Finite Group Databasebeta

← #28520106

Subgroups — #28520106

Order 15104.

2494 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273704C211yesmaximal, characteristic
2C23×Dic59⋊C4C211yesmaximal, characteristic
3C2×#16837322C212yesmaximal, complemented
4C2×#16837275C211yesmaximal, characteristic
5#21422360C212yesmaximal, complemented
6#21422359C212yesmaximal, complemented
7#21422347C212yesmaximal, complemented
8#21422318C211yesmaximal, characteristic
9#21422318C211yesmaximal, characteristic
10#21422318C211yesmaximal, characteristic
11C2×C59×#385C211yesmaximal, characteristic
12C23×Dic118C2211yescharacteristic
13C24×Dic59C2211yescharacteristic
14C24×Dic59C2211yescharacteristic
15C2×#14273704—24no—
16C2×#14273704—24no—
17C2×#14273704—24no—
18C22×C4⋊Dic59C2211yescharacteristic
19C22×Dic59⋊C4—24no—
20C22×Dic59⋊C4—28no—
21C22×Dic59⋊C4C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×Dic59⋊C4C2212yes—
24C22×Dic59⋊C4C2212yes—
25C22×Dic59⋊C4C2212yes—
26C22×C22⋊Dic59C2211yescharacteristic
27C22×C22⋊Dic59C2211yescharacteristic
28#16837322—28no—
29#16837275—24no—
30C2×C59⋊#95C2212yes—
31C2×C59⋊#95C2212yes—
32C2×C59⋊#95C2212yes—
33C2×C59⋊#95C2212yes—
34C2×C59⋊#95C2212yes—
35C2×C59⋊#95C2212yes—
36C2×C59⋊#95C2212yes—
37C24×C4×C59C2211yescharacteristic
38C22×C4⋊C4×C59C2212yes—
39C22×C22⋊C4×C59C2211yescharacteristic
40C22×C22⋊C4×C59C2211yescharacteristic
41C59×#385—24no—
42C2×#95×C59C2212yes—
43C22×Dic118—22no—
44C22×Dic118—22no—
45C22×Dic118—22no—
46C22×Dic118—24no—
47C22×Dic118—42no—
48C23×Dic59—22no—
49C23×Dic59—22no—
50C23×Dic59—24no—
51C23×Dic59—24no—
52C23×Dic59—22no—
53C23×Dic59—22no—
54C23×Dic59—24no—
55C23×Dic59—42no—
56C23×Dic59D414yes—
57C23×Dic59Q814yescomplemented
58C23×Dic59C2311yescharacteristic
59C23×Dic59C2311yescharacteristic
60C23×Dic59C2311yescharacteristic
61C23×Dic59C2312yes—
62C23×Dic59C2311yescharacteristic
63C23×Dic59C2312yes—
64#14273704—232no—
65C2×C4⋊Dic59—22no—
66C2×C4⋊Dic59—22no—
67C2×C4⋊Dic59—22no—
68C2×Dic59⋊C4—232no—
69C2×Dic59⋊C4—22no—
70C2×Dic59⋊C4—22no—
71C2×Dic59⋊C4—24no—
72C2×Dic59⋊C4—22no—
73C2×Dic59⋊C4—22no—
74C2×Dic59⋊C4—22no—
75C2×Dic59⋊C4—22no—
76C2×Dic59⋊C4—24no—
77C2×Dic59⋊C4—24no—
78C2×Dic59⋊C4—24no—
79C2×Dic59⋊C4—24no—
80C2×Dic59⋊C4—24no—
81C2×Dic59⋊C4—24no—
82C2×Dic59⋊C4—42no—
83C2×Dic59⋊C4D418yes—
84C2×C22⋊Dic59—22no—
85C2×C22⋊Dic59—22no—
86C2×C22⋊Dic59—22no—
87C2×C22⋊Dic59—22no—
88C2×C22⋊Dic59D414yes—
89C2×C22⋊Dic59Q814yescomplemented
90C59⋊#95—24no—
91C59⋊#95—24no—
92C59⋊#95—24no—
93C59⋊#95—24no—
94C59⋊#95—24no—
95C59⋊#95—24no—
96C59⋊#95—42no—
97C25×C59C2311yescharacteristic
98C23×C4×C59—22no—
99C23×C4×C59—24no—
100C23×C4×C59—22no—
101C23×C4×C59—22no—
102C23×C4×C59—42no—
103C23×C4×C59C2311yescharacteristic
104C23×C4×C59C2312yes—
105C23×C4×C59C2311yescharacteristic
106C23×C4×C59C2312yes—
107C2×C4⋊C4×C59—24no—
108C2×C4⋊C4×C59—24no—
109C2×C4⋊C4×C59—42no—
110C2×C22⋊C4×C59—22no—
111C2×C22⋊C4×C59—22no—
112C2×C22⋊C4×C59—22no—
113C2×C22⋊C4×C59—22no—
114C2×C22⋊C4×C59D414yes—
115C2×C22⋊C4×C59Q814yescomplemented
116#95×C59—24no—
117C24×C59—22no—
118C24×C59—22no—
119C24×C59—22no—
120C24×C59—22no—
121C24×C59C2×D412yes—
122C24×C59C2×D412yes—
123C24×C59C2×D412yes—
124C24×C59C2×Q812yes—
125C24×C59C2×Q812yes—
126C24×C59C2×Q812yes—
127C24×C59#4112yes—
128C24×C59C2411yescharacteristic
129C22×C4×C59—28no—
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—22no—
137C22×C4×C59—22no—
138C22×C4×C59—22no—
139C22×C4×C59—22no—
140C22×C4×C59—22no—
141C22×C4×C59—22no—
142C22×C4×C59—22no—
143C22×C4×C59—22no—
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—48no—
151C22×C4×C59—48no—
152C22×C4×C59—44no—
153C22×C4×C59—44no—
154C22×C4×C59C2×D414yes—
155C22×C4×C59C2×D412yes—
156C22×C4×C59C2×D412yes—
157C22×C4×C59C2×Q814yes—
158C22×Dic59—28no—
159C22×Dic59—216no—
160C22×Dic59—28no—
161C22×Dic59—28no—
162C22×Dic59—22no—
163C22×Dic59—22no—
164C22×Dic59—21no—
165C22×Dic59—21no—
166C22×Dic59—22no—
167C22×Dic59—22no—
168C22×Dic59—22no—
169C22×Dic59—216no—
170C22×Dic59—28no—
171C22×Dic59—22no—
172C22×Dic59—22no—
173C22×Dic59—22no—
174C22×Dic59—21no—
175C22×Dic59—21no—
176C22×Dic59—21no—
177C22×Dic59—21no—
178C22×Dic59—22no—
179C22×Dic59—21no—
180C22×Dic59—21no—
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×Dic59—28no—
190C22×Dic59—44no—
191C22×Dic59—48no—
192C22×Dic59—48no—
193C22×Dic59C2×D412yes—
194C22×Dic59C2×D412yes—
195C22×Dic59C2×D412yes—
196C22×Dic59C2×D414yes—
197C22×Dic59C2×D412yes—
198C22×Dic59C2×D414yes—
199C22×Dic59C2×Q814yes—
200C22×Dic59C2×Q814yes—
201C22×Dic59#4114yes—
202C2×Dic118—28no—
203C2×Dic118—48no—
204C2×Dic118—48no—
205C2×Dic118—44no—
206C2×Dic118—44no—
207C4⋊C4×C59—48no—
208C22⋊C4×C59—28no—
209C22⋊C4×C59—28no—
210C22⋊Dic59—28no—
211C22⋊Dic59—28no—
212C4⋊Dic59—28no—
213Dic59⋊C4—216no—
214Dic59⋊C4—28no—
215Dic59⋊C4—28no—
216Dic59⋊C4—216no—
217Dic59⋊C4—48no—
218C23×C59—22no—
219C23×C59—24no—
220C23×C59—22no—
221C23×C59—24no—
222C23×C59—22no—
223C23×C59—22no—
224C23×C59—24no—
225C23×C59—24no—
226C23×C59—24no—
227C23×C59—24no—
228C23×C59—24no—
229C23×C59—24no—
230C23×C59—24no—
231C23×C59—24no—
232C23×C59—24no—
233C23×C59—24no—
234C23×C59#12014yes—
235C23×C59C22⋊Q814yes—
236C23×C59C22⋊Q814yes—
237C23×C59C22⋊Q814yes—
238C23×C59C4⋊Q814yes—
239C23×C59C4⋊Q814yes—
240C23×C59C4⋊Q814yes—
241C23×C59C22×D411yescharacteristic
242C23×C59C22×D412yes—
243C23×C59C22×D411yescharacteristic
244C23×C59C22×D411yescharacteristic
245C23×C59C22×Q811yescharacteristic
246C23×C59C22×Q811yescharacteristic
247C23×C59C22×Q811yescharacteristic
248C23×C59C2×#4112yes—
249C23×C59C2×#4111yescharacteristic
250C23×C59H(5,𝔽2)12yes—
251C23×C592−1+412yes—
252C2×C4×C59—24no—
253C2×C4×C59—22no—
254C2×C4×C59—22no—
255C2×C4×C59—24no—
256C2×C4×C59—24no—
257C2×C4×C59—24no—
258C2×C4×C59—24no—
259C2×C4×C59—24no—
260C2×C4×C59—24no—
261C2×C4×C59—24no—
262C2×C4×C59—416no—
263C2×C4×C59—41no—
264C2×C4×C59—42no—
265C2×C4×C59—41no—
266C2×C4×C59—42no—
267C2×C4×C59—41no—
268C2×C4×C59—42no—
269C2×C4×C59—41no—
270C2×C4×C59—42no—
271C2×C4×C59—42no—
272C2×C4×C59—42no—
273C2×C4×C59—42no—
274C2×C4×C59—42no—
275C2×C4×C59—42no—
276C2×C4×C59—42no—
277C2×Dic59—232no—
278C2×Dic59—24no—
279C2×Dic59—22no—
280C2×Dic59—24no—
281C2×Dic59—24no—
282C2×Dic59—24no—
283C2×Dic59—24no—
284C2×Dic59—24no—
285C2×Dic59—22no—
286C2×Dic59—24no—
287C2×Dic59—24no—
288C2×Dic59—22no—
289C2×Dic59—22no—
290C2×Dic59—22no—
291C2×Dic59—22no—
292C2×Dic59—24no—
293C2×Dic59—22no—
294C2×Dic59—24no—
295C2×Dic59—24no—
296C2×Dic59—24no—
297C2×Dic59—24no—
298C2×Dic59—416no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301C2×Dic59—42no—
302C2×Dic59—41no—
303C2×Dic59—41no—
304C2×Dic59—42no—
305C2×Dic59—42no—
306C2×Dic59—42no—
307C2×Dic59—42no—
308C2×Dic59—42no—
309C2×Dic59—42no—
310C2×Dic59—42no—
311C2×Dic59#12014yes—
312C2×Dic59C22⋊Q818yescomplemented
313Dic118—416no—
314#14720—591nomaximal, Sylow
315C22×C59—24no—
316C22×C59—24no—
317C22×C59—24no—
318C22×C59—24no—
319C22×C59—24no—
320C22×C59—24no—
321C22×C59—28no—
322C22×C59—28no—
323C22×C59—28no—
324C22×C59—28no—
325C22×C59#39518yescomplemented
326C22×C59C2×#12011yescharacteristic
327C22×C59C2×#12011yescharacteristic
328C22×C59C2×C22⋊Q812yes—
329C22×C59C2×C22⋊Q811yescharacteristic
330C22×C59C2×C22⋊Q811yescharacteristic
331C22×C59C2×C22⋊Q811yescharacteristic
332C22×C59#52511yescharacteristic
333C22×C59#52512yes—
334C22×C59C2×C4⋊Q811yescharacteristic
335C22×C59C2×C4⋊Q811yescharacteristic
336C22×C59C2×C4⋊Q811yescharacteristic
337C22×C59#53411yescharacteristic
338C22×C59#53611yescharacteristic
339C22×C59#53912yes—
340C22×C59#54412yes—
341C22×C59D4212yes—
342C22×C59D4212yes—
343C22×C59#54712yes—
344C22×C59#54712yes—
345C22×C59D4×Q812yes—
346C22×C59D4×Q812yes—
347C22×C59#55412yes—
348C22×C59#55412yes—
349C4×C59—42no—
350C4×C59—44no—
351C4×C59—42no—
352C4×C59—44no—
353Dic59—28no—
354Dic59—24no—
355Dic59—42no—
356Dic59—42no—
357Dic59—42no—
358Dic59—44no—
359C22×C22⋊Q8—591no—
360C23×C4⋊C4—591no—
361C2×#395—592no—
362C2×#385—591no—
363C2×#385D5911yescharacteristic
364#1444—592no—
365#1444—592no—
366#1441—592no—
367C22⋊#95—591no—
368C22⋊#95—591no—
369C22⋊#95—591no—
370C2×C59—28no—
371C2×C59C2×#39511yescharacteristic
372C2×C59#240311yescharacteristic
373C2×C59#240611yescharacteristic
374C2×C59#243411yescharacteristic
375C2×C59#244012yes—
376C2×C59#244012yes—
377C2×C59#244912yes—
378C2×C59#244912yes—
379C2×C59#258311yescharacteristic
380C2×C59#262711yescharacteristic
381C2×C59#284811yescharacteristic
382C23×Q8—591no—
383C24×C4—591no—
384C24×C4—591no—
385C24×C4C2×D5911yescharacteristic
386C2×C22⋊Q8—1184no—
387C2×C22⋊Q8—1184no—
388C2×C22⋊Q8—1184no—
389C22×C4⋊C4—592no—
390C22×C4⋊C4—592no—
391C22×C4⋊C4—591no—
392C22×C4⋊C4—591no—
393C22×C4⋊C4—591no—
394C22×C4⋊C4—592no—
395C22×C4⋊C4—1188no—
396C22×C4⋊C4—1184no—
397C22×C4⋊C4C2×D5912yes—
398C22×C22⋊C4—591no—
399C22×C22⋊C4—591no—
400C22×C22⋊C4C2×D5911yescharacteristic
401C22×C22⋊C4C2×D5911yescharacteristic
402#395—1188no—
403#385—24no—
404#385—1184no—
405C2×#95—592no—
406C2×#95—592no—
407C2×#95—592no—
408C2×#95—592no—
409C2×#95—592no—
410C2×#95—592no—
411C2×#95—592no—
412C2×#95C2×D5912yes—
413C59#1472011yescharacteristic, complemented, Sylow
414C25C22×D5911yescharacteristic
415C22×Q8—1182no—
416C22×Q8—1182no—
417C22×Q8—1184no—
418C22×Q8—1182no—
419C22×Q8—2362no—
420C23×C4—22no—
421C23×C4—24no—
422C23×C4—22no—
423C23×C4—22no—
424C23×C4—42no—
425C23×C4—591no—
426C23×C4—592no—
427C23×C4—594no—
428C23×C4—591no—
429C23×C4—591no—
430C23×C4—592no—
431C23×C4—591no—
432C23×C4—594no—
433C23×C4—1184no—
434C23×C4—1184no—
435C23×C4—1184no—
436C23×C4—1182no—
437C23×C4—1182no—
438C23×C4—1182no—
439C23×C4—1182no—
440C23×C4—2362no—
441C23×C4C22×D5912yes—
442C23×C4C22×D5912yes—
443C23×C4C22×D5911yescharacteristic
444C23×C4C22×D5911yescharacteristic
445C22⋊Q8—11832no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—598no—
450C2×C4⋊C4—1184no—
451C2×C4⋊C4—1184no—
452C2×C4⋊C4—1184no—
453C2×C4⋊C4—1184no—
454C2×C4⋊C4—1182no—
455C2×C4⋊C4—1182no—
456C2×C4⋊C4—1182no—
457C2×C4⋊C4—1182no—
458C2×C4⋊C4—1182no—
459C2×C4⋊C4—1182no—
460C2×C4⋊C4—11832no—
461C2×C4⋊C4—1184no—
462C2×C4⋊C4—1182no—
463C2×C4⋊C4—1182no—
464C2×C4⋊C4—1182no—
465C2×C4⋊C4—1184no—
466C2×C4⋊C4—1184no—
467C2×C4⋊C4—2362no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—594no—
473C2×C22⋊C4—594no—
474C2×C22⋊C4—1182no—
475C2×C22⋊C4—1182no—
476C2×C22⋊C4—1182no—
477C2×C22⋊C4—1182no—
478C2×C22⋊C4Dic11814yescomplemented
479C2×C22⋊C4C22⋊D5914yes—
480#95—24no—
481#95—1184no—
482#95—1184no—
483#95—1184no—
484#95—1184no—
485#95—1184no—
486#95—1184no—
487#95—2362no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24C2×Dic11812yes—
493C24#1174568512yes—
494C24D4×D5912yes—
495C24D4×D5912yes—
496C24Q8×D5912yes—
497C24Q8×D5912yes—
498C24C2×C22⋊D5912yes—
499C24C23×D5911yescharacteristic
500C2×Q8—1188no—
501C2×Q8—2368no—
502C2×Q8—2364no—
503C2×Q8—2368no—
504C2×Q8—2364no—
505C22×C4—28no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—594no—
531C22×C4—594no—
532C22×C4—592no—
533C22×C4—594no—
534C22×C4—594no—
535C22×C4—592no—
536C22×C4—592no—
537C22×C4—592no—
538C22×C4—594no—
539C22×C4—11816no—
540C22×C4—1188no—
541C22×C4—1188no—
542C22×C4—1188no—
543C22×C4—11816no—
544C22×C4—1188no—
545C22×C4—1182no—
546C22×C4—1182no—
547C22×C4—1181no—
548C22×C4—1181no—
549C22×C4—1182no—
550C22×C4—1182no—
551C22×C4—1182no—
552C22×C4—1188no—
553C22×C4—1182no—
554C22×C4—1182no—
555C22×C4—1182no—
556C22×C4—1181no—
557C22×C4—1181no—
558C22×C4—1182no—
559C22×C4—1181no—
560C22×C4—1181no—
561C22×C4—1181no—
562C22×C4—1181no—
563C22×C4—1182no—
564C22×C4—1182no—
565C22×C4—1182no—
566C22×C4—1182no—
567C22×C4—1182no—
568C22×C4—1182no—
569C22×C4—1182no—
570C22×C4—1182no—
571C22×C4—2364no—
572C22×C4—2368no—
573C22×C4—2368no—
574C22×C4C2×Dic11814yes—
575C22×C4D4×D5914yes—
576C22×C4C2×C22⋊D5912yes—
577C22×C4C2×C22⋊D5912yes—
578C4⋊C4—48no—
579C4⋊C4—11816no—
580C4⋊C4—11816no—
581C4⋊C4—1188no—
582C4⋊C4—1188no—
583C4⋊C4—1188no—
584C4⋊C4—2368no—
585C22⋊C4—28no—
586C22⋊C4—28no—
587C22⋊C4—1188no—
588C22⋊C4—1188no—
589C23—24no—
590C23—22no—
591C23—24no—
592C23—22no—
593C23—22no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—22no—
605C23#1427369514yes—
606C23#1427370514yes—
607C23#1427370514yes—
608C23#1427370614yes—
609C23#1427372514yes—
610C23#1427372614yes—
611C23#1427372614yes—
612C23C2×D4×D5912yes—
613C23C2×D4×D5911yescharacteristic
614C23C2×D4×D5911yescharacteristic
615C23C22×C22⋊D5911yescharacteristic
616C23C2×Q8×D5911yescharacteristic
617C23C2×Q8×D5911yescharacteristic
618C23C22×Dic11811yescharacteristic
619C23#41×D5912yes—
620C23C2×#1174568511yescharacteristic
621C23#1427377212yes—
622C23#1427377412yes—
623Q8—23616no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—416no—
635C2×C4—41no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—41no—
648C2×C4—42no—
649C2×C4—598no—
650C2×C4—594no—
651C2×C4—11832no—
652C2×C4—1184no—
653C2×C4—1184no—
654C2×C4—1184no—
655C2×C4—1184no—
656C2×C4—1184no—
657C2×C4—1182no—
658C2×C4—1184no—
659C2×C4—1184no—
660C2×C4—1184no—
661C2×C4—1182no—
662C2×C4—1184no—
663C2×C4—1182no—
664C2×C4—1184no—
665C2×C4—1184no—
666C2×C4—1184no—
667C2×C4—1184no—
668C2×C4—1182no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—1182no—
672C2×C4—23616no—
673C2×C4—2361no—
674C2×C4—2362no—
675C2×C4—2361no—
676C2×C4—2361no—
677C2×C4—2362no—
678C2×C4—2362no—
679C2×C4—2362no—
680C2×C4—2362no—
681C2×C4—2362no—
682C2×C4—2362no—
683C2×C4—2362no—
684C2×C4—2361no—
685C22—24no—
686C22—24no—
687C22—28no—
688C22—28no—
689C22—24no—
690C22—28no—
691C22—28no—
692C22—24no—
693C22—24no—
694C22—24no—
695C22#1683732218yescomplemented
696C22#120×D5911yescharacteristic
697C22C2×#1427369511yescharacteristic
698C22C22⋊Q8×D5912yes—
699C22C2×#1427370511yescharacteristic
700C22C2×#1427370511yescharacteristic
701C22C2×#1427370611yescharacteristic
702C22#1683791011yescharacteristic
703C22#1683791112yes—
704C22C2×#1427372511yescharacteristic
705C22C2×#1427372611yescharacteristic
706C22C2×#1427372611yescharacteristic
707C22#1683796211yescharacteristic
708C22#1683797411yescharacteristic
709C22#1683799412yes—
710C22#1683803112yes—
711C22#1683803412yes—
712C22D4×C22⋊D5912yes—
713C22#1683805012yes—
714C22#1683805112yes—
715C22#1683806512yes—
716C22D4×Dic11812yes—
717C22#1683810612yes—
718C22#1683811112yes—
719C4—44no—
720C4—44no—
721C4—42no—
722C4—42no—
723C4—1188no—
724C4—1184no—
725C4—2364no—
726C4—2362no—
727C4—2362no—
728C4—2362no—
729C2—28no—
730C2C2×#1683732211yescharacteristic
731C2#2142740711yescharacteristic
732C2#2142742811yescharacteristic
733C2#2142773811yescharacteristic
734C2#2142779512yes—
735C2#2142779712yes—
736C2#2142789912yes—
737C2#2142790712yes—
738C2#2142947511yescharacteristic
739C2#2142991511yescharacteristic
740C2#2143238211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutator, socle, cosocleC24×C59C24
FittingC2×C59×#385C2
prime radicalC25×C59C23
hypercenterC2×#385D59
hypocenterC59#14720
LCSG ▷ C24×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C2×#16837322C2semidirect
5. #21422360C2semidirect
6. #21422359C2semidirect
7. #21422347C2semidirect
57. C23×Dic59Q8semidirect
89. C2×C22⋊Dic59Q8semidirect
115. C2×C22⋊C4×C59Q8semidirect
312. C2×Dic59C22⋊Q8semidirect
325. C22×C59#395semidirect
413. C59#14720semidirect
478. C2×C22⋊C4Dic118semidirect
695. C22#16837322semidirect

Maximal subgroups

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

subgroupindex
C22×#142737042
C23×Dic59⋊C42
C2×#168373222
C2×#168372752
#214223602
#214223592
#214223472
#214223182
C2×C59×#3852
#1472059