Finite Group Databasebeta

← #28516010

Subgroups — #28516010

Order 15104.

2062 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
1C2×#16837305C211yesmaximal, characteristic
2C2×#16837301C211yesmaximal, characteristic, complemented
3C2×#16837288C211yesmaximal, characteristic, complemented
4C2×#16837262C211yesmaximal, characteristic, complemented
5#21422349C211yesmaximal, characteristic, complemented
6#21422341C211yesmaximal, characteristic, complemented
7#21422341C211yesmaximal, characteristic, complemented
8#21422341C211yesmaximal, characteristic, complemented
9#21422341C211yesmaximal, characteristic, complemented
10#21422337C211yesmaximal, characteristic
11#21422333C211yesmaximal, characteristic, complemented
12#21422333C211yesmaximal, characteristic, complemented
13#21422328C211yesmaximal, characteristic, complemented
14#21422319C211yesmaximal, characteristic, complemented
15C22×#123×C59C211yesmaximal, characteristic
16C22×C4⋊Dic59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×C4⋊Dic59C2211yescharacteristic
19C22×C4⋊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×C4×Dic59C2211yescharacteristic
29C22×C4×Dic59C2211yescharacteristic
30#16837305—24no—
31#16837301—24no—
32#16837288—24no—
33#16837262—24no—
34C2×C59⋊#95C2211yescharacteristic
35C2×C59⋊#95C2211yescharacteristic
36C2×C59⋊#95C2211yescharacteristic
37C2×C59⋊#95C2211yescharacteristic
38C2×C59⋊#95C2211yescharacteristic
39C2×C59⋊#95C2211yescharacteristic
40C2×C59⋊#95C2211yescharacteristic
41C2×C59⋊#95C2211yescharacteristic
42C2×C59⋊#95C2211yescharacteristic
43C2×C59⋊#95C2211yescharacteristic
44C2×C59⋊#95C2211yescharacteristic
45C2×C59⋊#95C2211yescharacteristic
46C2×C59⋊#95C2211yescharacteristic
47C2×C59⋊#95C2211yescharacteristic
48C23×D4×C59C2211yescharacteristic
49C24×C4×C59C2211yescharacteristic
50C2×#123×C59—24no—
51C2×#123×C59—24no—
52C2×#123×C59C418yescomplemented
53C22×C4⋊C4×C59C2211yescharacteristic
54C22×C4⋊C4×C59C2211yescharacteristic
55C22×C22⋊C4×C59C2211yescharacteristic
56C22×C22⋊C4×C59C2211yescharacteristic
57C22×C22⋊C4×C59C2211yescharacteristic
58C23×Dic59C2311yescharacteristic
59C23×Dic59C2311yescharacteristic
60C23×Dic59C2311yescharacteristic
61C23×Dic59C2311yescharacteristic
62C23×Dic59C2311yescharacteristic
63C23×Dic59C2311yescharacteristic
64C23×Dic59C2311yescharacteristic
65C23×Dic59C2311yescharacteristic
66C2×C4⋊Dic59—22no—
67C2×C4⋊Dic59—22no—
68C2×C4⋊Dic59—22no—
69C2×C4⋊Dic59—22no—
70C2×C4⋊Dic59—22no—
71C2×C4⋊Dic59—22no—
72C2×C4⋊Dic59—22no—
73C2×C4⋊Dic59—41no—
74C2×C4⋊Dic59—41no—
75C2×C4⋊Dic59—41no—
76C2×C4⋊Dic59—41no—
77C2×C4⋊Dic59—41no—
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—41no—
88C2×C22⋊Dic59—41no—
89C2×C22⋊Dic59—41no—
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⋊Dic59D414yes—
102C2×C4×Dic59—22no—
103C2×C4×Dic59—22no—
104C2×C4×Dic59—22no—
105C2×C4×Dic59—41no—
106C2×C4×Dic59—41no—
107C2×C4×Dic59—41no—
108C59⋊#95—22no—
109C59⋊#95—22no—
110C59⋊#95—22no—
111C59⋊#95—22no—
112C59⋊#95—22no—
113C59⋊#95—22no—
114C59⋊#95—22no—
115C59⋊#95—22no—
116C59⋊#95—22no—
117C59⋊#95—22no—
118C59⋊#95—41no—
119C59⋊#95—41no—
120C59⋊#95—41no—
121C59⋊#95—41no—
122C25×C59C2311yescharacteristic
123C25×C59C2311yescharacteristic
124C22×D4×C59—22no—
125C22×D4×C59—22no—
126C22×D4×C59—22no—
127C22×D4×C59—22no—
128C22×D4×C59—41no—
129C22×D4×C59—41no—
130C22×D4×C59C2×C414yes—
131C23×C4×C59—22no—
132C23×C4×C59—22no—
133C23×C4×C59—22no—
134C23×C4×C59—22no—
135C23×C4×C59—41no—
136C23×C4×C59—41no—
137C23×C4×C59C2×C414yes—
138C23×C4×C59C2311yescharacteristic
139C23×C4×C59C2311yescharacteristic
140C23×C4×C59C2311yescharacteristic
141C23×C4×C59C2311yescharacteristic
142C23×C4×C59C2311yescharacteristic
143#123×C59—232no—
144C2×C4⋊C4×C59—22no—
145C2×C4⋊C4×C59—22no—
146C2×C4⋊C4×C59C2×C414yes—
147C2×C4⋊C4×C59C2×C414yes—
148C2×C4⋊C4×C59D414yes—
149C2×C4⋊C4×C59D414yes—
150C2×C22⋊C4×C59—22no—
151C2×C22⋊C4×C59—22no—
152C2×C22⋊C4×C59—22no—
153C2×C22⋊C4×C59—22no—
154C2×C22⋊C4×C59—22no—
155C2×C22⋊C4×C59—22no—
156C2×C22⋊C4×C59C2×C414yes—
157C2×C22⋊C4×C59C2×C414yes—
158C2×C22⋊C4×C59C2×C414yes—
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—28no—
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—28no—
223C22×C4×C59—44no—
224C22×C4×C59—44no—
225C22×C4×C59—44no—
226C22×C4×C59—44no—
227C22×C4×C59—44no—
228C22×C4×C59C22×C412yes—
229C22×C4×C59C22×C412yes—
230C22×C4×C59C22×C412yes—
231C22×C4×C59C22×C412yes—
232C22×C4×C59C22×C412yes—
233C22×C4×C59C2×D412yes—
234C22×C4×C59C2×D412yes—
235C22×C4×C59C2×D412yes—
236C22×C4×C59C2×D412yes—
237C22×C4×C59C2×D412yes—
238C22×C4×C59C2×D412yes—
239C22×Dic59—21no—
240C22×Dic59—21no—
241C22×Dic59—21no—
242C22×Dic59—21no—
243C22×Dic59—21no—
244C22×Dic59—21no—
245C22×Dic59—21no—
246C22×Dic59—21no—
247C22×Dic59—21no—
248C22×Dic59—21no—
249C22×Dic59—21no—
250C22×Dic59—21no—
251C22×Dic59—21no—
252C22×Dic59—21no—
253C22×Dic59—21no—
254C22×Dic59—21no—
255C22×Dic59—21no—
256C22×Dic59—21no—
257C22×Dic59—21no—
258C22×Dic59—21no—
259C22×Dic59—21no—
260C22×Dic59—21no—
261C22×Dic59—21no—
262C22×Dic59—21no—
263C22×Dic59—21no—
264C22×Dic59—21no—
265C22×Dic59—21no—
266C22×Dic59—21no—
267C22×Dic59—21no—
268C22×Dic59—21no—
269C22×Dic59—21no—
270C22×Dic59—21no—
271C22×Dic59—21no—
272C22×Dic59—21no—
273C22×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×Dic59C2×D412yes—
292C22×Dic59C2×D412yes—
293C22×Dic59#4112yes—
294C22×Dic59#4112yes—
295C4⋊C4×C59—28no—
296C4⋊C4×C59C22⋊C4116yescomplemented
297C22⋊C4×C59—28no—
298C22⋊C4×C59—28no—
299C22⋊C4×C59—28no—
300C22⋊Dic59—44no—
301C22⋊Dic59—44no—
302C22⋊Dic59—44no—
303C22⋊Dic59—44no—
304C22⋊Dic59—44no—
305C22⋊Dic59—44no—
306C22⋊Dic59—44no—
307C22⋊Dic59—44no—
308C4⋊Dic59—44no—
309C4⋊Dic59—44no—
310C4⋊Dic59—44no—
311C4⋊Dic59—44no—
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×C59H(5,𝔽2)11yescharacteristic
392C23×C59H(5,𝔽2)11yescharacteristic
393C23×C59H(5,𝔽2)11yescharacteristic
394C23×C59H(5,𝔽2)11yescharacteristic
395C23×C59H(5,𝔽2)11yescharacteristic
396C23×C592−1+411yescharacteristic
397C23×C592−1+411yescharacteristic
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—22no—
419C2×C4×C59—22no—
420C2×C4×C59—22no—
421C2×C4×C59—22no—
422C2×C4×C59—22no—
423C2×C4×C59—22no—
424C2×C4×C59—416no—
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×C59C2×C22⋊C414yes—
435C2×C4×C59C2×C22⋊C414yes—
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—41no—
449C2×Dic59—41no—
450C2×Dic59—41no—
451C2×Dic59—41no—
452C2×Dic59—41no—
453C2×Dic59—41no—
454C2×Dic59—41no—
455C2×Dic59—41no—
456C2×Dic59—41no—
457C2×Dic59—41no—
458C2×Dic59—41no—
459C2×Dic59—41no—
460C2×Dic59—41no—
461C2×Dic59—41no—
462C2×Dic59—41no—
463C2×Dic59—41no—
464C2×Dic59—41no—
465C2×Dic59—41no—
466C2×Dic59—41no—
467C2×Dic59—41no—
468C2×Dic59—41no—
469C2×Dic59—41no—
470C2×Dic59—41no—
471C2×Dic59—41no—
472C2×Dic59—41no—
473C2×Dic59—41no—
474C2×Dic59—41no—
475C2×Dic59—41no—
476C2×Dic59—41no—
477C2×Dic59—41no—
478C2×Dic59—41no—
479C2×Dic59—41no—
480C2×Dic59—41no—
481C2×Dic59—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—
492#14360—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×C59#51811yescharacteristic
527C22×C59#52011yescharacteristic
528C22×C59#52011yescharacteristic
529C22×C59#52011yescharacteristic
530C22×C59#53411yescharacteristic
531C22×C59#53511yescharacteristic
532C22×C59#53611yescharacteristic
533C22×C59#53611yescharacteristic
534C22×C59#53711yescharacteristic
535C22×C59#53711yescharacteristic
536C22×C59#53811yescharacteristic
537C22×C59#53911yescharacteristic
538C22×C59#53911yescharacteristic
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#55211yescharacteristic
554C22×C59#56011yescharacteristic
555C22×C59#56211yescharacteristic
556C22×C59#56211yescharacteristic
557C22×C59#56311yescharacteristic
558C4×C59—24no—
559C4×C59—24no—
560C4×C59—24no—
561C4×C59—42no—
562C4×C59—42no—
563Dic59—42no—
564Dic59—42no—
565Dic59—42no—
566Dic59—42no—
567Dic59—81no—
568Dic59—81no—
569Dic59—81no—
570Dic59—81no—
571C22×#123D5911yescharacteristic
572C2×#390—591no—
573C2×#389—591no—
574C2×#387—591no—
575C2×#380—591no—
576#1441—591no—
577#1439—591no—
578#1439—591no—
579#1439—591no—
580#1439—591no—
581#1438—591no—
582#1437—591no—
583#1437—591no—
584#1436—591no—
585C22⋊#95—591no—
586C2×C59—44no—
587C2×C59—82no—
588C2×C59#231111yescharacteristic
589C2×C59#232211yescharacteristic
590C2×C59#233511yescharacteristic
591C2×C59D4×C22⋊C411yescharacteristic
592C2×C59#234111yescharacteristic
593C2×C59#235911yescharacteristic
594C2×C59#237611yescharacteristic
595C2×C59#267311yescharacteristic
596C2×C59#267411yescharacteristic
597C2×C59#268111yescharacteristic
598C2×C59#268211yescharacteristic
599C2×C59#269411yescharacteristic
600C2×C59#269611yescharacteristic
601C2×C59#270511yescharacteristic
602C2×C59#270711yescharacteristic
603C23×D4C2×D5911yescharacteristic
604C24×C4C2×D5911yescharacteristic
605C2×#123—24no—
606C2×#123—24no—
607C2×#123Dic5918yescomplemented
608C22×C4⋊C4—591no—
609C22×C4⋊C4—591no—
610C22×C4⋊C4—591no—
611C22×C4⋊C4—591no—
612C22×C4⋊C4C2×D5911yescharacteristic
613C22×C4⋊C4C2×D5911yescharacteristic
614C22×C22⋊C4—591no—
615C22×C22⋊C4—591no—
616C22×C22⋊C4—591no—
617C22×C22⋊C4—591no—
618C22×C22⋊C4—591no—
619C22×C22⋊C4—591no—
620C22×C22⋊C4—591no—
621C22×C22⋊C4—591no—
622C22×C22⋊C4C2×D5911yescharacteristic
623C22×C22⋊C4C2×D5911yescharacteristic
624C22×C22⋊C4C2×D5911yescharacteristic
625C22×C42—591no—
626C22×C42—591no—
627#390—1184no—
628#389—1184no—
629#387—1184no—
630#380—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#1436011yescharacteristic, 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×D4C2×Dic5914yes—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—41no—
660C23×C4—41no—
661C23×C4—591no—
662C23×C4—591no—
663C23×C4—591no—
664C23×C4—591no—
665C23×C4—591no—
666C23×C4—591no—
667C23×C4—591no—
668C23×C4—591no—
669C23×C4C2×Dic5914yes—
670C23×C4C22×D5911yescharacteristic
671C23×C4C22×D5911yescharacteristic
672C23×C4C22×D5911yescharacteristic
673C23×C4C22×D5911yescharacteristic
674C23×C4C22×D5911yescharacteristic
675#123—232no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—1182no—
679C2×C4⋊C4—1182no—
680C2×C4⋊C4—1182no—
681C2×C4⋊C4—1182no—
682C2×C4⋊C4—1182no—
683C2×C4⋊C4—1182no—
684C2×C4⋊C4—1182no—
685C2×C4⋊C4—2361no—
686C2×C4⋊C4—2361no—
687C2×C4⋊C4—2361no—
688C2×C4⋊C4—2361no—
689C2×C4⋊C4—2361no—
690C2×C4⋊C4C2×Dic5914yes—
691C2×C4⋊C4C2×Dic5914yes—
692C2×C4⋊C4C22⋊D5914yes—
693C2×C4⋊C4C22⋊D5914yes—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—594no—
701C2×C22⋊C4—1182no—
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—2361no—
711C2×C22⋊C4—2361no—
712C2×C22⋊C4—2361no—
713C2×C22⋊C4—2361no—
714C2×C22⋊C4—2361no—
715C2×C22⋊C4—2361no—
716C2×C22⋊C4—2361no—
717C2×C22⋊C4—2361no—
718C2×C22⋊C4—2361no—
719C2×C22⋊C4—2361no—
720C2×C22⋊C4—2361no—
721C2×C22⋊C4—2361no—
722C2×C22⋊C4—2361no—
723C2×C22⋊C4—2361no—
724C2×C22⋊C4C2×Dic5914yes—
725C2×C22⋊C4C2×Dic5914yes—
726C2×C22⋊C4C2×Dic5914yes—
727C2×C42—1182no—
728C2×C42—1182no—
729C2×C42—1182no—
730C2×C42—2361no—
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—
773C24D4×D5912yes—
774C24#1174568712yes—
775C24C22×Dic5912yes—
776C24C22×Dic5912yes—
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—28no—
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—28no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—592no—
817C22×C4—592no—
818C22×C4—592no—
819C22×C4—592no—
820C22×C4—1181no—
821C22×C4—1181no—
822C22×C4—1181no—
823C22×C4—1181no—
824C22×C4—1181no—
825C22×C4—1181no—
826C22×C4—1181no—
827C22×C4—1181no—
828C22×C4—1181no—
829C22×C4—1181no—
830C22×C4—1181no—
831C22×C4—1181no—
832C22×C4—1181no—
833C22×C4—1181no—
834C22×C4—1181no—
835C22×C4—1181no—
836C22×C4—1181no—
837C22×C4—1181no—
838C22×C4—1181no—
839C22×C4—1181no—
840C22×C4—1181no—
841C22×C4—1181no—
842C22×C4—1181no—
843C22×C4—1181no—
844C22×C4—1181no—
845C22×C4—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—1181no—
871C22×C4—1181no—
872C22×C4C22×Dic5912yes—
873C22×C4C22×Dic5912yes—
874C22×C4C22×Dic5912yes—
875C22×C4C22×Dic5912yes—
876C22×C4C22×Dic5912yes—
877C22×C4C2×C22⋊D5912yes—
878C22×C4C2×C22⋊D5912yes—
879C22×C4C2×C22⋊D5912yes—
880C22×C4C2×C22⋊D5912yes—
881C22×C4C2×C22⋊D5912yes—
882C22×C4C2×C22⋊D5912yes—
883C4⋊C4—28no—
884C4⋊C4—2364no—
885C4⋊C4—2364no—
886C4⋊C4—2364no—
887C4⋊C4—2364no—
888C4⋊C4C22⋊Dic59116yescomplemented
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—2364no—
893C22⋊C4—2364no—
894C22⋊C4—2364no—
895C22⋊C4—2364no—
896C22⋊C4—2364no—
897C22⋊C4—2364no—
898C22⋊C4—2364no—
899C22⋊C4—2364no—
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—
971C23D4×Dic5914yes—
972C23C23×Dic5911yescharacteristic
973C23C2×D4×D5911yescharacteristic
974C23C22×C22⋊D5911yescharacteristic
975C23C22×C22⋊D5911yescharacteristic
976C23#41×D5911yescharacteristic
977C23#41×D5911yescharacteristic
978C23C2×#1174568711yescharacteristic
979C23#1427377211yescharacteristic
980C23#1427377211yescharacteristic
981C23#1427377311yescharacteristic
982C23#1427377311yescharacteristic
983C23#1427377311yescharacteristic
984C23#1427377411yescharacteristic
985C23#1427377411yescharacteristic
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—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—416no—
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—1182no—
1022C2×C4—1182no—
1023C2×C4—1182no—
1024C2×C4—1182no—
1025C2×C4—1182no—
1026C2×C4—1182no—
1027C2×C4—1182no—
1028C2×C4—1182no—
1029C2×C4—1182no—
1030C2×C4—1182no—
1031C2×C4—1182no—
1032C2×C4—1182no—
1033C2×C4—2361no—
1034C2×C4—2361no—
1035C2×C4—2361no—
1036C2×C4—2361no—
1037C2×C4—2361no—
1038C2×C4—2361no—
1039C2×C4—2361no—
1040C2×C4—2361no—
1041C2×C4—2361no—
1042C2×C4—2361no—
1043C2×C4—2361no—
1044C2×C4—2361no—
1045C2×C4—2361no—
1046C2×C4—2361no—
1047C2×C4—2361no—
1048C2×C4—2361no—
1049C2×C4—2361no—
1050C2×C4—2361no—
1051C2×C4—2361no—
1052C2×C4—2361no—
1053C2×C4—2361no—
1054C2×C4—2361no—
1055C2×C4—2361no—
1056C2×C4—2361no—
1057C2×C4—2361no—
1058C2×C4—2361no—
1059C2×C4—2361no—
1060C2×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×C4C2×C22⋊Dic5914yes—
1078C2×C4C2×C22⋊Dic5914yes—
1079C2×C4C2×C22⋊Dic5914yes—
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—
1110C22C22×C22⋊Dic5911yescharacteristic
1111C22C2×D4×Dic5911yescharacteristic
1112C22#41×Dic5911yescharacteristic
1113C22#1683787711yescharacteristic
1114C22#1683788511yescharacteristic
1115C22#1683788511yescharacteristic
1116C22#1683788511yescharacteristic
1117C22#1683796311yescharacteristic
1118C22#1683796611yescharacteristic
1119C22#1683797311yescharacteristic
1120C22#1683797411yescharacteristic
1121C22#1683798011yescharacteristic
1122C22#1683798011yescharacteristic
1123C22#1683798811yescharacteristic
1124C22#1683799511yescharacteristic
1125C22#1683799611yescharacteristic
1126C22#1683799611yescharacteristic
1127C22#1683800411yescharacteristic
1128C22#1683802011yescharacteristic
1129C22D4×C22⋊D5911yescharacteristic
1130C22D4×C22⋊D5911yescharacteristic
1131C22#1683804411yescharacteristic
1132C22#1683804611yescharacteristic
1133C22#1683804611yescharacteristic
1134C22#1683805011yescharacteristic
1135C22#1683805911yescharacteristic
1136C22#1683805911yescharacteristic
1137C22#1683807111yescharacteristic
1138C22#1683807111yescharacteristic
1139C22#1683807511yescharacteristic
1140C22#1683808911yescharacteristic
1141C22#1683814211yescharacteristic
1142C22#1683814911yescharacteristic
1143C22#1683814911yescharacteristic
1144C22#1683815511yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—24no—
1148C4—42no—
1149C4—42no—
1150C4—4721no—
1151C4—4721no—
1152C4—4721no—
1153C4—4721no—
1154C4—2362no—
1155C4—2362no—
1156C4—2362no—
1157C4—2362no—
1158C2—44no—
1159C2—82no—
1160C2#2142668811yescharacteristic
1161C2#2142676811yescharacteristic
1162C2#2142689011yescharacteristic
1163C2D4×C22⋊Dic5911yescharacteristic
1164C2#2142693711yescharacteristic
1165C2#2142709211yescharacteristic
1166C2#2142724411yescharacteristic
1167C2#2143036211yescharacteristic
1168C2#2143037711yescharacteristic
1169C2#2143044811yescharacteristic
1170C2#2143046111yescharacteristic
1171C2#2143061211yescharacteristic
1172C2#2143064211yescharacteristic
1173C2#2143076511yescharacteristic
1174C2#2143079511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC22×#123×C59C2
socle, cosocleC24×C59C24
prime radicalC23×D4×C59C22
hypercenterC22×#123D59
hypocenterC59#14360
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
2. C2×#16837301C2semidirect
3. C2×#16837288C2semidirect
4. C2×#16837262C2semidirect
5. #21422349C2semidirect
6. #21422341C2semidirect
7. #21422341C2semidirect
8. #21422341C2semidirect
9. #21422341C2semidirect
11. #21422333C2semidirect
12. #21422333C2semidirect
13. #21422328C2semidirect
14. #21422319C2semidirect
52. C2×#123×C59C4semidirect
296. C4⋊C4×C59C22⋊C4semidirect
607. C2×#123Dic59semidirect
645. C59#14360semidirect
888. C4⋊C4C22⋊Dic59semidirect

Maximal subgroups

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

subgroupindex
C2×#168373052
C2×#168373012
C2×#168372882
C2×#168372622
#214223492
#214223412
#214223372
#214223332
#214223282
#214223192
C22×#123×C592
#1436059