Finite Group Databasebeta

← #28514164

Subgroups — #28514164

Order 15104.

2422 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic59C211yesmaximal, characteristic
2C2×#16837301C211yesmaximal, characteristic, complemented
3C2×#16837295C211yesmaximal, characteristic, complemented
4C2×#16837277C211yesmaximal, characteristic, complemented
5C2×#16837277C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×Dic59C211yesmaximal, characteristic, complemented
7#21422345C211yesmaximal, characteristic, complemented
8#21422341C211yesmaximal, characteristic, complemented
9#21422337C211yesmaximal, characteristic
10#21422333C211yesmaximal, characteristic, complemented
11#21422330C211yesmaximal, characteristic, complemented
12#21422330C211yesmaximal, characteristic, complemented
13#21422328C211yesmaximal, characteristic, complemented
14#21422318C211yesmaximal, characteristic, complemented
15C2×C59×#394C211yesmaximal, characteristic
16C24×Dic59C2211yescharacteristic
17C24×Dic59C2211yescharacteristic
18C2×D4×Dic59—24no—
19C2×D4×Dic59—24no—
20C2×D4×Dic59—24no—
21C22×C4⋊Dic59C2211yescharacteristic
22C22×C4⋊Dic59C2211yescharacteristic
23C22×C4⋊Dic59C2211yescharacteristic
24C22×C4⋊Dic59C2211yescharacteristic
25C22×C22⋊Dic59C2211yescharacteristic
26C22×C22⋊Dic59C2211yescharacteristic
27C22×C22⋊Dic59C2211yescharacteristic
28C22×C22⋊Dic59C2211yescharacteristic
29C22×C22⋊Dic59C2211yescharacteristic
30C22×C22⋊Dic59C2211yescharacteristic
31C22×C4×Dic59C2211yescharacteristic
32C22×C4×Dic59C2211yescharacteristic
33C22×C4×Dic59C2211yescharacteristic
34#16837301—24no—
35#16837295—24no—
36#16837277—24no—
37#16837277—24no—
38C22⋊C4×Dic59—24no—
39C2×C59⋊#95C2211yescharacteristic
40C2×C59⋊#95C2211yescharacteristic
41C2×C59⋊#95C2211yescharacteristic
42C2×C59⋊#95C2211yescharacteristic
43C2×C59⋊#95C2211yescharacteristic
44C2×C59⋊#95C2211yescharacteristic
45C2×C59⋊#95C2211yescharacteristic
46C2×C59⋊#95C2211yescharacteristic
47C2×C59⋊#95C2211yescharacteristic
48C2×C59⋊#95C2211yescharacteristic
49C2×C59⋊#95C2211yescharacteristic
50C2×C59⋊#95C2211yescharacteristic
51C2×C59⋊#95C2211yescharacteristic
52C23×D4×C59C2211yescharacteristic
53C22×C4⋊C4×C59C2211yescharacteristic
54C22×C22⋊C4×C59C2211yescharacteristic
55C22×C22⋊C4×C59C2211yescharacteristic
56C22×C22⋊C4×C59C2211yescharacteristic
57C22×C22⋊C4×C59C2211yescharacteristic
58C59×#394C418yescomplemented
59C2×#95×C59C2211yescharacteristic
60C23×Dic59—22no—
61C23×Dic59—22no—
62C23×Dic59—22no—
63C23×Dic59—22no—
64C23×Dic59—22no—
65C23×Dic59—22no—
66C23×Dic59—22no—
67C23×Dic59—22no—
68C23×Dic59—22no—
69C23×Dic59—41no—
70C23×Dic59—41no—
71C23×Dic59—41no—
72C23×Dic59—41no—
73C23×Dic59D414yes—
74C23×Dic59C2311yescharacteristic
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2311yescharacteristic
79C23×Dic59C2311yescharacteristic
80C23×Dic59C2311yescharacteristic
81C23×Dic59C2311yescharacteristic
82D4×Dic59—232no—
83C2×C4⋊Dic59—22no—
84C2×C4⋊Dic59—22no—
85C2×C4⋊Dic59—22no—
86C2×C4⋊Dic59—22no—
87C2×C4⋊Dic59—22no—
88C2×C4⋊Dic59—22no—
89C2×C4⋊Dic59—22no—
90C2×C4⋊Dic59—22no—
91C2×C4⋊Dic59—22no—
92C2×C4⋊Dic59—22no—
93C2×C4⋊Dic59—41no—
94C2×C4⋊Dic59D414yes—
95C2×C22⋊Dic59—22no—
96C2×C22⋊Dic59—22no—
97C2×C22⋊Dic59—22no—
98C2×C22⋊Dic59—22no—
99C2×C22⋊Dic59—22no—
100C2×C22⋊Dic59—22no—
101C2×C22⋊Dic59—22no—
102C2×C22⋊Dic59—22no—
103C2×C22⋊Dic59—22no—
104C2×C22⋊Dic59—22no—
105C2×C22⋊Dic59—22no—
106C2×C22⋊Dic59—22no—
107C2×C22⋊Dic59—22no—
108C2×C22⋊Dic59—41no—
109C2×C22⋊Dic59—41no—
110C2×C22⋊Dic59—41no—
111C2×C22⋊Dic59—41no—
112C2×C22⋊Dic59D414yes—
113C2×C4×Dic59—22no—
114C2×C4×Dic59—22no—
115C2×C4×Dic59—22no—
116C2×C4×Dic59—22no—
117C2×C4×Dic59—22no—
118C2×C4×Dic59—22no—
119C2×C4×Dic59—22no—
120C2×C4×Dic59—41no—
121C2×C4×Dic59—41no—
122C59⋊#95—22no—
123C59⋊#95—22no—
124C59⋊#95—22no—
125C59⋊#95—22no—
126C59⋊#95—22no—
127C59⋊#95—22no—
128C59⋊#95—22no—
129C59⋊#95—22no—
130C59⋊#95—22no—
131C59⋊#95—22no—
132C59⋊#95—22no—
133C59⋊#95—41no—
134C59⋊#95D414yescomplemented
135C25×C59C2311yescharacteristic
136C25×C59C2311yescharacteristic
137C22×D4×C59—22no—
138C22×D4×C59—22no—
139C22×D4×C59—22no—
140C22×D4×C59—22no—
141C22×D4×C59—22no—
142C22×D4×C59—22no—
143C22×D4×C59C2×C414yes—
144C23×C4×C59C2311yescharacteristic
145C23×C4×C59C2311yescharacteristic
146C23×C4×C59C2311yescharacteristic
147C23×C4×C59C2311yescharacteristic
148C23×C4×C59C2311yescharacteristic
149C2×C4⋊C4×C59—22no—
150C2×C4⋊C4×C59—22no—
151C2×C4⋊C4×C59C2×C414yescomplemented
152C2×C22⋊C4×C59—22no—
153C2×C22⋊C4×C59—22no—
154C2×C22⋊C4×C59—22no—
155C2×C22⋊C4×C59—22no—
156C2×C22⋊C4×C59—22no—
157C2×C22⋊C4×C59—22no—
158C2×C22⋊C4×C59—22no—
159C2×C22⋊C4×C59—22no—
160C2×C22⋊C4×C59C2×C414yescomplemented
161C2×C22⋊C4×C59C2×C414yescomplemented
162C2×C22⋊C4×C59C2×C414yescomplemented
163C2×C22⋊C4×C59C2×C414yescomplemented
164#95×C59C2×C414yescomplemented
165C24×C59—21no—
166C24×C59—21no—
167C24×C59—21no—
168C24×C59—21no—
169C24×C59—21no—
170C24×C59—21no—
171C24×C59—21no—
172C24×C59—21no—
173C24×C59—21no—
174C24×C59—21no—
175C24×C59—21no—
176C24×C59—21no—
177C24×C59—21no—
178C24×C59—21no—
179C24×C59—21no—
180C24×C59—21no—
181C24×C59—21no—
182C24×C59—21no—
183C24×C59—21no—
184C24×C59—21no—
185C24×C59—21no—
186C24×C59—21no—
187C24×C59—21no—
188C24×C59—21no—
189C24×C59C22×C412yes—
190C24×C59C22×C412yes—
191C24×C59C2×D412yes—
192C24×C59C2×D412yes—
193C24×C59#4112yes—
194C24×C59#4112yes—
195C24×C59C2411yescharacteristic
196C2×D4×C59—28no—
197C2×D4×C59—28no—
198C2×D4×C59—28no—
199C2×D4×C59—28no—
200C2×D4×C59—28no—
201C2×D4×C59—28no—
202C2×D4×C59—28no—
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—21no—
218C22×C4×C59—21no—
219C22×C4×C59—21no—
220C22×C4×C59—21no—
221C22×C4×C59—21no—
222C22×C4×C59—21no—
223C22×C4×C59—21no—
224C22×C4×C59—21no—
225C22×C4×C59—21no—
226C22×C4×C59—21no—
227C22×C4×C59—21no—
228C22×C4×C59—21no—
229C22×C4×C59C22×C412yes—
230C22×C4×C59C22×C412yes—
231C22×C4×C59C22×C412yes—
232C22×C4×C59C22×C412yes—
233C22×C4×C59C22×C412yes—
234C22×C4×C59C2×D412yes—
235C22×C4×C59C2×D412yes—
236C22×C4×C59#4112yes—
237C22×C4×C59#4112yes—
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—28no—
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—28no—
272C22×Dic59—28no—
273C22×Dic59—21no—
274C22×Dic59—21no—
275C22×Dic59—21no—
276C22×Dic59—21no—
277C22×Dic59—21no—
278C22×Dic59—21no—
279C22×Dic59—21no—
280C22×Dic59—21no—
281C22×Dic59—21no—
282C22×Dic59—21no—
283C22×Dic59—21no—
284C22×Dic59—21no—
285C22×Dic59—21no—
286C22×Dic59—21no—
287C22×Dic59—44no—
288C22×Dic59—44no—
289C22×Dic59—44no—
290C22×Dic59—44no—
291C22×Dic59—44no—
292C22×Dic59—44no—
293C22×Dic59—44no—
294C22×Dic59—44no—
295C22×Dic59—44no—
296C22×Dic59—44no—
297C22×Dic59—44no—
298C22×Dic59C2×D412yes—
299C22×Dic59C2×D412yes—
300C22×Dic59C2×D412yes—
301C22×Dic59C2×D412yes—
302C22×Dic59C2×D412yes—
303C22×Dic59C2×D412yes—
304C22×Dic59C2×D412yes—
305C22×Dic59C2×D412yes—
306C22×Dic59#4112yes—
307C22×Dic59#4112yes—
308C4⋊C4×C59—28no—
309C22⋊C4×C59—28no—
310C22⋊C4×C59—28no—
311C22⋊C4×C59—28no—
312C22⋊C4×C59—28no—
313C22⋊Dic59—28no—
314C22⋊Dic59—28no—
315C22⋊Dic59—28no—
316C22⋊Dic59—44no—
317C22⋊Dic59—44no—
318C22⋊Dic59—44no—
319C4⋊Dic59—28no—
320C4⋊Dic59—44no—
321C4⋊Dic59—44no—
322C4⋊Dic59—44no—
323C4×Dic59—28no—
324C4×Dic59—44no—
325C4×Dic59—44no—
326C23×C59—22no—
327C23×C59—22no—
328C23×C59—22no—
329C23×C59—22no—
330C23×C59—22no—
331C23×C59—22no—
332C23×C59—22no—
333C23×C59—22no—
334C23×C59—22no—
335C23×C59—22no—
336C23×C59—22no—
337C23×C59—22no—
338C23×C59—22no—
339C23×C59—22no—
340C23×C59—22no—
341C23×C59—22no—
342C23×C59—22no—
343C23×C59—22no—
344C23×C59—22no—
345C23×C59—22no—
346C23×C59—22no—
347C23×C59—22no—
348C23×C59—22no—
349C23×C59—22no—
350C23×C59—22no—
351C23×C59—22no—
352C23×C59—22no—
353C23×C59—22no—
354C23×C59—22no—
355C23×C59—22no—
356C23×C59—22no—
357C23×C59—22no—
358C23×C59—22no—
359C23×C59—22no—
360C23×C59—22no—
361C23×C59—22no—
362C23×C59—41no—
363C23×C59—41no—
364C23×C59—41no—
365C23×C59—41no—
366C23×C59—41no—
367C23×C59—41no—
368C23×C59—41no—
369C23×C59—41no—
370C23×C59—41no—
371C23×C59—41no—
372C23×C59—41no—
373C23×C59—41no—
374C23×C59—41no—
375C23×C59—41no—
376C23×C59—41no—
377C23×C59—41no—
378C23×C59—41no—
379C23×C59—41no—
380C23×C59—41no—
381C23×C59—41no—
382C23×C59—41no—
383C23×C59—41no—
384C23×C59—41no—
385C23×C59—41no—
386C23×C59—41no—
387C23×C59—41no—
388C23×C59—41no—
389C23×C59—41no—
390C23×C59—41no—
391C23×C59—41no—
392C23×C59—41no—
393C23×C59—41no—
394C23×C59C4×D414yes—
395C23×C59C4×D414yes—
396C23×C59C23×C411yescharacteristic
397C23×C59C22×D411yescharacteristic
398C23×C59C22×D411yescharacteristic
399C23×C59C22×D411yescharacteristic
400C23×C59C22×D411yescharacteristic
401C23×C59C2×#4111yescharacteristic
402C23×C59C2×#4111yescharacteristic
403C23×C59C2×#4111yescharacteristic
404C23×C59C2×#4111yescharacteristic
405C23×C59C2×#4111yescharacteristic
406C23×C59C2×#4111yescharacteristic
407C23×C59H(5,𝔽2)11yescharacteristic
408C23×C59H(5,𝔽2)11yescharacteristic
409C23×C592−1+411yescharacteristic
410C23×C592−1+411yescharacteristic
411D4×C59—232no—
412C2×C4×C59—22no—
413C2×C4×C59—22no—
414C2×C4×C59—22no—
415C2×C4×C59—22no—
416C2×C4×C59—22no—
417C2×C4×C59—22no—
418C2×C4×C59—22no—
419C2×C4×C59—22no—
420C2×C4×C59—22no—
421C2×C4×C59—22no—
422C2×C4×C59—22no—
423C2×C4×C59—22no—
424C2×C4×C59—22no—
425C2×C4×C59—22no—
426C2×C4×C59—22no—
427C2×C4×C59—22no—
428C2×C4×C59—22no—
429C2×C4×C59—22no—
430C2×C4×C59—22no—
431C2×C4×C59—22no—
432C2×C4×C59—22no—
433C2×C4×C59—41no—
434C2×C4×C59—41no—
435C2×C4×C59—41no—
436C2×C4×C59—41no—
437C2×C4×C59—41no—
438C2×C4×C59—41no—
439C2×C4×C59—41no—
440C2×C4×C59—41no—
441C2×C4×C59—41no—
442C2×C4×C59—41no—
443C2×C4×C59—41no—
444C2×C4×C59—41no—
445C2×C4×C59C4×D414yes—
446C2×C4×C59C4×D414yescomplemented
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—22no—
461C2×Dic59—22no—
462C2×Dic59—22no—
463C2×Dic59—22no—
464C2×Dic59—22no—
465C2×Dic59—22no—
466C2×Dic59—22no—
467C2×Dic59—22no—
468C2×Dic59—22no—
469C2×Dic59—22no—
470C2×Dic59—22no—
471C2×Dic59—416no—
472C2×Dic59—416no—
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×Dic59—41no—
485C2×Dic59—41no—
486C2×Dic59—41no—
487C2×Dic59—41no—
488C2×Dic59—41no—
489C2×Dic59—41no—
490C2×Dic59—41no—
491C2×Dic59—41no—
492C2×Dic59—41no—
493C2×Dic59—41no—
494C2×Dic59—41no—
495C2×Dic59—41no—
496C2×Dic59—41no—
497C2×Dic59—41no—
498C2×Dic59—41no—
499C2×Dic59—41no—
500C2×Dic59—41no—
501C2×Dic59—41no—
502C2×Dic59—41no—
503C2×Dic59#12014yes—
504C2×Dic59#12114yes—
505#14185—591nomaximal, Sylow
506C22×C59—24no—
507C22×C59—24no—
508C22×C59—24no—
509C22×C59—24no—
510C22×C59—24no—
511C22×C59—24no—
512C22×C59—42no—
513C22×C59—42no—
514C22×C59—42no—
515C22×C59—42no—
516C22×C59—42no—
517C22×C59—42no—
518C22×C59—42no—
519C22×C59—42no—
520C22×C59—42no—
521C22×C59—42no—
522C22×C59—42no—
523C22×C59—42no—
524C22×C59—42no—
525C22×C59—42no—
526C22×C59—42no—
527C22×C59—42no—
528C22×C59—42no—
529C22×C59—42no—
530C22×C59—42no—
531C22×C59—42no—
532C22×C59—42no—
533C22×C59—42no—
534C22×C59—42no—
535C22×C59—42no—
536C22×C59C2×C4×D411yescharacteristic
537C22×C59C2×C4×D411yescharacteristic
538C22×C59C2×C4×D411yescharacteristic
539C22×C59C2×C4×D411yescharacteristic
540C22×C59C4×#4111yescharacteristic
541C22×C59#52011yescharacteristic
542C22×C59#52011yescharacteristic
543C22×C59C2×#12011yescharacteristic
544C22×C59C2×#12111yescharacteristic
545C22×C59#52511yescharacteristic
546C22×C59#52511yescharacteristic
547C22×C59#52511yescharacteristic
548C22×C59#52511yescharacteristic
549C22×C59#52911yescharacteristic
550C22×C59#53211yescharacteristic
551C22×C59#53411yescharacteristic
552C22×C59#53611yescharacteristic
553C22×C59#53911yescharacteristic
554C22×C59#53911yescharacteristic
555C22×C59D4211yescharacteristic
556C22×C59D4211yescharacteristic
557C22×C59#54611yescharacteristic
558C22×C59#54611yescharacteristic
559C22×C59#54711yescharacteristic
560C22×C59#54711yescharacteristic
561C22×C59#54711yescharacteristic
562C22×C59#54811yescharacteristic
563C22×C59#54811yescharacteristic
564C22×C59#54811yescharacteristic
565C22×C59#55111yescharacteristic
566C22×C59#55211yescharacteristic
567C22×C59#55311yescharacteristic
568C22×C59#55311yescharacteristic
569C22×C59#55611yescharacteristic
570C22×C59#55911yescharacteristic
571C4×C59—24no—
572C4×C59—24no—
573C4×C59—42no—
574C4×C59—42no—
575C4×C59—42no—
576Dic59—24no—
577Dic59—24no—
578Dic59—42no—
579Dic59—42no—
580Dic59—42no—
581Dic59—42no—
582Dic59—81no—
583Dic59—81no—
584C22×C4×D4—591no—
585C2×#394D5911yescharacteristic
586C2×#389—591no—
587C2×#388—591no—
588C2×#385—591no—
589C2×#385—591no—
590C2×C4×C22⋊C4—591no—
591#1440—591no—
592#1439—591no—
593#1438—591no—
594#1437—591no—
595#1436—591no—
596#1436—591no—
597#1436—591no—
598C22⋊#95—591no—
599C2×C59—44no—
600C2×C59—44no—
601C2×C59C4×#12011yescharacteristic
602C2×C59C4×#12111yescharacteristic
603C2×C59#232211yescharacteristic
604C2×C59#235911yescharacteristic
605C2×C59#236111yescharacteristic
606C2×C59#236111yescharacteristic
607C2×C59#236711yescharacteristic
608C2×C59#241011yescharacteristic
609C2×C59#241511yescharacteristic
610C2×C59#243211yescharacteristic
611C2×C59#245511yescharacteristic
612C2×C59#246011yescharacteristic
613C2×C59#246311yescharacteristic
614C2×C59#246611yescharacteristic
615C2×C59#260211yescharacteristic
616C23×D4C2×D5911yescharacteristic
617C24×C4—591no—
618C24×C4—591no—
619C2×C4×D4—1184no—
620C2×C4×D4—1184no—
621C2×C4×D4—1184no—
622C22×C4⋊C4—591no—
623C22×C4⋊C4—591no—
624C22×C4⋊C4—591no—
625C22×C4⋊C4—591no—
626C22×C4⋊C4C2×D5911yescharacteristic
627C22×C22⋊C4—591no—
628C22×C22⋊C4—591no—
629C22×C22⋊C4—591no—
630C22×C22⋊C4—591no—
631C22×C22⋊C4—591no—
632C22×C22⋊C4—591no—
633C22×C22⋊C4C2×D5911yescharacteristic
634C22×C22⋊C4C2×D5911yescharacteristic
635C22×C22⋊C4C2×D5911yescharacteristic
636C22×C22⋊C4C2×D5911yescharacteristic
637C22×C42—591no—
638C22×C42—591no—
639C22×C42—591no—
640#394Dic5918yescomplemented
641#389—1184no—
642#388—1184no—
643#385—1184no—
644#385—1184no—
645C4×C22⋊C4—1184no—
646C2×#95—591no—
647C2×#95—591no—
648C2×#95—591no—
649C2×#95—591no—
650C2×#95—591no—
651C2×#95—591no—
652C2×#95—591no—
653C2×#95—591no—
654C2×#95—591no—
655C2×#95—591no—
656C2×#95—591no—
657C2×#95—591no—
658C2×#95—591no—
659C2×#95C2×D5911yescharacteristic
660C59#1418511yescharacteristic, complemented, Sylow
661C25C22×D5911yescharacteristic
662C25C22×D5911yescharacteristic
663C22×D4—22no—
664C22×D4—22no—
665C22×D4—22no—
666C22×D4—22no—
667C22×D4—22no—
668C22×D4—22no—
669C22×D4C2×Dic5914yes—
670C23×C4—591no—
671C23×C4—591no—
672C23×C4—591no—
673C23×C4—591no—
674C23×C4—591no—
675C23×C4—591no—
676C23×C4—594no—
677C23×C4—591no—
678C23×C4—591no—
679C23×C4—1182no—
680C23×C4—1182no—
681C23×C4—1182no—
682C23×C4—1182no—
683C23×C4—1182no—
684C23×C4—1182no—
685C23×C4—1182no—
686C23×C4—1182no—
687C23×C4—1182no—
688C23×C4—2361no—
689C23×C4—2361no—
690C23×C4—2361no—
691C23×C4—2361no—
692C23×C4C22×D5911yescharacteristic
693C23×C4C22×D5911yescharacteristic
694C23×C4C22×D5911yescharacteristic
695C23×C4C22×D5911yescharacteristic
696C23×C4C22×D5911yescharacteristic
697C4×D4—11832no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—594no—
701C2×C4⋊C4—1182no—
702C2×C4⋊C4—1182no—
703C2×C4⋊C4—1182no—
704C2×C4⋊C4—1182no—
705C2×C4⋊C4—1182no—
706C2×C4⋊C4—1182no—
707C2×C4⋊C4—1182no—
708C2×C4⋊C4—1182no—
709C2×C4⋊C4—1182no—
710C2×C4⋊C4—1182no—
711C2×C4⋊C4—2361no—
712C2×C4⋊C4C2×Dic5914yescomplemented
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—594no—
722C2×C22⋊C4—1182no—
723C2×C22⋊C4—1182no—
724C2×C22⋊C4—1182no—
725C2×C22⋊C4—1182no—
726C2×C22⋊C4—1182no—
727C2×C22⋊C4—1182no—
728C2×C22⋊C4—1182no—
729C2×C22⋊C4—1182no—
730C2×C22⋊C4—1182no—
731C2×C22⋊C4—1182no—
732C2×C22⋊C4—1182no—
733C2×C22⋊C4—1182no—
734C2×C22⋊C4—1182no—
735C2×C22⋊C4—2361no—
736C2×C22⋊C4—2361no—
737C2×C22⋊C4—2361no—
738C2×C22⋊C4—2361no—
739C2×C22⋊C4C2×Dic5914yescomplemented
740C2×C22⋊C4C2×Dic5914yescomplemented
741C2×C22⋊C4C2×Dic5914yescomplemented
742C2×C22⋊C4C2×Dic5914yescomplemented
743C2×C42—1182no—
744C2×C42—1182no—
745C2×C42—1182no—
746C2×C42—1182no—
747C2×C42—1182no—
748C2×C42—1182no—
749C2×C42—1182no—
750C2×C42—2361no—
751C2×C42—2361no—
752#95—594no—
753#95—1182no—
754#95—1182no—
755#95—1182no—
756#95—1182no—
757#95—1182no—
758#95—1182no—
759#95—1182no—
760#95—1182no—
761#95—1182no—
762#95—1182no—
763#95—1182no—
764#95—2361no—
765#95C2×Dic5914yescomplemented
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24D4×D5912yes—
791C24D4×D5912yes—
792C24#1174568712yes—
793C24#1174568712yes—
794C24C22×Dic5912yes—
795C24C22×Dic5912yes—
796C24C23×D5911yescharacteristic
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—28no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—592no—
831C22×C4—592no—
832C22×C4—592no—
833C22×C4—592no—
834C22×C4—592no—
835C22×C4—592no—
836C22×C4—592no—
837C22×C4—592no—
838C22×C4—592no—
839C22×C4—592no—
840C22×C4—1188no—
841C22×C4—1188no—
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—1188no—
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—1181no—
863C22×C4—1181no—
864C22×C4—1181no—
865C22×C4—1181no—
866C22×C4—1181no—
867C22×C4—1181no—
868C22×C4—1181no—
869C22×C4—1181no—
870C22×C4—1181no—
871C22×C4—1181no—
872C22×C4—1181no—
873C22×C4—1181no—
874C22×C4—1181no—
875C22×C4—1181no—
876C22×C4—1181no—
877C22×C4—1181no—
878C22×C4—1181no—
879C22×C4—1181no—
880C22×C4—1181no—
881C22×C4—1181no—
882C22×C4—1181no—
883C22×C4—1181no—
884C22×C4—1181no—
885C22×C4—1181no—
886C22×C4—1181no—
887C22×C4—1181no—
888C22×C4—1181no—
889C22×C4—2364no—
890C22×C4—2364no—
891C22×C4—2364no—
892C22×C4—2364no—
893C22×C4—2364no—
894C22×C4—2364no—
895C22×C4—2364no—
896C22×C4—2364no—
897C22×C4—2364no—
898C22×C4—2364no—
899C22×C4—2364no—
900C22×C4D4×D5912yes—
901C22×C4D4×D5912yes—
902C22×C4#1174568712yes—
903C22×C4#1174568712yes—
904C22×C4C22×Dic5912yes—
905C22×C4C22×Dic5912yes—
906C22×C4C22×Dic5912yes—
907C22×C4C22×Dic5912yes—
908C22×C4C22×Dic5912yes—
909C4⋊C4—28no—
910C4⋊C4—1188no—
911C4⋊C4—2364no—
912C4⋊C4—2364no—
913C4⋊C4—2364no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—1188no—
919C22⋊C4—1188no—
920C22⋊C4—1188no—
921C22⋊C4—2364no—
922C22⋊C4—2364no—
923C22⋊C4—2364no—
924C42—1188no—
925C42—2364no—
926C42—2364no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23D4×Dic5914yes—
996C23D4×Dic5914yes—
997C23C23×Dic5911yescharacteristic
998C23C2×D4×D5911yescharacteristic
999C23C2×D4×D5911yescharacteristic
1000C23C2×D4×D5911yescharacteristic
1001C23C2×D4×D5911yescharacteristic
1002C23#41×D5911yescharacteristic
1003C23#41×D5911yescharacteristic
1004C23C2×#1174568711yescharacteristic
1005C23C2×#1174568711yescharacteristic
1006C23C2×#1174568711yescharacteristic
1007C23C2×#1174568711yescharacteristic
1008C23#1427377311yescharacteristic
1009C23#1427377311yescharacteristic
1010C23#1427377411yescharacteristic
1011C23#1427377411yescharacteristic
1012D4—232no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—594no—
1047C2×C4—594no—
1048C2×C4—1182no—
1049C2×C4—1182no—
1050C2×C4—1182no—
1051C2×C4—1182no—
1052C2×C4—1182no—
1053C2×C4—1182no—
1054C2×C4—1182no—
1055C2×C4—1182no—
1056C2×C4—1182no—
1057C2×C4—1182no—
1058C2×C4—1182no—
1059C2×C4—1182no—
1060C2×C4—1182no—
1061C2×C4—1182no—
1062C2×C4—1182no—
1063C2×C4—1182no—
1064C2×C4—1182no—
1065C2×C4—1182no—
1066C2×C4—1182no—
1067C2×C4—1182no—
1068C2×C4—1182no—
1069C2×C4—1182no—
1070C2×C4—1182no—
1071C2×C4—1182no—
1072C2×C4—23616no—
1073C2×C4—23616no—
1074C2×C4—2361no—
1075C2×C4—2361no—
1076C2×C4—2361no—
1077C2×C4—2361no—
1078C2×C4—2361no—
1079C2×C4—2361no—
1080C2×C4—2361no—
1081C2×C4—2361no—
1082C2×C4—2361no—
1083C2×C4—2361no—
1084C2×C4—2361no—
1085C2×C4—2361no—
1086C2×C4—2361no—
1087C2×C4—2361no—
1088C2×C4—2361no—
1089C2×C4—2361no—
1090C2×C4—2361no—
1091C2×C4—2361no—
1092C2×C4—2361no—
1093C2×C4—2361no—
1094C2×C4—2361no—
1095C2×C4—2361no—
1096C2×C4—2361no—
1097C2×C4—2361no—
1098C2×C4—2361no—
1099C2×C4—2361no—
1100C2×C4—2361no—
1101C2×C4—2361no—
1102C2×C4—2361no—
1103C2×C4—2361no—
1104C2×C4D4×Dic5914yes—
1105C2×C4D4×Dic5914yescomplemented
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—24no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22C2×D4×Dic5911yescharacteristic
1137C22C2×D4×Dic5911yescharacteristic
1138C22C2×D4×Dic5911yescharacteristic
1139C22C2×D4×Dic5911yescharacteristic
1140C22#41×Dic5911yescharacteristic
1141C22#1683788511yescharacteristic
1142C22#1683788511yescharacteristic
1143C22#120×D5911yescharacteristic
1144C22#121×D5911yescharacteristic
1145C22#1683790811yescharacteristic
1146C22#1683790811yescharacteristic
1147C22#1683790811yescharacteristic
1148C22#1683791211yescharacteristic
1149C22#1683793311yescharacteristic
1150C22#1683794711yescharacteristic
1151C22#1683796311yescharacteristic
1152C22#1683797411yescharacteristic
1153C22#1683799611yescharacteristic
1154C22#1683799611yescharacteristic
1155C22#1683803611yescharacteristic
1156C22#1683803611yescharacteristic
1157C22#1683804411yescharacteristic
1158C22#1683804511yescharacteristic
1159C22#1683805011yescharacteristic
1160C22#1683805211yescharacteristic
1161C22#1683805211yescharacteristic
1162C22#1683805811yescharacteristic
1163C22#1683805811yescharacteristic
1164C22#1683806011yescharacteristic
1165C22#1683807511yescharacteristic
1166C22#1683808911yescharacteristic
1167C22#1683810411yescharacteristic
1168C22#1683810411yescharacteristic
1169C22#1683812111yescharacteristic
1170C22#1683813411yescharacteristic
1171C4—24no—
1172C4—24no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—1184no—
1177C4—1184no—
1178C4—4721no—
1179C4—4721no—
1180C4—2362no—
1181C4—2362no—
1182C4—2362no—
1183C4—2362no—
1184C2—44no—
1185C2—44no—
1186C2#120×Dic5911yescharacteristic
1187C2#121×Dic5911yescharacteristic
1188C2#2142676811yescharacteristic
1189C2#2142709211yescharacteristic
1190C2#2142711611yescharacteristic
1191C2#2142711611yescharacteristic
1192C2#2142717111yescharacteristic
1193C2#2142746511yescharacteristic
1194C2#2142751811yescharacteristic
1195C2#2142771911yescharacteristic
1196C2#2142797411yescharacteristic
1197C2#2142804311yescharacteristic
1198C2#2142808811yescharacteristic
1199C2#2142812711yescharacteristic
1200C2#2142970911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C59×#394C2
socle, cosocleC24×C59C24
prime radicalC23×D4×C59C22
hypercenterC2×#394D59
hypocenterC59#14185
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C2×#16837301C2semidirect
3. C2×#16837295C2semidirect
4. C2×#16837277C2semidirect
5. C2×#16837277C2semidirect
6. C2×C22⋊C4×Dic59C2semidirect
7. #21422345C2semidirect
8. #21422341C2semidirect
10. #21422333C2semidirect
11. #21422330C2semidirect
12. #21422330C2semidirect
13. #21422328C2semidirect
14. #21422318C2semidirect
58. C59×#394C4semidirect
134. C59⋊#95D4semidirect
151. C2×C4⋊C4×C59C2×C4semidirect
160. C2×C22⋊C4×C59C2×C4semidirect
161. C2×C22⋊C4×C59C2×C4semidirect
162. C2×C22⋊C4×C59C2×C4semidirect
163. C2×C22⋊C4×C59C2×C4semidirect
164. #95×C59C2×C4semidirect
446. C2×C4×C59C4×D4semidirect
640. #394Dic59semidirect
660. C59#14185semidirect
712. C2×C4⋊C4C2×Dic59semidirect
739. C2×C22⋊C4C2×Dic59semidirect
740. C2×C22⋊C4C2×Dic59semidirect
741. C2×C22⋊C4C2×Dic59semidirect
742. C2×C22⋊C4C2×Dic59semidirect
765. #95C2×Dic59semidirect
1105. C2×C4D4×Dic59semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic592
C2×#168373012
C2×#168372952
C2×#168372772
C2×C22⋊C4×Dic592
#214223452
#214223412
#214223372
#214223332
#214223302
#214223282
#214223182
C2×C59×#3942
#1418559