Finite Group Databasebeta

← #28616195

Subgroups — #28616195

Order 15104.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837445C211yesmaximal, characteristic, complemented
2C2×#16837403C211yesmaximal, characteristic, complemented
3C2×#16837403C211yesmaximal, characteristic, complemented
4C2×#16837366C211yesmaximal, characteristic, complemented
5C2×#16837262C211yesmaximal, characteristic, complemented
6#21425296C212yesmaximal, complemented
7#21425289C212yesmaximal, complemented
8#21425282C212yesmaximal, complemented
9#21425275C212yesmaximal, complemented
10#21423817C211yesmaximal, characteristic, complemented
11C2×C59×#525C211yesmaximal, characteristic
12C22×#11745664C2211yescharacteristic
13C22×#11745664C2211yescharacteristic
14C22×C4⋊Dic59C2211yescharacteristic
15C22×C4⋊Dic59C2211yescharacteristic
16C22×C22⋊Dic59—21no—
17#16837445—24no—
18C2×#14273660C2212yescomplemented
19C2×#14273658C2212yescomplemented
20#16837403—24no—
21#16837403—24no—
22C2×#14273651C2212yescomplemented
23C2×#14273651C2212yescomplemented
24C2×#14273648C2212yescomplemented
25C2×#14273648C2212yescomplemented
26#16837366—24no—
27C2×C22⋊(C59⋊C8)C2212yes—
28C2×C22⋊(C59⋊C8)C2212yes—
29#16837262—21no—
30#16837262—21no—
31#16837262C2212yes—
32#16837262C2212yes—
33C2×C59⋊#95—21no—
34#16837164C2212yescomplemented
35#16837164C2212yescomplemented
36C22×#41×C59C2211yescharacteristic
37C24×C4×C59C2211yescharacteristic
38C59×#525—24no—
39C59×#525—24no—
40C2×#123×C59—21no—
41C2×C22⋊Q8×C59C2211yescharacteristic
42C2×C22⋊Q8×C59C2211yescharacteristic
43C2×#121×C59C2211yescharacteristic
44C2×#121×C59C2211yescharacteristic
45C2×#120×C59—21no—
46C2×C4×D4×C59—21no—
47C2×C4×D4×C59—21no—
48C2×#117×C59C2211yescharacteristic
49C23×Dic59—21no—
50C23×Dic59—21no—
51C2×#11745664—22no—
52C2×#11745664—22no—
53C2×#11745664—22no—
54C2×#11745664—22no—
55C2×#11745664—22no—
56C2×#11745664D414yescomplemented
57C22×C59⋊C8C2312yes—
58C22×C59⋊C8C2312yes—
59C2×C4⋊Dic59—22no—
60C2×C4⋊Dic59—22no—
61C2×C4⋊Dic59—22no—
62C2×C4⋊Dic59—22no—
63C2×C4⋊Dic59—21no—
64C2×C4⋊Dic59—21no—
65C2×C4⋊Dic59C2312yes—
66C2×C4⋊Dic59C2312yes—
67C2×C22⋊Dic59—22no—
68C2×C22⋊Dic59—22no—
69C2×C22⋊Dic59—44no—
70#14273660—24no—
71#14273658—24no—
72#14273651—24no—
73#14273651—24no—
74#14273648—24no—
75#14273648—24no—
76C22⋊(C59⋊C8)—24no—
77C22⋊(C59⋊C8)—24no—
78C59⋊#95—22no—
79C59⋊#95—22no—
80C25×C59D411yescharacteristic
81C2×#41×C59—22no—
82C2×#41×C59—22no—
83C2×#41×C59—22no—
84C2×#41×C59—22no—
85C2×#41×C59—22no—
86C2×#41×C59D414yes—
87C22×Q8×C59C2311yescharacteristic
88C22×D4×C59—21no—
89C22×D4×C59—21no—
90C22×D4×C59—21no—
91C22×D4×C59C2311yescharacteristic
92C23×C4×C59—21no—
93C23×C4×C59—22no—
94C23×C4×C59—22no—
95C23×C4×C59—22no—
96C23×C4×C59—22no—
97C23×C4×C59—22no—
98C23×C4×C59—22no—
99C23×C4×C59D411yescharacteristic
100C23×C4×C59D411yescharacteristic
101C23×C4×C59D411yescharacteristic
102C23×C4×C59C2311yescharacteristic
103C23×C4×C59C2311yescharacteristic
104C23×C4×C59C2311yescharacteristic
105#123×C59—28no—
106C22⋊Q8×C59—22no—
107C22⋊Q8×C59—22no—
108C22⋊Q8×C59—22no—
109C22⋊Q8×C59—22no—
110#121×C59—22no—
111#121×C59—22no—
112#121×C59—22no—
113#121×C59—22no—
114#120×C59—28no—
115C4×D4×C59—28no—
116C4×D4×C59—28no—
117#117×C59—22no—
118#117×C59D414yes—
119C2×C4⋊C4×C59—21no—
120C2×C4⋊C4×C59—21no—
121C2×C4⋊C4×C59C2311yescharacteristic
122C2×C4⋊C4×C59C2311yescharacteristic
123C2×C22⋊C4×C59—21no—
124C2×C22⋊C4×C59—21no—
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59—21no—
127C2×C22⋊C4×C59—21no—
128C2×C42×C59—21no—
129C24×C59—22no—
130C24×C59—22no—
131C24×C59—22no—
132C24×C59—22no—
133C24×C59—22no—
134C24×C59—21no—
135C24×C59—41no—
136C24×C59—41no—
137C24×C59C2×D411yescharacteristic
138C24×C59C2×D411yescharacteristic
139C24×C59C2×D411yescharacteristic
140#41×C59—28no—
141#41×C59—28no—
142#41×C59—44no—
143#41×C59—44no—
144C2×Q8×C59—21no—
145C2×Q8×C59—21no—
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×C59—21no—
149C2×Q8×C59C2×D412yes—
150C2×D4×C59—24no—
151C2×D4×C59—24no—
152C2×D4×C59—24no—
153C2×D4×C59—21no—
154C2×D4×C59—21no—
155C2×D4×C59—21no—
156C2×D4×C59—21no—
157C2×D4×C59—21no—
158C2×D4×C59—42no—
159C2×D4×C59—42no—
160C2×D4×C59—42no—
161C2×D4×C59—42no—
162C2×D4×C59—42no—
163C2×D4×C59—42no—
164C2×D4×C59C2×D412yes—
165C22×C4×C59—22no—
166C22×C4×C59—22no—
167C22×C4×C59—22no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—22no—
172C22×C4×C59—22no—
173C22×C4×C59—24no—
174C22×C4×C59—22no—
175C22×C4×C59—22no—
176C22×C4×C59—22no—
177C22×C4×C59—22no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—44no—
191C22×C4×C59—44no—
192C22×C4×C59—42no—
193C22×C4×C59—44no—
194C22×C4×C59—42no—
195C22×C4×C59—44no—
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2×D412yes—
200C22×C4×C59C2×D412yes—
201C22×C4×C59C2×D412yes—
202C22×C4×C59#4112yes—
203C22×C4×C59#4112yes—
204C22×C4×C59#4112yes—
205C22×C4×C59C2411yescharacteristic
206C22×Dic59—22no—
207C22×Dic59—22no—
208C22×Dic59—42no—
209C22×Dic59—42no—
210C22×Dic59—42no—
211C22×Dic59—42no—
212C22×Dic59—42no—
213C22×Dic59—42no—
214C4⋊C4×C59—24no—
215C4⋊C4×C59—24no—
216C4⋊C4×C59—21no—
217C4⋊C4×C59—21no—
218C4⋊C4×C59C2×D412yes—
219C4⋊C4×C59C2×D412yes—
220C22⋊C4×C59—24no—
221C22⋊C4×C59—24no—
222C22⋊C4×C59—24no—
223C22⋊C4×C59—24no—
224C22⋊C4×C59—24no—
225C42×C59—24no—
226C22⋊Dic59—44no—
227C22⋊Dic59—44no—
228C4⋊Dic59—22no—
229C4⋊Dic59—22no—
230C4⋊Dic59—22no—
231C4⋊Dic59—22no—
232C4⋊Dic59—42no—
233C4⋊Dic59—42no—
234#11745664—28no—
235#11745664—44no—
236C2×C59⋊C8—22no—
237C2×C59⋊C8—22no—
238C2×C59⋊C8—22no—
239C2×C59⋊C8—22no—
240C2×C59⋊C8—22no—
241C2×C59⋊C8C2×D414yes—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59—28no—
247C23×C59—21no—
248C23×C59—21no—
249C23×C59—21no—
250C23×C59—21no—
251C23×C59—21no—
252C23×C59—21no—
253C23×C59—21no—
254C23×C59—21no—
255C23×C59—21no—
256C23×C59—21no—
257C23×C59—21no—
258C23×C59—21no—
259C23×C59—22no—
260C23×C59—44no—
261C23×C59—44no—
262C23×C59—44no—
263C23×C59—44no—
264C23×C59—44no—
265C23×C59—44no—
266C23×C59—41no—
267C23×C59—41no—
268C23×C59—41no—
269C23×C59—41no—
270C23×C59—41no—
271C23×C59—41no—
272C23×C59#12012yes—
273C23×C59#12112yes—
274C23×C59#12312yes—
275C23×C59AGL(1,ℤ/8)12yes—
276C23×C59#13712yes—
277C23×C59C22×D411yescharacteristic
278Q8×C59—22no—
279Q8×C59—22no—
280Q8×C59—41no—
281Q8×C59—41no—
282D4×C59—22no—
283D4×C59—22no—
284D4×C59—48no—
285D4×C59—48no—
286D4×C59—48no—
287D4×C59—41no—
288D4×C59—41no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—21no—
292C2×C4×C59—21no—
293C2×C4×C59—22no—
294C2×C4×C59—21no—
295C2×C4×C59—21no—
296C2×C4×C59—21no—
297C2×C4×C59—21no—
298C2×C4×C59—41no—
299C2×C4×C59—41no—
300C2×C4×C59—41no—
301C2×C4×C59—41no—
302C2×C4×C59—41no—
303C2×C4×C59—41no—
304C2×C4×C59—44no—
305C2×C4×C59—41no—
306C2×C4×C59—41no—
307C2×C4×C59—41no—
308C2×C4×C59—41no—
309C2×C4×C59—41no—
310C2×C4×C59—41no—
311C2×C4×C59—41no—
312C2×C4×C59—41no—
313C2×C4×C59—44no—
314C2×C4×C59—44no—
315C2×C4×C59—48no—
316C2×C4×C59#12012yes—
317C2×C4×C59#12114yes—
318C2×C4×C59#12114yes—
319C2×C4×C59#12112yes—
320C2×C4×C59#12314yes—
321C2×C4×C59#12312yes—
322C2×C4×C59#12414yes—
323C2×C4×C59C22×D411yescharacteristic
324C2×C4×C59C22×D411yescharacteristic
325C2×C4×C59C22×D411yescharacteristic
326C2×C4×C59C2×#4111yescharacteristic
327C2×C4×C59C2×#4111yescharacteristic
328C2×C4×C59C2×#4111yescharacteristic
329C2×Dic59—42no—
330C2×Dic59—42no—
331C2×Dic59—42no—
332C2×Dic59—42no—
333C2×Dic59—42no—
334C2×Dic59—42no—
335C2×Dic59—84no—
336C2×Dic59—84no—
337C59⋊C8—24no—
338C59⋊C8—42no—
339#23482—591nomaximal, Sylow
340C22×C59—22no—
341C22×C59—22no—
342C22×C59—22no—
343C22×C59—22no—
344C22×C59—22no—
345C22×C59—22no—
346C22×C59—22no—
347C22×C59—22no—
348C22×C59—22no—
349C22×C59—22no—
350C22×C59—22no—
351C22×C59—22no—
352C22×C59—416no—
353C22×C59—41no—
354C22×C59—41no—
355C22×C59—41no—
356C22×C59—41no—
357C22×C59—41no—
358C22×C59—41no—
359C22×C59—41no—
360C22×C59—41no—
361C22×C59—42no—
362C22×C59—42no—
363C22×C59—42no—
364C22×C59—81no—
365C22×C59—81no—
366C22×C59—81no—
367C22×C59—81no—
368C22×C59#39414yes—
369C22×C59C2×#12011yescharacteristic
370C22×C59C2×#12111yescharacteristic
371C22×C59C2×#12311yescharacteristic
372C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
373C22×C59C2×#13711yescharacteristic
374C22×C59#57511yescharacteristic
375C22×C59#57511yescharacteristic
376C4×C59—41no—
377C4×C59—41no—
378C4×C59—42no—
379C4×C59—42no—
380C4×C59—42no—
381C4×C59#39414yes—
382C4×C59C2×#12111yescharacteristic
383C4×C59C2×#12111yescharacteristic
384C4×C59C2×#12311yescharacteristic
385C4×C59C2×#12411yescharacteristic
386Dic59—82no—
387Dic59—82no—
388C2×#525D5911yescharacteristic
389C2×#428—591no—
390C2×#417—591no—
391C2×#417—591no—
392C2×#407—591no—
393C2×#380—591no—
394#2036—592no—
395#2035—592no—
396#2034—592no—
397#2033—592no—
398#1736—591no—
399C2×C59—24no—
400C2×C59—42no—
401C2×C59—42no—
402C2×C59—82no—
403C2×C59C2×#39411yescharacteristic
404C2×C59#300611yescharacteristic
405C2×C59#300711yescharacteristic
406C2×C59#305511yescharacteristic
407C2×C59#305611yescharacteristic
408C2×C59#309211yescharacteristic
409C2×C59#309311yescharacteristic
410C22×#41C2×D5911yescharacteristic
411C24×C4C2×D5911yescharacteristic
412C22×M16—591no—
413C22×M16—591no—
414#525—24no—
415#525—24no—
416C2×#123—21no—
417C2×C22⋊Q8C2×D5911yescharacteristic
418C2×C22⋊Q8C2×D5911yescharacteristic
419C2×#121C2×D5911yescharacteristic
420C2×#121C2×D5911yescharacteristic
421C2×#120—21no—
422C2×C4×D4—21no—
423C2×C4×D4—21no—
424C2×#117C2×D5911yescharacteristic
425C22×C4⋊C4—591no—
426C22×C4⋊C4—591no—
427C22×C22⋊C4—1181no—
428#428—1184no—
429C2×#107—592no—
430C2×#106—592no—
431#417—1184no—
432#417—1184no—
433C2×#103—592no—
434C2×#103—592no—
435C2×#102—592no—
436C2×#102—592no—
437#407—1184no—
438C2×C22⋊C8—592no—
439C2×C22⋊C8—592no—
440#380—592no—
441#380—592no—
442#380—1181no—
443#380—1181no—
444C2×#95—1181no—
445#340—592no—
446#340—592no—
447C59#2348211yescharacteristic, complemented, Sylow
448C25C22⋊D5911yescharacteristic
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41C22⋊D5914yes—
455C22×Q8C22×D5911yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4C22×D5911yescharacteristic
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—21no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—1181no—
468C23×C4—1181no—
469C23×C4C22⋊D5911yescharacteristic
470C23×C4C22⋊D5911yescharacteristic
471C23×C4C22⋊D5911yescharacteristic
472C23×C4C22×D5911yescharacteristic
473C23×C4C22×D5911yescharacteristic
474C23×C4C22×D5911yescharacteristic
475C2×M16—594no—
476C2×M16—1182no—
477C2×M16—1182no—
478C2×M16—1182no—
479C2×M16—1182no—
480C2×M16—1182no—
481C22×C8—592no—
482C22×C8—592no—
483#123—28no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#121—22no—
492#120—28no—
493C4×D4—28no—
494C4×D4—28no—
495#117—22no—
496#117C22⋊D5914yes—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—592no—
500C2×C4⋊C4—592no—
501C2×C4⋊C4—1182no—
502C2×C4⋊C4—1182no—
503C2×C4⋊C4—1182no—
504C2×C4⋊C4—1182no—
505C2×C4⋊C4—1181no—
506C2×C4⋊C4—1181no—
507C2×C4⋊C4C22×D5911yescharacteristic
508C2×C4⋊C4C22×D5911yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—1182no—
515C2×C22⋊C4—1182no—
516C2×C22⋊C4—2364no—
517C2×C42—21no—
518#107—1184no—
519#106—1184no—
520#103—1184no—
521#103—1184no—
522#102—1184no—
523#102—1184no—
524C22⋊C8—1184no—
525C22⋊C8—1184no—
526#95—1182no—
527#95—1182no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—21no—
534C24—41no—
535C24—41no—
536C24C2×C22⋊D5911yescharacteristic
537C24C2×C22⋊D5911yescharacteristic
538C24C2×C22⋊D5911yescharacteristic
539#41—28no—
540#41—28no—
541#41—44no—
542#41—44no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×C22⋊D5912yes—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4C2×C22⋊D5912yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—42no—
592C22×C4—44no—
593C22×C4—42no—
594C22×C4—44no—
595C22×C4—1182no—
596C22×C4—1182no—
597C22×C4—2362no—
598C22×C4—2362no—
599C22×C4—2362no—
600C22×C4—2362no—
601C22×C4—2362no—
602C22×C4—2362no—
603C22×C4D4×D5912yes—
604C22×C4#1174568712yes—
605C22×C4#1174568712yes—
606C22×C4#1174568712yes—
607C22×C4C2×C22⋊D5911yescharacteristic
608C22×C4C2×C22⋊D5911yescharacteristic
609C22×C4C2×C22⋊D5911yescharacteristic
610C22×C4C2×C22⋊D5912yes—
611C22×C4C2×C22⋊D5912yes—
612C22×C4C23×D5911yescharacteristic
613M16—1188no—
614M16—2364no—
615C2×C8—594no—
616C2×C8—1182no—
617C2×C8—1182no—
618C2×C8—1182no—
619C2×C8—1182no—
620C2×C8—1182no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—1182no—
626C4⋊C4—1182no—
627C4⋊C4—1182no—
628C4⋊C4—1182no—
629C4⋊C4—2362no—
630C4⋊C4—2362no—
631C4⋊C4C2×C22⋊D5912yes—
632C4⋊C4C2×C22⋊D5912yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—2364no—
639C22⋊C4—2364no—
640C42—24no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—28no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23#1427369612yes—
672C23#1427369912yes—
673C23#1427370812yes—
674C23#1427375212yes—
675C23#1427375712yes—
676C23C22×C22⋊D5911yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—48no—
685D4—48no—
686D4—41no—
687D4—41no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—44no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—48no—
715C2×C4—4724no—
716C2×C4—4724no—
717C2×C4—2362no—
718C2×C4—2362no—
719C2×C4—2362no—
720C2×C4—2362no—
721C2×C4—2362no—
722C2×C4—2362no—
723C2×C4#1427369612yes—
724C2×C4#1427369814yes—
725C2×C4#1427369914yes—
726C2×C4#1427369912yes—
727C2×C4#1427370814yes—
728C2×C4#1427370812yes—
729C2×C4#1427371414yes—
730C2×C4C2×D4×D5911yescharacteristic
731C2×C4C22×C22⋊D5911yescharacteristic
732C2×C4C22×C22⋊D5911yescharacteristic
733C2×C4C2×#1174568711yescharacteristic
734C2×C4C2×#1174568711yescharacteristic
735C2×C4C2×#1174568711yescharacteristic
736C8—1184no—
737C8—2362no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22#1683731614yes—
767C22C2×#1427369611yescharacteristic
768C22C2×#1427369911yescharacteristic
769C22C2×#1427370811yescharacteristic
770C22C2×#1427375211yescharacteristic
771C22C2×#1427375711yescharacteristic
772C22#1683820011yescharacteristic
773C22#1683820011yescharacteristic
774C4—42no—
775C4—42no—
776C4—41no—
777C4—41no—
778C4—42no—
779C4—4722no—
780C4—4722no—
781C4#1683731614yes—
782C4C2×#1427369811yescharacteristic
783C4C2×#1427369911yescharacteristic
784C4C2×#1427370811yescharacteristic
785C4C2×#1427371411yescharacteristic
786C2—24no—
787C2—42no—
788C2—42no—
789C2—82no—
790C2C2×#1683731611yescharacteristic
791C2#2143334811yescharacteristic
792C2#2143335611yescharacteristic
793C2#2143371711yescharacteristic
794C2#2143372811yescharacteristic
795C2#2143401611yescharacteristic
796C2#2143402511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
Fitting, prime radicalC2×C59×#525C2
socleC23×C59C22×D4
hypercenterC2×#525D59
hypocenterC59#23482
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#16837445C2semidirect
2. C2×#16837403C2semidirect
3. C2×#16837403C2semidirect
4. C2×#16837366C2semidirect
5. C2×#16837262C2semidirect
6. #21425296C2semidirect
7. #21425289C2semidirect
8. #21425282C2semidirect
9. #21425275C2semidirect
10. #21423817C2semidirect
18. C2×#14273660C22semidirect
19. C2×#14273658C22semidirect
22. C2×#14273651C22semidirect
23. C2×#14273651C22semidirect
24. C2×#14273648C22semidirect
25. C2×#14273648C22semidirect
34. #16837164C22semidirect
35. #16837164C22semidirect
56. C2×#11745664D4semidirect
447. C59#23482semidirect

Maximal subgroups

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

subgroupindex
C2×#168374452
C2×#168374032
C2×#168373662
C2×#168372622
#214252962
#214252892
#214252822
#214252752
#214238172
C2×C59×#5252
#2348259