Finite Group Databasebeta

← C2×#21436438 #29467096

Subgroups — C2×#21436438 #29467096

Order 15104.

2374 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838053C211yesmaximal, characteristic, complemented
2C2×#16838052C211yesmaximal, characteristic, complemented
3#21436438C2116yesmaximal, direct product factor
4C2×#16837806C211yesmaximal, characteristic, complemented
5C2×#16837717C211yesmaximal, characteristic, complemented
6C2×#16837716C211yesmaximal, characteristic, complemented
7C2×#16837714C211yesmaximal, characteristic, complemented
8C2×#16837681C211yesmaximal, characteristic, complemented
9C2×#16837680C211yesmaximal, characteristic, complemented
10C2×#16837637C211yesmaximal, characteristic, complemented
11C2×#16837636C211yesmaximal, characteristic, complemented
12C2×#16837482C211yesmaximal, characteristic, complemented
13C2×(C22⋊D59)⋊C8C211yesmaximal, characteristic, complemented
14C22×#14273660C211yesmaximal, characteristic, complemented
15C2×#107×D59C211yesmaximal, characteristic, complemented
16C2×C59×#480C211yesmaximal, characteristic, complemented
17C22×#11745685—21no—
18C22×#11745687—21no—
19C22×#11745669C2211yescharacteristic
20C23×C59⋊C8C2211yescharacteristic
21C22×C8×D59C2211yescharacteristic
22#16838053—24no—
23#16838053C2218yescomplemented
24#16838052—24no—
25#16838052C2218yescomplemented
26C2×#14273726C2211yescharacteristic
27C2×#14273726C2211yescharacteristic
28C2×#14273712—21no—
29C2×#14273710—21no—
30C2×#14273709—21no—
31C2×#14273708—21no—
32C2×#14273705—21no—
33C2×#14273704—21no—
34C2×#14273702C2211yescharacteristic
35C2×#14273701C2211yescharacteristic
36C2×#14273698C2211yescharacteristic
37C2×D4×Dic59C2211yescharacteristic
38C2×#14273689C2211yescharacteristic
39C2×C4×C22⋊D59C2211yescharacteristic
40C22×C4⋊Dic59C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic
42C2×C4⋊C4×D59C2211yescharacteristic
43#16837806C2218yescomplemented
44#16837717C2218yescomplemented
45#16837716C2218yescomplemented
46#16837714C2218yescomplemented
47#16837681C2218yescomplemented
48#16837680C2218yescomplemented
49#16837637C2218yescomplemented
50#16837636C2218yescomplemented
51#16837482C2218yescomplemented
52(C22⋊D59)⋊C8C2218yescomplemented
53C2×#14273661C2211yescharacteristic
54C2×#14273661C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273660C2211yescharacteristic
58C2×#14273660C2211yescharacteristic
59C2×#14273660C2211yescharacteristic
60C2×#14273660C2218yescomplemented
61#107×D59C2218yescomplemented
62C2×Dic59⋊C8C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×#14273647C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×#121×C59C2211yescharacteristic
70C22×C4⋊C4×C59C2211yescharacteristic
71C59×#480C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#107×C59C2211yescharacteristic
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C2×#11745685—28no—
78C2×#11745685—48no—
79C2×#11745687—28no—
80C2×#11745687—48no—
81C22×Dic118—21no—
82C22×Dic118—21no—
83C22×D236—21no—
84C22×D236C2311yescharacteristic
85C22×C22⋊D59—21no—
86C22×C22⋊D59—21no—
87C22×C22⋊D59D411yescharacteristic
88C23×Dic59—21no—
89C23×Dic59—21no—
90C22×C4×D59—21no—
91C22×C4×D59—21no—
92C22×C4×D59—21no—
93C22×C4×D59C2311yescharacteristic
94C2×#11745669—24no—
95C2×#11745669C2314yes—
96C22×C59⋊C8—24no—
97C22×C59⋊C8C2314yes—
98C22×C59⋊C8C2311yescharacteristic
99C22×C59⋊C8C2311yescharacteristic
100C2×C8×D59—24no—
101C2×C8×D59C2314yes—
102#14273726—22no—
103#14273726—22no—
104#14273726C2314yes—
105#14273726C2314yes—
106#14273712—28no—
107#14273710—28no—
108#14273709—28no—
109#14273708—28no—
110#14273705—28no—
111#14273704—28no—
112#14273702—22no—
113#14273702C2314yes—
114#14273701—22no—
115#14273701C2314yes—
116#14273698—22no—
117#14273698C2314yes—
118D4×Dic59—22no—
119D4×Dic59C2314yes—
120#14273689—22no—
121#14273689C2314yes—
122C4×C22⋊D59D414yes—
123C4×C22⋊D59C2314yes—
124C2×C4⋊Dic59—21no—
125C2×C4⋊Dic59—22no—
126C2×C4⋊Dic59C2311yescharacteristic
127C2×C4⋊Dic59C2311yescharacteristic
128C2×C4⋊Dic59C2311yescharacteristic
129C2×C4⋊Dic59C2314yes—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4D411yescharacteristic
135C4⋊C4×D59—22no—
136C4⋊C4×D59—22no—
137C4⋊C4×D59C2314yes—
138C4⋊C4×D59C2314yes—
139C2×C22⋊Dic59—21no—
140C2×C22⋊Dic59—21no—
141C2×C22⋊Dic59D411yescharacteristic
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4—21no—
144C2×(C2×D59)⋊C4—21no—
145C2×(C2×D59)⋊C4D411yescharacteristic
146C2×C4×Dic59C2311yescharacteristic
147#14273661C2314yes—
148#14273661C2314yes—
149#14273660C2314yes—
150#14273660C2314yes—
151#14273660C2314yes—
152#14273660C2314yes—
153#14273660C2314yes—
154Dic59⋊C8C2314yes—
155#14273649C2314yes—
156#14273649C2314yes—
157#14273648C2314yes—
158#14273647C2314yes—
159(C2×D59)⋊C8C2314yes—
160C8×Dic59C2314yes—
161C22×D4×C59—21no—
162C22×D4×C59C2311yescharacteristic
163C23×C4×C59—21no—
164C23×C4×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167#121×C59—22no—
168#121×C59C2314yes—
169C2×C4⋊C4×C59—21no—
170C2×C4⋊C4×C59—22no—
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C4⋊C4×C59C2314yes—
175C2×C22⋊C4×C59—21no—
176#107×C59C2314yes—
177#107×C59C2314yes—
178#102×C59C2314yes—
179#102×C59C2314yes—
180C22⋊C8×C59C2314yes—
181C24×C59—21no—
182C24×C59C2×D411yescharacteristic
183C23×D59—21no—
184C23×D59C2×D411yescharacteristic
185C2×D4×C59—24no—
186C2×D4×C59—21no—
187C2×D4×C59—22no—
188C2×D4×C59—22no—
189C2×D4×C59—44no—
190C2×D4×C59C2412yes—
191C22×C4×C59—22no—
192C22×C4×C59—22no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—24no—
197C22×C4×C59—44no—
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2×D412yes—
200C22×C4×C59C2412yes—
201C22×C4×C59C2411yescharacteristic
202C2×C22⋊D59—24no—
203C2×C22⋊D59—24no—
204C2×C22⋊D59—44no—
205C2×C22⋊D59—44no—
206C2×C22⋊D59D818yescomplemented
207C2×C22⋊D59C2×D414yes—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C22×Dic59—21no—
211C22×Dic59—24no—
212C22×Dic59—24no—
213C22×Dic59—44no—
214C22×Dic59—44no—
215C22×Dic59C2×D411yescharacteristic
216C22×Dic59C2×D411yescharacteristic
217C22×Dic59C2×D411yescharacteristic
218#11745687—432no—
219#11745685—432no—
220C2×D236—22no—
221C2×D236—22no—
222C2×D236—24no—
223C2×D236—21no—
224C2×D236—44no—
225C2×D236C2412yes—
226C2×C4×D59—22no—
227C2×C4×D59—22no—
228C2×C4×D59—24no—
229C2×C4×D59—24no—
230C2×C4×D59—24no—
231C2×C4×D59—44no—
232C2×C4×D59—44no—
233C2×C4×D59—44no—
234C2×C4×D59C2×D412yes—
235C2×C4×D59C2412yes—
236C2×Dic118—24no—
237C2×Dic118—24no—
238C2×Dic118—44no—
239C2×Dic118—44no—
240C2×C8×C59—22no—
241C2×C8×C59—22no—
242C2×C8×C59C2412yes—
243C2×C8×C59C2412yes—
244C4⋊C4×C59—21no—
245C4⋊C4×C59—21no—
246C4⋊C4×C59—24no—
247C4⋊C4×C59—21no—
248C4⋊C4×C59C2412yes—
249C4⋊C4×C59C2412yes—
250C4⋊C4×C59C2412yes—
251C22⋊C4×C59—24no—
252C22⋊Dic59—24no—
253C22⋊Dic59—24no—
254C22⋊Dic59C2×D414yes—
255#11745669—28no—
256(C2×D59)⋊C4—24no—
257(C2×D59)⋊C4—24no—
258(C2×D59)⋊C4—24no—
259(C2×D59)⋊C4C2×D414yes—
260C4⋊Dic59—21no—
261C4⋊Dic59—21no—
262C4⋊Dic59—21no—
263C4⋊Dic59—24no—
264C4⋊Dic59C2412yes—
265C4⋊Dic59C2412yes—
266C4⋊Dic59C2412yes—
267Dic59⋊C4—24no—
268Dic59⋊C4—24no—
269Dic59⋊C4—24no—
270Dic59⋊C4—24no—
271Dic59⋊C4C2×D414yes—
272C4×Dic59C2×D412yes—
273C4×Dic59C2412yes—
274C2×C59⋊C8—22no—
275C2×C59⋊C8—28no—
276C2×C59⋊C8#4114yescomplemented
277C2×C59⋊C8C2412yes—
278C2×C59⋊C8C2412yes—
279C8×D59—28no—
280C23×C59—22no—
281C23×C59—22no—
282C23×C59—22no—
283C23×C59—42no—
284C23×C59—42no—
285C23×C59—42no—
286C23×C59C2×D814yes—
287C23×C59C22×D412yes—
288C23×C59C22×D411yescharacteristic
289C22×D59—22no—
290C22×D59—22no—
291C22×D59—22no—
292C22×D59—42no—
293C22×D59—42no—
294C22×D59—42no—
295C22×D59C2×D814yes—
296C22×D59C22×D412yes—
297D4×C59—22no—
298D4×C59—22no—
299D4×C59—48no—
300D4×C59—42no—
301C2×C4×C59—22no—
302C2×C4×C59—24no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—42no—
309C2×C4×C59—42no—
310C2×C4×C59—42no—
311C2×C4×C59—48no—
312C2×C4×C59C22×D412yes—
313C2×C4×C59C22×D411yescharacteristic
314C2×C4×C59C2×#4112yes—
315C2×C4×C592−1+412yes—
316C2×C4×C59C2511yescharacteristic
317C22⋊D59—48no—
318C22⋊D59—48no—
319C22⋊D59C2×D8116yescomplemented
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—42no—
326C2×Dic59—42no—
327C2×Dic59—42no—
328C2×Dic59—48no—
329C2×Dic59—48no—
330C2×Dic59C2×D814yes—
331C2×Dic59C22×D412yes—
332C2×Dic59C22×D412yes—
333C2×Dic59C22×D412yes—
334D236—22no—
335D236—22no—
336D236—48no—
337D236—42no—
338C4×D59—24no—
339C4×D59—22no—
340C4×D59—22no—
341C4×D59—48no—
342C4×D59—48no—
343C4×D59—48no—
344Dic118—48no—
345Dic118—48no—
346C8×C59—22no—
347C8×C59—22no—
348C59⋊C8—22no—
349C59⋊C8C2×#4114yescomplemented
350C2×#3334—591nomaximal, Sylow
351C22×C59—28no—
352C22×C59—22no—
353C22×C59—22no—
354C22×C59—42no—
355C22×C59—42no—
356C22×C59—42no—
357C22×C59—84no—
358C22×C59#54712yes—
359C22×C59C22×D814yes—
360C22×C59C22×D812yes—
361C22×C59#57812yes—
362C22×C59C23×D411yescharacteristic
363C2×D59—28no—
364C2×D59—22no—
365C2×D59—22no—
366C2×D59—42no—
367C2×D59—42no—
368C2×D59—42no—
369C2×D59—84no—
370C2×D59C22×D814yes—
371C4×C59—22no—
372C4×C59—42no—
373C4×C59—42no—
374C4×C59—42no—
375C4×C59#54712yes—
376C4×C59C22×#4111yescharacteristic
377C4×C59C2×2−1+411yescharacteristic
378Dic59—22no—
379Dic59—22no—
380Dic59—42no—
381Dic59—42no—
382Dic59—42no—
383Dic59C22×D814yes—
384C2×#547—591no—
385C2×#547—591no—
386#3334—5916no—
387C2×#500—591no—
388C2×#480—591no—
389C2×#480—591no—
390C2×#480—591no—
391C2×#480D5911yescharacteristic, complemented
392C2×#474—591no—
393C2×#474—591no—
394C2×#466—591no—
395C2×#466—591no—
396C2×C4×D8—591no—
397C2×C8×D4—591no—
398C22×#107—591no—
399C22×#107—591no—
400C2×C59—24no—
401C2×C59—82no—
402C2×C59#333414yescomplemented
403C2×C59C2×#54711yescharacteristic
404C2×C59C23×D811yescharacteristic
405C2×C59C2×#57811yescharacteristic
406D59—24no—
407D59—82no—
408C22×#41—1181no—
409C22×#41—1181no—
410C22×D8—591no—
411C23×C8—591no—
412C23×C8—591no—
413#547—598no—
414#547—598no—
415#547—1184no—
416#547—1184no—
417C2×C4⋊Q8—591no—
418C2×C4⋊Q8—591no—
419C2×#123—1181no—
420C2×#123—1181no—
421C2×#123—1181no—
422C2×#123—1181no—
423C2×C22⋊Q8—1181no—
424C2×C22⋊Q8—1181no—
425C2×#121—591no—
426C2×#121—591no—
427C2×#121—591no—
428C2×#121C2×D5911yescharacteristic
429C2×C4×D4—591no—
430C2×C4×D4—591no—
431C2×C4×D4—591no—
432C22×C4⋊C4—591no—
433C22×C4⋊C4—591no—
434C22×C4⋊C4—591no—
435C22×C4⋊C4C2×D5911yescharacteristic
436#500—598no—
437#480—598no—
438#480—598no—
439#480—598no—
440#480C2×D5918yescomplemented
441#474—598no—
442#474—598no—
443#466—598no—
444#466—598no—
445C4×D8—598no—
446C8×D4—598no—
447C2×#107—591no—
448C2×#107—591no—
449C2×#107—598no—
450C2×#107—591no—
451C2×#107—591no—
452C2×#107—591no—
453C2×#107—591no—
454C2×#107—591no—
455C2×#107—598no—
456C2×#107C2×D5911yescharacteristic
457C2×#107C2×D5911yescharacteristic
458C2×C4⋊C8—591no—
459C2×#102—591no—
460C2×#102—591no—
461C2×#102—591no—
462C2×#102—591no—
463C2×#102C2×D5911yescharacteristic
464C2×#102C2×D5911yescharacteristic
465C2×C22⋊C8—591no—
466C2×C22⋊C8C2×D5911yescharacteristic
467C2×C4×C8—591no—
468C59C2×#333411yescharacteristic, complemented, Sylow
469C2×#41—1188no—
470C2×#41—1188no—
471C2×#41—2368no—
472C2×#41—2368no—
473C22×Q8—1181no—
474C22×Q8—1181no—
475C22×D4—21no—
476C22×D4—591no—
477C22×D4—591no—
478C22×D4—1181no—
479C22×D4—1181no—
480C22×D4—1181no—
481C22×D4C22×D5911yescharacteristic
482C23×C4—21no—
483C23×C4—591no—
484C23×C4—1181no—
485C23×C4—1181no—
486C23×C4—1181no—
487C23×C4—1181no—
488C23×C4—1181no—
489C23×C4C22×D5911yescharacteristic
490C2×D8—594no—
491C2×D8—1184no—
492C22×C8—591no—
493C22×C8—591no—
494C22×C8—594no—
495C22×C8—594no—
496C22×C8—1184no—
497C22×C8—1184no—
498C22×C8C22×D5911yescharacteristic
499C22×C8C22×D5911yescharacteristic
500C4⋊Q8—594no—
501C4⋊Q8—594no—
502C4⋊Q8—1182no—
503C4⋊Q8—1182no—
504#123—1188no—
505#123—1188no—
506#123—1188no—
507#123—1188no—
508C22⋊Q8—1188no—
509C22⋊Q8—1188no—
510#121—22no—
511#121—594no—
512#121—594no—
513#121—594no—
514#121—1182no—
515#121—1182no—
516#121—1182no—
517#121C22×D5914yes—
518C4×D4—594no—
519C4×D4—594no—
520C4×D4—594no—
521C4×D4—594no—
522C4×D4—1182no—
523C4×D4—1182no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—591no—
527C2×C4⋊C4—591no—
528C2×C4⋊C4—591no—
529C2×C4⋊C4—591no—
530C2×C4⋊C4—594no—
531C2×C4⋊C4—594no—
532C2×C4⋊C4—594no—
533C2×C4⋊C4—1182no—
534C2×C4⋊C4—1182no—
535C2×C4⋊C4—1181no—
536C2×C4⋊C4—1181no—
537C2×C4⋊C4—1181no—
538C2×C4⋊C4—1181no—
539C2×C4⋊C4—1181no—
540C2×C4⋊C4—1182no—
541C2×C4⋊C4C22×D5911yescharacteristic
542C2×C4⋊C4C22×D5911yescharacteristic
543C2×C4⋊C4C22×D5911yescharacteristic
544C2×C4⋊C4C22×D5914yes—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—591no—
547C2×C22⋊C4—591no—
548C2×C22⋊C4—1181no—
549C2×C22⋊C4—1181no—
550C2×C22⋊C4—1181no—
551C2×C22⋊C4—1181no—
552C2×C22⋊C4—1181no—
553C2×C42—591no—
554#107—594no—
555#107—594no—
556#107—594no—
557#107—594no—
558#107—594no—
559#107—594no—
560#107—594no—
561#107C22×D5914yes—
562#107C22×D5914yes—
563C4⋊C8—594no—
564#102—594no—
565#102—594no—
566#102—594no—
567#102—594no—
568#102C22×D5914yes—
569#102C22×D5914yes—
570C22⋊C8—594no—
571C22⋊C8C22×D5914yes—
572C4×C8—594no—
573C24—21no—
574C24—591no—
575C24—1181no—
576C24D4×D5911yescharacteristic
577#41—23632no—
578#41—23632no—
579C2×Q8—1184no—
580C2×Q8—1184no—
581C2×Q8—2364no—
582C2×Q8—2364no—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—44no—
588C2×D4—598no—
589C2×D4—594no—
590C2×D4—592no—
591C2×D4—1184no—
592C2×D4—1184no—
593C2×D4—1184no—
594C2×D4—1181no—
595C2×D4—1182no—
596C2×D4—1182no—
597C2×D4—2364no—
598C2×D4—2364no—
599C2×D4—2364no—
600C2×D4C23×D5912yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—44no—
608C22×C4—591no—
609C22×C4—591no—
610C22×C4—591no—
611C22×C4—592no—
612C22×C4—592no—
613C22×C4—1184no—
614C22×C4—1184no—
615C22×C4—1184no—
616C22×C4—1184no—
617C22×C4—1182no—
618C22×C4—1182no—
619C22×C4—1184no—
620C22×C4—1181no—
621C22×C4—1181no—
622C22×C4—1181no—
623C22×C4—2364no—
624C22×C4—2364no—
625C22×C4—2364no—
626C22×C4—2364no—
627C22×C4—2364no—
628C22×C4D4×D5912yes—
629C22×C4D4×D5911yescharacteristic
630C22×C4C23×D5912yes—
631C22×C4C23×D5911yescharacteristic
632D8—1188no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—594no—
636C2×C8—592no—
637C2×C8—592no—
638C2×C8—1188no—
639C2×C8—1188no—
640C2×C8—1182no—
641C2×C8C23×D5912yes—
642C2×C8C23×D5912yes—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—594no—
648C4⋊C4—592no—
649C4⋊C4—592no—
650C4⋊C4—592no—
651C4⋊C4—1184no—
652C4⋊C4—1184no—
653C4⋊C4—1184no—
654C4⋊C4—1184no—
655C4⋊C4—1181no—
656C4⋊C4—1181no—
657C4⋊C4—1181no—
658C4⋊C4—1184no—
659C4⋊C4C23×D5912yes—
660C4⋊C4C23×D5912yes—
661C4⋊C4C23×D5912yes—
662C22⋊C4—24no—
663C22⋊C4—594no—
664C22⋊C4—594no—
665C22⋊C4—1184no—
666C22⋊C4—1184no—
667C22⋊C4—1184no—
668C22⋊C4—1184no—
669C22⋊C4—1184no—
670C42—592no—
671C42—592no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—594no—
679C23—592no—
680C23—1182no—
681C23—1182no—
682C23—1182no—
683C23—2362no—
684C23—2362no—
685C23—2362no—
686C23D8×D5914yes—
687C23C2×D4×D5912yes—
688C23C2×D4×D5911yescharacteristic
689Q8—2368no—
690Q8—2368no—
691D4—22no—
692D4—22no—
693D4—48no—
694D4—42no—
695D4—5916no—
696D4—1182no—
697D4—1182no—
698D4—2368no—
699D4—2368no—
700D4—2368no—
701D4—2362no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—48no—
712C2×C4—42no—
713C2×C4—594no—
714C2×C4—592no—
715C2×C4—592no—
716C2×C4—592no—
717C2×C4—1182no—
718C2×C4—1182no—
719C2×C4—1182no—
720C2×C4—1182no—
721C2×C4—1184no—
722C2×C4—1182no—
723C2×C4—1182no—
724C2×C4—1182no—
725C2×C4—2368no—
726C2×C4—2368no—
727C2×C4—2368no—
728C2×C4—2368no—
729C2×C4—2362no—
730C2×C4—2362no—
731C2×C4—2362no—
732C2×C4—2368no—
733C2×C4C2×D4×D5912yes—
734C2×C4C2×D4×D5911yescharacteristic
735C2×C4#41×D5912yes—
736C2×C4#1427377412yes—
737C2×C4C24×D5911yescharacteristic
738C8—22no—
739C8—22no—
740C8—594no—
741C8—1182no—
742C22—28no—
743C22—22no—
744C22—22no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—84no—
749C22—594no—
750C22—1188no—
751C22—1182no—
752C22—1182no—
753C22—4724no—
754C22—2362no—
755C22—2362no—
756C22—2362no—
757C22#1683805012yes—
758C22C2×D8×D5914yes—
759C22C2×D8×D5912yes—
760C22#1683821812yes—
761C22C22×D4×D5911yescharacteristic
762C4—22no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—594no—
767C4—1182no—
768C4—1182no—
769C4—2362no—
770C4—2362no—
771C4—2362no—
772C4#1683805012yes—
773C4C2×#41×D5911yescharacteristic
774C4C2×#1427377411yescharacteristic
775C2—24no—
776C2—82no—
777C2—1184no—
778C2—4722no—
779C2#2143643814yesdirect product factor
780C2C2×#1683805011yescharacteristic
781C2C22×D8×D5911yescharacteristic
782C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#480C2
socleC23×C59C22×D4
hypercenterC2×#480D59
hypocenterC59C2×#3334
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#16838053C2semidirect
2. C2×#16838052C2semidirect
3. #21436438C2direct (N × H)
4. C2×#16837806C2semidirect
5. C2×#16837717C2semidirect
6. C2×#16837716C2semidirect
7. C2×#16837714C2semidirect
8. C2×#16837681C2semidirect
9. C2×#16837680C2semidirect
10. C2×#16837637C2semidirect
11. C2×#16837636C2semidirect
12. C2×#16837482C2semidirect
13. C2×(C22⋊D59)⋊C8C2semidirect
14. C22×#14273660C2semidirect
15. C2×#107×D59C2semidirect
16. C2×C59×#480C2semidirect
23. #16838053C22semidirect
25. #16838052C22semidirect
43. #16837806C22semidirect
44. #16837717C22semidirect
45. #16837716C22semidirect
46. #16837714C22semidirect
47. #16837681C22semidirect
48. #16837680C22semidirect
49. #16837637C22semidirect
50. #16837636C22semidirect
51. #16837482C22semidirect
52. (C22⋊D59)⋊C8C22semidirect
60. C2×#14273660C22semidirect
61. #107×D59C22semidirect
71. C59×#480C22semidirect
206. C2×C22⋊D59D8semidirect
276. C2×C59⋊C8#41semidirect
319. C22⋊D59C2×D8semidirect
349. C59⋊C8C2×#41semidirect
391. C2×#480D59semidirect
402. C2×C59#3334semidirect
440. #480C2×D59semidirect
468. C59C2×#3334semidirect
779. C2#21436438direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380532
C2×#168380522
#214364382
C2×#168378062
C2×#168377172
C2×#168377162
C2×#168377142
C2×#168376812
C2×#168376802
C2×#168376372
C2×#168376362
C2×#168374822
C2×(C22⋊D59)⋊C82
C22×#142736602
C2×#107×D592
C2×C59×#4802
C2×#333459