Finite Group Databasebeta

← #28511484

Subgroups — #28511484

Order 15104.

2266 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273707C211yesmaximal, characteristic
2C22×C4×Dic118C211yesmaximal, characteristic, complemented
3C2×#16837307C211yesmaximal, characteristic, complemented
4C2×#16837259C211yesmaximal, characteristic
5C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic
6#21422348C212yesmaximal, complemented
7#21422340C212yesmaximal
8#21422332C212yesmaximal
9#21422330C212yesmaximal, complemented
10#21422325C211yesmaximal, characteristic, complemented
11C59×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×Dic118C2211yescharacteristic
13C23×C4×D59C2211yescharacteristic
14C2×#14273707—24no—
15C2×#14273707—24no—
16C2×#14273707C418yescomplemented
17C2×C4×Dic118—24no—
18C2×C4×Dic118—24no—
19C2×C4×Dic118—24no—
20C22×C4⋊Dic59C2212yes—
21C22×C4⋊Dic59C2211yescharacteristic
22C22×Dic59⋊C4C2212yes—
23C22×(C2×D59)⋊C4C2211yescharacteristic
24C22×(C2×D59)⋊C4C2212yes—
25C22×(C2×D59)⋊C4C2212yes—
26C22×(C2×D59)⋊C4C2211yescharacteristic
27C22×C4×Dic59C2212yes—
28C22×C4×Dic59C2211yescharacteristic
29#16837307—24no—
30#16837259—24no—
31C4×(C2×D59)⋊C4—24no—
32C2×C59⋊#95C2212yes—
33C2×C59⋊#95C2212yes—
34C2×C59⋊#95C2211yescharacteristic
35C2×C59⋊#95C2212yes—
36C2×C59⋊#95C2212yes—
37C2×C59⋊#95C2211yescharacteristic
38C2×C59⋊#95C2212yes—
39C22×C4⋊C4×C59C2211yescharacteristic
40C22×C4⋊C4×C59C2211yescharacteristic
41C22×C42×C59C2211yescharacteristic
42C2×#95×C59C2212yes—
43C2×#95×C59C2212yes—
44C24×D59C2311yescharacteristic
45C22×Dic118—22no—
46C22×Dic118—22no—
47C22×Dic118—22no—
48C22×Dic118—22no—
49C22×Dic118C2×C414yes—
50C22×Dic118D414yes—
51C22×Dic118D414yes—
52C23×Dic59C2311yescharacteristic
53C23×Dic59C2312yes—
54C23×Dic59C2311yescharacteristic
55C23×Dic59C2311yescharacteristic
56C23×Dic59C2312yes—
57C22×C4×D59—22no—
58C22×C4×D59—22no—
59C22×C4×D59—22no—
60C22×C4×D59—22no—
61C22×C4×D59—22no—
62C22×C4×D59—22no—
63C22×C4×D59C2×C414yes—
64#14273707—232no—
65C4×Dic118—232no—
66C2×C4⋊Dic59—22no—
67C2×C4⋊Dic59—22no—
68C2×C4⋊Dic59—24no—
69C2×C4⋊Dic59—24no—
70C2×C4⋊Dic59C2×C418yes—
71C2×C4⋊Dic59D414yes—
72C2×Dic59⋊C4—24no—
73C2×Dic59⋊C4—24no—
74C2×Dic59⋊C4—24no—
75C2×(C2×D59)⋊C4—22no—
76C2×(C2×D59)⋊C4—22no—
77C2×(C2×D59)⋊C4—22no—
78C2×(C2×D59)⋊C4—22no—
79C2×(C2×D59)⋊C4—24no—
80C2×(C2×D59)⋊C4—24no—
81C2×(C2×D59)⋊C4—22no—
82C2×(C2×D59)⋊C4—24no—
83C2×(C2×D59)⋊C4—24no—
84C2×(C2×D59)⋊C4—42no—
85C2×(C2×D59)⋊C4C2×C418yes—
86C2×(C2×D59)⋊C4Q814yescomplemented
87C2×C4×Dic59—24no—
88C2×C4×Dic59—24no—
89C2×C4×Dic59—24no—
90C2×C4×Dic59—22no—
91C2×C4×Dic59—22no—
92C2×C4×Dic59—22no—
93C59⋊#95—22no—
94C59⋊#95—22no—
95C59⋊#95—24no—
96C59⋊#95—24no—
97C59⋊#95—24no—
98C59⋊#95—24no—
99C59⋊#95—42no—
100C23×C4×C59C2312yes—
101C23×C4×C59C2312yes—
102C23×C4×C59C2311yescharacteristic
103C23×C4×C59C2311yescharacteristic
104C23×C4×C59C2311yescharacteristic
105C2×C4⋊C4×C59—22no—
106C2×C4⋊C4×C59—22no—
107C2×C4⋊C4×C59—22no—
108C2×C4⋊C4×C59—22no—
109C2×C4⋊C4×C59—22no—
110C2×C4⋊C4×C59C2×C414yes—
111C2×C42×C59—22no—
112C2×C42×C59—22no—
113C2×C42×C59D414yes—
114#95×C59—24no—
115#95×C59—42no—
116C24×C59C2411yescharacteristic
117C23×D59—21no—
118C23×D59—21no—
119C23×D59—21no—
120C23×D59—21no—
121C23×D59—21no—
122C23×D59—21no—
123C23×D59—21no—
124C23×D59—21no—
125C23×D59—21no—
126C23×D59—21no—
127C23×D59—21no—
128C23×D59—21no—
129C23×D59C22×C412yes—
130C23×D59C2×Q812yes—
131C23×D59#4112yes—
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—22no—
140C22×C4×C59—22no—
141C22×C4×C59—22no—
142C22×C4×C59—21no—
143C22×C4×C59—21no—
144C22×C4×C59—21no—
145C22×C4×C59—22no—
146C22×C4×C59—22no—
147C22×C4×C59—21no—
148C22×C4×C59—22no—
149C22×C4×C59—22no—
150C22×C4×C59—22no—
151C22×C4×C59—22no—
152C22×C4×C59—22no—
153C22×C4×C59—22no—
154C22×C4×C59—22no—
155C22×C4×C59C22×C414yes—
156C22×C4×C59C22×C412yes—
157C22×C4×C59C2×D412yes—
158C22×C4×C59C2×D412yes—
159C22×C4×C59C2×D412yes—
160C22×C4×C59C2×D412yes—
161C22×C4×C59C2×D412yes—
162C22×C4×C59C2×D412yes—
163C22×C4×C59C2×Q812yes—
164C22×C4×C59#4112yes—
165C22×C4×C59#4112yes—
166C22×C4×C59#4112yes—
167C22×Dic59—22no—
168C22×Dic59—22no—
169C22×Dic59—22no—
170C22×Dic59—22no—
171C22×Dic59—21no—
172C22×Dic59—21no—
173C22×Dic59—21no—
174C22×Dic59—21no—
175C22×Dic59—21no—
176C22×Dic59—21no—
177C22×Dic59—22no—
178C22×Dic59—22no—
179C22×Dic59—21no—
180C22×Dic59—21no—
181C22×Dic59—22no—
182C22×Dic59—21no—
183C22×Dic59—21no—
184C22×Dic59—21no—
185C22×Dic59—21no—
186C22×Dic59—22no—
187C22×Dic59—21no—
188C22×Dic59—21no—
189C22×Dic59—21no—
190C22×Dic59—22no—
191C22×Dic59—22no—
192C22×Dic59—21no—
193C22×Dic59—21no—
194C22×Dic59—21no—
195C22×Dic59C22×C412yes—
196C22×Dic59C22×C414yes—
197C22×Dic59C2×D414yes—
198C22×Dic59C2×D414yes—
199C22×Dic59C2×D414yes—
200C22×Dic59C2×Q812yes—
201C22×Dic59#4112yes—
202C2×C4×D59—28no—
203C2×C4×D59—28no—
204C2×C4×D59—28no—
205C2×C4×D59—44no—
206C2×C4×D59—44no—
207C2×C4×D59—44no—
208C2×C4×D59—44no—
209C2×Dic118—28no—
210C2×Dic118—28no—
211C2×Dic118—28no—
212C2×Dic118—28no—
213C2×Dic118—28no—
214C2×Dic118—28no—
215C2×Dic118C22⋊C4116yescomplemented
216C4⋊C4×C59—28no—
217C4⋊C4×C59—44no—
218C42×C59—28no—
219(C2×D59)⋊C4—28no—
220(C2×D59)⋊C4—28no—
221(C2×D59)⋊C4—216no—
222(C2×D59)⋊C4—48no—
223C4⋊Dic59—28no—
224C4⋊Dic59—216no—
225Dic59⋊C4—216no—
226C4×Dic59—216no—
227C4×Dic59—44no—
228C23×C59C23×C411yescharacteristic
229C23×C59C22×D411yescharacteristic
230C23×C59C22×D411yescharacteristic
231C23×C59C22×D411yescharacteristic
232C23×C59C22×D411yescharacteristic
233C23×C59C22×Q811yescharacteristic
234C23×C59C2×#4111yescharacteristic
235C23×C59C2×#4111yescharacteristic
236C23×C59C2×#4111yescharacteristic
237C23×C59C2×#4111yescharacteristic
238C23×C59C2×#4111yescharacteristic
239C23×C59H(5,𝔽2)11yescharacteristic
240C23×C592−1+411yescharacteristic
241C23×C592−1+411yescharacteristic
242C23×C592−1+411yescharacteristic
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—22no—
256C22×D59—22no—
257C22×D59—22no—
258C22×D59—22no—
259C22×D59—22no—
260C22×D59—22no—
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×D59—41no—
272C22×D59—41no—
273C22×D59—41no—
274C22×D59—41no—
275C22×D59—41no—
276C22×D59—41no—
277C22×D59C4×Q814yescomplemented
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—24no—
285C2×C4×C59—24no—
286C2×C4×C59—24no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—41no—
291C2×C4×C59—41no—
292C2×C4×C59—42no—
293C2×C4×C59—42no—
294C2×C4×C59—41no—
295C2×C4×C59—42no—
296C2×C4×C59—41no—
297C2×C4×C59—42no—
298C2×C4×C59—42no—
299C2×C4×C59—42no—
300C2×C4×C59—42no—
301C2×C4×C59—42no—
302C2×C4×C59—42no—
303C2×C4×C59—42no—
304C2×C4×C59—42no—
305C2×C4×C59C2×C22⋊C414yes—
306C2×C4×C59C4×D414yes—
307C2×C4×C59C4×D414yes—
308C2×C4×C59#12014yes—
309C2×C4×C59#12114yes—
310C2×C4×C59#12114yes—
311C2×C4×C59C22⋊Q814yescomplemented
312C2×C4×C59#12314yes—
313C2×Dic59—24no—
314C2×Dic59—24no—
315C2×Dic59—24no—
316C2×Dic59—24no—
317C2×Dic59—24no—
318C2×Dic59—24no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—24no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—24no—
326C2×Dic59—24no—
327C2×Dic59—22no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—41no—
332C2×Dic59—41no—
333C2×Dic59—41no—
334C2×Dic59—41no—
335C2×Dic59—41no—
336C2×Dic59—41no—
337C2×Dic59—42no—
338C2×Dic59—41no—
339C2×Dic59—42no—
340C2×Dic59—41no—
341C2×Dic59—41no—
342C2×Dic59—42no—
343C2×Dic59—42no—
344C2×Dic59—41no—
345C2×Dic59—41no—
346C2×Dic59—41no—
347C2×Dic59C2×C22⋊C418yes—
348C4×D59—416no—
349Dic118—232no—
350#13969—591nomaximal, Sylow
351C22×C59C22×C22⋊C411yescharacteristic
352C22×C59C2×C4×D411yescharacteristic
353C22×C59C2×C4×D411yescharacteristic
354C22×C59C2×C4×Q811yescharacteristic
355C22×C59C4×#4111yescharacteristic
356C22×C59#51911yescharacteristic
357C22×C59#52011yescharacteristic
358C22×C59C2×#12011yescharacteristic
359C22×C59C2×#12111yescharacteristic
360C22×C59C2×#12111yescharacteristic
361C22×C59C2×C22⋊Q811yescharacteristic
362C22×C59C2×#12311yescharacteristic
363C22×C59#52511yescharacteristic
364C22×C59#52911yescharacteristic
365C22×C59#53311yescharacteristic
366C22×C59#53611yescharacteristic
367C22×C59#53711yescharacteristic
368C22×C59#54111yescharacteristic
369C22×C59#54211yescharacteristic
370C22×C59#54611yescharacteristic
371C22×C59#54711yescharacteristic
372C22×C59#54811yescharacteristic
373C22×C59#54811yescharacteristic
374C22×C59#54811yescharacteristic
375C22×C59#54811yescharacteristic
376C22×C59#54811yescharacteristic
377C22×C59D4×Q811yescharacteristic
378C22×C59D4×Q811yescharacteristic
379C22×C59D4×Q811yescharacteristic
380C22×C59#55011yescharacteristic
381C22×C59#55011yescharacteristic
382C22×C59#55211yescharacteristic
383C22×C59#55211yescharacteristic
384C22×C59#55411yescharacteristic
385C22×C59#55611yescharacteristic
386C2×D59—24no—
387C2×D59—24no—
388C2×D59—24no—
389C2×D59—42no—
390C2×D59—42no—
391C2×D59—42no—
392C2×D59—42no—
393C2×D59—42no—
394C2×D59—42no—
395C2×D59—42no—
396C2×D59—42no—
397C2×D59—42no—
398C2×D59—42no—
399C2×D59—42no—
400C2×D59—42no—
401C4×C59—24no—
402C4×C59—44no—
403C4×C59—42no—
404C4×C59—82no—
405C4×C59#38618yes—
406Dic59—28no—
407Dic59—44no—
408Dic59—42no—
409Dic59—42no—
410Dic59—42no—
411C22×C22⋊Q8—591no—
412C22×C4×Q8—591no—
413C2×#391—591no—
414C2×#380—591no—
415C2×C4×C22⋊C4—591no—
416#1441—592no—
417#1439—592no—
418#1437—592no—
419#1436—592no—
420C4⋊#95—591no—
421C4⋊#95D5911yescharacteristic, complemented
422C2×C59C2×#38611yescharacteristic
423C2×C59C4×C22⋊Q811yescharacteristic
424C2×C59#232311yescharacteristic
425C2×C59Q8×C22⋊C411yescharacteristic
426C2×C59#234111yescharacteristic
427C2×C59#236011yescharacteristic
428C2×C59#236211yescharacteristic
429C2×C59#240711yescharacteristic
430C2×C59#240911yescharacteristic
431C2×C59#242111yescharacteristic
432C2×C59#242311yescharacteristic
433C2×C59#242611yescharacteristic
434C2×C59#242911yescharacteristic
435C2×C59#253611yescharacteristic
436C2×C59#253811yescharacteristic
437D59—44no—
438C23×Q8—591no—
439C24×C4—591no—
440C2×C22⋊Q8—598no—
441C2×C22⋊Q8—1184no—
442C2×C22⋊Q8—1184no—
443C2×C4×Q8—1184no—
444C2×C4×Q8—1184no—
445C2×C4×Q8—1184no—
446C22×C4⋊C4—591no—
447C22×C4⋊C4—592no—
448C22×C4⋊C4—592no—
449C22×C4⋊C4C2×D5911yescharacteristic
450C22×C4⋊C4C2×D5911yescharacteristic
451C22×C22⋊C4—592no—
452C22×C22⋊C4—591no—
453C22×C22⋊C4—591no—
454C22×C22⋊C4—592no—
455C22×C42—592no—
456C22×C42—591no—
457C22×C42C2×D5911yescharacteristic
458#391—1184no—
459#380—1184no—
460C4×C22⋊C4—1184no—
461C2×#95—592no—
462C2×#95—591no—
463C2×#95—592no—
464C2×#95—592no—
465C2×#95—592no—
466C2×#95—591no—
467C2×#95—592no—
468C2×#95C2×D5912yes—
469C2×#95C2×D5912yes—
470C59#1396911yescharacteristic, complemented, Sylow
471C25—591no—
472C22×Q8—594no—
473C22×Q8—594no—
474C22×Q8—594no—
475C22×Q8—1182no—
476C22×Q8—1182no—
477C22×Q8—1182no—
478C22×Q8—1182no—
479C23×C4—592no—
480C23×C4—592no—
481C23×C4—591no—
482C23×C4—591no—
483C23×C4—591no—
484C23×C4—594no—
485C23×C4—1182no—
486C23×C4—1182no—
487C23×C4—1182no—
488C23×C4—1182no—
489C23×C4—1182no—
490C23×C4—1182no—
491C23×C4C22×D5912yes—
492C23×C4C22×D5912yes—
493C23×C4C22×D5911yescharacteristic
494C23×C4C22×D5911yescharacteristic
495C23×C4C22×D5911yescharacteristic
496C22⋊Q8—11832no—
497C4×Q8—11832no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—598no—
504C2×C4⋊C4—594no—
505C2×C4⋊C4—1184no—
506C2×C4⋊C4—1184no—
507C2×C4⋊C4—1184no—
508C2×C4⋊C4—1184no—
509C2×C4⋊C4—1184no—
510C2×C4⋊C4—1182no—
511C2×C4⋊C4—1182no—
512C2×C4⋊C4C4×D5914yes—
513C2×C22⋊C4—598no—
514C2×C22⋊C4—594no—
515C2×C22⋊C4—1184no—
516C2×C22⋊C4—1184no—
517C2×C22⋊C4—1182no—
518C2×C22⋊C4—1182no—
519C2×C22⋊C4—1182no—
520C2×C22⋊C4—1182no—
521C2×C22⋊C4—1182no—
522C2×C22⋊C4—1184no—
523C2×C22⋊C4—1184no—
524C2×C22⋊C4—2362no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—1184no—
528C2×C42—1184no—
529C2×C42—1184no—
530C2×C42—1182no—
531C2×C42—1182no—
532C2×C42—1182no—
533C2×C42D23614yes—
534#95—24no—
535#95—42no—
536#95—1184no—
537#95—1184no—
538#95—1184no—
539#95—1184no—
540#95—1182no—
541#95—1182no—
542#95—2362no—
543C24—592no—
544C24—592no—
545C24—592no—
546C24—1181no—
547C24—1181no—
548C24—1181no—
549C24—1181no—
550C24—1181no—
551C24—1181no—
552C24—1181no—
553C24—1181no—
554C24—1181no—
555C24—1181no—
556C24—1181no—
557C24—1181no—
558C24C23×D5911yescharacteristic
559C2×Q8—5916no—
560C2×Q8—1188no—
561C2×Q8—1188no—
562C2×Q8—1188no—
563C2×Q8—1188no—
564C2×Q8—1188no—
565C2×Q8—1188no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—594no—
590C22×C4—594no—
591C22×C4—594no—
592C22×C4—592no—
593C22×C4—594no—
594C22×C4—592no—
595C22×C4—592no—
596C22×C4—1182no—
597C22×C4—1182no—
598C22×C4—1182no—
599C22×C4—1182no—
600C22×C4—1181no—
601C22×C4—1181no—
602C22×C4—1181no—
603C22×C4—1182no—
604C22×C4—1181no—
605C22×C4—1181no—
606C22×C4—1181no—
607C22×C4—1181no—
608C22×C4—1181no—
609C22×C4—1182no—
610C22×C4—1182no—
611C22×C4—1181no—
612C22×C4—1182no—
613C22×C4—1181no—
614C22×C4—1181no—
615C22×C4—1181no—
616C22×C4—1181no—
617C22×C4—1181no—
618C22×C4—1181no—
619C22×C4—1182no—
620C22×C4—1181no—
621C22×C4—1181no—
622C22×C4—1182no—
623C22×C4—1181no—
624C22×C4—1188no—
625C22×C4—1188no—
626C22×C4—1188no—
627C22×C4—2364no—
628C22×C4—2364no—
629C22×C4—2364no—
630C22×C4—2364no—
631C22×C4C2×C4×D5914yes—
632C22×C4C2×C4×D5912yes—
633C22×C4C2×D23612yes—
634C22×C4C2×D23612yes—
635C22×C4C2×D23612yes—
636C22×C4#1174568512yes—
637C22×C4D4×D5912yes—
638C22×C4D4×D5912yes—
639C22×C4D4×D5912yes—
640C22×C4#1174568712yes—
641C22×C4Q8×D5912yes—
642C22×C4#1174568912yes—
643C4⋊C4—28no—
644C4⋊C4—44no—
645C4⋊C4—11816no—
646C4⋊C4—11816no—
647C4⋊C4—1188no—
648C22⋊C4—11816no—
649C22⋊C4—1188no—
650C22⋊C4—1188no—
651C22⋊C4—2368no—
652C42—28no—
653C42—11816no—
654C42—2364no—
655C23—594no—
656C23—1182no—
657C23—1182no—
658C23—1182no—
659C23—1182no—
660C23—1182no—
661C23—1182no—
662C23—1182no—
663C23—1182no—
664C23—1182no—
665C23—1182no—
666C23—1182no—
667C23—1182no—
668C23—1182no—
669C23—1182no—
670C23—1182no—
671C23—1182no—
672C23—1182no—
673C23—1182no—
674C23—2361no—
675C23—2361no—
676C23—2361no—
677C23—2361no—
678C23—2361no—
679C23—2361no—
680C23—2361no—
681C23—2361no—
682C23—2361no—
683C23—2361no—
684C23—2361no—
685C23—2361no—
686C23—2361no—
687C23—2361no—
688C23—2361no—
689C23—2361no—
690C23C22×C4×D5911yescharacteristic
691C23C2×D4×D5911yescharacteristic
692C23C2×D4×D5911yescharacteristic
693C23C2×D4×D5911yescharacteristic
694C23C22×D23611yescharacteristic
695C23C2×Q8×D5911yescharacteristic
696C23#41×D5911yescharacteristic
697C23#41×D5911yescharacteristic
698C23C2×#1174568711yescharacteristic
699C23C2×#1174568511yescharacteristic
700C23C2×#1174568911yescharacteristic
701C23#1427377211yescharacteristic
702C23#1427377411yescharacteristic
703C23#1427377411yescharacteristic
704C23#1427377511yescharacteristic
705Q8—11832no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—598no—
734C2×C4—1184no—
735C2×C4—1184no—
736C2×C4—1184no—
737C2×C4—1184no—
738C2×C4—1184no—
739C2×C4—1184no—
740C2×C4—1184no—
741C2×C4—1182no—
742C2×C4—1182no—
743C2×C4—1184no—
744C2×C4—1184no—
745C2×C4—1182no—
746C2×C4—1182no—
747C2×C4—1182no—
748C2×C4—1182no—
749C2×C4—1182no—
750C2×C4—1182no—
751C2×C4—1182no—
752C2×C4—2361no—
753C2×C4—2361no—
754C2×C4—2361no—
755C2×C4—2361no—
756C2×C4—2361no—
757C2×C4—2361no—
758C2×C4—2362no—
759C2×C4—2361no—
760C2×C4—2361no—
761C2×C4—2362no—
762C2×C4—2361no—
763C2×C4—2362no—
764C2×C4—2362no—
765C2×C4—2361no—
766C2×C4—2361no—
767C2×C4—2361no—
768C2×C4—23616no—
769C2×C4C22⋊C4×D5914yes—
770C2×C4#1427368914yes—
771C2×C4C4×D23614yes—
772C2×C4#1427369714yes—
773C2×C4#1427370014yes—
774C2×C4#1427370214yes—
775C2×C4#1427370714yescomplemented
776C2×C4#1427371214yes—
777C22—1184no—
778C22—1184no—
779C22—1184no—
780C22—2362no—
781C22—2362no—
782C22—2362no—
783C22—2362no—
784C22—2362no—
785C22—2362no—
786C22—2362no—
787C22—2362no—
788C22—2362no—
789C22—2362no—
790C22—2362no—
791C22—2362no—
792C22C2×C22⋊C4×D5911yescharacteristic
793C22C2×#1427368911yescharacteristic
794C22C2×C4×D23611yescharacteristic
795C22C4×Q8×D5911yescharacteristic
796C22C4×#1174568711yescharacteristic
797C22#1683787811yescharacteristic
798C22#1683788111yescharacteristic
799C22C2×#1427369711yescharacteristic
800C22C2×#1427370011yescharacteristic
801C22C2×#1427370211yescharacteristic
802C22C2×#1427370711yescharacteristic
803C22C2×#1427371211yescharacteristic
804C22#1683791411yescharacteristic
805C22#1683793411yescharacteristic
806C22#1683795611yescharacteristic
807C22#1683797811yescharacteristic
808C22#1683798311yescharacteristic
809C22#1683801011yescharacteristic
810C22#1683801711yescharacteristic
811C22#1683804911yescharacteristic
812C22#1683805411yescharacteristic
813C22#1683805811yescharacteristic
814C22#1683805811yescharacteristic
815C22#1683806011yescharacteristic
816C22#1683806011yescharacteristic
817C22#1683806211yescharacteristic
818C22#1683806511yescharacteristic
819C22#1683806511yescharacteristic
820C22#1683806711yescharacteristic
821C22#1683807011yescharacteristic
822C22#1683807211yescharacteristic
823C22#1683809011yescharacteristic
824C22#1683809011yescharacteristic
825C22#1683811311yescharacteristic
826C22#1683812611yescharacteristic
827C4—24no—
828C4—42no—
829C4—44no—
830C4—82no—
831C4—1188no—
832C4—2362no—
833C4—2362no—
834C4—2362no—
835C4—2364no—
836C4#1683728018yes—
837C2—2364no—
838C2C2×#1683728011yescharacteristic
839C2C4×#1427370711yescharacteristic
840C2#2142677911yescharacteristic
841C2#2142693011yescharacteristic
842C2#2142693511yescharacteristic
843C2#2142710011yescharacteristic
844C2#2142712211yescharacteristic
845C2#2142744211yescharacteristic
846C2#2142746211yescharacteristic
847C2#2142760011yescharacteristic
848C2#2142762211yescharacteristic
849C2#2142766311yescharacteristic
850C2#2142769611yescharacteristic
851C2#2142900611yescharacteristic
852C2#2142901911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×C4⋊#95C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenterC4⋊#95D59
hypocenterC59#13969
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic118C2semidirect
3. C2×#16837307C2semidirect
6. #21422348C2semidirect
9. #21422330C2semidirect
10. #21422325C2semidirect
11. C59×C4⋊#95C2semidirect
16. C2×#14273707C4semidirect
86. C2×(C2×D59)⋊C4Q8semidirect
215. C2×Dic118C22⋊C4semidirect
277. C22×D59C4×Q8semidirect
311. C2×C4×C59C22⋊Q8semidirect
421. C4⋊#95D59semidirect
470. C59#13969semidirect
775. C2×C4#14273707semidirect

Maximal subgroups

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

subgroupindex
C22×#142737072
C22×C4×Dic1182
C2×#168373072
C2×#168372592
C2×C4×(C2×D59)⋊C42
#214223482
#214223402
#214223322
#214223302
#214223252
C59×C4⋊#952
#1396959