Finite Group Databasebeta

← C2×#21436196 #29465347

Subgroups — C2×#21436196 #29465347

Order 15104.

2126 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838086C211yesmaximal, characteristic, complemented
2C2×#16838051C211yesmaximal, characteristic
3#21436196C2116yesmaximal, direct product factor
4C2×#16837769C211yesmaximal, characteristic, complemented
5C2×#16837736C211yesmaximal, characteristic, complemented
6C2×#16837744C211yesmaximal, characteristic, complemented
7C2×#16837704C211yesmaximal, characteristic, complemented
8C2×#16837657C211yesmaximal, characteristic, complemented
9C2×#16837641C211yesmaximal, characteristic, complemented
10C2×#16837610C211yesmaximal, characteristic, complemented
11C2×#16837561C211yesmaximal, characteristic, complemented
12C2×#16837503C211yesmaximal, characteristic, complemented
13C2×#16837470C211yesmaximal, characteristic, complemented
14C2×#16837400C211yesmaximal, characteristic, complemented
15C2×#16837398C211yesmaximal, characteristic, complemented
16C2×C59×#452C211yesmaximal, characteristic, complemented
17C22×#11745687C2211yescharacteristic
18C22×#11745672C2211yescharacteristic
19C22×#11745659C2211yescharacteristic
20C23×C59⋊C8C2211yescharacteristic
21#16838086—24no—
22#16838086C2218yescomplemented
23#16838051—24no—
24#16838051C2218yes—
25C2×#14273725C2211yescharacteristic
26C2×#14273720—21no—
27C2×#14273718C2211yescharacteristic
28C2×#14273717—21no—
29C2×#14273710—21no—
30C2×#14273709—21no—
31C2×#14273708—21no—
32C2×#14273706C2211yescharacteristic
33C2×#14273703C2211yescharacteristic
34C2×#14273703C2211yescharacteristic
35C2×#14273699—21no—
36C2×Q8×Dic59C2211yescharacteristic
37C2×D4×Dic59C2211yescharacteristic
38C2×C4×C22⋊D59C2211yescharacteristic
39C2×#14273686C2211yescharacteristic
40C2×#14273685—21no—
41C22×Dic59⋊C4—21no—
42C2×C4⋊C4×D59C2211yescharacteristic
43#16837769C2218yescomplemented
44#16837744C2218yescomplemented
45#16837736C2218yescomplemented
46#16837704C2218yescomplemented
47#16837657C2218yescomplemented
48#16837641C2218yescomplemented
49#16837610C2218yescomplemented
50#16837561C2218yescomplemented
51#16837503C2218yescomplemented
52#16837470C2218yescomplemented
53C2×#14273661C2211yescharacteristic
54C2×#14273660C2211yescharacteristic
55C2×#14273659C2211yescharacteristic
56C2×Dic59⋊C8C2211yescharacteristic
57#16837400C2218yescomplemented
58#16837398C2218yescomplemented
59C2×#14273652C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273651C2211yescharacteristic
64C2×#14273650C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×#14273648C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
69C22×#41×C59C2211yescharacteristic
70C22×Q16×C59C2211yescharacteristic
71C22×SD16×C59C2211yescharacteristic
72C2×C22⋊Q8×C59C2211yescharacteristic
73C59×#452C2218yescomplemented
74C2×#103×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C2×#11745687—24no—
78C2×#11745687—22no—
79C2×#11745687—42no—
80C2×#11745687C2314yes—
81C22×Dic118C2311yescharacteristic
82C22×C22⋊D59—21no—
83C22×C22⋊D59D411yescharacteristic
84C23×Dic59—21no—
85C23×Dic59—21no—
86C22×C4×D59—21no—
87C22×C4×D59C2311yescharacteristic
88C2×#11745672—42no—
89C2×#11745672C2314yes—
90C2×#11745659—42no—
91C2×#11745659C2314yes—
92C22×C59⋊C8—42no—
93C22×C59⋊C8C2311yescharacteristic
94C22×C59⋊C8C2311yescharacteristic
95C22×C59⋊C8C2314yes—
96#14273725—22no—
97#14273725C2314yes—
98#14273720—28no—
99#14273718—22no—
100#14273718C2314yes—
101#14273717—28no—
102#14273710—28no—
103#14273709—28no—
104#14273708—28no—
105#14273706—22no—
106#14273706C2314yes—
107#14273703—22no—
108#14273703—22no—
109#14273703C2314yes—
110#14273703C2314yes—
111#14273699—28no—
112Q8×Dic59—22no—
113Q8×Dic59C2314yes—
114D4×Dic59—22no—
115D4×Dic59C2314yes—
116C4×C22⋊D59D414yes—
117C4×C22⋊D59C2314yes—
118#14273686—22no—
119#14273686C2314yes—
120#14273685—28no—
121C2×C4⋊Dic59—21no—
122C2×C4⋊Dic59—21no—
123C2×C4⋊Dic59C2311yescharacteristic
124C2×C4⋊Dic59C2311yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—28no—
134C2×Dic59⋊C4D411yescharacteristic
135C4⋊C4×D59—22no—
136C4⋊C4×D59C2314yes—
137C2×C22⋊Dic59—21no—
138C2×C22⋊Dic59—21no—
139C2×C22⋊Dic59—21no—
140C2×C22⋊Dic59D411yescharacteristic
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4D411yescharacteristic
144C2×C4×Dic59—21no—
145C2×C4×Dic59—21no—
146C2×C4×Dic59C2311yescharacteristic
147#14273661C2314yes—
148#14273660C2314yes—
149#14273659C2314yes—
150Dic59⋊C8C2314yes—
151#14273652C2314yes—
152#14273652C2314yes—
153#14273651C2314yes—
154#14273651C2314yes—
155#14273651C2314yes—
156#14273650C2314yes—
157#14273648C2314yes—
158#14273648C2314yes—
159(C2×D59)⋊C8C2314yes—
160#14273637C2314yes—
161C2×#41×C59—22no—
162C2×#41×C59—24no—
163C2×#41×C59—42no—
164C2×#41×C59C2314yes—
165C22×Q8×C59C2311yescharacteristic
166C22×Q8×C59C2311yescharacteristic
167C22×D4×C59—21no—
168C22×D4×C59C2311yescharacteristic
169C23×C4×C59—21no—
170C23×C4×C59C2311yescharacteristic
171C2×Q16×C59—42no—
172C2×Q16×C59C2314yes—
173C2×SD16×C59—24no—
174C2×SD16×C59C2314yes—
175C22×C8×C59C2311yescharacteristic
176C22×C8×C59C2311yescharacteristic
177C22⋊Q8×C59—22no—
178C22⋊Q8×C59C2314yes—
179C2×C4⋊C4×C59—21no—
180C2×C4⋊C4×C59C2311yescharacteristic
181C2×C22⋊C4×C59—21no—
182#103×C59C2314yes—
183#102×C59C2314yes—
184C22⋊C8×C59C2314yes—
185C24×C59—21no—
186C24×C59C2×D411yescharacteristic
187C23×D59C2×D411yescharacteristic
188#41×C59—28no—
189#41×C59—44no—
190#41×C59—48no—
191C2×Q8×C59—21no—
192C2×Q8×C59—21no—
193C2×Q8×C59—22no—
194C2×Q8×C59—22no—
195C2×Q8×C59—22no—
196C2×Q8×C59—22no—
197C2×Q8×C59C2412yes—
198C2×Q8×C59C2412yes—
199C2×D4×C59—24no—
200C2×D4×C59—21no—
201C2×D4×C59—22no—
202C2×D4×C59—44no—
203C2×D4×C59#4114yes—
204C2×D4×C59C2412yes—
205C22×C4×C59—22no—
206C22×C4×C59—22no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—24no—
211C22×C4×C59—44no—
212C22×C4×C59C2×D411yescharacteristic
213C22×C4×C59C2×D412yes—
214C22×C4×C59C2412yes—
215C22×C4×C59C2411yescharacteristic
216C2×C22⋊D59—24no—
217C2×C22⋊D59—42no—
218C2×C22⋊D59—44no—
219C2×C22⋊D59C2×D414yes—
220C22×Dic59—21no—
221C22×Dic59—21no—
222C22×Dic59—21no—
223C22×Dic59—21no—
224C22×Dic59—24no—
225C22×Dic59—24no—
226C22×Dic59—44no—
227C22×Dic59—44no—
228C22×Dic59C2×D411yescharacteristic
229C22×Dic59C2×D411yescharacteristic
230C22×Dic59C2×D411yescharacteristic
231#11745687—28no—
232#11745687—44no—
233#11745687—48no—
234C2×C4×D59—22no—
235C2×C4×D59—22no—
236C2×C4×D59—24no—
237C2×C4×D59—44no—
238C2×C4×D59C2×D412yes—
239C2×C4×D59C2412yes—
240C2×Dic118—22no—
241C2×Dic118—22no—
242C2×Dic118—21no—
243C2×Dic118C2412yes—
244Q16×C59—44no—
245SD16×C59—28no—
246C2×C8×C59—22no—
247C2×C8×C59—22no—
248C2×C8×C59C2412yes—
249C2×C8×C59C2412yes—
250C4⋊C4×C59—24no—
251C4⋊C4×C59—21no—
252C4⋊C4×C59C2412yes—
253C22⋊C4×C59—24no—
254C22⋊Dic59—24no—
255C22⋊Dic59—24no—
256C22⋊Dic59—24no—
257C22⋊Dic59C2×D414yes—
258#11745672—44no—
259(C2×D59)⋊C4—24no—
260(C2×D59)⋊C4—24no—
261(C2×D59)⋊C4C2×D414yes—
262C4⋊Dic59—21no—
263C4⋊Dic59—21no—
264C4⋊Dic59—21no—
265C4⋊Dic59—24no—
266C4⋊Dic59—24no—
267C4⋊Dic59C2412yes—
268C4⋊Dic59C2412yes—
269C4⋊Dic59C2412yes—
270Dic59⋊C4—24no—
271Dic59⋊C4—24no—
272Dic59⋊C4—24no—
273Dic59⋊C4—24no—
274Dic59⋊C4—24no—
275Dic59⋊C4—24no—
276Dic59⋊C4—24no—
277Dic59⋊C4C2×D414yes—
278C4×Dic59—24no—
279C4×Dic59—24no—
280C4×Dic59C2×D412yes—
281C4×Dic59C2412yes—
282C2×C59⋊C8—22no—
283C2×C59⋊C8—22no—
284C2×C59⋊C8—44no—
285C2×C59⋊C8C2412yes—
286C2×C59⋊C8C2412yes—
287#11745659—44no—
288C23×C59—24no—
289C23×C59—22no—
290C23×C59—22no—
291C23×C59—22no—
292C23×C59—22no—
293C23×C59—42no—
294C23×C59—42no—
295C23×C59C22×D412yes—
296C23×C59C22×D411yescharacteristic
297C22×D59—22no—
298C22×D59—22no—
299C22×D59—22no—
300C22×D59C22×D412yes—
301Q8×C59—22no—
302Q8×C59—22no—
303Q8×C59—22no—
304Q8×C59—22no—
305Q8×C59—42no—
306Q8×C59—42no—
307D4×C59—24no—
308D4×C59—22no—
309D4×C59—48no—
310D4×C59C2×#4114yes—
311C2×C4×C59—22no—
312C2×C4×C59—24no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—22no—
318C2×C4×C59—48no—
319C2×C4×C59—42no—
320C2×C4×C59—42no—
321C2×C4×C59—42no—
322C2×C4×C59C22×D412yes—
323C2×C4×C59C22×D411yescharacteristic
324C2×C4×C59C2×#4112yes—
325C2×C4×C59H(5,𝔽2)12yes—
326C2×C4×C59C2511yescharacteristic
327C22⋊D59—44no—
328C22⋊D59—48no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—22no—
333C2×Dic59—22no—
334C2×Dic59—22no—
335C2×Dic59—22no—
336C2×Dic59—48no—
337C2×Dic59—48no—
338C2×Dic59—42no—
339C2×Dic59—42no—
340C2×Dic59—42no—
341C2×Dic59—42no—
342C2×Dic59C22×D412yes—
343C2×Dic59C22×D412yes—
344C2×Dic59C22×D412yes—
345C4×D59—24no—
346C4×D59—22no—
347C4×D59—22no—
348C4×D59—48no—
349Dic118—22no—
350Dic118—22no—
351Dic118—42no—
352C8×C59—22no—
353C8×C59—22no—
354C59⋊C8—22no—
355C59⋊C8—22no—
356C2×#3315—591nomaximal, Sylow
357C22×C59—24no—
358C22×C59—22no—
359C22×C59—22no—
360C22×C59—22no—
361C22×C59—44no—
362C22×C59—48no—
363C22×C59—42no—
364C22×C59—42no—
365C22×C59#54612yes—
366C22×C59#57512yes—
367C22×C59#57812yes—
368C22×C59C23×D411yescharacteristic
369C2×D59—22no—
370C2×D59—22no—
371C2×D59—22no—
372C2×D59—44no—
373C4×C59—22no—
374C4×C59—42no—
375C4×C59—42no—
376C4×C59—42no—
377C4×C59#54612yes—
378C4×C59C22×#4111yescharacteristic
379C4×C59C2×H(5,𝔽2)11yescharacteristic
380Dic59—22no—
381Dic59—22no—
382Dic59—22no—
383Dic59—42no—
384Dic59—42no—
385Dic59—42no—
386Dic59—42no—
387C2×#552—591no—
388C2×#547—591no—
389#3315—5916no—
390C2×#491—591no—
391C2×#484—591no—
392C2×#485—591no—
393C2×#478—591no—
394C2×#470—591no—
395C2×#467—591no—
396C2×#462—591no—
397C2×#452—591no—
398C2×#452D5911yescharacteristic, complemented
399C2×#440—591no—
400C2×#435—591no—
401C2×#417—591no—
402C2×#416—591no—
403C2×C59—42no—
404C2×C59—44no—
405C2×C59#331514yescomplemented
406C2×C59C2×#54611yescharacteristic
407C2×C59C2×#57511yescharacteristic
408C2×C59C2×#57811yescharacteristic
409D59—42no—
410C22×#41—591no—
411C22×#41C2×D5911yescharacteristic
412C22×Q16—591no—
413C22×Q16C2×D5911yescharacteristic
414C22×SD16C2×D5911yescharacteristic
415C22×M16—591no—
416C23×C8—591no—
417#552—598no—
418#552—1184no—
419#547—598no—
420#547—1184no—
421C2×C4⋊Q8—591no—
422C2×#126—1181no—
423C2×#125—591no—
424C2×#125—1181no—
425C2×#123—1181no—
426C2×#123—1181no—
427C2×#123—1181no—
428C2×C22⋊Q8—591no—
429C2×C22⋊Q8—591no—
430C2×C22⋊Q8—591no—
431C2×C22⋊Q8C2×D5911yescharacteristic
432C2×#121—1181no—
433C2×C4×Q8—591no—
434C2×C4×D4—591no—
435C2×C4×D4—591no—
436C2×#117—591no—
437C2×#117—1181no—
438C22×C4⋊C4—591no—
439C22×C4⋊C4—1181no—
440#491—598no—
441#485—598no—
442#484—598no—
443#478—598no—
444#470—598no—
445#467—598no—
446#462—598no—
447#452—598no—
448#452C2×D5918yescomplemented
449#440—598no—
450#435—598no—
451C2×#107—591no—
452C2×#107—591no—
453C2×#106—591no—
454C2×C4⋊C8—591no—
455#417—598no—
456#416—598no—
457C2×#103—591no—
458C2×#103—591no—
459C2×#103—591no—
460C2×#103—591no—
461C2×#103—591no—
462C2×#103—591no—
463C2×#103C2×D5911yescharacteristic
464C2×#102—591no—
465C2×#102—591no—
466C2×#102C2×D5911yescharacteristic
467C2×C22⋊C8—591no—
468C2×C22⋊C8C2×D5911yescharacteristic
469C2×#97—591no—
470C59C2×#331511yescharacteristic, complemented, Sylow
471C2×#41—22no—
472C2×#41—24no—
473C2×#41—42no—
474C2×#41—594no—
475C2×#41—1182no—
476C2×#41—1184no—
477C2×#41—2362no—
478C2×#41C22×D5914yes—
479C22×Q8—591no—
480C22×Q8C22×D5911yescharacteristic
481C22×Q8C22×D5911yescharacteristic
482C22×D4—21no—
483C22×D4—591no—
484C22×D4—1181no—
485C22×D4C22×D5911yescharacteristic
486C23×C4—21no—
487C23×C4—591no—
488C23×C4—1181no—
489C23×C4—1181no—
490C23×C4—1181no—
491C23×C4C22×D5911yescharacteristic
492C2×Q16—42no—
493C2×Q16—594no—
494C2×Q16—2362no—
495C2×Q16C22×D5914yes—
496C2×SD16—24no—
497C2×SD16C22×D5914yes—
498C2×M16—594no—
499C2×M16—2362no—
500C22×C8—591no—
501C22×C8—591no—
502C22×C8—594no—
503C22×C8—2362no—
504C22×C8C22×D5911yescharacteristic
505C22×C8C22×D5911yescharacteristic
506C4⋊Q8—594no—
507C4⋊Q8—1182no—
508#126—1188no—
509#125—594no—
510#125—1182no—
511#125—1188no—
512#123—1188no—
513#123—1188no—
514#123—1188no—
515C22⋊Q8—22no—
516C22⋊Q8—594no—
517C22⋊Q8—594no—
518C22⋊Q8—594no—
519C22⋊Q8—1182no—
520C22⋊Q8—1182no—
521C22⋊Q8—1182no—
522C22⋊Q8C22×D5914yes—
523#121—1188no—
524C4×Q8—594no—
525C4×Q8—1182no—
526C4×D4—594no—
527C4×D4—594no—
528C4×D4—594no—
529C4×D4—1182no—
530#117—594no—
531#117—1188no—
532#117—1182no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—591no—
535C2×C4⋊C4—591no—
536C2×C4⋊C4—591no—
537C2×C4⋊C4—591no—
538C2×C4⋊C4—594no—
539C2×C4⋊C4—1182no—
540C2×C4⋊C4—1188no—
541C2×C4⋊C4—1181no—
542C2×C4⋊C4—1181no—
543C2×C4⋊C4—1181no—
544C2×C4⋊C4—1181no—
545C2×C4⋊C4—1181no—
546C2×C4⋊C4—1181no—
547C2×C4⋊C4—1181no—
548C2×C4⋊C4—1181no—
549C2×C4⋊C4—1181no—
550C2×C4⋊C4C22×D5911yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—591no—
553C2×C22⋊C4—591no—
554C2×C22⋊C4—1181no—
555C2×C22⋊C4—1181no—
556C2×C22⋊C4—1181no—
557C2×C22⋊C4—1181no—
558C2×C22⋊C4—1181no—
559C2×C42—591no—
560C2×C42—1181no—
561C2×C42—1181no—
562#107—594no—
563#107—594no—
564#106—594no—
565C4⋊C8—594no—
566#103—594no—
567#103—594no—
568#103—594no—
569#103—594no—
570#103—594no—
571#103—594no—
572#103C22×D5914yes—
573#102—594no—
574#102—594no—
575#102C22×D5914yes—
576C22⋊C8—594no—
577C22⋊C8C22×D5914yes—
578#97—594no—
579C24—21no—
580C24—591no—
581C24D4×D5911yescharacteristic
582#41—28no—
583#41—44no—
584#41—48no—
585#41—1188no—
586#41—2364no—
587#41—2368no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—592no—
595C2×Q8—1181no—
596C2×Q8—1182no—
597C2×Q8—1182no—
598C2×Q8C23×D5912yes—
599C2×Q8C23×D5912yes—
600C2×D4—24no—
601C2×D4—21no—
602C2×D4—22no—
603C2×D4—44no—
604C2×D4—594no—
605C2×D4—1184no—
606C2×D4—2362no—
607C2×D4—2364no—
608C2×D4#1174568714yes—
609C2×D4C23×D5912yes—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—44no—
617C22×C4—591no—
618C22×C4—591no—
619C22×C4—591no—
620C22×C4—592no—
621C22×C4—592no—
622C22×C4—1184no—
623C22×C4—1184no—
624C22×C4—1184no—
625C22×C4—1182no—
626C22×C4—1182no—
627C22×C4—1181no—
628C22×C4—1181no—
629C22×C4—1181no—
630C22×C4—1181no—
631C22×C4—2364no—
632C22×C4—2364no—
633C22×C4—2364no—
634C22×C4D4×D5912yes—
635C22×C4D4×D5911yescharacteristic
636C22×C4C23×D5912yes—
637C22×C4C23×D5911yescharacteristic
638Q16—44no—
639Q16—2364no—
640SD16—28no—
641M16—2364no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—592no—
645C2×C8—592no—
646C2×C8—1182no—
647C2×C8—1182no—
648C2×C8—2364no—
649C2×C8C23×D5912yes—
650C2×C8C23×D5912yes—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—594no—
654C4⋊C4—592no—
655C4⋊C4—592no—
656C4⋊C4—592no—
657C4⋊C4—1184no—
658C4⋊C4—1184no—
659C4⋊C4—1184no—
660C4⋊C4—1184no—
661C4⋊C4—1184no—
662C4⋊C4—1184no—
663C4⋊C4—1184no—
664C4⋊C4—1184no—
665C4⋊C4—1181no—
666C4⋊C4—1181no—
667C4⋊C4—1181no—
668C4⋊C4—1184no—
669C4⋊C4C23×D5912yes—
670C22⋊C4—24no—
671C22⋊C4—594no—
672C22⋊C4—594no—
673C22⋊C4—1184no—
674C22⋊C4—1184no—
675C22⋊C4—1184no—
676C22⋊C4—1184no—
677C22⋊C4—1184no—
678C42—592no—
679C42—592no—
680C42—1184no—
681C42—1184no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—24no—
687C23—42no—
688C23—42no—
689C23—592no—
690C23—1182no—
691C23—1182no—
692C23—1182no—
693C23C2×D4×D5912yes—
694C23C2×D4×D5911yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—42no—
701Q8—1182no—
702Q8—1182no—
703Q8—2362no—
704D4—22no—
705D4—24no—
706D4—48no—
707D4—2364no—
708D4—2368no—
709D4C2×#1174568714yes—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—592no—
722C2×C4—592no—
723C2×C4—592no—
724C2×C4—1182no—
725C2×C4—1182no—
726C2×C4—1182no—
727C2×C4—1182no—
728C2×C4—1182no—
729C2×C4—1184no—
730C2×C4—1182no—
731C2×C4—1182no—
732C2×C4—1182no—
733C2×C4—1182no—
734C2×C4—2368no—
735C2×C4—2368no—
736C2×C4—2368no—
737C2×C4—2362no—
738C2×C4—2362no—
739C2×C4—2362no—
740C2×C4—2362no—
741C2×C4C2×D4×D5912yes—
742C2×C4C2×D4×D5911yescharacteristic
743C2×C4C2×#1174568712yes—
744C2×C4#1427377212yes—
745C2×C4C24×D5911yescharacteristic
746C8—22no—
747C8—22no—
748C8—1182no—
749C8—1182no—
750C22—22no—
751C22—24no—
752C22—22no—
753C22—22no—
754C22—44no—
755C22—48no—
756C22—42no—
757C22—42no—
758C22—1182no—
759C22—1182no—
760C22—1182no—
761C22—2364no—
762C22#1683803912yes—
763C22#1683819912yes—
764C22#1683821812yes—
765C22C22×D4×D5911yescharacteristic
766C4—22no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—1182no—
771C4—1182no—
772C4—1182no—
773C4—2362no—
774C4—2362no—
775C4—2362no—
776C4—2362no—
777C4#1683803912yes—
778C4C22×#1174568711yescharacteristic
779C4C2×#1427377211yescharacteristic
780C2—42no—
781C2—44no—
782C2—2362no—
783C2#2143619614yesdirect product factor
784C2C2×#1683803911yescharacteristic
785C2C2×#1683819911yescharacteristic
786C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#452C2
socleC23×C59C22×D4
prime radicalC2×#16838051C2
hypercenterC2×#452D59
hypocenterC59C2×#3315
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#16838086C2semidirect
3. #21436196C2direct (N × H)
4. C2×#16837769C2semidirect
5. C2×#16837736C2semidirect
6. C2×#16837744C2semidirect
7. C2×#16837704C2semidirect
8. C2×#16837657C2semidirect
9. C2×#16837641C2semidirect
10. C2×#16837610C2semidirect
11. C2×#16837561C2semidirect
12. C2×#16837503C2semidirect
13. C2×#16837470C2semidirect
14. C2×#16837400C2semidirect
15. C2×#16837398C2semidirect
16. C2×C59×#452C2semidirect
22. #16838086C22semidirect
43. #16837769C22semidirect
44. #16837744C22semidirect
45. #16837736C22semidirect
46. #16837704C22semidirect
47. #16837657C22semidirect
48. #16837641C22semidirect
49. #16837610C22semidirect
50. #16837561C22semidirect
51. #16837503C22semidirect
52. #16837470C22semidirect
57. #16837400C22semidirect
58. #16837398C22semidirect
73. C59×#452C22semidirect
398. C2×#452D59semidirect
405. C2×C59#3315semidirect
448. #452C2×D59semidirect
470. C59C2×#3315semidirect
783. C2#21436196direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380862
C2×#168380512
#214361962
C2×#168377692
C2×#168377362
C2×#168377442
C2×#168377042
C2×#168376572
C2×#168376412
C2×#168376102
C2×#168375612
C2×#168375032
C2×#168374702
C2×#168374002
C2×#168373982
C2×C59×#4522
C2×#331559