Finite Group Databasebeta

← #29473521

Subgroups — #29473521

Order 15104.

2234 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838048C211yesmaximal, characteristic
2#21436171C218yesmaximal, complemented
3#21435607C218yesmaximal, complemented
4#21435095C212yesmaximal, complemented
5#21434898C212yesmaximal, complemented
6#21434868C212yesmaximal, complemented
7#21434191C212yesmaximal, complemented
8#21433354C212yesmaximal, complemented
9C2×#16837552C212yesmaximal, complemented
10#21433125C211yesmaximal, characteristic, complemented
11C59×#3501C211yesmaximal, characteristic, complemented
12C22×#11745685C2211yescharacteristic
13C23×D236C2211yescharacteristic
14C2×#14273758C2214yescomplemented
15C22×#11745671C2214yescomplemented
16#16838048—24no—
17#16838048C2218yes—
18C2×#14273715C2211yescharacteristic
19C2×#14273712—21no—
20C2×#14273706C2211yescharacteristic
21C2×#14273701C2211yescharacteristic
22C2×#14273700—21no—
23C2×#14273695—21no—
24C2×C4×D236C2211yescharacteristic
25C2×C22⋊C4×D59—21no—
26#16837794C2214yescomplemented
27#16837764C2214yescomplemented
28#16837737C2214yescomplemented
29#16837735C2214yescomplemented
30#16837715C2214yescomplemented
31#16837679C2214yescomplemented
32#16837650C2218yescomplemented
33#16837641C2218yescomplemented
34#16837624C2218yescomplemented
35#16837604C2214yescomplemented
36#16837562C2218yescomplemented
37#16837558C2214yescomplemented
38#16837557C2214yescomplemented
39#16837552C2214yes—
40#16837552C2214yes—
41#16837552C2218yescomplemented
42#16837541C2214yescomplemented
43#16837500C2218yescomplemented
44#16837474C2218yescomplemented
45#16837459C2212yescomplemented
46#16837401C2214yescomplemented
47C2×#14273647C2214yescomplemented
48#16837366C2212yescomplemented
49C2×C22⋊(C59⋊C8)C2212yes—
50C59×#554—24no—
51C59×#554C2214yescomplemented
52D4×Q8×C59C2214yescomplemented
53C59×#544—21no—
54C59×#543—21no—
55C59×#543—21no—
56C59×#533C2212yescomplemented
57C2×C22⋊Q8×C59C2212yes—
58C2×C22⋊Q8×C59C2212yescomplemented
59C59×#518—21no—
60C2×C4×D4×C59C2211yescharacteristic
61C24×D59—21no—
62C2×#11745685—22no—
63C2×#11745685—44no—
64C2×#11745685C2314yes—
65C22×Dic118C2311yescharacteristic
66C22×D236—21no—
67C22×D236—22no—
68C22×D236—44no—
69C22×D236C2311yescharacteristic
70C22×D236C2314yes—
71C22×D236C2311yescharacteristic
72C22×C22⋊D59—21no—
73C22×C22⋊D59—21no—
74C22×C4×D59—21no—
75C22×C4×D59—21no—
76#14273758—48no—
77C2×#11745672C2318yescomplemented
78C2×#11745671—48no—
79C2×#11745671C2318yes—
80C2×#11745671C2318yes—
81C2×#11745664C2314yescomplemented
82C22×C59⋊C8C2314yes—
83#14273715—22no—
84#14273715C2314yes—
85#14273712—28no—
86#14273706—22no—
87#14273706C2314yes—
88#14273701—22no—
89#14273701C2314yes—
90#14273700—28no—
91#14273695—28no—
92C4×D236—22no—
93C4×D236C2314yes—
94C2×C4⋊Dic59C2311yescharacteristic
95C2×Dic59⋊C4—21no—
96C2×C22⋊Dic59—21no—
97C2×(C2×D59)⋊C4—21no—
98C2×(C2×D59)⋊C4—21no—
99C2×(C2×D59)⋊C4—21no—
100C2×(C2×D59)⋊C4—21no—
101C22⋊C4×D59—28no—
102#14273660C2318yescomplemented
103C4⋊(C59⋊C8)C2314yescomplemented
104#14273651C2318yescomplemented
105#14273650C2318yescomplemented
106#14273647C2318yes—
107#14273647C2318yes—
108C22⋊(C59⋊C8)C2314yes—
109C22⋊(C59⋊C8)C2314yes—
110C22⋊(C59⋊C8)C2314yescomplemented
111#14273638C2314yescomplemented
112C22×Q8×C59C2312yes—
113C22×Q8×C59C2312yescomplemented
114C22×D4×C59D411yescharacteristic
115C23×C4×C59C2311yescharacteristic
116C23×C4×C59C2311yescharacteristic
117C4⋊Q8×C59—24no—
118C4⋊Q8×C59C2312yescomplemented
119C4⋊Q8×C59C2312yescomplemented
120#125×C59—24no—
121#125×C59—22no—
122C22⋊Q8×C59—22no—
123C22⋊Q8×C59—22no—
124C22⋊Q8×C59—22no—
125C22⋊Q8×C59—22no—
126C22⋊Q8×C59—22no—
127C22⋊Q8×C59—24no—
128C22⋊Q8×C59—24no—
129C22⋊Q8×C59—24no—
130C22⋊Q8×C59—24no—
131C22⋊Q8×C59C2314yes—
132C22⋊Q8×C59C2314yes—
133C22⋊Q8×C59C2314yescomplemented
134C4×Q8×C59—22no—
135C4×Q8×C59C2314yescomplemented
136C4×D4×C59—24no—
137C4×D4×C59—24no—
138C4×D4×C59D414yes—
139C4×D4×C59C2314yes—
140#117×C59—22no—
141C2×C4⋊C4×C59—22no—
142C2×C4⋊C4×C59—22no—
143C2×C4⋊C4×C59D411yescharacteristic
144C2×C4⋊C4×C59C2312yes—
145C2×C4⋊C4×C59C2312yescomplemented
146C2×C22⋊C4×C59—22no—
147C2×C22⋊C4×C59—22no—
148C2×C22⋊C4×C59D411yescharacteristic
149C2×C22⋊C4×C59D411yescharacteristic
150C2×C42×C59C2311yescharacteristic
151C24×C59C2×D411yescharacteristic
152C24×C59C2×D411yescharacteristic
153C23×D59—21no—
154C23×D59—21no—
155C23×D59—24no—
156C23×D59—44no—
157C23×D59—44no—
158C23×D59—82no—
159C2×Q8×C59—22no—
160C2×Q8×C59—22no—
161C2×Q8×C59—22no—
162C2×Q8×C59—44no—
163C2×Q8×C59—44no—
164C2×Q8×C59C2414yes—
165C2×D4×C59—24no—
166C2×D4×C59C2×D414yes—
167C22×C4×C59—22no—
168C22×C4×C59—22no—
169C22×C4×C59—22no—
170C22×C4×C59—22no—
171C22×C4×C59—42no—
172C22×C4×C59—42no—
173C22×C4×C59C2×D411yescharacteristic
174C22×C4×C59C2×D411yescharacteristic
175C22×C4×C59C2×D411yescharacteristic
176C22×C4×C59C2×D411yescharacteristic
177C22×C4×C59C2×D412yes—
178C22×C4×C59C2×D412yes—
179C22×C4×C59C2411yescharacteristic
180C22×C4×C59C2412yes—
181C22×C4×C59C2412yes—
182C2×C22⋊D59—24no—
183C2×C22⋊D59—24no—
184C2×C22⋊D59—44no—
185C2×C22⋊D59—82no—
186C22×Dic59—21no—
187C22×Dic59—21no—
188#11745685—28no—
189#11745685—44no—
190#11745685—48no—
191C2×D236—21no—
192C2×D236—24no—
193C2×D236—28no—
194C2×D236—24no—
195C2×D236—21no—
196C2×D236—44no—
197C2×D236—42no—
198C2×D236—48no—
199C2×D236—44no—
200C2×D236C2412yes—
201C2×D236C2412yes—
202C2×C4×D59—24no—
203C2×C4×D59—24no—
204C2×C4×D59—44no—
205C2×C4×D59—82no—
206C2×Dic118—21no—
207C2×Dic118—42no—
208C2×Dic118C2412yes—
209C4⋊C4×C59—24no—
210C4⋊C4×C59—24no—
211C4⋊C4×C59—24no—
212C4⋊C4×C59—22no—
213C4⋊C4×C59—22no—
214C4⋊C4×C59—22no—
215C4⋊C4×C59—22no—
216C4⋊C4×C59—22no—
217C4⋊C4×C59—24no—
218C4⋊C4×C59C2×D414yes—
219C4⋊C4×C59C2414yes—
220C22⋊C4×C59—24no—
221C22⋊C4×C59—24no—
222C22⋊C4×C59—24no—
223C22⋊C4×C59C2×D414yes—
224C22⋊C4×C59C2×D414yes—
225C42×C59—24no—
226C42×C59C2×D412yes—
227C42×C59C2412yes—
228C22⋊Dic59—24no—
229#11745672—48no—
230#11745671—216no—
231#11745671—48no—
232(C2×D59)⋊C4—24no—
233(C2×D59)⋊C4—24no—
234(C2×D59)⋊C4—24no—
235(C2×D59)⋊C4—24no—
236C4⋊Dic59—21no—
237C4⋊Dic59C2412yes—
238Dic59⋊C4—24no—
239#11745664—44no—
240C2×C59⋊C8—44no—
241C2×C59⋊C8C2418yes—
242C23×C59—22no—
243C23×C59—41no—
244C23×C59—41no—
245C23×C59—41no—
246C23×C59—41no—
247C23×C59#13714yescomplemented
248C23×C59C22×D412yes—
249C23×C59C22×D412yes—
250C23×C59C22×D411yescharacteristic
251C22×D59—24no—
252C22×D59—22no—
253C22×D59—22no—
254C22×D59—48no—
255C22×D59—42no—
256C22×D59—42no—
257C22×D59—42no—
258C22×D59—42no—
259C22×D59—48no—
260C22×D59—42no—
261C22×D59—84no—
262C22×D59—816no—
263Q8×C59—28no—
264Q8×C59—82no—
265Q8×C59—82no—
266Q8×C59—82no—
267D4×C59—28no—
268C2×C4×C59—22no—
269C2×C4×C59—24no—
270C2×C4×C59—24no—
271C2×C4×C59—22no—
272C2×C4×C59—24no—
273C2×C4×C59—24no—
274C2×C4×C59—41no—
275C2×C4×C59—41no—
276C2×C4×C59—42no—
277C2×C4×C59—41no—
278C2×C4×C59—42no—
279C2×C4×C59—82no—
280C2×C4×C59—82no—
281C2×C4×C59—82no—
282C2×C4×C59—82no—
283C2×C4×C59C22×D412yes—
284C2×C4×C59C22×D411yescharacteristic
285C2×C4×C59C22×D412yes—
286C2×C4×C59C22×D412yes—
287C2×C4×C59C22×D412yes—
288C2×C4×C59C2511yescharacteristic
289C22⋊D59—48no—
290C22⋊D59—84no—
291C2×Dic59—22no—
292C2×Dic59—22no—
293C2×Dic59—42no—
294C2×Dic59—42no—
295D236—24no—
296D236—22no—
297D236—24no—
298D236—48no—
299D236—42no—
300D236H(5,𝔽2)14yes—
301C4×D59—48no—
302C4×D59—84no—
303Dic118—24no—
304Dic118—42no—
305C59⋊C8—28no—
306#61570—591nomaximal, Sylow
307C22×C59—21no—
308C22×C59—22no—
309C22×C59—21no—
310C22×C59—22no—
311C22×C59—22no—
312C22×C59—22no—
313C22×C59—22no—
314C22×C59—44no—
315C22×C59—82no—
316C22×C59C2×#13712yes—
317C22×C59C2×#13714yes—
318C22×C59C23×D411yescharacteristic
319C2×D59—24no—
320C2×D59—48no—
321C2×D59—42no—
322C2×D59—42no—
323C2×D59—42no—
324C2×D59—42no—
325C2×D59—42no—
326C2×D59—816no—
327C2×D59—84no—
328C4×C59—22no—
329C4×C59—21no—
330C4×C59—22no—
331C4×C59—22no—
332C4×C59—22no—
333C4×C59—44no—
334C4×C59—44no—
335C4×C59C2×H(5,𝔽2)12yes—
336Dic59—42no—
337Dic59—42no—
338#3501D5911yescharacteristic, complemented
339C2×#546—591no—
340#3314—598no—
341#3266—598no—
342#3215—592no—
343#3193—592no—
344#3189—592no—
345#3110—592no—
346#3007—592no—
347C2×#450—592no—
348#2973—591no—
349C2×C59—22no—
350C2×C59—24no—
351C2×C59—42no—
352C2×C59#348411yescharacteristic
353C2×C59C22×#13711yescharacteristic
354C2×C59#358511yescharacteristic
355D59—44no—
356D59—82no—
357C22×#41—591no—
358C23×D4—591no—
359C2×#137—594no—
360C22×SD16—594no—
361#554—24no—
362#554C2×D5914yescomplemented
363D4×Q8C2×D5914yescomplemented
364#546—598no—
365#546—1184no—
366#544—21no—
367#543—21no—
368#543—21no—
369#533C2×D5912yescomplemented
370C2×#124—591no—
371C2×#123—1181no—
372C2×C22⋊Q8—591no—
373C2×C22⋊Q8C2×D5912yes—
374C2×C22⋊Q8C2×D5912yescomplemented
375C2×#121—591no—
376C2×#121—1181no—
377C2×#120—1181no—
378#518—21no—
379C2×C4×D4—591no—
380C2×C4×D4C2×D5911yescharacteristic
381C22×C22⋊C4—1181no—
382#497—594no—
383#489—594no—
384#484—594no—
385#484—594no—
386#480—594no—
387#474—594no—
388#468—598no—
389#467—598no—
390#464—598no—
391#461—594no—
392#452—598no—
393#451—594no—
394#451—594no—
395#450—594no—
396#450—594no—
397#450—598no—
398#448—594no—
399#440—598no—
400#435—598no—
401#432—592no—
402#417—594no—
403C2×#102—594no—
404#407—592no—
405C2×C22⋊C8—592no—
406C59#6157011yescharacteristic, complemented, Sylow
407C25—1181no—
408C2×#41—594no—
409C2×#41—1182no—
410C2×#41—2364no—
411C22×Q8—591no—
412C22×Q8C22×D5912yes—
413C22×Q8C22×D5912yescomplemented
414C22×D4—591no—
415C22×D4—594no—
416C22×D4—591no—
417C22×D4—1181no—
418C22×D4—1181no—
419C22×D4—1181no—
420C22×D4—1182no—
421C22×D4—2364no—
422C22×D4C22⋊D5911yescharacteristic
423C23×C4—1181no—
424C23×C4—1181no—
425C23×C4C22×D5911yescharacteristic
426C23×C4C22×D5911yescharacteristic
427#137—2368no—
428C2×Q16—598no—
429C2×SD16—598no—
430C2×SD16—598no—
431C2×SD16—2368no—
432C2×M16—594no—
433C22×C8—594no—
434C4⋊Q8—24no—
435C4⋊Q8C22×D5912yescomplemented
436C4⋊Q8C22×D5912yescomplemented
437#125—24no—
438#125—22no—
439#124—594no—
440#124—1182no—
441#123—1188no—
442C22⋊Q8—22no—
443C22⋊Q8—22no—
444C22⋊Q8—22no—
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C22⋊Q8—24no—
448C22⋊Q8—24no—
449C22⋊Q8—24no—
450C22⋊Q8—24no—
451C22⋊Q8—594no—
452C22⋊Q8—1182no—
453C22⋊Q8C22×D5914yes—
454C22⋊Q8C22×D5914yes—
455C22⋊Q8C22×D5914yescomplemented
456#121—594no—
457#121—1182no—
458#121—1188no—
459#120—1188no—
460C4×Q8—22no—
461C4×Q8C22×D5914yescomplemented
462C4×D4—24no—
463C4×D4—24no—
464C4×D4—594no—
465C4×D4—1182no—
466C4×D4C22⋊D5914yes—
467C4×D4C22×D5914yes—
468#117—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—591no—
472C2×C4⋊C4—1181no—
473C2×C4⋊C4C22⋊D5911yescharacteristic
474C2×C4⋊C4C22×D5912yes—
475C2×C4⋊C4C22×D5912yescomplemented
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—1181no—
479C2×C22⋊C4—1181no—
480C2×C22⋊C4—1181no—
481C2×C22⋊C4—1181no—
482C2×C22⋊C4—1181no—
483C2×C22⋊C4—1188no—
484C2×C22⋊C4C22⋊D5911yescharacteristic
485C2×C22⋊C4C22⋊D5911yescharacteristic
486C2×C42C22×D5911yescharacteristic
487#107—598no—
488C4⋊C8—594no—
489#103—598no—
490#103—598no—
491#102—598no—
492#102—598no—
493C22⋊C8—594no—
494C22⋊C8—594no—
495C22⋊C8—594no—
496#97—594no—
497C24—1181no—
498C24—1184no—
499C24—1181no—
500C24—4722no—
501C24—2364no—
502C24—2364no—
503C24C2×C22⋊D5911yescharacteristic
504C24C2×C22⋊D5911yescharacteristic
505#41—1188no—
506#41—2364no—
507#41—2368no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—22no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×Q8—592no—
514C2×Q8—1181no—
515C2×Q8—2362no—
516C2×Q8C23×D5914yes—
517C2×D4—24no—
518C2×D4—592no—
519C2×D4—592no—
520C2×D4—1184no—
521C2×D4—1188no—
522C2×D4—1184no—
523C2×D4—1184no—
524C2×D4—1181no—
525C2×D4—1184no—
526C2×D4—1181no—
527C2×D4—4722no—
528C2×D4—2364no—
529C2×D4—2362no—
530C2×D4—2368no—
531C2×D4—2364no—
532C2×D4—2364no—
533C2×D4C2×C22⋊D5914yes—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—1181no—
541C22×C4—1181no—
542C22×C4—1184no—
543C22×C4—1184no—
544C22×C4—4722no—
545C22×C4—2364no—
546C22×C4C2×C22⋊D5911yescharacteristic
547C22×C4C2×C22⋊D5911yescharacteristic
548C22×C4C2×C22⋊D5911yescharacteristic
549C22×C4C2×C22⋊D5911yescharacteristic
550C22×C4C2×C22⋊D5912yes—
551C22×C4C2×C22⋊D5912yes—
552C22×C4C23×D5911yescharacteristic
553C22×C4C23×D5912yes—
554C22×C4C23×D5912yes—
555Q16—2368no—
556SD16—11816no—
557SD16—2368no—
558M16—2364no—
559C2×C8—598no—
560C2×C8—2364no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—24no—
570C4⋊C4—592no—
571C4⋊C4—1181no—
572C4⋊C4—1184no—
573C4⋊C4C2×C22⋊D5914yes—
574C4⋊C4C23×D5914yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—1184no—
579C22⋊C4—1184no—
580C22⋊C4—1184no—
581C22⋊C4—1184no—
582C22⋊C4—1184no—
583C22⋊C4C2×C22⋊D5914yes—
584C22⋊C4C2×C22⋊D5914yes—
585C42—24no—
586C42C2×C22⋊D5912yes—
587C42C23×D5912yes—
588C23—22no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—1184no—
594C23—1182no—
595C23—1182no—
596C23—4724no—
597C23—47216no—
598C23—2368no—
599C23—2362no—
600C23—2362no—
601C23—2362no—
602C23—2362no—
603C23—2368no—
604C23—2362no—
605C23#1427375814yescomplemented
606C23C22×C22⋊D5912yes—
607C23C22×C22⋊D5911yescharacteristic
608C23C22×C22⋊D5912yes—
609Q8—28no—
610Q8—82no—
611Q8—82no—
612Q8—82no—
613Q8—1184no—
614Q8—2362no—
615D4—28no—
616D4—594no—
617D4—1184no—
618D4—1182no—
619D4—1184no—
620D4—4724no—
621D4—2368no—
622D4—2362no—
623D4—2368no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—41no—
631C2×C4—42no—
632C2×C4—41no—
633C2×C4—42no—
634C2×C4—41no—
635C2×C4—82no—
636C2×C4—82no—
637C2×C4—82no—
638C2×C4—82no—
639C2×C4—1182no—
640C2×C4—1182no—
641C2×C4—4724no—
642C2×C4—2368no—
643C2×C4—2362no—
644C2×C4—2362no—
645C2×C4C22×C22⋊D5912yes—
646C2×C4C22×C22⋊D5911yescharacteristic
647C2×C4C22×C22⋊D5912yes—
648C2×C4C22×C22⋊D5912yes—
649C2×C4C22×C22⋊D5912yes—
650C2×C4C24×D5911yescharacteristic
651C8—1188no—
652C22—21no—
653C22—22no—
654C22—21no—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—22no—
659C22—44no—
660C22—82no—
661C22—1184no—
662C22—4724no—
663C22—47216no—
664C22—2368no—
665C22—2362no—
666C22—2362no—
667C22—2362no—
668C22—2362no—
669C22—2362no—
670C22C2×#1427375812yes—
671C22C2×#1427375814yes—
672C22C23×C22⋊D5911yescharacteristic
673C4—21no—
674C4—22no—
675C4—22no—
676C4—22no—
677C4—22no—
678C4—44no—
679C4—44no—
680C4—2362no—
681C4—2362no—
682C4H(5,𝔽2)×D5912yes—
683C2—22no—
684C2—24no—
685C2—42no—
686C2—4722no—
687C2—2364no—
688C2#2143772711yescharacteristic
689C2C22×#1427375811yescharacteristic
690C2#2143887511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC59×#3501C2
socleC22×C59C23×D4
prime radicalC2×#16838048C2
hypercenter#3501D59
hypocenterC59#61570
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3501

Complements

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

NH ≅ G/Ntype
2. #21436171C2semidirect
3. #21435607C2semidirect
4. #21435095C2semidirect
5. #21434898C2semidirect
6. #21434868C2semidirect
7. #21434191C2semidirect
8. #21433354C2semidirect
9. C2×#16837552C2semidirect
10. #21433125C2semidirect
11. C59×#3501C2semidirect
14. C2×#14273758C22semidirect
15. C22×#11745671C22semidirect
26. #16837794C22semidirect
27. #16837764C22semidirect
28. #16837737C22semidirect
29. #16837735C22semidirect
30. #16837715C22semidirect
31. #16837679C22semidirect
32. #16837650C22semidirect
33. #16837641C22semidirect
34. #16837624C22semidirect
35. #16837604C22semidirect
36. #16837562C22semidirect
37. #16837558C22semidirect
38. #16837557C22semidirect
41. #16837552C22semidirect
42. #16837541C22semidirect
43. #16837500C22semidirect
44. #16837474C22semidirect
45. #16837459C22semidirect
46. #16837401C22semidirect
47. C2×#14273647C22semidirect
48. #16837366C22semidirect
51. C59×#554C22semidirect
52. D4×Q8×C59C22semidirect
56. C59×#533C22semidirect
58. C2×C22⋊Q8×C59C22semidirect
77. C2×#11745672C23semidirect
81. C2×#11745664C23semidirect
102. #14273660C23semidirect
103. C4⋊(C59⋊C8)C23semidirect
104. #14273651C23semidirect
105. #14273650C23semidirect
110. C22⋊(C59⋊C8)C23semidirect
111. #14273638C23semidirect
113. C22×Q8×C59C23semidirect
118. C4⋊Q8×C59C23semidirect
119. C4⋊Q8×C59C23semidirect
133. C22⋊Q8×C59C23semidirect
135. C4×Q8×C59C23semidirect
145. C2×C4⋊C4×C59C23semidirect
247. C23×C59#137semidirect
338. #3501D59semidirect
362. #554C2×D59semidirect
363. D4×Q8C2×D59semidirect
369. #533C2×D59semidirect
374. C2×C22⋊Q8C2×D59semidirect
406. C59#61570semidirect
413. C22×Q8C22×D59semidirect
435. C4⋊Q8C22×D59semidirect
436. C4⋊Q8C22×D59semidirect
455. C22⋊Q8C22×D59semidirect
461. C4×Q8C22×D59semidirect
475. C2×C4⋊C4C22×D59semidirect
605. C23#14273758semidirect

Maximal subgroups

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

subgroupindex
C2×#168380482
#214361712
#214356072
#214350952
#214348982
#214348682
#214341912
#214333542
C2×#168375522
#214331252
C59×#35012
#6157059