Finite Group Databasebeta

← C2×#21435344 #29460873

Subgroups — C2×#21435344 #29460873

Order 15104.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838032C211yesmaximal, characteristic, complemented
2C2×#16838006C211yesmaximal, characteristic
3#21435344C2116yesmaximal, direct product factor
4C2×#16837811C211yesmaximal, characteristic, complemented
5C2×#16837801C211yesmaximal, characteristic, complemented
6C2×#16837748C211yesmaximal, characteristic, complemented
7C2×#16837719C211yesmaximal, characteristic, complemented
8C2×#16837725C211yesmaximal, characteristic, complemented
9C2×#16837724C211yesmaximal, characteristic, complemented
10C2×#16837714C211yesmaximal, characteristic, complemented
11C2×#16837704C211yesmaximal, characteristic, complemented
12C2×#16837700C211yesmaximal, characteristic, complemented
13C2×#16837690C211yesmaximal, characteristic, complemented
14C2×#16837680C211yesmaximal, characteristic, complemented
15C2×#16837464C211yesmaximal, characteristic, complemented
16C2×C59×#490C211yesmaximal, characteristic, complemented
17#16838032—24no—
18#16838032C2218yescomplemented
19#16838006—24no—
20#16838006C2218yes—
21C2×#14273727C2211yescharacteristic
22C2×#14273726—21no—
23C2×#14273726C2211yescharacteristic
24C2×#14273719C2211yescharacteristic
25C2×#14273718C2211yescharacteristic
26C2×#14273717—21no—
27C2×#14273708—21no—
28C2×#14273708—21no—
29C2×#14273707—21no—
30C2×#14273705—21no—
31C2×#14273699—21no—
32C2×#14273699—21no—
33C2×#14273698C2211yescharacteristic
34C2×#14273698C2211yescharacteristic
35C2×D4×Dic59C2211yescharacteristic
36C2×D4×Dic59C2211yescharacteristic
37C2×#14273685C2211yescharacteristic
38C2×#14273684C2211yescharacteristic
39C2×C4⋊C4×D59C2211yescharacteristic
40#16837811C2218yescomplemented
41#16837801C2218yescomplemented
42#16837748C2218yescomplemented
43#16837725C2218yescomplemented
44#16837724C2218yescomplemented
45#16837719C2218yescomplemented
46#16837714C2218yescomplemented
47#16837704C2218yescomplemented
48#16837700C2218yescomplemented
49#16837690C2218yescomplemented
50#16837680C2218yescomplemented
51#16837464C2218yescomplemented
52C2×#14273661C2211yescharacteristic
53C2×#14273661C2211yescharacteristic
54C2×#14273660C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273659C2211yescharacteristic
57C2×#14273659C2211yescharacteristic
58C2×#14273658C2211yescharacteristic
59C2×#14273658C2211yescharacteristic
60C2×Dic59⋊C8C2211yescharacteristic
61C2×Dic59⋊C8C2211yescharacteristic
62C2×#14273648C2211yescharacteristic
63C2×#14273648C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×(C2×D59)⋊C8C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C4×C59⋊C8C2211yescharacteristic
69C2×#127×C59C2211yescharacteristic
70C2×#125×C59C2211yescharacteristic
71C59×#490C2218yescomplemented
72C2×#102×C59C2211yescharacteristic
73C2×#102×C59C2211yescharacteristic
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×C22⋊D59—21no—
80C22×C22⋊D59—21no—
81C23×Dic59—21no—
82C23×Dic59—21no—
83C22×C4×D59—21no—
84C22×C4×D59C2311yescharacteristic
85C22×C59⋊C8C2311yescharacteristic
86C22×C59⋊C8C2311yescharacteristic
87#14273727—22no—
88#14273727C2314yes—
89#14273726—28no—
90#14273726—22no—
91#14273726C2314yes—
92#14273719—22no—
93#14273719C2314yes—
94#14273718—22no—
95#14273718C2314yes—
96#14273717—28no—
97#14273708—28no—
98#14273708—28no—
99#14273707—28no—
100#14273705—28no—
101#14273699—28no—
102#14273699—28no—
103#14273698—22no—
104#14273698—22no—
105#14273698C2314yes—
106#14273698C2314yes—
107D4×Dic59—22no—
108D4×Dic59—22no—
109D4×Dic59C2314yes—
110D4×Dic59C2314yes—
111#14273685—22no—
112#14273685C2314yes—
113#14273684D414yes—
114#14273684C2314yes—
115C2×C4⋊Dic59—21no—
116C2×C4⋊Dic59—21no—
117C2×C4⋊Dic59C2311yescharacteristic
118C2×C4⋊Dic59C2311yescharacteristic
119C2×C4⋊Dic59C2311yescharacteristic
120C2×C4⋊Dic59C2311yescharacteristic
121C2×Dic59⋊C4—21no—
122C2×Dic59⋊C4—21no—
123C2×Dic59⋊C4—21no—
124C2×Dic59⋊C4—21no—
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4D411yescharacteristic
127C2×Dic59⋊C4D411yescharacteristic
128C4⋊C4×D59—22no—
129C4⋊C4×D59C2314yes—
130C2×C22⋊Dic59—21no—
131C2×C22⋊Dic59—21no—
132C2×C22⋊Dic59—21no—
133C2×C22⋊Dic59—21no—
134C2×(C2×D59)⋊C4—21no—
135C2×(C2×D59)⋊C4D411yescharacteristic
136C2×(C2×D59)⋊C4D411yescharacteristic
137C2×C4×Dic59—21no—
138C2×C4×Dic59C2311yescharacteristic
139#14273661C2314yes—
140#14273661C2314yes—
141#14273660C2314yes—
142#14273660C2314yes—
143#14273659C2314yes—
144#14273659C2314yes—
145#14273658C2314yes—
146#14273658C2314yes—
147Dic59⋊C8C2314yes—
148Dic59⋊C8C2314yes—
149#14273648C2314yes—
150#14273648C2314yes—
151#14273648C2314yes—
152#14273648C2314yes—
153(C2×D59)⋊C8C2314yes—
154(C2×D59)⋊C8C2314yes—
155C4×C59⋊C8C2314yes—
156C22×D4×C59—21no—
157C22×D4×C59—21no—
158C22×D4×C59C2311yescharacteristic
159C22×D4×C59C2311yescharacteristic
160C22×C8×C59C2311yescharacteristic
161C22×C8×C59C2311yescharacteristic
162#127×C59—22no—
163#127×C59C2314yes—
164#125×C59—22no—
165#125×C59C2314yes—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C42×C59C2311yescharacteristic
171#102×C59C2314yes—
172#102×C59C2314yes—
173#102×C59C2314yes—
174#102×C59C2314yes—
175#97×C59C2314yes—
176C24×C59—21no—
177C24×C59—21no—
178C23×D59C2×D411yescharacteristic
179C2×D4×C59—21no—
180C2×D4×C59—21no—
181C2×D4×C59—24no—
182C2×D4×C59—24no—
183C2×D4×C59—22no—
184C2×D4×C59—22no—
185C2×D4×C59—22no—
186C2×D4×C59—22no—
187C2×D4×C59—82no—
188C2×D4×C59—82no—
189C2×D4×C59C2412yes—
190C2×D4×C59C2412yes—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2×D411yescharacteristic
195C22×C4×C59C2411yescharacteristic
196C2×C22⋊D59—24no—
197C2×C22⋊D59—24no—
198C2×C22⋊D59—82no—
199C2×C22⋊D59—82no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—24no—
205C22×Dic59—24no—
206C22×Dic59—82no—
207C22×Dic59—82no—
208C22×Dic59C2×D411yescharacteristic
209C22×Dic59C2×D411yescharacteristic
210C22×Dic59C2×D411yescharacteristic
211C2×C4×D59—22no—
212C2×C4×D59—22no—
213C2×C4×D59—24no—
214C2×C4×D59—82no—
215C2×C4×D59C2×D412yes—
216C2×C4×D59C2412yes—
217C2×Dic118—24no—
218C2×Dic118—24no—
219C2×Dic118—82no—
220C2×Dic118—82no—
221C2×C8×C59—22no—
222C2×C8×C59—22no—
223C2×C8×C59C2412yes—
224C2×C8×C59C2412yes—
225C4⋊C4×C59—24no—
226C4⋊C4×C59—24no—
227C4⋊C4×C59—21no—
228C4⋊C4×C59—21no—
229C4⋊C4×C59C2412yes—
230C4⋊C4×C59C2412yes—
231C42×C59C2×D412yes—
232C42×C59C2412yes—
233C22⋊Dic59—24no—
234C22⋊Dic59—24no—
235C22⋊Dic59—24no—
236C22⋊Dic59—24no—
237(C2×D59)⋊C4—24no—
238(C2×D59)⋊C4C2×D414yes—
239(C2×D59)⋊C4C2×D414yes—
240C4⋊Dic59—21no—
241C4⋊Dic59—24no—
242C4⋊Dic59—21no—
243C4⋊Dic59—21no—
244C4⋊Dic59—21no—
245C4⋊Dic59—24no—
246C4⋊Dic59C2412yes—
247C4⋊Dic59C2412yes—
248C4⋊Dic59C2412yes—
249C4⋊Dic59C2412yes—
250Dic59⋊C4—24no—
251Dic59⋊C4—24no—
252Dic59⋊C4—24no—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4C2×D414yes—
256Dic59⋊C4C2×D414yes—
257C4×Dic59—24no—
258C4×Dic59C2×D412yes—
259C4×Dic59C2412yes—
260C2×C59⋊C8—22no—
261C2×C59⋊C8—22no—
262C2×C59⋊C8C2412yes—
263C2×C59⋊C8C2412yes—
264C23×C59—22no—
265C23×C59—22no—
266C23×C59—42no—
267C23×C59—42no—
268C23×C59—42no—
269C23×C59—42no—
270C23×C59—42no—
271C23×C59—42no—
272C23×C59C22×D411yescharacteristic
273C22×D59—22no—
274C22×D59—22no—
275C22×D59—22no—
276C22×D59C22×D412yes—
277D4×C59—22no—
278D4×C59—22no—
279D4×C59—22no—
280D4×C59—22no—
281D4×C59—42no—
282D4×C59—42no—
283D4×C59—84no—
284D4×C59—84no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—42no—
290C2×C4×C59—42no—
291C2×C4×C59C22×D412yes—
292C2×C4×C59C22×D412yes—
293C2×C4×C59C22×D411yescharacteristic
294C2×C4×C592−1+412yes—
295C2×C4×C592−1+412yes—
296C2×C4×C59C2511yescharacteristic
297C22⋊D59—84no—
298C22⋊D59—84no—
299C2×Dic59—22no—
300C2×Dic59—22no—
301C2×Dic59—22no—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—42no—
307C2×Dic59—42no—
308C2×Dic59—42no—
309C2×Dic59—42no—
310C2×Dic59—84no—
311C2×Dic59—84no—
312C2×Dic59C22×D412yes—
313C2×Dic59C22×D412yes—
314C2×Dic59C22×D412yes—
315C4×D59—24no—
316C4×D59—22no—
317C4×D59—22no—
318C4×D59—84no—
319Dic118—84no—
320Dic118—84no—
321C8×C59—22no—
322C8×C59—22no—
323C59⋊C8—22no—
324C59⋊C8—22no—
325C2×#3241—591nomaximal, Sylow
326C22×C59—42no—
327C22×C59—42no—
328C22×C59—42no—
329C22×C59—42no—
330C22×C59—42no—
331C22×C59—42no—
332C22×C59—84no—
333C22×C59—84no—
334C22×C59#53612yes—
335C22×C59#57612yes—
336C22×C59#57712yes—
337C22×C59C23×D411yescharacteristic
338C2×D59—22no—
339C2×D59—22no—
340C2×D59—22no—
341C2×D59—44no—
342C4×C59—22no—
343C4×C59—22no—
344C4×C59—42no—
345C4×C59—42no—
346C4×C59#53612yes—
347C4×C59C2×2−1+411yescharacteristic
348C4×C59C2×2−1+411yescharacteristic
349Dic59—22no—
350Dic59—22no—
351Dic59—22no—
352Dic59—42no—
353Dic59—42no—
354Dic59—42no—
355Dic59—42no—
356C2×#544—591no—
357C2×#540—591no—
358#3241—5916no—
359C2×#501—591no—
360C2×#499—591no—
361C2×#490D5911yescharacteristic, complemented
362C2×#486—591no—
363C2×#481—591no—
364C2×#482—591no—
365C2×#482—591no—
366C2×#480—591no—
367C2×#478—591no—
368C2×#478—591no—
369C2×#476—591no—
370C2×#474—591no—
371C2×#433—591no—
372C2×C59—82no—
373C2×C59—82no—
374C2×C59#324114yescomplemented
375C2×C59C2×#53611yescharacteristic
376C2×C59C2×#57611yescharacteristic
377C2×C59C2×#57711yescharacteristic
378D59—42no—
379#544—598no—
380#544—1184no—
381#540—598no—
382#540—1184no—
383C2×C4⋊Q8—591no—
384C2×C4⋊Q8—591no—
385C2×C4⋊Q8—1181no—
386C2×#127C2×D5911yescharacteristic
387C2×#125—591no—
388C2×#125—591no—
389C2×#125—1181no—
390C2×#125C2×D5911yescharacteristic
391C2×#123—1181no—
392C2×#123—1181no—
393C2×C22⋊Q8—1181no—
394C2×C22⋊Q8—1181no—
395C2×#121—591no—
396C2×#121—591no—
397C2×#121—1181no—
398C2×#121—1181no—
399C2×C4×D4—591no—
400C2×C4×D4—591no—
401C2×#117—591no—
402C2×#117—591no—
403C22×C4⋊C4—591no—
404#501—598no—
405#499—598no—
406#490C2×D5918yescomplemented
407#486—598no—
408#482—598no—
409#482—598no—
410#481—598no—
411#480—598no—
412#478—598no—
413#478—598no—
414#476—598no—
415#474—598no—
416#433—598no—
417C2×#107—591no—
418C2×#107—591no—
419C2×#107—591no—
420C2×#107—591no—
421C2×#106—591no—
422C2×#106—591no—
423C2×#106—591no—
424C2×#106—591no—
425C2×C4⋊C8—591no—
426C2×C4⋊C8—591no—
427C2×#102—591no—
428C2×#102—591no—
429C2×#102—591no—
430C2×#102—591no—
431C2×#102C2×D5911yescharacteristic
432C2×#102C2×D5911yescharacteristic
433C2×#102C2×D5911yescharacteristic
434C2×#102C2×D5911yescharacteristic
435C2×C22⋊C8—591no—
436C2×C22⋊C8—591no—
437C2×#97C2×D5911yescharacteristic
438C2×C4×C8—591no—
439C59C2×#324111yescharacteristic, complemented, Sylow
440C22×Q8—1181no—
441C22×Q8—1181no—
442C22×D4—21no—
443C22×D4—21no—
444C22×D4—1181no—
445C22×D4—1181no—
446C22×D4C22×D5911yescharacteristic
447C22×D4C22×D5911yescharacteristic
448C23×C4—591no—
449C23×C4—1181no—
450C23×C4—1181no—
451C23×C4—1181no—
452C22×C8—591no—
453C22×C8—591no—
454C22×C8C22×D5911yescharacteristic
455C22×C8C22×D5911yescharacteristic
456C4⋊Q8—594no—
457C4⋊Q8—594no—
458C4⋊Q8—1182no—
459C4⋊Q8—1188no—
460C4⋊Q8—1182no—
461#127—22no—
462#127C22×D5914yes—
463#125—22no—
464#125—594no—
465#125—594no—
466#125—1182no—
467#125—1188no—
468#125—1182no—
469#125C22×D5914yes—
470#123—1188no—
471#123—1188no—
472C22⋊Q8—1188no—
473C22⋊Q8—1188no—
474#121—594no—
475#121—594no—
476#121—1188no—
477#121—1188no—
478#121—1182no—
479#121—1182no—
480C4×D4—594no—
481C4×D4—594no—
482C4×D4—1182no—
483C4×D4—1182no—
484#117—594no—
485#117—594no—
486#117—594no—
487#117—1182no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—591no—
491C2×C4⋊C4—591no—
492C2×C4⋊C4—591no—
493C2×C4⋊C4—591no—
494C2×C4⋊C4—591no—
495C2×C4⋊C4—591no—
496C2×C4⋊C4—594no—
497C2×C4⋊C4—1182no—
498C2×C4⋊C4—1181no—
499C2×C4⋊C4—1181no—
500C2×C4⋊C4—1181no—
501C2×C4⋊C4—1181no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4—1181no—
505C2×C4⋊C4C22×D5911yescharacteristic
506C2×C4⋊C4C22×D5911yescharacteristic
507C2×C22⋊C4—591no—
508C2×C22⋊C4—591no—
509C2×C22⋊C4—1181no—
510C2×C22⋊C4—1181no—
511C2×C22⋊C4—1181no—
512C2×C22⋊C4—1181no—
513C2×C22⋊C4—1181no—
514C2×C42—591no—
515C2×C42—1181no—
516C2×C42C22×D5911yescharacteristic
517#107—594no—
518#107—594no—
519#107—594no—
520#107—594no—
521#106—594no—
522#106—594no—
523#106—594no—
524#106—594no—
525C4⋊C8—594no—
526C4⋊C8—594no—
527#102—594no—
528#102—594no—
529#102—594no—
530#102—594no—
531#102C22×D5914yes—
532#102C22×D5914yes—
533#102C22×D5914yes—
534#102C22×D5914yes—
535C22⋊C8—594no—
536C22⋊C8—594no—
537#97C22×D5914yes—
538C4×C8—594no—
539C24—21no—
540C24—21no—
541C24—591no—
542C2×Q8—1184no—
543C2×Q8—1184no—
544C2×Q8—4722no—
545C2×Q8—4722no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4—1184no—
557C2×D4—1184no—
558C2×D4—4722no—
559C2×D4—4722no—
560C2×D4C23×D5912yes—
561C2×D4C23×D5912yes—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—591no—
565C22×C4—591no—
566C22×C4—591no—
567C22×C4—592no—
568C22×C4—592no—
569C22×C4—1184no—
570C22×C4—1184no—
571C22×C4—1184no—
572C22×C4—1182no—
573C22×C4—1182no—
574C22×C4—1181no—
575C22×C4—1181no—
576C22×C4—1181no—
577C22×C4—1181no—
578C22×C4—4722no—
579C22×C4—4722no—
580C22×C4—4722no—
581C22×C4D4×D5911yescharacteristic
582C22×C4D4×D5911yescharacteristic
583C22×C4C23×D5911yescharacteristic
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—592no—
587C2×C8—592no—
588C2×C8—1182no—
589C2×C8—1182no—
590C2×C8C23×D5912yes—
591C2×C8C23×D5912yes—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—594no—
597C4⋊C4—594no—
598C4⋊C4—592no—
599C4⋊C4—592no—
600C4⋊C4—592no—
601C4⋊C4—592no—
602C4⋊C4—1184no—
603C4⋊C4—1184no—
604C4⋊C4—1184no—
605C4⋊C4—1184no—
606C4⋊C4—1181no—
607C4⋊C4—1181no—
608C4⋊C4—1181no—
609C4⋊C4—1181no—
610C4⋊C4—1184no—
611C4⋊C4—1184no—
612C4⋊C4—1184no—
613C4⋊C4C23×D5912yes—
614C4⋊C4C23×D5912yes—
615C22⋊C4—594no—
616C22⋊C4—594no—
617C22⋊C4—1184no—
618C22⋊C4—1184no—
619C22⋊C4—1184no—
620C22⋊C4—1184no—
621C22⋊C4—1184no—
622C42—592no—
623C42—592no—
624C42—1184no—
625C42D4×D5912yes—
626C42C23×D5912yes—
627C23—22no—
628C23—22no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—592no—
636C23—1182no—
637C23—1182no—
638C23—1182no—
639C23C2×D4×D5911yescharacteristic
640Q8—4724no—
641Q8—4724no—
642D4—22no—
643D4—22no—
644D4—22no—
645D4—22no—
646D4—42no—
647D4—42no—
648D4—84no—
649D4—84no—
650D4—4724no—
651D4—4724no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—592no—
659C2×C4—592no—
660C2×C4—592no—
661C2×C4—1182no—
662C2×C4—1182no—
663C2×C4—1182no—
664C2×C4—1184no—
665C2×C4—1182no—
666C2×C4—1182no—
667C2×C4—1182no—
668C2×C4—1182no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—4724no—
672C2×C4—4724no—
673C2×C4—4724no—
674C2×C4—2362no—
675C2×C4—2362no—
676C2×C4—2362no—
677C2×C4—2362no—
678C2×C4C2×D4×D5912yes—
679C2×C4C2×D4×D5912yes—
680C2×C4C2×D4×D5911yescharacteristic
681C2×C4#1427377412yes—
682C2×C4#1427377412yes—
683C2×C4C24×D5911yescharacteristic
684C8—22no—
685C8—22no—
686C8—1182no—
687C8—1182no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—84no—
695C22—84no—
696C22—1182no—
697C22—1182no—
698C22—1182no—
699C22—2364no—
700C22#1683797212yes—
701C22#1683820612yes—
702C22#1683821212yes—
703C22C22×D4×D5911yescharacteristic
704C4—22no—
705C4—22no—
706C4—42no—
707C4—42no—
708C4—1182no—
709C4—1182no—
710C4—1182no—
711C4—2362no—
712C4—2362no—
713C4—2362no—
714C4—2362no—
715C4#1683797212yes—
716C4C2×#1427377411yescharacteristic
717C4C2×#1427377411yescharacteristic
718C2—82no—
719C2—82no—
720C2—2362no—
721C2#2143534414yesdirect product factor
722C2C2×#1683797211yescharacteristic
723C2C2×#1683820611yescharacteristic
724C2C2×#1683821211yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#490C2
socleC23×C59C22×D4
prime radicalC2×#16838006C2
hypercenterC2×#490D59
hypocenterC59C2×#3241
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#16838032C2semidirect
3. #21435344C2direct (N × H)
4. C2×#16837811C2semidirect
5. C2×#16837801C2semidirect
6. C2×#16837748C2semidirect
7. C2×#16837719C2semidirect
8. C2×#16837725C2semidirect
9. C2×#16837724C2semidirect
10. C2×#16837714C2semidirect
11. C2×#16837704C2semidirect
12. C2×#16837700C2semidirect
13. C2×#16837690C2semidirect
14. C2×#16837680C2semidirect
15. C2×#16837464C2semidirect
16. C2×C59×#490C2semidirect
18. #16838032C22semidirect
40. #16837811C22semidirect
41. #16837801C22semidirect
42. #16837748C22semidirect
43. #16837725C22semidirect
44. #16837724C22semidirect
45. #16837719C22semidirect
46. #16837714C22semidirect
47. #16837704C22semidirect
48. #16837700C22semidirect
49. #16837690C22semidirect
50. #16837680C22semidirect
51. #16837464C22semidirect
71. C59×#490C22semidirect
361. C2×#490D59semidirect
374. C2×C59#3241semidirect
406. #490C2×D59semidirect
439. C59C2×#3241semidirect
721. C2#21435344direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380322
C2×#168380062
#214353442
C2×#168378112
C2×#168378012
C2×#168377482
C2×#168377192
C2×#168377252
C2×#168377242
C2×#168377142
C2×#168377042
C2×#168377002
C2×#168376902
C2×#168376802
C2×#168374642
C2×C59×#4902
C2×#324159