Finite Group Databasebeta

← #28511553

Subgroups — #28511553

Order 15104.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic59C211yesmaximal, characteristic
2C2×#16837282C211yesmaximal, characteristic
3C2×#16837277C211yesmaximal, characteristic, complemented
4C2×#16837277C211yesmaximal, characteristic, complemented
5C2×#16837262C211yesmaximal, characteristic, complemented
6C22×C59⋊#95C211yesmaximal, characteristic, complemented
7#21422361C211yesmaximal, characteristic, complemented
8#21422353C211yesmaximal, characteristic, complemented
9#21422341C211yesmaximal, characteristic, complemented
10#21422341C211yesmaximal, characteristic, complemented
11#21422330C211yesmaximal, characteristic, complemented
12#21422330C211yesmaximal, characteristic, complemented
13#21422318C211yesmaximal, characteristic, complemented
14#21422318C211yesmaximal, characteristic, complemented
15C2×C59×#386C211yesmaximal, characteristic
16C24×Dic59C2211yescharacteristic
17C24×Dic59C2211yescharacteristic
18C24×Dic59C2211yescharacteristic
19C2×D4×Dic59—24no—
20C2×D4×Dic59—24no—
21C2×D4×Dic59—24no—
22C22×C4⋊Dic59C2211yescharacteristic
23C22×C4⋊Dic59C2211yescharacteristic
24C22×C4⋊Dic59C2211yescharacteristic
25C22×C4⋊Dic59C2211yescharacteristic
26C22×C4⋊Dic59C2211yescharacteristic
27C22×C22⋊Dic59C2211yescharacteristic
28C22×C22⋊Dic59C2211yescharacteristic
29C22×C22⋊Dic59C2211yescharacteristic
30C22×C22⋊Dic59C2211yescharacteristic
31C22×C22⋊Dic59C2211yescharacteristic
32C22×C4×Dic59C2211yescharacteristic
33#16837282—24no—
34#16837277—24no—
35#16837277—24no—
36#16837262—24no—
37C2×C59⋊#95—24no—
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
48C2×C59⋊#95C2211yescharacteristic
49C2×C59⋊#95C2211yescharacteristic
50C2×C59⋊#95C2211yescharacteristic
51C2×C59⋊#95C2211yescharacteristic
52C23×D4×C59C2211yescharacteristic
53C24×C4×C59C2211yescharacteristic
54C22×C22⋊C4×C59C2211yescharacteristic
55C22×C22⋊C4×C59C2211yescharacteristic
56C22×C22⋊C4×C59C2211yescharacteristic
57C59×#386C418yescomplemented
58C2×#95×C59C2211yescharacteristic
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—22no—
70C23×Dic59—22no—
71C23×Dic59—22no—
72C23×Dic59—22no—
73C23×Dic59—22no—
74C23×Dic59—41no—
75C23×Dic59—41no—
76C23×Dic59—41no—
77C23×Dic59—41no—
78C23×Dic59—41no—
79C23×Dic59—41no—
80C23×Dic59D414yes—
81C23×Dic59C2311yescharacteristic
82C23×Dic59C2311yescharacteristic
83C23×Dic59C2311yescharacteristic
84C23×Dic59C2311yescharacteristic
85C23×Dic59C2311yescharacteristic
86C23×Dic59C2311yescharacteristic
87C23×Dic59C2311yescharacteristic
88C23×Dic59C2311yescharacteristic
89D4×Dic59—232no—
90C2×C4⋊Dic59—22no—
91C2×C4⋊Dic59—22no—
92C2×C4⋊Dic59—22no—
93C2×C4⋊Dic59—22no—
94C2×C4⋊Dic59—22no—
95C2×C4⋊Dic59—22no—
96C2×C4⋊Dic59—22no—
97C2×C4⋊Dic59—22no—
98C2×C4⋊Dic59—22no—
99C2×C4⋊Dic59—22no—
100C2×C4⋊Dic59—22no—
101C2×C4⋊Dic59—41no—
102C2×C4⋊Dic59—41no—
103C2×C4⋊Dic59—41no—
104C2×C4⋊Dic59—41no—
105C2×C22⋊Dic59—22no—
106C2×C22⋊Dic59—22no—
107C2×C22⋊Dic59—22no—
108C2×C22⋊Dic59—22no—
109C2×C22⋊Dic59—22no—
110C2×C22⋊Dic59—22no—
111C2×C22⋊Dic59—22no—
112C2×C22⋊Dic59—22no—
113C2×C22⋊Dic59—22no—
114C2×C22⋊Dic59—22no—
115C2×C22⋊Dic59—22no—
116C2×C22⋊Dic59—22no—
117C2×C22⋊Dic59—41no—
118C2×C22⋊Dic59—41no—
119C2×C22⋊Dic59D414yes—
120C2×C4×Dic59—22no—
121C2×C4×Dic59—22no—
122C2×C4×Dic59—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—22no—
134C59⋊#95—41no—
135C59⋊#95—41no—
136C59⋊#95D414yescomplemented
137C25×C59C2311yescharacteristic
138C25×C59C2311yescharacteristic
139C22×D4×C59—22no—
140C22×D4×C59—22no—
141C22×D4×C59—22no—
142C22×D4×C59—22no—
143C22×D4×C59C2×C414yes—
144C22×D4×C59D414yes—
145C22×D4×C59Q814yes—
146C23×C4×C59—22no—
147C23×C4×C59—22no—
148C23×C4×C59—22no—
149C23×C4×C59—22no—
150C23×C4×C59—41no—
151C23×C4×C59—41no—
152C23×C4×C59C2×C414yescomplemented
153C23×C4×C59C2311yescharacteristic
154C23×C4×C59C2311yescharacteristic
155C23×C4×C59C2311yescharacteristic
156C23×C4×C59C2311yescharacteristic
157C23×C4×C59C2311yescharacteristic
158C2×C22⋊C4×C59—22no—
159C2×C22⋊C4×C59—22no—
160C2×C22⋊C4×C59—22no—
161C2×C22⋊C4×C59—22no—
162C2×C22⋊C4×C59—41no—
163C2×C22⋊C4×C59—41no—
164C2×C22⋊C4×C59C2×C414yescomplemented
165C2×C22⋊C4×C59C2×C414yescomplemented
166C2×C22⋊C4×C59C2×C414yescomplemented
167#95×C59C2×C414yescomplemented
168#95×C59C2×C414yescomplemented
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×C59C2×D412yes—
194C24×C59C2×D412yes—
195C24×C59C2×Q812yes—
196C24×C59C2×Q812yes—
197C24×C59#4112yes—
198C24×C59#4112yes—
199C24×C59C2411yescharacteristic
200C2×D4×C59—28no—
201C2×D4×C59—28no—
202C2×D4×C59—28no—
203C2×D4×C59—28no—
204C2×D4×C59—28no—
205C2×D4×C59—28no—
206C2×D4×C59C4⋊C4116yescomplemented
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—28no—
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×C59—21no—
230C22×C4×C59—21no—
231C22×C4×C59—21no—
232C22×C4×C59—21no—
233C22×C4×C59—21no—
234C22×C4×C59—28no—
235C22×C4×C59—44no—
236C22×C4×C59—44no—
237C22×C4×C59—44no—
238C22×C4×C59—44no—
239C22×C4×C59—44no—
240C22×C4×C59C22×C412yes—
241C22×C4×C59C22×C412yes—
242C22×C4×C59C22×C412yes—
243C22×C4×C59C22×C412yes—
244C22×C4×C59C22×C412yes—
245C22×C4×C59C2×D412yes—
246C22×C4×C59C2×D412yes—
247C22×C4×C59C2×Q812yes—
248C22×C4×C59#4112yes—
249C22×Dic59—21no—
250C22×Dic59—21no—
251C22×Dic59—21no—
252C22×Dic59—21no—
253C22×Dic59—28no—
254C22×Dic59—28no—
255C22×Dic59—28no—
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×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—28no—
287C22×Dic59—21no—
288C22×Dic59—21no—
289C22×Dic59—21no—
290C22×Dic59—21no—
291C22×Dic59—21no—
292C22×Dic59—21no—
293C22×Dic59—21no—
294C22×Dic59—21no—
295C22×Dic59—21no—
296C22×Dic59—21no—
297C22×Dic59—21no—
298C22×Dic59—21no—
299C22×Dic59—21no—
300C22×Dic59—21no—
301C22×Dic59—44no—
302C22×Dic59—44no—
303C22×Dic59—44no—
304C22×Dic59—44no—
305C22×Dic59—44no—
306C22×Dic59—44no—
307C22×Dic59—44no—
308C22×Dic59—44no—
309C22×Dic59—44no—
310C22×Dic59—44no—
311C22×Dic59—44no—
312C22×Dic59—44no—
313C22×Dic59—44no—
314C22×Dic59—44no—
315C22×Dic59—44no—
316C22×Dic59—44no—
317C22×Dic59—44no—
318C22×Dic59C2×D412yes—
319C22×Dic59C2×D412yes—
320C22×Dic59C2×D412yes—
321C22×Dic59C2×D412yes—
322C22×Dic59C2×D412yes—
323C22×Dic59C2×D412yes—
324C22×Dic59#4112yes—
325C22×Dic59#4112yes—
326C22⋊C4×C59—28no—
327C22⋊C4×C59—28no—
328C22⋊C4×C59—44no—
329C22⋊Dic59—28no—
330C22⋊Dic59—28no—
331C22⋊Dic59—44no—
332C22⋊Dic59—44no—
333C22⋊Dic59—44no—
334C4⋊Dic59—28no—
335C4⋊Dic59—44no—
336C4⋊Dic59—44no—
337C4⋊Dic59—44no—
338C4⋊Dic59—44no—
339C4×Dic59—28no—
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—22no—
363C23×C59—22no—
364C23×C59—22no—
365C23×C59—22no—
366C23×C59—22no—
367C23×C59—22no—
368C23×C59—22no—
369C23×C59—22no—
370C23×C59—22no—
371C23×C59—22no—
372C23×C59—22no—
373C23×C59—22no—
374C23×C59—22no—
375C23×C59—22no—
376C23×C59—22no—
377C23×C59—22no—
378C23×C59—22no—
379C23×C59—22no—
380C23×C59—22no—
381C23×C59—22no—
382C23×C59—22no—
383C23×C59—22no—
384C23×C59—22no—
385C23×C59—22no—
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×C59—41no—
395C23×C59—41no—
396C23×C59—41no—
397C23×C59—41no—
398C23×C59—41no—
399C23×C59—41no—
400C23×C59—41no—
401C23×C59—41no—
402C23×C59C2×C4⋊C414yes—
403C23×C59C2×C4⋊C414yes—
404C23×C59C4×D414yes—
405C23×C59C4×D414yes—
406C23×C59#12014yes—
407C23×C59C22⋊Q814yes—
408C23×C59C22⋊Q814yes—
409C23×C59#12314yes—
410C23×C59C23×C411yescharacteristic
411C23×C59C22×D411yescharacteristic
412C23×C59C22×D411yescharacteristic
413C23×C59C22×D411yescharacteristic
414C23×C59C22×D411yescharacteristic
415C23×C59C22×Q811yescharacteristic
416C23×C59C2×#4111yescharacteristic
417C23×C59C2×#4111yescharacteristic
418C23×C59C2×#4111yescharacteristic
419C23×C59C2×#4111yescharacteristic
420C23×C59C2×#4111yescharacteristic
421C23×C59H(5,𝔽2)11yescharacteristic
422C23×C59H(5,𝔽2)11yescharacteristic
423C23×C59H(5,𝔽2)11yescharacteristic
424C23×C592−1+411yescharacteristic
425D4×C59—232no—
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—22no—
434C2×C4×C59—22no—
435C2×C4×C59—22no—
436C2×C4×C59—22no—
437C2×C4×C59—22no—
438C2×C4×C59—22no—
439C2×C4×C59—22no—
440C2×C4×C59—22no—
441C2×C4×C59—22no—
442C2×C4×C59—22no—
443C2×C4×C59—22no—
444C2×C4×C59—22no—
445C2×C4×C59—22no—
446C2×C4×C59—22no—
447C2×C4×C59—416no—
448C2×C4×C59—41no—
449C2×C4×C59—41no—
450C2×C4×C59—41no—
451C2×C4×C59—41no—
452C2×C4×C59—41no—
453C2×C4×C59—41no—
454C2×C4×C59—41no—
455C2×C4×C59—41no—
456C2×C4×C59—41no—
457C2×C4×C59—41no—
458C2×C4×C59—41no—
459C2×C4×C59—41no—
460C2×C4×C59C2×C4⋊C414yes—
461C2×C4×C59C4×D414yescomplemented
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—22no—
472C2×Dic59—22no—
473C2×Dic59—22no—
474C2×Dic59—22no—
475C2×Dic59—22no—
476C2×Dic59—22no—
477C2×Dic59—22no—
478C2×Dic59—22no—
479C2×Dic59—22no—
480C2×Dic59—22no—
481C2×Dic59—22no—
482C2×Dic59—22no—
483C2×Dic59—416no—
484C2×Dic59—416no—
485C2×Dic59—416no—
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—41no—
504C2×Dic59—41no—
505C2×Dic59—41no—
506C2×Dic59—41no—
507C2×Dic59—41no—
508C2×Dic59—41no—
509C2×Dic59—41no—
510C2×Dic59—41no—
511C2×Dic59—41no—
512C2×Dic59—41no—
513C2×Dic59—41no—
514C2×Dic59—41no—
515C2×Dic59—41no—
516C2×Dic59—41no—
517C2×Dic59—41no—
518C2×Dic59—41no—
519C2×Dic59—41no—
520C2×Dic59#12114yes—
521#13975—591nomaximal, Sylow
522C22×C59—24no—
523C22×C59—24no—
524C22×C59—24no—
525C22×C59—24no—
526C22×C59—24no—
527C22×C59—24no—
528C22×C59—24no—
529C22×C59—24no—
530C22×C59—24no—
531C22×C59—24no—
532C22×C59—24no—
533C22×C59—24no—
534C22×C59—24no—
535C22×C59—24no—
536C22×C59—24no—
537C22×C59—24no—
538C22×C59—24no—
539C22×C59—42no—
540C22×C59—42no—
541C22×C59—42no—
542C22×C59—42no—
543C22×C59—42no—
544C22×C59—42no—
545C22×C59—42no—
546C22×C59—42no—
547C22×C59—42no—
548C22×C59—42no—
549C22×C59—42no—
550C22×C59—42no—
551C22×C59#38518yescomplemented
552C22×C59C22×C4⋊C411yescharacteristic
553C22×C59C2×C4×D411yescharacteristic
554C22×C59C2×C4×D411yescharacteristic
555C22×C59C2×C4×D411yescharacteristic
556C22×C59C4×#4111yescharacteristic
557C22×C59#51811yescharacteristic
558C22×C59#52011yescharacteristic
559C22×C59C2×#12011yescharacteristic
560C22×C59C2×#12111yescharacteristic
561C22×C59C2×C22⋊Q811yescharacteristic
562C22×C59C2×C22⋊Q811yescharacteristic
563C22×C59C2×#12311yescharacteristic
564C22×C59#52511yescharacteristic
565C22×C59#52911yescharacteristic
566C22×C59#53211yescharacteristic
567C22×C59#53411yescharacteristic
568C22×C59#53711yescharacteristic
569C22×C59#53811yescharacteristic
570C22×C59#53911yescharacteristic
571C22×C59D4211yescharacteristic
572C22×C59D4211yescharacteristic
573C22×C59#54611yescharacteristic
574C22×C59#54611yescharacteristic
575C22×C59#54611yescharacteristic
576C22×C59#54611yescharacteristic
577C22×C59#54611yescharacteristic
578C22×C59#54711yescharacteristic
579C22×C59#54711yescharacteristic
580C22×C59D4×Q811yescharacteristic
581C22×C59#55111yescharacteristic
582C22×C59#55111yescharacteristic
583C22×C59#55211yescharacteristic
584C22×C59#55411yescharacteristic
585C22×C59#55411yescharacteristic
586C22×C59#55411yescharacteristic
587C4×C59—24no—
588C4×C59—24no—
589C4×C59—42no—
590C4×C59—42no—
591C4×C59—42no—
592Dic59—24no—
593Dic59—42no—
594Dic59—42no—
595Dic59—42no—
596Dic59—42no—
597Dic59—42no—
598Dic59—81no—
599Dic59—81no—
600C22×C4×D4—591no—
601C2×#386—591no—
602C2×#386D5911yescharacteristic
603C2×#385—591no—
604C2×#385—591no—
605C2×#380—591no—
606C22×#95—591no—
607#1444—591no—
608#1442—591no—
609#1439—591no—
610#1439—591no—
611#1436—591no—
612#1436—591no—
613C22⋊#95—591no—
614C22⋊#95—591no—
615C2×C59—28no—
616C2×C59—44no—
617C2×C59C2×#38511yescharacteristic
618C2×C59C4×#12111yescharacteristic
619C2×C59#232511yescharacteristic
620C2×C59D4×C4⋊C411yescharacteristic
621C2×C59#234911yescharacteristic
622C2×C59#235811yescharacteristic
623C2×C59#235911yescharacteristic
624C2×C59#241011yescharacteristic
625C2×C59#241711yescharacteristic
626C2×C59#241811yescharacteristic
627C2×C59#241911yescharacteristic
628C2×C59#243011yescharacteristic
629C2×C59#244911yescharacteristic
630C2×C59#245011yescharacteristic
631C2×C59#256411yescharacteristic
632C23×D4C2×D5911yescharacteristic
633C24×C4—591no—
634C24×C4—591no—
635C24×C4—591no—
636C24×C4C2×D5911yescharacteristic
637C2×C4×D4—1184no—
638C2×C4×D4—1184no—
639C2×C4×D4—1184no—
640C22×C4⋊C4—591no—
641C22×C4⋊C4—591no—
642C22×C4⋊C4—591no—
643C22×C4⋊C4—591no—
644C22×C4⋊C4—591no—
645C22×C22⋊C4—591no—
646C22×C22⋊C4—591no—
647C22×C22⋊C4—591no—
648C22×C22⋊C4—591no—
649C22×C22⋊C4—591no—
650C22×C22⋊C4C2×D5911yescharacteristic
651C22×C22⋊C4C2×D5911yescharacteristic
652C22×C22⋊C4C2×D5911yescharacteristic
653C22×C42—591no—
654#386—1184no—
655#386Dic5918yescomplemented
656#385—1184no—
657#385—1184no—
658#380—1184no—
659C2×#95—591no—
660C2×#95—591no—
661C2×#95—591no—
662C2×#95—591no—
663C2×#95—591no—
664C2×#95—591no—
665C2×#95—591no—
666C2×#95—591no—
667C2×#95—591no—
668C2×#95—591no—
669C2×#95—591no—
670C2×#95—591no—
671C2×#95—591no—
672C2×#95—591no—
673C2×#95—1184no—
674C2×#95C2×D5911yescharacteristic
675C2×#95C2×D5911yescharacteristic
676C59#1397511yescharacteristic, complemented, Sylow
677C25C22×D5911yescharacteristic
678C25C22×D5911yescharacteristic
679C22×D4—22no—
680C22×D4—22no—
681C22×D4—22no—
682C22×D4—22no—
683C22×D4Dic11814yes—
684C22×D4D23614yes—
685C22×D4C2×Dic5914yes—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—22no—
690C23×C4—41no—
691C23×C4—41no—
692C23×C4—591no—
693C23×C4—591no—
694C23×C4—591no—
695C23×C4—591no—
696C23×C4—591no—
697C23×C4—591no—
698C23×C4—594no—
699C23×C4—591no—
700C23×C4—591no—
701C23×C4—1182no—
702C23×C4—1182no—
703C23×C4—1182no—
704C23×C4—1182no—
705C23×C4—1182no—
706C23×C4—1182no—
707C23×C4—1182no—
708C23×C4—1182no—
709C23×C4—1182no—
710C23×C4—1182no—
711C23×C4—1182no—
712C23×C4—1182no—
713C23×C4—1182no—
714C23×C4—1182no—
715C23×C4—2361no—
716C23×C4—2361no—
717C23×C4—2361no—
718C23×C4—2361no—
719C23×C4—2361no—
720C23×C4—2361no—
721C23×C4C2×Dic5914yescomplemented
722C23×C4C22×D5911yescharacteristic
723C23×C4C22×D5911yescharacteristic
724C23×C4C22×D5911yescharacteristic
725C23×C4C22×D5911yescharacteristic
726C23×C4C22×D5911yescharacteristic
727C4×D4—11832no—
728C2×C4⋊C4—1182no—
729C2×C4⋊C4—1182no—
730C2×C4⋊C4—1182no—
731C2×C4⋊C4—1182no—
732C2×C4⋊C4—1182no—
733C2×C4⋊C4—1182no—
734C2×C4⋊C4—1182no—
735C2×C4⋊C4—1182no—
736C2×C4⋊C4—1182no—
737C2×C4⋊C4—1182no—
738C2×C4⋊C4—1182no—
739C2×C4⋊C4—2361no—
740C2×C4⋊C4—2361no—
741C2×C4⋊C4—2361no—
742C2×C4⋊C4—2361no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—41no—
748C2×C22⋊C4—41no—
749C2×C22⋊C4—594no—
750C2×C22⋊C4—1182no—
751C2×C22⋊C4—1182no—
752C2×C22⋊C4—1182no—
753C2×C22⋊C4—1182no—
754C2×C22⋊C4—1182no—
755C2×C22⋊C4—1182no—
756C2×C22⋊C4—1182no—
757C2×C22⋊C4—1182no—
758C2×C22⋊C4—1182no—
759C2×C22⋊C4—1182no—
760C2×C22⋊C4—1182no—
761C2×C22⋊C4—1182no—
762C2×C22⋊C4—2361no—
763C2×C22⋊C4—2361no—
764C2×C22⋊C4C2×Dic5914yescomplemented
765C2×C22⋊C4C2×Dic5914yescomplemented
766C2×C22⋊C4C2×Dic5914yescomplemented
767C2×C42—1182no—
768C2×C42—1182no—
769C2×C42—1182no—
770#95—594no—
771#95—1182no—
772#95—1182no—
773#95—1182no—
774#95—1182no—
775#95—1182no—
776#95—1182no—
777#95—1182no—
778#95—1182no—
779#95—1182no—
780#95—1182no—
781#95—1182no—
782#95—2361no—
783#95—2361no—
784#95C2×Dic5914yescomplemented
785#95C2×Dic5914yescomplemented
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24C2×Dic11812yes—
807C24C2×Dic11812yes—
808C24C2×D23612yes—
809C24C2×D23612yes—
810C24D4×D5912yes—
811C24D4×D5912yes—
812C24#1174568712yes—
813C24#1174568712yes—
814C24C22×Dic5912yes—
815C24C22×Dic5912yes—
816C24C23×D5911yescharacteristic
817C2×D4—28no—
818C2×D4—28no—
819C2×D4—28no—
820C2×D4—28no—
821C2×D4—28no—
822C2×D4—28no—
823C2×D4C4⋊Dic59116yescomplemented
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—28no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—28no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—592no—
858C22×C4—592no—
859C22×C4—592no—
860C22×C4—592no—
861C22×C4—592no—
862C22×C4—592no—
863C22×C4—592no—
864C22×C4—592no—
865C22×C4—1188no—
866C22×C4—1181no—
867C22×C4—1181no—
868C22×C4—1181no—
869C22×C4—1181no—
870C22×C4—1188no—
871C22×C4—1188no—
872C22×C4—1188no—
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—1181no—
890C22×C4—1181no—
891C22×C4—1181no—
892C22×C4—1181no—
893C22×C4—1181no—
894C22×C4—1181no—
895C22×C4—1181no—
896C22×C4—1181no—
897C22×C4—1181no—
898C22×C4—1181no—
899C22×C4—1181no—
900C22×C4—1181no—
901C22×C4—1181no—
902C22×C4—1181no—
903C22×C4—1181no—
904C22×C4—1181no—
905C22×C4—1181no—
906C22×C4—1181no—
907C22×C4—1181no—
908C22×C4—1181no—
909C22×C4—1181no—
910C22×C4—1181no—
911C22×C4—1181no—
912C22×C4—1181no—
913C22×C4—1181no—
914C22×C4—1181no—
915C22×C4—1181no—
916C22×C4—1181no—
917C22×C4—2364no—
918C22×C4—2364no—
919C22×C4—2364no—
920C22×C4—2364no—
921C22×C4—2364no—
922C22×C4—2364no—
923C22×C4—2364no—
924C22×C4—2364no—
925C22×C4—2364no—
926C22×C4—2364no—
927C22×C4—2364no—
928C22×C4—2364no—
929C22×C4—2364no—
930C22×C4—2364no—
931C22×C4—2364no—
932C22×C4—2364no—
933C22×C4—2364no—
934C22×C4C2×Dic11812yes—
935C22×C4C2×D23612yes—
936C22×C4D4×D5912yes—
937C22×C4#1174568712yes—
938C22×C4C22×Dic5912yes—
939C22×C4C22×Dic5912yes—
940C22×C4C22×Dic5912yes—
941C22×C4C22×Dic5912yes—
942C22×C4C22×Dic5912yes—
943C4⋊C4—1188no—
944C4⋊C4—2364no—
945C4⋊C4—2364no—
946C4⋊C4—2364no—
947C4⋊C4—2364no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—44no—
951C22⋊C4—1188no—
952C22⋊C4—1188no—
953C22⋊C4—2364no—
954C22⋊C4—2364no—
955C22⋊C4—2364no—
956C42—1188no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23C2×C4⋊Dic5914yes—
1020C23C2×C4⋊Dic5914yes—
1021C23D4×Dic5914yes—
1022C23D4×Dic5914yes—
1023C23#1427369714yes—
1024C23#1427370414yes—
1025C23#1427370414yes—
1026C23#1427371114yes—
1027C23C23×Dic5911yescharacteristic
1028C23C2×D4×D5911yescharacteristic
1029C23C2×D4×D5911yescharacteristic
1030C23C2×D4×D5911yescharacteristic
1031C23C22×D23611yescharacteristic
1032C23C22×Dic11811yescharacteristic
1033C23#41×D5911yescharacteristic
1034C23#41×D5911yescharacteristic
1035C23C2×#1174568711yescharacteristic
1036C23C2×#1174568711yescharacteristic
1037C23C2×#1174568711yescharacteristic
1038C23#1427377211yescharacteristic
1039C23#1427377211yescharacteristic
1040C23#1427377311yescharacteristic
1041C23#1427377411yescharacteristic
1042D4—232no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—416no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—594no—
1078C2×C4—1182no—
1079C2×C4—1182no—
1080C2×C4—1182no—
1081C2×C4—1182no—
1082C2×C4—1182no—
1083C2×C4—1182no—
1084C2×C4—1182no—
1085C2×C4—1182no—
1086C2×C4—1182no—
1087C2×C4—1182no—
1088C2×C4—1182no—
1089C2×C4—1182no—
1090C2×C4—1182no—
1091C2×C4—1182no—
1092C2×C4—1182no—
1093C2×C4—1182no—
1094C2×C4—1182no—
1095C2×C4—1182no—
1096C2×C4—1182no—
1097C2×C4—1182no—
1098C2×C4—1182no—
1099C2×C4—23616no—
1100C2×C4—23616no—
1101C2×C4—2361no—
1102C2×C4—2361no—
1103C2×C4—2361no—
1104C2×C4—2361no—
1105C2×C4—2361no—
1106C2×C4—2361no—
1107C2×C4—2361no—
1108C2×C4—2361no—
1109C2×C4—2361no—
1110C2×C4—2361no—
1111C2×C4—2361no—
1112C2×C4—2361no—
1113C2×C4—2361no—
1114C2×C4—2361no—
1115C2×C4—23616no—
1116C2×C4—2361no—
1117C2×C4—2361no—
1118C2×C4—2361no—
1119C2×C4—2361no—
1120C2×C4—2361no—
1121C2×C4—2361no—
1122C2×C4—2361no—
1123C2×C4—2361no—
1124C2×C4—2361no—
1125C2×C4—2361no—
1126C2×C4—2361no—
1127C2×C4—2361no—
1128C2×C4—2361no—
1129C2×C4—2361no—
1130C2×C4—2361no—
1131C2×C4—2361no—
1132C2×C4—2361no—
1133C2×C4—2361no—
1134C2×C4—2361no—
1135C2×C4—2361no—
1136C2×C4C2×C4⋊Dic5914yes—
1137C2×C4D4×Dic5914yescomplemented
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—24no—
1153C22—24no—
1154C22—24no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22#1683727718yescomplemented
1168C22C22×C4⋊Dic5911yescharacteristic
1169C22C2×D4×Dic5911yescharacteristic
1170C22C2×D4×Dic5911yescharacteristic
1171C22C2×D4×Dic5911yescharacteristic
1172C22#41×Dic5911yescharacteristic
1173C22#1683787711yescharacteristic
1174C22#1683788511yescharacteristic
1175C22C2×#1427369711yescharacteristic
1176C22#121×D5911yescharacteristic
1177C22C2×#1427370411yescharacteristic
1178C22C2×#1427370411yescharacteristic
1179C22C2×#1427371111yescharacteristic
1180C22#1683791211yescharacteristic
1181C22#1683793311yescharacteristic
1182C22#1683794711yescharacteristic
1183C22#1683796011yescharacteristic
1184C22#1683797911yescharacteristic
1185C22#1683798911yescharacteristic
1186C22#1683799711yescharacteristic
1187C22#1683803411yescharacteristic
1188C22D4×D23611yescharacteristic
1189C22#1683803911yescharacteristic
1190C22#1683803911yescharacteristic
1191C22#1683804411yescharacteristic
1192C22#1683804711yescharacteristic
1193C22#1683804711yescharacteristic
1194C22#1683805011yescharacteristic
1195C22#1683805611yescharacteristic
1196C22D4×Dic11811yescharacteristic
1197C22#1683807511yescharacteristic
1198C22#1683808311yescharacteristic
1199C22#1683808911yescharacteristic
1200C22#1683810911yescharacteristic
1201C22#1683811111yescharacteristic
1202C22#1683811111yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—1184no—
1209C4—4721no—
1210C4—4721no—
1211C4—2362no—
1212C4—2362no—
1213C4—2362no—
1214C4—2362no—
1215C4—2362no—
1216C2—28no—
1217C2—44no—
1218C2C2×#1683727711yescharacteristic
1219C2#121×Dic5911yescharacteristic
1220C2#2142680111yescharacteristic
1221C2D4×C4⋊Dic5911yescharacteristic
1222C2#2142700611yescharacteristic
1223C2#2142708011yescharacteristic
1224C2#2142709211yescharacteristic
1225C2#2142746911yescharacteristic
1226C2#2142754411yescharacteristic
1227C2#2142755611yescharacteristic
1228C2#2142757111yescharacteristic
1229C2#2142770411yescharacteristic
1230C2#2142790911yescharacteristic
1231C2#2142792411yescharacteristic
1232C2#2142928011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C59×#386C2
socle, cosocleC24×C59C24
prime radicalC23×D4×C59C22
hypercenterC2×#386D59
hypocenterC59#13975
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#16837277C2semidirect
4. C2×#16837277C2semidirect
5. C2×#16837262C2semidirect
6. C22×C59⋊#95C2semidirect
7. #21422361C2semidirect
8. #21422353C2semidirect
9. #21422341C2semidirect
10. #21422341C2semidirect
11. #21422330C2semidirect
12. #21422330C2semidirect
13. #21422318C2semidirect
14. #21422318C2semidirect
57. C59×#386C4semidirect
136. C59⋊#95D4semidirect
152. C23×C4×C59C2×C4semidirect
164. C2×C22⋊C4×C59C2×C4semidirect
165. C2×C22⋊C4×C59C2×C4semidirect
166. C2×C22⋊C4×C59C2×C4semidirect
167. #95×C59C2×C4semidirect
168. #95×C59C2×C4semidirect
206. C2×D4×C59C4⋊C4semidirect
461. C2×C4×C59C4×D4semidirect
551. C22×C59#385semidirect
655. #386Dic59semidirect
676. C59#13975semidirect
721. C23×C4C2×Dic59semidirect
764. C2×C22⋊C4C2×Dic59semidirect
765. C2×C22⋊C4C2×Dic59semidirect
766. C2×C22⋊C4C2×Dic59semidirect
784. #95C2×Dic59semidirect
785. #95C2×Dic59semidirect
823. C2×D4C4⋊Dic59semidirect
1137. C2×C4D4×Dic59semidirect
1167. C22#16837277semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic592
C2×#168372822
C2×#168372772
C2×#168372622
C22×C59⋊#952
#214223612
#214223532
#214223412
#214223302
#214223182
C2×C59×#3862
#1397559