Finite Group Databasebeta

← C2×#21435345 #29460874

Subgroups — C2×#21435345 #29460874

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×#16838033C211yesmaximal, characteristic, complemented
2C2×#16838005C211yesmaximal, characteristic
3#21435345C2116yesmaximal, direct product factor
4C2×#16837810C211yesmaximal, characteristic, complemented
5C2×#16837803C211yesmaximal, characteristic, complemented
6C2×#16837765C211yesmaximal, characteristic, complemented
7C2×#16837747C211yesmaximal, characteristic, complemented
8C2×#16837720C211yesmaximal, characteristic, complemented
9C2×#16837727C211yesmaximal, characteristic, complemented
10C2×#16837723C211yesmaximal, characteristic, complemented
11C2×#16837705C211yesmaximal, characteristic, complemented
12C2×#16837700C211yesmaximal, characteristic, complemented
13C2×#16837690C211yesmaximal, characteristic, complemented
14C2×#16837681C211yesmaximal, characteristic, complemented
15C2×#16837460C211yesmaximal, characteristic, complemented
16C2×C59×#480C211yesmaximal, characteristic, complemented
17#16838033—24no—
18#16838033C2218yescomplemented
19#16838005—24no—
20#16838005C2218yes—
21C2×#14273726—21no—
22C2×#14273726C2211yescharacteristic
23C2×#14273726C2211yescharacteristic
24C2×#14273723C2211yescharacteristic
25C2×#14273718—21no—
26C2×#14273718C2211yescharacteristic
27C2×#14273718C2211yescharacteristic
28C2×#14273718C2211yescharacteristic
29C2×#14273711—21no—
30C2×#14273709—21no—
31C2×#14273706—21no—
32C2×#14273706—21no—
33C2×#14273701C2211yescharacteristic
34C2×#14273699—21no—
35C2×#14273698—21no—
36C2×D4×Dic59C2211yescharacteristic
37C2×#14273689C2211yescharacteristic
38C2×#14273686C2211yescharacteristic
39C2×#14273686C2211yescharacteristic
40#16837810C2218yescomplemented
41#16837803C2218yescomplemented
42#16837765C2218yescomplemented
43#16837747C2218yescomplemented
44#16837727C2218yescomplemented
45#16837723C2218yescomplemented
46#16837720C2218yescomplemented
47#16837705C2218yescomplemented
48#16837700C2218yescomplemented
49#16837690C2218yescomplemented
50#16837681C2218yescomplemented
51#16837460C2218yescomplemented
52C2×#14273661C2211yescharacteristic
53C2×#14273660C2211yescharacteristic
54C2×#14273659C2211yescharacteristic
55C2×#14273658C2211yescharacteristic
56C2×#14273658C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×#14273649C2211yescharacteristic
61C2×#14273649C2211yescharacteristic
62C2×#14273648C2211yescharacteristic
63C2×#14273648C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
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
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×D236C2311yescharacteristic
80C22×C22⋊D59—21no—
81C22×C22⋊D59—21no—
82C22×C22⋊D59—21no—
83C23×Dic59—21no—
84C22×C4×D59—21no—
85C22×C59⋊C8C2311yescharacteristic
86C22×C59⋊C8C2311yescharacteristic
87#14273726—28no—
88#14273726—22no—
89#14273726—22no—
90#14273726C2314yes—
91#14273726C2314yes—
92#14273723—22no—
93#14273723C2314yes—
94#14273718—28no—
95#14273718—22no—
96#14273718—22no—
97#14273718—22no—
98#14273718C2314yes—
99#14273718C2314yes—
100#14273718C2314yes—
101#14273711—28no—
102#14273709—28no—
103#14273706—28no—
104#14273706—28no—
105#14273701—22no—
106#14273701C2314yes—
107#14273699—28no—
108#14273698—28no—
109D4×Dic59—22no—
110D4×Dic59C2314yes—
111#14273689—22no—
112#14273689C2314yes—
113#14273686—22no—
114#14273686D414yes—
115#14273686C2314yes—
116#14273686C2314yes—
117C2×C4⋊Dic59—21no—
118C2×C4⋊Dic59—21no—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59D411yescharacteristic
121C2×C4⋊Dic59D411yescharacteristic
122C2×C4⋊Dic59C2311yescharacteristic
123C2×C4⋊Dic59C2311yescharacteristic
124C2×C4⋊Dic59C2311yescharacteristic
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×C22⋊Dic59—21no—
131C2×C22⋊Dic59—21no—
132C2×C22⋊Dic59D411yescharacteristic
133C2×C22⋊Dic59D411yescharacteristic
134C2×(C2×D59)⋊C4—21no—
135C2×(C2×D59)⋊C4—21no—
136C2×C4×Dic59—21no—
137C2×C4×Dic59C2311yescharacteristic
138C2×C4×Dic59C2311yescharacteristic
139#14273661C2314yes—
140#14273660C2314yes—
141#14273659C2314yes—
142#14273658C2314yes—
143#14273658C2314yes—
144#14273658C2314yes—
145Dic59⋊C8C2314yes—
146Dic59⋊C8C2314yes—
147#14273649C2314yes—
148#14273649C2314yes—
149#14273648C2314yes—
150#14273648C2314yes—
151#14273647C2314yes—
152#14273647C2314yes—
153C22⋊(C59⋊C8)C2314yes—
154#14273637C2314yes—
155C8×Dic59C2314yes—
156C22×D4×C59—21no—
157C22×D4×C59C2311yescharacteristic
158C23×C4×C59—21no—
159C23×C4×C59C2311yescharacteristic
160C22×C8×C59C2311yescharacteristic
161C22×C8×C59C2311yescharacteristic
162#121×C59—22no—
163#121×C59C2314yes—
164C2×C4⋊C4×C59—21no—
165C2×C4⋊C4×C59—22no—
166C2×C4⋊C4×C59C2311yescharacteristic
167C2×C4⋊C4×C59C2311yescharacteristic
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C4⋊C4×C59C2314yes—
170C2×C22⋊C4×C59—21no—
171#107×C59C2314yes—
172#107×C59C2314yes—
173#102×C59C2314yes—
174#102×C59C2314yes—
175C22⋊C8×C59C2314yes—
176C24×C59—21no—
177C24×C59C2×D411yescharacteristic
178C23×D59—21no—
179C2×D4×C59—24no—
180C2×D4×C59—21no—
181C2×D4×C59—22no—
182C2×D4×C59—22no—
183C2×D4×C59—82no—
184C2×D4×C59C2412yes—
185C22×C4×C59—22no—
186C22×C4×C59—22no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—24no—
191C22×C4×C59—82no—
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D412yes—
194C22×C4×C59C2412yes—
195C22×C4×C59C2411yescharacteristic
196C2×C22⋊D59—24no—
197C2×C22⋊D59—24no—
198C2×C22⋊D59—24no—
199C2×C22⋊D59—82no—
200C2×C22⋊D59—82no—
201C2×C22⋊D59—82no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—24no—
206C22×Dic59—82no—
207C22×Dic59C2×D411yescharacteristic
208C22×Dic59C2×D411yescharacteristic
209C22×Dic59C2×D411yescharacteristic
210C22×Dic59C2×D411yescharacteristic
211C2×D236—22no—
212C2×D236—22no—
213C2×D236—21no—
214C2×D236C2412yes—
215C2×C4×D59—24no—
216C2×C4×D59—82no—
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—21no—
227C4⋊C4×C59—21no—
228C4⋊C4×C59—21no—
229C4⋊C4×C59C2412yes—
230C4⋊C4×C59C2412yes—
231C4⋊C4×C59C2412yes—
232C22⋊C4×C59—24no—
233C22⋊Dic59—24no—
234C22⋊Dic59—24no—
235C22⋊Dic59C2×D414yes—
236C22⋊Dic59C2×D414yes—
237(C2×D59)⋊C4—24no—
238(C2×D59)⋊C4—24no—
239C4⋊Dic59—21no—
240C4⋊Dic59—21no—
241C4⋊Dic59—21no—
242C4⋊Dic59—24no—
243C4⋊Dic59—24no—
244C4⋊Dic59—24no—
245C4⋊Dic59C2×D414yes—
246C4⋊Dic59C2×D414yes—
247C4⋊Dic59C2412yes—
248C4⋊Dic59C2412yes—
249C4⋊Dic59C2412yes—
250Dic59⋊C4—24no—
251Dic59⋊C4—24no—
252Dic59⋊C4—24no—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255C4×Dic59—24no—
256C4×Dic59C2×D412yes—
257C4×Dic59C2×D412yes—
258C4×Dic59C2412yes—
259C4×Dic59C2412yes—
260C2×C59⋊C8—22no—
261C2×C59⋊C8—22no—
262C2×C59⋊C8C2412yes—
263C2×C59⋊C8C2412yes—
264C23×C59—22no—
265C23×C59—22no—
266C23×C59—22no—
267C23×C59—22no—
268C23×C59—42no—
269C23×C59—42no—
270C23×C59—42no—
271C23×C59C22×D412yes—
272C23×C59C22×D411yescharacteristic
273C22×D59—22no—
274C22×D59—42no—
275C22×D59—42no—
276C22×D59—42no—
277D4×C59—22no—
278D4×C59—22no—
279D4×C59—42no—
280D4×C59—84no—
281C2×C4×C59—22no—
282C2×C4×C59—24no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—42no—
289C2×C4×C59—42no—
290C2×C4×C59—42no—
291C2×C4×C59—84no—
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—
299C22⋊D59—84no—
300C2×Dic59—22no—
301C2×Dic59—22no—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—42no—
308C2×Dic59—42no—
309C2×Dic59—42no—
310C2×Dic59—84no—
311C2×Dic59C22×D412yes—
312C2×Dic59C22×D412yes—
313C2×Dic59C22×D412yes—
314C2×Dic59C22×D412yes—
315D236—22no—
316D236—22no—
317D236—42no—
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—22no—
327C22×C59—22no—
328C22×C59—22no—
329C22×C59—44no—
330C22×C59—42no—
331C22×C59—42no—
332C22×C59—42no—
333C22×C59—84no—
334C22×C59#53612yes—
335C22×C59#57612yes—
336C22×C59#57712yes—
337C22×C59C23×D411yescharacteristic
338C2×D59—42no—
339C2×D59—42no—
340C2×D59—42no—
341C2×D59—84no—
342C4×C59—22no—
343C4×C59—42no—
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—22no—
353Dic59—42no—
354Dic59—42no—
355Dic59—42no—
356C2×#544—591no—
357C2×#540—591no—
358#3241—5916no—
359C2×#501—591no—
360C2×#499—591no—
361C2×#490—591no—
362C2×#486—591no—
363C2×#481—591no—
364C2×#482—591no—
365C2×#482—591no—
366C2×#480D5911yescharacteristic, complemented
367C2×#478—591no—
368C2×#478—591no—
369C2×#476—591no—
370C2×#474—591no—
371C2×#433—591no—
372C2×C59—42no—
373C2×C59—82no—
374C2×C59#324114yescomplemented
375C2×C59C2×#53611yescharacteristic
376C2×C59C2×#57611yescharacteristic
377C2×C59C2×#57711yescharacteristic
378D59—82no—
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×#127—591no—
387C2×#125—591no—
388C2×#125—591no—
389C2×#125—591no—
390C2×#125—1181no—
391C2×#123—1181no—
392C2×#123—1181no—
393C2×C22⋊Q8—1181no—
394C2×C22⋊Q8—1181no—
395C2×#121—591no—
396C2×#121—1181no—
397C2×#121—1181no—
398C2×#121C2×D5911yescharacteristic
399C2×C4×D4—591no—
400C2×C4×D4—591no—
401C2×#117—591no—
402C2×#117—591no—
403C22×C4⋊C4C2×D5911yescharacteristic
404#501—598no—
405#499—598no—
406#490—598no—
407#486—598no—
408#482—598no—
409#482—598no—
410#481—598no—
411#480C2×D5918yescomplemented
412#478—598no—
413#478—598no—
414#476—598no—
415#474—598no—
416#433—598no—
417C2×#107—591no—
418C2×#107—591no—
419C2×#107C2×D5911yescharacteristic
420C2×#107C2×D5911yescharacteristic
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×#102—591no—
432C2×#102—591no—
433C2×#102C2×D5911yescharacteristic
434C2×#102C2×D5911yescharacteristic
435C2×C22⋊C8—591no—
436C2×C22⋊C8C2×D5911yescharacteristic
437C2×#97—591no—
438C2×C4×C8—591no—
439C59C2×#324111yescharacteristic, complemented, Sylow
440C22×Q8—1181no—
441C22×Q8—1181no—
442C22×D4—21no—
443C22×D4—591no—
444C22×D4—1181no—
445C22×D4—1181no—
446C22×D4—1181no—
447C22×D4C22×D5911yescharacteristic
448C23×C4—21no—
449C23×C4—1181no—
450C23×C4—1181no—
451C23×C4C22×D5911yescharacteristic
452C22×C8—591no—
453C22×C8—591no—
454C22×C8C22×D5911yescharacteristic
455C22×C8C22×D5911yescharacteristic
456C4⋊Q8—594no—
457C4⋊Q8—594no—
458C4⋊Q8—1182no—
459C4⋊Q8—1182no—
460C4⋊Q8—1188no—
461#127—594no—
462#127—1182no—
463#125—594no—
464#125—594no—
465#125—594no—
466#125—1182no—
467#125—1182no—
468#125—1182no—
469#125—1188no—
470#123—1188no—
471#123—1188no—
472C22⋊Q8—1188no—
473C22⋊Q8—1188no—
474#121—22no—
475#121—594no—
476#121—1188no—
477#121—1188no—
478#121—1182no—
479#121C22×D5914yes—
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—22no—
490C2×C4⋊C4—591no—
491C2×C4⋊C4—591no—
492C2×C4⋊C4—591no—
493C2×C4⋊C4—591no—
494C2×C4⋊C4—591no—
495C2×C4⋊C4—1181no—
496C2×C4⋊C4—1181no—
497C2×C4⋊C4—1181no—
498C2×C4⋊C4—1181no—
499C2×C4⋊C4—1181no—
500C2×C4⋊C4—1181no—
501C2×C4⋊C4—1181no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4C22×D5911yescharacteristic
504C2×C4⋊C4C22×D5911yescharacteristic
505C2×C4⋊C4C22×D5914yes—
506C2×C4⋊C4C22×D5911yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—591no—
509C2×C22⋊C4—591no—
510C2×C22⋊C4—1181no—
511C2×C22⋊C4—1181no—
512C2×C22⋊C4—1181no—
513C2×C22⋊C4—1181no—
514C2×C42—591no—
515C2×C42—591no—
516C2×C42—1181no—
517#107—594no—
518#107—594no—
519#107C22×D5914yes—
520#107C22×D5914yes—
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#102—594no—
532#102—594no—
533#102C22×D5914yes—
534#102C22×D5914yes—
535C22⋊C8—594no—
536C22⋊C8C22×D5914yes—
537#97—594no—
538C4×C8—594no—
539C24—21no—
540C24—1181no—
541C24D4×D5911yescharacteristic
542C2×Q8—1184no—
543C2×Q8—1184no—
544C2×Q8—4722no—
545C2×Q8—4722no—
546C2×D4—24no—
547C2×D4—21no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—82no—
551C2×D4—592no—
552C2×D4—1184no—
553C2×D4—1184no—
554C2×D4—1184no—
555C2×D4—1181no—
556C2×D4—1182no—
557C2×D4—1182no—
558C2×D4—4722no—
559C2×D4—4722no—
560C2×D4—4722no—
561C2×D4C23×D5912yes—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—82no—
569C22×C4—591no—
570C22×C4—591no—
571C22×C4—591no—
572C22×C4—591no—
573C22×C4—1184no—
574C22×C4—1184no—
575C22×C4—1181no—
576C22×C4—1181no—
577C22×C4—1181no—
578C22×C4—4722no—
579C22×C4—4722no—
580C22×C4D4×D5912yes—
581C22×C4D4×D5911yescharacteristic
582C22×C4C23×D5912yes—
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—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—594no—
597C4⋊C4—594no—
598C4⋊C4—592no—
599C4⋊C4—592no—
600C4⋊C4—592no—
601C4⋊C4—1184no—
602C4⋊C4—1184no—
603C4⋊C4—1184no—
604C4⋊C4—1184no—
605C4⋊C4—1184no—
606C4⋊C4—1184no—
607C4⋊C4—1184no—
608C4⋊C4—1184no—
609C4⋊C4—1181no—
610C4⋊C4—1181no—
611C4⋊C4—1181no—
612C4⋊C4C23×D5912yes—
613C4⋊C4C23×D5912yes—
614C4⋊C4C23×D5912yes—
615C22⋊C4—24no—
616C22⋊C4—594no—
617C22⋊C4—594no—
618C22⋊C4—1184no—
619C22⋊C4—1184no—
620C22⋊C4—1184no—
621C22⋊C4—1184no—
622C42—592no—
623C42—592no—
624C42—592no—
625C42—592no—
626C42—1184no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—1182no—
635C23—2362no—
636C23—2362no—
637C23—2362no—
638C23C2×D4×D5912yes—
639C23C2×D4×D5911yescharacteristic
640Q8—4724no—
641Q8—4724no—
642D4—22no—
643D4—22no—
644D4—42no—
645D4—84no—
646D4—1182no—
647D4—1182no—
648D4—4724no—
649D4—4724no—
650D4—4724no—
651D4—2362no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—84no—
663C2×C4—592no—
664C2×C4—592no—
665C2×C4—592no—
666C2×C4—592no—
667C2×C4—1182no—
668C2×C4—1182no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—1182no—
672C2×C4—1182no—
673C2×C4—1182no—
674C2×C4—4724no—
675C2×C4—4724no—
676C2×C4—2362no—
677C2×C4—2362no—
678C2×C4—2362no—
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—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—84no—
696C22—4724no—
697C22—2362no—
698C22—2362no—
699C22—2362no—
700C22#1683797412yes—
701C22#1683820312yes—
702C22#1683821112yes—
703C22C22×D4×D5911yescharacteristic
704C4—22no—
705C4—42no—
706C4—42no—
707C4—42no—
708C4—1182no—
709C4—1182no—
710C4—1182no—
711C4—1182no—
712C4—2362no—
713C4—2362no—
714C4—2362no—
715C4#1683797412yes—
716C4C2×#1427377411yescharacteristic
717C4C2×#1427377411yescharacteristic
718C2—42no—
719C2—82no—
720C2—4722no—
721C2#2143534514yesdirect product factor
722C2C2×#1683797411yescharacteristic
723C2C2×#1683820311yescharacteristic
724C2C2×#1683821111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#480C2
socleC23×C59C22×D4
prime radicalC2×#16838005C2
hypercenterC2×#480D59
hypocenterC59C2×#3241
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×#16838033C2semidirect
3. #21435345C2direct (N × H)
4. C2×#16837810C2semidirect
5. C2×#16837803C2semidirect
6. C2×#16837765C2semidirect
7. C2×#16837747C2semidirect
8. C2×#16837720C2semidirect
9. C2×#16837727C2semidirect
10. C2×#16837723C2semidirect
11. C2×#16837705C2semidirect
12. C2×#16837700C2semidirect
13. C2×#16837690C2semidirect
14. C2×#16837681C2semidirect
15. C2×#16837460C2semidirect
16. C2×C59×#480C2semidirect
18. #16838033C22semidirect
40. #16837810C22semidirect
41. #16837803C22semidirect
42. #16837765C22semidirect
43. #16837747C22semidirect
44. #16837727C22semidirect
45. #16837723C22semidirect
46. #16837720C22semidirect
47. #16837705C22semidirect
48. #16837700C22semidirect
49. #16837690C22semidirect
50. #16837681C22semidirect
51. #16837460C22semidirect
71. C59×#480C22semidirect
366. C2×#480D59semidirect
374. C2×C59#3241semidirect
411. #480C2×D59semidirect
439. C59C2×#3241semidirect
721. C2#21435345direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380332
C2×#168380052
#214353452
C2×#168378102
C2×#168378032
C2×#168377652
C2×#168377472
C2×#168377202
C2×#168377272
C2×#168377232
C2×#168377052
C2×#168377002
C2×#168376902
C2×#168376812
C2×#168374602
C2×C59×#4802
C2×#324159