Finite Group Databasebeta

← #28611392

Subgroups — #28611392

Order 15104.

1054 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837631C211yesmaximal, characteristic
2C2×#16837504C211yesmaximal, characteristic, complemented
3C22×#14273661C211yesmaximal, characteristic, complemented
4#21427110C211yesmaximal, characteristic
5#21427099C211yesmaximal, characteristic, complemented
6#21424977C211yesmaximal, characteristic, complemented
7#21424839C211yesmaximal, characteristic, complemented
8#21424738C211yesmaximal, characteristic, complemented
9#21424717C211yesmaximal, characteristic, complemented
10#21424411C211yesmaximal, characteristic
11#21424401C211yesmaximal, characteristic, complemented
12#21424353C211yesmaximal, characteristic, complemented
13#21424346C211yesmaximal, characteristic, complemented
14#21423993C211yesmaximal, characteristic, complemented
15C59×#1752C211yesmaximal, characteristic, complemented
16C22×#11745660C2211yescharacteristic
17C2×#14273706C2211yescharacteristic
18C2×#14273701C2211yescharacteristic
19C2×C4×Dic118C2211yescharacteristic
20C2×C4×D236C2211yescharacteristic
21C2×(C22⋊D59)⋊C4—21no—
22C22×C4⋊Dic59C2211yescharacteristic
23C22×C4⋊Dic59C2211yescharacteristic
24#16837631C418yescomplemented
25#16837504—24no—
26C2×#14273661—24no—
27C2×#14273661C2211yescharacteristic
28C2×#14273661C2211yescharacteristic
29C2×#14273661C2211yescharacteristic
30C2×#14273661C2211yescharacteristic
31C2×#14273659C2211yescharacteristic
32C2×#14273652C2211yescharacteristic
33C2×#14273652C2211yescharacteristic
34C2×#14273652C2211yescharacteristic
35C2×#14273649C2211yescharacteristic
36C2×#14273649C2211yescharacteristic
37C2×#14273649C2211yescharacteristic
38#16837308C2211yescharacteristic
39#16837304C2211yescharacteristic
40#16837300C2211yescharacteristic
41#16837300C2211yescharacteristic
42#16837299—21no—
43#16837294—21no—
44#16837289—21no—
45#16837279—21no—
46#16837276—21no—
47#16837274—21no—
48C4×C4⋊Dic59C2211yescharacteristic
49C4×C4⋊Dic59C2211yescharacteristic
50C22⋊C4×Dic59—21no—
51#16837165C2211yescharacteristic
52#16837165C2211yescharacteristic
53#16837165C2211yescharacteristic
54#16837165C2211yescharacteristic
55C23×C8×C59C2211yescharacteristic
56C2×C22⋊C8×C59C2211yescharacteristic
57C2×#97×C59C2211yescharacteristic
58C2×#97×C59C2211yescharacteristic
59C4×C22⋊C4×C59C2211yescharacteristic
60C59×#336C2211yescharacteristic
61C59×#336C2211yescharacteristic
62C22×Dic118C2311yescharacteristic
63C22×D236C2311yescharacteristic
64C22×C22⋊D59—21no—
65C23×Dic59—21no—
66C23×Dic59—21no—
67C22×C4×D59—21no—
68C2×#11745660—22no—
69C2×#11745660—22no—
70C2×#11745660C2×C414yescomplemented
71#14273706—22no—
72#14273706C2×C414yescomplemented
73#14273701—22no—
74#14273701C2×C414yes—
75C4×Dic118—22no—
76C4×Dic118—41no—
77C4×D236—22no—
78C4×D236—41no—
79(C22⋊D59)⋊C4—44no—
80C2×C4⋊Dic59—22no—
81C2×C4⋊Dic59—22no—
82C2×C4⋊Dic59—21no—
83C2×C4⋊Dic59—21no—
84C2×C4⋊Dic59—41no—
85C2×C4⋊Dic59—41no—
86C2×C4⋊Dic59C2311yescharacteristic
87C2×C4⋊Dic59C2311yescharacteristic
88C2×C4⋊Dic59C2311yescharacteristic
89C2×C4⋊Dic59C2311yescharacteristic
90C2×C4⋊Dic59C2311yescharacteristic
91C2×C4⋊Dic59C2311yescharacteristic
92C2×Dic59⋊C4—21no—
93C2×Dic59⋊C4—21no—
94C2×Dic59⋊C4—21no—
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—
101C2×C4×Dic59—21no—
102C2×C4×Dic59—21no—
103C2×C4×Dic59—21no—
104#14273661—22no—
105#14273661—22no—
106#14273661—22no—
107#14273661D414yescomplemented
108#14273659C2×C414yescomplemented
109#14273652—22no—
110#14273652—41no—
111#14273652C2×C414yescomplemented
112#14273649—22no—
113#14273649—41no—
114#14273649C2×C414yescomplemented
115C59⋊#95—21no—
116C59⋊#95—21no—
117C59⋊#95—21no—
118C59⋊#95—21no—
119C59⋊#95—21no—
120C59⋊#95—21no—
121C23×C4×C59C2311yescharacteristic
122C22×C8×C59—22no—
123C22×C8×C59—22no—
124C22×C8×C59C2×C414yescomplemented
125C22×C8×C59C2311yescharacteristic
126C22×C8×C59C2311yescharacteristic
127C22×C8×C59C2311yescharacteristic
128C22×C8×C59C2311yescharacteristic
129C2×C22⋊C4×C59D411yescharacteristic
130C2×C22⋊C4×C59D411yescharacteristic
131C2×C42×C59C2311yescharacteristic
132C2×C42×C59C2311yescharacteristic
133C22⋊C8×C59—22no—
134#97×C59—22no—
135#97×C59—22no—
136#95×C59D411yescharacteristic
137#95×C59D411yescharacteristic
138C24×C59C2×D411yescharacteristic
139C23×D59—21no—
140C22×C4×C59—21no—
141C22×C4×C59—21no—
142C22×C4×C59—21no—
143C22×C4×C59—21no—
144C22×C4×C59C22×C412yes—
145C22×C4×C59C2×D411yescharacteristic
146C22×C4×C59C2×D411yescharacteristic
147C22×C4×C59C2×D411yescharacteristic
148C22×C4×C59C2×D411yescharacteristic
149C22×C4×C59C2×D411yescharacteristic
150C22×C4×C59#4112yes—
151C22×C4×C59C2411yescharacteristic
152C2×C22⋊D59—24no—
153C2×C22⋊D59—42no—
154C2×C22⋊D59—42no—
155C22×Dic59—21no—
156C22×Dic59—21no—
157C22×Dic59—21no—
158C22×Dic59—21no—
159C22×Dic59—21no—
160C22×Dic59—21no—
161C22×Dic59—21no—
162C22×Dic59—42no—
163C22×Dic59—42no—
164C22×Dic59—42no—
165C22×Dic59—42no—
166C22×Dic59—81no—
167C22×Dic59—81no—
168C2×D236—21no—
169C2×D236—21no—
170C2×D236—21no—
171C2×D236—21no—
172C2×D236—21no—
173C2×D236C22×C412yes—
174C2×C4×D59—42no—
175C2×C4×D59—42no—
176C2×C4×D59—81no—
177C2×Dic118—21no—
178C2×Dic118—21no—
179C2×Dic118—21no—
180C2×Dic118—21no—
181C2×Dic118—21no—
182C2×Dic118C22×C412yes—
183C2×C8×C59—21no—
184C2×C8×C59—21no—
185C2×C8×C59—28no—
186C2×C8×C59—21no—
187C2×C8×C59—21no—
188C2×C8×C59—21no—
189C2×C8×C59—21no—
190C2×C8×C59—21no—
191C2×C8×C59—21no—
192C2×C8×C59C22×C412yes—
193C2×C8×C59C22×C412yes—
194C2×C8×C59C2×D412yes—
195C2×C8×C59#4112yes—
196C22⋊C4×C59—22no—
197C22⋊C4×C59—22no—
198C42×C59—21no—
199C42×C59—21no—
200C42×C59—21no—
201C42×C59—21no—
202C22⋊Dic59—24no—
203(C2×D59)⋊C4—24no—
204(C2×D59)⋊C4—42no—
205(C2×D59)⋊C4—42no—
206(C2×D59)⋊C4—81no—
207C4⋊Dic59—21no—
208C4⋊Dic59—21no—
209C4⋊Dic59—21no—
210C4⋊Dic59—21no—
211C4⋊Dic59—21no—
212C4⋊Dic59—21no—
213C4⋊Dic59—21no—
214C4⋊Dic59—21no—
215C4⋊Dic59—42no—
216C4⋊Dic59—42no—
217C4⋊Dic59C22×C412yes—
218C4⋊Dic59C22×C412yes—
219C4⋊Dic59C2×D412yes—
220C4⋊Dic59C2×D412yes—
221Dic59⋊C4—24no—
222Dic59⋊C4—42no—
223Dic59⋊C4—42no—
224Dic59⋊C4—81no—
225C4×Dic59—42no—
226C4×Dic59—42no—
227C4×Dic59—81no—
228#11745660—28no—
229C23×C59—21no—
230C23×C59—21no—
231C23×C59—21no—
232C23×C59—21no—
233C23×C59C4×D412yes—
234C23×C59AGL(1,ℤ/8)12yes—
235C23×C59#13712yes—
236C23×C59C22×D411yescharacteristic
237C22×D59—22no—
238C22×D59—41no—
239C22×D59—41no—
240C22×D59—41no—
241C22×D59—41no—
242C22×D59—41no—
243C22×D59—41no—
244C2×C4×C59—21no—
245C2×C4×C59—21no—
246C2×C4×C59—22no—
247C2×C4×C59—22no—
248C2×C4×C59—22no—
249C2×C4×C59—22no—
250C2×C4×C59—21no—
251C2×C4×C59—21no—
252C2×C4×C59—21no—
253C2×C4×C59—21no—
254C2×C4×C59—21no—
255C2×C4×C59—21no—
256C2×C4×C59—21no—
257C2×C4×C59—21no—
258C2×C4×C59—21no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59C4×D412yes—
263C2×C4×C59C23×C411yescharacteristic
264C2×C4×C59C22×D411yescharacteristic
265C2×C4×C59C2×#4111yescharacteristic
266C2×C4×C59C2×#4111yescharacteristic
267C2×C4×C59H(5,𝔽2)11yescharacteristic
268C2×C4×C592−1+411yescharacteristic
269C22⋊D59—48no—
270C2×Dic59—22no—
271C2×Dic59—22no—
272C2×Dic59—22no—
273C2×Dic59—22no—
274C2×Dic59—22no—
275C2×Dic59—41no—
276C2×Dic59—41no—
277C2×Dic59—41no—
278C2×Dic59—41no—
279C2×Dic59—41no—
280C2×Dic59—41no—
281C2×Dic59—41no—
282C2×Dic59—41no—
283C2×Dic59—41no—
284C2×Dic59—41no—
285C2×Dic59—41no—
286C2×Dic59—41no—
287C2×Dic59—41no—
288C2×Dic59—41no—
289C2×Dic59—41no—
290C2×Dic59—41no—
291C2×Dic59—84no—
292C2×Dic59—84no—
293D236—22no—
294D236—22no—
295D236—41no—
296D236—41no—
297C4×D59—84no—
298Dic118—22no—
299Dic118—22no—
300Dic118—41no—
301Dic118—41no—
302C8×C59—22no—
303C8×C59—41no—
304C8×C59—41no—
305C8×C59C4×D414yescomplemented
306#23032—591nomaximal, Sylow
307C22×C59—22no—
308C22×C59—22no—
309C22×C59—22no—
310C22×C59—22no—
311C22×C59—22no—
312C22×C59—22no—
313C22×C59#44014yescomplemented
314C22×C59C2×C4×D411yescharacteristic
315C22×C59D4211yescharacteristic
316C22×C59#54711yescharacteristic
317C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
318C22×C59C2×#13711yescharacteristic
319C22×C59#57611yescharacteristic
320C22×C59#57811yescharacteristic
321C2×D59—42no—
322C2×D59—42no—
323C2×D59—42no—
324C2×D59—81no—
325C2×D59—81no—
326C2×D59—81no—
327C2×D59—81no—
328C4×C59—22no—
329C4×C59—41no—
330C4×C59—41no—
331C4×C59—41no—
332C4×C59—41no—
333C4×C59C2×C4×D411yescharacteristic
334C4×C59#52011yescharacteristic
335C4×C59#54811yescharacteristic
336C4×C59#55311yescharacteristic
337Dic59—42no—
338Dic59—42no—
339Dic59—42no—
340Dic59—42no—
341Dic59—42no—
342Dic59—81no—
343Dic59—81no—
344C2×#465—591no—
345C2×#440—591no—
346C22×#107—591no—
347#2361—591no—
348#2360—591no—
349#1973—591no—
350#1944—591no—
351#1928—591no—
352#1925—591no—
353#1874—591no—
354#1872—591no—
355#1863—591no—
356#1862—591no—
357#1776—591no—
358#1752D5911yescharacteristic, complemented
359C2×C59—24no—
360C2×C59#236111yescharacteristic
361C2×C59C2×#44011yescharacteristic
362C2×C59#295111yescharacteristic
363C2×C59#326411yescharacteristic
364C2×C59#327011yescharacteristic
365C2×C59#334311yescharacteristic
366C2×C59#334611yescharacteristic
367D59—82no—
368C22×SD16—591no—
369C23×C8C2×D5911yescharacteristic
370C2×C22⋊Q8—591no—
371C2×#121—591no—
372C2×C4×Q8—591no—
373C2×C4×D4—591no—
374C2×C4×D4—1181no—
375C22×C4⋊C4—591no—
376C22×C4⋊C4—591no—
377#465—598no—
378#440—1184no—
379C2×#107—591no—
380C2×#107—591no—
381C2×#107—591no—
382C2×#107—591no—
383C2×#107—1184no—
384C2×#106—591no—
385C2×#103—591no—
386C2×#103—591no—
387C2×#103—591no—
388C2×#102—591no—
389C2×#102—591no—
390C2×#102—591no—
391C2×C22⋊C8C2×D5911yescharacteristic
392C2×#97C2×D5911yescharacteristic
393C2×#97C2×D5911yescharacteristic
394#391—591no—
395#390—591no—
396#389—591no—
397#389—591no—
398#389—1181no—
399#388—1181no—
400#387—1181no—
401#386—1181no—
402#385—1181no—
403#385—1181no—
404C4×C4⋊C4—591no—
405C4×C4⋊C4—591no—
406C4×C22⋊C4—1181no—
407C4×C22⋊C4C2×D5911yescharacteristic
408#340—591no—
409#340—591no—
410#340—591no—
411#340—591no—
412#336C2×D5911yescharacteristic
413#336C2×D5911yescharacteristic
414C59#2303211yescharacteristic, complemented, Sylow
415C22×Q8—591no—
416C22×D4—591no—
417C22×D4—1181no—
418C23×C4—1181no—
419C23×C4—1181no—
420C23×C4—1181no—
421C23×C4C22×D5911yescharacteristic
422C2×SD16—594no—
423C2×SD16—1182no—
424C2×SD16—1182no—
425C22×C8—22no—
426C22×C8—22no—
427C22×C8C4×D5914yescomplemented
428C22×C8C22×D5911yescharacteristic
429C22×C8C22×D5911yescharacteristic
430C22×C8C22×D5911yescharacteristic
431C22×C8C22×D5911yescharacteristic
432C22⋊Q8—594no—
433C22⋊Q8—1182no—
434#121—594no—
435#121—1182no—
436C4×Q8—1182no—
437C4×Q8—2361no—
438C4×D4—1182no—
439C4×D4—2361no—
440C4×D4—2364no—
441C2×C4⋊C4—591no—
442C2×C4⋊C4—591no—
443C2×C4⋊C4—591no—
444C2×C4⋊C4—591no—
445C2×C4⋊C4—591no—
446C2×C4⋊C4—591no—
447C2×C4⋊C4—1182no—
448C2×C4⋊C4—1182no—
449C2×C4⋊C4—1181no—
450C2×C4⋊C4—1181no—
451C2×C4⋊C4—1181no—
452C2×C4⋊C4—1181no—
453C2×C4⋊C4—1181no—
454C2×C4⋊C4—1181no—
455C2×C4⋊C4—2361no—
456C2×C4⋊C4—2361no—
457C2×C22⋊C4—1181no—
458C2×C22⋊C4—1181no—
459C2×C22⋊C4—1181no—
460C2×C22⋊C4—1181no—
461C2×C22⋊C4—1181no—
462C2×C22⋊C4D23611yescharacteristic
463C2×C22⋊C4D23611yescharacteristic
464C2×C42—1181no—
465C2×C42—1181no—
466C2×C42—1181no—
467C2×C42C22×D5911yescharacteristic
468C2×C42C22×D5911yescharacteristic
469#107—594no—
470#107—1182no—
471#107—1182no—
472#107—1182no—
473#106—594no—
474#103—594no—
475#103—1182no—
476#103—2361no—
477#102—594no—
478#102—1182no—
479#102—2361no—
480C22⋊C8—22no—
481#97—22no—
482#97—22no—
483#95—1181no—
484#95—1181no—
485#95—1181no—
486#95—1181no—
487#95—1181no—
488#95—1181no—
489#95D23611yescharacteristic
490#95D23611yescharacteristic
491C24—1181no—
492C24C2×D23611yescharacteristic
493C2×Q8—592no—
494C2×Q8—1181no—
495C2×Q8—1181no—
496C2×Q8—1181no—
497C2×Q8—1181no—
498C2×Q8—1181no—
499C2×D4—592no—
500C2×D4—1184no—
501C2×D4—1181no—
502C2×D4—1181no—
503C2×D4—1181no—
504C2×D4—1181no—
505C2×D4—1181no—
506C2×D4—2362no—
507C2×D4—2362no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—1181no—
513C22×C4—1181no—
514C22×C4—1181no—
515C22×C4—1181no—
516C22×C4—1181no—
517C22×C4—1181no—
518C22×C4—1181no—
519C22×C4—4721no—
520C22×C4—4721no—
521C22×C4—4721no—
522C22×C4—2362no—
523C22×C4—2362no—
524C22×C4—2362no—
525C22×C4—2362no—
526C22×C4—2362no—
527C22×C4—2362no—
528C22×C4C2×C4×D5912yes—
529C22×C4C2×D23611yescharacteristic
530C22×C4C2×D23611yescharacteristic
531C22×C4C2×D23611yescharacteristic
532C22×C4C2×D23611yescharacteristic
533C22×C4C2×D23611yescharacteristic
534C22×C4#1174568512yes—
535C22×C4C23×D5911yescharacteristic
536SD16—1188no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—28no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8C2×C4×D5912yes—
547C2×C8C2×C4×D5912yes—
548C2×C8D4×D5912yes—
549C2×C8#1174568712yes—
550C4⋊C4—592no—
551C4⋊C4—592no—
552C4⋊C4—592no—
553C4⋊C4—592no—
554C4⋊C4—1184no—
555C4⋊C4—1181no—
556C4⋊C4—1181no—
557C4⋊C4—1181no—
558C4⋊C4—1181no—
559C4⋊C4—1181no—
560C4⋊C4—1181no—
561C4⋊C4—1181no—
562C4⋊C4—1181no—
563C4⋊C4—4721no—
564C4⋊C4—2362no—
565C4⋊C4—2362no—
566C4⋊C4—2362no—
567C4⋊C4—2362no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—1184no—
571C22⋊C4—1184no—
572C22⋊C4—4721no—
573C22⋊C4—2362no—
574C22⋊C4—2362no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—4721no—
580C42—2362no—
581C42—2362no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—1182no—
587C23—2361no—
588C23—2361no—
589C23—2361no—
590C23—2361no—
591C23—2361no—
592C23—2361no—
593C23C4×D23612yes—
594C23#1427375512yes—
595C23#1427376012yes—
596C23C22×D23611yescharacteristic
597Q8—1182no—
598Q8—1182no—
599Q8—2361no—
600Q8—2361no—
601D4—1182no—
602D4—1182no—
603D4—2368no—
604D4—2361no—
605D4—2361no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—1182no—
625C2×C4—1182no—
626C2×C4—1182no—
627C2×C4—1182no—
628C2×C4—1182no—
629C2×C4—4724no—
630C2×C4—4724no—
631C2×C4—4724no—
632C2×C4—2361no—
633C2×C4—2361no—
634C2×C4—2361no—
635C2×C4—2361no—
636C2×C4—2361no—
637C2×C4—2361no—
638C2×C4—2361no—
639C2×C4—2361no—
640C2×C4—2361no—
641C2×C4—2361no—
642C2×C4—2361no—
643C2×C4—2361no—
644C2×C4—2361no—
645C2×C4—2361no—
646C2×C4—2361no—
647C2×C4—2361no—
648C2×C4C4×D23612yes—
649C2×C4C22×C4×D5911yescharacteristic
650C2×C4C2×D4×D5911yescharacteristic
651C2×C4C2×#1174568711yescharacteristic
652C2×C4C2×#1174568511yescharacteristic
653C2×C4#1427377311yescharacteristic
654C2×C4#1427377411yescharacteristic
655C8—22no—
656C8—41no—
657C8—41no—
658C8(C22⋊D59)⋊C414yescomplemented
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—4721no—
666C22—4721no—
667C22—4721no—
668C22—4721no—
669C22—2362no—
670C22—2362no—
671C22—2362no—
672C22#1683750414yescomplemented
673C22C2×C4×D23611yescharacteristic
674C22D4×D23611yescharacteristic
675C22#1683805611yescharacteristic
676C22C2×#1427375511yescharacteristic
677C22C2×#1427376011yescharacteristic
678C22#1683820711yescharacteristic
679C22#1683821911yescharacteristic
680C4—22no—
681C4—41no—
682C4—41no—
683C4—41no—
684C4—41no—
685C4—4721no—
686C4—4721no—
687C4—2362no—
688C4—2362no—
689C4—2362no—
690C4—2362no—
691C4—2362no—
692C4C2×(C22⋊D59)⋊C411yescharacteristic
693C4#1683788211yescharacteristic
694C4#1683806111yescharacteristic
695C4#1683809811yescharacteristic
696C2—24no—
697C2—4722no—
698C2#2142711011yescharacteristic
699C2C2×#1683750411yescharacteristic
700C2#2143297311yescharacteristic
701C2#2143558111yescharacteristic
702C2#2143567111yescharacteristic
703C2#2143653811yescharacteristic
704C2#2143658311yescharacteristic
subgroupG/H
centerC23C22×D236
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1752C2
socleC23×C59C22×D4
prime radicalC2×#14273701C22
cosocleC22×C4×C59C24
hypercenter#1752D59
hypocenterC59#23032
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1752

Complements

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

NH ≅ G/Ntype
2. C2×#16837504C2semidirect
3. C22×#14273661C2semidirect
5. #21427099C2semidirect
6. #21424977C2semidirect
7. #21424839C2semidirect
8. #21424738C2semidirect
9. #21424717C2semidirect
11. #21424401C2semidirect
12. #21424353C2semidirect
13. #21424346C2semidirect
14. #21423993C2semidirect
15. C59×#1752C2semidirect
24. #16837631C4semidirect
70. C2×#11745660C2×C4semidirect
72. #14273706C2×C4semidirect
107. #14273661D4semidirect
108. #14273659C2×C4semidirect
111. #14273652C2×C4semidirect
114. #14273649C2×C4semidirect
124. C22×C8×C59C2×C4semidirect
305. C8×C59C4×D4semidirect
313. C22×C59#440semidirect
358. #1752D59semidirect
414. C59#23032semidirect
427. C22×C8C4×D59semidirect
658. C8(C22⋊D59)⋊C4semidirect
672. C22#16837504semidirect

Maximal subgroups

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

subgroupindex
C2×#168376312
C2×#168375042
C22×#142736612
#214271102
#214270992
#214249772
#214248392
#214247382
#214247172
#214244112
#214244012
#214243532
#214243462
#214239932
C59×#17522
#2303259