Finite Group Databasebeta

← C2×#21435554 #29461651

Subgroups — C2×#21435554 #29461651

Order 15104.

1882 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838021C211yesmaximal, characteristic, complemented
2C2×#16838017C211yesmaximal, characteristic, complemented
3#21435554C2116yesmaximal, direct product factor
4C2×#16837698C211yesmaximal, characteristic, complemented
5C2×#16837695C211yesmaximal, characteristic, complemented
6C2×#16837682C211yesmaximal, characteristic, complemented
7C2×#16837680C211yesmaximal, characteristic, complemented
8C2×#16837647C211yesmaximal, characteristic, complemented
9C2×#16837645C211yesmaximal, characteristic, complemented
10C2×#16837642C211yesmaximal, characteristic, complemented
11C2×#16837635C211yesmaximal, characteristic
12C2×#16837622C211yesmaximal, characteristic, complemented
13C2×#16837621C211yesmaximal, characteristic, complemented
14C2×#16837615C211yesmaximal, characteristic, complemented
15C2×#16837427C211yesmaximal, characteristic, complemented
16C2×C59×#463C211yesmaximal, characteristic, complemented
17C22×#11745672C2211yescharacteristic
18C22×#11745670C2211yescharacteristic
19C22×#11745659C2211yescharacteristic
20C22×C8×D59C2211yescharacteristic
21#16838021—24no—
22#16838021C2218yescomplemented
23#16838017—24no—
24#16838017C2218yescomplemented
25C2×#14273727C2211yescharacteristic
26C2×#14273726C2211yescharacteristic
27C2×#14273720—21no—
28C2×#14273720—21no—
29C2×#14273714C2211yescharacteristic
30C2×#14273713—21no—
31C2×#14273713—21no—
32C2×#14273711—21no—
33C2×#14273710—21no—
34C2×#14273707C2211yescharacteristic
35C2×#14273706—21no—
36C2×#14273704—21no—
37C2×#14273703C2211yescharacteristic
38C2×#14273698C2211yescharacteristic
39C2×#14273698C2211yescharacteristic
40C2×Q8×Dic59C2211yescharacteristic
41C2×C4×Dic118C2211yescharacteristic
42C2×D4×Dic59C2211yescharacteristic
43C2×#14273684C2211yescharacteristic
44#16837698C2218yescomplemented
45#16837695C2218yescomplemented
46#16837682C2218yescomplemented
47#16837680C2218yescomplemented
48#16837647C2218yescomplemented
49#16837645C2218yescomplemented
50#16837642C2218yescomplemented
51#16837635C2218yes—
52#16837622C2218yescomplemented
53#16837621C2218yescomplemented
54#16837615C2218yescomplemented
55C2×#14273661C2211yescharacteristic
56C2×#14273661C2211yescharacteristic
57C2×#14273660C2211yescharacteristic
58C2×#14273660C2211yescharacteristic
59#16837427C2218yescomplemented
60C2×C4⋊(C59⋊C8)C2211yescharacteristic
61C2×Dic59⋊C8C2211yescharacteristic
62C2×Dic59⋊C8C2211yescharacteristic
63C2×#14273652C2211yescharacteristic
64C2×#14273652C2211yescharacteristic
65C2×#14273651C2211yescharacteristic
66C2×#14273648C2211yescharacteristic
67C2×#14273648C2211yescharacteristic
68C2×#14273648C2211yescharacteristic
69C22×SD16×C59C2211yescharacteristic
70C22×D8×C59C2211yescharacteristic
71C2×#124×C59C2211yescharacteristic
72C2×C4×D4×C59C2211yescharacteristic
73C59×#463C2218yescomplemented
74C2×C4⋊C8×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118C2311yescharacteristic
80C22×C22⋊D59—21no—
81C22×C22⋊D59—21no—
82C23×Dic59—21no—
83C22×C4×D59C2311yescharacteristic
84C2×#11745672—42no—
85C2×#11745672C2314yes—
86C2×#11745670—42no—
87C2×#11745670C2314yes—
88C2×#11745659—42no—
89C2×#11745659C2314yes—
90C22×C59⋊C8C2311yescharacteristic
91C22×C59⋊C8C2311yescharacteristic
92C2×C8×D59—42no—
93C2×C8×D59C2314yes—
94#14273727—22no—
95#14273727C2314yes—
96#14273726—22no—
97#14273726C2314yes—
98#14273720—28no—
99#14273720—28no—
100#14273714—22no—
101#14273714C2314yes—
102#14273713—28no—
103#14273713—28no—
104#14273711—28no—
105#14273710—28no—
106#14273707—22no—
107#14273707C2314yes—
108#14273706—28no—
109#14273704—28no—
110#14273703—22no—
111#14273703C2314yes—
112#14273698—22no—
113#14273698—22no—
114#14273698C2314yes—
115#14273698C2314yes—
116Q8×Dic59—22no—
117Q8×Dic59C2314yes—
118C4×Dic118—22no—
119C4×Dic118C2314yes—
120D4×Dic59—22no—
121D4×Dic59C2314yes—
122#14273684D414yes—
123#14273684C2314yes—
124C2×C4⋊Dic59—21no—
125C2×C4⋊Dic59—21no—
126C2×C4⋊Dic59—21no—
127C2×C4⋊Dic59C2311yescharacteristic
128C2×C4⋊Dic59C2311yescharacteristic
129C2×C4⋊Dic59C2311yescharacteristic
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4D411yescharacteristic
134C2×Dic59⋊C4D411yescharacteristic
135C2×C22⋊Dic59—21no—
136C2×C22⋊Dic59—21no—
137C2×C22⋊Dic59—21no—
138C2×C22⋊Dic59—21no—
139C2×C22⋊Dic59—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4D411yescharacteristic
143C2×(C2×D59)⋊C4D411yescharacteristic
144C2×C4×Dic59—21no—
145C2×C4×Dic59—21no—
146C2×C4×Dic59C2311yescharacteristic
147#14273661C2314yes—
148#14273661C2314yes—
149#14273660C2314yes—
150#14273660C2314yes—
151C4⋊(C59⋊C8)C2314yes—
152Dic59⋊C8C2314yes—
153Dic59⋊C8C2314yes—
154#14273652C2314yes—
155#14273652C2314yes—
156#14273651C2314yes—
157#14273648C2314yes—
158#14273648C2314yes—
159#14273648C2314yes—
160C22×Q8×C59C2311yescharacteristic
161C22×D4×C59C2311yescharacteristic
162C22×D4×C59C2311yescharacteristic
163C23×C4×C59—21no—
164C2×SD16×C59—42no—
165C2×SD16×C59C2314yes—
166C2×D8×C59—42no—
167C2×D8×C59C2314yes—
168C22×C8×C59C2311yescharacteristic
169C22×C8×C59C2311yescharacteristic
170#124×C59—22no—
171#124×C59C2314yes—
172C4×D4×C59—22no—
173C4×D4×C59C2314yes—
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C22⋊C4×C59—21no—
176C2×C22⋊C4×C59—21no—
177C2×C22⋊C4×C59—21no—
178C2×C42×C59C2311yescharacteristic
179C4⋊C8×C59C2314yes—
180#103×C59C2314yes—
181#102×C59C2314yes—
182C24×C59—21no—
183C24×C59—21no—
184C23×D59C2×D411yescharacteristic
185C2×Q8×C59—21no—
186C2×Q8×C59—22no—
187C2×Q8×C59—22no—
188C2×Q8×C59C2412yes—
189C2×D4×C59—21no—
190C2×D4×C59—21no—
191C2×D4×C59—22no—
192C2×D4×C59—22no—
193C2×D4×C59—22no—
194C2×D4×C59—22no—
195C2×D4×C59C2412yes—
196C2×D4×C59C2412yes—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—24no—
200C22×C4×C59—82no—
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2×D411yescharacteristic
203C22×C4×C59C2411yescharacteristic
204C2×C22⋊D59—24no—
205C2×C22⋊D59—24no—
206C2×C22⋊D59—82no—
207C2×C22⋊D59—82no—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59—24no—
213C22×Dic59—82no—
214C22×Dic59C2×D411yescharacteristic
215C22×Dic59C2×D411yescharacteristic
216C22×Dic59C2×D411yescharacteristic
217C2×C4×D59—22no—
218C2×C4×D59—22no—
219C2×C4×D59C2×D412yes—
220C2×C4×D59C2412yes—
221C2×Dic118—22no—
222C2×Dic118—22no—
223C2×Dic118—21no—
224C2×Dic118—24no—
225C2×Dic118—24no—
226C2×Dic118—82no—
227C2×Dic118—82no—
228C2×Dic118C2412yes—
229SD16×C59—44no—
230D8×C59—44no—
231C2×C8×C59—22no—
232C2×C8×C59—22no—
233C2×C8×C59C2412yes—
234C2×C8×C59C2412yes—
235C4⋊C4×C59—21no—
236C4⋊C4×C59C2412yes—
237C22⋊C4×C59—24no—
238C22⋊C4×C59—24no—
239C22⋊C4×C59—24no—
240C42×C59C2×D412yes—
241C42×C59C2412yes—
242C22⋊Dic59—24no—
243C22⋊Dic59—24no—
244C22⋊Dic59—24no—
245C22⋊Dic59—24no—
246C22⋊Dic59—24no—
247#11745672—44no—
248#11745670—44no—
249(C2×D59)⋊C4—24no—
250(C2×D59)⋊C4—24no—
251(C2×D59)⋊C4C2×D414yes—
252(C2×D59)⋊C4C2×D414yes—
253C4⋊Dic59—24no—
254C4⋊Dic59—21no—
255C4⋊Dic59—21no—
256C4⋊Dic59—21no—
257C4⋊Dic59—24no—
258C4⋊Dic59—24no—
259C4⋊Dic59C2412yes—
260C4⋊Dic59C2412yes—
261C4⋊Dic59C2412yes—
262Dic59⋊C4—24no—
263Dic59⋊C4—24no—
264Dic59⋊C4—24no—
265Dic59⋊C4C2×D414yes—
266Dic59⋊C4C2×D414yes—
267C4×Dic59—24no—
268C4×Dic59—24no—
269C4×Dic59C2×D412yes—
270C4×Dic59C2412yes—
271C2×C59⋊C8—22no—
272C2×C59⋊C8—22no—
273C2×C59⋊C8C2412yes—
274C2×C59⋊C8C2412yes—
275#11745659—44no—
276C8×D59—44no—
277C23×C59—22no—
278C23×C59—22no—
279C23×C59—42no—
280C23×C59—42no—
281C23×C59—42no—
282C23×C59—42no—
283C23×C59—42no—
284C23×C59—42no—
285C23×C59C22×D411yescharacteristic
286C22×D59—22no—
287C22×D59—22no—
288C22×D59—22no—
289C22×D59C22×D412yes—
290Q8×C59—22no—
291Q8×C59—22no—
292Q8×C59—42no—
293D4×C59—22no—
294D4×C59—22no—
295D4×C59—22no—
296D4×C59—22no—
297D4×C59—42no—
298D4×C59—42no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—42no—
304C2×C4×C59—42no—
305C2×C4×C59—84no—
306C2×C4×C59C22×D412yes—
307C2×C4×C59C22×D412yes—
308C2×C4×C59C22×D411yescharacteristic
309C2×C4×C59H(5,𝔽2)12yes—
310C2×C4×C592−1+412yes—
311C2×C4×C59C2511yescharacteristic
312C22⋊D59—84no—
313C22⋊D59—84no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—42no—
322C2×Dic59—42no—
323C2×Dic59—42no—
324C2×Dic59—42no—
325C2×Dic59—84no—
326C2×Dic59C22×D412yes—
327C2×Dic59C22×D412yes—
328C2×Dic59C22×D412yes—
329C4×D59—24no—
330C4×D59—22no—
331C4×D59—22no—
332Dic118—22no—
333Dic118—22no—
334Dic118—42no—
335Dic118—84no—
336Dic118—84no—
337C8×C59—22no—
338C8×C59—22no—
339C59⋊C8—22no—
340C59⋊C8—22no—
341C2×#3262—591nomaximal, Sylow
342C22×C59—42no—
343C22×C59—42no—
344C22×C59—42no—
345C22×C59—42no—
346C22×C59—42no—
347C22×C59—42no—
348C22×C59—84no—
349C22×C59—84no—
350C22×C59#53712yes—
351C22×C59#57612yes—
352C22×C59#57812yes—
353C22×C59C23×D411yescharacteristic
354C2×D59—22no—
355C2×D59—22no—
356C2×D59—22no—
357C2×D59—44no—
358C4×C59—22no—
359C4×C59—22no—
360C4×C59—42no—
361C4×C59—42no—
362C4×C59#53712yes—
363C4×C59C2×H(5,𝔽2)11yescharacteristic
364C4×C59C2×2−1+411yescharacteristic
365Dic59—22no—
366Dic59—22no—
367Dic59—22no—
368Dic59—42no—
369Dic59—42no—
370Dic59—42no—
371Dic59—42no—
372C2×#542—591no—
373C2×#542—591no—
374#3262—5916no—
375C2×#477—591no—
376C2×#477—591no—
377C2×#474—591no—
378C2×#474—591no—
379C2×#468—591no—
380C2×#468—591no—
381C2×#467—591no—
382C2×#466—591no—
383C2×#464—591no—
384C2×#464—591no—
385C2×#463—591no—
386C2×#463D5911yescharacteristic, complemented
387C2×#424—591no—
388C2×C59—82no—
389C2×C59—82no—
390C2×C59#326214yescomplemented
391C2×C59C2×#53711yescharacteristic
392C2×C59C2×#57611yescharacteristic
393C2×C59C2×#57811yescharacteristic
394D59—42no—
395C22×Q16—591no—
396C22×SD16—591no—
397C22×SD16C2×D5911yescharacteristic
398C22×D8C2×D5911yescharacteristic
399C22×M16—591no—
400C23×C8—591no—
401#542—598no—
402#542—598no—
403#542—1184no—
404#542—1184no—
405C2×C4⋊Q8—591no—
406C2×C4⋊Q8—591no—
407C2×#126—1181no—
408C2×#126—1181no—
409C2×#124—591no—
410C2×#124—1181no—
411C2×#124—1181no—
412C2×#124C2×D5911yescharacteristic
413C2×#123—1181no—
414C2×#123—1181no—
415C2×C22⋊Q8—591no—
416C2×C22⋊Q8—591no—
417C2×C22⋊Q8—1181no—
418C2×C22⋊Q8—1181no—
419C2×#121—591no—
420C2×#121—591no—
421C2×C4×Q8—591no—
422C2×C4×Q8—591no—
423C2×C4×D4—591no—
424C2×C4×D4C2×D5911yescharacteristic
425C2×#117—591no—
426#477—598no—
427#477—598no—
428#474—598no—
429#474—598no—
430#468—598no—
431#468—598no—
432#467—598no—
433#466—598no—
434#464—598no—
435#464—598no—
436#463—598no—
437#463C2×D5918yescomplemented
438C2×#107—591no—
439C2×#107—591no—
440C2×#107—591no—
441C2×#107—591no—
442#424—598no—
443C2×C4⋊C8—591no—
444C2×C4⋊C8—591no—
445C2×C4⋊C8—591no—
446C2×C4⋊C8C2×D5911yescharacteristic
447C2×#103—591no—
448C2×#103—591no—
449C2×#103—591no—
450C2×#103C2×D5911yescharacteristic
451C2×#102—591no—
452C2×#102—591no—
453C2×#102—591no—
454C2×#102C2×D5911yescharacteristic
455C59C2×#326211yescharacteristic, complemented, Sylow
456C22×Q8—591no—
457C22×Q8—1181no—
458C22×Q8—1181no—
459C22×Q8C22×D5911yescharacteristic
460C22×D4—1181no—
461C22×D4—1181no—
462C22×D4C22×D5911yescharacteristic
463C22×D4C22×D5911yescharacteristic
464C23×C4—21no—
465C23×C4—591no—
466C23×C4—1181no—
467C2×Q16—594no—
468C2×Q16—2362no—
469C2×SD16—42no—
470C2×SD16—594no—
471C2×SD16—2362no—
472C2×SD16C22×D5914yes—
473C2×D8—42no—
474C2×D8C22×D5914yes—
475C2×M16—594no—
476C2×M16—2362no—
477C22×C8—591no—
478C22×C8—591no—
479C22×C8—594no—
480C22×C8—2362no—
481C22×C8C22×D5911yescharacteristic
482C22×C8C22×D5911yescharacteristic
483C4⋊Q8—594no—
484C4⋊Q8—594no—
485C4⋊Q8—1182no—
486C4⋊Q8—1182no—
487#126—1188no—
488#126—1188no—
489#124—22no—
490#124—594no—
491#124—1182no—
492#124—1188no—
493#124—1188no—
494#124C22×D5914yes—
495#123—1188no—
496#123—1188no—
497C22⋊Q8—594no—
498C22⋊Q8—594no—
499C22⋊Q8—1188no—
500C22⋊Q8—1182no—
501C22⋊Q8—1188no—
502C22⋊Q8—1182no—
503#121—594no—
504#121—594no—
505#121—1182no—
506#121—1182no—
507C4×Q8—594no—
508C4×Q8—594no—
509C4×Q8—1182no—
510C4×Q8—1182no—
511C4×D4—22no—
512C4×D4—594no—
513C4×D4—1182no—
514C4×D4C22×D5914yes—
515#117—594no—
516#117—594no—
517C2×C4⋊C4—591no—
518C2×C4⋊C4—591no—
519C2×C4⋊C4—591no—
520C2×C4⋊C4—591no—
521C2×C4⋊C4—591no—
522C2×C4⋊C4—1181no—
523C2×C4⋊C4—1181no—
524C2×C4⋊C4—1181no—
525C2×C4⋊C4—1181no—
526C2×C4⋊C4—1181no—
527C2×C4⋊C4—1181no—
528C2×C4⋊C4C22×D5911yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—591no—
533C2×C22⋊C4—591no—
534C2×C22⋊C4—1181no—
535C2×C22⋊C4—1181no—
536C2×C22⋊C4—1181no—
537C2×C22⋊C4—1181no—
538C2×C22⋊C4—1181no—
539C2×C22⋊C4—1181no—
540C2×C22⋊C4—1181no—
541C2×C42—591no—
542C2×C42—1181no—
543C2×C42—1181no—
544C2×C42C22×D5911yescharacteristic
545#107—594no—
546#107—594no—
547#107—594no—
548#107—594no—
549C4⋊C8—594no—
550C4⋊C8—594no—
551C4⋊C8—594no—
552C4⋊C8C22×D5914yes—
553#103—594no—
554#103—594no—
555#103—594no—
556#103C22×D5914yes—
557#102—594no—
558#102—594no—
559#102—594no—
560#102C22×D5914yes—
561C24—21no—
562C24—21no—
563C24—591no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—592no—
568C2×Q8—1184no—
569C2×Q8—1184no—
570C2×Q8—1181no—
571C2×Q8—1182no—
572C2×Q8—1182no—
573C2×Q8—4722no—
574C2×Q8—4722no—
575C2×Q8C23×D5912yes—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—1184no—
583C2×D4—1184no—
584C2×D4—4722no—
585C2×D4—4722no—
586C2×D4C23×D5912yes—
587C2×D4C23×D5912yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—82no—
592C22×C4—591no—
593C22×C4—591no—
594C22×C4—591no—
595C22×C4—592no—
596C22×C4—592no—
597C22×C4—1184no—
598C22×C4—1182no—
599C22×C4—1182no—
600C22×C4—1181no—
601C22×C4—1181no—
602C22×C4—1181no—
603C22×C4—1181no—
604C22×C4—4722no—
605C22×C4D4×D5911yescharacteristic
606C22×C4D4×D5911yescharacteristic
607C22×C4C23×D5911yescharacteristic
608Q16—2364no—
609SD16—44no—
610SD16—2364no—
611D8—44no—
612M16—2364no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—592no—
616C2×C8—592no—
617C2×C8—1182no—
618C2×C8—1182no—
619C2×C8—2364no—
620C2×C8C23×D5912yes—
621C2×C8C23×D5912yes—
622C4⋊C4—21no—
623C4⋊C4—594no—
624C4⋊C4—594no—
625C4⋊C4—592no—
626C4⋊C4—592no—
627C4⋊C4—592no—
628C4⋊C4—1184no—
629C4⋊C4—1184no—
630C4⋊C4—1184no—
631C4⋊C4—1184no—
632C4⋊C4—1181no—
633C4⋊C4—1181no—
634C4⋊C4—1181no—
635C4⋊C4—1184no—
636C4⋊C4—1184no—
637C4⋊C4C23×D5912yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—594no—
642C22⋊C4—594no—
643C22⋊C4—1184no—
644C22⋊C4—1184no—
645C22⋊C4—1184no—
646C22⋊C4—1184no—
647C22⋊C4—1184no—
648C22⋊C4—1184no—
649C22⋊C4—1184no—
650C42—592no—
651C42—592no—
652C42—1184no—
653C42—1184no—
654C42D4×D5912yes—
655C42C23×D5912yes—
656C23—22no—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—592no—
665C23—1182no—
666C23—1182no—
667C23—1182no—
668C23C2×D4×D5911yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—1182no—
673Q8—1182no—
674Q8—4724no—
675Q8—4724no—
676Q8—2362no—
677D4—22no—
678D4—22no—
679D4—22no—
680D4—22no—
681D4—42no—
682D4—42no—
683D4—4724no—
684D4—4724no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—84no—
692C2×C4—592no—
693C2×C4—592no—
694C2×C4—592no—
695C2×C4—1182no—
696C2×C4—1182no—
697C2×C4—1182no—
698C2×C4—1182no—
699C2×C4—1182no—
700C2×C4—1184no—
701C2×C4—1182no—
702C2×C4—1182no—
703C2×C4—1182no—
704C2×C4—1182no—
705C2×C4—4724no—
706C2×C4—2362no—
707C2×C4—2362no—
708C2×C4—2362no—
709C2×C4—2362no—
710C2×C4C2×D4×D5912yes—
711C2×C4C2×D4×D5912yes—
712C2×C4C2×D4×D5911yescharacteristic
713C2×C4#1427377212yes—
714C2×C4#1427377412yes—
715C2×C4C24×D5911yescharacteristic
716C8—22no—
717C8—22no—
718C8—1182no—
719C8—1182no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—84no—
727C22—84no—
728C22—1182no—
729C22—1182no—
730C22—1182no—
731C22—2364no—
732C22#1683798112yes—
733C22#1683820612yes—
734C22#1683821612yes—
735C22C22×D4×D5911yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—1182no—
741C4—1182no—
742C4—1182no—
743C4—2362no—
744C4—2362no—
745C4—2362no—
746C4—2362no—
747C4#1683798112yes—
748C4C2×#1427377211yescharacteristic
749C4C2×#1427377411yescharacteristic
750C2—82no—
751C2—82no—
752C2—2362no—
753C2#2143555414yesdirect product factor
754C2C2×#1683798111yescharacteristic
755C2C2×#1683820611yescharacteristic
756C2C2×#1683821611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#463C2
socleC23×C59C22×D4
prime radicalC2×#16837635C2
hypercenterC2×#463D59
hypocenterC59C2×#3262
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#16838021C2semidirect
2. C2×#16838017C2semidirect
3. #21435554C2direct (N × H)
4. C2×#16837698C2semidirect
5. C2×#16837695C2semidirect
6. C2×#16837682C2semidirect
7. C2×#16837680C2semidirect
8. C2×#16837647C2semidirect
9. C2×#16837645C2semidirect
10. C2×#16837642C2semidirect
12. C2×#16837622C2semidirect
13. C2×#16837621C2semidirect
14. C2×#16837615C2semidirect
15. C2×#16837427C2semidirect
16. C2×C59×#463C2semidirect
22. #16838021C22semidirect
24. #16838017C22semidirect
44. #16837698C22semidirect
45. #16837695C22semidirect
46. #16837682C22semidirect
47. #16837680C22semidirect
48. #16837647C22semidirect
49. #16837645C22semidirect
50. #16837642C22semidirect
52. #16837622C22semidirect
53. #16837621C22semidirect
54. #16837615C22semidirect
59. #16837427C22semidirect
73. C59×#463C22semidirect
386. C2×#463D59semidirect
390. C2×C59#3262semidirect
437. #463C2×D59semidirect
455. C59C2×#3262semidirect
753. C2#21435554direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380212
C2×#168380172
#214355542
C2×#168376982
C2×#168376952
C2×#168376822
C2×#168376802
C2×#168376472
C2×#168376452
C2×#168376422
C2×#168376352
C2×#168376222
C2×#168376212
C2×#168376152
C2×#168374272
C2×C59×#4632
C2×#326259