Finite Group Databasebeta

← #28636896

Subgroups — #28636896

Order 15104.

940 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837730C211yesmaximal, characteristic, complemented
2C2×#16837633C211yesmaximal, characteristic
3#21428567C211yesmaximal, characteristic
4#21425572C211yesmaximal, characteristic, complemented
5#21425504C211yesmaximal, characteristic, complemented
6#21425467C211yesmaximal, characteristic, complemented
7#21425411C211yesmaximal, characteristic, complemented
8#21424859C211yesmaximal, characteristic, complemented
9#21424723C211yesmaximal, characteristic, complemented
10#21424451C211yesmaximal, characteristic, complemented
11#21424413C211yesmaximal, characteristic
12#21424276C211yesmaximal, characteristic, complemented
13#21424101C211yesmaximal, characteristic, complemented
14C2×#16837164C211yesmaximal, characteristic, complemented
15C59×#2360C211yesmaximal, characteristic, complemented
16C22×#11745671C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18C2×#14273711—21no—
19C2×#14273711—21no—
20C2×#14273701C2211yescharacteristic
21C22×C4⋊Dic59C2211yescharacteristic
22#16837730—24no—
23#16837633—24no—
24C2×#14273658C2211yescharacteristic
25C2×#14273658C2211yescharacteristic
26C2×#14273658C2211yescharacteristic
27C2×C4⋊(C59⋊C8)C2211yescharacteristic
28C2×C4⋊(C59⋊C8)C2211yescharacteristic
29C2×#14273651C2211yescharacteristic
30C2×#14273651C2211yescharacteristic
31C2×#14273651C2211yescharacteristic
32C2×#14273647C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×#14273647C2211yescharacteristic
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36#16837339—21no—
37#16837339—21no—
38#16837304C2211yescharacteristic
39#16837304C2211yescharacteristic
40#16837272C2211yescharacteristic
41#16837272C2211yescharacteristic
42#16837164C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837157C2211yescharacteristic
49#16837157C2211yescharacteristic
50C2×C22⋊Q8×C59C2211yescharacteristic
51C2×C4×Q8×C59C2211yescharacteristic
52C22×C4⋊C4×C59C2211yescharacteristic
53C59×#391C2211yescharacteristic
54C59×#389—21no—
55C59×#389C2211yescharacteristic
56C59×#387—21no—
57C59×#385—21no—
58C4×C4⋊C4×C59C2211yescharacteristic
59C4×C22⋊C4×C59—21no—
60C4×C22⋊C4×C59C2211yescharacteristic
61C22×D236C2311yescharacteristic
62C22×C22⋊D59—21no—
63C23×Dic59—21no—
64C2×#11745671—22no—
65C2×#11745671—22no—
66C2×#11745671—41no—
67C22×C59⋊C8—22no—
68C22×C59⋊C8—22no—
69C22×C59⋊C8—41no—
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74#14273711—44no—
75#14273711—44no—
76#14273701—22no—
77#14273701—22no—
78C2×C4⋊Dic59—22no—
79C2×C4⋊Dic59—22no—
80C2×C4⋊Dic59—21no—
81C2×C4⋊Dic59—21no—
82C2×C4⋊Dic59—21no—
83C2×C4⋊Dic59—21no—
84C2×C4⋊Dic59—21no—
85C2×C4⋊Dic59C2311yescharacteristic
86C2×C4⋊Dic59C2311yescharacteristic
87C2×C4⋊Dic59C2311yescharacteristic
88C2×(C2×D59)⋊C4—21no—
89C2×(C2×D59)⋊C4—21no—
90C2×(C2×D59)⋊C4—21no—
91C2×(C2×D59)⋊C4—21no—
92C2×(C2×D59)⋊C4—21no—
93#14273658—22no—
94#14273658—22no—
95#14273658—22no—
96C4⋊(C59⋊C8)—22no—
97C4⋊(C59⋊C8)—41no—
98#14273651—22no—
99#14273651—22no—
100#14273651—22no—
101#14273647—22no—
102#14273647—22no—
103#14273647—41no—
104C22⋊(C59⋊C8)—22no—
105C22×Q8×C59C2311yescharacteristic
106C23×C4×C59—21no—
107C23×C4×C59C2311yescharacteristic
108C22⋊Q8×C59—22no—
109C22⋊Q8×C59D414yes—
110C4×Q8×C59—22no—
111C4×Q8×C59—41no—
112C2×C4⋊C4×C59—21no—
113C2×C4⋊C4×C59—22no—
114C2×C4⋊C4×C59—21no—
115C2×C4⋊C4×C59—21no—
116C2×C4⋊C4×C59—21no—
117C2×C4⋊C4×C59—41no—
118C2×C4⋊C4×C59C2311yescharacteristic
119C2×C4⋊C4×C59C2311yescharacteristic
120C2×C4⋊C4×C59C2311yescharacteristic
121C2×C22⋊C4×C59—21no—
122C2×C22⋊C4×C59D411yescharacteristic
123C2×C22⋊C4×C59D411yescharacteristic
124C2×C42×C59—21no—
125C2×C42×C59—21no—
126C2×C42×C59C2311yescharacteristic
127C2×C42×C59C2311yescharacteristic
128#95×C59—21no—
129#95×C59—21no—
130#95×C59—21no—
131#95×C59—21no—
132#95×C59D411yescharacteristic
133#95×C59D411yescharacteristic
134C24×C59C2×D411yescharacteristic
135C23×D59—21no—
136C2×Q8×C59—21no—
137C2×Q8×C59—21no—
138C2×Q8×C59—21no—
139C2×Q8×C59—21no—
140C2×Q8×C59—21no—
141C2×Q8×C59C2×D412yes—
142C22×C4×C59—21no—
143C22×C4×C59—21no—
144C22×C4×C59—21no—
145C22×C4×C59—21no—
146C22×C4×C59—21no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—42no—
151C22×C4×C59—42no—
152C22×C4×C59—81no—
153C22×C4×C59C2×D411yescharacteristic
154C22×C4×C59C2×D411yescharacteristic
155C22×C4×C59C2×D411yescharacteristic
156C22×C4×C59C2×D412yes—
157C22×C4×C59C2×D411yescharacteristic
158C22×C4×C59C2×D411yescharacteristic
159C22×C4×C59#4112yes—
160C22×C4×C59C2411yescharacteristic
161C2×C22⋊D59—42no—
162C2×C22⋊D59—42no—
163C2×C22⋊D59—42no—
164C22×Dic59—21no—
165C22×Dic59—21no—
166C22×Dic59—21no—
167C22×Dic59—42no—
168C22×Dic59—42no—
169C22×Dic59—42no—
170C2×D236—21no—
171C2×D236—21no—
172C2×D236—21no—
173C2×D236—21no—
174C2×D236—21no—
175C2×D236—21no—
176C4⋊C4×C59—24no—
177C4⋊C4×C59—21no—
178C4⋊C4×C59—21no—
179C4⋊C4×C59—21no—
180C4⋊C4×C59—21no—
181C4⋊C4×C59—42no—
182C4⋊C4×C59—42no—
183C4⋊C4×C59—81no—
184C4⋊C4×C59C2×D412yes—
185C4⋊C4×C59#4112yes—
186C22⋊C4×C59—24no—
187C22⋊C4×C59—22no—
188C22⋊C4×C59SD1614yescomplemented
189C42×C59—21no—
190C42×C59—21no—
191C42×C59—21no—
192C42×C59—21no—
193C42×C59—42no—
194C42×C59—81no—
195#11745671—44no—
196(C2×D59)⋊C4—42no—
197(C2×D59)⋊C4—42no—
198(C2×D59)⋊C4—42no—
199(C2×D59)⋊C4—42no—
200(C2×D59)⋊C4—42no—
201C4⋊Dic59—21no—
202C4⋊Dic59—21no—
203C4⋊Dic59—21no—
204C4⋊Dic59—21no—
205C4⋊Dic59—21no—
206C4⋊Dic59—21no—
207C4⋊Dic59—42no—
208C4⋊Dic59—42no—
209C4⋊Dic59—42no—
210C4⋊Dic59—42no—
211C4⋊Dic59—42no—
212C2×C59⋊C8—21no—
213C2×C59⋊C8—21no—
214C2×C59⋊C8—21no—
215C2×C59⋊C8—21no—
216C2×C59⋊C8—21no—
217C2×C59⋊C8—21no—
218C2×C59⋊C8—21no—
219C2×C59⋊C8—21no—
220C2×C59⋊C8—21no—
221C2×C59⋊C8—21no—
222C2×C59⋊C8—21no—
223C2×C59⋊C8—44no—
224C2×C59⋊C8#4112yes—
225C23×C59—21no—
226C23×C59—21no—
227C23×C59—21no—
228C23×C59—21no—
229C23×C59#12112yes—
230C23×C59C2×SD1612yes—
231C23×C59AGL(1,ℤ/8)12yes—
232C23×C59C22×D411yescharacteristic
233C22×D59—41no—
234C22×D59—41no—
235C22×D59—41no—
236C22×D59—41no—
237C22×D59—41no—
238C22×D59—41no—
239C22×D59—41no—
240Q8×C59—22no—
241Q8×C59—22no—
242Q8×C59—41no—
243Q8×C59—41no—
244C2×C4×C59—21no—
245C2×C4×C59—21no—
246C2×C4×C59—21no—
247C2×C4×C59—21no—
248C2×C4×C59—21no—
249C2×C4×C59—21no—
250C2×C4×C59—22no—
251C2×C4×C59—22no—
252C2×C4×C59—22no—
253C2×C4×C59—22no—
254C2×C4×C59—22no—
255C2×C4×C59—22no—
256C2×C4×C59—21no—
257C2×C4×C59—22no—
258C2×C4×C59—21no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—41no—
264C2×C4×C59—41no—
265C2×C4×C59—41no—
266C2×C4×C59—41no—
267C2×C4×C59—41no—
268C2×C4×C59—41no—
269C2×C4×C59—41no—
270C2×C4×C59—41no—
271C2×C4×C59—41no—
272C2×C4×C59—84no—
273C2×C4×C59#12112yes—
274C2×C4×C59C2×SD1612yes—
275C2×C4×C59C2×SD1612yes—
276C2×C4×C59C22×D411yescharacteristic
277C2×C4×C59C2×#4111yescharacteristic
278C2×C4×C59C2×#4111yescharacteristic
279C2×C4×C59C2×#4111yescharacteristic
280C2×C4×C59H(5,𝔽2)11yescharacteristic
281C2×C4×C592−1+411yescharacteristic
282C22⋊D59—84no—
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—41no—
292C2×Dic59—84no—
293D236—41no—
294D236—41no—
295D236—41no—
296D236—41no—
297C59⋊C8—22no—
298C59⋊C8—41no—
299C59⋊C8—41no—
300C59⋊C8—41no—
301#25204—591nomaximal, Sylow
302C22×C59—22no—
303C22×C59—22no—
304C22×C59—22no—
305C22×C59—22no—
306C22×C59—22no—
307C22×C59—22no—
308C22×C59#46014yes—
309C22×C59C2×#12111yescharacteristic
310C22×C59#54611yescharacteristic
311C22×C59#54711yescharacteristic
312C22×C59C22×SD1611yescharacteristic
313C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C59#57711yescharacteristic
315C22×C59#57811yescharacteristic
316C2×D59—81no—
317C2×D59—81no—
318C2×D59—81no—
319C2×D59—81no—
320C2×D59—81no—
321C2×D59—81no—
322C2×D59—81no—
323C4×C59—22no—
324C4×C59—22no—
325C4×C59—22no—
326C4×C59—41no—
327C4×C59—42no—
328C4×C59—42no—
329C4×C59—41no—
330C4×C59—42no—
331C4×C59—81no—
332C4×C59#52911yescharacteristic
333C4×C59#53911yescharacteristic
334C4×C59#54611yescharacteristic
335C4×C59#54711yescharacteristic
336Dic59—81no—
337Dic59—81no—
338Dic59—81no—
339C2×#483—591no—
340C2×#465—591no—
341#2501—591no—
342#2360D5911yescharacteristic, complemented
343#2084—591no—
344#2072—591no—
345#2065—591no—
346#2055—591no—
347#1948—591no—
348#1926—591no—
349#1880—591no—
350#1874—591no—
351#1850—591no—
352#1803—591no—
353C2×#340—591no—
354C2×C59—24no—
355C2×C59#242511yescharacteristic
356C2×C59C2×#46011yescharacteristic
357C2×C59#304611yescharacteristic
358C2×C59#329811yescharacteristic
359C2×C59#330611yescharacteristic
360C2×C59#333511yescharacteristic
361C2×C59#334311yescharacteristic
362D59—161no—
363C22×SD16—591no—
364C23×C8—591no—
365C2×#123—1181no—
366C2×#123—1181no—
367C2×C22⋊Q8C2×D5911yescharacteristic
368C2×#121—591no—
369C2×C4×Q8C2×D5911yescharacteristic
370C22×C4⋊C4—591no—
371C22×C4⋊C4C2×D5911yescharacteristic
372#483—1184no—
373#465—1184no—
374C2×#106—591no—
375C2×#106—591no—
376C2×#106—591no—
377C2×C4⋊C8—591no—
378C2×C4⋊C8—591no—
379C2×#103—591no—
380C2×#103—591no—
381C2×#103—591no—
382C2×#102—591no—
383C2×#102—591no—
384C2×#102—591no—
385C2×C22⋊C8—591no—
386#399—1181no—
387#399—1181no—
388#391C2×D5911yescharacteristic
389#390—591no—
390#390—591no—
391#389—21no—
392#389C2×D5911yescharacteristic
393#387—21no—
394#385—21no—
395#384—591no—
396#384—591no—
397C4×C4⋊C4C2×D5911yescharacteristic
398C4×C22⋊C4—21no—
399C4×C22⋊C4C2×D5911yescharacteristic
400#340—591no—
401#340—591no—
402#340—591no—
403#340—591no—
404#340—591no—
405#340—591no—
406#336—591no—
407#336—591no—
408C59#2520411yescharacteristic, complemented, Sylow
409C22×Q8C22×D5911yescharacteristic
410C22×D4—591no—
411C22×D4—1181no—
412C23×C4—21no—
413C23×C4—1181no—
414C23×C4C22×D5911yescharacteristic
415C2×SD16—1182no—
416C2×SD16—1182no—
417C2×SD16—2361no—
418C22×C8—591no—
419C22×C8—591no—
420C22×C8—591no—
421C22×C8—591no—
422C22×C8—1182no—
423C22×C8—1182no—
424C22×C8—2361no—
425#123—2364no—
426#123—2364no—
427C22⋊Q8—22no—
428C22⋊Q8D23614yes—
429#121—1182no—
430#121—1182no—
431C4×Q8—22no—
432C4×Q8—41no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—41no—
439C2×C4⋊C4—591no—
440C2×C4⋊C4—591no—
441C2×C4⋊C4—591no—
442C2×C4⋊C4—1182no—
443C2×C4⋊C4—1182no—
444C2×C4⋊C4—1181no—
445C2×C4⋊C4—1181no—
446C2×C4⋊C4—1181no—
447C2×C4⋊C4—1181no—
448C2×C4⋊C4—1181no—
449C2×C4⋊C4C22×D5911yescharacteristic
450C2×C4⋊C4C22×D5911yescharacteristic
451C2×C4⋊C4C22×D5911yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—1181no—
454C2×C22⋊C4—1181no—
455C2×C22⋊C4—1181no—
456C2×C22⋊C4—1181no—
457C2×C22⋊C4—1181no—
458C2×C22⋊C4C22⋊D5911yescharacteristic
459C2×C22⋊C4C22⋊D5911yescharacteristic
460C2×C42—21no—
461C2×C42—21no—
462C2×C42C22×D5911yescharacteristic
463C2×C42C22×D5911yescharacteristic
464#106—1182no—
465#106—1182no—
466#106—1182no—
467C4⋊C8—1182no—
468C4⋊C8—2361no—
469#103—1182no—
470#103—1182no—
471#103—1182no—
472#102—1182no—
473#102—1182no—
474#102—2361no—
475C22⋊C8—1182no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95C22⋊D5911yescharacteristic
481#95C22⋊D5911yescharacteristic
482C24—1181no—
483C24C2×C22⋊D5911yescharacteristic
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8C2×D23612yes—
490C2×D4—1181no—
491C2×D4—1181no—
492C2×D4—1181no—
493C2×D4—1181no—
494C2×D4—1181no—
495C2×D4—1181no—
496C2×D4—2362no—
497C2×D4—2362no—
498C2×D4—2362no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—81no—
510C22×C4—1181no—
511C22×C4—1181no—
512C22×C4—1181no—
513C22×C4—2362no—
514C22×C4—2362no—
515C22×C4—2362no—
516C22×C4C2×D23612yes—
517C22×C4#1174568512yes—
518C22×C4C2×C22⋊D5911yescharacteristic
519C22×C4C2×C22⋊D5911yescharacteristic
520C22×C4C2×C22⋊D5911yescharacteristic
521C22×C4C2×C22⋊D5911yescharacteristic
522C22×C4C2×C22⋊D5911yescharacteristic
523C22×C4C23×D5911yescharacteristic
524SD16—2364no—
525C2×C8—592no—
526C2×C8—1181no—
527C2×C8—1181no—
528C2×C8—1181no—
529C2×C8—1181no—
530C2×C8—1181no—
531C2×C8—1181no—
532C2×C8—1181no—
533C2×C8—1181no—
534C2×C8—1181no—
535C2×C8—1181no—
536C2×C8—1181no—
537C2×C8—2364no—
538C4⋊C4—24no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—81no—
546C4⋊C4—1181no—
547C4⋊C4—1181no—
548C4⋊C4—1181no—
549C4⋊C4—1181no—
550C4⋊C4—1181no—
551C4⋊C4—1181no—
552C4⋊C4—2362no—
553C4⋊C4—2362no—
554C4⋊C4—2362no—
555C4⋊C4—2362no—
556C4⋊C4—2362no—
557C4⋊C4C2×D23612yes—
558C4⋊C4#1174568712yes—
559C22⋊C4—24no—
560C22⋊C4—22no—
561C22⋊C4—2362no—
562C22⋊C4—2362no—
563C22⋊C4—2362no—
564C22⋊C4—2362no—
565C22⋊C4—2362no—
566C22⋊C4#1174567114yescomplemented
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—42no—
572C42—81no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—2361no—
578C23—2361no—
579C23—2361no—
580C23—2361no—
581C23—2361no—
582C23—2361no—
583C23—2361no—
584C23#1427370112yes—
585C23C2×#1174567112yes—
586C23#1427375212yes—
587C23C22×C22⋊D5911yescharacteristic
588Q8—22no—
589Q8—22no—
590Q8—41no—
591Q8—41no—
592D4—4724no—
593D4—2361no—
594D4—2361no—
595D4—2361no—
596D4—2361no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—84no—
626C2×C4—4724no—
627C2×C4—2361no—
628C2×C4—2361no—
629C2×C4—2361no—
630C2×C4—2361no—
631C2×C4—2361no—
632C2×C4—2361no—
633C2×C4—2361no—
634C2×C4—2361no—
635C2×C4—2361no—
636C2×C4#1427370112yes—
637C2×C4C2×#1174567112yes—
638C2×C4C2×#1174567112yes—
639C2×C4C22×D23611yescharacteristic
640C2×C4#41×D5911yescharacteristic
641C2×C4C2×#1174568711yescharacteristic
642C2×C4C2×#1174568511yescharacteristic
643C2×C4#1427377211yescharacteristic
644C2×C4#1427377411yescharacteristic
645C8—1182no—
646C8—2361no—
647C8—2361no—
648C8—2361no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—4721no—
656C22—4721no—
657C22—4721no—
658C22—4721no—
659C22—4721no—
660C22—4721no—
661C22—4721no—
662C22#1683760214yes—
663C22C2×#1427370111yescharacteristic
664C22#1683804611yescharacteristic
665C22#1683805111yescharacteristic
666C22C22×#1174567111yescharacteristic
667C22C2×#1427375211yescharacteristic
668C22#1683821311yescharacteristic
669C22#1683821711yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—42no—
674C4—41no—
675C4—41no—
676C4—42no—
677C4—42no—
678C4—81no—
679C4—4721no—
680C4—4721no—
681C4—4721no—
682C4#1683793211yescharacteristic
683C4#1683799411yescharacteristic
684C4#1683804711yescharacteristic
685C4#1683805611yescharacteristic
686C2—24no—
687C2—9441no—
688C2#2142764111yescharacteristic
689C2C2×#1683760211yescharacteristic
690C2#2143364611yescharacteristic
691C2#2143596111yescharacteristic
692C2#2143605711yescharacteristic
693C2#2143644711yescharacteristic
694C2#2143653611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2360C2
socleC23×C59C22×D4
prime radicalC2×#14273701C22
hypercenter#2360D59
hypocenterC59#25204
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
1. C2×#16837730C2semidirect
4. #21425572C2semidirect
5. #21425504C2semidirect
6. #21425467C2semidirect
7. #21425411C2semidirect
8. #21424859C2semidirect
9. #21424723C2semidirect
10. #21424451C2semidirect
12. #21424276C2semidirect
13. #21424101C2semidirect
14. C2×#16837164C2semidirect
15. C59×#2360C2semidirect
188. C22⋊C4×C59SD16semidirect
342. #2360D59semidirect
408. C59#25204semidirect
566. C22⋊C4#11745671semidirect

Maximal subgroups

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

subgroupindex
C2×#168377302
C2×#168376332
#214285672
#214255722
#214255042
#214254672
#214254112
#214248592
#214247232
#214244512
#214244132
#214242762
#214241012
C2×#168371642
C59×#23602
#2520459