prime radicalC23×C22⋊D59C22
hypercenterC22⋊#95D59
hypocenterC59#13832
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. #21422333C2semidirect
5. #21422333C2semidirect
6. #21422332C2semidirect
7. #21422332C2semidirect
8. #21422331C2semidirect
9. #21422327C2semidirect
10. #21422322C2semidirect
11. #21422320C2semidirect
12. #21422319C2semidirect
13. (C2×D59)⋊#95C2semidirect
14. (C2×D59)⋊#95C2semidirect
15. C59×C22⋊#95C2semidirect
30. #16837302C4semidirect
31. #16837281C4semidirect
32. #16837278C4semidirect
75. C22×C4×D59C2×C4semidirect
78. C2×Dic59⋊C4C2×C4semidirect
86. C2×C22⋊Dic59C2×C4semidirect
87. C2×C22⋊Dic59C2×C4semidirect
100. C2×(C2×D59)⋊C4C2×C4semidirect
101. C2×(C2×D59)⋊C4C2×C4semidirect
102. C2×(C2×D59)⋊C4C2×C4semidirect
111. C2×C4×Dic59C2×C4semidirect
122. C59⋊#95C2×C4semidirect
123. C59⋊#95C2×C4semidirect
124. C59⋊#95C2×C4semidirect
125. C59⋊#95C2×C4semidirect
133. C23×C4×C59C2×C4semidirect
145. C2×C22⋊C4×C59C2×C4semidirect
236. C2×C22⋊D59C42semidirect
579. C22⋊#95D59semidirect
635. C59#13832semidirect
665. C23×C4C4×D59semidirect
704. C2×C22⋊C4C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168373022
C2×#168372812
C2×#168372782
#214223332
#214223322
#214223312
#214223272
#214223222
#214223202
#214223192
(C2×D59)⋊#952
C59×C22⋊#952
#1383259