Finite Group Databasebeta

← C2×#428×D59 #29452340

Subgroups — C2×#428×D59 #29452340

Order 15104.

3182 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D59C211yesmaximal, characteristic
2C2×#117×D59C211yesmaximal, characteristic
3C22×C4⋊C4×D59C211yesmaximal, characteristic
4C2×#16837445C211yesmaximal, characteristic, complemented
5C2×#16837444C211yesmaximal, characteristic, complemented
6C2×#16837443C212yesmaximal, complemented
7C2×#16837442C211yesmaximal, characteristic, complemented
8C2×#16837441C212yesmaximal, complemented
9#428×D59C2116yesmaximal, direct product factor
10C2×#107×D59C212yesmaximal, complemented
11C2×#106×D59C212yesmaximal, complemented
12C2×C59×#428C211yesmaximal, characteristic, complemented
13C23×C4×D59—21no—
14C23×C4×D59C2211yescharacteristic
15C22×#11745664C2211yescharacteristic
16C22×#11745659C2212yes—
17C2×M16×D59C4116yescomplemented
18C2×M16×D59C2218yes—
19C22×C8×D59C2212yes—
20C2×#14273686C2211yescharacteristic
21C2×#14273685C2211yescharacteristic
22C2×#14273685C2211yescharacteristic
23C2×#14273684—21no—
24C2×#14273683—21no—
25#117×D59—24no—
26#117×D59C2218yes—
27C22×C4⋊Dic59C2211yescharacteristic
28C22×Dic59⋊C4—21no—
29C2×C4⋊C4×D59—21no—
30C2×C4⋊C4×D59—24no—
31C2×C4⋊C4×D59—21no—
32C2×C4⋊C4×D59C2212yes—
33C2×C4⋊C4×D59C2218yes—
34C2×C4⋊C4×D59C2212yes—
35C2×C4⋊C4×D59C2211yescharacteristic
36C2×C4⋊C4×D59C2211yescharacteristic
37C2×C22⋊C4×D59—21no—
38C2×C42×D59—21no—
39#16837445C2218yescomplemented
40#16837444C2218yescomplemented
41#16837443C22116yescomplemented
42#16837442C2218yescomplemented
43#16837441C22116yescomplemented
44C2×#14273661C2212yescomplemented
45C2×#14273660C2212yescomplemented
46C2×#14273660C2212yescomplemented
47#107×D59C22116yescomplemented
48C2×#14273659C2212yescomplemented
49C2×#14273658C2212yescomplemented
50C2×#14273658C2212yescomplemented
51#106×D59C22116yescomplemented
52C22×M16×C59C2211yescharacteristic
53C2×#117×C59C2211yescharacteristic
54C22×C4⋊C4×C59C2211yescharacteristic
55C59×#428C2218yescomplemented
56C2×#107×C59C2212yescomplemented
57C2×#106×C59C2212yescomplemented
58C24×D59D411yescharacteristic
59C23×Dic59—21no—
60C23×Dic59D411yescharacteristic
61C22×C4×D59—28no—
62C22×C4×D59—22no—
63C22×C4×D59—22no—
64C22×C4×D59—21no—
65C22×C4×D59—21no—
66C22×C4×D59—48no—
67C22×C4×D59C2×C418yes—
68C22×C4×D59D411yescharacteristic
69C22×C4×D59D414yes—
70C22×C4×D59D411yescharacteristic
71C22×C4×D59Q818yes—
72C22×C4×D59C2311yescharacteristic
73C22×C4×D59C2314yes—
74C22×C4×D59C2311yescharacteristic
75C2×#11745664C2×C418yescomplemented
76C2×#11745664C2314yes—
77C2×#11745659C2×C4116yescomplemented
78C2×#11745659C2318yes—
79M16×D59C2×C4164yescomplemented
80C22×C59⋊C8C2312yes—
81C2×C8×D59C2×C4116yescomplemented
82C2×C8×D59C2318yes—
83#14273686—22no—
84#14273686C2314yes—
85#14273685—22no—
86#14273685—22no—
87#14273685C2314yes—
88#14273685C2314yes—
89#14273684—28no—
90#14273683—28no—
91C2×C4⋊Dic59—21no—
92C2×C4⋊Dic59—22no—
93C2×C4⋊Dic59C2311yescharacteristic
94C2×C4⋊Dic59C2312yes—
95C2×C4⋊Dic59C2311yescharacteristic
96C2×C4⋊Dic59C2314yes—
97C2×Dic59⋊C4—22no—
98C2×Dic59⋊C4—22no—
99C2×Dic59⋊C4—28no—
100C2×Dic59⋊C4—21no—
101C2×Dic59⋊C4—21no—
102C4⋊C4×D59—28no—
103C4⋊C4×D59—24no—
104C4⋊C4×D59—28no—
105C4⋊C4×D59—24no—
106C4⋊C4×D59—22no—
107C4⋊C4×D59—22no—
108C4⋊C4×D59C2314yes—
109C4⋊C4×D59C2318yes—
110C4⋊C4×D59C2314yes—
111C4⋊C4×D59C2318yes—
112C2×C22⋊Dic59—21no—
113C2×(C2×D59)⋊C4—21no—
114C2×(C2×D59)⋊C4—21no—
115C22⋊C4×D59—28no—
116C2×C4×Dic59—21no—
117C2×C4×Dic59—21no—
118C2×C4×Dic59—21no—
119C42×D59—28no—
120#14273661C2318yescomplemented
121#14273660C2318yescomplemented
122#14273660C2318yescomplemented
123#14273659C2318yescomplemented
124#14273658C2318yescomplemented
125#14273658C2318yescomplemented
126C23×C4×C59—21no—
127C23×C4×C59C2311yescharacteristic
128C2×M16×C59C2×C418yescomplemented
129C2×M16×C59C2314yes—
130C22×C8×C59C2312yes—
131#117×C59—22no—
132#117×C59C2314yes—
133C2×C4⋊C4×C59—21no—
134C2×C4⋊C4×C59—22no—
135C2×C4⋊C4×C59C2311yescharacteristic
136C2×C4⋊C4×C59C2312yes—
137C2×C4⋊C4×C59C2311yescharacteristic
138C2×C4⋊C4×C59C2314yes—
139C2×C22⋊C4×C59—21no—
140C2×C42×C59—21no—
141#107×C59C2318yescomplemented
142#106×C59C2318yescomplemented
143C24×C59C2×D411yescharacteristic
144C23×D59—24no—
145C23×D59—24no—
146C23×D59C4⋊C418yes—
147C23×D59C2×D414yes—
148C23×D59C2×D411yescharacteristic
149C23×D59C2×D411yescharacteristic
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—24no—
153C22×C4×C59—22no—
154C22×C4×C59—44no—
155C22×C4×C59C22×C414yes—
156C22×C4×C59C2×D411yescharacteristic
157C22×C4×C59C2×D412yes—
158C22×C4×C59C2×Q814yes—
159C22×C4×C59C2411yescharacteristic
160C22×C4×C59C2412yes—
161C22×Dic59—21no—
162C22×Dic59—21no—
163C22×Dic59—24no—
164C22×Dic59—22no—
165C22×Dic59—44no—
166C22×Dic59C4⋊C418yes—
167C22×Dic59C2×D411yescharacteristic
168C22×Dic59C2×D411yescharacteristic
169C22×Dic59C2×D414yes—
170C2×C4×D59—24no—
171C2×C4×D59—24no—
172C2×C4×D59—28no—
173C2×C4×D59—28no—
174C2×C4×D59—48no—
175C2×C4×D59—432no—
176C2×C4×D59—44no—
177C2×C4×D59—48no—
178C2×C4×D59—44no—
179C2×C4×D59C4⋊C4132yes—
180C2×C4×D59C4⋊C418yes—
181C2×C4×D59C4⋊C418yes—
182C2×C4×D59C22×C414yes—
183C2×C4×D59C22×C4116yes—
184C2×C4×D59C22×C414yes—
185C2×C4×D59C2×D414yes—
186C2×C4×D59C2×D412yes—
187C2×C4×D59C2×D414yes—
188C2×C4×D59C2×D412yes—
189C2×C4×D59C2×Q8116yes—
190C2×C4×D59C2×Q814yes—
191C2×C4×D59C2×Q814yes—
192C2×C4×D59C2412yes—
193C2×C4×D59C2412yes—
194M16×C59C22×C4116yescomplemented
195C2×C8×C59C22×C418yescomplemented
196C2×C8×C59C2414yes—
197C4⋊C4×C59—24no—
198C4⋊C4×C59—22no—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—21no—
201C4⋊C4×C59C2412yes—
202C4⋊C4×C59C2414yes—
203C4⋊C4×C59C2412yes—
204C22⋊C4×C59—24no—
205C42×C59—24no—
206C22⋊Dic59—24no—
207(C2×D59)⋊C4—24no—
208(C2×D59)⋊C4—24no—
209C4⋊Dic59—24no—
210C4⋊Dic59—22no—
211C4⋊Dic59—21no—
212C4⋊Dic59—21no—
213C4⋊Dic59C2412yes—
214C4⋊Dic59C2414yes—
215C4⋊Dic59C2412yes—
216Dic59⋊C4—28no—
217Dic59⋊C4—28no—
218Dic59⋊C4—24no—
219Dic59⋊C4—24no—
220C4×Dic59—24no—
221C4×Dic59—24no—
222C4×Dic59—24no—
223#11745664C22×C4116yescomplemented
224C2×C59⋊C8C22×C418yescomplemented
225C2×C59⋊C8C2414yes—
226#11745659C22×C4132yescomplemented
227C8×D59C22×C4132yescomplemented
228C23×C59—22no—
229C23×C59—22no—
230C23×C59C2×C4⋊C414yes—
231C23×C59C22×D412yes—
232C23×C59C22×D411yescharacteristic
233C22×D59—22no—
234C22×D59—22no—
235C22×D59—28no—
236C22×D59—28no—
237C22×D59—232no—
238C22×D59C2×C4⋊C414yes—
239C22×D59C2×C4⋊C4116yes—
240C22×D59C2×C4⋊C414yes—
241C22×D59AGL(1,ℤ/8)14yes—
242C22×D59#13714yes—
243C22×D59C22×D412yes—
244C22×D59C22×D412yes—
245C2×C4×C59—22no—
246C2×C4×C59—22no—
247C2×C4×C59—24no—
248C2×C4×C59—48no—
249C2×C4×C59—44no—
250C2×C4×C59—42no—
251C2×C4×C59—42no—
252C2×C4×C59C2×C4⋊C418yes—
253C2×C4×C59C2×C4⋊C414yes—
254C2×C4×C59C23×C412yes—
255C2×C4×C59C23×C414yes—
256C2×C4×C59C22×D412yes—
257C2×C4×C59C22×D411yescharacteristic
258C2×C4×C59C22×Q814yes—
259C2×C4×C59C22×Q812yes—
260C2×C4×C59C2511yescharacteristic
261C2×Dic59—22no—
262C2×Dic59—22no—
263C2×Dic59—24no—
264C2×Dic59—48no—
265C2×Dic59—44no—
266C2×Dic59—42no—
267C2×Dic59—42no—
268C2×Dic59C2×C4⋊C4116yes—
269C2×Dic59C2×C4⋊C414yes—
270C2×Dic59C2×C4⋊C414yes—
271C2×Dic59C22×D412yes—
272C2×Dic59C22×D412yes—
273C4×D59—416no—
274C4×D59—48no—
275C4×D59—416no—
276C4×D59—48no—
277C4×D59C2×C4⋊C4116yes—
278C4×D59C2×C4⋊C418yes—
279C4×D59C2×C4⋊C418yes—
280C4×D59C2×C4⋊C4116yes—
281C4×D59C23×C414yes—
282C4×D59C23×C414yes—
283C4×D59C22×Q814yes—
284C4×D59C22×Q814yes—
285C8×C59C23×C418yescomplemented
286C59⋊C8C23×C418yescomplemented
287C22×#428—591nomaximal, Sylow
288C22×C59—28no—
289C22×C59—22no—
290C22×C59—22no—
291C22×C59C22×C4⋊C414yes—
292C22×C59C22×C4⋊C412yes—
293C22×C59C2×AGL(1,ℤ/8)12yes—
294C22×C59C2×#13712yes—
295C22×C59C23×D411yescharacteristic
296C2×D59—28no—
297C2×D59—22no—
298C2×D59—22no—
299C2×D59—232no—
300C2×D59#428116yesdirect product factor
301C2×D59C22×C4⋊C414yes—
302C2×D59C22×C4⋊C414yes—
303C2×D59C2×AGL(1,ℤ/8)14yes—
304C2×D59C2×#13714yes—
305C4×C59—44no—
306C4×C59—42no—
307C4×C59—42no—
308C4×C59C22×C4⋊C412yes—
309C4×C59C22×C4⋊C414yes—
310C4×C59C24×C411yescharacteristic
311C4×C59C23×Q811yescharacteristic
312Dic59—44no—
313Dic59—42no—
314Dic59—42no—
315Dic59C22×C4⋊C414yes—
316Dic59C22×C4⋊C414yes—
317C23×M16—591no—
318C22×#117—591no—
319C23×C4⋊C4—591no—
320C2×#428—5916no—
321C2×#428—592no—
322C2×#428—592no—
323C2×#428—591no—
324C2×#428—591no—
325C2×#428—591no—
326C2×#428D5911yescharacteristic, direct product factor
327C22×#107—592no—
328C22×#106—592no—
329C2×C59—24no—
330C2×C59C2×#42814yescomplemented
331C2×C59C23×C4⋊C411yescharacteristic
332C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
333C2×C59C22×#13711yescharacteristic
334D59—24no—
335D59C2×#42818yesdirect product factor
336C24×C4—591no—
337C24×C4—1181no—
338C22×M16—591no—
339C22×M16—5916no—
340C22×M16—598no—
341C22×M16—592no—
342C22×M16C2×D5911yescharacteristic
343C23×C8—592no—
344C2×#117—591no—
345C2×#117—598no—
346C2×#117—591no—
347C2×#117—591no—
348C2×#117—1181no—
349C2×#117—1181no—
350C2×#117—1184no—
351C2×#117C2×D5911yescharacteristic
352C22×C4⋊C4—591no—
353C22×C4⋊C4—591no—
354C22×C4⋊C4—592no—
355C22×C4⋊C4—591no—
356C22×C4⋊C4—592no—
357C22×C4⋊C4—598no—
358C22×C4⋊C4—1184no—
359C22×C4⋊C4—1181no—
360C22×C4⋊C4—1181no—
361C22×C4⋊C4—1181no—
362C22×C4⋊C4C2×D5911yescharacteristic
363C22×C22⋊C4—1181no—
364C22×C42—1181no—
365#428—598no—
366#428—598no—
367#428—598no—
368#428—5916no—
369#428—5916no—
370#428C2×D5918yesdirect product factor
371C2×#107—592no—
372C2×#107—592no—
373C2×#107—592no—
374C2×#107—5916no—
375C2×#107C2×D5912yescomplemented
376C2×#106—592no—
377C2×#106—592no—
378C2×#106—592no—
379C2×#106—5916no—
380C2×#106C2×D5912yescomplemented
381C59C22×#42811yescharacteristic, complemented, Sylow
382C25—591no—
383C23×C4—21no—
384C23×C4—591no—
385C23×C4—598no—
386C23×C4—594no—
387C23×C4—591no—
388C23×C4—591no—
389C23×C4—598no—
390C23×C4—591no—
391C23×C4—594no—
392C23×C4—591no—
393C23×C4—1181no—
394C23×C4—1181no—
395C23×C4—1188no—
396C23×C4—1182no—
397C23×C4—1182no—
398C23×C4—1181no—
399C23×C4—2368no—
400C23×C4C22×D5911yescharacteristic
401C2×M16—598no—
402C2×M16—594no—
403C2×M16—5964no—
404C2×M16—5916no—
405C2×M16—598no—
406C2×M16C4×D5918yescomplemented
407C2×M16C22×D5914yes—
408C22×C8—592no—
409C22×C8—5916no—
410C22×C8—598no—
411C22×C8C22×D5912yes—
412#117—22no—
413#117—594no—
414#117—594no—
415#117—594no—
416#117—1188no—
417#117—1188no—
418#117—1182no—
419#117—1182no—
420#117—1182no—
421#117C22×D5914yes—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—592no—
425C2×C4⋊C4—594no—
426C2×C4⋊C4—591no—
427C2×C4⋊C4—591no—
428C2×C4⋊C4—598no—
429C2×C4⋊C4—598no—
430C2×C4⋊C4—594no—
431C2×C4⋊C4—594no—
432C2×C4⋊C4—1188no—
433C2×C4⋊C4—1184no—
434C2×C4⋊C4—1188no—
435C2×C4⋊C4—1184no—
436C2×C4⋊C4—1182no—
437C2×C4⋊C4—1182no—
438C2×C4⋊C4—1188no—
439C2×C4⋊C4—1182no—
440C2×C4⋊C4—1182no—
441C2×C4⋊C4—1181no—
442C2×C4⋊C4—1181no—
443C2×C4⋊C4—1182no—
444C2×C4⋊C4—1181no—
445C2×C4⋊C4C22×D5912yes—
446C2×C4⋊C4C22×D5914yes—
447C2×C4⋊C4C22×D5911yescharacteristic
448C2×C4⋊C4C22×D5911yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—1188no—
451C2×C22⋊C4—1181no—
452C2×C22⋊C4—1181no—
453C2×C22⋊C4—1181no—
454C2×C42—21no—
455C2×C42—1188no—
456C2×C42—1181no—
457C2×C42—1181no—
458C2×C42—1181no—
459#107—598no—
460#107—598no—
461#107—598no—
462#107C22×D5918yescomplemented
463#106—598no—
464#106—598no—
465#106—598no—
466#106C22×D5918yescomplemented
467C24—591no—
468C24—598no—
469C24—594no—
470C24—591no—
471C24—1184no—
472C24—1184no—
473C24D4×D5911yescharacteristic
474C22×C4—24no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—44no—
479C22×C4—598no—
480C22×C4—594no—
481C22×C4—591no—
482C22×C4—591no—
483C22×C4—598no—
484C22×C4—5932no—
485C22×C4—598no—
486C22×C4—594no—
487C22×C4—5916no—
488C22×C4—594no—
489C22×C4—594no—
490C22×C4—592no—
491C22×C4—592no—
492C22×C4—594no—
493C22×C4—594no—
494C22×C4—5916no—
495C22×C4—594no—
496C22×C4—592no—
497C22×C4—592no—
498C22×C4—1184no—
499C22×C4—1184no—
500C22×C4—1188no—
501C22×C4—1188no—
502C22×C4—1184no—
503C22×C4—1181no—
504C22×C4—1181no—
505C22×C4—1182no—
506C22×C4—2368no—
507C22×C4—2364no—
508C22×C4—2364no—
509C22×C4—23632no—
510C22×C4—2368no—
511C22×C4—2364no—
512C22×C4C2×C4×D5914yes—
513C22×C4D4×D5912yes—
514C22×C4D4×D5911yescharacteristic
515C22×C4Q8×D5914yes—
516C22×C4C23×D5912yes—
517C22×C4C23×D5911yescharacteristic
518M16—5916no—
519M16—5932no—
520M16C2×C4×D59116yescomplemented
521C2×C8—598no—
522C2×C8—594no—
523C2×C8—5932no—
524C2×C8C2×C4×D5918yescomplemented
525C2×C8C23×D5914yes—
526C4⋊C4—24no—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—592no—
531C4⋊C4—594no—
532C4⋊C4—592no—
533C4⋊C4—1188no—
534C4⋊C4—1188no—
535C4⋊C4—1184no—
536C4⋊C4—1184no—
537C4⋊C4—1184no—
538C4⋊C4—1182no—
539C4⋊C4—1181no—
540C4⋊C4—1181no—
541C4⋊C4C23×D5912yes—
542C4⋊C4C23×D5914yes—
543C4⋊C4C23×D5912yes—
544C22⋊C4—24no—
545C22⋊C4—1184no—
546C22⋊C4—1184no—
547C22⋊C4—1184no—
548C42—24no—
549C42—1184no—
550C42—1184no—
551C42—1184no—
552C23—22no—
553C23—22no—
554C23—594no—
555C23—594no—
556C23—592no—
557C23—594no—
558C23—592no—
559C23—5916no—
560C23—594no—
561C23—1188no—
562C23—11832no—
563C23—1188no—
564C23—1182no—
565C23—1182no—
566C23C4⋊C4×D5914yes—
567C23C2×D4×D5912yes—
568C23C2×D4×D5911yescharacteristic
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—48no—
573C2×C4—44no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—592no—
577C2×C4—592no—
578C2×C4—5916no—
579C2×C4—594no—
580C2×C4—594no—
581C2×C4—594no—
582C2×C4—594no—
583C2×C4—594no—
584C2×C4—594no—
585C2×C4—598no—
586C2×C4—5916no—
587C2×C4—598no—
588C2×C4—5916no—
589C2×C4—1182no—
590C2×C4—1182no—
591C2×C4—1184no—
592C2×C4—2368no—
593C2×C4—2368no—
594C2×C4—23616no—
595C2×C4—23616no—
596C2×C4—2368no—
597C2×C4—2362no—
598C2×C4—2364no—
599C2×C4—2362no—
600C2×C4C4⋊C4×D5918yes—
601C2×C4C4⋊C4×D5914yes—
602C2×C4C22×C4×D5912yes—
603C2×C4C22×C4×D5914yes—
604C2×C4C2×D4×D5912yes—
605C2×C4C2×D4×D5911yescharacteristic
606C2×C4C2×Q8×D5914yes—
607C2×C4C2×Q8×D5912yes—
608C2×C4C24×D5911yescharacteristic
609C8—598no—
610C8C22×C4×D5918yescomplemented
611C22—28no—
612C22—22no—
613C22—22no—
614C22—594no—
615C22—5916no—
616C22—594no—
617C22—594no—
618C22—594no—
619C22—11832no—
620C22—1188no—
621C22—1182no—
622C22—1182no—
623C22C2×C4⋊C4×D5914yes—
624C22C2×C4⋊C4×D5912yes—
625C22AGL(1,ℤ/8)×D5912yes—
626C22#137×D5912yes—
627C22C22×D4×D5911yescharacteristic
628C4—44no—
629C4—42no—
630C4—42no—
631C4—594no—
632C4—594no—
633C4—2364no—
634C4—2362no—
635C4—2362no—
636C4C2×C4⋊C4×D5912yes—
637C4C2×C4⋊C4×D5914yes—
638C4C23×C4×D5911yescharacteristic
639C4C22×Q8×D5911yescharacteristic
640C2—24no—
641C2—598no—
642C2—1184no—
643C2#428×D5914yesdirect product factor
644C2C22×C4⋊C4×D5911yescharacteristic
645C2C2×AGL(1,ℤ/8)×D5911yescharacteristic
646C2C2×#137×D5911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC4×C59C24×C4
FrattiniC2×C4C24×D59
FittingC2×C59×#428C2
socleC23×C59C22×D4
prime radicalC24×D59D4
cosocleC2×C4×C59C25
hypercenterC2×#428D59
hypocenterC59C22×#428
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
4. C2×#16837445C2semidirect
5. C2×#16837444C2semidirect
6. C2×#16837443C2semidirect
7. C2×#16837442C2semidirect
8. C2×#16837441C2semidirect
9. #428×D59C2direct (N × H)
10. C2×#107×D59C2semidirect
11. C2×#106×D59C2semidirect
12. C2×C59×#428C2semidirect
17. C2×M16×D59C4semidirect
39. #16837445C22semidirect
40. #16837444C22semidirect
41. #16837443C22semidirect
42. #16837442C22semidirect
43. #16837441C22semidirect
44. C2×#14273661C22semidirect
45. C2×#14273660C22semidirect
46. C2×#14273660C22semidirect
47. #107×D59C22semidirect
48. C2×#14273659C22semidirect
49. C2×#14273658C22semidirect
50. C2×#14273658C22semidirect
51. #106×D59C22semidirect
55. C59×#428C22semidirect
56. C2×#107×C59C22semidirect
57. C2×#106×C59C22semidirect
75. C2×#11745664C2×C4semidirect
77. C2×#11745659C2×C4semidirect
79. M16×D59C2×C4semidirect
81. C2×C8×D59C2×C4semidirect
120. #14273661C23semidirect
121. #14273660C23semidirect
122. #14273660C23semidirect
123. #14273659C23semidirect
124. #14273658C23semidirect
125. #14273658C23semidirect
128. C2×M16×C59C2×C4semidirect
141. #107×C59C23semidirect
142. #106×C59C23semidirect
194. M16×C59C22×C4semidirect
195. C2×C8×C59C22×C4semidirect
223. #11745664C22×C4semidirect
224. C2×C59⋊C8C22×C4semidirect
226. #11745659C22×C4semidirect
227. C8×D59C22×C4semidirect
285. C8×C59C23×C4semidirect
286. C59⋊C8C23×C4semidirect
300. C2×D59#428direct (N × H)
326. C2×#428D59direct (N × H)
330. C2×C59C2×#428semidirect
335. D59C2×#428direct (N × H)
370. #428C2×D59direct (N × H)
375. C2×#107C2×D59semidirect
380. C2×#106C2×D59semidirect
381. C59C22×#428semidirect
406. C2×M16C4×D59semidirect
462. #107C22×D59semidirect
466. #106C22×D59semidirect
520. M16C2×C4×D59semidirect
524. C2×C8C2×C4×D59semidirect
610. C8C22×C4×D59semidirect
643. C2#428×D59direct (N × H)

Maximal subgroups

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

subgroupindex
C22×M16×D592
C2×#117×D592
C22×C4⋊C4×D592
C2×#168374452
C2×#168374442
C2×#168374432
C2×#168374422
C2×#168374412
#428×D592
C2×#107×D592
C2×#106×D592
C2×C59×#4282
C22×#42859