Finite Group Databasebeta

← #28493969

Subgroups — #28493969

Order 15104.

1518 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273685C211yesmaximal, characteristic
2C22×(C2×D59)⋊C8C211yesmaximal, characteristic
3C2×#16837259C211yesmaximal, characteristic
4C2×#16837165C211yesmaximal, characteristic, complemented
5C2×#16837164C211yesmaximal, characteristic, complemented
6C2×#16837164C211yesmaximal, characteristic, complemented
7C2×C59×#340C211yesmaximal, characteristic, complemented
8C23×C4×D59C2211yescharacteristic
9C23×C59⋊C8C2211yescharacteristic
10C2×#14273685—22no—
11C2×#14273685—22no—
12C2×#14273685—22no—
13C2×#14273685—22no—
14C2×#14273685—22no—
15C2×#14273685C414yescomplemented
16C22×C4⋊Dic59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×(C2×D59)⋊C4—21no—
19C22×(C2×D59)⋊C4—21no—
20C22×C4×Dic59—21no—
21C2×(C2×D59)⋊C8—22no—
22C2×(C2×D59)⋊C8—22no—
23C2×(C2×D59)⋊C8C414yescomplemented
24#16837259—22no—
25#16837259C414yescomplemented
26C2×C59⋊#95—21no—
27#16837165—22no—
28#16837164—22no—
29#16837164—22no—
30C23×C8×C59C2211yescharacteristic
31C22×C4⋊C4×C59C2211yescharacteristic
32C22×C4⋊C4×C59C2211yescharacteristic
33C59×#340—22no—
34C24×D59D411yescharacteristic
35C23×Dic59—21no—
36C23×Dic59—21no—
37C23×Dic59D411yescharacteristic
38C22×C4×D59—21no—
39C22×C4×D59—21no—
40C22×C4×D59—21no—
41C22×C4×D59—21no—
42C22×C4×D59—21no—
43C22×C4×D59—21no—
44C22×C4×D59—21no—
45C22×C4×D59—21no—
46C22×C4×D59C2×C412yes—
47C22×C4×D59C2×C412yes—
48C22×C4×D59C2×C412yes—
49C22×C4×D59D412yes—
50C22×C4×D59D412yes—
51C22×C4×D59Q812yes—
52C22×C59⋊C8—21no—
53C22×C59⋊C8—21no—
54C22×C59⋊C8—21no—
55C22×C59⋊C8—21no—
56C22×C59⋊C8—21no—
57C22×C59⋊C8—21no—
58C22×C59⋊C8C2×C412yes—
59#14273685—28no—
60#14273685—28no—
61#14273685—28no—
62#14273685—28no—
63C2×C4⋊Dic59—21no—
64C2×C4⋊Dic59—21no—
65C2×C4⋊Dic59—21no—
66C2×C4⋊Dic59—21no—
67C2×C4⋊Dic59—21no—
68C2×C4⋊Dic59—21no—
69C2×C4⋊Dic59—21no—
70C2×C4⋊Dic59—21no—
71C2×C4⋊Dic59C2×C412yes—
72C2×C4⋊Dic59C2×C412yes—
73C2×C4⋊Dic59D412yes—
74C2×C4⋊Dic59D412yes—
75C2×(C2×D59)⋊C4—24no—
76C2×(C2×D59)⋊C4—24no—
77C2×(C2×D59)⋊C4—24no—
78C2×(C2×D59)⋊C4—24no—
79C2×(C2×D59)⋊C4—42no—
80C2×(C2×D59)⋊C4—42no—
81C2×C4×Dic59—24no—
82C2×C4×Dic59—24no—
83C2×C4×Dic59—24no—
84(C2×D59)⋊C8—28no—
85C59⋊#95—24no—
86C23×C4×C59—21no—
87C23×C4×C59—21no—
88C23×C4×C59C2311yescharacteristic
89C22×C8×C59—21no—
90C22×C8×C59—21no—
91C22×C8×C59—21no—
92C22×C8×C59—21no—
93C22×C8×C59—21no—
94C22×C8×C59—21no—
95C22×C8×C59C2×C412yes—
96C2×C4⋊C4×C59—21no—
97C2×C4⋊C4×C59—21no—
98C2×C4⋊C4×C59—21no—
99C2×C4⋊C4×C59—21no—
100C2×C4⋊C4×C59—21no—
101C2×C4⋊C4×C59—21no—
102C2×C4⋊C4×C59—21no—
103C2×C4⋊C4×C59—21no—
104C2×C4⋊C4×C59C2×C412yes—
105C2×C4⋊C4×C59C2×C412yes—
106C2×C4⋊C4×C59D412yes—
107C2×C4⋊C4×C59D412yes—
108C24×C59C2×D411yescharacteristic
109C23×D59—21no—
110C23×D59—21no—
111C23×D59—21no—
112C23×D59—21no—
113C23×D59—21no—
114C23×D59—21no—
115C23×D59—21no—
116C23×D59—21no—
117C23×D59—21no—
118C23×D59—21no—
119C23×D59—21no—
120C23×D59—21no—
121C23×D59C22⋊C412yes—
122C23×D59C22⋊C412yes—
123C23×D59C4⋊C412yes—
124C22×C4×C59—22no—
125C22×C4×C59—22no—
126C22×C4×C59—22no—
127C22×C4×C59—22no—
128C22×C4×C59—41no—
129C22×C4×C59—41no—
130C22×C4×C59—41no—
131C22×C4×C59—41no—
132C22×C4×C59—41no—
133C22×C4×C59—41no—
134C22×C4×C59—41no—
135C22×C4×C59—41no—
136C22×C4×C59—41no—
137C22×C4×C59—41no—
138C22×C4×C59C22×C411yescharacteristic
139C22×C4×C59C22×C411yescharacteristic
140C22×C4×C59C22×C411yescharacteristic
141C22×C4×C59C2×D411yescharacteristic
142C22×C4×C59C2×D411yescharacteristic
143C22×C4×C59C2×D411yescharacteristic
144C22×C4×C59C2×D411yescharacteristic
145C22×C4×C59C2×D411yescharacteristic
146C22×C4×C59C2×D411yescharacteristic
147C22×C4×C59C2×Q811yescharacteristic
148C22×C4×C59#4111yescharacteristic
149C22×C4×C59#4111yescharacteristic
150C22×C4×C59#4111yescharacteristic
151C22×C4×C59#4111yescharacteristic
152C22×Dic59—21no—
153C22×Dic59—21no—
154C22×Dic59—21no—
155C22×Dic59—21no—
156C22×Dic59—22no—
157C22×Dic59—22no—
158C22×Dic59—22no—
159C22×Dic59—22no—
160C22×Dic59—41no—
161C22×Dic59—41no—
162C22×Dic59—41no—
163C22×Dic59—41no—
164C22×Dic59—41no—
165C22×Dic59—41no—
166C22×Dic59—41no—
167C22×Dic59—41no—
168C22×Dic59—41no—
169C22×Dic59—41no—
170C22×Dic59C22⋊C412yes—
171C22×Dic59C22⋊C412yes—
172C22×Dic59C4⋊C412yes—
173C2×C4×D59—22no—
174C2×C4×D59—22no—
175C2×C4×D59—22no—
176C2×C4×D59—22no—
177C2×C4×D59—22no—
178C2×C4×D59—22no—
179C2×C4×D59—22no—
180C2×C4×D59—22no—
181C2×C4×D59—22no—
182C2×C4×D59—22no—
183C2×C4×D59—22no—
184C2×C4×D59—22no—
185C2×C4×D59—22no—
186C2×C4×D59—22no—
187C2×C4×D59—22no—
188C2×C4×D59—22no—
189C2×C4×D59—22no—
190C2×C4×D59—22no—
191C2×C4×D59—22no—
192C2×C4×D59—22no—
193C2×C4×D59—22no—
194C2×C4×D59—22no—
195C2×C4×D59—22no—
196C2×C4×D59—22no—
197C2×C4×D59C4214yes—
198C2×C4×D59C22⋊C414yes—
199C2×C4×D59C4⋊C414yes—
200C2×C4×D59C4⋊C414yes—
201C2×C8×C59—22no—
202C2×C8×C59—22no—
203C2×C8×C59—22no—
204C2×C8×C59—41no—
205C2×C8×C59—41no—
206C2×C8×C59—41no—
207C2×C8×C59—41no—
208C4⋊C4×C59—22no—
209C4⋊C4×C59—22no—
210C4⋊C4×C59—22no—
211C4⋊C4×C59—22no—
212C4⋊C4×C59—22no—
213C4⋊C4×C59—41no—
214C4⋊C4×C59—41no—
215C4⋊C4×C59C22⋊C414yescomplemented
216(C2×D59)⋊C4—216no—
217(C2×D59)⋊C4—48no—
218C4⋊Dic59—22no—
219C4⋊Dic59—22no—
220C4⋊Dic59—22no—
221C4⋊Dic59—22no—
222C4⋊Dic59—22no—
223C4⋊Dic59—41no—
224C4⋊Dic59—41no—
225C4⋊Dic59C22⋊C414yescomplemented
226C4×Dic59—216no—
227C2×C59⋊C8—22no—
228C2×C59⋊C8—22no—
229C2×C59⋊C8—22no—
230C2×C59⋊C8—41no—
231C2×C59⋊C8—41no—
232C2×C59⋊C8—41no—
233C2×C59⋊C8—41no—
234C23×C59C2×C22⋊C411yescharacteristic
235C23×C59C2×C22⋊C411yescharacteristic
236C23×C59C2×C4⋊C411yescharacteristic
237C23×C59#12011yescharacteristic
238C23×C59#12011yescharacteristic
239C23×C59#12311yescharacteristic
240C23×C59#12311yescharacteristic
241C23×C59#13511yescharacteristic
242C23×C59#13511yescharacteristic
243C23×C59#13511yescharacteristic
244C23×C59#13511yescharacteristic
245C23×C59AGL(1,ℤ/8)11yescharacteristic
246C23×C59AGL(1,ℤ/8)11yescharacteristic
247C23×C59#13711yescharacteristic
248C23×C59#13711yescharacteristic
249C22×D59—22no—
250C22×D59—22no—
251C22×D59—22no—
252C22×D59—22no—
253C22×D59—22no—
254C22×D59—22no—
255C22×D59—22no—
256C22×D59—22no—
257C22×D59—22no—
258C22×D59—22no—
259C22×D59—22no—
260C22×D59—22no—
261C22×D59—22no—
262C22×D59—22no—
263C22×D59—22no—
264C22×D59—22no—
265C22×D59—22no—
266C22×D59—22no—
267C22×D59—41no—
268C22×D59—41no—
269C22×D59—41no—
270C22×D59—41no—
271C22×D59—41no—
272C22×D59—41no—
273C22×D59—41no—
274C22×D59—41no—
275C22×D59—41no—
276C22×D59—41no—
277C22×D59—41no—
278C22×D59—41no—
279C22×D59—41no—
280C22×D59—41no—
281C22×D59—41no—
282C22×D59—41no—
283C22×D59#9514yes—
284C2×C4×C59—24no—
285C2×C4×C59—42no—
286C2×C4×C59—42no—
287C2×C4×C59—42no—
288C2×C4×C59—42no—
289C2×C4×C59—42no—
290C2×C4×C59—42no—
291C2×C4×C59—42no—
292C2×C4×C59—42no—
293C2×C4×C59—42no—
294C2×C4×C59—81no—
295C2×C4×C59—81no—
296C2×C4×C59—81no—
297C2×C4×C59—81no—
298C2×C4×C59C2×C4211yescharacteristic
299C2×C4×C59C2×C22⋊C411yescharacteristic
300C2×C4×C59C2×C22⋊C411yescharacteristic
301C2×C4×C59C2×C22⋊C411yescharacteristic
302C2×C4×C59C2×C4⋊C411yescharacteristic
303C2×C4×C59C2×C4⋊C411yescharacteristic
304C2×C4×C59#11711yescharacteristic
305C2×C4×C59#11711yescharacteristic
306C2×C4×C59C4×D411yescharacteristic
307C2×C4×C59C4×D411yescharacteristic
308C2×C4×C59C4×D411yescharacteristic
309C2×C4×C59C4×D411yescharacteristic
310C2×C4×C59C4×D411yescharacteristic
311C2×C4×C59C4×D411yescharacteristic
312C2×C4×C59C4×D411yescharacteristic
313C2×C4×C59C4×D411yescharacteristic
314C2×C4×C59#12011yescharacteristic
315C2×C4×C59#12011yescharacteristic
316C2×C4×C59#12111yescharacteristic
317C2×C4×C59#12111yescharacteristic
318C2×C4×C59#12111yescharacteristic
319C2×C4×C59#12111yescharacteristic
320C2×C4×C59C22⋊Q811yescharacteristic
321C2×C4×C59C22⋊Q811yescharacteristic
322C2×C4×C59C22⋊Q811yescharacteristic
323C2×C4×C59C22⋊Q811yescharacteristic
324C2×C4×C59#12311yescharacteristic
325C2×C4×C59#12311yescharacteristic
326C2×Dic59—22no—
327C2×Dic59—22no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—24no—
333C2×Dic59—42no—
334C2×Dic59—42no—
335C2×Dic59—42no—
336C2×Dic59—42no—
337C2×Dic59—42no—
338C2×Dic59—42no—
339C2×Dic59—42no—
340C2×Dic59—42no—
341C2×Dic59—42no—
342C2×Dic59—81no—
343C2×Dic59—81no—
344C2×Dic59—81no—
345C2×Dic59—81no—
346C2×Dic59#9514yes—
347C4×D59—24no—
348C4×D59—24no—
349C4×D59—24no—
350C4×D59—24no—
351C4×D59—24no—
352C4×D59—24no—
353C4×D59—24no—
354C4×D59—24no—
355C8×C59—42no—
356C59⋊C8—42no—
357#10731—591nomaximal, Sylow
358C22×C59C2×#9511yescharacteristic
359C22×C59#37911yescharacteristic
360C22×C59#38111yescharacteristic
361C22×C59#38511yescharacteristic
362C22×C59#38511yescharacteristic
363C22×C59#38611yescharacteristic
364C22×C59#38611yescharacteristic
365C22×C59#41611yescharacteristic
366C22×C59#41611yescharacteristic
367C22×C59#41611yescharacteristic
368C22×C59#41611yescharacteristic
369C22×C59#41711yescharacteristic
370C22×C59#41711yescharacteristic
371C22×C59#41811yescharacteristic
372C22×C59#41911yescharacteristic
373C22×C59#42711yescharacteristic
374C22×C59#42711yescharacteristic
375C22×C59#42811yescharacteristic
376C22×C59#42811yescharacteristic
377C22×C59#44911yescharacteristic
378C22×C59#44911yescharacteristic
379C22×C59#44911yescharacteristic
380C22×C59#44911yescharacteristic
381C22×C59#45211yescharacteristic
382C22×C59#45211yescharacteristic
383C22×C59#45211yescharacteristic
384C22×C59#45211yescharacteristic
385C22×C59#48211yescharacteristic
386C22×C59#48211yescharacteristic
387C22×C59#48211yescharacteristic
388C22×C59#48211yescharacteristic
389C22×C59#48511yescharacteristic
390C22×C59#48511yescharacteristic
391C22×C59#48511yescharacteristic
392C22×C59#48511yescharacteristic
393C2×D59—24no—
394C2×D59—24no—
395C2×D59—24no—
396C2×D59—42no—
397C2×D59—42no—
398C2×D59—42no—
399C2×D59—42no—
400C2×D59—42no—
401C2×D59—42no—
402C2×D59—42no—
403C2×D59—42no—
404C2×D59—42no—
405C2×D59—42no—
406C2×D59—42no—
407C2×D59—42no—
408C4×C59—44no—
409C4×C59—82no—
410C4×C59C4×C22⋊C411yescharacteristic
411C4×C59C4×C22⋊C411yescharacteristic
412C4×C59#38011yescharacteristic
413C4×C59#38011yescharacteristic
414C4×C59#38511yescharacteristic
415C4×C59#38511yescharacteristic
416C4×C59#38611yescharacteristic
417C4×C59#38611yescharacteristic
418Dic59—24no—
419Dic59—44no—
420Dic59—82no—
421C22×#117—591no—
422C22×C22⋊C8—591no—
423C2×#380—591no—
424C2×#340—591no—
425C2×#340—591no—
426C2×#340—591no—
427C2×#340D5911yescharacteristic, complemented
428C2×C59C22⋊#9511yescharacteristic
429C2×C59#173511yescharacteristic
430C2×C59#173611yescharacteristic
431C2×C59#178811yescharacteristic
432C2×C59#178811yescharacteristic
433C2×C59#182511yescharacteristic
434C2×C59#182511yescharacteristic
435C2×C59#185411yescharacteristic
436C2×C59#185411yescharacteristic
437C2×C59#185411yescharacteristic
438C2×C59#185411yescharacteristic
439C2×C59#187311yescharacteristic
440C2×C59#187311yescharacteristic
441C2×C59#187511yescharacteristic
442C2×C59#187511yescharacteristic
443D59—44no—
444C24×C4—591no—
445C23×C8—591no—
446C23×C8C2×D5911yescharacteristic
447C2×#117—594no—
448C2×#117—1182no—
449C2×#117—1182no—
450C2×#117—1182no—
451C2×#117—1182no—
452C2×#117—1182no—
453C22×C4⋊C4—591no—
454C22×C4⋊C4—591no—
455C22×C4⋊C4C2×D5911yescharacteristic
456C22×C4⋊C4C2×D5911yescharacteristic
457C22×C22⋊C4—1181no—
458C22×C22⋊C4—1181no—
459C22×C42—1181no—
460C2×C22⋊C8—594no—
461C2×C22⋊C8—1182no—
462C2×C22⋊C8—1182no—
463#380—594no—
464#380—1182no—
465C2×#95—1181no—
466#340—22no—
467#340—1182no—
468#340—1182no—
469#340—1182no—
470C59#1073111yescharacteristic, complemented, Sylow
471C25—591no—
472C23×C4—21no—
473C23×C4—21no—
474C23×C4—591no—
475C23×C4—592no—
476C23×C4—592no—
477C23×C4—592no—
478C23×C4—592no—
479C23×C4—592no—
480C23×C4—592no—
481C23×C4—1181no—
482C23×C4—1181no—
483C23×C4—1181no—
484C23×C4—1181no—
485C23×C4—1181no—
486C23×C4—1181no—
487C23×C4—1181no—
488C23×C4—1181no—
489C23×C4—1181no—
490C23×C4—1181no—
491C23×C4C22×D5911yescharacteristic
492C22×C8—21no—
493C22×C8—21no—
494C22×C8—21no—
495C22×C8—21no—
496C22×C8—21no—
497C22×C8—21no—
498C22×C8—592no—
499C22×C8—1181no—
500C22×C8—1181no—
501C22×C8—1181no—
502C22×C8—1181no—
503C22×C8—1181no—
504C22×C8—1181no—
505C22×C8C4×D5912yes—
506#117—1188no—
507#117—1188no—
508#117—1188no—
509#117—1188no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—592no—
519C2×C4⋊C4—592no—
520C2×C4⋊C4—592no—
521C2×C4⋊C4—592no—
522C2×C4⋊C4—1181no—
523C2×C4⋊C4—1181no—
524C2×C4⋊C4—1181no—
525C2×C4⋊C4—1181no—
526C2×C4⋊C4—1181no—
527C2×C4⋊C4—1181no—
528C2×C4⋊C4—1181no—
529C2×C4⋊C4—1181no—
530C2×C4⋊C4C4×D5912yes—
531C2×C4⋊C4C4×D5912yes—
532C2×C4⋊C4D23612yes—
533C2×C4⋊C4C22⋊D5912yes—
534C2×C22⋊C4—1184no—
535C2×C22⋊C4—1184no—
536C2×C22⋊C4—1184no—
537C2×C22⋊C4—1184no—
538C2×C22⋊C4—2362no—
539C2×C22⋊C4—2362no—
540C2×C42—1184no—
541C2×C42—1184no—
542C2×C42—1184no—
543C22⋊C8—1188no—
544#95—1184no—
545C24—592no—
546C24—592no—
547C24—592no—
548C24—1181no—
549C24—1181no—
550C24—1181no—
551C24—1181no—
552C24—1181no—
553C24—1181no—
554C24—1181no—
555C24—1181no—
556C24—1181no—
557C24—1181no—
558C24—1181no—
559C24—1181no—
560C24D4×D5911yescharacteristic
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—592no—
576C22×C4—592no—
577C22×C4—592no—
578C22×C4—594no—
579C22×C4—594no—
580C22×C4—594no—
581C22×C4—594no—
582C22×C4—1181no—
583C22×C4—1181no—
584C22×C4—1181no—
585C22×C4—1181no—
586C22×C4—1182no—
587C22×C4—1182no—
588C22×C4—1182no—
589C22×C4—1182no—
590C22×C4—1182no—
591C22×C4—1182no—
592C22×C4—1182no—
593C22×C4—1182no—
594C22×C4—1182no—
595C22×C4—1182no—
596C22×C4—1182no—
597C22×C4—1182no—
598C22×C4—1182no—
599C22×C4—1182no—
600C22×C4—1182no—
601C22×C4—1182no—
602C22×C4—1182no—
603C22×C4—1182no—
604C22×C4—1182no—
605C22×C4—1182no—
606C22×C4—1182no—
607C22×C4—1182no—
608C22×C4—1182no—
609C22×C4—1182no—
610C22×C4—1182no—
611C22×C4—1182no—
612C22×C4—1182no—
613C22×C4—1182no—
614C22×C4—2361no—
615C22×C4—2361no—
616C22×C4—2361no—
617C22×C4—2361no—
618C22×C4—2361no—
619C22×C4—2361no—
620C22×C4—2361no—
621C22×C4—2361no—
622C22×C4—2361no—
623C22×C4—2361no—
624C22×C4C2×C4×D5911yescharacteristic
625C22×C4C2×C4×D5911yescharacteristic
626C22×C4C2×C4×D5911yescharacteristic
627C22×C4C2×D23611yescharacteristic
628C22×C4#1174568511yescharacteristic
629C22×C4#1174568511yescharacteristic
630C22×C4D4×D5911yescharacteristic
631C22×C4D4×D5911yescharacteristic
632C22×C4D4×D5911yescharacteristic
633C22×C4D4×D5911yescharacteristic
634C22×C4#1174568711yescharacteristic
635C22×C4Q8×D5911yescharacteristic
636C22×C4#1174568911yescharacteristic
637C22×C4C2×C22⋊D5911yescharacteristic
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—1182no—
646C2×C8—1182no—
647C2×C8—1182no—
648C2×C8—2361no—
649C2×C8—2361no—
650C2×C8—2361no—
651C2×C8—2361no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—594no—
660C4⋊C4—1182no—
661C4⋊C4—1182no—
662C4⋊C4—1182no—
663C4⋊C4—1182no—
664C4⋊C4—1182no—
665C4⋊C4—2361no—
666C4⋊C4—2361no—
667C4⋊C4(C2×D59)⋊C414yescomplemented
668C22⋊C4—11816no—
669C22⋊C4—2368no—
670C42—11816no—
671C23—594no—
672C23—1182no—
673C23—1182no—
674C23—1182no—
675C23—1182no—
676C23—1182no—
677C23—1182no—
678C23—1182no—
679C23—1182no—
680C23—1182no—
681C23—1182no—
682C23—1182no—
683C23—1182no—
684C23—1182no—
685C23—1182no—
686C23—1182no—
687C23—1182no—
688C23—1182no—
689C23—1182no—
690C23—2361no—
691C23—2361no—
692C23—2361no—
693C23—2361no—
694C23—2361no—
695C23—2361no—
696C23—2361no—
697C23—2361no—
698C23—2361no—
699C23—2361no—
700C23—2361no—
701C23—2361no—
702C23—2361no—
703C23—2361no—
704C23—2361no—
705C23—2361no—
706C23C22⋊C4×D5911yescharacteristic
707C23C22⋊C4×D5911yescharacteristic
708C23C4⋊C4×D5911yescharacteristic
709C23#1427369511yescharacteristic
710C23#1427369711yescharacteristic
711C23#1427370911yescharacteristic
712C23#1427371211yescharacteristic
713C23#1427374611yescharacteristic
714C23#1427374811yescharacteristic
715C23#1427374811yescharacteristic
716C23#1427375011yescharacteristic
717C23#1427375111yescharacteristic
718C23#1427375411yescharacteristic
719C23#1427375611yescharacteristic
720C23#1427375911yescharacteristic
721C2×C4—24no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—594no—
736C2×C4—1182no—
737C2×C4—1182no—
738C2×C4—1182no—
739C2×C4—1182no—
740C2×C4—1182no—
741C2×C4—1182no—
742C2×C4—1184no—
743C2×C4—1184no—
744C2×C4—1184no—
745C2×C4—1184no—
746C2×C4—1184no—
747C2×C4—1184no—
748C2×C4—1184no—
749C2×C4—1184no—
750C2×C4—1184no—
751C2×C4—4721no—
752C2×C4—4721no—
753C2×C4—4721no—
754C2×C4—4721no—
755C2×C4—2362no—
756C2×C4—2362no—
757C2×C4—2362no—
758C2×C4—2362no—
759C2×C4—2362no—
760C2×C4—2362no—
761C2×C4—2362no—
762C2×C4—2362no—
763C2×C4—2362no—
764C2×C4C42×D5911yescharacteristic
765C2×C4C22⋊C4×D5911yescharacteristic
766C2×C4C22⋊C4×D5911yescharacteristic
767C2×C4C2×(C2×D59)⋊C411yescharacteristic
768C2×C4C4⋊C4×D5911yescharacteristic
769C2×C4C4⋊C4×D5911yescharacteristic
770C2×C4#1427368411yescharacteristic
771C2×C4#1427368511yescharacteristic
772C2×C4(C22⋊D59)⋊C411yescharacteristic
773C2×C4(C22⋊D59)⋊C411yescharacteristic
774C2×C4C4×C22⋊D5911yescharacteristic
775C2×C4C4×C22⋊D5911yescharacteristic
776C2×C4#1427368911yescharacteristic
777C2×C4#1427368911yescharacteristic
778C2×C4C4×D23611yescharacteristic
779C2×C4C4×D23611yescharacteristic
780C2×C4#1427369511yescharacteristic
781C2×C4#1427369711yescharacteristic
782C2×C4#1427369811yescharacteristic
783C2×C4#1427370011yescharacteristic
784C2×C4#1427370011yescharacteristic
785C2×C4#1427370211yescharacteristic
786C2×C4#1427370311yescharacteristic
787C2×C4#1427370511yescharacteristic
788C2×C4#1427370511yescharacteristic
789C2×C4#1427370711yescharacteristic
790C2×C4#1427370911yescharacteristic
791C2×C4#1427371211yescharacteristic
792C8—42no—
793C8—2362no—
794C22—1184no—
795C22—1184no—
796C22—1184no—
797C22—2362no—
798C22—2362no—
799C22—2362no—
800C22—2362no—
801C22—2362no—
802C22—2362no—
803C22—2362no—
804C22—2362no—
805C22—2362no—
806C22—2362no—
807C22—2362no—
808C22—2362no—
809C22#95×D5911yescharacteristic
810C22#1683725711yescharacteristic
811C22#1683726411yescharacteristic
812C22#1683727311yescharacteristic
813C22#1683727611yescharacteristic
814C22#1683727811yescharacteristic
815C22#1683728011yescharacteristic
816C22#1683739511yescharacteristic
817C22#1683739511yescharacteristic
818C22#1683739711yescharacteristic
819C22#1683739711yescharacteristic
820C22#1683740011yescharacteristic
821C22#1683740211yescharacteristic
822C22#1683740511yescharacteristic
823C22#1683740911yescharacteristic
824C22#1683743711yescharacteristic
825C22#1683743911yescharacteristic
826C22#1683744111yescharacteristic
827C22#1683744311yescharacteristic
828C22#1683754411yescharacteristic
829C22#1683754611yescharacteristic
830C22#1683754811yescharacteristic
831C22#1683755011yescharacteristic
832C22#1683756111yescharacteristic
833C22#1683756311yescharacteristic
834C22#1683756511yescharacteristic
835C22#1683756711yescharacteristic
836C22#1683772411yescharacteristic
837C22#1683772511yescharacteristic
838C22#1683772811yescharacteristic
839C22#1683772911yescharacteristic
840C22#1683774111yescharacteristic
841C22#1683774211yescharacteristic
842C22#1683774511yescharacteristic
843C22#1683774611yescharacteristic
844C4—44no—
845C4—82no—
846C4—1184no—
847C4—4722no—
848C4—2364no—
849C4#1683724911yescharacteristic
850C4C4×(C2×D59)⋊C411yescharacteristic
851C4#1683725911yescharacteristic
852C4#1683726111yescharacteristic
853C4#1683727311yescharacteristic
854C4#1683727611yescharacteristic
855C4#1683727811yescharacteristic
856C4#1683728011yescharacteristic
857C2—2364no—
858C2(C2×D59)⋊#9511yescharacteristic
859C2#2142381111yescharacteristic
860C2#2142381411yescharacteristic
861C2#2142403311yescharacteristic
862C2#2142403511yescharacteristic
863C2#2142418911yescharacteristic
864C2#2142419011yescharacteristic
865C2#2142429211yescharacteristic
866C2#2142429411yescharacteristic
867C2#2142429611yescharacteristic
868C2#2142429811yescharacteristic
869C2#2142440511yescharacteristic
870C2#2142440711yescharacteristic
871C2#2142441511yescharacteristic
872C2#2142441711yescharacteristic
subgroupG/H
centerC24D4×D59
commutatorC2×C4×C59C2×C42
FrattiniC23×C4C22×D59
FittingC2×C59×#340C2
socleC24×C59C2×D4
prime radicalC24×D59D4
cosocleC23×C4×C59C23
hypercenterC2×#340D59
hypocenterC59#10731
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. C2×#16837165C2semidirect
5. C2×#16837164C2semidirect
6. C2×#16837164C2semidirect
7. C2×C59×#340C2semidirect
15. C2×#14273685C4semidirect
23. C2×(C2×D59)⋊C8C4semidirect
25. #16837259C4semidirect
215. C4⋊C4×C59C22⋊C4semidirect
225. C4⋊Dic59C22⋊C4semidirect
427. C2×#340D59semidirect
470. C59#10731semidirect
667. C4⋊C4(C2×D59)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#142736852
C22×(C2×D59)⋊C82
C2×#168372592
C2×#168371652
C2×#168371642
C2×C59×#3402
#1073159