Finite Group Databasebeta

← #28515114

Subgroups — #28515114

Order 15104.

1926 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273684C211yesmaximal, characteristic
2C2×#16837298C211yesmaximal, characteristic, complemented
3C2×#16837259C211yesmaximal, characteristic
4C2×#16837259C211yesmaximal, characteristic
5#21422359C212yesmaximal, complemented
6#21422354C212yesmaximal, complemented
7#21422340C212yesmaximal
8#21422338C212yesmaximal
9#21422326C211yesmaximal, characteristic, complemented
10#21422325C211yesmaximal, characteristic, complemented
11C2×C59×#389C211yesmaximal, characteristic, complemented
12C23×C4×D59C2211yescharacteristic
13C2×#14273684—24no—
14C2×#14273684—24no—
15C2×#14273684—24no—
16C22×C4⋊Dic59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×Dic59⋊C4C2211yescharacteristic
19C22×Dic59⋊C4C2211yescharacteristic
20C22×Dic59⋊C4C2212yes—
21C22×(C2×D59)⋊C4C2211yescharacteristic
22C22×(C2×D59)⋊C4C2211yescharacteristic
23C22×(C2×D59)⋊C4C2212yes—
24C22×(C2×D59)⋊C4C2212yes—
25C22×C4×Dic59C2211yescharacteristic
26#16837298—24no—
27#16837259—24no—
28#16837259C418yescomplemented
29C2×C59⋊#95C2212yes—
30C2×C59⋊#95C2212yes—
31C2×C59⋊#95C2212yes—
32C2×C59⋊#95C2212yes—
33C2×C59⋊#95C2212yes—
34C2×C59⋊#95C2212yes—
35C2×C59⋊#95C2212yes—
36C22×C4⋊C4×C59C2211yescharacteristic
37C22×C4⋊C4×C59C2211yescharacteristic
38C22×C4⋊C4×C59C2212yes—
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×D59C2×C414yes—
53C22×C4×D59D414yes—
54C22×C4×D59Q814yes—
55#14273684—232no—
56C2×C4⋊Dic59—22no—
57C2×C4⋊Dic59—22no—
58C2×C4⋊Dic59—22no—
59C2×C4⋊Dic59—22no—
60C2×C4⋊Dic59—22no—
61C2×C4⋊Dic59C2×C414yes—
62C2×Dic59⋊C4—22no—
63C2×Dic59⋊C4—22no—
64C2×Dic59⋊C4—22no—
65C2×Dic59⋊C4—22no—
66C2×Dic59⋊C4—22no—
67C2×Dic59⋊C4—22no—
68C2×Dic59⋊C4—24no—
69C2×Dic59⋊C4—42no—
70C2×Dic59⋊C4—42no—
71C2×(C2×D59)⋊C4—22no—
72C2×(C2×D59)⋊C4—22no—
73C2×(C2×D59)⋊C4—22no—
74C2×(C2×D59)⋊C4—22no—
75C2×(C2×D59)⋊C4—22no—
76C2×(C2×D59)⋊C4—22no—
77C2×(C2×D59)⋊C4—24no—
78C2×(C2×D59)⋊C4—42no—
79C2×(C2×D59)⋊C4—42no—
80C2×(C2×D59)⋊C4—42no—
81C2×(C2×D59)⋊C4—42no—
82C2×(C2×D59)⋊C4C2×C418yes—
83C2×C4×Dic59—22no—
84C2×C4×Dic59—22no—
85C2×C4×Dic59D414yes—
86C59⋊#95—24no—
87C59⋊#95—24no—
88C59⋊#95—42no—
89C59⋊#95—42no—
90C59⋊#95—42no—
91C59⋊#95—42no—
92C59⋊#95C2×C418yes—
93C23×C4×C59C2312yes—
94C23×C4×C59C2312yes—
95C23×C4×C59C2311yescharacteristic
96C23×C4×C59C2311yescharacteristic
97C23×C4×C59C2311yescharacteristic
98C2×C4⋊C4×C59—22no—
99C2×C4⋊C4×C59—22no—
100C2×C4⋊C4×C59—24no—
101C2×C4⋊C4×C59—22no—
102C2×C4⋊C4×C59—22no—
103C2×C4⋊C4×C59—22no—
104C2×C4⋊C4×C59—42no—
105C2×C4⋊C4×C59—42no—
106C2×C4⋊C4×C59C2×C414yes—
107C2×C42×C59—22no—
108C2×C42×C59—22no—
109C2×C42×C59D414yes—
110#95×C59—24no—
111C24×C59C2411yescharacteristic
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×D59—21no—
124C23×D59C22×C412yes—
125C23×D59C2×D412yes—
126C23×D59C2×Q812yes—
127C22×C4×C59—22no—
128C22×C4×C59—21no—
129C22×C4×C59—21no—
130C22×C4×C59—21no—
131C22×C4×C59—21no—
132C22×C4×C59—22no—
133C22×C4×C59—21no—
134C22×C4×C59—21no—
135C22×C4×C59—22no—
136C22×C4×C59—22no—
137C22×C4×C59—21no—
138C22×C4×C59—21no—
139C22×C4×C59—22no—
140C22×C4×C59—22no—
141C22×C4×C59—21no—
142C22×C4×C59—21no—
143C22×C4×C59—21no—
144C22×C4×C59—21no—
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×C59—22no—
152C22×C4×C59C22×C414yes—
153C22×C4×C59C22×C412yes—
154C22×C4×C59C2×D412yes—
155C22×C4×C59C2×D412yes—
156C22×C4×C59C2×D412yes—
157C22×C4×C59C2×D412yes—
158C22×C4×C59C2×D412yes—
159C22×C4×C59C2×Q812yes—
160C22×C4×C59#4112yes—
161C22×C4×C59#4112yes—
162C22×Dic59—21no—
163C22×Dic59—21no—
164C22×Dic59—21no—
165C22×Dic59—21no—
166C22×Dic59—22no—
167C22×Dic59—21no—
168C22×Dic59—21no—
169C22×Dic59—21no—
170C22×Dic59—21no—
171C22×Dic59—22no—
172C22×Dic59—21no—
173C22×Dic59—21no—
174C22×Dic59—22no—
175C22×Dic59—22no—
176C22×Dic59—22no—
177C22×Dic59—21no—
178C22×Dic59—21no—
179C22×Dic59—22no—
180C22×Dic59—21no—
181C22×Dic59—21no—
182C22×Dic59—21no—
183C22×Dic59—21no—
184C22×Dic59—22no—
185C22×Dic59—22no—
186C22×Dic59—22no—
187C22×Dic59—22no—
188C22×Dic59—22no—
189C22×Dic59—22no—
190C22×Dic59—22no—
191C22×Dic59C22×C414yes—
192C22×Dic59C22×C412yes—
193C22×Dic59C2×D412yes—
194C22×Dic59C2×D412yes—
195C22×Dic59C2×D412yes—
196C22×Dic59C2×Q812yes—
197C2×C4×D59—28no—
198C2×C4×D59—28no—
199C2×C4×D59—28no—
200C2×C4×D59—28no—
201C2×C4×D59—28no—
202C2×C4×D59—28no—
203C2×C4×D59C4⋊C4116yescomplemented
204C4⋊C4×C59—28no—
205C4⋊C4×C59—48no—
206C4⋊C4×C59—44no—
207C42×C59—28no—
208(C2×D59)⋊C4—28no—
209(C2×D59)⋊C4—28no—
210(C2×D59)⋊C4—48no—
211(C2×D59)⋊C4—48no—
212C4⋊Dic59—28no—
213C4⋊Dic59—44no—
214Dic59⋊C4—28no—
215Dic59⋊C4—28no—
216Dic59⋊C4—48no—
217C4×Dic59—28no—
218C23×C59C23×C411yescharacteristic
219C23×C59C22×D411yescharacteristic
220C23×C59C22×D411yescharacteristic
221C23×C59C22×D411yescharacteristic
222C23×C59C22×Q811yescharacteristic
223C23×C59C2×#4111yescharacteristic
224C23×C59C2×#4111yescharacteristic
225C23×C59H(5,𝔽2)11yescharacteristic
226C23×C59H(5,𝔽2)11yescharacteristic
227C23×C59H(5,𝔽2)11yescharacteristic
228C23×C59H(5,𝔽2)11yescharacteristic
229C23×C592−1+411yescharacteristic
230C23×C592−1+411yescharacteristic
231C23×C592−1+411yescharacteristic
232C23×C592−1+411yescharacteristic
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—22no—
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×D59—41no—
267C22×D59C2×C4⋊C414yes—
268C2×C4×C59—24no—
269C2×C4×C59—24no—
270C2×C4×C59—24no—
271C2×C4×C59—22no—
272C2×C4×C59—22no—
273C2×C4×C59—22no—
274C2×C4×C59—22no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—42no—
278C2×C4×C59—41no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—42no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
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×C59—42no—
296C2×C4×C59C2×C4⋊C414yes—
297C2×C4×C59C4×D414yes—
298C2×C4×C59C4×D414yes—
299C2×C4×C59#12014yes—
300C2×C4×C59C22⋊Q814yes—
301C2×C4×C59C22⋊Q814yes—
302C2×C4×C59#12314yes—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—24no—
310C2×Dic59—24no—
311C2×Dic59—24no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—42no—
319C2×Dic59—41no—
320C2×Dic59—41no—
321C2×Dic59—41no—
322C2×Dic59—41no—
323C2×Dic59—41no—
324C2×Dic59—41no—
325C2×Dic59—41no—
326C2×Dic59—42no—
327C2×Dic59—41no—
328C2×Dic59—42no—
329C2×Dic59—42no—
330C2×Dic59—42no—
331C2×Dic59—42no—
332C2×Dic59—42no—
333C2×Dic59—42no—
334C2×Dic59—42no—
335C2×Dic59—42no—
336C2×Dic59—42no—
337C2×Dic59C2×C4⋊C414yes—
338C4×D59—232no—
339#14264—591nomaximal, Sylow
340C22×C59C22×C4⋊C411yescharacteristic
341C22×C59C2×C4×D411yescharacteristic
342C22×C59C2×C4×D411yescharacteristic
343C22×C59#51811yescharacteristic
344C22×C59#51911yescharacteristic
345C22×C59#52011yescharacteristic
346C22×C59#52011yescharacteristic
347C22×C59C2×#12011yescharacteristic
348C22×C59C2×C22⋊Q811yescharacteristic
349C22×C59C2×C22⋊Q811yescharacteristic
350C22×C59C2×#12311yescharacteristic
351C22×C59#53511yescharacteristic
352C22×C59#53511yescharacteristic
353C22×C59#53511yescharacteristic
354C22×C59#53611yescharacteristic
355C22×C59#53611yescharacteristic
356C22×C59#53611yescharacteristic
357C22×C59#53711yescharacteristic
358C22×C59#53711yescharacteristic
359C22×C59#53711yescharacteristic
360C22×C59#53711yescharacteristic
361C22×C59#53711yescharacteristic
362C22×C59#53711yescharacteristic
363C22×C59#54011yescharacteristic
364C22×C59#54011yescharacteristic
365C22×C59#54111yescharacteristic
366C22×C59#54111yescharacteristic
367C22×C59#54211yescharacteristic
368C22×C59#54211yescharacteristic
369C22×C59#54211yescharacteristic
370C22×C59#54211yescharacteristic
371C22×C59#54411yescharacteristic
372C22×C59#54411yescharacteristic
373C22×C59#54411yescharacteristic
374C22×C59#54411yescharacteristic
375C2×D59—24no—
376C2×D59—24no—
377C2×D59—24no—
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—
389C2×D59—42no—
390C4×C59—44no—
391C4×C59—42no—
392C4×C59—42no—
393C4×C59—82no—
394C4×C59#38518yes—
395Dic59—24no—
396Dic59—44no—
397Dic59—42no—
398Dic59—42no—
399Dic59—82no—
400C22×#117—591no—
401C2×#389—591no—
402C2×#389D5911yescharacteristic, complemented
403C2×#380—591no—
404C2×#380—591no—
405#1444—592no—
406#1442—592no—
407#1439—592no—
408#1439—592no—
409C4⋊#95—591no—
410C4⋊#95—591no—
411C2×C59C2×#38511yescharacteristic
412C2×C59#231611yescharacteristic
413C2×C59#231711yescharacteristic
414C2×C59#232311yescharacteristic
415C2×C59#232311yescharacteristic
416C2×C59#232411yescharacteristic
417C2×C59#232411yescharacteristic
418C2×C59#261511yescharacteristic
419C2×C59#261611yescharacteristic
420C2×C59#262411yescharacteristic
421C2×C59#262511yescharacteristic
422C2×C59#262811yescharacteristic
423C2×C59#262811yescharacteristic
424C2×C59#262911yescharacteristic
425C2×C59#262911yescharacteristic
426D59—44no—
427C24×C4—591no—
428C2×#117—1184no—
429C2×#117—1184no—
430C2×#117—1184no—
431C22×C4⋊C4—591no—
432C22×C4⋊C4—591no—
433C22×C4⋊C4—591no—
434C22×C4⋊C4—591no—
435C22×C4⋊C4—592no—
436C22×C4⋊C4C2×D5911yescharacteristic
437C22×C4⋊C4C2×D5911yescharacteristic
438C22×C4⋊C4C2×D5912yes—
439C22×C22⋊C4—592no—
440C22×C22⋊C4—591no—
441C22×C22⋊C4—591no—
442C22×C22⋊C4—592no—
443C22×C42—591no—
444C22×C42C2×D5911yescharacteristic
445#389—24no—
446#389—1184no—
447#380—598no—
448#380—1184no—
449C2×#95—592no—
450C2×#95—592no—
451C2×#95—592no—
452C2×#95—592no—
453C2×#95—592no—
454C2×#95—592no—
455C2×#95—592no—
456C2×#95C2×D5912yes—
457C59#1426411yescharacteristic, complemented, Sylow
458C25—591no—
459C23×C4—591no—
460C23×C4—594no—
461C23×C4—594no—
462C23×C4—594no—
463C23×C4—591no—
464C23×C4—592no—
465C23×C4—591no—
466C23×C4—592no—
467C23×C4—1182no—
468C23×C4—1182no—
469C23×C4—1182no—
470C23×C4—1182no—
471C23×C4C22×D5912yes—
472C23×C4C22×D5912yes—
473C23×C4C22×D5911yescharacteristic
474C23×C4C22×D5911yescharacteristic
475C23×C4C22×D5911yescharacteristic
476#117—11832no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—594no—
486C2×C4⋊C4—1182no—
487C2×C4⋊C4—1182no—
488C2×C4⋊C4—1182no—
489C2×C4⋊C4—1182no—
490C2×C4⋊C4—1182no—
491C2×C4⋊C4—1182no—
492C2×C4⋊C4—1182no—
493C2×C4⋊C4—1182no—
494C2×C4⋊C4—1184no—
495C2×C4⋊C4—1182no—
496C2×C4⋊C4—1182no—
497C2×C4⋊C4—1182no—
498C2×C4⋊C4—2362no—
499C2×C4⋊C4—2362no—
500C2×C4⋊C4C4×D5914yes—
501C2×C22⋊C4—598no—
502C2×C22⋊C4—1182no—
503C2×C22⋊C4—1182no—
504C2×C22⋊C4—1182no—
505C2×C22⋊C4—1182no—
506C2×C22⋊C4—1182no—
507C2×C22⋊C4—1182no—
508C2×C22⋊C4—1184no—
509C2×C22⋊C4—2362no—
510C2×C22⋊C4—2362no—
511C2×C22⋊C4—2362no—
512C2×C22⋊C4—2362no—
513C2×C42—22no—
514C2×C42—22no—
515C2×C42—594no—
516C2×C42—1182no—
517C2×C42—1182no—
518C2×C42C22⋊D5914yes—
519#95—24no—
520#95—598no—
521#95—1184no—
522#95—1184no—
523#95—2362no—
524#95—2362no—
525#95—2362no—
526#95—2362no—
527C24—592no—
528C24—592no—
529C24—592no—
530C24—1181no—
531C24—1181no—
532C24—1181no—
533C24—1181no—
534C24—1181no—
535C24—1181no—
536C24—1181no—
537C24—1181no—
538C24—1181no—
539C24—1181no—
540C24—1181no—
541C24—1181no—
542C24C23×D5911yescharacteristic
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—592no—
569C22×C4—592no—
570C22×C4—592no—
571C22×C4—5916no—
572C22×C4—594no—
573C22×C4—592no—
574C22×C4—592no—
575C22×C4—1181no—
576C22×C4—1181no—
577C22×C4—1181no—
578C22×C4—1181no—
579C22×C4—1188no—
580C22×C4—1188no—
581C22×C4—1188no—
582C22×C4—1188no—
583C22×C4—1188no—
584C22×C4—1188no—
585C22×C4—1182no—
586C22×C4—1181no—
587C22×C4—1181no—
588C22×C4—1181no—
589C22×C4—1181no—
590C22×C4—1182no—
591C22×C4—1181no—
592C22×C4—1182no—
593C22×C4—1181no—
594C22×C4—1181no—
595C22×C4—1182no—
596C22×C4—1182no—
597C22×C4—1181no—
598C22×C4—1181no—
599C22×C4—1181no—
600C22×C4—1181no—
601C22×C4—1181no—
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×C4C2×C4×D5914yes—
611C22×C4C2×C4×D5912yes—
612C22×C4#1174568512yes—
613C22×C4D4×D5912yes—
614C22×C4D4×D5912yes—
615C22×C4Q8×D5912yes—
616C22×C4#1174568912yes—
617C22×C4C2×C22⋊D5912yes—
618C22×C4C2×C22⋊D5912yes—
619C22×C4C2×C22⋊D5912yes—
620C4⋊C4—28no—
621C4⋊C4—48no—
622C4⋊C4—44no—
623C4⋊C4—1188no—
624C4⋊C4—1188no—
625C4⋊C4—1188no—
626C4⋊C4—2368no—
627C4⋊C4—2364no—
628C22⋊C4—1188no—
629C22⋊C4—1188no—
630C22⋊C4—2368no—
631C22⋊C4—2368no—
632C42—28no—
633C42—1188no—
634C23—594no—
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—1182no—
652C23—1182no—
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—
667C23—2361no—
668C23—2361no—
669C23C22×C4×D5911yescharacteristic
670C23C2×D4×D5911yescharacteristic
671C23C2×D4×D5911yescharacteristic
672C23C22×C22⋊D5911yescharacteristic
673C23C2×Q8×D5911yescharacteristic
674C23C2×#1174568511yescharacteristic
675C23C2×#1174568911yescharacteristic
676C23#1427377211yescharacteristic
677C23#1427377211yescharacteristic
678C23#1427377311yescharacteristic
679C23#1427377311yescharacteristic
680C23#1427377411yescharacteristic
681C23#1427377411yescharacteristic
682C23#1427377511yescharacteristic
683C23#1427377511yescharacteristic
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—594no—
713C2×C4—1182no—
714C2×C4—1182no—
715C2×C4—1182no—
716C2×C4—1182no—
717C2×C4—1182no—
718C2×C4—1182no—
719C2×C4—11832no—
720C2×C4—1182no—
721C2×C4—1182no—
722C2×C4—1182no—
723C2×C4—1182no—
724C2×C4—1184no—
725C2×C4—1184no—
726C2×C4—1184no—
727C2×C4—1182no—
728C2×C4—1182no—
729C2×C4—2362no—
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—2361no—
742C2×C4—2361no—
743C2×C4—2361no—
744C2×C4—2361no—
745C2×C4—2362no—
746C2×C4—2362no—
747C2×C4—2362no—
748C2×C4C4⋊C4×D5914yes—
749C2×C4C4×C22⋊D5914yes—
750C2×C4#1427368914yes—
751C2×C4#1427369514yes—
752C2×C4#1427370314yes—
753C2×C4#1427370514yes—
754C2×C4#1427371214yes—
755C22—1184no—
756C22—1184no—
757C22—1184no—
758C22—2362no—
759C22—2362no—
760C22—2362no—
761C22—2362no—
762C22—2362no—
763C22—2362no—
764C22—2362no—
765C22—2362no—
766C22—2362no—
767C22—2362no—
768C22—2362no—
769C22—2362no—
770C22C2×C4⋊C4×D5911yescharacteristic
771C22C2×C4×C22⋊D5911yescharacteristic
772C22C2×#1427368911yescharacteristic
773C22#1683787411yescharacteristic
774C22#1683787811yescharacteristic
775C22#1683788111yescharacteristic
776C22#1683788411yescharacteristic
777C22C2×#1427369511yescharacteristic
778C22C2×#1427370311yescharacteristic
779C22C2×#1427370511yescharacteristic
780C22C2×#1427371211yescharacteristic
781C22#1683796811yescharacteristic
782C22#1683796811yescharacteristic
783C22#1683796911yescharacteristic
784C22#1683797511yescharacteristic
785C22#1683797511yescharacteristic
786C22#1683797611yescharacteristic
787C22#1683798011yescharacteristic
788C22#1683798011yescharacteristic
789C22#1683798111yescharacteristic
790C22#1683798111yescharacteristic
791C22#1683798211yescharacteristic
792C22#1683798211yescharacteristic
793C22#1683800311yescharacteristic
794C22#1683800811yescharacteristic
795C22#1683801011yescharacteristic
796C22#1683801511yescharacteristic
797C22#1683801711yescharacteristic
798C22#1683802411yescharacteristic
799C22#1683802611yescharacteristic
800C22#1683802611yescharacteristic
801C22#1683802911yescharacteristic
802C22#1683802911yescharacteristic
803C22#1683803211yescharacteristic
804C22#1683803211yescharacteristic
805C4—42no—
806C4—42no—
807C4—44no—
808C4—82no—
809C4—1184no—
810C4—4722no—
811C4—2362no—
812C4—2362no—
813C4—2364no—
814C4#1683727318yes—
815C2—2364no—
816C2C2×#1683727311yescharacteristic
817C2#2142671111yescharacteristic
818C2#2142671811yescharacteristic
819C2#2142677211yescharacteristic
820C2#2142677611yescharacteristic
821C2#2142678311yescharacteristic
822C2#2142678711yescharacteristic
823C2#2142982111yescharacteristic
824C2#2142982611yescharacteristic
825C2#2142989011yescharacteristic
826C2#2142989811yescharacteristic
827C2#2142991811yescharacteristic
828C2#2142992311yescharacteristic
829C2#2142992711yescharacteristic
830C2#2142993111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C59×#389C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenterC2×#389D59
hypocenterC59#14264
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#16837298C2semidirect
5. #21422359C2semidirect
6. #21422354C2semidirect
9. #21422326C2semidirect
10. #21422325C2semidirect
11. C2×C59×#389C2semidirect
28. #16837259C4semidirect
203. C2×C4×D59C4⋊C4semidirect
402. C2×#389D59semidirect
457. C59#14264semidirect

Maximal subgroups

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

subgroupindex
C22×#142736842
C2×#168372982
C2×#168372592
#214223592
#214223542
#214223402
#214223382
#214223262
#214223252
C2×C59×#3892
#1426459