Finite Group Databasebeta

← #28645863

Subgroups — #28645863

Order 15104.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837689C211yesmaximal, characteristic, complemented
2C22×#14273647C211yesmaximal, characteristic
3C22⋊C4×D236C211yesmaximal, characteristic
4#21425630C211yesmaximal, characteristic, complemented
5#21425467C211yesmaximal, characteristic, complemented
6#21425467C211yesmaximal, characteristic, complemented
7#21425229C211yesmaximal, characteristic, complemented
8#21424356C211yesmaximal, characteristic, complemented
9#21424356C211yesmaximal, characteristic, complemented
10#21424289C211yesmaximal, characteristic, complemented
11#21424276C211yesmaximal, characteristic, complemented
12#21424119C211yesmaximal, characteristic, complemented
13#21424093C211yesmaximal, characteristic, complemented
14#21424026C211yesmaximal, characteristic
15C59×#2440C211yesmaximal, characteristic, complemented
16C23×D236C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18C2×C4×D236C2211yescharacteristic
19C2×C4×D236C2211yescharacteristic
20C2×C22⋊C4×D59—21no—
21#16837689—24no—
22C2×#14273658C2211yescharacteristic, complemented
23C2×#14273658C2211yescharacteristic, complemented
24C2×#14273658C2211yescharacteristic, complemented
25C2×#14273658C2211yescharacteristic, complemented
26C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
27C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
28C2×#14273647—24no—
29C2×#14273647C2211yescharacteristic
30C2×#14273647C2211yescharacteristic
31C2×#14273647C2211yescharacteristic
32C2×#14273647C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×#14273647C2211yescharacteristic
35C2×#14273647C2211yescharacteristic
36C2×#14273647C2211yescharacteristic
37C2×C22⋊(C59⋊C8)C2211yescharacteristic
38#16837304C2211yescharacteristic
39#16837304C2211yescharacteristic
40#16837280—21no—
41#16837280—21no—
42#16837262C2211yescharacteristic
43#16837257—21no—
44#16837164C2211yescharacteristic, complemented
45#16837164C2211yescharacteristic, complemented
46#16837164C2211yescharacteristic, complemented
47#16837164C2211yescharacteristic, complemented
48#16837157C2211yescharacteristic, complemented
49#16837157C2211yescharacteristic, complemented
50C2×C4⋊Q8×C59C2211yescharacteristic, complemented
51C2×C22⋊Q8×C59—21no—
52C22×C4⋊C4×C59C2211yescharacteristic
53C59×#398—21no—
54C59×#395—21no—
55C59×#389C2211yescharacteristic, complemented
56C59×#389C2211yescharacteristic, complemented
57C59×#385—21no—
58C59×#384C2211yescharacteristic, complemented
59C59×#380C2211yescharacteristic
60C4×C22⋊C4×C59C2211yescharacteristic
61C24×D59—21no—
62C22×D236—22no—
63C22×D236—22no—
64C22×D236—21no—
65C22×D236—22no—
66C22×D236—41no—
67C22×D236—41no—
68C22×D236Q814yescomplemented
69C22×D236C2311yescharacteristic
70C22×D236C2311yescharacteristic
71C22×C4×D59—21no—
72C22×C4×D59—21no—
73C22×C59⋊C8—22no—
74C22×C59⋊C8—22no—
75C22×C59⋊C8—41no—
76C22×C59⋊C8C2311yescharacteristic
77C22×C59⋊C8C2311yescharacteristic
78C22×C59⋊C8C2311yescharacteristic
79C22×C59⋊C8C2311yescharacteristic
80C4×D236—22no—
81C4×D236—22no—
82C4×D236—41no—
83C4×D236—41no—
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C4⋊Dic59C2311yescharacteristic
86C2×C22⋊Dic59—21no—
87C2×(C2×D59)⋊C4—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×(C2×D59)⋊C4—21no—
90C2×(C2×D59)⋊C4—21no—
91C2×(C2×D59)⋊C4—21no—
92C2×(C2×D59)⋊C4—21no—
93C22⋊C4×D59—44no—
94#14273658—22no—
95#14273658—22no—
96#14273658—41no—
97#14273658—41no—
98C4⋊(C59⋊C8)—22no—
99C4⋊(C59⋊C8)—41no—
100#14273647—22no—
101#14273647—22no—
102#14273647—22no—
103#14273647—22no—
104#14273647—22no—
105#14273647—41no—
106#14273647—41no—
107#14273647D414yes—
108C22⋊(C59⋊C8)—22no—
109C59⋊#95—21no—
110C22×Q8×C59—21no—
111C23×C4×C59—21no—
112C23×C4×C59C2311yescharacteristic
113C4⋊Q8×C59—22no—
114C4⋊Q8×C59—41no—
115C22⋊Q8×C59—44no—
116C2×C4⋊C4×C59—22no—
117C2×C4⋊C4×C59—21no—
118C2×C4⋊C4×C59—21no—
119C2×C4⋊C4×C59—21no—
120C2×C4⋊C4×C59—21no—
121C2×C4⋊C4×C59—21no—
122C2×C4⋊C4×C59—21no—
123C2×C4⋊C4×C59—41no—
124C2×C4⋊C4×C59C2311yescharacteristic
125C2×C4⋊C4×C59C2311yescharacteristic
126C2×C4⋊C4×C59C2311yescharacteristic
127C2×C4⋊C4×C59C2311yescharacteristic
128C2×C22⋊C4×C59—21no—
129C2×C22⋊C4×C59D411yescharacteristic
130C2×C22⋊C4×C59D411yescharacteristic
131C2×C42×C59C2311yescharacteristic
132C2×C42×C59C2311yescharacteristic
133#95×C59—21no—
134#95×C59—21no—
135#95×C59—21no—
136#95×C59D411yescharacteristic
137#95×C59D411yescharacteristic
138C24×C59C2×D411yescharacteristic
139C23×D59—21no—
140C23×D59—21no—
141C23×D59—24no—
142C23×D59—42no—
143C23×D59—42no—
144C23×D59—42no—
145C23×D59—42no—
146C23×D59—81no—
147C23×D59—81no—
148C2×Q8×C59—42no—
149C2×Q8×C59—42no—
150C2×Q8×C59—81no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—42no—
160C22×C4×C59—42no—
161C22×C4×C59—81no—
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59C2×D411yescharacteristic
166C22×C4×C59C2×D411yescharacteristic
167C22×C4×C59C2×Q812yes—
168C22×C4×C59#4112yes—
169C22×C4×C59C2411yescharacteristic
170C22×Dic59—21no—
171C22×Dic59—21no—
172C2×D236—21no—
173C2×D236—21no—
174C2×D236—21no—
175C2×D236—21no—
176C2×D236—21no—
177C2×D236—21no—
178C2×D236—21no—
179C2×D236—28no—
180C2×D236—24no—
181C2×D236—21no—
182C2×D236—44no—
183C2×D236—44no—
184C2×D236—44no—
185C2×D236—42no—
186C2×D236—42no—
187C2×D236C2×D412yes—
188C2×D236C2×Q812yes—
189C2×D236C2×Q812yes—
190C2×D236#4112yes—
191C2×C4×D59—42no—
192C2×C4×D59—42no—
193C2×C4×D59—42no—
194C2×C4×D59—42no—
195C2×C4×D59—81no—
196C2×C4×D59—81no—
197C4⋊C4×C59—21no—
198C4⋊C4×C59—21no—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—21no—
201C4⋊C4×C59—21no—
202C4⋊C4×C59—21no—
203C4⋊C4×C59—21no—
204C4⋊C4×C59—42no—
205C4⋊C4×C59—42no—
206C4⋊C4×C59—42no—
207C4⋊C4×C59—42no—
208C4⋊C4×C59—42no—
209C4⋊C4×C59—81no—
210C4⋊C4×C59C2×D412yes—
211C22⋊C4×C59—22no—
212C22⋊C4×C59—42no—
213C22⋊C4×C59SD1614yes—
214C42×C59—21no—
215C42×C59—21no—
216C42×C59—21no—
217C42×C59—21no—
218C22⋊Dic59—42no—
219(C2×D59)⋊C4—42no—
220(C2×D59)⋊C4—42no—
221(C2×D59)⋊C4—42no—
222(C2×D59)⋊C4—42no—
223(C2×D59)⋊C4—81no—
224(C2×D59)⋊C4—81no—
225C4⋊Dic59—21no—
226C4⋊Dic59—21no—
227C4⋊Dic59—21no—
228C4⋊Dic59—21no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8—21no—
240C2×C59⋊C8—44no—
241C2×C59⋊C8C2×D412yes—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59C22⋊Q812yes—
247C23×C59C2×SD1612yes—
248C23×C59AGL(1,ℤ/8)12yes—
249C23×C59C22×D411yescharacteristic
250C22×D59—22no—
251C22×D59—22no—
252C22×D59—22no—
253C22×D59—22no—
254C22×D59—48no—
255C22×D59—41no—
256C22×D59—41no—
257C22×D59—41no—
258C22×D59—41no—
259C22×D59—41no—
260C22×D59—41no—
261C22×D59—41no—
262C22×D59—41no—
263C22×D59—41no—
264C22×D59—41no—
265C22×D59—48no—
266C22×D59—84no—
267C22×D59—84no—
268C22×D59—84no—
269C22×D59—84no—
270C22×D59—84no—
271Q8×C59—84no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—21no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—21no—
283C2×C4×C59—22no—
284C2×C4×C59—21no—
285C2×C4×C59—21no—
286C2×C4×C59—21no—
287C2×C4×C59—21no—
288C2×C4×C59—21no—
289C2×C4×C59—41no—
290C2×C4×C59—41no—
291C2×C4×C59—41no—
292C2×C4×C59—41no—
293C2×C4×C59—41no—
294C2×C4×C59—41no—
295C2×C4×C59—41no—
296C2×C4×C59—41no—
297C2×C4×C59—41no—
298C2×C4×C59—41no—
299C2×C4×C59—41no—
300C2×C4×C59—84no—
301C2×C4×C59C22⋊Q812yes—
302C2×C4×C59C2×SD1612yes—
303C2×C4×C59C2×SD1612yes—
304C2×C4×C59C22×D411yescharacteristic
305C2×C4×C59C22×Q811yescharacteristic
306C2×C4×C59C2×#4111yescharacteristic
307C2×C4×C59C2×#4111yescharacteristic
308C2×C4×C59H(5,𝔽2)11yescharacteristic
309C2×C4×C59H(5,𝔽2)11yescharacteristic
310C2×Dic59—41no—
311C2×Dic59—41no—
312C2×Dic59—41no—
313C2×Dic59—41no—
314C2×Dic59—41no—
315C2×Dic59—41no—
316D236—22no—
317D236—22no—
318D236—22no—
319D236—22no—
320D236—22no—
321D236—48no—
322D236—41no—
323D236—41no—
324D236C22⋊Q814yescomplemented
325C4×D59—84no—
326C4×D59—84no—
327C59⋊C8—22no—
328C59⋊C8—41no—
329C59⋊C8—41no—
330C59⋊C8—41no—
331#25958—591nomaximal, Sylow
332C22×C59—22no—
333C22×C59—22no—
334C22×C59—22no—
335C22×C59—22no—
336C22×C59—22no—
337C22×C59—22no—
338C22×C59#47614yescomplemented
339C22×C59C2×C22⋊Q811yescharacteristic
340C22×C59D4211yescharacteristic
341C22×C59#54611yescharacteristic
342C22×C59C22×SD1611yescharacteristic
343C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
344C22×C59#57611yescharacteristic
345C22×C59#57711yescharacteristic
346C2×D59—24no—
347C2×D59—42no—
348C2×D59—42no—
349C2×D59—42no—
350C2×D59—42no—
351C2×D59—42no—
352C2×D59—42no—
353C2×D59—42no—
354C2×D59—42no—
355C2×D59—42no—
356C2×D59—816no—
357C2×D59—81no—
358C2×D59—81no—
359C2×D59—81no—
360C2×D59—81no—
361C4×C59—22no—
362C4×C59—22no—
363C4×C59—22no—
364C4×C59—41no—
365C4×C59—42no—
366C4×C59—41no—
367C4×C59—81no—
368C4×C59—81no—
369C4×C59—81no—
370C4×C59C2×C22⋊Q811yescharacteristic
371C4×C59#54311yescharacteristic
372C4×C59#54611yescharacteristic
373C4×C59#55111yescharacteristic
374Dic59—81no—
375Dic59—81no—
376C2×#476—591no—
377C22×#102—591no—
378#2440D5911yescharacteristic, complemented
379D4×C22⋊C4—591no—
380#2094—591no—
381#2065—591no—
382#2065—591no—
383#2023—591no—
384#1864—591no—
385#1864—591no—
386#1853—591no—
387#1850—591no—
388#1807—591no—
389#1802—591no—
390#1786—591no—
391C2×C59—24no—
392C2×C59#243711yescharacteristic
393C2×C59C2×#47611yescharacteristic
394C2×C59#308111yescharacteristic
395C2×C59#326411yescharacteristic
396C2×C59D4×SD1611yescharacteristic
397C2×C59#329511yescharacteristic
398C2×C59#330611yescharacteristic
399D59—44no—
400D59—82no—
401C23×D4—591no—
402C23×C8—591no—
403C2×C4⋊Q8C2×D5911yescharacteristic, complemented
404C2×C22⋊Q8—21no—
405C2×C4×D4—591no—
406C2×C4×D4—591no—
407C22×C4⋊C4C2×D5911yescharacteristic
408C22×C22⋊C4—1181no—
409#476—1184no—
410C2×#106—591no—
411C2×#106—591no—
412C2×#106—591no—
413C2×#106—591no—
414C2×C4⋊C8—591no—
415C2×C4⋊C8—591no—
416C2×#102—591no—
417C2×#102—591no—
418C2×#102—591no—
419C2×#102—591no—
420C2×#102—591no—
421C2×#102—591no—
422C2×#102—591no—
423C2×#102—591no—
424C2×#102—1184no—
425C2×C22⋊C8—591no—
426#398—21no—
427#395—21no—
428#390—591no—
429#390—591no—
430#389C2×D5911yescharacteristic, complemented
431#389C2×D5911yescharacteristic, complemented
432#386—1181no—
433#386—1181no—
434#385—21no—
435#384C2×D5911yescharacteristic, complemented
436#380—591no—
437#380C2×D5911yescharacteristic
438#379—1181no—
439C4×C22⋊C4C2×D5911yescharacteristic
440#340—591no—
441#340—591no—
442#340—591no—
443#340—591no—
444#336—591no—
445#336—591no—
446C59#2595811yescharacteristic, complemented, Sylow
447C25—1181no—
448C22×Q8—21no—
449C22×D4—594no—
450C22×D4—591no—
451C22×D4—591no—
452C22×D4—1182no—
453C22×D4—1182no—
454C22×D4—1182no—
455C22×D4—1181no—
456C22×D4—2361no—
457C22×D4—2361no—
458C23×C4—21no—
459C23×C4—1181no—
460C23×C4—1181no—
461C23×C4C22×D5911yescharacteristic
462C22×C8—591no—
463C22×C8—591no—
464C22×C8—591no—
465C22×C8—591no—
466C22×C8—1182no—
467C22×C8—1182no—
468C22×C8—2361no—
469C4⋊Q8—22no—
470C4⋊Q8—41no—
471C22⋊Q8—44no—
472C4×D4—1182no—
473C4×D4—1182no—
474C4×D4—2361no—
475C4×D4—2361no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—41no—
484C2×C4⋊C4—591no—
485C2×C4⋊C4—591no—
486C2×C4⋊C4C22×D5911yescharacteristic
487C2×C4⋊C4C22×D5911yescharacteristic
488C2×C4⋊C4C22×D5911yescharacteristic
489C2×C4⋊C4C22×D5911yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—1181no—
492C2×C22⋊C4—1181no—
493C2×C22⋊C4—1181no—
494C2×C22⋊C4—1181no—
495C2×C22⋊C4—1181no—
496C2×C22⋊C4—1181no—
497C2×C22⋊C4—1181no—
498C2×C22⋊C4—2364no—
499C2×C22⋊C4C22⋊D5911yescharacteristic
500C2×C22⋊C4C22⋊D5911yescharacteristic
501C2×C42C22×D5911yescharacteristic
502C2×C42C22×D5911yescharacteristic
503#106—1182no—
504#106—1182no—
505#106—2361no—
506#106—2361no—
507C4⋊C8—1182no—
508C4⋊C8—2361no—
509#102—594no—
510#102—1182no—
511#102—1182no—
512#102—1182no—
513#102—1182no—
514#102—1182no—
515#102—2361no—
516#102—2361no—
517C22⋊C8—1182no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—1181no—
522#95C22⋊D5911yescharacteristic
523#95C22⋊D5911yescharacteristic
524C24—1181no—
525C24—1184no—
526C24—1181no—
527C24—4721no—
528C24—4721no—
529C24—2362no—
530C24—2362no—
531C24—2362no—
532C24—2362no—
533C24C2×C22⋊D5911yescharacteristic
534C2×Q8—42no—
535C2×Q8—42no—
536C2×Q8—81no—
537C2×D4—592no—
538C2×D4—592no—
539C2×D4—592no—
540C2×D4—592no—
541C2×D4—1188no—
542C2×D4—1184no—
543C2×D4—1181no—
544C2×D4—1181no—
545C2×D4—1181no—
546C2×D4—1181no—
547C2×D4—1181no—
548C2×D4—1181no—
549C2×D4—1181no—
550C2×D4—1181no—
551C2×D4—2364no—
552C2×D4—2364no—
553C2×D4—2364no—
554C2×D4—2362no—
555C2×D4—2362no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4—1181no—
568C22×C4—1181no—
569C22×C4—4721no—
570C22×C4—4721no—
571C22×C4—2362no—
572C22×C4—2362no—
573C22×C4—2362no—
574C22×C4—2362no—
575C22×C4Q8×D5912yes—
576C22×C4#1174568912yes—
577C22×C4C2×C22⋊D5911yescharacteristic
578C22×C4C2×C22⋊D5911yescharacteristic
579C22×C4C2×C22⋊D5911yescharacteristic
580C22×C4C2×C22⋊D5911yescharacteristic
581C22×C4C2×C22⋊D5911yescharacteristic
582C22×C4C23×D5911yescharacteristic
583C2×C8—592no—
584C2×C8—1181no—
585C2×C8—1181no—
586C2×C8—1181no—
587C2×C8—1181no—
588C2×C8—1181no—
589C2×C8—1181no—
590C2×C8—1181no—
591C2×C8—1181no—
592C2×C8—1181no—
593C2×C8—1181no—
594C2×C8—1181no—
595C2×C8—2364no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—81no—
609C4⋊C4—1181no—
610C4⋊C4—1181no—
611C4⋊C4—1181no—
612C4⋊C4—1181no—
613C4⋊C4D4×D5912yes—
614C22⋊C4—22no—
615C22⋊C4—42no—
616C22⋊C4—4721no—
617C22⋊C4—4721no—
618C22⋊C4—2362no—
619C22⋊C4—2362no—
620C22⋊C4—2362no—
621C22⋊C4—2362no—
622C22⋊C4—2362no—
623C22⋊C4#1174567114yes—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—1182no—
633C23—1182no—
634C23—1182no—
635C23—1182no—
636C23—4724no—
637C23—4724no—
638C23—4724no—
639C23—4724no—
640C23—4724no—
641C23—2368no—
642C23—2361no—
643C23—2361no—
644C23—2368no—
645C23—2361no—
646C23—2361no—
647C23—2361no—
648C23—2361no—
649C23—2361no—
650C23—2361no—
651C23—2361no—
652C23—2361no—
653C23#1427370312yes—
654C23C2×#1174567112yes—
655C23#1427375312yes—
656C23C22×C22⋊D5911yescharacteristic
657Q8—84no—
658D4—594no—
659D4—1182no—
660D4—1182no—
661D4—1182no—
662D4—1182no—
663D4—1182no—
664D4—2368no—
665D4—2361no—
666D4—2361no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—84no—
696C2×C4—4724no—
697C2×C4—4724no—
698C2×C4—2361no—
699C2×C4—2361no—
700C2×C4—2361no—
701C2×C4—2361no—
702C2×C4—2361no—
703C2×C4—2361no—
704C2×C4#1427370312yes—
705C2×C4C2×#1174567112yes—
706C2×C4C2×#1174567112yes—
707C2×C4C2×D4×D5911yescharacteristic
708C2×C4C2×Q8×D5911yescharacteristic
709C2×C4#41×D5911yescharacteristic
710C2×C4C2×#1174568911yescharacteristic
711C2×C4#1427377211yescharacteristic
712C2×C4#1427377311yescharacteristic
713C8—1182no—
714C8—2361no—
715C8—2361no—
716C8—2361no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—1184no—
724C22—47216no—
725C22—4721no—
726C22—4721no—
727C22—4721no—
728C22—4721no—
729C22—2362no—
730C22—2362no—
731C22—2362no—
732C22—2362no—
733C22—2362no—
734C22—2362no—
735C22—2362no—
736C22—2362no—
737C22—2362no—
738C22#1683768914yescomplemented
739C22C2×#1427370311yescharacteristic
740C22D4×C22⋊D5911yescharacteristic
741C22#1683804011yescharacteristic
742C22C22×#1174567111yescharacteristic
743C22C2×#1427375311yescharacteristic
744C22#1683820511yescharacteristic
745C22#1683821011yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—41no—
751C4—42no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4—4721no—
756C4—4721no—
757C4C22⋊Q8×D5911yescharacteristic
758C4#1683802711yescharacteristic
759C4#1683804311yescharacteristic
760C4#1683807911yescharacteristic
761C2—24no—
762C2—4722no—
763C2—2364no—
764C2#2142775911yescharacteristic
765C2C2×#1683768911yescharacteristic
766C2#2143392111yescharacteristic
767C2#2143557211yescharacteristic
768C2D4×#1174567111yescharacteristic
769C2#2143591411yescharacteristic
770C2#2143605111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2440C2
socleC23×C59C22×D4
prime radicalC23×D236C22
hypercenter#2440D59
hypocenterC59#25958
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2440

Complements

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

NH ≅ G/Ntype
1. C2×#16837689C2semidirect
4. #21425630C2semidirect
5. #21425467C2semidirect
6. #21425467C2semidirect
7. #21425229C2semidirect
8. #21424356C2semidirect
9. #21424356C2semidirect
10. #21424289C2semidirect
11. #21424276C2semidirect
12. #21424119C2semidirect
13. #21424093C2semidirect
15. C59×#2440C2semidirect
22. C2×#14273658C22semidirect
23. C2×#14273658C22semidirect
24. C2×#14273658C22semidirect
25. C2×#14273658C22semidirect
26. C2×C4⋊(C59⋊C8)C22semidirect
27. C2×C4⋊(C59⋊C8)C22semidirect
44. #16837164C22semidirect
45. #16837164C22semidirect
46. #16837164C22semidirect
47. #16837164C22semidirect
48. #16837157C22semidirect
49. #16837157C22semidirect
50. C2×C4⋊Q8×C59C22semidirect
55. C59×#389C22semidirect
56. C59×#389C22semidirect
58. C59×#384C22semidirect
68. C22×D236Q8semidirect
324. D236C22⋊Q8semidirect
338. C22×C59#476semidirect
378. #2440D59semidirect
403. C2×C4⋊Q8C2×D59semidirect
430. #389C2×D59semidirect
431. #389C2×D59semidirect
435. #384C2×D59semidirect
446. C59#25958semidirect
738. C22#16837689semidirect

Maximal subgroups

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

subgroupindex
C2×#168376892
C22×#142736472
C22⋊C4×D2362
#214256302
#214254672
#214252292
#214243562
#214242892
#214242762
#214241192
#214240932
#214240262
C59×#24402
#2595859