Finite Group Databasebeta

← #28513122

Subgroups — #28513122

Order 15104.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273708C211yesmaximal, characteristic
2C2×#16837283C211yesmaximal, characteristic, complemented
3C2×C4×Dic59⋊C4C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic59C211yesmaximal, characteristic, complemented
5#21422346C211yesmaximal, characteristic, complemented
6#21422339C211yesmaximal, characteristic, complemented
7#21422339C211yesmaximal, characteristic, complemented
8#21422337C211yesmaximal, characteristic
9#21422333C211yesmaximal, characteristic, complemented
10#21422333C211yesmaximal, characteristic, complemented
11#21422333C211yesmaximal, characteristic, complemented
12#21422333C211yesmaximal, characteristic, complemented
13#21422329C211yesmaximal, characteristic, complemented
14#21422318C211yesmaximal, characteristic, complemented
15C2×C59×#390C211yesmaximal, characteristic
16C24×Dic59C2211yescharacteristic
17C2×#14273708—24no—
18C2×#14273708—24no—
19C2×#14273708C418yescomplemented
20C22×Dic59⋊C4C2211yescharacteristic
21C22×Dic59⋊C4C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×C22⋊Dic59C2211yescharacteristic
24C22×C22⋊Dic59C2211yescharacteristic
25C22×C22⋊Dic59C2211yescharacteristic
26C22×C22⋊Dic59C2211yescharacteristic
27C22×C22⋊Dic59C2211yescharacteristic
28C22×C22⋊Dic59C2211yescharacteristic
29C22×C22⋊Dic59C2211yescharacteristic
30C22×C4×Dic59C2211yescharacteristic
31C22×C4×Dic59C2211yescharacteristic
32C22×C4×Dic59C2211yescharacteristic
33#16837283—24no—
34C4×Dic59⋊C4—24no—
35C22⋊C4×Dic59—24no—
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
48C2×C59⋊#95C2211yescharacteristic
49C2×C59⋊#95C2211yescharacteristic
50C23×D4×C59C2211yescharacteristic
51C22×C4⋊C4×C59C2211yescharacteristic
52C22×C22⋊C4×C59C2211yescharacteristic
53C22×C22⋊C4×C59C2211yescharacteristic
54C22×C22⋊C4×C59C2211yescharacteristic
55C22×C22⋊C4×C59C2211yescharacteristic
56C22×C42×C59C2211yescharacteristic
57C59×#390—24no—
58C23×Dic59—22no—
59C23×Dic59—22no—
60C23×Dic59—22no—
61C23×Dic59—22no—
62C23×Dic59—41no—
63C23×Dic59—41no—
64C23×Dic59C2×C414yes—
65C23×Dic59C2311yescharacteristic
66C23×Dic59C2311yescharacteristic
67C23×Dic59C2311yescharacteristic
68C23×Dic59C2311yescharacteristic
69C23×Dic59C2311yescharacteristic
70C23×Dic59C2311yescharacteristic
71C23×Dic59C2311yescharacteristic
72C23×Dic59C2311yescharacteristic
73#14273708—232no—
74C2×Dic59⋊C4—22no—
75C2×Dic59⋊C4—22no—
76C2×Dic59⋊C4—22no—
77C2×Dic59⋊C4—22no—
78C2×Dic59⋊C4—22no—
79C2×Dic59⋊C4C2×C414yes—
80C2×Dic59⋊C4C2×C414yes—
81C2×Dic59⋊C4D414yes—
82C2×Dic59⋊C4D414yes—
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—22no—
91C2×C22⋊Dic59—22no—
92C2×C22⋊Dic59—22no—
93C2×C22⋊Dic59—22no—
94C2×C22⋊Dic59—22no—
95C2×C22⋊Dic59—22no—
96C2×C22⋊Dic59—22no—
97C2×C22⋊Dic59—41no—
98C2×C22⋊Dic59—41no—
99C2×C22⋊Dic59—41no—
100C2×C22⋊Dic59—41no—
101C2×C22⋊Dic59C2×C414yes—
102C2×C22⋊Dic59C2×C414yes—
103C2×C22⋊Dic59C2×C414yes—
104C2×C4×Dic59—22no—
105C2×C4×Dic59—22no—
106C2×C4×Dic59—22no—
107C2×C4×Dic59—22no—
108C2×C4×Dic59—22no—
109C2×C4×Dic59—22no—
110C2×C4×Dic59—22no—
111C2×C4×Dic59—41no—
112C2×C4×Dic59—41no—
113C59⋊#95—22no—
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—22no—
123C59⋊#95—41no—
124C59⋊#95—41no—
125C59⋊#95—41no—
126C59⋊#95—41no—
127C25×C59C2311yescharacteristic
128C25×C59C2311yescharacteristic
129C22×D4×C59—22no—
130C22×D4×C59—22no—
131C22×D4×C59—22no—
132C22×D4×C59—22no—
133C22×D4×C59—41no—
134C22×D4×C59—41no—
135C22×D4×C59C2×C414yes—
136C23×C4×C59C2311yescharacteristic
137C23×C4×C59C2311yescharacteristic
138C23×C4×C59C2311yescharacteristic
139C23×C4×C59C2311yescharacteristic
140C23×C4×C59C2311yescharacteristic
141C2×C4⋊C4×C59—22no—
142C2×C4⋊C4×C59—22no—
143C2×C4⋊C4×C59—41no—
144C2×C22⋊C4×C59—22no—
145C2×C22⋊C4×C59—22no—
146C2×C22⋊C4×C59—22no—
147C2×C22⋊C4×C59—22no—
148C2×C22⋊C4×C59—22no—
149C2×C22⋊C4×C59—22no—
150C2×C22⋊C4×C59—22no—
151C2×C22⋊C4×C59—22no—
152C2×C22⋊C4×C59—22no—
153C2×C22⋊C4×C59—41no—
154C2×C22⋊C4×C59—41no—
155C2×C22⋊C4×C59D414yes—
156C2×C42×C59—22no—
157C2×C42×C59—22no—
158C2×C42×C59—41no—
159C24×C59—21no—
160C24×C59—21no—
161C24×C59—21no—
162C24×C59—21no—
163C24×C59—21no—
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×C59C22×C412yes—
186C24×C59C22×C412yes—
187C24×C59C2×D412yes—
188C24×C59#4112yes—
189C24×C59C2411yescharacteristic
190C2×D4×C59—28no—
191C2×D4×C59—28no—
192C2×D4×C59—44no—
193C2×D4×C59—44no—
194C2×D4×C59—44no—
195C2×D4×C59—44no—
196C2×D4×C59—44no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—21no—
213C22×C4×C59—21no—
214C22×C4×C59—21no—
215C22×C4×C59—21no—
216C22×C4×C59—21no—
217C22×C4×C59—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×C59C22×C412yes—
225C22×C4×C59C2×D412yes—
226C22×C4×C59C2×D412yes—
227C22×C4×C59C2×D412yes—
228C22×C4×C59C2×D412yes—
229C22×C4×C59#4112yes—
230C22×C4×C59#4112yes—
231C22×C4×C59#4112yes—
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—28no—
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—28no—
272C22×Dic59—21no—
273C22×Dic59—21no—
274C22×Dic59—21no—
275C22×Dic59—21no—
276C22×Dic59—21no—
277C22×Dic59—21no—
278C22×Dic59—21no—
279C22×Dic59—44no—
280C22×Dic59—44no—
281C22×Dic59—44no—
282C22×Dic59—44no—
283C22×Dic59—44no—
284C22×Dic59C22×C412yes—
285C22×Dic59C22×C412yes—
286C22×Dic59C22×C412yes—
287C22×Dic59C22×C412yes—
288C22×Dic59C2×D412yes—
289C22×Dic59C2×D412yes—
290C22×Dic59C2×D412yes—
291C22×Dic59C2×D412yes—
292C22×Dic59#4112yes—
293C22×Dic59#4112yes—
294C22×Dic59#4112yes—
295C4⋊C4×C59—44no—
296C22⋊C4×C59—28no—
297C22⋊C4×C59—44no—
298C22⋊C4×C59—44no—
299C22⋊C4×C59—44no—
300C42×C59—44no—
301C22⋊Dic59—28no—
302C22⋊Dic59—28no—
303C22⋊Dic59—28no—
304C22⋊Dic59—28no—
305C22⋊Dic59—44no—
306C22⋊Dic59—44no—
307C22⋊Dic59—44no—
308Dic59⋊C4—28no—
309Dic59⋊C4—28no—
310Dic59⋊C4C22⋊C4116yescomplemented
311C4×Dic59—28no—
312C4×Dic59—44no—
313C4×Dic59—44no—
314C23×C59—22no—
315C23×C59—22no—
316C23×C59—22no—
317C23×C59—22no—
318C23×C59—22no—
319C23×C59—22no—
320C23×C59—22no—
321C23×C59—22no—
322C23×C59—22no—
323C23×C59—22no—
324C23×C59—22no—
325C23×C59—22no—
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—41no—
340C23×C59—41no—
341C23×C59—41no—
342C23×C59—41no—
343C23×C59—41no—
344C23×C59—41no—
345C23×C59—41no—
346C23×C59—41no—
347C23×C59—41no—
348C23×C59—41no—
349C23×C59—41no—
350C23×C59—41no—
351C23×C59—41no—
352C23×C59—41no—
353C23×C59—41no—
354C23×C59—41no—
355C23×C59—41no—
356C23×C59—41no—
357C23×C59—41no—
358C23×C59—41no—
359C23×C59—41no—
360C23×C59—41no—
361C23×C59—41no—
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×C59C4×D414yes—
384C23×C59C23×C411yescharacteristic
385C23×C59C22×D411yescharacteristic
386C23×C59C22×D411yescharacteristic
387C23×C59C22×D411yescharacteristic
388C23×C59C2×#4111yescharacteristic
389C23×C59C2×#4111yescharacteristic
390C23×C59C2×#4111yescharacteristic
391C23×C59C2×#4111yescharacteristic
392C23×C59C2×#4111yescharacteristic
393C23×C59C2×#4111yescharacteristic
394C23×C59C2×#4111yescharacteristic
395C23×C59H(5,𝔽2)11yescharacteristic
396C23×C59H(5,𝔽2)11yescharacteristic
397C23×C59H(5,𝔽2)11yescharacteristic
398C23×C592−1+411yescharacteristic
399D4×C59—416no—
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—22no—
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—41no—
419C2×C4×C59—41no—
420C2×C4×C59—41no—
421C2×C4×C59—41no—
422C2×C4×C59—41no—
423C2×C4×C59—41no—
424C2×C4×C59—41no—
425C2×C4×C59—41no—
426C2×C4×C59—41no—
427C2×C4×C59—41no—
428C2×C4×C59—41no—
429C2×C4×C59—41no—
430C2×C4×C59—41no—
431C2×C4×C59—41no—
432C2×C4×C59—41no—
433C2×C4×C59C2×C22⋊C414yes—
434C2×C4×C59#12314yescomplemented
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—22no—
455C2×Dic59—22no—
456C2×Dic59—22no—
457C2×Dic59—22no—
458C2×Dic59—22no—
459C2×Dic59—22no—
460C2×Dic59—22no—
461C2×Dic59—22no—
462C2×Dic59—416no—
463C2×Dic59—41no—
464C2×Dic59—41no—
465C2×Dic59—41no—
466C2×Dic59—41no—
467C2×Dic59—41no—
468C2×Dic59—41no—
469C2×Dic59—41no—
470C2×Dic59—41no—
471C2×Dic59—41no—
472C2×Dic59—41no—
473C2×Dic59—41no—
474C2×Dic59—41no—
475C2×Dic59—41no—
476C2×Dic59—41no—
477C2×Dic59—41no—
478C2×Dic59—41no—
479C2×Dic59—41no—
480C2×Dic59—41no—
481C2×Dic59—41no—
482C2×Dic59—41no—
483C2×Dic59—41no—
484C2×Dic59—41no—
485C2×Dic59—41no—
486C2×Dic59—41no—
487C2×Dic59—41no—
488C2×Dic59—41no—
489C2×Dic59—41no—
490C2×Dic59C2×C22⋊C414yes—
491C2×Dic59C2×C22⋊C414yes—
492#14095—591nomaximal, Sylow
493C22×C59—24no—
494C22×C59—24no—
495C22×C59—24no—
496C22×C59—42no—
497C22×C59—42no—
498C22×C59—42no—
499C22×C59—42no—
500C22×C59—42no—
501C22×C59—42no—
502C22×C59—42no—
503C22×C59—42no—
504C22×C59—42no—
505C22×C59—42no—
506C22×C59—42no—
507C22×C59—42no—
508C22×C59—42no—
509C22×C59—42no—
510C22×C59—42no—
511C22×C59—42no—
512C22×C59—42no—
513C22×C59—42no—
514C22×C59—42no—
515C22×C59—81no—
516C22×C59—81no—
517C22×C59—81no—
518C22×C59—81no—
519C22×C59—81no—
520C22×C59—81no—
521C22×C59—81no—
522C22×C59—81no—
523C22×C59C22×C22⋊C411yescharacteristic
524C22×C59C2×C4×D411yescharacteristic
525C22×C59C4×#4111yescharacteristic
526C22×C59C4×#4111yescharacteristic
527C22×C59C4×#4111yescharacteristic
528C22×C59#51811yescharacteristic
529C22×C59#52011yescharacteristic
530C22×C59C2×#12311yescharacteristic
531C22×C59#52511yescharacteristic
532C22×C59#52511yescharacteristic
533C22×C59#52511yescharacteristic
534C22×C59#52911yescharacteristic
535C22×C59#52911yescharacteristic
536C22×C59#53211yescharacteristic
537C22×C59#53211yescharacteristic
538C22×C59#53811yescharacteristic
539C22×C59#53911yescharacteristic
540C22×C59#54011yescharacteristic
541C22×C59#54211yescharacteristic
542C22×C59D4211yescharacteristic
543C22×C59D4211yescharacteristic
544C22×C59#54611yescharacteristic
545C22×C59#54611yescharacteristic
546C22×C59#54611yescharacteristic
547C22×C59#54711yescharacteristic
548C22×C59#54811yescharacteristic
549C22×C59#54811yescharacteristic
550C22×C59#55011yescharacteristic
551C22×C59#55011yescharacteristic
552C22×C59#55111yescharacteristic
553C22×C59#55111yescharacteristic
554C22×C59#55211yescharacteristic
555C22×C59#55311yescharacteristic
556C22×C59#55311yescharacteristic
557C22×C59#55911yescharacteristic
558C4×C59—24no—
559C4×C59—24no—
560C4×C59—42no—
561C4×C59—42no—
562C4×C59—81no—
563Dic59—24no—
564Dic59—24no—
565Dic59—42no—
566Dic59—42no—
567Dic59—42no—
568Dic59—42no—
569Dic59—42no—
570Dic59—81no—
571C22×#123—591no—
572C2×#390D5911yescharacteristic
573C2×#387—591no—
574C2×C4×C4⋊C4—591no—
575C2×C4×C22⋊C4—591no—
576#1441—591no—
577#1439—591no—
578#1439—591no—
579#1438—591no—
580#1437—591no—
581#1437—591no—
582#1437—591no—
583#1437—591no—
584#1436—591no—
585C22⋊#95—591no—
586C2×C59—44no—
587C2×C59—82no—
588C2×C59#229711yescharacteristic
589C2×C59C4×#12311yescharacteristic
590C2×C59#233511yescharacteristic
591C2×C59D4×C22⋊C411yescharacteristic
592C2×C59#234111yescharacteristic
593C2×C59#235911yescharacteristic
594C2×C59#237411yescharacteristic
595C2×C59#244311yescharacteristic
596C2×C59#244511yescharacteristic
597C2×C59#245611yescharacteristic
598C2×C59#245811yescharacteristic
599C2×C59#246111yescharacteristic
600C2×C59#247111yescharacteristic
601C2×C59#255411yescharacteristic
602C2×C59#255811yescharacteristic
603C23×D4C2×D5911yescharacteristic
604C24×C4—591no—
605C2×#123—598no—
606C2×#123—1184no—
607C2×#123—1184no—
608C22×C4⋊C4—591no—
609C22×C4⋊C4—591no—
610C22×C4⋊C4—591no—
611C22×C4⋊C4C2×D5911yescharacteristic
612C22×C22⋊C4—591no—
613C22×C22⋊C4—591no—
614C22×C22⋊C4—591no—
615C22×C22⋊C4—591no—
616C22×C22⋊C4—591no—
617C22×C22⋊C4—591no—
618C22×C22⋊C4—591no—
619C22×C22⋊C4C2×D5911yescharacteristic
620C22×C22⋊C4C2×D5911yescharacteristic
621C22×C22⋊C4C2×D5911yescharacteristic
622C22×C22⋊C4C2×D5911yescharacteristic
623C22×C42—591no—
624C22×C42—591no—
625C22×C42—591no—
626C22×C42C2×D5911yescharacteristic
627#390—24no—
628#387—1184no—
629C4×C4⋊C4—1184no—
630C4×C22⋊C4—1184no—
631C2×#95—591no—
632C2×#95—591no—
633C2×#95—591no—
634C2×#95—591no—
635C2×#95—591no—
636C2×#95—591no—
637C2×#95—591no—
638C2×#95—591no—
639C2×#95—591no—
640C2×#95—591no—
641C2×#95—591no—
642C2×#95—591no—
643C2×#95—591no—
644C2×#95—591no—
645C59#1409511yescharacteristic, complemented, Sylow
646C25C22×D5911yescharacteristic
647C25C22×D5911yescharacteristic
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—22no—
651C22×D4—22no—
652C22×D4—41no—
653C22×D4—41no—
654C22×D4C4×D5914yes—
655C23×C4—591no—
656C23×C4—591no—
657C23×C4—591no—
658C23×C4—591no—
659C23×C4—591no—
660C23×C4—591no—
661C23×C4—591no—
662C23×C4—594no—
663C23×C4—591no—
664C23×C4—1182no—
665C23×C4—1182no—
666C23×C4—1182no—
667C23×C4—1182no—
668C23×C4—2361no—
669C23×C4—2361no—
670C23×C4C22×D5911yescharacteristic
671C23×C4C22×D5911yescharacteristic
672C23×C4C22×D5911yescharacteristic
673C23×C4C22×D5911yescharacteristic
674C23×C4C22×D5911yescharacteristic
675#123—11832no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—41no—
679C2×C4⋊C4—594no—
680C2×C4⋊C4—594no—
681C2×C4⋊C4—594no—
682C2×C4⋊C4—594no—
683C2×C4⋊C4—1182no—
684C2×C4⋊C4—1182no—
685C2×C4⋊C4—1182no—
686C2×C4⋊C4—1182no—
687C2×C4⋊C4—1182no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—594no—
700C2×C22⋊C4—594no—
701C2×C22⋊C4—594no—
702C2×C22⋊C4—1182no—
703C2×C22⋊C4—1182no—
704C2×C22⋊C4—1182no—
705C2×C22⋊C4—1182no—
706C2×C22⋊C4—1182no—
707C2×C22⋊C4—1182no—
708C2×C22⋊C4—1182no—
709C2×C22⋊C4—1182no—
710C2×C22⋊C4—1182no—
711C2×C22⋊C4—1182no—
712C2×C22⋊C4—1182no—
713C2×C22⋊C4—1182no—
714C2×C22⋊C4—1182no—
715C2×C22⋊C4—1182no—
716C2×C22⋊C4—2361no—
717C2×C22⋊C4—2361no—
718C2×C22⋊C4—2361no—
719C2×C22⋊C4—2361no—
720C2×C22⋊C4C22⋊D5914yes—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—41no—
724C2×C42—1182no—
725C2×C42—1182no—
726C2×C42—1182no—
727C2×C42—1182no—
728C2×C42—1182no—
729C2×C42—1182no—
730C2×C42—1182no—
731C2×C42—2361no—
732C2×C42—2361no—
733#95—1182no—
734#95—1182no—
735#95—1182no—
736#95—1182no—
737#95—1182no—
738#95—1182no—
739#95—1182no—
740#95—1182no—
741#95—1182no—
742#95—1182no—
743#95—2361no—
744#95—2361no—
745#95—2361no—
746#95—2361no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24C2×C4×D5912yes—
774C24C2×C4×D5912yes—
775C24#1174568512yes—
776C24C2×C22⋊D5912yes—
777C24C23×D5911yescharacteristic
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—592no—
813C22×C4—592no—
814C22×C4—592no—
815C22×C4—592no—
816C22×C4—592no—
817C22×C4—592no—
818C22×C4—592no—
819C22×C4—592no—
820C22×C4—592no—
821C22×C4—592no—
822C22×C4—592no—
823C22×C4—1188no—
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—1188no—
833C22×C4—1181no—
834C22×C4—1181no—
835C22×C4—1181no—
836C22×C4—1181no—
837C22×C4—1181no—
838C22×C4—1181no—
839C22×C4—1181no—
840C22×C4—1181no—
841C22×C4—1181no—
842C22×C4—1181no—
843C22×C4—1181no—
844C22×C4—1181no—
845C22×C4—1181no—
846C22×C4—1181no—
847C22×C4—1181no—
848C22×C4—1181no—
849C22×C4—1181no—
850C22×C4—1181no—
851C22×C4—1181no—
852C22×C4—1181no—
853C22×C4—1181no—
854C22×C4—1181no—
855C22×C4—1181no—
856C22×C4—1181no—
857C22×C4—1181no—
858C22×C4—1181no—
859C22×C4—1181no—
860C22×C4—1181no—
861C22×C4—1181no—
862C22×C4—1181no—
863C22×C4—1181no—
864C22×C4—1181no—
865C22×C4—1181no—
866C22×C4—1181no—
867C22×C4—1181no—
868C22×C4—1181no—
869C22×C4—1181no—
870C22×C4—2364no—
871C22×C4—2364no—
872C22×C4—2364no—
873C22×C4—2364no—
874C22×C4—2364no—
875C22×C4C2×C4×D5912yes—
876C22×C4D4×D5912yes—
877C22×C4D4×D5912yes—
878C22×C4#1174568712yes—
879C22×C4#1174568712yes—
880C22×C4#1174568712yes—
881C22×C4C2×C22⋊D5912yes—
882C22×C4C2×C22⋊D5912yes—
883C4⋊C4—44no—
884C4⋊C4—5916no—
885C4⋊C4—1188no—
886C4⋊C4—1188no—
887C22⋊C4—28no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—1188no—
892C22⋊C4—1188no—
893C22⋊C4—1188no—
894C22⋊C4—1188no—
895C22⋊C4—2364no—
896C22⋊C4—2364no—
897C22⋊C4—2364no—
898C42—44no—
899C42—1188no—
900C42—2364no—
901C42—2364no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23C4×C22⋊D5914yes—
972C23C22×C4×D5911yescharacteristic
973C23C2×D4×D5911yescharacteristic
974C23C2×D4×D5911yescharacteristic
975C23C22×C22⋊D5911yescharacteristic
976C23#41×D5911yescharacteristic
977C23#41×D5911yescharacteristic
978C23#41×D5911yescharacteristic
979C23C2×#1174568711yescharacteristic
980C23C2×#1174568711yescharacteristic
981C23C2×#1174568711yescharacteristic
982C23C2×#1174568511yescharacteristic
983C23#1427377211yescharacteristic
984C23#1427377211yescharacteristic
985C23#1427377211yescharacteristic
986C23#1427377411yescharacteristic
987D4—416no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—594no—
1022C2×C4—594no—
1023C2×C4—1182no—
1024C2×C4—1182no—
1025C2×C4—1182no—
1026C2×C4—1182no—
1027C2×C4—1182no—
1028C2×C4—1182no—
1029C2×C4—1182no—
1030C2×C4—1182no—
1031C2×C4—1182no—
1032C2×C4—1182no—
1033C2×C4—1182no—
1034C2×C4—1182no—
1035C2×C4—1182no—
1036C2×C4—1182no—
1037C2×C4—1182no—
1038C2×C4—1182no—
1039C2×C4—1182no—
1040C2×C4—1182no—
1041C2×C4—1182no—
1042C2×C4—1182no—
1043C2×C4—1182no—
1044C2×C4—1182no—
1045C2×C4—1182no—
1046C2×C4—1182no—
1047C2×C4—1182no—
1048C2×C4—1182no—
1049C2×C4—1182no—
1050C2×C4—23616no—
1051C2×C4—2361no—
1052C2×C4—2361no—
1053C2×C4—2361no—
1054C2×C4—2361no—
1055C2×C4—2361no—
1056C2×C4—2361no—
1057C2×C4—2361no—
1058C2×C4—2361no—
1059C2×C4—2361no—
1060C2×C4—2361no—
1061C2×C4—2361no—
1062C2×C4—2361no—
1063C2×C4—2361no—
1064C2×C4—2361no—
1065C2×C4—2361no—
1066C2×C4—2361no—
1067C2×C4—2361no—
1068C2×C4—2361no—
1069C2×C4—2361no—
1070C2×C4—2361no—
1071C2×C4—2361no—
1072C2×C4—2361no—
1073C2×C4—2361no—
1074C2×C4—2361no—
1075C2×C4—2361no—
1076C2×C4—2361no—
1077C2×C4—2361no—
1078C2×C4C22⋊C4×D5914yes—
1079C2×C4#1427370814yescomplemented
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22C2×C22⋊C4×D5911yescharacteristic
1111C22C2×C4×C22⋊D5911yescharacteristic
1112C22C4×#1174568711yescharacteristic
1113C22C4×#1174568711yescharacteristic
1114C22C4×#1174568711yescharacteristic
1115C22#1683787511yescharacteristic
1116C22#1683788111yescharacteristic
1117C22C2×#1427370811yescharacteristic
1118C22#1683790911yescharacteristic
1119C22#1683791211yescharacteristic
1120C22#1683791211yescharacteristic
1121C22#1683793211yescharacteristic
1122C22#1683793211yescharacteristic
1123C22#1683795011yescharacteristic
1124C22#1683795111yescharacteristic
1125C22#1683798411yescharacteristic
1126C22#1683799711yescharacteristic
1127C22#1683800611yescharacteristic
1128C22#1683801611yescharacteristic
1129C22D4×C22⋊D5911yescharacteristic
1130C22D4×C22⋊D5911yescharacteristic
1131C22#1683804211yescharacteristic
1132C22#1683804211yescharacteristic
1133C22#1683804611yescharacteristic
1134C22#1683805111yescharacteristic
1135C22#1683805811yescharacteristic
1136C22#1683806011yescharacteristic
1137C22#1683807011yescharacteristic
1138C22#1683807211yescharacteristic
1139C22#1683808111yescharacteristic
1140C22#1683808211yescharacteristic
1141C22#1683809211yescharacteristic
1142C22#1683809511yescharacteristic
1143C22#1683809511yescharacteristic
1144C22#1683813811yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—42no—
1148C4—42no—
1149C4—81no—
1150C4—1184no—
1151C4—1184no—
1152C4—4721no—
1153C4—2362no—
1154C4—2362no—
1155C4—2362no—
1156C4—2362no—
1157C4—2362no—
1158C2—44no—
1159C2—82no—
1160C2#2142658311yescharacteristic
1161C2C4×#1427370811yescharacteristic
1162C2#2142688311yescharacteristic
1163C2C22⋊C4×C22⋊D5911yescharacteristic
1164C2#2142693511yescharacteristic
1165C2#2142708211yescharacteristic
1166C2#2142723111yescharacteristic
1167C2#2142782711yescharacteristic
1168C2#2142785711yescharacteristic
1169C2#2142799311yescharacteristic
1170C2#2142802311yescharacteristic
1171C2#2142805911yescharacteristic
1172C2#2142821211yescharacteristic
1173C2#2142916111yescharacteristic
1174C2#2142921511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C59×#390C2
socle, cosocleC24×C59C24
prime radicalC23×D4×C59C22
hypercenterC2×#390D59
hypocenterC59#14095
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#16837283C2semidirect
3. C2×C4×Dic59⋊C4C2semidirect
4. C2×C22⋊C4×Dic59C2semidirect
5. #21422346C2semidirect
6. #21422339C2semidirect
7. #21422339C2semidirect
9. #21422333C2semidirect
10. #21422333C2semidirect
11. #21422333C2semidirect
12. #21422333C2semidirect
13. #21422329C2semidirect
14. #21422318C2semidirect
19. C2×#14273708C4semidirect
310. Dic59⋊C4C22⋊C4semidirect
434. C2×C4×C59#123semidirect
645. C59#14095semidirect
1079. C2×C4#14273708semidirect

Maximal subgroups

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

subgroupindex
C22×#142737082
C2×#168372832
C2×C4×Dic59⋊C42
C2×C22⋊C4×Dic592
#214223462
#214223392
#214223372
#214223332
#214223292
#214223182
C2×C59×#3902
#1409559