Finite Group Databasebeta

← #28514347

Subgroups — #28514347

Order 15104.

1954 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837318C211yesmaximal, characteristic
2C2×#16837278C211yesmaximal, characteristic
3C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic, complemented
4C2×#16837249C211yesmaximal, characteristic, complemented
5#21422344C211yesmaximal, characteristic, complemented
6#21422338C211yesmaximal, characteristic, complemented
7#21422335C211yesmaximal, characteristic
8#21422333C211yesmaximal, characteristic, complemented
9#21422333C211yesmaximal, characteristic, complemented
10#21422333C211yesmaximal, characteristic, complemented
11#21422330C211yesmaximal, characteristic, complemented
12#21422325C211yesmaximal, characteristic, complemented
13#21422323C211yesmaximal, characteristic, complemented
14#21422320C211yesmaximal, characteristic, complemented
15C2×C59×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D59C2211yescharacteristic
17C23×C4×D59C2211yescharacteristic
18C22×C4⋊Dic59C2211yescharacteristic
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#16837318C418yescomplemented
31#16837278—24no—
32C4×(C2×D59)⋊C4—24no—
33#16837249—24no—
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×C22⋊C4×C59C2211yescharacteristic
50C22×C22⋊C4×C59C2211yescharacteristic
51C22×C22⋊C4×C59C2211yescharacteristic
52C22×C42×C59C2211yescharacteristic
53C59×#388—24no—
54C2×#95×C59C2211yescharacteristic
55C2×#95×C59C2211yescharacteristic
56C24×D59C2311yescharacteristic
57C22×C22⋊D59—22no—
58C22×C22⋊D59—22no—
59C22×C22⋊D59—41no—
60C22×C22⋊D59—41no—
61C22×C22⋊D59—41no—
62C22×C22⋊D59—41no—
63C22×C22⋊D59C2×C414yes—
64C23×Dic59C2311yescharacteristic
65C23×Dic59C2311yescharacteristic
66C23×Dic59C2311yescharacteristic
67C23×Dic59C2311yescharacteristic
68C23×Dic59C2311yescharacteristic
69C23×Dic59C2311yescharacteristic
70C23×Dic59C2311yescharacteristic
71C22×C4×D59—22no—
72C22×C4×D59—22no—
73C22×C4×D59—22no—
74C22×C4×D59—22no—
75C22×C4×D59—41no—
76C22×C4×D59—41no—
77C22×C4×D59D414yes—
78C2×C4⋊Dic59—41no—
79C2×C4⋊Dic59—41no—
80C2×C4⋊Dic59C2×C414yescomplemented
81C2×C22⋊Dic59—22no—
82C2×C22⋊Dic59—22no—
83C2×C22⋊Dic59—22no—
84C2×C22⋊Dic59—22no—
85C2×C22⋊Dic59—22no—
86C2×C22⋊Dic59—41no—
87C2×C22⋊Dic59—41no—
88C2×C22⋊Dic59—41no—
89C2×C22⋊Dic59C2×C414yescomplemented
90C2×(C2×D59)⋊C4—22no—
91C2×(C2×D59)⋊C4—22no—
92C2×(C2×D59)⋊C4—22no—
93C2×(C2×D59)⋊C4—22no—
94C2×(C2×D59)⋊C4—22no—
95C2×(C2×D59)⋊C4—22no—
96C2×(C2×D59)⋊C4—22no—
97C2×(C2×D59)⋊C4—22no—
98C2×(C2×D59)⋊C4—22no—
99C2×(C2×D59)⋊C4—22no—
100C2×(C2×D59)⋊C4—22no—
101C2×(C2×D59)⋊C4—41no—
102C2×(C2×D59)⋊C4—41no—
103C2×(C2×D59)⋊C4C2×C414yes—
104C2×(C2×D59)⋊C4C2×C414yes—
105C2×C4×Dic59—22no—
106C2×C4×Dic59—22no—
107C2×C4×Dic59—22no—
108C2×C4×Dic59—22no—
109C2×C4×Dic59—22no—
110C2×C4×Dic59—41no—
111C2×C4×Dic59—41no—
112C2×C4×Dic59—41no—
113C2×C4×Dic59—41no—
114C59⋊#95—22no—
115C59⋊#95—22no—
116C59⋊#95—22no—
117C59⋊#95—22no—
118C59⋊#95—22no—
119C59⋊#95—22no—
120C59⋊#95—22no—
121C59⋊#95—22no—
122C59⋊#95—41no—
123C59⋊#95—41no—
124C59⋊#95—41no—
125C59⋊#95—41no—
126C59⋊#95—41no—
127C59⋊#95C2×C414yescomplemented
128C25×C59C2311yescharacteristic
129C23×C4×C59C2311yescharacteristic
130C23×C4×C59C2311yescharacteristic
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C2×C4⋊C4×C59—22no—
136C2×C4⋊C4×C59—22no—
137C2×C4⋊C4×C59—41no—
138C2×C22⋊C4×C59—22no—
139C2×C22⋊C4×C59—22no—
140C2×C22⋊C4×C59—22no—
141C2×C22⋊C4×C59—22no—
142C2×C22⋊C4×C59—22no—
143C2×C22⋊C4×C59—22no—
144C2×C22⋊C4×C59—22no—
145C2×C22⋊C4×C59—41no—
146C2×C22⋊C4×C59C2×C414yescomplemented
147C2×C42×C59—22no—
148C2×C42×C59—22no—
149C2×C42×C59—22no—
150#95×C59—22no—
151#95×C59D414yescomplemented
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×C59—21no—
163C24×C59—21no—
164C24×C59—21no—
165C24×C59—21no—
166C24×C59C22×C412yes—
167C24×C59C2411yescharacteristic
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×D59—21no—
179C23×D59—21no—
180C23×D59C22×C412yes—
181C23×D59C2×D412yes—
182C23×D59#4112yes—
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×C59C22×C412yes—
217C22×C4×C59C22×C412yes—
218C22×C4×C59C2×D412yes—
219C22×C4×C59C2×D412yes—
220C22×C4×C59C2×D412yes—
221C22×C4×C59C2×D412yes—
222C22×C4×C59#4112yes—
223C22×C4×C59#4112yes—
224C22×C4×C59#4112yes—
225C2×C22⋊D59—28no—
226C2×C22⋊D59—44no—
227C2×C22⋊D59—44no—
228C2×C22⋊D59—44no—
229C2×C22⋊D59—44no—
230C2×C22⋊D59—44no—
231C2×C22⋊D59—44no—
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×Dic59—21no—
270C22×Dic59—21no—
271C22×Dic59—21no—
272C22×Dic59—21no—
273C22×Dic59C22×C412yes—
274C22×Dic59C22×C412yes—
275C22×Dic59C22×C412yes—
276C22×Dic59C2×D412yes—
277C22×Dic59#4112yes—
278C22×Dic59#4112yes—
279C22×Dic59#4112yes—
280C22×Dic59#4112yes—
281C2×C4×D59—28no—
282C2×C4×D59—28no—
283C2×C4×D59—44no—
284C2×C4×D59—44no—
285C2×C4×D59—44no—
286C2×C4×D59—44no—
287C2×C4×D59—44no—
288C4⋊C4×C59—44no—
289C22⋊C4×C59—28no—
290C22⋊C4×C59—44no—
291C22⋊C4×C59—44no—
292C42×C59—44no—
293C22⋊Dic59—44no—
294C22⋊Dic59—44no—
295C22⋊Dic59—44no—
296(C2×D59)⋊C4—28no—
297(C2×D59)⋊C4—28no—
298(C2×D59)⋊C4—28no—
299(C2×D59)⋊C4—28no—
300(C2×D59)⋊C4—44no—
301C4⋊Dic59—44no—
302C4×Dic59—44no—
303C4×Dic59—44no—
304C4×Dic59—44no—
305C23×C59—22no—
306C23×C59—22no—
307C23×C59—22no—
308C23×C59—22no—
309C23×C59—22no—
310C23×C59—22no—
311C23×C59—22no—
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×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×C59C23×C411yescharacteristic
341C23×C59C22×D411yescharacteristic
342C23×C59C22×D411yescharacteristic
343C23×C59C2×#4111yescharacteristic
344C23×C59C2×#4111yescharacteristic
345C23×C59C2×#4111yescharacteristic
346C23×C59C2×#4111yescharacteristic
347C23×C59C2×#4111yescharacteristic
348C23×C59C2×#4111yescharacteristic
349C23×C59C2×#4111yescharacteristic
350C23×C59C2×#4111yescharacteristic
351C23×C59H(5,𝔽2)11yescharacteristic
352C23×C59H(5,𝔽2)11yescharacteristic
353C23×C59H(5,𝔽2)11yescharacteristic
354C23×C59H(5,𝔽2)11yescharacteristic
355C22×D59—22no—
356C22×D59—22no—
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—41no—
374C22×D59—41no—
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×D59C4×D414yes—
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—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—22no—
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×C59C4×D414yes—
431C2×C4×C59#12114yes—
432C22⋊D59—416no—
433C2×Dic59—22no—
434C2×Dic59—22no—
435C2×Dic59—22no—
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—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—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#12314yes—
482C4×D59—416no—
483#14199—591nomaximal, Sylow
484C22×C59—42no—
485C22×C59—42no—
486C22×C59—42no—
487C22×C59—42no—
488C22×C59—42no—
489C22×C59—42no—
490C22×C59—42no—
491C22×C59—81no—
492C22×C59—81no—
493C22×C59—81no—
494C22×C59—81no—
495C22×C59—81no—
496C22×C59—81no—
497C22×C59—81no—
498C22×C59—81no—
499C22×C59C2×C4×D411yescharacteristic
500C22×C59C2×C4×D411yescharacteristic
501C22×C59C4×#4111yescharacteristic
502C22×C59C4×#4111yescharacteristic
503C22×C59C4×#4111yescharacteristic
504C22×C59#51811yescharacteristic
505C22×C59#51811yescharacteristic
506C22×C59C2×#12111yescharacteristic
507C22×C59C2×#12311yescharacteristic
508C22×C59#52511yescharacteristic
509C22×C59#52511yescharacteristic
510C22×C59#52911yescharacteristic
511C22×C59#52911yescharacteristic
512C22×C59#52911yescharacteristic
513C22×C59#53211yescharacteristic
514C22×C59#53411yescharacteristic
515C22×C59#53511yescharacteristic
516C22×C59#53811yescharacteristic
517C22×C59#53811yescharacteristic
518C22×C59#54611yescharacteristic
519C22×C59#54611yescharacteristic
520C22×C59#54611yescharacteristic
521C22×C59#55011yescharacteristic
522C22×C59#55111yescharacteristic
523C22×C59#55111yescharacteristic
524C22×C59#55111yescharacteristic
525C22×C59#55311yescharacteristic
526C22×C59#55311yescharacteristic
527C22×C59#55311yescharacteristic
528C22×C59#55311yescharacteristic
529C22×C59#55311yescharacteristic
530C22×C59#55511yescharacteristic
531C22×C59#55511yescharacteristic
532C22×C59#55511yescharacteristic
533C22×C59#55911yescharacteristic
534C2×D59—24no—
535C2×D59—24no—
536C2×D59—24no—
537C2×D59—42no—
538C2×D59—42no—
539C2×D59—42no—
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—
549C4×C59—24no—
550C4×C59—24no—
551C4×C59—42no—
552C4×C59—42no—
553C4×C59—42no—
554C4×C59—81no—
555Dic59—24no—
556Dic59—42no—
557Dic59—42no—
558Dic59—42no—
559Dic59—42no—
560Dic59—42no—
561Dic59—81no—
562C2×#394—591no—
563C2×#388D5911yescharacteristic, complemented
564C2×#386—591no—
565C2×C4×C22⋊C4—591no—
566C2×C4×C22⋊C4—591no—
567#1440—591no—
568#1439—591no—
569#1438—591no—
570#1437—591no—
571#1437—591no—
572#1437—591no—
573#1436—591no—
574C4⋊#95—591no—
575#1434—591no—
576#1434—591no—
577C2×C59—82no—
578C2×C59C4×#12111yescharacteristic
579C2×C59C4×#12311yescharacteristic
580C2×C59#232111yescharacteristic
581C2×C59#236311yescharacteristic
582C2×C59#236411yescharacteristic
583C2×C59#237211yescharacteristic
584C2×C59#237411yescharacteristic
585C2×C59#241211yescharacteristic
586C2×C59#241411yescharacteristic
587C2×C59#245911yescharacteristic
588C2×C59#246711yescharacteristic
589C2×C59#250011yescharacteristic
590C2×C59#251811yescharacteristic
591C2×C59#251811yescharacteristic
592C2×C59#260211yescharacteristic
593D59—44no—
594C23×D4—591no—
595C24×C4—591no—
596C22×C4⋊C4—591no—
597C22×C4⋊C4C2×D5911yescharacteristic
598C22×C22⋊C4—591no—
599C22×C22⋊C4—591no—
600C22×C22⋊C4—591no—
601C22×C22⋊C4—591no—
602C22×C22⋊C4—591no—
603C22×C22⋊C4—591no—
604C22×C22⋊C4—591no—
605C22×C22⋊C4—591no—
606C22×C22⋊C4C2×D5911yescharacteristic
607C22×C22⋊C4C2×D5911yescharacteristic
608C22×C22⋊C4C2×D5911yescharacteristic
609C22×C42—591no—
610C22×C42—591no—
611C22×C42—591no—
612C22×C42C2×D5911yescharacteristic
613#394—598no—
614#388—24no—
615#386—1184no—
616C4×C22⋊C4—1184no—
617C4×C22⋊C4—1184no—
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×#95—591no—
632C2×#95C2×D5911yescharacteristic
633C2×#95C2×D5911yescharacteristic
634C59#1419911yescharacteristic, complemented, Sylow
635C25—591no—
636C25C22×D5911yescharacteristic
637C22×D4—594no—
638C22×D4—1182no—
639C22×D4—1182no—
640C22×D4—2361no—
641C22×D4—2361no—
642C22×D4—2361no—
643C22×D4—2361no—
644C23×C4—591no—
645C23×C4—591no—
646C23×C4—591no—
647C23×C4—591no—
648C23×C4—591no—
649C23×C4—591no—
650C23×C4—594no—
651C23×C4—591no—
652C23×C4—1182no—
653C23×C4—1182no—
654C23×C4—1182no—
655C23×C4—1182no—
656C23×C4—2361no—
657C23×C4—2361no—
658C23×C4C22×D5911yescharacteristic
659C23×C4C22×D5911yescharacteristic
660C23×C4C22×D5911yescharacteristic
661C23×C4C22×D5911yescharacteristic
662C23×C4C22×D5911yescharacteristic
663C23×C4C22×D5911yescharacteristic
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—41no—
667C2×C4⋊C4—594no—
668C2×C4⋊C4—2361no—
669C2×C4⋊C4—2361no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—41no—
678C2×C22⋊C4—594no—
679C2×C22⋊C4—594no—
680C2×C22⋊C4—594no—
681C2×C22⋊C4—1182no—
682C2×C22⋊C4—1182no—
683C2×C22⋊C4—1182no—
684C2×C22⋊C4—1182no—
685C2×C22⋊C4—1182no—
686C2×C22⋊C4—1182no—
687C2×C22⋊C4—1182no—
688C2×C22⋊C4—1182no—
689C2×C22⋊C4—1182no—
690C2×C22⋊C4—1182no—
691C2×C22⋊C4—1182no—
692C2×C22⋊C4—1182no—
693C2×C22⋊C4—1182no—
694C2×C22⋊C4—1182no—
695C2×C22⋊C4—1182no—
696C2×C22⋊C4—1182no—
697C2×C22⋊C4—2361no—
698C2×C22⋊C4—2361no—
699C2×C22⋊C4—2361no—
700C2×C22⋊C4—2361no—
701C2×C22⋊C4—2361no—
702C2×C22⋊C4C4×D5914yescomplemented
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—22no—
706C2×C42—1182no—
707C2×C42—1182no—
708C2×C42—1182no—
709C2×C42—1182no—
710C2×C42—1182no—
711C2×C42—2361no—
712C2×C42—2361no—
713C2×C42—2361no—
714C2×C42—2361no—
715#95—22no—
716#95—594no—
717#95—1182no—
718#95—1182no—
719#95—1182no—
720#95—1182no—
721#95—1182no—
722#95—1182no—
723#95—1182no—
724#95—1182no—
725#95—2361no—
726#95—2361no—
727#95—2361no—
728#95—2361no—
729#95—2361no—
730#95C22⋊D5914yescomplemented
731C24—21no—
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—21no—
745C24—592no—
746C24—592no—
747C24—592no—
748C24—1181no—
749C24—1181no—
750C24—1181no—
751C24—1181no—
752C24—1181no—
753C24—1181no—
754C24—1181no—
755C24—1181no—
756C24—1181no—
757C24—1181no—
758C24—1181no—
759C24—1181no—
760C24C2×C4×D5912yes—
761C24C23×D5911yescharacteristic
762C2×D4—1188no—
763C2×D4—2364no—
764C2×D4—2364no—
765C2×D4—2364no—
766C2×D4—2364no—
767C2×D4—2364no—
768C2×D4—2364no—
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—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—592no—
803C22×C4—592no—
804C22×C4—592no—
805C22×C4—592no—
806C22×C4—592no—
807C22×C4—592no—
808C22×C4—592no—
809C22×C4—592no—
810C22×C4—1188no—
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×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—1188no—
846C22×C4—1181no—
847C22×C4—1181no—
848C22×C4—1181no—
849C22×C4—1181no—
850C22×C4—1181no—
851C22×C4—1181no—
852C22×C4—1181no—
853C22×C4—2364no—
854C22×C4—2364no—
855C22×C4—2364no—
856C22×C4—2364no—
857C22×C4—2364no—
858C22×C4C2×C4×D5912yes—
859C22×C4C2×C4×D5912yes—
860C22×C4#1174568512yes—
861C22×C4D4×D5912yes—
862C22×C4#1174568712yes—
863C22×C4#1174568712yes—
864C22×C4C2×C22⋊D5912yes—
865C22×C4C2×C22⋊D5912yes—
866C22×C4C2×C22⋊D5912yes—
867C4⋊C4—44no—
868C4⋊C4—2364no—
869C22⋊C4—28no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—1188no—
873C22⋊C4—1188no—
874C22⋊C4—1188no—
875C22⋊C4—1188no—
876C22⋊C4—2364no—
877C22⋊C4—2364no—
878C22⋊C4—2364no—
879C22⋊C4—2364no—
880C42—44no—
881C42—2364no—
882C42—2364no—
883C42—2364no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
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—594no—
920C23—1182no—
921C23—1182no—
922C23—1182no—
923C23—1182no—
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—2361no—
939C23—2361no—
940C23—2361no—
941C23—2361no—
942C23—2361no—
943C23—2361no—
944C23—2361no—
945C23—2361no—
946C23—2361no—
947C23—2361no—
948C23—2361no—
949C23—2361no—
950C23—2361no—
951C23—2361no—
952C23—2361no—
953C23—2361no—
954C23C22×C4×D5911yescharacteristic
955C23C2×D4×D5911yescharacteristic
956C23C22×C22⋊D5911yescharacteristic
957C23#41×D5911yescharacteristic
958C23#41×D5911yescharacteristic
959C23#41×D5911yescharacteristic
960C23#41×D5911yescharacteristic
961C23#41×D5911yescharacteristic
962C23C2×#1174568711yescharacteristic
963C23C2×#1174568711yescharacteristic
964C23C2×#1174568511yescharacteristic
965C23#1427377211yescharacteristic
966C23#1427377311yescharacteristic
967C23#1427377311yescharacteristic
968C23#1427377311yescharacteristic
969D4—23616no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
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—41no—
992C2×C4—41no—
993C2×C4—41no—
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—594no—
1011C2×C4—1182no—
1012C2×C4—1182no—
1013C2×C4—1182no—
1014C2×C4—1182no—
1015C2×C4—1182no—
1016C2×C4—1182no—
1017C2×C4—1182no—
1018C2×C4—1182no—
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—23616no—
1033C2×C4—2361no—
1034C2×C4—2361no—
1035C2×C4—2361no—
1036C2×C4—2361no—
1037C2×C4—2361no—
1038C2×C4—2361no—
1039C2×C4—2361no—
1040C2×C4—2361no—
1041C2×C4—2361no—
1042C2×C4—2361no—
1043C2×C4—2361no—
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×C4C4×C22⋊D5914yes—
1061C2×C4#1427369814yes—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—1184no—
1078C22—1184no—
1079C22—1184no—
1080C22—2362no—
1081C22—2362no—
1082C22—2362no—
1083C22—2362no—
1084C22—2362no—
1085C22—2362no—
1086C22—2362no—
1087C22—2362no—
1088C22—2362no—
1089C22—2362no—
1090C22—2362no—
1091C22—2362no—
1092C22C4×D4×D5911yescharacteristic
1093C22C2×C4×C22⋊D5911yescharacteristic
1094C22C4×#1174568711yescharacteristic
1095C22C4×#1174568711yescharacteristic
1096C22#1683787011yescharacteristic
1097C22#1683787411yescharacteristic
1098C22#1683787611yescharacteristic
1099C22C2×#1427369811yescharacteristic
1100C22#123×D5911yescharacteristic
1101C22#1683790911yescharacteristic
1102C22#1683791211yescharacteristic
1103C22#1683793111yescharacteristic
1104C22#1683793411yescharacteristic
1105C22#1683793511yescharacteristic
1106C22#1683794911yescharacteristic
1107C22#1683796311yescharacteristic
1108C22#1683796811yescharacteristic
1109C22#1683798611yescharacteristic
1110C22#1683799111yescharacteristic
1111C22#1683804011yescharacteristic
1112C22#1683804011yescharacteristic
1113C22#1683804611yescharacteristic
1114C22#1683807111yescharacteristic
1115C22#1683807511yescharacteristic
1116C22#1683807511yescharacteristic
1117C22#1683807711yescharacteristic
1118C22#1683809611yescharacteristic
1119C22#1683809811yescharacteristic
1120C22#1683810111yescharacteristic
1121C22#1683810311yescharacteristic
1122C22#1683810411yescharacteristic
1123C22#1683811411yescharacteristic
1124C22#1683811511yescharacteristic
1125C22#1683811611yescharacteristic
1126C22#1683813411yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—81no—
1133C4—1184no—
1134C4—4721no—
1135C4—2362no—
1136C4—2362no—
1137C4—2362no—
1138C4—2362no—
1139C4—2362no—
1140C2—82no—
1141C2—2364no—
1142C2C4×#1427369811yescharacteristic
1143C2#2142662311yescharacteristic
1144C2#2142675811yescharacteristic
1145C2#2142713411yescharacteristic
1146C2#2142714111yescharacteristic
1147C2#2142720311yescharacteristic
1148C2#2142722611yescharacteristic
1149C2#2142748811yescharacteristic
1150C2#2142751011yescharacteristic
1151C2#2142802911yescharacteristic
1152C2#2142814311yescharacteristic
1153C2#2142855611yescharacteristic
1154C2#2142875811yescharacteristic
1155C2#2142876111yescharacteristic
1156C2#2142971411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C59×#388C2
socle, cosocleC24×C59C24
prime radicalC23×C22⋊D59C22
hypercenterC2×#388D59
hypocenterC59#14199
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C2×C4×(C2×D59)⋊C4C2semidirect
4. C2×#16837249C2semidirect
5. #21422344C2semidirect
6. #21422338C2semidirect
8. #21422333C2semidirect
9. #21422333C2semidirect
10. #21422333C2semidirect
11. #21422330C2semidirect
12. #21422325C2semidirect
13. #21422323C2semidirect
14. #21422320C2semidirect
15. C2×C59×#388C2semidirect
30. #16837318C4semidirect
80. C2×C4⋊Dic59C2×C4semidirect
89. C2×C22⋊Dic59C2×C4semidirect
127. C59⋊#95C2×C4semidirect
146. C2×C22⋊C4×C59C2×C4semidirect
151. #95×C59D4semidirect
563. C2×#388D59semidirect
634. C59#14199semidirect
702. C2×C22⋊C4C4×D59semidirect
730. #95C22⋊D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168373182
C2×#168372782
C2×C4×(C2×D59)⋊C42
C2×#168372492
#214223442
#214223382
#214223352
#214223332
#214223302
#214223252
#214223232
#214223202
C2×C59×#3882
#1419959