Finite Group Databasebeta

← #28525242

Subgroups — #28525242

Order 15104.

2038 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273726C211yesmaximal, characteristic, complemented
2C2×#16837315C212yesmaximal
3C2×#16837259C211yesmaximal, characteristic
4C2×#16837259C211yesmaximal, characteristic
5C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic
6#21422366C212yesmaximal, complemented
7#21422351C212yesmaximal, complemented
8#21422340C212yesmaximal
9#21422326C211yesmaximal, characteristic, complemented
10#21422325C211yesmaximal, characteristic, complemented
11C59×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×Dic118C2212yes—
13C23×C4×D59C2211yescharacteristic
14C2×#14273726—24no—
15C2×#14273726—24no—
16C2×#14273726—24no—
17C22×C4⋊Dic59C2211yescharacteristic
18C22×C4⋊Dic59C2211yescharacteristic
19C22×Dic59⋊C4C2212yes—
20C22×(C2×D59)⋊C4C2212yes—
21C22×(C2×D59)⋊C4C2212yes—
22C22×(C2×D59)⋊C4C2211yescharacteristic
23C22×(C2×D59)⋊C4C2211yescharacteristic
24C22×C4×Dic59C2211yescharacteristic
25#16837315—28no—
26#16837259—24no—
27#16837259—24no—
28C4×(C2×D59)⋊C4—24no—
29C2×C59⋊#95C2212yes—
30C2×C59⋊#95C2211yescharacteristic
31C2×C59⋊#95C2212yes—
32C2×C59⋊#95C2212yes—
33C2×C59⋊#95C2212yes—
34C2×C59⋊#95C2211yescharacteristic
35C2×C59⋊#95C2212yes—
36C2×C59⋊#95C2212yes—
37C22×C4⋊C4×C59C2211yescharacteristic
38C22×C4⋊C4×C59C2211yescharacteristic
39C22×C42×C59C2211yescharacteristic
40C2×#95×C59C2212yes—
41C2×#95×C59C2212yes—
42C24×D59C2311yescharacteristic
43C22×Dic118—24no—
44C22×Dic118—24no—
45C22×Dic118—24no—
46C22×Dic118—24no—
47C22×Dic118—24no—
48C22×Dic118—42no—
49C22×Dic118—42no—
50C23×Dic59C2312yes—
51C23×Dic59C2312yes—
52C23×Dic59C2311yescharacteristic
53C23×Dic59C2311yescharacteristic
54C23×Dic59C2311yescharacteristic
55C22×C4×D59—22no—
56C22×C4×D59—22no—
57C22×C4×D59—22no—
58C22×C4×D59—22no—
59C22×C4×D59—22no—
60C22×C4×D59—22no—
61C22×C4×D59Q814yescomplemented
62#14273726—232no—
63C2×C4⋊Dic59—22no—
64C2×C4⋊Dic59—22no—
65C2×C4⋊Dic59—22no—
66C2×C4⋊Dic59—22no—
67C2×C4⋊Dic59—22no—
68C2×C4⋊Dic59D414yes—
69C2×Dic59⋊C4—24no—
70C2×Dic59⋊C4—24no—
71C2×Dic59⋊C4—24no—
72C2×(C2×D59)⋊C4—22no—
73C2×(C2×D59)⋊C4—22no—
74C2×(C2×D59)⋊C4—22no—
75C2×(C2×D59)⋊C4—22no—
76C2×(C2×D59)⋊C4—24no—
77C2×(C2×D59)⋊C4—24no—
78C2×(C2×D59)⋊C4—24no—
79C2×(C2×D59)⋊C4—24no—
80C2×(C2×D59)⋊C4—42no—
81C2×(C2×D59)⋊C4—42no—
82C2×(C2×D59)⋊C4D414yes—
83C2×(C2×D59)⋊C4Q814yescomplemented
84C2×C4×Dic59—22no—
85C2×C4×Dic59—22no—
86C2×C4×Dic59D414yes—
87C59⋊#95—24no—
88C59⋊#95—24no—
89C59⋊#95—22no—
90C59⋊#95—22no—
91C59⋊#95—24no—
92C59⋊#95—24no—
93C59⋊#95—24no—
94C59⋊#95—42no—
95C23×C4×C59C2312yes—
96C23×C4×C59C2312yes—
97C23×C4×C59C2311yescharacteristic
98C23×C4×C59C2311yescharacteristic
99C23×C4×C59C2311yescharacteristic
100C2×C4⋊C4×C59—22no—
101C2×C4⋊C4×C59—22no—
102C2×C4⋊C4×C59—22no—
103C2×C4⋊C4×C59—22no—
104C2×C4⋊C4×C59—22no—
105C2×C4⋊C4×C59D414yes—
106C2×C42×C59—22no—
107C2×C42×C59—22no—
108C2×C42×C59—22no—
109#95×C59—24no—
110#95×C59—42no—
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×D59C2×D412yes—
125C23×D59C2×Q812yes—
126C23×D59C2×Q812yes—
127C22×C4×C59—22no—
128C22×C4×C59—21no—
129C22×C4×C59—21no—
130C22×C4×C59—22no—
131C22×C4×C59—22no—
132C22×C4×C59—21no—
133C22×C4×C59—21no—
134C22×C4×C59—21no—
135C22×C4×C59—21no—
136C22×C4×C59—21no—
137C22×C4×C59—21no—
138C22×C4×C59—22no—
139C22×C4×C59—21no—
140C22×C4×C59—22no—
141C22×C4×C59—21no—
142C22×C4×C59—22no—
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×C59C2×D414yes—
153C22×C4×C59C2×D412yes—
154C22×C4×C59C2×D412yes—
155C22×C4×C59C2×D412yes—
156C22×C4×C59C2×D412yes—
157C22×C4×C59C2×Q812yes—
158C22×C4×C59C2×Q812yes—
159C22×C4×C59#4112yes—
160C22×C4×C59#4112yes—
161C22×C4×C59#4112yes—
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—21no—
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×Dic59—22no—
189C22×Dic59C2×D414yes—
190C22×Dic59C2×D412yes—
191C22×Dic59C2×D412yes—
192C22×Dic59C2×D412yes—
193C22×Dic59C2×Q812yes—
194C22×Dic59C2×Q812yes—
195C22×Dic59#4112yes—
196C22×Dic59#4112yes—
197C2×C4×D59—28no—
198C2×C4×D59—28no—
199C2×C4×D59—28no—
200C2×C4×D59—44no—
201C2×C4×D59—44no—
202C2×C4×D59—44no—
203C2×C4×D59—44no—
204C2×Dic118—216no—
205C2×Dic118—48no—
206C2×Dic118—48no—
207C2×Dic118—48no—
208C2×Dic118—48no—
209C2×Dic118—48no—
210C2×Dic118—48no—
211C4⋊C4×C59—28no—
212C4⋊C4×C59—44no—
213C42×C59—44no—
214(C2×D59)⋊C4—28no—
215(C2×D59)⋊C4—28no—
216(C2×D59)⋊C4—48no—
217(C2×D59)⋊C4—48no—
218C4⋊Dic59—28no—
219C4⋊Dic59—44no—
220Dic59⋊C4—216no—
221C4×Dic59—28no—
222C23×C59C22×D411yescharacteristic
223C23×C59C22×D411yescharacteristic
224C23×C59C22×D411yescharacteristic
225C23×C59C22×D411yescharacteristic
226C23×C59C22×Q811yescharacteristic
227C23×C59C22×Q811yescharacteristic
228C23×C59C2×#4111yescharacteristic
229C23×C59C2×#4111yescharacteristic
230C23×C59C2×#4111yescharacteristic
231C23×C59C2×#4111yescharacteristic
232C23×C59C2×#4111yescharacteristic
233C23×C59H(5,𝔽2)11yescharacteristic
234C23×C59H(5,𝔽2)11yescharacteristic
235C23×C592−1+411yescharacteristic
236C23×C592−1+411yescharacteristic
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—22no—
252C22×D59—22no—
253C22×D59—22no—
254C22×D59—22no—
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×D59—41no—
268C22×D59—41no—
269C22×D59—41no—
270C22×D59—41no—
271C22×D59C4⋊Q814yescomplemented
272C2×C4×C59—24no—
273C2×C4×C59—22no—
274C2×C4×C59—22no—
275C2×C4×C59—24no—
276C2×C4×C59—24no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
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—41no—
290C2×C4×C59—41no—
291C2×C4×C59—41no—
292C2×C4×C59—41no—
293C2×C4×C59—42no—
294C2×C4×C59—42no—
295C2×C4×C59—42no—
296C2×C4×C59—42no—
297C2×C4×C59—42no—
298C2×C4×C59—42no—
299C2×C4×C59—42no—
300C2×C4×C59#12014yes—
301C2×C4×C59C22⋊Q814yes—
302C2×C4×C59C22⋊Q814yes—
303C2×C4×C59C22⋊Q814yes—
304C2×C4×C59#12414yes—
305C2×C4×C59#12414yes—
306C2×C4×C59#12414yes—
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—22no—
318C2×Dic59—22no—
319C2×Dic59—24no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—24no—
324C2×Dic59—24no—
325C2×Dic59—41no—
326C2×Dic59—42no—
327C2×Dic59—41no—
328C2×Dic59—41no—
329C2×Dic59—41no—
330C2×Dic59—42no—
331C2×Dic59—42no—
332C2×Dic59—42no—
333C2×Dic59—42no—
334C2×Dic59—42no—
335C2×Dic59—42no—
336C2×Dic59—42no—
337C2×Dic59—42no—
338C2×Dic59—42no—
339C2×Dic59—42no—
340C2×Dic59#12114yes—
341C2×Dic59C22⋊Q814yes—
342C4×D59—416no—
343Dic118—432no—
344#15125—591nomaximal, Sylow
345C22×C59C2×#12011yescharacteristic
346C22×C59C2×#12111yescharacteristic
347C22×C59C2×C22⋊Q811yescharacteristic
348C22×C59C2×C22⋊Q811yescharacteristic
349C22×C59C2×C22⋊Q811yescharacteristic
350C22×C59C2×C22⋊Q811yescharacteristic
351C22×C59C2×#12411yescharacteristic
352C22×C59C2×#12411yescharacteristic
353C22×C59C2×#12411yescharacteristic
354C22×C59C2×C4⋊Q811yescharacteristic
355C22×C59#53211yescharacteristic
356C22×C59#53311yescharacteristic
357C22×C59#53311yescharacteristic
358C22×C59#53511yescharacteristic
359C22×C59#53611yescharacteristic
360C22×C59#54211yescharacteristic
361C22×C59#54211yescharacteristic
362C22×C59#54411yescharacteristic
363C22×C59#54411yescharacteristic
364C22×C59D4211yescharacteristic
365C22×C59D4211yescharacteristic
366C22×C59#54611yescharacteristic
367C22×C59#54611yescharacteristic
368C22×C59#54711yescharacteristic
369C22×C59#54711yescharacteristic
370C22×C59#54811yescharacteristic
371C22×C59#54811yescharacteristic
372C22×C59D4×Q811yescharacteristic
373C22×C59D4×Q811yescharacteristic
374C22×C59#55411yescharacteristic
375C22×C59#55411yescharacteristic
376C22×C59#55511yescharacteristic
377C22×C59#55511yescharacteristic
378C22×C59#55611yescharacteristic
379C22×C59#55611yescharacteristic
380C2×D59—24no—
381C2×D59—24no—
382C2×D59—24no—
383C2×D59—42no—
384C2×D59—42no—
385C2×D59—42no—
386C2×D59—42no—
387C2×D59—42no—
388C2×D59—42no—
389C2×D59—42no—
390C2×D59—42no—
391C2×D59—42no—
392C2×D59—42no—
393C2×D59—42no—
394C2×D59—42no—
395C4×C59—42no—
396C4×C59—44no—
397C4×C59—42no—
398C4×C59—82no—
399C4×C59#39318yescomplemented
400Dic59—24no—
401Dic59—24no—
402Dic59—42no—
403Dic59—44no—
404Dic59—82no—
405C22×C4⋊Q8—591no—
406C2×#393—592no—
407C2×#380—591no—
408C2×#380—591no—
409C2×C4×C22⋊C4—591no—
410#1446—592no—
411#1442—592no—
412#1439—592no—
413C4⋊#95—591no—
414C4⋊#95—591no—
415C4⋊#95D5911yescharacteristic, complemented
416C2×C59C2×#39311yescharacteristic
417C2×C59#240811yescharacteristic
418C2×C59#240911yescharacteristic
419C2×C59#243911yescharacteristic
420C2×C59#243911yescharacteristic
421C2×C59#244011yescharacteristic
422C2×C59#244011yescharacteristic
423C2×C59#249111yescharacteristic
424C2×C59#249111yescharacteristic
425C2×C59#249211yescharacteristic
426C2×C59#249211yescharacteristic
427C2×C59#254711yescharacteristic
428C2×C59#256311yescharacteristic
429C2×C59#262811yescharacteristic
430C2×C59#285711yescharacteristic
431D59—44no—
432C23×Q8—592no—
433C24×C4—591no—
434C2×C4⋊Q8—1184no—
435C2×C4⋊Q8—1184no—
436C2×C4⋊Q8—1184no—
437C22×C4⋊C4—591no—
438C22×C4⋊C4—592no—
439C22×C4⋊C4—591no—
440C22×C4⋊C4C2×D5911yescharacteristic
441C22×C4⋊C4C2×D5911yescharacteristic
442C22×C22⋊C4—591no—
443C22×C22⋊C4—591no—
444C22×C22⋊C4—592no—
445C22×C22⋊C4—592no—
446C22×C42—591no—
447C22×C42C2×D5911yescharacteristic
448#393—1188no—
449#380—1184no—
450#380—1184no—
451C4×C22⋊C4—1184no—
452C2×#95—592no—
453C2×#95—592no—
454C2×#95—592no—
455C2×#95—591no—
456C2×#95—592no—
457C2×#95—592no—
458C2×#95—591no—
459C2×#95—592no—
460C2×#95C2×D5912yes—
461C2×#95C2×D5912yes—
462C59#1512511yescharacteristic, complemented, Sylow
463C25—591no—
464C22×Q8—1184no—
465C22×Q8—1184no—
466C22×Q8—1184no—
467C22×Q8—1184no—
468C22×Q8—1184no—
469C22×Q8—2362no—
470C22×Q8—2362no—
471C23×C4—591no—
472C23×C4—591no—
473C23×C4—592no—
474C23×C4—591no—
475C23×C4—594no—
476C23×C4—592no—
477C23×C4—1182no—
478C23×C4—1182no—
479C23×C4—1182no—
480C23×C4—1182no—
481C23×C4—1182no—
482C23×C4—1182no—
483C23×C4C22×D5912yes—
484C23×C4C22×D5912yes—
485C23×C4C22×D5911yescharacteristic
486C23×C4C22×D5911yescharacteristic
487C23×C4C22×D5911yescharacteristic
488C4⋊Q8—11832no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—594no—
495C2×C4⋊C4—1184no—
496C2×C4⋊C4—1184no—
497C2×C4⋊C4—1184no—
498C2×C4⋊C4—1182no—
499C2×C4⋊C4—1182no—
500C2×C4⋊C4—1182no—
501C2×C4⋊C4—1182no—
502C2×C4⋊C4—1182no—
503C2×C4⋊C4D23614yes—
504C2×C22⋊C4—594no—
505C2×C22⋊C4—594no—
506C2×C22⋊C4—1182no—
507C2×C22⋊C4—1182no—
508C2×C22⋊C4—1182no—
509C2×C22⋊C4—1182no—
510C2×C22⋊C4—1184no—
511C2×C22⋊C4—1184no—
512C2×C22⋊C4—1184no—
513C2×C22⋊C4—1184no—
514C2×C22⋊C4—2362no—
515C2×C22⋊C4—2362no—
516C2×C42—22no—
517C2×C42—22no—
518C2×C42—22no—
519C2×C42—594no—
520C2×C42—1182no—
521C2×C42—1182no—
522#95—24no—
523#95—42no—
524#95—1184no—
525#95—1182no—
526#95—1182no—
527#95—1184no—
528#95—1184no—
529#95—1184no—
530#95—1184no—
531#95—2362no—
532C24—592no—
533C24—592no—
534C24—592no—
535C24—1181no—
536C24—1181no—
537C24—1181no—
538C24—1181no—
539C24—1181no—
540C24—1181no—
541C24—1181no—
542C24—1181no—
543C24—1181no—
544C24—1181no—
545C24—1181no—
546C24—1181no—
547C24C23×D5911yescharacteristic
548C2×Q8—11816no—
549C2×Q8—2368no—
550C2×Q8—2368no—
551C2×Q8—2368no—
552C2×Q8—2368no—
553C2×Q8—2368no—
554C2×Q8—2368no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—592no—
581C22×C4—592no—
582C22×C4—592no—
583C22×C4—592no—
584C22×C4—592no—
585C22×C4—592no—
586C22×C4—594no—
587C22×C4—592no—
588C22×C4—1181no—
589C22×C4—1181no—
590C22×C4—1181no—
591C22×C4—1181no—
592C22×C4—1181no—
593C22×C4—1181no—
594C22×C4—1181no—
595C22×C4—1181no—
596C22×C4—1181no—
597C22×C4—1181no—
598C22×C4—1182no—
599C22×C4—1182no—
600C22×C4—1181no—
601C22×C4—1182no—
602C22×C4—1182no—
603C22×C4—1181no—
604C22×C4—1181no—
605C22×C4—1181no—
606C22×C4—1182no—
607C22×C4—1182no—
608C22×C4—1188no—
609C22×C4—1188no—
610C22×C4—1188no—
611C22×C4—1182no—
612C22×C4—1182no—
613C22×C4—1182no—
614C22×C4—1182no—
615C22×C4—1182no—
616C22×C4—1182no—
617C22×C4—1182no—
618C22×C4—2364no—
619C22×C4—2364no—
620C22×C4—2364no—
621C22×C4—2364no—
622C22×C4C2×D23614yes—
623C22×C4C2×D23612yes—
624C22×C4#1174568512yes—
625C22×C4#1174568512yes—
626C22×C4D4×D5912yes—
627C22×C4D4×D5912yes—
628C22×C4D4×D5912yes—
629C22×C4#1174568712yes—
630C22×C4Q8×D5912yes—
631C22×C4Q8×D5912yes—
632C4⋊C4—28no—
633C4⋊C4—44no—
634C4⋊C4—11816no—
635C4⋊C4—1188no—
636C4⋊C4—2364no—
637C22⋊C4—1188no—
638C22⋊C4—1188no—
639C22⋊C4—2368no—
640C22⋊C4—2368no—
641C42—44no—
642C42—1188no—
643C23—594no—
644C23—1182no—
645C23—1182no—
646C23—1182no—
647C23—1182no—
648C23—1182no—
649C23—1182no—
650C23—1182no—
651C23—1182no—
652C23—1182no—
653C23—1182no—
654C23—1182no—
655C23—1182no—
656C23—1182no—
657C23—1182no—
658C23—1182no—
659C23—1182no—
660C23—1182no—
661C23—1182no—
662C23—2361no—
663C23—2361no—
664C23—2361no—
665C23—2361no—
666C23—2361no—
667C23—2361no—
668C23—2361no—
669C23—2361no—
670C23—2361no—
671C23—2361no—
672C23—2361no—
673C23—2361no—
674C23—2361no—
675C23—2361no—
676C23—2361no—
677C23—2361no—
678C23C2×D4×D5911yescharacteristic
679C23C2×D4×D5911yescharacteristic
680C23C2×D4×D5911yescharacteristic
681C23C22×D23611yescharacteristic
682C23C2×Q8×D5911yescharacteristic
683C23C2×Q8×D5911yescharacteristic
684C23#41×D5911yescharacteristic
685C23#41×D5911yescharacteristic
686C23C2×#1174568711yescharacteristic
687C23C2×#1174568511yescharacteristic
688C23C2×#1174568511yescharacteristic
689C23#1427377211yescharacteristic
690C23#1427377311yescharacteristic
691C23#1427377411yescharacteristic
692C23#1427377511yescharacteristic
693Q8—23632no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—594no—
723C2×C4—594no—
724C2×C4—1182no—
725C2×C4—1182no—
726C2×C4—1182no—
727C2×C4—1182no—
728C2×C4—1182no—
729C2×C4—1182no—
730C2×C4—1182no—
731C2×C4—1182no—
732C2×C4—1182no—
733C2×C4—1182no—
734C2×C4—1182no—
735C2×C4—1182no—
736C2×C4—1184no—
737C2×C4—1182no—
738C2×C4—1182no—
739C2×C4—1182no—
740C2×C4—1184no—
741C2×C4—1184no—
742C2×C4—2362no—
743C2×C4—2362no—
744C2×C4—2362no—
745C2×C4—2362no—
746C2×C4—2362no—
747C2×C4—2362no—
748C2×C4—2362no—
749C2×C4—2361no—
750C2×C4—2362no—
751C2×C4—2361no—
752C2×C4—2361no—
753C2×C4—2361no—
754C2×C4—2362no—
755C2×C4—2362no—
756C2×C4—2362no—
757C2×C4—23616no—
758C2×C4#1427369714yes—
759C2×C4#1427370514yes—
760C2×C4#1427370514yes—
761C2×C4#1427370714yes—
762C2×C4#1427371314yes—
763C2×C4#1427371314yes—
764C2×C4#1427371514yes—
765C22—1184no—
766C22—1184no—
767C22—1184no—
768C22—2362no—
769C22—2362no—
770C22—2362no—
771C22—2362no—
772C22—2362no—
773C22—2362no—
774C22—2362no—
775C22—2362no—
776C22—2362no—
777C22—2362no—
778C22—2362no—
779C22—2362no—
780C22C2×#1427369711yescharacteristic
781C22#121×D5911yescharacteristic
782C22C22⋊Q8×D5911yescharacteristic
783C22C2×#1427370511yescharacteristic
784C22C2×#1427370511yescharacteristic
785C22C2×#1427370711yescharacteristic
786C22C2×#1427371311yescharacteristic
787C22C2×#1427371311yescharacteristic
788C22C2×#1427371511yescharacteristic
789C22C4⋊Q8×D5911yescharacteristic
790C22#1683794911yescharacteristic
791C22#1683795611yescharacteristic
792C22#1683795811yescharacteristic
793C22#1683796811yescharacteristic
794C22#1683797511yescharacteristic
795C22#1683801711yescharacteristic
796C22#1683802411yescharacteristic
797C22#1683802911yescharacteristic
798C22#1683803211yescharacteristic
799C22#1683803711yescharacteristic
800C22D4×D23611yescharacteristic
801C22#1683804511yescharacteristic
802C22#1683804711yescharacteristic
803C22#1683805211yescharacteristic
804C22#1683805311yescharacteristic
805C22#1683806011yescharacteristic
806C22#1683806411yescharacteristic
807C22#1683806711yescharacteristic
808C22Q8×D23611yescharacteristic
809C22#1683810711yescharacteristic
810C22#1683811011yescharacteristic
811C22#1683811511yescharacteristic
812C22#1683811611yescharacteristic
813C22#1683812011yescharacteristic
814C22#1683812311yescharacteristic
815C4—42no—
816C4—42no—
817C4—44no—
818C4—82no—
819C4—1184no—
820C4—1184no—
821C4—4722no—
822C4—2362no—
823C4—2364no—
824C4#1683731518yescomplemented
825C2—2364no—
826C2C2×#1683731511yescharacteristic
827C2#2142745011yescharacteristic
828C2#2142745911yescharacteristic
829C2#2142778511yescharacteristic
830C2#2142779011yescharacteristic
831C2#2142779611yescharacteristic
832C2#2142780111yescharacteristic
833C2#2142845311yescharacteristic
834C2#2142846011yescharacteristic
835C2#2142846411yescharacteristic
836C2#2142847111yescharacteristic
837C2#2142909011yescharacteristic
838C2#2142926611yescharacteristic
839C2#2142992311yescharacteristic
840C2#2143244711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutator, socle, cosocleC24×C59C24
FittingC59×C4⋊#95C2
prime radicalC24×D59C23
hypercenterC4⋊#95D59
hypocenterC59#15125
LCSG ▷ C24×C59 ▷ C59
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
1. C22×#14273726C2semidirect
6. #21422366C2semidirect
7. #21422351C2semidirect
9. #21422326C2semidirect
10. #21422325C2semidirect
11. C59×C4⋊#95C2semidirect
61. C22×C4×D59Q8semidirect
83. C2×(C2×D59)⋊C4Q8semidirect
271. C22×D59C4⋊Q8semidirect
399. C4×C59#393semidirect
415. C4⋊#95D59semidirect
462. C59#15125semidirect
824. C4#16837315semidirect

Maximal subgroups

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

subgroupindex
C22×#142737262
C2×#168373152
C2×#168372592
C2×C4×(C2×D59)⋊C42
#214223662
#214223512
#214223402
#214223262
#214223252
C59×C4⋊#952
#1512559