Finite Group Databasebeta

← C2×#21436164 #29465425

Subgroups — C2×#21436164 #29465425

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×#16838122C211yesmaximal, characteristic, complemented
2C2×#16838061C211yesmaximal, characteristic
3#21436164C2116yesmaximal, direct product factor
4C2×#16837762C211yesmaximal, characteristic, complemented
5C2×#16837744C211yesmaximal, characteristic, complemented
6C2×#16837727C211yesmaximal, characteristic, complemented
7C2×#16837698C211yesmaximal, characteristic, complemented
8C2×#16837648C211yesmaximal, characteristic, complemented
9C2×#16837643C211yesmaximal, characteristic, complemented
10C2×#16837625C211yesmaximal, characteristic, complemented
11C2×#16837566C211yesmaximal, characteristic, complemented
12C2×#16837560C211yesmaximal, characteristic, complemented
13C2×#16837510C211yesmaximal, characteristic, complemented
14C2×#16837412C211yesmaximal, characteristic, complemented
15C2×#16837399C211yesmaximal, characteristic, complemented
16C2×C59×#435C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C23×Dic118C2211yescharacteristic
19C22×Dic236C2211yescharacteristic
20C22×Dic236C2211yescharacteristic
21C22×#11745660C2211yescharacteristic
22#16838122—24no—
23#16838122C2218yescomplemented
24#16838061—24no—
25#16838061C2218yes—
26C2×#14273727C2211yescharacteristic
27C2×#14273720—21no—
28C2×#14273720—21no—
29C2×#14273715C2211yescharacteristic
30C2×#14273714—21no—
31C2×#14273713—21no—
32C2×#14273706C2211yescharacteristic
33C2×#14273706C2211yescharacteristic
34C2×#14273706C2211yescharacteristic
35C2×#14273705—21no—
36C2×#14273701C2211yescharacteristic
37C2×#14273699—21no—
38C2×C4×Dic118C2211yescharacteristic
39C2×C4×Dic118C2211yescharacteristic
40C2×#14273692—21no—
41C2×(C22⋊D59)⋊C4—21no—
42C2×#14273686C2211yescharacteristic
43C2×#14273686C2211yescharacteristic
44#16837762C2218yescomplemented
45#16837744C2218yescomplemented
46#16837727C2218yescomplemented
47#16837698C2218yescomplemented
48#16837648C2218yescomplemented
49#16837643C2218yescomplemented
50#16837625C2218yescomplemented
51#16837566C2218yescomplemented
52#16837560C2218yescomplemented
53#16837510C2218yescomplemented
54C2×#14273661C2211yescharacteristic
55C2×#14273661C2211yescharacteristic
56C2×#14273659C2211yescharacteristic
57#16837412C2218yescomplemented
58#16837399C2218yescomplemented
59C2×#14273652C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273652C2211yescharacteristic
63C2×#14273652C2211yescharacteristic
64C2×#14273652C2211yescharacteristic
65C2×#14273652C2211yescharacteristic
66C2×#14273649C2211yescharacteristic
67C2×#14273649C2211yescharacteristic
68C2×#14273649C2211yescharacteristic
69C22×M16×C59C2211yescharacteristic
70C23×C8×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic
72C59×#435C2218yescomplemented
73C2×C4⋊C8×C59C2211yescharacteristic
74C2×C22⋊C8×C59C2211yescharacteristic
75C2×C22⋊C8×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic
77C2×#11745685—22no—
78C2×#11745685—24no—
79C2×#11745685—42no—
80C2×#11745685C2314yes—
81C22×Dic118—24no—
82C22×Dic118—21no—
83C22×Dic118—21no—
84C22×Dic118—22no—
85C22×Dic118—42no—
86C22×Dic118C2311yescharacteristic
87C22×Dic118C2311yescharacteristic
88C22×Dic118C2314yes—
89C22×Dic118C2311yescharacteristic
90C22×D236C2311yescharacteristic
91C22×C22⋊D59—21no—
92C22×C22⋊D59—21no—
93C23×Dic59—21no—
94C22×C4×D59—21no—
95C2×Dic236—24no—
96C2×Dic236—42no—
97C2×Dic236C2314yes—
98C2×Dic236C2314yes—
99C2×#11745660—42no—
100C2×#11745660C2314yes—
101#14273727—22no—
102#14273727C2314yes—
103#14273720—28no—
104#14273720—28no—
105#14273715—22no—
106#14273715C2314yes—
107#14273714—28no—
108#14273713—28no—
109#14273706—22no—
110#14273706—22no—
111#14273706—22no—
112#14273706C2314yes—
113#14273706C2314yes—
114#14273706C2314yes—
115#14273705—28no—
116#14273701—22no—
117#14273701C2314yes—
118#14273699—28no—
119C4×Dic118—22no—
120C4×Dic118—22no—
121C4×Dic118C2314yes—
122C4×Dic118C2314yes—
123#14273692—28no—
124(C22⋊D59)⋊C4—28no—
125#14273686—22no—
126#14273686—22no—
127#14273686C2314yes—
128#14273686C2314yes—
129C2×C4⋊Dic59—21no—
130C2×C4⋊Dic59C2311yescharacteristic
131C2×C4⋊Dic59C2311yescharacteristic
132C2×C4⋊Dic59C2311yescharacteristic
133C2×C4⋊Dic59C2311yescharacteristic
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4—21no—
139C2×C22⋊Dic59—21no—
140C2×C22⋊Dic59—21no—
141C2×C22⋊Dic59—21no—
142C2×C22⋊Dic59—21no—
143C2×C22⋊Dic59—21no—
144C2×(C2×D59)⋊C4—21no—
145C2×(C2×D59)⋊C4—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×C4×Dic59—21no—
148C2×C4×Dic59—21no—
149C2×C4×Dic59—21no—
150C2×C4×Dic59—21no—
151#14273661C2314yes—
152#14273661C2314yes—
153#14273659C2314yes—
154#14273652C2314yes—
155#14273652C2314yes—
156#14273652C2314yes—
157#14273652C2314yes—
158#14273652C2314yes—
159#14273652C2314yes—
160#14273652C2314yes—
161#14273649C2314yes—
162#14273649C2314yes—
163#14273649C2314yes—
164C22×D4×C59D411yescharacteristic
165C23×C4×C59C2311yescharacteristic
166C23×C4×C59C2311yescharacteristic
167C2×M16×C59—42no—
168C2×M16×C59C2314yes—
169C22×C8×C59—42no—
170C22×C8×C59C2311yescharacteristic
171C22×C8×C59C2311yescharacteristic
172C22×C8×C59C2311yescharacteristic
173C22×C8×C59C2311yescharacteristic
174C22×C8×C59C2314yes—
175C4×D4×C59D414yes—
176C4×D4×C59C2314yes—
177C2×C4⋊C4×C59D411yescharacteristic
178C2×C22⋊C4×C59D411yescharacteristic
179C2×C22⋊C4×C59D411yescharacteristic
180C2×C42×C59C2311yescharacteristic
181C4⋊C8×C59C2314yes—
182C22⋊C8×C59C2314yes—
183C22⋊C8×C59C2314yes—
184#97×C59C2314yes—
185C24×C59C2×D411yescharacteristic
186C24×C59C2×D411yescharacteristic
187C23×D59—21no—
188C2×D4×C59—42no—
189C2×D4×C59C2×D414yes—
190C22×C4×C59—22no—
191C22×C4×C59—22no—
192C22×C4×C59—22no—
193C22×C4×C59—22no—
194C22×C4×C59C2×D411yescharacteristic
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D412yes—
199C22×C4×C59C2×D412yes—
200C22×C4×C59C2412yes—
201C22×C4×C59C2412yes—
202C22×C4×C59C2411yescharacteristic
203C2×C22⋊D59—24no—
204C2×C22⋊D59—24no—
205C2×C22⋊D59—44no—
206C2×C22⋊D59—44no—
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—24no—
215C22×Dic59—44no—
216#11745685—28no—
217#11745685—44no—
218#11745685—48no—
219C2×D236—22no—
220C2×D236—22no—
221C2×D236—21no—
222C2×D236C2412yes—
223C2×C4×D59—24no—
224C2×C4×D59—44no—
225C2×Dic118—21no—
226C2×Dic118—22no—
227C2×Dic118—22no—
228C2×Dic118—22no—
229C2×Dic118—22no—
230C2×Dic118—22no—
231C2×Dic118—28no—
232C2×Dic118—24no—
233C2×Dic118—21no—
234C2×Dic118—24no—
235C2×Dic118—21no—
236C2×Dic118—44no—
237C2×Dic118—48no—
238C2×Dic118—44no—
239C2×Dic118—44no—
240C2×Dic118#4114yes—
241C2×Dic118C2412yes—
242C2×Dic118C2412yes—
243C2×Dic118C2412yes—
244M16×C59—44no—
245C2×C8×C59—22no—
246C2×C8×C59—22no—
247C2×C8×C59—22no—
248C2×C8×C59—22no—
249C2×C8×C59—44no—
250C2×C8×C59C2412yes—
251C2×C8×C59C2412yes—
252C2×C8×C59C2412yes—
253C2×C8×C59C2412yes—
254C4⋊C4×C59C2×D414yes—
255C22⋊C4×C59C2×D414yes—
256C22⋊C4×C59C2×D414yes—
257C42×C59C2×D412yes—
258C42×C59C2412yes—
259C22⋊Dic59—24no—
260C22⋊Dic59—24no—
261C22⋊Dic59—24no—
262C22⋊Dic59—24no—
263C22⋊Dic59—24no—
264(C2×D59)⋊C4—24no—
265(C2×D59)⋊C4—24no—
266(C2×D59)⋊C4—24no—
267C4⋊Dic59—24no—
268C4⋊Dic59—21no—
269C4⋊Dic59—21no—
270C4⋊Dic59—21no—
271C4⋊Dic59—21no—
272C4⋊Dic59C2412yes—
273C4⋊Dic59C2412yes—
274C4⋊Dic59C2412yes—
275C4⋊Dic59C2412yes—
276Dic59⋊C4—24no—
277Dic59⋊C4—24no—
278Dic59⋊C4—24no—
279Dic59⋊C4—24no—
280Dic59⋊C4—24no—
281C4×Dic59—24no—
282C4×Dic59—24no—
283C4×Dic59—24no—
284C4×Dic59—24no—
285Dic236—28no—
286Dic236—44no—
287#11745660—44no—
288C23×C59—22no—
289C23×C59—22no—
290C23×C59—22no—
291C23×C59—22no—
292C23×C59—22no—
293C23×C59—22no—
294C23×C59C22×D412yes—
295C23×C59C22×D412yes—
296C23×C59C22×D411yescharacteristic
297C22×D59—22no—
298C22×D59—42no—
299C22×D59—42no—
300C22×D59—42no—
301D4×C59—44no—
302C2×C4×C59—22no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—24no—
307C2×C4×C59—24no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59C22×D412yes—
313C2×C4×C59C22×D412yes—
314C2×C4×C59C22×D412yes—
315C2×C4×C59C22×D412yes—
316C2×C4×C59C22×D411yescharacteristic
317C2×C4×C59C2×#4112yes—
318C2×C4×C59H(5,𝔽2)12yes—
319C2×C4×C59C2511yescharacteristic
320C22⋊D59—48no—
321C22⋊D59—48no—
322C2×Dic59—24no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—22no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—48no—
331C2×Dic59—42no—
332C2×Dic59—42no—
333C2×Dic59—42no—
334C2×Dic59—42no—
335C2×Dic59—42no—
336C2×Dic59—42no—
337D236—22no—
338D236—22no—
339D236—42no—
340C4×D59—48no—
341Dic118—24no—
342Dic118—22no—
343Dic118—22no—
344Dic118—22no—
345Dic118—22no—
346Dic118—22no—
347Dic118—48no—
348Dic118—48no—
349Dic118—42no—
350Dic118—42no—
351Dic118C2×#4114yes—
352C8×C59—22no—
353C8×C59—22no—
354C8×C59—22no—
355C8×C59—22no—
356C2×#3313—591nomaximal, Sylow
357C22×C59—22no—
358C22×C59—22no—
359C22×C59—22no—
360C22×C59—22no—
361C22×C59—22no—
362C22×C59—22no—
363C22×C59—44no—
364C22×C59—44no—
365C22×C59#54612yes—
366C22×C59#57512yes—
367C22×C59#57812yes—
368C22×C59C23×D411yescharacteristic
369C2×D59—42no—
370C2×D59—42no—
371C2×D59—42no—
372C2×D59—84no—
373C4×C59—22no—
374C4×C59—22no—
375C4×C59—22no—
376C4×C59—22no—
377C4×C59#54612yes—
378C4×C59C22×#4111yescharacteristic
379C4×C59C2×H(5,𝔽2)11yescharacteristic
380Dic59—24no—
381Dic59—42no—
382Dic59—42no—
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×#435D5911yescharacteristic, complemented
401C2×#419—591no—
402C2×#416—591no—
403C2×C59—42no—
404C2×C59—42no—
405C2×C59#331314yescomplemented
406C2×C59C2×#54611yescharacteristic
407C2×C59C2×#57511yescharacteristic
408C2×C59C2×#57811yescharacteristic
409D59—82no—
410C22×#41—591no—
411C23×Q8—591no—
412C22×Q16—591no—
413C22×Q16—591no—
414C22×SD16—591no—
415C22×M16C2×D5911yescharacteristic
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—1181no—
437C2×C4×D4C2×D5911yescharacteristic
438C2×#117—591no—
439C2×#117—591no—
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#435C2×D5918yescomplemented
451C2×#107—591no—
452C2×#107—591no—
453C2×#106—591no—
454C2×C4⋊C8C2×D5911yescharacteristic
455#419—598no—
456#416—598no—
457C2×#103—591no—
458C2×#103—591no—
459C2×#103—591no—
460C2×#103—591no—
461C2×#103—591no—
462C2×#103—591no—
463C2×#103—591no—
464C2×#102—591no—
465C2×#102—591no—
466C2×#102—591no—
467C2×C22⋊C8C2×D5911yescharacteristic
468C2×C22⋊C8C2×D5911yescharacteristic
469C2×#97C2×D5911yescharacteristic
470C59C2×#331311yescharacteristic, complemented, Sylow
471C2×#41—594no—
472C2×#41—1184no—
473C2×#41—1182no—
474C2×#41—2362no—
475C22×Q8—591no—
476C22×Q8—591no—
477C22×Q8—591no—
478C22×Q8—594no—
479C22×Q8—1184no—
480C22×Q8—1181no—
481C22×Q8—1181no—
482C22×Q8—1182no—
483C22×Q8—2362no—
484C22×D4—591no—
485C22×D4—1181no—
486C22×D4—1181no—
487C22×D4D23611yescharacteristic
488C23×C4—1181no—
489C23×C4—1181no—
490C23×C4C22×D5911yescharacteristic
491C23×C4C22×D5911yescharacteristic
492C2×Q16—594no—
493C2×Q16—594no—
494C2×Q16—1184no—
495C2×Q16—2362no—
496C2×SD16—594no—
497C2×SD16—2362no—
498C2×M16—42no—
499C2×M16C22×D5914yes—
500C22×C8—42no—
501C22×C8C22×D5911yescharacteristic
502C22×C8C22×D5911yescharacteristic
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—1188no—
512#124—1188no—
513#124—1182no—
514C22⋊Q8—594no—
515C22⋊Q8—594no—
516C22⋊Q8—594no—
517C22⋊Q8—1182no—
518C22⋊Q8—1182no—
519C22⋊Q8—1182no—
520C22⋊Q8—1188no—
521#121—594no—
522#121—1188no—
523#121—1182no—
524C4×Q8—594no—
525C4×Q8—594no—
526C4×Q8—1188no—
527C4×Q8—1182no—
528C4×Q8—1182no—
529C4×D4—1188no—
530C4×D4D23614yes—
531C4×D4C22×D5914yes—
532#117—594no—
533#117—594no—
534#117—1182no—
535#117—1182no—
536C2×C4⋊C4—591no—
537C2×C4⋊C4—591no—
538C2×C4⋊C4—591no—
539C2×C4⋊C4—591no—
540C2×C4⋊C4—1181no—
541C2×C4⋊C4—1181no—
542C2×C4⋊C4—1181no—
543C2×C4⋊C4—1181no—
544C2×C4⋊C4—1181no—
545C2×C4⋊C4—1181no—
546C2×C4⋊C4D23611yescharacteristic
547C2×C22⋊C4—1181no—
548C2×C22⋊C4—1181no—
549C2×C22⋊C4—1181no—
550C2×C22⋊C4—1181no—
551C2×C22⋊C4—1181no—
552C2×C22⋊C4—1181no—
553C2×C22⋊C4—1181no—
554C2×C22⋊C4—1181no—
555C2×C22⋊C4D23611yescharacteristic
556C2×C22⋊C4D23611yescharacteristic
557C2×C42—1181no—
558C2×C42—1181no—
559C2×C42—1181no—
560C2×C42—1181no—
561C2×C42C22×D5911yescharacteristic
562#107—594no—
563#107—594no—
564#106—594no—
565C4⋊C8C22×D5914yes—
566#103—594no—
567#103—594no—
568#103—594no—
569#103—594no—
570#103—594no—
571#103—594no—
572#103—594no—
573#102—594no—
574#102—594no—
575#102—594no—
576C22⋊C8C22×D5914yes—
577C22⋊C8C22×D5914yes—
578#97C22×D5914yes—
579C24—1181no—
580C24C2×D23611yescharacteristic
581C24C2×D23611yescharacteristic
582#41—1188no—
583#41—2364no—
584#41—2368no—
585C2×Q8—594no—
586C2×Q8—592no—
587C2×Q8—592no—
588C2×Q8—592no—
589C2×Q8—1188no—
590C2×Q8—1181no—
591C2×Q8—1181no—
592C2×Q8—1184no—
593C2×Q8—1184no—
594C2×Q8—1181no—
595C2×Q8—1182no—
596C2×Q8—1182no—
597C2×Q8—1182no—
598C2×Q8—1182no—
599C2×Q8—1182no—
600C2×Q8—2364no—
601C2×Q8—2364no—
602C2×Q8—2368no—
603C2×Q8—2364no—
604C2×D4—42no—
605C2×D4—592no—
606C2×D4—1184no—
607C2×D4—1184no—
608C2×D4—1181no—
609C2×D4—1182no—
610C2×D4—1182no—
611C2×D4—2364no—
612C2×D4—2364no—
613C2×D4C2×D23614yes—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—1181no—
619C22×C4—1184no—
620C22×C4—1181no—
621C22×C4—1181no—
622C22×C4—1181no—
623C22×C4—1181no—
624C22×C4—1181no—
625C22×C4—1181no—
626C22×C4—1184no—
627C22×C4—2364no—
628C22×C4—2364no—
629C22×C4C2×D23612yes—
630C22×C4C2×D23612yes—
631C22×C4C2×D23611yescharacteristic
632C22×C4C2×D23611yescharacteristic
633C22×C4C2×D23611yescharacteristic
634C22×C4C2×D23611yescharacteristic
635C22×C4C23×D5912yes—
636C22×C4C23×D5912yes—
637C22×C4C23×D5911yescharacteristic
638Q16—1188no—
639Q16—2364no—
640SD16—2364no—
641M16—44no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—44no—
647C2×C8C23×D5912yes—
648C2×C8C23×D5912yes—
649C2×C8C23×D5912yes—
650C2×C8C23×D5912yes—
651C4⋊C4—592no—
652C4⋊C4—592no—
653C4⋊C4—592no—
654C4⋊C4—592no—
655C4⋊C4—1181no—
656C4⋊C4—1181no—
657C4⋊C4—1181no—
658C4⋊C4—1181no—
659C4⋊C4—1184no—
660C4⋊C4—1184no—
661C4⋊C4—1184no—
662C4⋊C4—1184no—
663C4⋊C4—1184no—
664C4⋊C4—1184no—
665C4⋊C4C2×D23614yes—
666C22⋊C4—1184no—
667C22⋊C4—1184no—
668C22⋊C4—1184no—
669C22⋊C4—1184no—
670C22⋊C4—1184no—
671C22⋊C4—1184no—
672C22⋊C4—1184no—
673C22⋊C4—1184no—
674C22⋊C4C2×D23614yes—
675C22⋊C4C2×D23614yes—
676C42—1184no—
677C42—1184no—
678C42—1184no—
679C42—1184no—
680C42C2×D23612yes—
681C42C23×D5912yes—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—1182no—
689C23—2362no—
690C23—2362no—
691C23—2362no—
692C23C22×D23612yes—
693C23C22×D23612yes—
694C23C22×D23611yescharacteristic
695Q8—594no—
696Q8—1182no—
697Q8—1184no—
698Q8—1182no—
699Q8—1182no—
700Q8—1182no—
701Q8—1182no—
702Q8—2368no—
703Q8—2368no—
704Q8—2362no—
705Q8—2362no—
706D4—44no—
707D4—1182no—
708D4—1182no—
709D4—2368no—
710D4—2368no—
711D4—2362no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—1182no—
723C2×C4—1184no—
724C2×C4—1182no—
725C2×C4—1182no—
726C2×C4—1182no—
727C2×C4—1182no—
728C2×C4—1182no—
729C2×C4—1182no—
730C2×C4—2368no—
731C2×C4—2368no—
732C2×C4—2362no—
733C2×C4—2362no—
734C2×C4—2362no—
735C2×C4—2362no—
736C2×C4—2362no—
737C2×C4—2362no—
738C2×C4C22×D23612yes—
739C2×C4C22×D23612yes—
740C2×C4C22×D23612yes—
741C2×C4C22×D23612yes—
742C2×C4C22×D23611yescharacteristic
743C2×C4#41×D5912yes—
744C2×C4#1427377212yes—
745C2×C4C24×D5911yescharacteristic
746C8—22no—
747C8—22no—
748C8—22no—
749C8—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—44no—
758C22—4724no—
759C22—2362no—
760C22—2362no—
761C22—2362no—
762C22#1683804712yes—
763C22#1683820212yes—
764C22#1683821912yes—
765C22C23×D23611yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—1184no—
771C4—2362no—
772C4—2362no—
773C4—2362no—
774C4—2362no—
775C4—2362no—
776C4—2362no—
777C4#1683804712yes—
778C4C2×#41×D5911yescharacteristic
779C4C2×#1427377211yescharacteristic
780C2—42no—
781C2—42no—
782C2—4722no—
783C2#2143616414yesdirect product factor
784C2C2×#1683804711yescharacteristic
785C2C2×#1683820211yescharacteristic
786C2C2×#1683821911yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#435C2
socleC23×C59C22×D4
prime radicalC2×#16838061C2
hypercenterC2×#435D59
hypocenterC59C2×#3313
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16838122C2semidirect
3. #21436164C2direct (N × H)
4. C2×#16837762C2semidirect
5. C2×#16837744C2semidirect
6. C2×#16837727C2semidirect
7. C2×#16837698C2semidirect
8. C2×#16837648C2semidirect
9. C2×#16837643C2semidirect
10. C2×#16837625C2semidirect
11. C2×#16837566C2semidirect
12. C2×#16837560C2semidirect
13. C2×#16837510C2semidirect
14. C2×#16837412C2semidirect
15. C2×#16837399C2semidirect
16. C2×C59×#435C2semidirect
23. #16838122C22semidirect
44. #16837762C22semidirect
45. #16837744C22semidirect
46. #16837727C22semidirect
47. #16837698C22semidirect
48. #16837648C22semidirect
49. #16837643C22semidirect
50. #16837625C22semidirect
51. #16837566C22semidirect
52. #16837560C22semidirect
53. #16837510C22semidirect
57. #16837412C22semidirect
58. #16837399C22semidirect
72. C59×#435C22semidirect
400. C2×#435D59semidirect
405. C2×C59#3313semidirect
450. #435C2×D59semidirect
470. C59C2×#3313semidirect
783. C2#21436164direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381222
C2×#168380612
#214361642
C2×#168377622
C2×#168377442
C2×#168377272
C2×#168376982
C2×#168376482
C2×#168376432
C2×#168376252
C2×#168375662
C2×#168375602
C2×#168375102
C2×#168374122
C2×#168373992
C2×C59×#4352
C2×#331359