Finite Group Databasebeta

← #28518040

Subgroups — #28518040

Order 15104.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837305C211yesmaximal, characteristic, complemented
2C2×#16837295C211yesmaximal, characteristic, complemented
3C2×#16837282C211yesmaximal, characteristic, complemented
4C2×#16837282C211yesmaximal, characteristic, complemented
5#21422353C211yesmaximal, characteristic, complemented
6#21422345C211yesmaximal, characteristic, complemented
7#21422337C211yesmaximal, characteristic, complemented
8#21422337C211yesmaximal, characteristic, complemented
9#21422337C211yesmaximal, characteristic, complemented
10#21422333C211yesmaximal, characteristic, complemented
11#21422333C211yesmaximal, characteristic, complemented
12#21422333C211yesmaximal, characteristic, complemented
13#21422321C211yesmaximal, characteristic, complemented
14#21422318C211yesmaximal, characteristic, complemented
15C2×C59×#392C211yesmaximal, characteristic
16C24×Dic59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×C22⋊Dic59C2211yescharacteristic
19C22×C22⋊Dic59C2211yescharacteristic
20C22×C22⋊Dic59C2211yescharacteristic
21C22×C22⋊Dic59C2211yescharacteristic
22C22×C22⋊Dic59C2211yescharacteristic
23C22×C22⋊Dic59C2211yescharacteristic
24C22×C22⋊Dic59C2211yescharacteristic
25C22×C22⋊Dic59C2211yescharacteristic
26C22×C22⋊Dic59C2211yescharacteristic
27C22×C22⋊Dic59C2211yescharacteristic
28C22×C22⋊Dic59C2211yescharacteristic
29C22×C4×Dic59C2211yescharacteristic
30C22×C4×Dic59C2211yescharacteristic
31#16837305—24no—
32#16837295—24no—
33#16837282—24no—
34#16837282—24no—
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
48C23×D4×C59C2211yescharacteristic
49C23×D4×C59C2211yescharacteristic
50C23×D4×C59C2211yescharacteristic
51C22×C22⋊C4×C59C2211yescharacteristic
52C22×C22⋊C4×C59C2211yescharacteristic
53C22×C22⋊C4×C59C2211yescharacteristic
54C59×#392C418yescomplemented
55C2×#95×C59C2211yescharacteristic
56C23×Dic59—22no—
57C23×Dic59—22no—
58C23×Dic59—22no—
59C23×Dic59—41no—
60C23×Dic59—41no—
61C23×Dic59—41no—
62C23×Dic59—41no—
63C23×Dic59C2311yescharacteristic
64C23×Dic59C2311yescharacteristic
65C23×Dic59C2311yescharacteristic
66C23×Dic59C2311yescharacteristic
67C23×Dic59C2311yescharacteristic
68C23×Dic59C2311yescharacteristic
69C23×Dic59C2311yescharacteristic
70C23×Dic59C2311yescharacteristic
71C2×C4⋊Dic59—22no—
72C2×C4⋊Dic59—22no—
73C2×C4⋊Dic59—41no—
74C2×C22⋊Dic59—22no—
75C2×C22⋊Dic59—22no—
76C2×C22⋊Dic59—22no—
77C2×C22⋊Dic59—22no—
78C2×C22⋊Dic59—22no—
79C2×C22⋊Dic59—22no—
80C2×C22⋊Dic59—22no—
81C2×C22⋊Dic59—22no—
82C2×C22⋊Dic59—22no—
83C2×C22⋊Dic59—22no—
84C2×C22⋊Dic59—22no—
85C2×C22⋊Dic59—22no—
86C2×C22⋊Dic59—22no—
87C2×C22⋊Dic59—22no—
88C2×C22⋊Dic59—22no—
89C2×C22⋊Dic59—22no—
90C2×C22⋊Dic59—41no—
91C2×C22⋊Dic59—41no—
92C2×C22⋊Dic59—41no—
93C2×C22⋊Dic59—41no—
94C2×C22⋊Dic59—41no—
95C2×C22⋊Dic59—41no—
96C2×C22⋊Dic59—41no—
97C2×C22⋊Dic59—41no—
98C2×C22⋊Dic59—41no—
99C2×C22⋊Dic59—41no—
100C2×C22⋊Dic59—41no—
101C2×C22⋊Dic59—41no—
102C2×C22⋊Dic59—41no—
103C2×C22⋊Dic59—41no—
104C2×C22⋊Dic59—41no—
105C2×C22⋊Dic59—41no—
106C2×C22⋊Dic59D414yescomplemented
107C2×C4×Dic59—22no—
108C2×C4×Dic59—22no—
109C2×C4×Dic59—22no—
110C2×C4×Dic59—41no—
111C2×C4×Dic59—41no—
112C2×C4×Dic59—41no—
113C59⋊#95—22no—
114C59⋊#95—22no—
115C59⋊#95—22no—
116C59⋊#95—22no—
117C59⋊#95—41no—
118C59⋊#95—41no—
119C59⋊#95—41no—
120C59⋊#95—41no—
121C59⋊#95—41no—
122C59⋊#95—41no—
123C59⋊#95—41no—
124C59⋊#95—41no—
125C59⋊#95D414yescomplemented
126C25×C59C2311yescharacteristic
127C25×C59C2311yescharacteristic
128C25×C59C2311yescharacteristic
129C22×D4×C59—22no—
130C22×D4×C59—22no—
131C22×D4×C59—22no—
132C22×D4×C59—22no—
133C22×D4×C59—22no—
134C22×D4×C59—22no—
135C22×D4×C59—41no—
136C22×D4×C59—41no—
137C22×D4×C59—41no—
138C22×D4×C59—41no—
139C22×D4×C59—41no—
140C22×D4×C59—41no—
141C22×D4×C59—41no—
142C22×D4×C59—41no—
143C22×D4×C59—41no—
144C22×D4×C59—41no—
145C22×D4×C59—41no—
146C22×D4×C59—41no—
147C22×D4×C59C2×C414yes—
148C22×D4×C59C2×C414yes—
149C22×D4×C59C2×C414yescomplemented
150C23×C4×C59C2311yescharacteristic
151C23×C4×C59C2311yescharacteristic
152C23×C4×C59C2311yescharacteristic
153C23×C4×C59C2311yescharacteristic
154C2×C22⋊C4×C59—22no—
155C2×C22⋊C4×C59—22no—
156C2×C22⋊C4×C59—41no—
157C2×C22⋊C4×C59—41no—
158C2×C22⋊C4×C59—41no—
159C2×C22⋊C4×C59—41no—
160C2×C22⋊C4×C59C2×C414yes—
161C2×C22⋊C4×C59C2×C414yescomplemented
162C2×C22⋊C4×C59C2×C414yescomplemented
163#95×C59C2×C414yescomplemented
164C24×C59—21no—
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×C59—21no—
190C24×C59—21no—
191C24×C59—21no—
192C24×C59—21no—
193C24×C59—21no—
194C24×C59—21no—
195C24×C59—21no—
196C24×C59—21no—
197C24×C59—21no—
198C24×C59—21no—
199C24×C59—21no—
200C24×C59—21no—
201C24×C59—21no—
202C24×C59—21no—
203C24×C59—21no—
204C24×C59C22×C412yes—
205C24×C59C22×C412yes—
206C24×C59C22×C412yes—
207C24×C59C2×D412yes—
208C24×C59#4112yes—
209C24×C59C2411yescharacteristic
210C2×D4×C59—28no—
211C2×D4×C59—28no—
212C2×D4×C59—28no—
213C2×D4×C59—44no—
214C2×D4×C59—44no—
215C2×D4×C59—44no—
216C2×D4×C59—44no—
217C2×D4×C59—44no—
218C2×D4×C59—44no—
219C2×D4×C59—44no—
220C2×D4×C59—44no—
221C2×D4×C59—44no—
222C2×D4×C59—44no—
223C2×D4×C59—44no—
224C2×D4×C59—44no—
225C2×D4×C59—44no—
226C2×D4×C59—44no—
227C2×D4×C59—44no—
228C2×D4×C59—44no—
229C2×D4×C59—44no—
230C2×D4×C59—44no—
231C22×C4×C59—21no—
232C22×C4×C59—21no—
233C22×C4×C59—21no—
234C22×C4×C59—21no—
235C22×C4×C59—21no—
236C22×C4×C59—21no—
237C22×C4×C59—21no—
238C22×C4×C59—21no—
239C22×C4×C59—21no—
240C22×C4×C59—21no—
241C22×C4×C59—21no—
242C22×C4×C59—21no—
243C22×C4×C59—21no—
244C22×C4×C59—21no—
245C22×C4×C59—21no—
246C22×C4×C59—21no—
247C22×C4×C59—21no—
248C22×C4×C59—21no—
249C22×C4×C59—21no—
250C22×C4×C59—21no—
251C22×C4×C59—21no—
252C22×C4×C59—21no—
253C22×C4×C59C22×C412yes—
254C22×C4×C59C22×C412yes—
255C22×C4×C59C22×C412yes—
256C22×C4×C59C22×C412yes—
257C22×C4×C59C2×D412yes—
258C22×C4×C59#4112yes—
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—21no—
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—21no—
302C22×Dic59—21no—
303C22×Dic59—21no—
304C22×Dic59—21no—
305C22×Dic59—21no—
306C22×Dic59—21no—
307C22×Dic59—21no—
308C22×Dic59—21no—
309C22×Dic59—44no—
310C22×Dic59—44no—
311C22×Dic59—44no—
312C22×Dic59—44no—
313C22×Dic59—44no—
314C22×Dic59—44no—
315C22×Dic59—44no—
316C22×Dic59C2×D412yes—
317C22×Dic59C2×D412yes—
318C22×Dic59C2×D412yes—
319C22×Dic59C2×D412yes—
320C22×Dic59#4112yes—
321C22×Dic59#4112yes—
322C22⋊C4×C59—28no—
323C22⋊C4×C59—44no—
324C22⋊C4×C59—44no—
325C22⋊Dic59—44no—
326C22⋊Dic59—44no—
327C22⋊Dic59—44no—
328C22⋊Dic59—44no—
329C22⋊Dic59—44no—
330C22⋊Dic59—44no—
331C22⋊Dic59—44no—
332C22⋊Dic59—44no—
333C22⋊Dic59—44no—
334C22⋊Dic59—44no—
335C22⋊Dic59—44no—
336C4⋊Dic59—44no—
337C4×Dic59—44no—
338C4×Dic59—44no—
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—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—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×C59—41no—
395C23×C59—41no—
396C23×C59—41no—
397C23×C59—41no—
398C23×C59—41no—
399C23×C59—41no—
400C23×C59—41no—
401C23×C59—41no—
402C23×C59—41no—
403C23×C59—41no—
404C23×C59—41no—
405C23×C59—41no—
406C23×C59—41no—
407C23×C59—41no—
408C23×C59—41no—
409C23×C59—41no—
410C23×C59—41no—
411C23×C59—41no—
412C23×C59—41no—
413C23×C59—41no—
414C23×C59—41no—
415C23×C59—41no—
416C23×C59—41no—
417C23×C59—41no—
418C23×C59—41no—
419C23×C59—41no—
420C23×C59—41no—
421C23×C59—41no—
422C23×C59—41no—
423C23×C59—41no—
424C23×C59—41no—
425C23×C59—41no—
426C23×C59—41no—
427C23×C59—41no—
428C23×C59—41no—
429C23×C59—41no—
430C23×C59—41no—
431C23×C59—41no—
432C23×C59—41no—
433C23×C59—41no—
434C23×C59—41no—
435C23×C59—41no—
436C23×C59—41no—
437C23×C59—41no—
438C23×C59—41no—
439C23×C59—41no—
440C23×C59—41no—
441C23×C59—41no—
442C23×C59—41no—
443C23×C59C4×D414yes—
444C23×C59C23×C411yescharacteristic
445C23×C59C22×D411yescharacteristic
446C23×C59C22×D411yescharacteristic
447C23×C59C2×#4111yescharacteristic
448C23×C59C2×#4111yescharacteristic
449C23×C59C2×#4111yescharacteristic
450C23×C59C2×#4111yescharacteristic
451C23×C59H(5,𝔽2)11yescharacteristic
452C23×C59H(5,𝔽2)11yescharacteristic
453C23×C59H(5,𝔽2)11yescharacteristic
454C23×C59H(5,𝔽2)11yescharacteristic
455C23×C59H(5,𝔽2)11yescharacteristic
456C23×C59H(5,𝔽2)11yescharacteristic
457C23×C59H(5,𝔽2)11yescharacteristic
458C23×C59H(5,𝔽2)11yescharacteristic
459D4×C59—416no—
460D4×C59—416no—
461D4×C59—416no—
462C2×C4×C59—22no—
463C2×C4×C59—22no—
464C2×C4×C59—22no—
465C2×C4×C59—22no—
466C2×C4×C59—22no—
467C2×C4×C59—22no—
468C2×C4×C59—22no—
469C2×C4×C59—22no—
470C2×C4×C59—22no—
471C2×C4×C59—22no—
472C2×C4×C59—22no—
473C2×C4×C59—22no—
474C2×C4×C59—22no—
475C2×C4×C59—22no—
476C2×C4×C59—22no—
477C2×C4×C59—41no—
478C2×C4×C59—41no—
479C2×C4×C59—41no—
480C2×C4×C59—41no—
481C2×C4×C59—41no—
482C2×C4×C59—41no—
483C2×C4×C59—41no—
484C2×C4×C59—41no—
485C2×C4×C59—41no—
486C2×C4×C59—41no—
487C2×C4×C59—41no—
488C2×C4×C59—41no—
489C2×C4×C59C4×D414yes—
490C2×Dic59—22no—
491C2×Dic59—22no—
492C2×Dic59—22no—
493C2×Dic59—22no—
494C2×Dic59—22no—
495C2×Dic59—22no—
496C2×Dic59—22no—
497C2×Dic59—22no—
498C2×Dic59—22no—
499C2×Dic59—22no—
500C2×Dic59—22no—
501C2×Dic59—22no—
502C2×Dic59—22no—
503C2×Dic59—22no—
504C2×Dic59—22no—
505C2×Dic59—22no—
506C2×Dic59—22no—
507C2×Dic59—22no—
508C2×Dic59—416no—
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—41no—
521C2×Dic59—41no—
522C2×Dic59—41no—
523C2×Dic59—41no—
524C2×Dic59—41no—
525C2×Dic59—41no—
526C2×Dic59—41no—
527C2×Dic59—41no—
528C2×Dic59—41no—
529C2×Dic59—41no—
530C2×Dic59—41no—
531C2×Dic59—41no—
532C2×Dic59—41no—
533C2×Dic59—41no—
534C2×Dic59—41no—
535C2×Dic59—41no—
536C2×Dic59—41no—
537C2×Dic59—41no—
538C2×Dic59—41no—
539C2×Dic59—41no—
540C2×Dic59—41no—
541C2×Dic59—41no—
542C2×Dic59—41no—
543C2×Dic59—41no—
544C2×Dic59—41no—
545C2×Dic59—41no—
546C2×Dic59—41no—
547#14520—591nomaximal, Sylow
548C22×C59—24no—
549C22×C59—24no—
550C22×C59—24no—
551C22×C59—42no—
552C22×C59—42no—
553C22×C59—42no—
554C22×C59—42no—
555C22×C59—42no—
556C22×C59—42no—
557C22×C59—42no—
558C22×C59—42no—
559C22×C59—42no—
560C22×C59—42no—
561C22×C59—42no—
562C22×C59—42no—
563C22×C59—42no—
564C22×C59—42no—
565C22×C59—42no—
566C22×C59—42no—
567C22×C59—42no—
568C22×C59—42no—
569C22×C59—42no—
570C22×C59—42no—
571C22×C59—42no—
572C22×C59—42no—
573C22×C59—42no—
574C22×C59—42no—
575C22×C59—42no—
576C22×C59—42no—
577C22×C59—81no—
578C22×C59—81no—
579C22×C59—81no—
580C22×C59—81no—
581C22×C59—81no—
582C22×C59—81no—
583C22×C59—81no—
584C22×C59—81no—
585C22×C59—81no—
586C22×C59—81no—
587C22×C59—81no—
588C22×C59—81no—
589C22×C59—81no—
590C22×C59—81no—
591C22×C59—81no—
592C22×C59—81no—
593C22×C59C2×C4×D411yescharacteristic
594C22×C59C2×C4×D411yescharacteristic
595C22×C59C4×#4111yescharacteristic
596C22×C59#51811yescharacteristic
597C22×C59#51811yescharacteristic
598C22×C59#51811yescharacteristic
599C22×C59#51811yescharacteristic
600C22×C59#53411yescharacteristic
601C22×C59#53511yescharacteristic
602C22×C59#53511yescharacteristic
603C22×C59#53511yescharacteristic
604C22×C59#53811yescharacteristic
605C22×C59#53811yescharacteristic
606C22×C59#53811yescharacteristic
607C22×C59#53811yescharacteristic
608C22×C59#54011yescharacteristic
609C22×C59#54011yescharacteristic
610C22×C59#54011yescharacteristic
611C22×C59#54011yescharacteristic
612C22×C59D4211yescharacteristic
613C22×C59#54611yescharacteristic
614C22×C59#54611yescharacteristic
615C22×C59#54611yescharacteristic
616C22×C59#54611yescharacteristic
617C22×C59#54611yescharacteristic
618C22×C59#55011yescharacteristic
619C22×C59#55111yescharacteristic
620C22×C59#55311yescharacteristic
621C22×C59#55311yescharacteristic
622C22×C59#55311yescharacteristic
623C22×C59#55511yescharacteristic
624C22×C59#56011yescharacteristic
625C22×C59#56011yescharacteristic
626C22×C59#56011yescharacteristic
627C22×C59H(3,𝔽4)11yescharacteristic
628C4×C59—24no—
629C4×C59—42no—
630C4×C59—42no—
631C4×C59—42no—
632Dic59—42no—
633Dic59—42no—
634Dic59—42no—
635Dic59—42no—
636Dic59—42no—
637Dic59—42no—
638Dic59—81no—
639Dic59—81no—
640C2×#392D5911yescharacteristic
641C2×#390—591no—
642C2×#388—591no—
643C2×#386—591no—
644C2×#386—591no—
645#1442—591no—
646#1440—591no—
647#1438—591no—
648#1438—591no—
649#1438—591no—
650#1437—591no—
651#1437—591no—
652#1437—591no—
653#1434—591no—
654C22⋊#95—591no—
655C2×C59—44no—
656C2×C59—82no—
657C2×C59—82no—
658C2×C59#232111yescharacteristic
659C2×C59#232811yescharacteristic
660C2×C59#233311yescharacteristic
661C2×C59#235811yescharacteristic
662C2×C59#236311yescharacteristic
663C2×C59#236411yescharacteristic
664C2×C59#237511yescharacteristic
665C2×C59#267011yescharacteristic
666C2×C59#267311yescharacteristic
667C2×C59#269911yescharacteristic
668C2×C59#270311yescharacteristic
669C2×C59#270311yescharacteristic
670C2×C59#271411yescharacteristic
671C2×C59#275311yescharacteristic
672C2×C59#275611yescharacteristic
673C23×D4C2×D5911yescharacteristic
674C23×D4C2×D5911yescharacteristic
675C23×D4C2×D5911yescharacteristic
676C24×C4—591no—
677C22×C4⋊C4—591no—
678C22×C22⋊C4—591no—
679C22×C22⋊C4—591no—
680C22×C22⋊C4—591no—
681C22×C22⋊C4—591no—
682C22×C22⋊C4—591no—
683C22×C22⋊C4—591no—
684C22×C22⋊C4—591no—
685C22×C22⋊C4—591no—
686C22×C22⋊C4—591no—
687C22×C22⋊C4—591no—
688C22×C22⋊C4—591no—
689C22×C22⋊C4C2×D5911yescharacteristic
690C22×C22⋊C4C2×D5911yescharacteristic
691C22×C22⋊C4C2×D5911yescharacteristic
692C22×C42—591no—
693C22×C42—591no—
694#392Dic5918yescomplemented
695#390—1184no—
696#388—1184no—
697#386—1184no—
698#386—1184no—
699C2×#95—591no—
700C2×#95—591no—
701C2×#95—591no—
702C2×#95—591no—
703C2×#95—591no—
704C2×#95—591no—
705C2×#95—591no—
706C2×#95—591no—
707C2×#95—591no—
708C2×#95—591no—
709C2×#95—591no—
710C2×#95—591no—
711C2×#95—591no—
712C2×#95C2×D5911yescharacteristic
713C59#1452011yescharacteristic, complemented, Sylow
714C25C22×D5911yescharacteristic
715C25C22×D5911yescharacteristic
716C25C22×D5911yescharacteristic
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4C2×Dic5914yes—
736C22×D4C2×Dic5914yes—
737C22×D4C2×Dic5914yescomplemented
738C23×C4—591no—
739C23×C4—591no—
740C23×C4—591no—
741C23×C4—591no—
742C23×C4—591no—
743C23×C4—591no—
744C23×C4—591no—
745C23×C4—591no—
746C23×C4—1182no—
747C23×C4—1182no—
748C23×C4—1182no—
749C23×C4—2361no—
750C23×C4—2361no—
751C23×C4—2361no—
752C23×C4—2361no—
753C23×C4C22×D5911yescharacteristic
754C23×C4C22×D5911yescharacteristic
755C23×C4C22×D5911yescharacteristic
756C23×C4C22×D5911yescharacteristic
757C2×C4⋊C4—1182no—
758C2×C4⋊C4—1182no—
759C2×C4⋊C4—2361no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—41no—
763C2×C22⋊C4—41no—
764C2×C22⋊C4—41no—
765C2×C22⋊C4—41no—
766C2×C22⋊C4—594no—
767C2×C22⋊C4—1182no—
768C2×C22⋊C4—1182no—
769C2×C22⋊C4—1182no—
770C2×C22⋊C4—1182no—
771C2×C22⋊C4—1182no—
772C2×C22⋊C4—1182no—
773C2×C22⋊C4—1182no—
774C2×C22⋊C4—1182no—
775C2×C22⋊C4—1182no—
776C2×C22⋊C4—1182no—
777C2×C22⋊C4—1182no—
778C2×C22⋊C4—1182no—
779C2×C22⋊C4—1182no—
780C2×C22⋊C4—1182no—
781C2×C22⋊C4—1182no—
782C2×C22⋊C4—1182no—
783C2×C22⋊C4—2361no—
784C2×C22⋊C4—2361no—
785C2×C22⋊C4—2361no—
786C2×C22⋊C4—2361no—
787C2×C22⋊C4—2361no—
788C2×C22⋊C4—2361no—
789C2×C22⋊C4—2361no—
790C2×C22⋊C4—2361no—
791C2×C22⋊C4—2361no—
792C2×C22⋊C4—2361no—
793C2×C22⋊C4—2361no—
794C2×C22⋊C4—2361no—
795C2×C22⋊C4—2361no—
796C2×C22⋊C4—2361no—
797C2×C22⋊C4—2361no—
798C2×C22⋊C4—2361no—
799C2×C22⋊C4C2×Dic5914yes—
800C2×C22⋊C4C2×Dic5914yescomplemented
801C2×C22⋊C4C2×Dic5914yescomplemented
802C2×C42—1182no—
803C2×C42—1182no—
804C2×C42—1182no—
805C2×C42—2361no—
806C2×C42—2361no—
807C2×C42—2361no—
808#95—594no—
809#95—1182no—
810#95—1182no—
811#95—1182no—
812#95—1182no—
813#95—2361no—
814#95—2361no—
815#95—2361no—
816#95—2361no—
817#95—2361no—
818#95—2361no—
819#95—2361no—
820#95—2361no—
821#95C2×Dic5914yescomplemented
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24D4×D5912yes—
863C24#1174568712yes—
864C24C22×Dic5912yes—
865C24C22×Dic5912yes—
866C24C22×Dic5912yes—
867C24C23×D5911yescharacteristic
868C2×D4—28no—
869C2×D4—28no—
870C2×D4—28no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—592no—
912C22×C4—592no—
913C22×C4—592no—
914C22×C4—592no—
915C22×C4—592no—
916C22×C4—592no—
917C22×C4—1181no—
918C22×C4—1181no—
919C22×C4—1181no—
920C22×C4—1181no—
921C22×C4—1181no—
922C22×C4—1181no—
923C22×C4—1181no—
924C22×C4—1181no—
925C22×C4—1181no—
926C22×C4—1181no—
927C22×C4—1181no—
928C22×C4—1181no—
929C22×C4—1181no—
930C22×C4—1181no—
931C22×C4—1181no—
932C22×C4—1181no—
933C22×C4—1181no—
934C22×C4—1181no—
935C22×C4—1181no—
936C22×C4—1181no—
937C22×C4—1181no—
938C22×C4—1181no—
939C22×C4—1181no—
940C22×C4—1181no—
941C22×C4—1181no—
942C22×C4—1181no—
943C22×C4—1181no—
944C22×C4—1181no—
945C22×C4—1181no—
946C22×C4—1181no—
947C22×C4—1181no—
948C22×C4—1181no—
949C22×C4—1181no—
950C22×C4—1181no—
951C22×C4—1181no—
952C22×C4—1181no—
953C22×C4—1181no—
954C22×C4—1181no—
955C22×C4—1181no—
956C22×C4—1181no—
957C22×C4—1181no—
958C22×C4—1181no—
959C22×C4—1181no—
960C22×C4—1181no—
961C22×C4—1181no—
962C22×C4—1181no—
963C22×C4—1181no—
964C22×C4—1181no—
965C22×C4—1181no—
966C22×C4—1181no—
967C22×C4—2364no—
968C22×C4—2364no—
969C22×C4—2364no—
970C22×C4—2364no—
971C22×C4—2364no—
972C22×C4—2364no—
973C22×C4—2364no—
974C22×C4D4×D5912yes—
975C22×C4#1174568712yes—
976C22×C4C22×Dic5912yes—
977C22×C4C22×Dic5912yes—
978C22×C4C22×Dic5912yes—
979C22×C4C22×Dic5912yes—
980C4⋊C4—2364no—
981C22⋊C4—28no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—2364no—
985C22⋊C4—2364no—
986C22⋊C4—2364no—
987C22⋊C4—2364no—
988C22⋊C4—2364no—
989C22⋊C4—2364no—
990C22⋊C4—2364no—
991C22⋊C4—2364no—
992C22⋊C4—2364no—
993C22⋊C4—2364no—
994C22⋊C4—2364no—
995C42—2364no—
996C42—2364no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23D4×Dic5914yes—
1102C23C23×Dic5911yescharacteristic
1103C23C2×D4×D5911yescharacteristic
1104C23C2×D4×D5911yescharacteristic
1105C23#41×D5911yescharacteristic
1106C23#41×D5911yescharacteristic
1107C23C2×#1174568711yescharacteristic
1108C23C2×#1174568711yescharacteristic
1109C23#1427377211yescharacteristic
1110C23#1427377211yescharacteristic
1111C23#1427377211yescharacteristic
1112C23#1427377211yescharacteristic
1113C23#1427377211yescharacteristic
1114C23#1427377211yescharacteristic
1115C23#1427377211yescharacteristic
1116C23#1427377211yescharacteristic
1117D4—416no—
1118D4—416no—
1119D4—416no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—1182no—
1148C2×C4—1182no—
1149C2×C4—1182no—
1150C2×C4—1182no—
1151C2×C4—1182no—
1152C2×C4—1182no—
1153C2×C4—1182no—
1154C2×C4—1182no—
1155C2×C4—1182no—
1156C2×C4—1182no—
1157C2×C4—1182no—
1158C2×C4—1182no—
1159C2×C4—1182no—
1160C2×C4—1182no—
1161C2×C4—1182no—
1162C2×C4—1182no—
1163C2×C4—1182no—
1164C2×C4—1182no—
1165C2×C4—2361no—
1166C2×C4—2361no—
1167C2×C4—2361no—
1168C2×C4—2361no—
1169C2×C4—2361no—
1170C2×C4—2361no—
1171C2×C4—2361no—
1172C2×C4—2361no—
1173C2×C4—2361no—
1174C2×C4—2361no—
1175C2×C4—2361no—
1176C2×C4—2361no—
1177C2×C4—2361no—
1178C2×C4—2361no—
1179C2×C4—23616no—
1180C2×C4—2361no—
1181C2×C4—2361no—
1182C2×C4—2361no—
1183C2×C4—2361no—
1184C2×C4—2361no—
1185C2×C4—2361no—
1186C2×C4—2361no—
1187C2×C4—2361no—
1188C2×C4—2361no—
1189C2×C4—2361no—
1190C2×C4—2361no—
1191C2×C4—2361no—
1192C2×C4—2361no—
1193C2×C4—2361no—
1194C2×C4—2361no—
1195C2×C4—2361no—
1196C2×C4—2361no—
1197C2×C4—2361no—
1198C2×C4—2361no—
1199C2×C4—2361no—
1200C2×C4—2361no—
1201C2×C4—2361no—
1202C2×C4—2361no—
1203C2×C4—2361no—
1204C2×C4D4×Dic5914yes—
1205C22—24no—
1206C22—24no—
1207C22—24no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22C2×D4×Dic5911yescharacteristic
1251C22C2×D4×Dic5911yescharacteristic
1252C22#41×Dic5911yescharacteristic
1253C22#1683787711yescharacteristic
1254C22#1683787711yescharacteristic
1255C22#1683787711yescharacteristic
1256C22#1683787711yescharacteristic
1257C22#1683796211yescharacteristic
1258C22#1683796511yescharacteristic
1259C22#1683796511yescharacteristic
1260C22#1683796711yescharacteristic
1261C22#1683798411yescharacteristic
1262C22#1683798411yescharacteristic
1263C22#1683798711yescharacteristic
1264C22#1683798711yescharacteristic
1265C22#1683800211yescharacteristic
1266C22#1683800211yescharacteristic
1267C22#1683800611yescharacteristic
1268C22#1683800611yescharacteristic
1269C22#1683803411yescharacteristic
1270C22#1683803911yescharacteristic
1271C22#1683803911yescharacteristic
1272C22#1683804111yescharacteristic
1273C22#1683804111yescharacteristic
1274C22#1683804911yescharacteristic
1275C22#1683807011yescharacteristic
1276C22#1683808311yescharacteristic
1277C22#1683809511yescharacteristic
1278C22#1683809511yescharacteristic
1279C22#1683809911yescharacteristic
1280C22#1683811611yescharacteristic
1281C22#1683814111yescharacteristic
1282C22#1683814111yescharacteristic
1283C22#1683814111yescharacteristic
1284C22#1683814511yescharacteristic
1285C4—24no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—4721no—
1290C4—4721no—
1291C4—2362no—
1292C4—2362no—
1293C4—2362no—
1294C4—2362no—
1295C4—2362no—
1296C4—2362no—
1297C2—44no—
1298C2—82no—
1299C2—82no—
1300C2#2142675711yescharacteristic
1301C2#2142682211yescharacteristic
1302C2#2142686311yescharacteristic
1303C2#2142708011yescharacteristic
1304C2#2142713811yescharacteristic
1305C2#2142714811yescharacteristic
1306C2#2142723711yescharacteristic
1307C2#2143032111yescharacteristic
1308C2#2143036411yescharacteristic
1309C2#2143068611yescharacteristic
1310C2#2143073211yescharacteristic
1311C2#2143074611yescharacteristic
1312C2#2143088511yescharacteristic
1313C2#2143137511yescharacteristic
1314C2#2143142011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
Fitting, prime radicalC2×C59×#392C2
socle, cosocleC24×C59C24
hypercenterC2×#392D59
hypocenterC59#14520
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C2×#16837305C2semidirect
2. C2×#16837295C2semidirect
3. C2×#16837282C2semidirect
4. C2×#16837282C2semidirect
5. #21422353C2semidirect
6. #21422345C2semidirect
7. #21422337C2semidirect
8. #21422337C2semidirect
9. #21422337C2semidirect
10. #21422333C2semidirect
11. #21422333C2semidirect
12. #21422333C2semidirect
13. #21422321C2semidirect
14. #21422318C2semidirect
54. C59×#392C4semidirect
106. C2×C22⋊Dic59D4semidirect
125. C59⋊#95D4semidirect
149. C22×D4×C59C2×C4semidirect
161. C2×C22⋊C4×C59C2×C4semidirect
162. C2×C22⋊C4×C59C2×C4semidirect
163. #95×C59C2×C4semidirect
694. #392Dic59semidirect
713. C59#14520semidirect
737. C22×D4C2×Dic59semidirect
800. C2×C22⋊C4C2×Dic59semidirect
801. C2×C22⋊C4C2×Dic59semidirect
821. #95C2×Dic59semidirect

Maximal subgroups

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

subgroupindex
C2×#168373052
C2×#168372952
C2×#168372822
#214223532
#214223452
#214223372
#214223332
#214223212
#214223182
C2×C59×#3922
#1452059