Finite Group Databasebeta

← #28525333

Subgroups — #28525333

Order 15104.

1814 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837337C212yesmaximal
2C2×#16837300C211yesmaximal, characteristic, complemented
3C2×#16837271C211yesmaximal, characteristic, complemented
4C2×#16837259C211yesmaximal, characteristic
5C2×#16837259C211yesmaximal, characteristic
6C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic
7#21422362C212yesmaximal, complemented
8#21422359C212yesmaximal, complemented
9#21422340C212yesmaximal
10#21422325C211yesmaximal, characteristic, complemented
11C2×C59×#389C211yesmaximal, characteristic, complemented
12C23×C4×D59C2211yescharacteristic
13C22×C4⋊Dic59C2211yescharacteristic
14C22×C4⋊Dic59C2211yescharacteristic
15C22×Dic59⋊C4C2212yes—
16C22×Dic59⋊C4C2212yes—
17C22×Dic59⋊C4C2212yes—
18C22×(C2×D59)⋊C4C2212yes—
19C22×(C2×D59)⋊C4C2212yes—
20C22×(C2×D59)⋊C4C2211yescharacteristic
21C22×(C2×D59)⋊C4C2211yescharacteristic
22C22×C4×Dic59C2211yescharacteristic
23#16837337—28no—
24#16837300—24no—
25#16837271—24no—
26#16837259—24no—
27#16837259—24no—
28C4×(C2×D59)⋊C4—24no—
29C2×C59⋊#95C2212yes—
30C2×C59⋊#95C2212yes—
31C2×C59⋊#95C2211yescharacteristic
32C2×C59⋊#95C2212yes—
33C2×C59⋊#95C2212yes—
34C2×C59⋊#95C2211yescharacteristic
35C2×C59⋊#95C2212yes—
36C22×C4⋊C4×C59C2211yescharacteristic
37C22×C4⋊C4×C59C2212yes—
38C22×C4⋊C4×C59C2211yescharacteristic
39C22×C42×C59C2211yescharacteristic
40C59×#389—24no—
41C2×#95×C59C2212yes—
42C24×D59C2311yescharacteristic
43C23×Dic59C2312yes—
44C23×Dic59C2312yes—
45C23×Dic59C2311yescharacteristic
46C23×Dic59C2311yescharacteristic
47C23×Dic59C2311yescharacteristic
48C22×C4×D59—22no—
49C22×C4×D59—22no—
50C22×C4×D59—22no—
51C22×C4×D59—22no—
52C22×C4×D59—22no—
53C22×C4×D59—22no—
54C22×C4×D59Q814yes—
55C2×C4⋊Dic59—22no—
56C2×C4⋊Dic59—22no—
57C2×C4⋊Dic59—22no—
58C2×C4⋊Dic59—22no—
59C2×C4⋊Dic59—22no—
60C2×C4⋊Dic59D414yes—
61C2×Dic59⋊C4—24no—
62C2×Dic59⋊C4—24no—
63C2×Dic59⋊C4—24no—
64C2×Dic59⋊C4—24no—
65C2×Dic59⋊C4—24no—
66C2×Dic59⋊C4—24no—
67C2×Dic59⋊C4—42no—
68C2×Dic59⋊C4—42no—
69C2×Dic59⋊C4—42no—
70C2×(C2×D59)⋊C4—22no—
71C2×(C2×D59)⋊C4—22no—
72C2×(C2×D59)⋊C4—22no—
73C2×(C2×D59)⋊C4—22no—
74C2×(C2×D59)⋊C4—24no—
75C2×(C2×D59)⋊C4—24no—
76C2×(C2×D59)⋊C4—24no—
77C2×(C2×D59)⋊C4—24no—
78C2×(C2×D59)⋊C4—42no—
79C2×(C2×D59)⋊C4—42no—
80C2×(C2×D59)⋊C4D414yes—
81C2×(C2×D59)⋊C4Q814yes—
82C2×C4×Dic59—22no—
83C2×C4×Dic59—22no—
84C2×C4×Dic59D414yes—
85C59⋊#95—24no—
86C59⋊#95—22no—
87C59⋊#95—22no—
88C59⋊#95—24no—
89C59⋊#95—24no—
90C59⋊#95—24no—
91C59⋊#95—24no—
92C23×C4×C59C2312yes—
93C23×C4×C59C2312yes—
94C23×C4×C59C2311yescharacteristic
95C23×C4×C59C2311yescharacteristic
96C23×C4×C59C2311yescharacteristic
97C2×C4⋊C4×C59—22no—
98C2×C4⋊C4×C59—22no—
99C2×C4⋊C4×C59—24no—
100C2×C4⋊C4×C59—22no—
101C2×C4⋊C4×C59—22no—
102C2×C4⋊C4×C59—22no—
103C2×C4⋊C4×C59—24no—
104C2×C4⋊C4×C59—42no—
105C2×C4⋊C4×C59D414yes—
106C2×C42×C59—22no—
107C2×C42×C59—22no—
108C2×C42×C59—22no—
109#95×C59—24no—
110C24×C59C2411yescharacteristic
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×D59—21no—
122C23×D59—21no—
123C23×D59C2×D412yes—
124C23×D59C2×Q812yes—
125C23×D59C2×Q812yes—
126C22×C4×C59—21no—
127C22×C4×C59—21no—
128C22×C4×C59—21no—
129C22×C4×C59—21no—
130C22×C4×C59—21no—
131C22×C4×C59—21no—
132C22×C4×C59—22no—
133C22×C4×C59—22no—
134C22×C4×C59—22no—
135C22×C4×C59—22no—
136C22×C4×C59—21no—
137C22×C4×C59—21no—
138C22×C4×C59—21no—
139C22×C4×C59—22no—
140C22×C4×C59—21no—
141C22×C4×C59—22no—
142C22×C4×C59—21no—
143C22×C4×C59—21no—
144C22×C4×C59—22no—
145C22×C4×C59—22no—
146C22×C4×C59—22no—
147C22×C4×C59—22no—
148C22×C4×C59—22no—
149C22×C4×C59—22no—
150C22×C4×C59—22no—
151C22×C4×C59C2×D412yes—
152C22×C4×C59C2×D414yes—
153C22×C4×C59C2×D412yes—
154C22×C4×C59C2×D412yes—
155C22×C4×C59C2×D412yes—
156C22×C4×C59C2×Q812yes—
157C22×C4×C59C2×Q812yes—
158C22×C4×C59#4112yes—
159C22×C4×C59#4112yes—
160C22×C4×C59#4112yes—
161C22×Dic59—21no—
162C22×Dic59—21no—
163C22×Dic59—21no—
164C22×Dic59—21no—
165C22×Dic59—21no—
166C22×Dic59—21no—
167C22×Dic59—21no—
168C22×Dic59—21no—
169C22×Dic59—21no—
170C22×Dic59—21no—
171C22×Dic59—21no—
172C22×Dic59—22no—
173C22×Dic59—22no—
174C22×Dic59—22no—
175C22×Dic59—22no—
176C22×Dic59—21no—
177C22×Dic59—21no—
178C22×Dic59—21no—
179C22×Dic59—22no—
180C22×Dic59—22no—
181C22×Dic59—22no—
182C22×Dic59—22no—
183C22×Dic59—22no—
184C22×Dic59—22no—
185C22×Dic59—22no—
186C22×Dic59—22no—
187C22×Dic59—22no—
188C22×Dic59C2×D414yes—
189C22×Dic59C2×D412yes—
190C22×Dic59C2×D412yes—
191C22×Dic59C2×D412yes—
192C22×Dic59C2×Q812yes—
193C22×Dic59C2×Q812yes—
194C22×Dic59#4112yes—
195C22×Dic59#4112yes—
196C2×C4×D59—28no—
197C2×C4×D59—28no—
198C2×C4×D59—28no—
199C2×C4×D59—44no—
200C2×C4×D59—44no—
201C2×C4×D59—44no—
202C2×C4×D59—44no—
203C4⋊C4×C59—28no—
204C4⋊C4×C59—48no—
205C4⋊C4×C59—44no—
206C42×C59—44no—
207(C2×D59)⋊C4—28no—
208(C2×D59)⋊C4—28no—
209(C2×D59)⋊C4—48no—
210(C2×D59)⋊C4—48no—
211C4⋊Dic59—28no—
212C4⋊Dic59—44no—
213Dic59⋊C4—48no—
214Dic59⋊C4—48no—
215Dic59⋊C4—48no—
216C4×Dic59—28no—
217C23×C59C22×D411yescharacteristic
218C23×C59C22×D411yescharacteristic
219C23×C59C22×D411yescharacteristic
220C23×C59C22×D411yescharacteristic
221C23×C59C22×Q811yescharacteristic
222C23×C59C22×Q811yescharacteristic
223C23×C59C2×#4111yescharacteristic
224C23×C59C2×#4111yescharacteristic
225C23×C59C2×#4111yescharacteristic
226C23×C59C2×#4111yescharacteristic
227C23×C59C2×#4111yescharacteristic
228C23×C59H(5,𝔽2)11yescharacteristic
229C23×C59H(5,𝔽2)11yescharacteristic
230C23×C592−1+411yescharacteristic
231C23×C592−1+411yescharacteristic
232C22×D59—22no—
233C22×D59—22no—
234C22×D59—22no—
235C22×D59—22no—
236C22×D59—22no—
237C22×D59—22no—
238C22×D59—22no—
239C22×D59—22no—
240C22×D59—22no—
241C22×D59—22no—
242C22×D59—22no—
243C22×D59—22no—
244C22×D59—22no—
245C22×D59—22no—
246C22×D59—22no—
247C22×D59—22no—
248C22×D59—22no—
249C22×D59—22no—
250C22×D59—41no—
251C22×D59—41no—
252C22×D59—41no—
253C22×D59—41no—
254C22×D59—41no—
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—41no—
266C22×D59C4⋊Q814yes—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
269C2×C4×C59—24no—
270C2×C4×C59—22no—
271C2×C4×C59—24no—
272C2×C4×C59—22no—
273C2×C4×C59—24no—
274C2×C4×C59—22no—
275C2×C4×C59—22no—
276C2×C4×C59—41no—
277C2×C4×C59—41no—
278C2×C4×C59—42no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—42no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—42no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
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—42no—
295C2×C4×C59C22⋊Q814yes—
296C2×C4×C59C22⋊Q814yes—
297C2×C4×C59C22⋊Q814yes—
298C2×C4×C59#12314yes—
299C2×C4×C59#12314yes—
300C2×C4×C59#12314yes—
301C2×C4×C59#12714yes—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—24no—
318C2×Dic59—24no—
319C2×Dic59—24no—
320C2×Dic59—41no—
321C2×Dic59—41no—
322C2×Dic59—41no—
323C2×Dic59—41no—
324C2×Dic59—42no—
325C2×Dic59—42no—
326C2×Dic59—42no—
327C2×Dic59—42no—
328C2×Dic59—42no—
329C2×Dic59—42no—
330C2×Dic59—42no—
331C2×Dic59—42no—
332C2×Dic59—42no—
333C2×Dic59—42no—
334C2×Dic59—42no—
335C2×Dic59#12114yes—
336C2×Dic59C22⋊Q814yes—
337C4×D59—416no—
338#15135—591nomaximal, Sylow
339C22×C59C2×#12111yescharacteristic
340C22×C59C2×C22⋊Q811yescharacteristic
341C22×C59C2×C22⋊Q811yescharacteristic
342C22×C59C2×C22⋊Q811yescharacteristic
343C22×C59C2×C22⋊Q811yescharacteristic
344C22×C59C2×#12311yescharacteristic
345C22×C59C2×#12311yescharacteristic
346C22×C59C2×#12311yescharacteristic
347C22×C59C2×#12711yescharacteristic
348C22×C59C2×C4⋊Q811yescharacteristic
349C22×C59#53211yescharacteristic
350C22×C59#53311yescharacteristic
351C22×C59#53311yescharacteristic
352C22×C59#53511yescharacteristic
353C22×C59#53611yescharacteristic
354C22×C59#54211yescharacteristic
355C22×C59#54211yescharacteristic
356C22×C59#54411yescharacteristic
357C22×C59#54411yescharacteristic
358C22×C59D4211yescharacteristic
359C22×C59D4211yescharacteristic
360C22×C59#54711yescharacteristic
361C22×C59#54711yescharacteristic
362C22×C59#54711yescharacteristic
363C22×C59#54711yescharacteristic
364C22×C59D4×Q811yescharacteristic
365C22×C59D4×Q811yescharacteristic
366C22×C59#55011yescharacteristic
367C22×C59#55011yescharacteristic
368C22×C59#55211yescharacteristic
369C22×C59#55211yescharacteristic
370C22×C59#55311yescharacteristic
371C22×C59#55311yescharacteristic
372C22×C59#55411yescharacteristic
373C22×C59#55411yescharacteristic
374C2×D59—24no—
375C2×D59—24no—
376C2×D59—24no—
377C2×D59—42no—
378C2×D59—42no—
379C2×D59—42no—
380C2×D59—42no—
381C2×D59—42no—
382C2×D59—42no—
383C2×D59—42no—
384C2×D59—42no—
385C2×D59—42no—
386C2×D59—42no—
387C2×D59—42no—
388C2×D59—42no—
389C4×C59—44no—
390C4×C59—42no—
391C4×C59—42no—
392C4×C59—82no—
393C4×C59#39918yescomplemented
394Dic59—24no—
395Dic59—24no—
396Dic59—42no—
397Dic59—44no—
398Dic59—82no—
399C2×#399—592no—
400C2×#389—591no—
401C2×#389D5911yescharacteristic, complemented
402C2×#384—591no—
403C2×#380—591no—
404C2×#380—591no—
405C2×C4×C22⋊C4—591no—
406#1445—592no—
407#1444—592no—
408#1439—592no—
409C4⋊#95—591no—
410C2×C59C2×#39911yescharacteristic
411C2×C59#242211yescharacteristic
412C2×C59#242211yescharacteristic
413C2×C59#242311yescharacteristic
414C2×C59#242311yescharacteristic
415C2×C59#244011yescharacteristic
416C2×C59#244011yescharacteristic
417C2×C59#244111yescharacteristic
418C2×C59#244111yescharacteristic
419C2×C59#248611yescharacteristic
420C2×C59#248711yescharacteristic
421C2×C59#254111yescharacteristic
422C2×C59#254211yescharacteristic
423C2×C59#262811yescharacteristic
424C2×C59#285711yescharacteristic
425D59—44no—
426C24×C4—591no—
427C22×C4⋊C4—591no—
428C22×C4⋊C4—592no—
429C22×C4⋊C4—591no—
430C22×C4⋊C4—592no—
431C22×C4⋊C4—592no—
432C22×C4⋊C4C2×D5911yescharacteristic
433C22×C4⋊C4C2×D5912yes—
434C22×C4⋊C4C2×D5911yescharacteristic
435C22×C22⋊C4—591no—
436C22×C22⋊C4—591no—
437C22×C22⋊C4—592no—
438C22×C22⋊C4—592no—
439C22×C42—591no—
440C22×C42C2×D5911yescharacteristic
441#399—1188no—
442#389—24no—
443#389—1184no—
444#384—1184no—
445#380—1184no—
446#380—1184no—
447C4×C22⋊C4—1184no—
448C2×#95—592no—
449C2×#95—592no—
450C2×#95—592no—
451C2×#95—591no—
452C2×#95—592no—
453C2×#95—592no—
454C2×#95—591no—
455C2×#95C2×D5912yes—
456C59#1513511yescharacteristic, complemented, Sylow
457C25—591no—
458C23×C4—591no—
459C23×C4—591no—
460C23×C4—592no—
461C23×C4—591no—
462C23×C4—594no—
463C23×C4—592no—
464C23×C4—1182no—
465C23×C4—1182no—
466C23×C4—1182no—
467C23×C4—1182no—
468C23×C4—1182no—
469C23×C4—1182no—
470C23×C4C22×D5912yes—
471C23×C4C22×D5911yescharacteristic
472C23×C4C22×D5911yescharacteristic
473C23×C4C22×D5912yes—
474C23×C4C22×D5911yescharacteristic
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—594no—
484C2×C4⋊C4—1182no—
485C2×C4⋊C4—1182no—
486C2×C4⋊C4—1184no—
487C2×C4⋊C4—1184no—
488C2×C4⋊C4—1184no—
489C2×C4⋊C4—1184no—
490C2×C4⋊C4—1184no—
491C2×C4⋊C4—1182no—
492C2×C4⋊C4—1182no—
493C2×C4⋊C4—1184no—
494C2×C4⋊C4—1182no—
495C2×C4⋊C4—2362no—
496C2×C4⋊C4—2362no—
497C2×C4⋊C4—2362no—
498C2×C4⋊C4C22⋊D5914yes—
499C2×C22⋊C4—594no—
500C2×C22⋊C4—594no—
501C2×C22⋊C4—1182no—
502C2×C22⋊C4—1182no—
503C2×C22⋊C4—1182no—
504C2×C22⋊C4—1182no—
505C2×C22⋊C4—1184no—
506C2×C22⋊C4—1184no—
507C2×C22⋊C4—1184no—
508C2×C22⋊C4—1184no—
509C2×C22⋊C4—2362no—
510C2×C22⋊C4—2362no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—22no—
514C2×C42—594no—
515C2×C42—1182no—
516C2×C42—1182no—
517#95—24no—
518#95—1184no—
519#95—1182no—
520#95—1182no—
521#95—1184no—
522#95—1184no—
523#95—1184no—
524#95—1184no—
525C24—592no—
526C24—592no—
527C24—592no—
528C24—1181no—
529C24—1181no—
530C24—1181no—
531C24—1181no—
532C24—1181no—
533C24—1181no—
534C24—1181no—
535C24—1181no—
536C24—1181no—
537C24—1181no—
538C24—1181no—
539C24—1181no—
540C24C23×D5911yescharacteristic
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—592no—
567C22×C4—592no—
568C22×C4—592no—
569C22×C4—592no—
570C22×C4—592no—
571C22×C4—592no—
572C22×C4—594no—
573C22×C4—592no—
574C22×C4—1181no—
575C22×C4—1181no—
576C22×C4—1181no—
577C22×C4—1181no—
578C22×C4—1181no—
579C22×C4—1181no—
580C22×C4—1181no—
581C22×C4—1181no—
582C22×C4—1181no—
583C22×C4—1181no—
584C22×C4—1182no—
585C22×C4—1181no—
586C22×C4—1182no—
587C22×C4—1182no—
588C22×C4—1181no—
589C22×C4—1181no—
590C22×C4—1182no—
591C22×C4—1181no—
592C22×C4—1182no—
593C22×C4—1182no—
594C22×C4—1188no—
595C22×C4—1188no—
596C22×C4—1188no—
597C22×C4—1182no—
598C22×C4—1182no—
599C22×C4—1182no—
600C22×C4—1182no—
601C22×C4—1182no—
602C22×C4—1182no—
603C22×C4—1182no—
604C22×C4—2364no—
605C22×C4—2364no—
606C22×C4—2364no—
607C22×C4—2364no—
608C22×C4#1174568512yes—
609C22×C4#1174568512yes—
610C22×C4D4×D5912yes—
611C22×C4D4×D5912yes—
612C22×C4D4×D5912yes—
613C22×C4Q8×D5912yes—
614C22×C4Q8×D5912yes—
615C22×C4#1174568912yes—
616C22×C4C2×C22⋊D5914yes—
617C22×C4C2×C22⋊D5912yes—
618C4⋊C4—28no—
619C4⋊C4—48no—
620C4⋊C4—44no—
621C4⋊C4—1188no—
622C4⋊C4—2368no—
623C4⋊C4—2368no—
624C4⋊C4—2368no—
625C4⋊C4—2364no—
626C22⋊C4—1188no—
627C22⋊C4—1188no—
628C22⋊C4—2368no—
629C22⋊C4—2368no—
630C42—44no—
631C42—1188no—
632C23—594no—
633C23—1182no—
634C23—1182no—
635C23—1182no—
636C23—1182no—
637C23—1182no—
638C23—1182no—
639C23—1182no—
640C23—1182no—
641C23—1182no—
642C23—1182no—
643C23—1182no—
644C23—1182no—
645C23—1182no—
646C23—1182no—
647C23—1182no—
648C23—1182no—
649C23—1182no—
650C23—1182no—
651C23—2361no—
652C23—2361no—
653C23—2361no—
654C23—2361no—
655C23—2361no—
656C23—2361no—
657C23—2361no—
658C23—2361no—
659C23—2361no—
660C23—2361no—
661C23—2361no—
662C23—2361no—
663C23—2361no—
664C23—2361no—
665C23—2361no—
666C23—2361no—
667C23C2×D4×D5911yescharacteristic
668C23C2×D4×D5911yescharacteristic
669C23C2×D4×D5911yescharacteristic
670C23C22×C22⋊D5911yescharacteristic
671C23C2×Q8×D5911yescharacteristic
672C23C2×Q8×D5911yescharacteristic
673C23#41×D5911yescharacteristic
674C23#41×D5911yescharacteristic
675C23C2×#1174568511yescharacteristic
676C23C2×#1174568511yescharacteristic
677C23C2×#1174568911yescharacteristic
678C23#1427377211yescharacteristic
679C23#1427377311yescharacteristic
680C23#1427377411yescharacteristic
681C23#1427377511yescharacteristic
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—594no—
711C2×C4—594no—
712C2×C4—1182no—
713C2×C4—1182no—
714C2×C4—1182no—
715C2×C4—1182no—
716C2×C4—1182no—
717C2×C4—1182no—
718C2×C4—1182no—
719C2×C4—1182no—
720C2×C4—1182no—
721C2×C4—1182no—
722C2×C4—1182no—
723C2×C4—1182no—
724C2×C4—1182no—
725C2×C4—1182no—
726C2×C4—1182no—
727C2×C4—1184no—
728C2×C4—1184no—
729C2×C4—1184no—
730C2×C4—2362no—
731C2×C4—2362no—
732C2×C4—2362no—
733C2×C4—2362no—
734C2×C4—2362no—
735C2×C4—2362no—
736C2×C4—2362no—
737C2×C4—2361no—
738C2×C4—2361no—
739C2×C4—2361no—
740C2×C4—2361no—
741C2×C4—2362no—
742C2×C4—2362no—
743C2×C4—2362no—
744C2×C4—2362no—
745C2×C4—23616no—
746C2×C4#1427370314yes—
747C2×C4#1427370514yes—
748C2×C4#1427370514yes—
749C2×C4#1427371014yes—
750C2×C4#1427371214yes—
751C2×C4#1427371214yes—
752C2×C4#1427372314yes—
753C22—1184no—
754C22—1184no—
755C22—1184no—
756C22—2362no—
757C22—2362no—
758C22—2362no—
759C22—2362no—
760C22—2362no—
761C22—2362no—
762C22—2362no—
763C22—2362no—
764C22—2362no—
765C22—2362no—
766C22—2362no—
767C22—2362no—
768C22#121×D5911yescharacteristic
769C22C22⋊Q8×D5911yescharacteristic
770C22C2×#1427370311yescharacteristic
771C22C2×#1427370511yescharacteristic
772C22C2×#1427370511yescharacteristic
773C22C2×#1427371011yescharacteristic
774C22C2×#1427371211yescharacteristic
775C22C2×#1427371211yescharacteristic
776C22C2×#1427372311yescharacteristic
777C22C4⋊Q8×D5911yescharacteristic
778C22#1683794911yescharacteristic
779C22#1683795611yescharacteristic
780C22#1683795811yescharacteristic
781C22#1683796811yescharacteristic
782C22#1683797511yescharacteristic
783C22#1683801711yescharacteristic
784C22#1683802411yescharacteristic
785C22#1683802911yescharacteristic
786C22#1683803211yescharacteristic
787C22D4×C22⋊D5911yescharacteristic
788C22#1683803611yescharacteristic
789C22#1683805111yescharacteristic
790C22#1683805411yescharacteristic
791C22#1683805511yescharacteristic
792C22#1683805711yescharacteristic
793C22#1683806511yescharacteristic
794C22Q8×C22⋊D5911yescharacteristic
795C22#1683807011yescharacteristic
796C22#1683807111yescharacteristic
797C22#1683809011yescharacteristic
798C22#1683809311yescharacteristic
799C22#1683810211yescharacteristic
800C22#1683810511yescharacteristic
801C22#1683811211yescharacteristic
802C22#1683811311yescharacteristic
803C4—42no—
804C4—42no—
805C4—44no—
806C4—82no—
807C4—1184no—
808C4—1184no—
809C4—4722no—
810C4—2362no—
811C4—2364no—
812C4#1683733718yescomplemented
813C2—2364no—
814C2C2×#1683733711yescharacteristic
815C2#2142760411yescharacteristic
816C2#2142761111yescharacteristic
817C2#2142761511yescharacteristic
818C2#2142762211yescharacteristic
819C2#2142779411yescharacteristic
820C2#2142780011yescharacteristic
821C2#2142780511yescharacteristic
822C2#2142781111yescharacteristic
823C2#2142840211yescharacteristic
824C2#2142841111yescharacteristic
825C2#2142903911yescharacteristic
826C2#2142904611yescharacteristic
827C2#2142992311yescharacteristic
828C2#2143244711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutator, socle, cosocleC24×C59C24
FittingC2×C59×#389C2
prime radicalC24×D59C23
hypercenterC2×#389D59
hypocenterC59#15135
LCSG ▷ C24×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#16837300C2semidirect
3. C2×#16837271C2semidirect
7. #21422362C2semidirect
8. #21422359C2semidirect
10. #21422325C2semidirect
11. C2×C59×#389C2semidirect
393. C4×C59#399semidirect
401. C2×#389D59semidirect
456. C59#15135semidirect
812. C4#16837337semidirect

Maximal subgroups

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

subgroupindex
C2×#168373372
C2×#168373002
C2×#168372712
C2×#168372592
C2×C4×(C2×D59)⋊C42
#214223622
#214223592
#214223402
#214223252
C2×C59×#3892
#1513559