Finite Group Databasebeta

← C2×#21435351 #29460880

Subgroups — C2×#21435351 #29460880

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×#16838030C211yesmaximal, characteristic, complemented
2C2×#16838007C211yesmaximal, characteristic
3#21435351C2116yesmaximal, direct product factor
4C2×#16837811C211yesmaximal, characteristic, complemented
5C2×#16837804C211yesmaximal, characteristic, complemented
6C2×#16837767C211yesmaximal, characteristic, complemented
7C2×#16837749C211yesmaximal, characteristic, complemented
8C2×#16837721C211yesmaximal, characteristic, complemented
9C2×#16837727C211yesmaximal, characteristic, complemented
10C2×#16837727C211yesmaximal, characteristic, complemented
11C2×#16837716C211yesmaximal, characteristic, complemented
12C2×#16837703C211yesmaximal, characteristic, complemented
13C2×#16837703C211yesmaximal, characteristic, complemented
14C2×#16837693C211yesmaximal, characteristic, complemented
15C2×#16837683C211yesmaximal, characteristic, complemented
16C2×C59×#433C211yesmaximal, characteristic, complemented
17#16838030—24no—
18#16838030C2218yescomplemented
19#16838007—24no—
20#16838007C2218yes—
21C2×#14273727C2211yescharacteristic
22C2×#14273727C2211yescharacteristic
23C2×#14273726—21no—
24C2×#14273724C2211yescharacteristic
25C2×#14273719C2211yescharacteristic
26C2×#14273719C2211yescharacteristic
27C2×#14273719C2211yescharacteristic
28C2×#14273718—21no—
29C2×#14273712—21no—
30C2×#14273712—21no—
31C2×#14273704—21no—
32C2×#14273704—21no—
33C2×#14273701C2211yescharacteristic
34C2×#14273701C2211yescharacteristic
35C2×#14273700—21no—
36C2×#14273700—21no—
37C2×C4×D236C2211yescharacteristic
38C2×C4×D236C2211yescharacteristic
39C2×#14273686C2211yescharacteristic
40C22×C4⋊Dic59C2211yescharacteristic
41#16837811C2218yescomplemented
42#16837804C2218yescomplemented
43#16837767C2218yescomplemented
44#16837749C2218yescomplemented
45#16837727C2218yescomplemented
46#16837727C2218yescomplemented
47#16837721C2218yescomplemented
48#16837716C2218yescomplemented
49#16837703C2218yescomplemented
50#16837703C2218yescomplemented
51#16837693C2218yescomplemented
52#16837683C2218yescomplemented
53C2×#14273661C2211yescharacteristic
54C2×#14273661C2211yescharacteristic
55C2×#14273661C2211yescharacteristic
56C2×#14273661C2211yescharacteristic
57C2×#14273659C2211yescharacteristic
58C2×#14273659C2211yescharacteristic
59C2×#14273659C2211yescharacteristic
60C2×#14273659C2211yescharacteristic
61C2×#14273649C2211yescharacteristic
62C2×#14273649C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273649C2211yescharacteristic
66C2×#14273649C2211yescharacteristic
67C2×#14273649C2211yescharacteristic
68C2×#14273649C2211yescharacteristic
69C2×#117×C59C2211yescharacteristic
70C59×#433C2218yescomplemented
71C2×C4⋊C8×C59C2211yescharacteristic
72C2×C4⋊C8×C59C2211yescharacteristic
73C2×C22⋊C8×C59C2211yescharacteristic
74C2×C22⋊C8×C59C2211yescharacteristic
75C2×#97×C59C2211yescharacteristic
76C2×C4×C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×D236—21no—
80C22×D236—21no—
81C22×D236C2311yescharacteristic
82C22×D236C2311yescharacteristic
83C22×C22⋊D59—21no—
84C22×C22⋊D59—21no—
85C23×Dic59—21no—
86C22×C4×D59—21no—
87C22×C4×D59—21no—
88#14273727—22no—
89#14273727—22no—
90#14273727C2314yes—
91#14273727C2314yes—
92#14273726—28no—
93#14273724—22no—
94#14273724C2314yes—
95#14273719—22no—
96#14273719—22no—
97#14273719—22no—
98#14273719C2314yes—
99#14273719C2314yes—
100#14273719C2314yes—
101#14273718—28no—
102#14273712—28no—
103#14273712—28no—
104#14273704—28no—
105#14273704—28no—
106#14273701—22no—
107#14273701—22no—
108#14273701C2314yes—
109#14273701C2314yes—
110#14273700—28no—
111#14273700—28no—
112C4×D236—22no—
113C4×D236—22no—
114C4×D236C2314yes—
115C4×D236C2314yes—
116#14273686—22no—
117#14273686C2314yes—
118C2×C4⋊Dic59—21no—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59—22no—
122C2×C4⋊Dic59C2311yescharacteristic
123C2×C4⋊Dic59C2311yescharacteristic
124C2×C4⋊Dic59C2311yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×C4⋊Dic59C2311yescharacteristic
128C2×C4⋊Dic59C2314yes—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×C22⋊Dic59—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×C4×Dic59—21no—
141#14273661C2314yes—
142#14273661C2314yes—
143#14273661C2314yes—
144#14273661C2314yes—
145#14273659C2314yes—
146#14273659C2314yes—
147#14273659C2314yes—
148#14273659C2314yes—
149#14273649C2314yes—
150#14273649C2314yes—
151#14273649C2314yes—
152#14273649C2314yes—
153#14273649C2314yes—
154#14273649C2314yes—
155#14273649C2314yes—
156#14273649C2314yes—
157C23×C4×C59C2311yescharacteristic
158C22×C8×C59C2311yescharacteristic
159C22×C8×C59C2311yescharacteristic
160C22×C8×C59C2311yescharacteristic
161C22×C8×C59C2311yescharacteristic
162#117×C59D414yes—
163#117×C59C2314yes—
164C2×C4⋊C4×C59D411yescharacteristic
165C2×C4⋊C4×C59D411yescharacteristic
166C2×C22⋊C4×C59D411yescharacteristic
167C2×C22⋊C4×C59D411yescharacteristic
168C2×C42×C59C2311yescharacteristic
169C2×C42×C59C2311yescharacteristic
170C4⋊C8×C59C2314yes—
171C4⋊C8×C59C2314yes—
172C22⋊C8×C59C2314yes—
173C22⋊C8×C59C2314yes—
174#97×C59C2314yes—
175C4×C8×C59C2314yes—
176C24×C59C2×D411yescharacteristic
177C23×D59—21no—
178C23×D59—21no—
179C22×C4×C59—22no—
180C22×C4×C59—22no—
181C22×C4×C59C2×D411yescharacteristic
182C22×C4×C59C2×D411yescharacteristic
183C22×C4×C59C2×D411yescharacteristic
184C22×C4×C59C2×D411yescharacteristic
185C22×C4×C59C2×D411yescharacteristic
186C22×C4×C59C2×D412yes—
187C22×C4×C59C2412yes—
188C22×C4×C59C2411yescharacteristic
189C2×C22⋊D59—24no—
190C2×C22⋊D59—24no—
191C2×C22⋊D59—82no—
192C2×C22⋊D59—82no—
193C22×Dic59—21no—
194C22×Dic59—21no—
195C22×Dic59—21no—
196C22×Dic59—21no—
197C22×Dic59—21no—
198C22×Dic59—21no—
199C22×Dic59—24no—
200C22×Dic59—82no—
201C2×D236—22no—
202C2×D236—22no—
203C2×D236—22no—
204C2×D236—22no—
205C2×D236—21no—
206C2×D236—21no—
207C2×D236—24no—
208C2×D236—24no—
209C2×D236—82no—
210C2×D236—82no—
211C2×D236C2412yes—
212C2×D236C2412yes—
213C2×C4×D59—24no—
214C2×C4×D59—24no—
215C2×C4×D59—82no—
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×C59—22no—
224C2×C8×C59—22no—
225C2×C8×C59C2412yes—
226C2×C8×C59C2412yes—
227C2×C8×C59C2412yes—
228C2×C8×C59C2412yes—
229C4⋊C4×C59C2×D414yes—
230C4⋊C4×C59C2×D414yes—
231C22⋊C4×C59C2×D414yes—
232C22⋊C4×C59C2×D414yes—
233C42×C59C2×D412yes—
234C42×C59C2×D412yes—
235C42×C59C2412yes—
236C42×C59C2412yes—
237C22⋊Dic59—24no—
238(C2×D59)⋊C4—24no—
239(C2×D59)⋊C4—24no—
240(C2×D59)⋊C4—24no—
241(C2×D59)⋊C4—24no—
242C4⋊Dic59—24no—
243C4⋊Dic59—21no—
244C4⋊Dic59—21no—
245C4⋊Dic59—24no—
246C4⋊Dic59—24no—
247C4⋊Dic59—21no—
248C4⋊Dic59—21no—
249C4⋊Dic59—21no—
250C4⋊Dic59—21no—
251C4⋊Dic59C2412yes—
252C4⋊Dic59C2412yes—
253C4⋊Dic59C2412yes—
254C4⋊Dic59C2412yes—
255C4⋊Dic59C2412yes—
256C4⋊Dic59C2412yes—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263C4×Dic59—24no—
264C23×C59—22no—
265C23×C59—22no—
266C23×C59—22no—
267C23×C59C22×D412yes—
268C23×C59C22×D411yescharacteristic
269C22×D59—22no—
270C22×D59—22no—
271C22×D59—42no—
272C22×D59—42no—
273C22×D59—42no—
274C22×D59—42no—
275C22×D59—42no—
276C22×D59—42no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—24no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59C22×D412yes—
286C2×C4×C59C22×D412yes—
287C2×C4×C59C22×D412yes—
288C2×C4×C59C22×D412yes—
289C2×C4×C59C22×D412yes—
290C2×C4×C59C22×D411yescharacteristic
291C2×C4×C592−1+412yes—
292C2×C4×C592−1+412yes—
293C2×C4×C59C2511yescharacteristic
294C22⋊D59—84no—
295C22⋊D59—84no—
296C2×Dic59—22no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—22no—
300C2×Dic59—22no—
301C2×Dic59—22no—
302C2×Dic59—42no—
303C2×Dic59—42no—
304C2×Dic59—42no—
305C2×Dic59—42no—
306C2×Dic59—42no—
307C2×Dic59—42no—
308C2×Dic59—84no—
309D236—22no—
310D236—22no—
311D236—22no—
312D236—22no—
313D236—42no—
314D236—42no—
315D236—84no—
316D236—84no—
317C4×D59—84no—
318C4×D59—84no—
319Dic118—84no—
320Dic118—84no—
321C8×C59—22no—
322C8×C59—22no—
323C8×C59—22no—
324C8×C59—22no—
325C2×#3241—591nomaximal, Sylow
326C22×C59—22no—
327C22×C59—22no—
328C22×C59—22no—
329C22×C59—44no—
330C22×C59#53612yes—
331C22×C59#57612yes—
332C22×C59#57712yes—
333C22×C59C23×D411yescharacteristic
334C2×D59—42no—
335C2×D59—42no—
336C2×D59—42no—
337C2×D59—42no—
338C2×D59—42no—
339C2×D59—42no—
340C2×D59—84no—
341C2×D59—84no—
342C4×C59—22no—
343C4×C59—22no—
344C4×C59—22no—
345C4×C59—22no—
346C4×C59—22no—
347C4×C59#53612yes—
348C4×C59C2×2−1+411yescharacteristic
349C4×C59C2×2−1+411yescharacteristic
350Dic59—42no—
351Dic59—42no—
352Dic59—42no—
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×#480—591no—
367C2×#478—591no—
368C2×#478—591no—
369C2×#476—591no—
370C2×#474—591no—
371C2×#433D5911yescharacteristic, complemented
372C2×C59—42no—
373C2×C59#324114yescomplemented
374C2×C59C2×#53611yescharacteristic
375C2×C59C2×#57611yescharacteristic
376C2×C59C2×#57711yescharacteristic
377D59—82no—
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—591no—
397C2×#121—1181no—
398C2×#121—1181no—
399C2×C4×D4—591no—
400C2×C4×D4—591no—
401C2×#117—591no—
402C2×#117C2×D5911yescharacteristic
403C22×C4⋊C4—591no—
404#501—598no—
405#499—598no—
406#490—598no—
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#433C2×D5918yescomplemented
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⋊C8C2×D5911yescharacteristic
426C2×C4⋊C8C2×D5911yescharacteristic
427C2×#102—591no—
428C2×#102—591no—
429C2×#102—591no—
430C2×#102—591no—
431C2×#102—591no—
432C2×#102—591no—
433C2×#102—591no—
434C2×#102—591no—
435C2×C22⋊C8C2×D5911yescharacteristic
436C2×C22⋊C8C2×D5911yescharacteristic
437C2×#97C2×D5911yescharacteristic
438C2×C4×C8C2×D5911yescharacteristic
439C59C2×#324111yescharacteristic, complemented, Sylow
440C22×Q8—1181no—
441C22×Q8—1181no—
442C22×D4—591no—
443C22×D4—591no—
444C22×D4—1181no—
445C22×D4—1181no—
446C22×D4—1181no—
447C22×D4—1181no—
448C23×C4—1181no—
449C23×C4—1181no—
450C23×C4—1181no—
451C23×C4C22×D5911yescharacteristic
452C22×C8C22×D5911yescharacteristic
453C22×C8C22×D5911yescharacteristic
454C22×C8C22×D5911yescharacteristic
455C22×C8C22×D5911yescharacteristic
456C4⋊Q8—594no—
457C4⋊Q8—594no—
458C4⋊Q8—1188no—
459C4⋊Q8—1182no—
460C4⋊Q8—1182no—
461#127—594no—
462#127—1182no—
463#125—594no—
464#125—594no—
465#125—594no—
466#125—1188no—
467#125—1182no—
468#125—1182no—
469#125—1182no—
470#123—1188no—
471#123—1188no—
472C22⋊Q8—1188no—
473C22⋊Q8—1188no—
474#121—594no—
475#121—594no—
476#121—1182no—
477#121—1182no—
478#121—1188no—
479#121—1188no—
480C4×D4—594no—
481C4×D4—594no—
482C4×D4—1182no—
483C4×D4—1182no—
484#117—594no—
485#117—1182no—
486#117D23614yes—
487#117C22×D5914yes—
488C2×C4⋊C4—591no—
489C2×C4⋊C4—591no—
490C2×C4⋊C4—594no—
491C2×C4⋊C4—591no—
492C2×C4⋊C4—591no—
493C2×C4⋊C4—591no—
494C2×C4⋊C4—591no—
495C2×C4⋊C4—1181no—
496C2×C4⋊C4—1182no—
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⋊C4—1181no—
504C2×C4⋊C4—1181no—
505C2×C4⋊C4D23611yescharacteristic
506C2×C4⋊C4D23611yescharacteristic
507C2×C22⋊C4—1181no—
508C2×C22⋊C4—1181no—
509C2×C22⋊C4—1181no—
510C2×C22⋊C4—1181no—
511C2×C22⋊C4—1181no—
512C2×C22⋊C4D23611yescharacteristic
513C2×C22⋊C4D23611yescharacteristic
514C2×C42—1181no—
515C2×C42C22×D5911yescharacteristic
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⋊C8C22×D5914yes—
526C4⋊C8C22×D5914yes—
527#102—594no—
528#102—594no—
529#102—594no—
530#102—594no—
531#102—594no—
532#102—594no—
533#102—594no—
534#102—594no—
535C22⋊C8C22×D5914yes—
536C22⋊C8C22×D5914yes—
537#97C22×D5914yes—
538C4×C8C22×D5914yes—
539C24—1181no—
540C24—1181no—
541C24C2×D23611yescharacteristic
542C2×Q8—1184no—
543C2×Q8—1184no—
544C2×Q8—4722no—
545C2×Q8—4722no—
546C2×D4—592no—
547C2×D4—592no—
548C2×D4—1184no—
549C2×D4—1184no—
550C2×D4—1184no—
551C2×D4—1184no—
552C2×D4—1181no—
553C2×D4—1181no—
554C2×D4—1182no—
555C2×D4—1182no—
556C2×D4—1182no—
557C2×D4—1182no—
558C2×D4—4722no—
559C2×D4—4722no—
560C2×D4—4722no—
561C2×D4—4722no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—1184no—
565C22×C4—1181no—
566C22×C4—1181no—
567C22×C4—1181no—
568C22×C4—1181no—
569C22×C4—1181no—
570C22×C4—1181no—
571C22×C4—1184no—
572C22×C4—1184no—
573C22×C4—4722no—
574C22×C4—4722no—
575C22×C4—4722no—
576C22×C4C2×D23612yes—
577C22×C4C2×D23611yescharacteristic
578C22×C4C2×D23611yescharacteristic
579C22×C4C2×D23611yescharacteristic
580C22×C4C2×D23611yescharacteristic
581C22×C4C2×D23611yescharacteristic
582C22×C4C23×D5912yes—
583C22×C4C23×D5911yescharacteristic
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8C23×D5912yes—
589C2×C8C23×D5912yes—
590C2×C8C23×D5912yes—
591C2×C8C23×D5912yes—
592C4⋊C4—592no—
593C4⋊C4—592no—
594C4⋊C4—592no—
595C4⋊C4—592no—
596C4⋊C4—592no—
597C4⋊C4—592no—
598C4⋊C4—1184no—
599C4⋊C4—1181no—
600C4⋊C4—1181no—
601C4⋊C4—1181no—
602C4⋊C4—1181no—
603C4⋊C4—1181no—
604C4⋊C4—1181no—
605C4⋊C4—1184no—
606C4⋊C4—1184no—
607C4⋊C4—1184no—
608C4⋊C4—1184no—
609C4⋊C4—1184no—
610C4⋊C4—1184no—
611C4⋊C4—1184no—
612C4⋊C4—1184no—
613C4⋊C4C2×D23614yes—
614C4⋊C4C2×D23614yes—
615C22⋊C4—1184no—
616C22⋊C4—1184no—
617C22⋊C4—1184no—
618C22⋊C4—1184no—
619C22⋊C4—1184no—
620C22⋊C4C2×D23614yes—
621C22⋊C4C2×D23614yes—
622C42—1184no—
623C42C2×D23612yes—
624C42C2×D23612yes—
625C42C23×D5912yes—
626C42C23×D5912yes—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—1182no—
631C23—1182no—
632C23—2362no—
633C23—2362no—
634C23—2362no—
635C23—2362no—
636C23—2362no—
637C23—2362no—
638C23C22×D23612yes—
639C23C22×D23611yescharacteristic
640Q8—4724no—
641Q8—4724no—
642D4—1182no—
643D4—1182no—
644D4—1182no—
645D4—1182no—
646D4—4724no—
647D4—4724no—
648D4—4724no—
649D4—4724no—
650D4—2362no—
651D4—2362no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—1182no—
661C2×C4—1182no—
662C2×C4—1182no—
663C2×C4—1182no—
664C2×C4—1182no—
665C2×C4—1182no—
666C2×C4—4724no—
667C2×C4—4724no—
668C2×C4—4724no—
669C2×C4—2362no—
670C2×C4—2362no—
671C2×C4—2362no—
672C2×C4—2362no—
673C2×C4—2362no—
674C2×C4—2362no—
675C2×C4C22×D23612yes—
676C2×C4C22×D23612yes—
677C2×C4C22×D23612yes—
678C2×C4C22×D23612yes—
679C2×C4C22×D23612yes—
680C2×C4C22×D23611yescharacteristic
681C2×C4#1427377412yes—
682C2×C4#1427377412yes—
683C2×C4C24×D5911yescharacteristic
684C8—22no—
685C8—22no—
686C8—22no—
687C8—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—4724no—
693C22—4724no—
694C22—2362no—
695C22—2362no—
696C22—2362no—
697C22—2362no—
698C22—2362no—
699C22—2362no—
700C22#1683797812yes—
701C22#1683820712yes—
702C22#1683821412yes—
703C22C23×D23611yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—2362no—
710C4—2362no—
711C4—2362no—
712C4—2362no—
713C4—2362no—
714C4—2362no—
715C4#1683797812yes—
716C4C2×#1427377411yescharacteristic
717C4C2×#1427377411yescharacteristic
718C2—42no—
719C2—4722no—
720C2—4722no—
721C2#2143535114yesdirect product factor
722C2C2×#1683797811yescharacteristic
723C2C2×#1683820711yescharacteristic
724C2C2×#1683821411yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#433C2
socleC23×C59C22×D4
prime radicalC2×#16838007C2
hypercenterC2×#433D59
hypocenterC59C2×#3241
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#16838030C2semidirect
3. #21435351C2direct (N × H)
4. C2×#16837811C2semidirect
5. C2×#16837804C2semidirect
6. C2×#16837767C2semidirect
7. C2×#16837749C2semidirect
8. C2×#16837721C2semidirect
9. C2×#16837727C2semidirect
10. C2×#16837727C2semidirect
11. C2×#16837716C2semidirect
12. C2×#16837703C2semidirect
13. C2×#16837703C2semidirect
14. C2×#16837693C2semidirect
15. C2×#16837683C2semidirect
16. C2×C59×#433C2semidirect
18. #16838030C22semidirect
41. #16837811C22semidirect
42. #16837804C22semidirect
43. #16837767C22semidirect
44. #16837749C22semidirect
45. #16837727C22semidirect
46. #16837727C22semidirect
47. #16837721C22semidirect
48. #16837716C22semidirect
49. #16837703C22semidirect
50. #16837703C22semidirect
51. #16837693C22semidirect
52. #16837683C22semidirect
70. C59×#433C22semidirect
371. C2×#433D59semidirect
373. C2×C59#3241semidirect
416. #433C2×D59semidirect
439. C59C2×#3241semidirect
721. C2#21435351direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380302
C2×#168380072
#214353512
C2×#168378112
C2×#168378042
C2×#168377672
C2×#168377492
C2×#168377212
C2×#168377272
C2×#168377162
C2×#168377032
C2×#168376932
C2×#168376832
C2×C59×#4332
C2×#324159