Finite Group Databasebeta

← C4×#16838071 #28748540

Subgroups — C4×#16838071 #28748540

Order 15104.

3420 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838071C211yesmaximal, characteristic
2C2×C4×#11745689C211yesmaximal, characteristic, complemented
3#21427158C213yesmaximal, complemented
4#21427134C213yesmaximal, complemented
5#21427130C213yesmaximal, complemented
6#21427046C213yesmaximal, complemented
7Q8×Dic59⋊C4C211yesmaximal, characteristic, complemented
8#21426937C211yesmaximal, characteristic, complemented
9#21426934C211yesmaximal, characteristic, complemented
10C4×#14273723C213yesmaximal, complemented
11C4×#14273701C213yesmaximal, complemented
12C4×#14273698C213yesmaximal, complemented
13C4×Q8×Dic59C211yesmaximal, characteristic, complemented
14C42×C22⋊D59C213yesmaximal, complemented
15C2×C4×#41×C59C211yesmaximal, characteristic, complemented
16C22×#11745689C2211yescharacteristic
17#16838071C4116yesdirect product factor
18C2×#14273723C2213yes—
19C2×#14273701C2213yes—
20C2×#14273698C2213yes—
21C4×#11745689—28no—
22C2×Q8×Dic59C2211yescharacteristic
23C2×Q8×Dic59C2211yescharacteristic
24C2×Q8×Dic59C2211yescharacteristic
25C2×C4×D236C2213yes—
26C2×#14273689C2213yes—
27C2×C4×C22⋊D59C2213yes—
28C2×C4×C22⋊D59C2213yes—
29C2×C4×C22⋊D59C2216yes—
30C2×C4×C22⋊D59C2213yes—
31C2×#14273685C2213yes—
32C2×C42×D59C2213yes—
33#16837305C2213yes—
34#16837305C2213yes—
35#16837304C2213yes—
36#16837303C2213yes—
37#16837302C2216yes—
38#16837302C2216yes—
39#16837300C2213yes—
40#16837298C2213yes—
41#16837293C2216yes—
42#16837290C2216yes—
43#16837281C2216yes—
44#16837278C2216yes—
45#16837271C2213yes—
46#16837262C2213yes—
47#16837259C2213yes—
48C4⋊C4×Dic59C2213yes—
49C4⋊C4×Dic59C2213yes—
50C4×Dic59⋊C4C2211yescharacteristic
51C4×Dic59⋊C4C2213yes—
52C4×Dic59⋊C4C2213yes—
53C4×C4⋊Dic59C2213yes—
54C4×(C2×D59)⋊C4C2213yes—
55C4×(C2×D59)⋊C4C2213yes—
56C4×(C2×D59)⋊C4C2213yes—
57C4×C22⋊Dic59C2213yes—
58C4×C22⋊Dic59C2213yes—
59C4×C22⋊Dic59C2213yes—
60C42×Dic59C2213yes—
61C22×#41×C59C2211yescharacteristic
62C4×#41×C59—28no—
63C2×C4×Q8×C59C2211yescharacteristic
64C2×C4×Q8×C59C2211yescharacteristic
65C2×C4×D4×C59C2213yes—
66C2×C4×D4×C59C2213yes—
67C2×#117×C59C2213yes—
68C22×C42×C59C2213yes—
69C2×#11745689—24no—
70C2×#11745689—24no—
71C2×#11745689C2×C418yescomplemented
72C22×D236C2313yes—
73C22×C22⋊D59C2313yes—
74C22×C22⋊D59C2316yes—
75C22×C4×D59C2313yes—
76C22×C4×D59C2313yes—
77C22×C4×D59C2313yes—
78#14273723C2×C4124yescomplemented
79#14273701C2×C4124yescomplemented
80#14273698C2×C4124yescomplemented
81Q8×Dic59—24no—
82Q8×Dic59—24no—
83Q8×Dic59C2×C418yescomplemented
84C4×D236—212no—
85#14273689—212no—
86C4×C22⋊D59—212no—
87C4×C22⋊D59—212no—
88C4×C22⋊D59—412no—
89C4×C22⋊D59C2×C4124yescomplemented
90#14273685—212no—
91C2×C4⋊Dic59C2313yes—
92C2×C4⋊Dic59C2313yes—
93C2×C4⋊Dic59C2313yes—
94C2×Dic59⋊C4C2313yes—
95C2×Dic59⋊C4C2316yes—
96C2×Dic59⋊C4C2311yescharacteristic
97C2×Dic59⋊C4C2311yescharacteristic
98C2×C22⋊Dic59C2313yes—
99C2×C22⋊Dic59C2313yes—
100C2×C22⋊Dic59C2316yes—
101C2×C22⋊Dic59C2313yes—
102C2×(C2×D59)⋊C4C2313yes—
103C2×(C2×D59)⋊C4C2313yes—
104C2×(C2×D59)⋊C4C2316yes—
105C2×(C2×D59)⋊C4C2316yes—
106C2×(C2×D59)⋊C4C2313yes—
107C2×C4×Dic59C2313yes—
108C2×C4×Dic59C2313yes—
109C2×C4×Dic59C2313yes—
110C2×C4×Dic59C2311yescharacteristic
111C2×C4×Dic59C2313yes—
112C2×C4×Dic59C2313yes—
113C2×C4×Dic59C2313yes—
114C2×C4×Dic59C2313yes—
115C2×C4×Dic59C2311yescharacteristic
116C42×D59—212no—
117C59⋊#95C2311yescharacteristic
118C59⋊#95C2311yescharacteristic
119C59⋊#95C2313yes—
120C59⋊#95C2313yes—
121C59⋊#95C2313yes—
122C59⋊#95C2313yes—
123C59⋊#95C2316yes—
124C2×#41×C59—24no—
125C2×#41×C59—24no—
126C2×#41×C59C2×C418yescomplemented
127C22×Q8×C59C2311yescharacteristic
128C22×D4×C59C2313yes—
129C23×C4×C59C2313yes—
130C23×C4×C59C2313yes—
131C23×C4×C59C2313yes—
132C4×Q8×C59—24no—
133C4×Q8×C59D418yescomplemented
134C4×D4×C59—212no—
135C4×D4×C59—212no—
136#117×C59—212no—
137C2×C4⋊C4×C59C2313yes—
138C2×C4⋊C4×C59C2313yes—
139C2×C22⋊C4×C59C2316yes—
140C2×C42×C59—212no—
141C2×C42×C59C2311yescharacteristic
142C2×C42×C59C2313yes—
143C2×C42×C59C2313yes—
144C2×C42×C59C2313yes—
145C24×C59C2413yes—
146C23×D59C2413yes—
147#41×C59—232no—
148C2×Q8×C59C22×C414yes—
149C2×Q8×C59C2×D414yes—
150C2×Q8×C59#4114yes—
151C2×D4×C59—26no—
152C2×D4×C59—26no—
153C2×D4×C59C22×C4112yes—
154C22×C4×C59—26no—
155C22×C4×C59—26no—
156C22×C4×C59—26no—
157C22×C4×C59—26no—
158C22×C4×C59—26no—
159C22×C4×C59—26no—
160C22×C4×C59—26no—
161C22×C4×C59—43no—
162C22×C4×C59C22×C4112yes—
163C22×C4×C59C2413yes—
164C22×C4×C59C2411yescharacteristic
165C22×C4×C59C2413yes—
166C22×C4×C59C2411yescharacteristic
167C22×C4×C59C2413yes—
168C22×C4×C59C2411yescharacteristic
169C2×C22⋊D59—26no—
170C2×C22⋊D59—26no—
171C2×C22⋊D59—46no—
172C2×C22⋊D59—46no—
173C2×C22⋊D59C22×C4112yes—
174C2×C22⋊D59C22×C4124yes—
175C22×Dic59C2413yes—
176C22×Dic59C2413yes—
177C22×Dic59C2411yescharacteristic
178C22×Dic59C2413yes—
179C22×Dic59C2411yescharacteristic
180C22×Dic59C2411yescharacteristic
181C22×Dic59C2411yescharacteristic
182#11745689—232no—
183C2×D236—26no—
184C2×D236—26no—
185C2×D236C22×C4112yes—
186C2×C4×D59—26no—
187C2×C4×D59—26no—
188C2×C4×D59—26no—
189C2×C4×D59—26no—
190C2×C4×D59—26no—
191C2×C4×D59—26no—
192C2×C4×D59—26no—
193C2×C4×D59—43no—
194C2×C4×D59C22×C4112yes—
195C4⋊C4×C59—26no—
196C4⋊C4×C59C2×D4112yes—
197C22⋊C4×C59—212no—
198C42×C59—22no—
199C42×C59—26no—
200C42×C59—26no—
201C42×C59C2×D4112yes—
202C22⋊Dic59—26no—
203C22⋊Dic59—26no—
204C22⋊Dic59—46no—
205C22⋊Dic59C22×C4112yes—
206(C2×D59)⋊C4—212no—
207(C2×D59)⋊C4—26no—
208(C2×D59)⋊C4—26no—
209(C2×D59)⋊C4—46no—
210(C2×D59)⋊C4C22×C4112yes—
211C4⋊Dic59—26no—
212C4⋊Dic59—26no—
213C4⋊Dic59C22×C4112yes—
214Dic59⋊C4—26no—
215Dic59⋊C4—46no—
216Dic59⋊C4C22×C414yes—
217Dic59⋊C4#4114yescomplemented
218C4×Dic59—22no—
219C4×Dic59—26no—
220C4×Dic59—26no—
221C4×Dic59—26no—
222C4×Dic59—26no—
223C4×Dic59—26no—
224C4×Dic59—43no—
225C4×Dic59C22×C4112yes—
226C4×Dic59#4114yescomplemented
227C23×C59—23no—
228C23×C59—23no—
229C23×C59—23no—
230C23×C59—23no—
231C23×C59—23no—
232C23×C59—23no—
233C23×C59C23×C416yes—
234C23×C59C2511yescharacteristic
235C22×D59—23no—
236C22×D59—23no—
237C22×D59—23no—
238C22×D59—23no—
239C22×D59—23no—
240C22×D59—23no—
241C22×D59C23×C416yes—
242Q8×C59C4×D4116yescomplemented
243D4×C59—224no—
244C2×C4×C59—21no—
245C2×C4×C59—21no—
246C2×C4×C59—23no—
247C2×C4×C59—21no—
248C2×C4×C59—23no—
249C2×C4×C59—21no—
250C2×C4×C59—224no—
251C2×C4×C59—23no—
252C2×C4×C59—23no—
253C2×C4×C59—23no—
254C2×C4×C59—412no—
255C2×C4×C59—412no—
256C2×C4×C59C23×C412yes—
257C2×C4×C59C23×C416yes—
258C2×C4×C59C22×D416yes—
259C2×C4×C59C22×D416yes—
260C2×C4×C59C22×D412yes—
261C2×C4×C59C2×#4112yes—
262C2×C4×C59C2×#4112yes—
263C2×C4×C59C2×#4116yes—
264C2×C4×C59H(5,𝔽2)12yes—
265C22⋊D59—224no—
266C22⋊D59—424no—
267C2×Dic59—21no—
268C2×Dic59—21no—
269C2×Dic59—21no—
270C2×Dic59—21no—
271C2×Dic59—23no—
272C2×Dic59—21no—
273C2×Dic59—23no—
274C2×Dic59—21no—
275C2×Dic59—23no—
276C2×Dic59—23no—
277C2×Dic59—23no—
278C2×Dic59—23no—
279C2×Dic59—23no—
280C2×Dic59—23no—
281C2×Dic59C23×C416yes—
282C2×Dic59C23×C412yes—
283C2×Dic59C23×C412yes—
284C2×Dic59C2×#4112yes—
285C2×Dic59C2×#4112yes—
286C2×Dic59C2×#4112yes—
287C2×Dic59C2×#4112yes—
288D236—224no—
289C4×D59—224no—
290C4×D59—412no—
291C4×D59—412no—
292C4×#550—591nomaximal, Sylow
293C22×C59—26no—
294C22×C59—26no—
295C22×C59—26no—
296C22×C59—43no—
297C22×C59—43no—
298C22×C59—43no—
299C22×C59—43no—
300C22×C59C24×C411yescharacteristic
301C22×C59C23×D411yescharacteristic
302C22×C59C22×#4111yescharacteristic
303C22×C59C22×#4111yescharacteristic
304C22×C59C22×#4111yescharacteristic
305C22×C59C2×H(5,𝔽2)11yescharacteristic
306C22×C59#58511yescharacteristic
307C2×D59—26no—
308C2×D59—26no—
309C2×D59—26no—
310C2×D59—43no—
311C2×D59—43no—
312C2×D59—43no—
313C2×D59—43no—
314C4×C59—22no—
315C4×C59—26no—
316C4×C59—22no—
317C4×C59—43no—
318C4×C59C2×C4×D4112yes—
319C4×C59#55014yescomplemented
320Dic59—22no—
321Dic59—26no—
322Dic59—22no—
323Dic59—22no—
324Dic59—43no—
325Dic59—43no—
326Dic59C4×#4114yescomplemented
327C2×#550—591no—
328C2×C4×#41—591no—
329C2×C4×#41D5911yescharacteristic, complemented
330#2366—593no—
331#2363—593no—
332#2363—593no—
333#2354—593no—
334Q8×C4⋊C4—591no—
335#2341—591no—
336#2341—591no—
337C4×#127—593no—
338C4×#121—593no—
339C4×#121—593no—
340C42×Q8—591no—
341C42×D4—593no—
342C2×C59—46no—
343C2×C59C22×C4×D411yescharacteristic
344C2×C59C2×C4×#4111yescharacteristic
345C2×C59C4×H(5,𝔽2)11yescharacteristic
346C2×C59C2×#55011yescharacteristic
347C2×C59D4×#4111yescharacteristic
348C2×C59#348011yescharacteristic
349C2×C59#348311yescharacteristic
350D59—46no—
351C22×#41—591no—
352C22×#41C2×D5911yescharacteristic
353#550—5916no—
354C2×#127—593no—
355C2×#121—593no—
356C2×#121—593no—
357C4×#41—28no—
358C4×#41—1188no—
359C2×C4×Q8—591no—
360C2×C4×Q8—591no—
361C2×C4×Q8—591no—
362C2×C4×Q8C2×D5911yescharacteristic
363C2×C4×Q8C2×D5911yescharacteristic
364C2×C4×D4—593no—
365C2×C4×D4—593no—
366C2×C4×D4—593no—
367C2×C4×D4—596no—
368C2×C4×D4—593no—
369C2×C4×D4—593no—
370C2×C4×D4C2×D5913yes—
371C2×C4×D4C2×D5913yes—
372C2×#117—593no—
373C2×#117C2×D5913yes—
374C22×C42—593no—
375C22×C42C2×D5913yes—
376#390—593no—
377#390—593no—
378#390—593no—
379#390—596no—
380#390—596no—
381#390—593no—
382#389—593no—
383#389—593no—
384#388—596no—
385#388—596no—
386#386—596no—
387#386—596no—
388#384—593no—
389#380—593no—
390#380—593no—
391C4×C4⋊C4—593no—
392C4×C4⋊C4—593no—
393C4×C4⋊C4—593no—
394C4×C4⋊C4—593no—
395C4×C4⋊C4—593no—
396C4×C4⋊C4—591no—
397C4×C22⋊C4—593no—
398C4×C22⋊C4—593no—
399C4×C22⋊C4—593no—
400C4×C22⋊C4—593no—
401C4×C22⋊C4—593no—
402C4×C22⋊C4—593no—
403C43—593no—
404C59C4×#55011yescharacteristic, complemented, Sylow
405C2×#41—24no—
406C2×#41—24no—
407C2×#41—598no—
408C2×#41—1184no—
409C2×#41—1184no—
410C2×#41C4×D5918yescomplemented
411C22×Q8C22×D5911yescharacteristic
412C22×D4—593no—
413C22×D4—596no—
414C22×D4—593no—
415C22×D4C22×D5913yes—
416C23×C4—593no—
417C23×C4—593no—
418C23×C4—593no—
419C23×C4C22×D5913yes—
420C23×C4C22×D5913yes—
421C23×C4C22×D5913yes—
422#127—5924no—
423#121—5924no—
424#121—5924no—
425C4×Q8—24no—
426C4×Q8—598no—
427C4×Q8—1184no—
428C4×Q8—1184no—
429C4×Q8C22⋊D5918yescomplemented
430C4×D4—212no—
431C4×D4—212no—
432C4×D4—5924no—
433C4×D4—11812no—
434C4×D4—11812no—
435C4×D4—11812no—
436C4×D4—11812no—
437C4×D4—23612no—
438#117—212no—
439#117—11812no—
440C2×C4⋊C4—591no—
441C2×C4⋊C4—591no—
442C2×C4⋊C4—593no—
443C2×C4⋊C4—593no—
444C2×C4⋊C4—593no—
445C2×C4⋊C4—593no—
446C2×C4⋊C4—596no—
447C2×C4⋊C4C22×D5913yes—
448C2×C4⋊C4C22×D5913yes—
449C2×C22⋊C4—593no—
450C2×C22⋊C4—593no—
451C2×C22⋊C4—593no—
452C2×C22⋊C4—593no—
453C2×C22⋊C4—596no—
454C2×C22⋊C4—593no—
455C2×C22⋊C4—593no—
456C2×C22⋊C4—596no—
457C2×C22⋊C4—596no—
458C2×C22⋊C4C22×D5916yes—
459C2×C42—212no—
460C2×C42—593no—
461C2×C42—591no—
462C2×C42—593no—
463C2×C42—593no—
464C2×C42—593no—
465C2×C42—593no—
466C2×C42—593no—
467C2×C42—591no—
468C2×C42—593no—
469C2×C42—11812no—
470C2×C42C22×D5913yes—
471C2×C42C22×D5913yes—
472C2×C42C22×D5911yescharacteristic
473C2×C42C22×D5913yes—
474#95—591no—
475#95—591no—
476#95—593no—
477#95—593no—
478#95—593no—
479#95—593no—
480#95—596no—
481C24—593no—
482C24C23×D5913yes—
483#41—232no—
484#41—11832no—
485C2×Q8C2×C4×D5914yes—
486C2×Q8#1174568514yes—
487C2×Q8C2×C22⋊D5914yes—
488C2×D4—26no—
489C2×D4—26no—
490C2×D4—5912no—
491C2×D4—5924no—
492C2×D4—5912no—
493C2×D4—1186no—
494C2×D4—1186no—
495C2×D4—1186no—
496C2×D4—1186no—
497C2×D4—2366no—
498C2×D4—2366no—
499C2×D4C2×C4×D59112yes—
500C22×C4—26no—
501C22×C4—26no—
502C22×C4—26no—
503C22×C4—26no—
504C22×C4—26no—
505C22×C4—26no—
506C22×C4—26no—
507C22×C4—43no—
508C22×C4—591no—
509C22×C4—591no—
510C22×C4—591no—
511C22×C4—593no—
512C22×C4—591no—
513C22×C4—5912no—
514C22×C4—593no—
515C22×C4—593no—
516C22×C4—1186no—
517C22×C4—1186no—
518C22×C4—1186no—
519C22×C4—1186no—
520C22×C4—1186no—
521C22×C4—1186no—
522C22×C4—1186no—
523C22×C4—2363no—
524C22×C4C2×C4×D59112yes—
525C22×C4C23×D5913yes—
526C22×C4C23×D5911yescharacteristic
527C22×C4C23×D5913yes—
528C22×C4C23×D5911yescharacteristic
529C22×C4C23×D5913yes—
530C22×C4C23×D5911yescharacteristic
531C4⋊C4—26no—
532C4⋊C4—594no—
533C4⋊C4—5912no—
534C4⋊C4—594no—
535C4⋊C4—1186no—
536C4⋊C4—1186no—
537C4⋊C4—1186no—
538C4⋊C4—2366no—
539C4⋊C4C2×C22⋊D59112yes—
540C22⋊C4—212no—
541C22⋊C4—5912no—
542C22⋊C4—5912no—
543C22⋊C4—1186no—
544C22⋊C4—1186no—
545C22⋊C4—1186no—
546C22⋊C4—11812no—
547C22⋊C4—1186no—
548C22⋊C4—2366no—
549C22⋊C4—2366no—
550C42—22no—
551C42—26no—
552C42—26no—
553C42—5912no—
554C42—594no—
555C42—1186no—
556C42—1182no—
557C42—1186no—
558C42—1186no—
559C42—1186no—
560C42—1186no—
561C42—2363no—
562C42C2×C22⋊D59112yes—
563C23—23no—
564C23—23no—
565C23—23no—
566C23—23no—
567C23—23no—
568C23—23no—
569C23—596no—
570C23—1183no—
571C23—1183no—
572C23—1183no—
573C23—1183no—
574C23—1183no—
575C23—1183no—
576C23C22×C4×D5916yes—
577C23C24×D5911yescharacteristic
578Q8C4×C22⋊D59116yescomplemented
579D4—224no—
580D4—11824no—
581D4—11824no—
582D4—23624no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—23no—
586C2×C4—21no—
587C2×C4—23no—
588C2×C4—21no—
589C2×C4—224no—
590C2×C4—23no—
591C2×C4—23no—
592C2×C4—23no—
593C2×C4—412no—
594C2×C4—412no—
595C2×C4—592no—
596C2×C4—592no—
597C2×C4—592no—
598C2×C4—596no—
599C2×C4—592no—
600C2×C4—592no—
601C2×C4—592no—
602C2×C4—1181no—
603C2×C4—1181no—
604C2×C4—1181no—
605C2×C4—1181no—
606C2×C4—1183no—
607C2×C4—1181no—
608C2×C4—1183no—
609C2×C4—1181no—
610C2×C4—11824no—
611C2×C4—1183no—
612C2×C4—1183no—
613C2×C4—1183no—
614C2×C4—1183no—
615C2×C4—1183no—
616C2×C4—1183no—
617C2×C4—23612no—
618C2×C4—23612no—
619C2×C4C22×C4×D5912yes—
620C2×C4C22×C4×D5916yes—
621C2×C4C22×C22⋊D5916yes—
622C2×C4C22×C22⋊D5912yes—
623C2×C4C22×C22⋊D5916yes—
624C2×C4#41×D5912yes—
625C2×C4#41×D5912yes—
626C2×C4C2×#1174568516yes—
627C2×C4#1427377312yes—
628C22—26no—
629C22—26no—
630C22—26no—
631C22—43no—
632C22—43no—
633C22—43no—
634C22—43no—
635C22—1186no—
636C22—1186no—
637C22—1186no—
638C22—2363no—
639C22—2363no—
640C22—2363no—
641C22—2363no—
642C22C23×C4×D5911yescharacteristic
643C22C23×C22⋊D5911yescharacteristic
644C22C2×#41×D5911yescharacteristic
645C22C2×#41×D5911yescharacteristic
646C22C22×#1174568511yescharacteristic
647C22C2×#1427377311yescharacteristic
648C22#1683823811yescharacteristic
649C4—22no—
650C4—22no—
651C4—26no—
652C4—43no—
653C4—594no—
654C4—1182no—
655C4—1186no—
656C4—1182no—
657C4—1182no—
658C4—2363no—
659C4—2363no—
660C4C2×C4×C22⋊D59112yes—
661C4#1683807114yesdirect product factor
662C2—46no—
663C2—2366no—
664C2C22×C4×C22⋊D5911yescharacteristic
665C2C4×#41×D5911yescharacteristic
666C2C4×#1427377311yescharacteristic
667C2C2×#1683807111yescharacteristic
668C2#41×C22⋊D5911yescharacteristic
669C2#2143769411yescharacteristic
670C2#2143772211yescharacteristic
subgroupG/H
centerC22×C4C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC2×C4×#41×C59C2
socle, cosocleC23×C59C25
prime radicalC2×#16838071C2
hypercenterC2×C4×#41D59
hypocenterC59C4×#550
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11745689C2semidirect
3. #21427158C2semidirect
4. #21427134C2semidirect
5. #21427130C2semidirect
6. #21427046C2semidirect
7. Q8×Dic59⋊C4C2semidirect
8. #21426937C2semidirect
9. #21426934C2semidirect
10. C4×#14273723C2semidirect
11. C4×#14273701C2semidirect
12. C4×#14273698C2semidirect
13. C4×Q8×Dic59C2semidirect
14. C42×C22⋊D59C2semidirect
15. C2×C4×#41×C59C2semidirect
17. #16838071C4direct (N × H)
71. C2×#11745689C2×C4semidirect
78. #14273723C2×C4semidirect
79. #14273701C2×C4semidirect
80. #14273698C2×C4semidirect
83. Q8×Dic59C2×C4semidirect
89. C4×C22⋊D59C2×C4semidirect
126. C2×#41×C59C2×C4semidirect
133. C4×Q8×C59D4semidirect
217. Dic59⋊C4#41semidirect
226. C4×Dic59#41semidirect
242. Q8×C59C4×D4semidirect
319. C4×C59#550semidirect
326. Dic59C4×#41semidirect
329. C2×C4×#41D59semidirect
404. C59C4×#550semidirect
410. C2×#41C4×D59semidirect
429. C4×Q8C22⋊D59semidirect
578. Q8C4×C22⋊D59semidirect
661. C4#16838071direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380712
C2×C4×#117456892
#214271582
#214271342
#214271302
#214270462
Q8×Dic59⋊C42
#214269372
#214269342
C4×#142737232
C4×#142737012
C4×#142736982
C4×Q8×Dic592
C42×C22⋊D592
C2×C4×#41×C592
C4×#55059