Finite Group Databasebeta

← #28604163

Subgroups — #28604163

Order 15104.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838048C211yesmaximal, characteristic
2C2×#16837474C211yesmaximal, characteristic, complemented
3C2×#16837401C211yesmaximal, characteristic, complemented
4C22×#14273647C211yesmaximal, characteristic, complemented
5#21425028C211yesmaximal, characteristic, complemented
6#21424910C211yesmaximal, characteristic, complemented
7#21424532C211yesmaximal, characteristic, complemented
8#21424517C211yesmaximal, characteristic, complemented
9#21424413C211yesmaximal, characteristic, complemented
10#21424403C211yesmaximal, characteristic, complemented
11#21424093C211yesmaximal, characteristic, complemented
12#21424034C211yesmaximal, characteristic, complemented
13#21424026C211yesmaximal, characteristic, complemented
14#21423924C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C59C211yesmaximal, characteristic, complemented
16C22×#11745685C2211yescharacteristic
17C23×D236C2211yescharacteristic
18C22×#11745664C2211yescharacteristic, complemented
19C23×C59⋊C8C2211yescharacteristic
20#16838048—24no—
21#16838048C418yescomplemented
22C2×#14273715C2211yescharacteristic
23C2×#14273712—21no—
24C2×#14273706C2211yescharacteristic
25C2×#14273701C2211yescharacteristic
26C2×#14273700—21no—
27C2×#14273695—21no—
28C2×C4×D236C2211yescharacteristic
29C2×C22⋊C4×D59—21no—
30#16837474—24no—
31C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
32#16837401—24no—
33C2×#14273650C2211yescharacteristic, complemented
34C2×#14273650C2211yescharacteristic, complemented
35C2×#14273650C2211yescharacteristic, complemented
36C2×#14273650C2211yescharacteristic, complemented
37C2×#14273647—24no—
38C2×#14273647C2211yescharacteristic
39C2×#14273647C2211yescharacteristic
40C2×#14273647C2211yescharacteristic
41C2×#14273647C2211yescharacteristic
42C2×#14273647C2211yescharacteristic
43C2×#14273647C2211yescharacteristic
44C2×#14273647C2211yescharacteristic
45C2×#14273647C2211yescharacteristic
46C2×C22⋊(C59⋊C8)C2211yescharacteristic
47C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
48C2×#14273638C2211yescharacteristic, complemented
49#16837164C2211yescharacteristic, complemented
50#16837164C2211yescharacteristic, complemented
51#16837164C2211yescharacteristic, complemented
52#16837164C2211yescharacteristic, complemented
53C2×C4×D4×C59—21no—
54C2×C4×D4×C59C2211yescharacteristic
55C22×C4⋊C4×C59C2211yescharacteristic
56C22×C4⋊C4×C59C2211yescharacteristic, complemented
57C59×#389—21no—
58C59×#385—21no—
59C59×#385—21no—
60C59×#384C2211yescharacteristic, complemented
61C59×#380C2211yescharacteristic
62C59×#380C2211yescharacteristic, complemented
63C4×C4⋊C4×C59C2211yescharacteristic, complemented
64C24×D59—21no—
65C2×#11745685—22no—
66C2×#11745685—22no—
67C2×#11745685—22no—
68C2×#11745685—41no—
69C2×#11745685—41no—
70C2×#11745685C2×C414yescomplemented
71C22×Dic118C2311yescharacteristic
72C22×D236—22no—
73C22×D236—22no—
74C22×D236—21no—
75C22×D236—22no—
76C22×D236—41no—
77C22×D236—41no—
78C22×D236C2×C414yescomplemented
79C22×D236C2311yescharacteristic
80C22×D236C2311yescharacteristic
81C22×C22⋊D59—21no—
82C22×C22⋊D59—21no—
83C22×C4×D59—21no—
84C22×C4×D59—21no—
85C2×#11745664—22no—
86C2×#11745664—22no—
87C2×#11745664—41no—
88C22×C59⋊C8—22no—
89C22×C59⋊C8—22no—
90C22×C59⋊C8—41no—
91C22×C59⋊C8C2311yescharacteristic
92C22×C59⋊C8C2311yescharacteristic
93C22×C59⋊C8C2311yescharacteristic
94C22×C59⋊C8C2311yescharacteristic
95#14273715—22no—
96#14273715C2×C414yescomplemented
97#14273712—28no—
98#14273706—22no—
99#14273706C2×C414yescomplemented
100#14273701—22no—
101#14273701C2×C414yescomplemented
102#14273700—28no—
103#14273695—28no—
104C4×D236—22no—
105C4×D236C2×C414yescomplemented
106C2×C4⋊Dic59C2311yescharacteristic
107C2×Dic59⋊C4—21no—
108C2×C22⋊Dic59—21no—
109C2×(C2×D59)⋊C4—21no—
110C2×(C2×D59)⋊C4—21no—
111C2×(C2×D59)⋊C4—21no—
112C2×(C2×D59)⋊C4—21no—
113C22⋊C4×D59—28no—
114C4⋊(C59⋊C8)—22no—
115#14273650—22no—
116#14273650—22no—
117#14273650—41no—
118#14273650—41no—
119#14273647—22no—
120#14273647—22no—
121#14273647—22no—
122#14273647—22no—
123#14273647—22no—
124#14273647—41no—
125#14273647—41no—
126#14273647D414yescomplemented
127C22⋊(C59⋊C8)—22no—
128C22⋊(C59⋊C8)—22no—
129#14273638—22no—
130C22×D4×C59D411yescharacteristic
131C23×C4×C59—21no—
132C23×C4×C59—21no—
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C4×D4×C59—44no—
136C4×D4×C59C2×C414yes—
137C4×D4×C59D414yes—
138C2×C4⋊C4×C59—22no—
139C2×C4⋊C4×C59—22no—
140C2×C4⋊C4×C59—21no—
141C2×C4⋊C4×C59—21no—
142C2×C4⋊C4×C59—21no—
143C2×C4⋊C4×C59—21no—
144C2×C4⋊C4×C59—41no—
145C2×C4⋊C4×C59—41no—
146C2×C4⋊C4×C59D411yescharacteristic
147C2×C4⋊C4×C59C2311yescharacteristic
148C2×C4⋊C4×C59C2311yescharacteristic
149C2×C4⋊C4×C59C2311yescharacteristic
150C2×C4⋊C4×C59C2311yescharacteristic
151C2×C22⋊C4×C59—21no—
152C2×C22⋊C4×C59—21no—
153C2×C22⋊C4×C59D411yescharacteristic
154C2×C22⋊C4×C59D411yescharacteristic
155C2×C42×C59—21no—
156C2×C42×C59C2311yescharacteristic
157#95×C59—21no—
158#95×C59—21no—
159#95×C59—21no—
160C24×C59C2×D411yescharacteristic
161C24×C59C2×D411yescharacteristic
162C23×D59—21no—
163C23×D59—21no—
164C23×D59—24no—
165C23×D59—42no—
166C23×D59—42no—
167C23×D59—42no—
168C23×D59—42no—
169C23×D59—81no—
170C23×D59—81no—
171C2×D4×C59—22no—
172C2×D4×C59—22no—
173C2×D4×C59C22⋊C414yes—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—42no—
187C22×C4×C59—42no—
188C22×C4×C59—42no—
189C22×C4×C59—42no—
190C22×C4×C59—81no—
191C22×C4×C59—81no—
192C22×C4×C59C22×C412yes—
193C22×C4×C59C22×C412yes—
194C22×C4×C59C2×D411yescharacteristic
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D412yes—
199C22×C4×C59C2×D412yes—
200C22×C4×C59C2411yescharacteristic
201C2×C22⋊D59—24no—
202C2×C22⋊D59—24no—
203C2×C22⋊D59—42no—
204C2×C22⋊D59—42no—
205C2×C22⋊D59—81no—
206C2×C22⋊D59—81no—
207C22×Dic59—21no—
208C22×Dic59—21no—
209#11745685—28no—
210#11745685—44no—
211#11745685—44no—
212#11745685—44no—
213C2×D236—21no—
214C2×D236—21no—
215C2×D236—21no—
216C2×D236—21no—
217C2×D236—21no—
218C2×D236—21no—
219C2×D236—21no—
220C2×D236—28no—
221C2×D236—24no—
222C2×D236—21no—
223C2×D236—44no—
224C2×D236—44no—
225C2×D236—44no—
226C2×D236—42no—
227C2×D236—42no—
228C2×D236C22×C412yes—
229C2×D236C22×C412yes—
230C2×D236C2×D412yes—
231C2×D236#4112yes—
232C2×C4×D59—24no—
233C2×C4×D59—24no—
234C2×C4×D59—42no—
235C2×C4×D59—42no—
236C2×C4×D59—81no—
237C2×C4×D59—81no—
238C2×Dic118—21no—
239C2×Dic118—21no—
240C2×Dic118—21no—
241C2×Dic118—21no—
242C2×Dic118—21no—
243C2×Dic118C22×C412yes—
244C4⋊C4×C59—21no—
245C4⋊C4×C59—21no—
246C4⋊C4×C59—21no—
247C4⋊C4×C59—21no—
248C4⋊C4×C59—21no—
249C4⋊C4×C59—21no—
250C4⋊C4×C59—21no—
251C4⋊C4×C59—42no—
252C4⋊C4×C59—42no—
253C4⋊C4×C59—42no—
254C4⋊C4×C59—81no—
255C4⋊C4×C59C22⋊C414yes—
256C4⋊C4×C59C2×D412yes—
257C22⋊C4×C59—42no—
258C22⋊C4×C59—42no—
259C22⋊C4×C59C22⋊C414yes—
260C22⋊C4×C59C22⋊C414yes—
261C42×C59—42no—
262C42×C59C22×C412yes—
263C42×C59C2×D412yes—
264C22⋊Dic59—24no—
265(C2×D59)⋊C4—24no—
266(C2×D59)⋊C4—24no—
267(C2×D59)⋊C4—24no—
268(C2×D59)⋊C4—24no—
269C4⋊Dic59—21no—
270C4⋊Dic59C22×C412yes—
271Dic59⋊C4—24no—
272#11745664—44no—
273C2×C59⋊C8—21no—
274C2×C59⋊C8—21no—
275C2×C59⋊C8—21no—
276C2×C59⋊C8—21no—
277C2×C59⋊C8—21no—
278C2×C59⋊C8—21no—
279C2×C59⋊C8—21no—
280C2×C59⋊C8—21no—
281C2×C59⋊C8—21no—
282C2×C59⋊C8—21no—
283C2×C59⋊C8—21no—
284C2×C59⋊C8—44no—
285C2×C59⋊C8C2×D412yes—
286C23×C59—21no—
287C23×C59—21no—
288C23×C59—21no—
289C23×C59—21no—
290C23×C59—21no—
291C23×C59—21no—
292C23×C59—21no—
293C23×C59—21no—
294C23×C59—21no—
295C23×C59—21no—
296C23×C59C2×C22⋊C412yes—
297C23×C59C2×C22⋊C412yes—
298C23×C59AGL(1,ℤ/8)12yes—
299C23×C59#13712yes—
300C23×C59C22×D411yescharacteristic
301C22×D59—22no—
302C22×D59—22no—
303C22×D59—22no—
304C22×D59—22no—
305C22×D59—48no—
306C22×D59—41no—
307C22×D59—41no—
308C22×D59—41no—
309C22×D59—41no—
310C22×D59—41no—
311C22×D59—41no—
312C22×D59—41no—
313C22×D59—41no—
314C22×D59—41no—
315C22×D59—41no—
316C22×D59—48no—
317C22×D59—84no—
318C22×D59—84no—
319C22×D59—84no—
320C22×D59—84no—
321C22×D59—84no—
322D4×C59—28no—
323C2×C4×C59—21no—
324C2×C4×C59—21no—
325C2×C4×C59—21no—
326C2×C4×C59—21no—
327C2×C4×C59—21no—
328C2×C4×C59—21no—
329C2×C4×C59—21no—
330C2×C4×C59—21no—
331C2×C4×C59—22no—
332C2×C4×C59—22no—
333C2×C4×C59—22no—
334C2×C4×C59—22no—
335C2×C4×C59—22no—
336C2×C4×C59—22no—
337C2×C4×C59—22no—
338C2×C4×C59—22no—
339C2×C4×C59—22no—
340C2×C4×C59—41no—
341C2×C4×C59—41no—
342C2×C4×C59—41no—
343C2×C4×C59—41no—
344C2×C4×C59—41no—
345C2×C4×C59—41no—
346C2×C4×C59—41no—
347C2×C4×C59—41no—
348C2×C4×C59—41no—
349C2×C4×C59—41no—
350C2×C4×C59—41no—
351C2×C4×C59—84no—
352C2×C4×C59—84no—
353C2×C4×C59C2×C22⋊C412yes—
354C2×C4×C59C2×C22⋊C412yes—
355C2×C4×C59C2×C22⋊C412yes—
356C2×C4×C59C2×C22⋊C412yes—
357C2×C4×C59C23×C411yescharacteristic
358C2×C4×C59C22×D411yescharacteristic
359C2×C4×C59C22×D411yescharacteristic
360C2×C4×C59C2×#4111yescharacteristic
361C2×C4×C59H(5,𝔽2)11yescharacteristic
362C2×C4×C59H(5,𝔽2)11yescharacteristic
363C22⋊D59—48no—
364C22⋊D59—84no—
365C2×Dic59—22no—
366C2×Dic59—22no—
367C2×Dic59—41no—
368C2×Dic59—41no—
369C2×Dic59—41no—
370C2×Dic59—41no—
371D236—22no—
372D236—22no—
373D236—22no—
374D236—22no—
375D236—22no—
376D236—48no—
377D236—41no—
378D236—41no—
379D236C4×D414yescomplemented
380C4×D59—48no—
381C4×D59—84no—
382Dic118—22no—
383Dic118—22no—
384Dic118—41no—
385Dic118—41no—
386C59⋊C8—22no—
387C59⋊C8—41no—
388C59⋊C8—41no—
389C59⋊C8—41no—
390#22419—591nomaximal, Sylow
391C22×C59—22no—
392C22×C59—22no—
393C22×C59—22no—
394C22×C59—22no—
395C22×C59—22no—
396C22×C59—22no—
397C22×C59—22no—
398C22×C59—22no—
399C22×C59—22no—
400C22×C59—41no—
401C22×C59—41no—
402C22×C59—41no—
403C22×C59—41no—
404C22×C59#41714yescomplemented
405C22×C59C22×C22⋊C411yescharacteristic
406C22×C59D4211yescharacteristic
407C22×C59#54611yescharacteristic
408C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C59C2×#13711yescharacteristic
410C22×C59#57611yescharacteristic
411C22×C59#57711yescharacteristic
412C2×D59—24no—
413C2×D59—42no—
414C2×D59—42no—
415C2×D59—42no—
416C2×D59—42no—
417C2×D59—42no—
418C2×D59—42no—
419C2×D59—42no—
420C2×D59—42no—
421C2×D59—42no—
422C2×D59—816no—
423C2×D59—81no—
424C2×D59—81no—
425C2×D59—81no—
426C2×D59—81no—
427C4×C59—22no—
428C4×C59—22no—
429C4×C59—22no—
430C4×C59—22no—
431C4×C59—42no—
432C4×C59—81no—
433C4×C59—81no—
434C4×C59—81no—
435C4×C59C2×C4×D411yescharacteristic
436C4×C59#51811yescharacteristic
437C4×C59D4211yescharacteristic
438C4×C59#54611yescharacteristic
439Dic59—42no—
440Dic59—42no—
441C2×#546—591no—
442C2×#435—591no—
443C2×#417—591no—
444C22×#102—591no—
445D4×C4⋊C4D5911yescharacteristic, complemented
446#1983—591no—
447#1959—591no—
448#1895—591no—
449#1892—591no—
450#1874—591no—
451#1872—591no—
452#1802—591no—
453#1788—591no—
454#1786—591no—
455#1762—591no—
456C2×C59—24no—
457C2×C59—42no—
458C2×C59D4×C22⋊C411yescharacteristic
459C2×C59C2×#41711yescharacteristic
460C2×C59#289711yescharacteristic
461C2×C59#326411yescharacteristic
462C2×C59#326611yescharacteristic
463C2×C59#330611yescharacteristic
464C2×C59#331411yescharacteristic
465D59—44no—
466D59—82no—
467C22×#41—591no—
468C23×D4—591no—
469C22×M16—591no—
470C23×C8—591no—
471#546—598no—
472#546—1184no—
473C2×#124—591no—
474C2×#123—1181no—
475C2×C22⋊Q8—591no—
476C2×#121—591no—
477C2×#121—1181no—
478C2×#120—1181no—
479C2×C4×D4—21no—
480C2×C4×D4—591no—
481C2×C4×D4C2×D5911yescharacteristic
482C22×C4⋊C4C2×D5911yescharacteristic
483C22×C4⋊C4C2×D5911yescharacteristic, complemented
484C22×C22⋊C4—1181no—
485#435—1184no—
486C2×C4⋊C8—591no—
487#417—1184no—
488C2×#103—591no—
489C2×#103—591no—
490C2×#103—591no—
491C2×#103—591no—
492C2×#102—591no—
493C2×#102—591no—
494C2×#102—591no—
495C2×#102—591no—
496C2×#102—591no—
497C2×#102—591no—
498C2×#102—591no—
499C2×#102—591no—
500C2×#102—1184no—
501C2×C22⋊C8—591no—
502C2×C22⋊C8—591no—
503C2×#97—591no—
504#389—21no—
505#385—21no—
506#385—21no—
507#384C2×D5911yescharacteristic, complemented
508#380C2×D5911yescharacteristic
509#380C2×D5911yescharacteristic, complemented
510C4×C4⋊C4C2×D5911yescharacteristic, complemented
511#340—591no—
512#340—591no—
513#340—591no—
514#340—591no—
515C59#2241911yescharacteristic, complemented, Sylow
516C25—1181no—
517C2×#41—594no—
518C2×#41—1182no—
519C2×#41—1182no—
520C2×#41—1182no—
521C2×#41—2361no—
522C2×#41—2361no—
523C22×Q8—591no—
524C22×D4—594no—
525C22×D4—591no—
526C22×D4—591no—
527C22×D4—1182no—
528C22×D4—1182no—
529C22×D4—1181no—
530C22×D4—1181no—
531C22×D4—1182no—
532C22×D4—1181no—
533C22×D4—2361no—
534C22×D4—2361no—
535C22×D4C22⋊D5911yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—1181no—
539C23×C4—1181no—
540C23×C4C22×D5911yescharacteristic
541C23×C4C22×D5911yescharacteristic
542C2×M16—1182no—
543C2×M16—1182no—
544C2×M16—2361no—
545C22×C8—591no—
546C22×C8—591no—
547C22×C8—591no—
548C22×C8—591no—
549C22×C8—1182no—
550C22×C8—1182no—
551C22×C8—2361no—
552#124—594no—
553#124—1182no—
554#123—1188no—
555C22⋊Q8—594no—
556C22⋊Q8—1182no—
557#121—594no—
558#121—1182no—
559#121—1188no—
560#120—1188no—
561C4×D4—44no—
562C4×D4—594no—
563C4×D4—1182no—
564C4×D4C4×D5914yes—
565C4×D4D23614yes—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—591no—
575C2×C4⋊C4—1181no—
576C2×C4⋊C4C22⋊D5911yescharacteristic
577C2×C4⋊C4C22×D5911yescharacteristic
578C2×C4⋊C4C22×D5911yescharacteristic
579C2×C4⋊C4C22×D5911yescharacteristic
580C2×C4⋊C4C22×D5911yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—1181no—
584C2×C22⋊C4—1181no—
585C2×C22⋊C4—1181no—
586C2×C22⋊C4—1181no—
587C2×C22⋊C4—1181no—
588C2×C22⋊C4—1188no—
589C2×C22⋊C4C22⋊D5911yescharacteristic
590C2×C22⋊C4C22⋊D5911yescharacteristic
591C2×C42—21no—
592C2×C42C22×D5911yescharacteristic
593C4⋊C8—1182no—
594#103—1182no—
595#103—1182no—
596#103—2361no—
597#103—2361no—
598#102—594no—
599#102—1182no—
600#102—1182no—
601#102—1182no—
602#102—1182no—
603#102—1182no—
604#102—2361no—
605#102—2361no—
606C22⋊C8—1182no—
607C22⋊C8—1182no—
608#97—1182no—
609#95—21no—
610#95—21no—
611#95—21no—
612C24—1181no—
613C24—1184no—
614C24—1181no—
615C24—4721no—
616C24—4721no—
617C24—2362no—
618C24—2362no—
619C24—2362no—
620C24—2362no—
621C24C2×C22⋊D5911yescharacteristic
622C24C2×C22⋊D5911yescharacteristic
623#41—1188no—
624#41—2364no—
625#41—2364no—
626#41—2364no—
627C2×Q8—592no—
628C2×Q8—1181no—
629C2×Q8—1181no—
630C2×Q8—1181no—
631C2×Q8—1181no—
632C2×Q8—1181no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—592no—
636C2×D4—592no—
637C2×D4—592no—
638C2×D4—592no—
639C2×D4—1188no—
640C2×D4—1184no—
641C2×D4—1184no—
642C2×D4—1184no—
643C2×D4—1181no—
644C2×D4—1181no—
645C2×D4—1181no—
646C2×D4—1181no—
647C2×D4—1181no—
648C2×D4—1181no—
649C2×D4—1181no—
650C2×D4—1181no—
651C2×D4—4721no—
652C2×D4—4721no—
653C2×D4—2364no—
654C2×D4—2364no—
655C2×D4—2364no—
656C2×D4—2362no—
657C2×D4—2362no—
658C2×D4—2362no—
659C2×D4—2362no—
660C2×D4(C2×D59)⋊C414yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—81no—
678C22×C4—81no—
679C22×C4—1181no—
680C22×C4—1181no—
681C22×C4—1184no—
682C22×C4—1184no—
683C22×C4—4721no—
684C22×C4—4721no—
685C22×C4—2362no—
686C22×C4—2362no—
687C22×C4C2×C4×D5912yes—
688C22×C4C2×C4×D5912yes—
689C22×C4C2×D23612yes—
690C22×C4C2×D23612yes—
691C22×C4C2×C22⋊D5911yescharacteristic
692C22×C4C2×C22⋊D5911yescharacteristic
693C22×C4C2×C22⋊D5911yescharacteristic
694C22×C4C2×C22⋊D5911yescharacteristic
695C22×C4C23×D5911yescharacteristic
696M16—2364no—
697C2×C8—592no—
698C2×C8—1181no—
699C2×C8—1181no—
700C2×C8—1181no—
701C2×C8—1181no—
702C2×C8—1181no—
703C2×C8—1181no—
704C2×C8—1181no—
705C2×C8—1181no—
706C2×C8—1181no—
707C2×C8—1181no—
708C2×C8—1181no—
709C2×C8—2364no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—42no—
718C4⋊C4—42no—
719C4⋊C4—42no—
720C4⋊C4—81no—
721C4⋊C4—592no—
722C4⋊C4—1184no—
723C4⋊C4—1181no—
724C4⋊C4(C2×D59)⋊C414yes—
725C4⋊C4D4×D5912yes—
726C22⋊C4—42no—
727C22⋊C4—42no—
728C22⋊C4—1184no—
729C22⋊C4—1184no—
730C22⋊C4—1184no—
731C22⋊C4—1184no—
732C22⋊C4—1184no—
733C22⋊C4(C2×D59)⋊C414yes—
734C22⋊C4(C2×D59)⋊C414yes—
735C42—42no—
736C42C2×C4×D5912yes—
737C42C2×D23612yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—1182no—
749C23—1182no—
750C23—1182no—
751C23—1182no—
752C23—4724no—
753C23—4724no—
754C23—4724no—
755C23—4724no—
756C23—4724no—
757C23—2368no—
758C23—2368no—
759C23—2361no—
760C23—2361no—
761C23—2361no—
762C23—2361no—
763C23—2361no—
764C23—2361no—
765C23—2361no—
766C23—2361no—
767C23—2361no—
768C23—2361no—
769C23C2×(C2×D59)⋊C412yes—
770C23C2×(C2×D59)⋊C412yes—
771C23#1427375312yes—
772C23#1427375812yes—
773C23C22×C22⋊D5911yescharacteristic
774Q8—1182no—
775Q8—1182no—
776Q8—2361no—
777Q8—2361no—
778D4—28no—
779D4—594no—
780D4—1182no—
781D4—1182no—
782D4—1182no—
783D4—1182no—
784D4—1182no—
785D4—4724no—
786D4—2368no—
787D4—2368no—
788D4—2361no—
789D4—2361no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—84no—
819C2×C4—84no—
820C2×C4—1182no—
821C2×C4—1182no—
822C2×C4—4724no—
823C2×C4—2368no—
824C2×C4—2361no—
825C2×C4—2361no—
826C2×C4—2361no—
827C2×C4—2361no—
828C2×C4C2×(C2×D59)⋊C412yes—
829C2×C4C2×(C2×D59)⋊C412yes—
830C2×C4C2×(C2×D59)⋊C412yes—
831C2×C4C2×(C2×D59)⋊C412yes—
832C2×C4C22×C4×D5911yescharacteristic
833C2×C4C2×D4×D5911yescharacteristic
834C2×C4C22×D23611yescharacteristic
835C2×C4#41×D5911yescharacteristic
836C2×C4#1427377211yescharacteristic
837C2×C4#1427377311yescharacteristic
838C8—1182no—
839C8—2361no—
840C8—2361no—
841C8—2361no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—1184no—
856C22—47216no—
857C22—4721no—
858C22—4721no—
859C22—4721no—
860C22—4721no—
861C22—2362no—
862C22—2362no—
863C22—2362no—
864C22—2362no—
865C22—2362no—
866C22—2362no—
867C22—2362no—
868C22—2362no—
869C22—2362no—
870C22#1683740114yescomplemented
871C22C22×(C2×D59)⋊C411yescharacteristic
872C22D4×C22⋊D5911yescharacteristic
873C22#1683804011yescharacteristic
874C22C2×#1427375311yescharacteristic
875C22C2×#1427375811yescharacteristic
876C22#1683820511yescharacteristic
877C22#1683821011yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—81no—
884C4—81no—
885C4—81no—
886C4—2362no—
887C4—2362no—
888C4C4×D4×D5911yescharacteristic
889C4#1683787411yescharacteristic
890C4D4×D23611yescharacteristic
891C4#1683804711yescharacteristic
892C2—24no—
893C2—42no—
894C2—4722no—
895C2—2364no—
896C2D4×(C2×D59)⋊C411yescharacteristic
897C2C2×#1683740111yescharacteristic
898C2#2143261911yescharacteristic
899C2#2143557211yescharacteristic
900C2#2143560711yescharacteristic
901C2#2143605111yescharacteristic
902C2#2143617111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingD4×C4⋊C4×C59C2
socleC23×C59C22×D4
prime radicalC2×#16838048C2
cosocleC22×C4×C59C24
hypercenterD4×C4⋊C4D59
hypocenterC59#22419
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16837474C2semidirect
3. C2×#16837401C2semidirect
4. C22×#14273647C2semidirect
5. #21425028C2semidirect
6. #21424910C2semidirect
7. #21424532C2semidirect
8. #21424517C2semidirect
9. #21424413C2semidirect
10. #21424403C2semidirect
11. #21424093C2semidirect
12. #21424034C2semidirect
13. #21424026C2semidirect
14. #21423924C2semidirect
15. D4×C4⋊C4×C59C2semidirect
18. C22×#11745664C22semidirect
21. #16838048C4semidirect
31. C2×C4⋊(C59⋊C8)C22semidirect
33. C2×#14273650C22semidirect
34. C2×#14273650C22semidirect
35. C2×#14273650C22semidirect
36. C2×#14273650C22semidirect
47. C2×C22⋊(C59⋊C8)C22semidirect
48. C2×#14273638C22semidirect
49. #16837164C22semidirect
50. #16837164C22semidirect
51. #16837164C22semidirect
52. #16837164C22semidirect
56. C22×C4⋊C4×C59C22semidirect
60. C59×#384C22semidirect
62. C59×#380C22semidirect
63. C4×C4⋊C4×C59C22semidirect
70. C2×#11745685C2×C4semidirect
78. C22×D236C2×C4semidirect
96. #14273715C2×C4semidirect
99. #14273706C2×C4semidirect
101. #14273701C2×C4semidirect
105. C4×D236C2×C4semidirect
126. #14273647D4semidirect
379. D236C4×D4semidirect
404. C22×C59#417semidirect
445. D4×C4⋊C4D59semidirect
483. C22×C4⋊C4C2×D59semidirect
507. #384C2×D59semidirect
509. #380C2×D59semidirect
510. C4×C4⋊C4C2×D59semidirect
515. C59#22419semidirect
870. C22#16837401semidirect

Maximal subgroups

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

subgroupindex
C2×#168380482
C2×#168374742
C2×#168374012
C22×#142736472
#214250282
#214249102
#214245322
#214245172
#214244132
#214244032
#214240932
#214240342
#214240262
#214239242
D4×C4⋊C4×C592
#2241959