Finite Group Databasebeta

← C2×#21436158 #29465419

Subgroups — C2×#21436158 #29465419

Order 15104.

2114 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×#16838120C211yesmaximal, characteristic, complemented
2C2×#16838059C211yesmaximal, characteristic
3#21436158C2116yesmaximal, direct product factor
4C2×#16837760C211yesmaximal, characteristic, complemented
5C2×#16837743C211yesmaximal, characteristic, complemented
6C2×#16837724C211yesmaximal, characteristic, complemented
7C2×#16837695C211yesmaximal, characteristic, complemented
8C2×#16837647C211yesmaximal, characteristic, complemented
9C2×#16837643C211yesmaximal, characteristic, complemented
10C2×#16837623C211yesmaximal, characteristic, complemented
11C2×#16837564C211yesmaximal, characteristic, complemented
12C2×#16837559C211yesmaximal, characteristic, complemented
13C2×#16837506C211yesmaximal, characteristic, complemented
14C2×#16837473C211yesmaximal, characteristic, complemented
15C2×#16837409C211yesmaximal, characteristic, complemented
16C2×C59×#416C211yesmaximal, characteristic, complemented
17C22×Q8×D59C2211yescharacteristic
18C22×Dic236C2211yescharacteristic
19C22×#11745672C2211yescharacteristic
20C22×#11745670C2211yescharacteristic
21C22×#11745659C2211yescharacteristic
22#16838120—24no—
23#16838120C2218yescomplemented
24#16838059—24no—
25#16838059C2218yes—
26C2×#14273726C2211yescharacteristic
27C2×#14273721—21no—
28C2×#14273720—21no—
29C2×#14273714—21no—
30C2×#14273714C2211yescharacteristic
31C2×#14273713—21no—
32C2×#14273707C2211yescharacteristic
33C2×#14273706—21no—
34C2×#14273706C2211yescharacteristic
35C2×#14273706C2211yescharacteristic
36C2×#14273698—21no—
37C2×#14273698C2211yescharacteristic
38C2×Q8×Dic59C2211yescharacteristic
39C2×C4×Dic118—21no—
40C2×#14273692C2211yescharacteristic
41C2×C4×C22⋊D59—21no—
42C2×C4×C22⋊D59C2211yescharacteristic
43C2×#14273685C2211yescharacteristic
44#16837760C2218yescomplemented
45#16837743C2218yescomplemented
46#16837724C2218yescomplemented
47#16837695C2218yescomplemented
48#16837647C2218yescomplemented
49#16837643C2218yescomplemented
50#16837623C2218yescomplemented
51#16837564C2218yescomplemented
52#16837559C2218yescomplemented
53#16837506C2218yescomplemented
54#16837473C2218yescomplemented
55C2×#14273661C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59#16837409C2218yescomplemented
60C2×#14273652C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273650C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
69C22×#41×C59C2211yescharacteristic
70C23×C8×C59C2211yescharacteristic
71C2×#117×C59C2211yescharacteristic
72C59×#416C2218yescomplemented
73C2×#103×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118C2311yescharacteristic
80C22×Dic118C2311yescharacteristic
81C2×Q8×D59—22no—
82C2×Q8×D59—24no—
83C2×Q8×D59—42no—
84C2×Q8×D59C2314yes—
85C22×C22⋊D59—21no—
86C22×C22⋊D59D411yescharacteristic
87C22×C4×D59—21no—
88C22×C4×D59C2311yescharacteristic
89C2×Dic236—42no—
90C2×Dic236C2314yes—
91C2×#11745672—24no—
92C2×#11745672C2314yes—
93C2×#11745670—42no—
94C2×#11745670C2314yes—
95C2×#11745659—42no—
96C2×#11745659C2314yes—
97C22×C59⋊C8C2311yescharacteristic
98C22×C59⋊C8C2311yescharacteristic
99#14273726—22no—
100#14273726C2314yes—
101#14273721—28no—
102#14273720—28no—
103#14273714—28no—
104#14273714—22no—
105#14273714C2314yes—
106#14273713—28no—
107#14273707—22no—
108#14273707C2314yes—
109#14273706—22no—
110#14273706—22no—
111#14273706—28no—
112#14273706C2314yes—
113#14273706C2314yes—
114#14273698—28no—
115#14273698—22no—
116#14273698C2314yes—
117Q8×Dic59—22no—
118Q8×Dic59C2314yes—
119C4×Dic118—28no—
120#14273692—22no—
121#14273692C2314yes—
122C4×C22⋊D59—28no—
123C4×C22⋊D59D414yes—
124C4×C22⋊D59C2314yes—
125#14273685—22no—
126#14273685C2314yes—
127C2×C4⋊Dic59—21no—
128C2×C4⋊Dic59—21no—
129C2×C4⋊Dic59C2311yescharacteristic
130C2×C4⋊Dic59C2311yescharacteristic
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4D411yescharacteristic
136C2×C22⋊Dic59—21no—
137C2×C22⋊Dic59—21no—
138C2×C22⋊Dic59—21no—
139C2×C22⋊Dic59—21no—
140C2×C22⋊Dic59—21no—
141C2×C22⋊Dic59D411yescharacteristic
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4—21no—
144C2×(C2×D59)⋊C4D411yescharacteristic
145C2×C4×Dic59—21no—
146C2×C4×Dic59—21no—
147C2×C4×Dic59—21no—
148C2×C4×Dic59C2311yescharacteristic
149#14273661C2314yes—
150#14273660C2314yes—
151#14273658C2314yes—
152Dic59⋊C8C2314yes—
153#14273652C2314yes—
154#14273652C2314yes—
155#14273651C2314yes—
156#14273650C2314yes—
157#14273650C2314yes—
158#14273648C2314yes—
159C22⋊(C59⋊C8)C2314yes—
160(C2×D59)⋊C8C2314yes—
161#14273637C2314yes—
162C2×#41×C59—22no—
163C2×#41×C59—24no—
164C2×#41×C59—42no—
165C2×#41×C59C2314yes—
166C22×Q8×C59C2311yescharacteristic
167C22×D4×C59—21no—
168C22×D4×C59C2311yescharacteristic
169C23×C4×C59—21no—
170C23×C4×C59C2311yescharacteristic
171C22×C8×C59—42no—
172C22×C8×C59C2311yescharacteristic
173C22×C8×C59C2311yescharacteristic
174C22×C8×C59C2314yes—
175#117×C59—22no—
176#117×C59C2314yes—
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C4⋊C4×C59C2311yescharacteristic
179C2×C22⋊C4×C59—21no—
180C2×C42×C59—21no—
181#103×C59C2314yes—
182#103×C59C2314yes—
183#102×C59C2314yes—
184#102×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—22no—
193C2×Q8×C59#4114yes—
194C2×Q8×C59C2412yes—
195C2×D4×C59—24no—
196C2×D4×C59—21no—
197C2×D4×C59—22no—
198C2×D4×C59—22no—
199C2×D4×C59—44no—
200C2×D4×C59C2412yes—
201C22×C4×C59—21no—
202C22×C4×C59—22no—
203C22×C4×C59—22no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—24no—
207C22×C4×C59—44no—
208C22×C4×C59C2×D411yescharacteristic
209C22×C4×C59C2×D412yes—
210C22×C4×C59C2412yes—
211C22×C4×C59C2411yescharacteristic
212C2×C22⋊D59—24no—
213C2×C22⋊D59—42no—
214C2×C22⋊D59—44no—
215C2×C22⋊D59C2×D414yes—
216C22×Dic59—21no—
217C22×Dic59—21no—
218C22×Dic59—21no—
219C22×Dic59—21no—
220C22×Dic59C2×D411yescharacteristic
221C22×Dic59C2×D411yescharacteristic
222C22×Dic59C2×D411yescharacteristic
223Q8×D59—28no—
224Q8×D59—44no—
225Q8×D59—48no—
226C2×C4×D59—22no—
227C2×C4×D59—22no—
228C2×C4×D59—24no—
229C2×C4×D59—44no—
230C2×C4×D59C2×D412yes—
231C2×C4×D59C2412yes—
232C2×Dic118—22no—
233C2×Dic118—22no—
234C2×Dic118—22no—
235C2×Dic118—22no—
236C2×Dic118—21no—
237C2×Dic118—21no—
238C2×Dic118—24no—
239C2×Dic118—24no—
240C2×Dic118—44no—
241C2×Dic118—44no—
242C2×Dic118C2412yes—
243C2×Dic118C2412yes—
244C2×C8×C59—22no—
245C2×C8×C59—22no—
246C2×C8×C59—44no—
247C2×C8×C59C2412yes—
248C2×C8×C59C2412yes—
249C4⋊C4×C59—21no—
250C4⋊C4×C59—21no—
251C4⋊C4×C59C2412yes—
252C4⋊C4×C59C2412yes—
253C22⋊C4×C59—24no—
254C42×C59—24no—
255C22⋊Dic59—24no—
256C22⋊Dic59—24no—
257C22⋊Dic59—24no—
258C22⋊Dic59—24no—
259C22⋊Dic59—24no—
260C22⋊Dic59C2×D414yes—
261#11745672—28no—
262#11745670—44no—
263(C2×D59)⋊C4—24no—
264(C2×D59)⋊C4—24no—
265(C2×D59)⋊C4C2×D414yes—
266C4⋊Dic59—21no—
267C4⋊Dic59—21no—
268C4⋊Dic59—24no—
269C4⋊Dic59—24no—
270C4⋊Dic59C2412yes—
271C4⋊Dic59C2412yes—
272Dic59⋊C4—24no—
273Dic59⋊C4—24no—
274Dic59⋊C4—24no—
275Dic59⋊C4—24no—
276Dic59⋊C4C2×D414yes—
277C4×Dic59—24no—
278C4×Dic59—24no—
279C4×Dic59—24no—
280C4×Dic59C2×D412yes—
281C4×Dic59C2412yes—
282C2×C59⋊C8—22no—
283C2×C59⋊C8—22no—
284C2×C59⋊C8C2412yes—
285C2×C59⋊C8C2412yes—
286Dic236—44no—
287#11745659—44no—
288C23×C59—22no—
289C23×C59—22no—
290C23×C59—22no—
291C23×C59—22no—
292C23×C59—42no—
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—24no—
302Q8×C59—22no—
303Q8×C59C2×#4114yes—
304D4×C59—22no—
305D4×C59—22no—
306D4×C59—48no—
307D4×C59—42no—
308C2×C4×C59—24no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—24no—
312C2×C4×C59—22no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—48no—
317C2×C4×C59—42no—
318C2×C4×C59—42no—
319C2×C4×C59C22×D412yes—
320C2×C4×C59C22×D411yescharacteristic
321C2×C4×C59C2×#4112yes—
322C2×C4×C59H(5,𝔽2)12yes—
323C2×C4×C59C2511yescharacteristic
324C22⋊D59—44no—
325C22⋊D59—48no—
326C2×Dic59—22no—
327C2×Dic59—22no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—22no—
333C2×Dic59—42no—
334C2×Dic59—42no—
335C2×Dic59—42no—
336C2×Dic59—42no—
337C2×Dic59C22×D412yes—
338C2×Dic59C22×D412yes—
339C2×Dic59C22×D412yes—
340C4×D59—24no—
341C4×D59—22no—
342C4×D59—22no—
343C4×D59—48no—
344Dic118—22no—
345Dic118—22no—
346Dic118—22no—
347Dic118—22no—
348Dic118—48no—
349Dic118—48no—
350Dic118—42no—
351Dic118—42no—
352C8×C59—22no—
353C8×C59—22no—
354C59⋊C8—22no—
355C59⋊C8—22no—
356C2×#3313—591nomaximal, Sylow
357C22×C59—22no—
358C22×C59—22no—
359C22×C59—22no—
360C22×C59—44no—
361C22×C59—42no—
362C22×C59—42no—
363C22×C59—42no—
364C22×C59—84no—
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—24no—
374C4×C59—22no—
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×#556—591no—
388C2×#548—591no—
389#3313—5916no—
390C2×#489—591no—
391C2×#485—591no—
392C2×#482—591no—
393C2×#477—591no—
394C2×#468—591no—
395C2×#467—591no—
396C2×#464—591no—
397C2×#452—591no—
398C2×#451—591no—
399C2×#441—591no—
400C2×#435—591no—
401C2×#419—591no—
402C2×#416D5911yescharacteristic, complemented
403C2×C59—42no—
404C2×C59—82no—
405C2×C59#331314yescomplemented
406C2×C59C2×#54611yescharacteristic
407C2×C59C2×#57511yescharacteristic
408C2×C59C2×#57811yescharacteristic
409D59—42no—
410C22×#41C2×D5911yescharacteristic
411C23×Q8—591no—
412C22×Q16—591no—
413C22×Q16—591no—
414C22×SD16—591no—
415C22×M16—591no—
416C23×C8C2×D5911yescharacteristic
417#556—598no—
418#556—1184no—
419#548—598no—
420#548—1184no—
421C2×C4⋊Q8—591no—
422C2×#126—1181no—
423C2×#126—1181no—
424C2×#124—591no—
425C2×#124—1181no—
426C2×#124—1181no—
427C2×C22⋊Q8—591no—
428C2×C22⋊Q8—591no—
429C2×C22⋊Q8—591no—
430C2×C22⋊Q8—1181no—
431C2×#121—591no—
432C2×#121—1181no—
433C2×C4×Q8—591no—
434C2×C4×Q8—591no—
435C2×C4×Q8—1181no—
436C2×C4×D4—591no—
437C2×C4×D4—1181no—
438C2×#117—591no—
439C2×#117C2×D5911yescharacteristic
440#489—598no—
441#485—598no—
442#482—598no—
443#477—598no—
444#468—598no—
445#467—598no—
446#464—598no—
447#452—598no—
448#451—598no—
449#441—598no—
450#435—598no—
451C2×#107—591no—
452C2×#107—591no—
453C2×#106—591no—
454C2×C4⋊C8—591no—
455#419—598no—
456#416C2×D5918yescomplemented
457C2×#103—591no—
458C2×#103—591no—
459C2×#103—591no—
460C2×#103—591no—
461C2×#103—591no—
462C2×#103C2×D5911yescharacteristic
463C2×#103C2×D5911yescharacteristic
464C2×#102—591no—
465C2×#102C2×D5911yescharacteristic
466C2×#102C2×D5911yescharacteristic
467C2×C22⋊C8—591no—
468C2×C22⋊C8—591no—
469C2×#97—591no—
470C59C2×#331311yescharacteristic, complemented, Sylow
471C2×#41—22no—
472C2×#41—24no—
473C2×#41—42no—
474C2×#41C22×D5914yes—
475C22×Q8—594no—
476C22×Q8—591no—
477C22×Q8—591no—
478C22×Q8—1181no—
479C22×Q8—1181no—
480C22×Q8—1182no—
481C22×Q8—1184no—
482C22×Q8—2362no—
483C22×Q8C22×D5911yescharacteristic
484C22×D4—21no—
485C22×D4—591no—
486C22×D4—1181no—
487C22×D4C22×D5911yescharacteristic
488C23×C4—21no—
489C23×C4—591no—
490C23×C4—1181no—
491C23×C4C22×D5911yescharacteristic
492C2×Q16—594no—
493C2×Q16—594no—
494C2×Q16—1184no—
495C2×Q16—2362no—
496C2×SD16—594no—
497C2×SD16—2362no—
498C2×M16—594no—
499C2×M16—2362no—
500C22×C8—42no—
501C22×C8—591no—
502C22×C8—591no—
503C22×C8C22×D5911yescharacteristic
504C22×C8C22×D5911yescharacteristic
505C22×C8C22×D5914yes—
506C4⋊Q8—594no—
507C4⋊Q8—1182no—
508#126—1188no—
509#126—1188no—
510#124—594no—
511#124—1182no—
512#124—1188no—
513#124—1188no—
514C22⋊Q8—594no—
515C22⋊Q8—594no—
516C22⋊Q8—594no—
517C22⋊Q8—1182no—
518C22⋊Q8—1188no—
519C22⋊Q8—1182no—
520C22⋊Q8—1182no—
521#121—594no—
522#121—1182no—
523#121—1188no—
524C4×Q8—594no—
525C4×Q8—594no—
526C4×Q8—1188no—
527C4×Q8—1182no—
528C4×Q8—1182no—
529C4×D4—594no—
530C4×D4—594no—
531C4×D4—1188no—
532#117—22no—
533#117—594no—
534#117—1182no—
535#117C22×D5914yes—
536C2×C4⋊C4—591no—
537C2×C4⋊C4—591no—
538C2×C4⋊C4—591no—
539C2×C4⋊C4—1181no—
540C2×C4⋊C4—1181no—
541C2×C4⋊C4—1181no—
542C2×C4⋊C4—1181no—
543C2×C4⋊C4—1181no—
544C2×C4⋊C4—1181no—
545C2×C4⋊C4C22×D5911yescharacteristic
546C2×C4⋊C4C22×D5911yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—591no—
549C2×C22⋊C4—591no—
550C2×C22⋊C4—1181no—
551C2×C22⋊C4—1181no—
552C2×C22⋊C4—1181no—
553C2×C22⋊C4—1181no—
554C2×C22⋊C4—1181no—
555C2×C22⋊C4—1181no—
556C2×C22⋊C4—1181no—
557C2×C42—21no—
558C2×C42—591no—
559C2×C42—1181no—
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#103C22×D5914yes—
572#103C22×D5914yes—
573#102—594no—
574#102C22×D5914yes—
575#102C22×D5914yes—
576C22⋊C8—594no—
577C22⋊C8—594no—
578#97—594no—
579C24—21no—
580C24—591no—
581C24D4×D5911yescharacteristic
582#41—28no—
583#41—44no—
584#41—48no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—592no—
588C2×Q8—592no—
589C2×Q8—1184no—
590C2×Q8—1184no—
591C2×Q8—1181no—
592C2×Q8—1181no—
593C2×Q8—1188no—
594C2×Q8—1182no—
595C2×Q8—1182no—
596C2×Q8—1182no—
597C2×Q8—1182no—
598C2×Q8—2364no—
599C2×Q8—2364no—
600C2×Q8—2364no—
601C2×Q8—2368no—
602C2×Q8#1174568514yes—
603C2×Q8C23×D5912yes—
604C2×D4—24no—
605C2×D4—21no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—44no—
609C2×D4—594no—
610C2×D4—1184no—
611C2×D4—2362no—
612C2×D4—2364no—
613C2×D4C23×D5912yes—
614C22×C4—21no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—44no—
621C22×C4—591no—
622C22×C4—591no—
623C22×C4—591no—
624C22×C4—592no—
625C22×C4—592no—
626C22×C4—1184no—
627C22×C4—1182no—
628C22×C4—1182no—
629C22×C4—1181no—
630C22×C4—1181no—
631C22×C4—1181no—
632C22×C4—1181no—
633C22×C4—2364no—
634C22×C4D4×D5912yes—
635C22×C4D4×D5911yescharacteristic
636C22×C4C23×D5912yes—
637C22×C4C23×D5911yescharacteristic
638Q16—1188no—
639Q16—2364no—
640SD16—2364no—
641M16—2364no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—44no—
645C2×C8—592no—
646C2×C8—592no—
647C2×C8—1182no—
648C2×C8—1182no—
649C2×C8C23×D5912yes—
650C2×C8C23×D5912yes—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—594no—
654C4⋊C4—592no—
655C4⋊C4—592no—
656C4⋊C4—1184no—
657C4⋊C4—1184no—
658C4⋊C4—1184no—
659C4⋊C4—1184no—
660C4⋊C4—1181no—
661C4⋊C4—1181no—
662C4⋊C4—1184no—
663C4⋊C4—1184no—
664C4⋊C4C23×D5912yes—
665C4⋊C4C23×D5912yes—
666C22⋊C4—24no—
667C22⋊C4—594no—
668C22⋊C4—594no—
669C22⋊C4—1184no—
670C22⋊C4—1184no—
671C22⋊C4—1184no—
672C22⋊C4—1184no—
673C22⋊C4—1184no—
674C22⋊C4—1184no—
675C22⋊C4—1184no—
676C42—24no—
677C42—592no—
678C42—592no—
679C42—1184no—
680C42—1184no—
681C42—1184no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—592no—
690C23—1182no—
691C23—1182no—
692C23—1182no—
693C23C2×D4×D5912yes—
694C23C2×D4×D5911yescharacteristic
695Q8—22no—
696Q8—24no—
697Q8—1182no—
698Q8—1182no—
699Q8—1182no—
700Q8—1182no—
701Q8—2368no—
702Q8—2368no—
703Q8—2362no—
704Q8—2362no—
705Q8C2×#1174568514yes—
706D4—22no—
707D4—22no—
708D4—48no—
709D4—42no—
710D4—2364no—
711D4—2368no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—48no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—592no—
724C2×C4—592no—
725C2×C4—592no—
726C2×C4—1182no—
727C2×C4—1182no—
728C2×C4—1182no—
729C2×C4—1182no—
730C2×C4—1182no—
731C2×C4—1184no—
732C2×C4—1182no—
733C2×C4—1182no—
734C2×C4—1182no—
735C2×C4—1182no—
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×#1174568512yes—
744C2×C4#1427377212yes—
745C2×C4C24×D5911yescharacteristic
746C8—22no—
747C8—22no—
748C8—1182no—
749C8—1182no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—84no—
758C22—1182no—
759C22—1182no—
760C22—1182no—
761C22—2364no—
762C22#1683804212yes—
763C22#1683819912yes—
764C22#1683821612yes—
765C22C22×D4×D5911yescharacteristic
766C4—22no—
767C4—24no—
768C4—42no—
769C4—42no—
770C4—1182no—
771C4—1182no—
772C4—1182no—
773C4—2362no—
774C4—2362no—
775C4—2362no—
776C4—2362no—
777C4#1683804212yes—
778C4C22×#1174568511yescharacteristic
779C4C2×#1427377211yescharacteristic
780C2—42no—
781C2—82no—
782C2—2362no—
783C2#2143615814yesdirect product factor
784C2C2×#1683804211yescharacteristic
785C2C2×#1683819911yescharacteristic
786C2C2×#1683821611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#416C2
socleC23×C59C22×D4
prime radicalC2×#16838059C2
hypercenterC2×#416D59
hypocenterC59C2×#3313
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#16838120C2semidirect
3. #21436158C2direct (N × H)
4. C2×#16837760C2semidirect
5. C2×#16837743C2semidirect
6. C2×#16837724C2semidirect
7. C2×#16837695C2semidirect
8. C2×#16837647C2semidirect
9. C2×#16837643C2semidirect
10. C2×#16837623C2semidirect
11. C2×#16837564C2semidirect
12. C2×#16837559C2semidirect
13. C2×#16837506C2semidirect
14. C2×#16837473C2semidirect
15. C2×#16837409C2semidirect
16. C2×C59×#416C2semidirect
23. #16838120C22semidirect
44. #16837760C22semidirect
45. #16837743C22semidirect
46. #16837724C22semidirect
47. #16837695C22semidirect
48. #16837647C22semidirect
49. #16837643C22semidirect
50. #16837623C22semidirect
51. #16837564C22semidirect
52. #16837559C22semidirect
53. #16837506C22semidirect
54. #16837473C22semidirect
59. #16837409C22semidirect
72. C59×#416C22semidirect
402. C2×#416D59semidirect
405. C2×C59#3313semidirect
456. #416C2×D59semidirect
470. C59C2×#3313semidirect
783. C2#21436158direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381202
C2×#168380592
#214361582
C2×#168377602
C2×#168377432
C2×#168377242
C2×#168376952
C2×#168376472
C2×#168376432
C2×#168376232
C2×#168375642
C2×#168375592
C2×#168375062
C2×#168374732
C2×#168374092
C2×C59×#4162
C2×#331359