Finite Group Databasebeta

← C2×#20286783 #28260828

Subgroups — C2×#20286783 #28260828

Order 13568.

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×#16811343C211yesmaximal, characteristic, complemented
2C2×#16811282C211yesmaximal, characteristic
3#20286783C2116yesmaximal, direct product factor
4C2×#16810983C211yesmaximal, characteristic, complemented
5C2×#16810965C211yesmaximal, characteristic, complemented
6C2×#16810948C211yesmaximal, characteristic, complemented
7C2×#16810919C211yesmaximal, characteristic, complemented
8C2×#16810869C211yesmaximal, characteristic, complemented
9C2×#16810864C211yesmaximal, characteristic, complemented
10C2×#16810846C211yesmaximal, characteristic, complemented
11C2×#16810787C211yesmaximal, characteristic, complemented
12C2×#16810781C211yesmaximal, characteristic, complemented
13C2×#16810731C211yesmaximal, characteristic, complemented
14C2×#16810633C211yesmaximal, characteristic, complemented
15C2×#16810620C211yesmaximal, characteristic, complemented
16C2×C53×#435C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C23×Dic106C2211yescharacteristic
19C22×Dic212C2211yescharacteristic
20C22×Dic212C2211yescharacteristic
21C22×#11719913C2211yescharacteristic
22#16811343—24no—
23#16811343C2218yescomplemented
24#16811282—24no—
25#16811282C2218yes—
26C2×#13133217C2211yescharacteristic
27C2×#13133210—21no—
28C2×#13133210—21no—
29C2×#13133205C2211yescharacteristic
30C2×#13133204—21no—
31C2×#13133203—21no—
32C2×#13133196C2211yescharacteristic
33C2×#13133196C2211yescharacteristic
34C2×#13133196C2211yescharacteristic
35C2×#13133195—21no—
36C2×#13133191C2211yescharacteristic
37C2×#13133189—21no—
38C2×C4×Dic106C2211yescharacteristic
39C2×C4×Dic106C2211yescharacteristic
40C2×#13133182—21no—
41C2×#13133177—21no—
42C2×#13133176C2211yescharacteristic
43C2×#13133176C2211yescharacteristic
44#16810983C2218yescomplemented
45#16810965C2218yescomplemented
46#16810948C2218yescomplemented
47#16810919C2218yescomplemented
48#16810869C2218yescomplemented
49#16810864C2218yescomplemented
50#16810846C2218yescomplemented
51#16810787C2218yescomplemented
52#16810781C2218yescomplemented
53#16810731C2218yescomplemented
54C2×#13133151C2211yescharacteristic
55C2×#13133151C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57#16810633C2218yescomplemented
58#16810620C2218yescomplemented
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133142C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2211yescharacteristic
65C2×#13133142C2211yescharacteristic
66C2×#13133139C2211yescharacteristic
67C2×#13133139C2211yescharacteristic
68C2×#13133139C2211yescharacteristic
69C22×M16×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#435C2218yescomplemented
73C2×C4⋊C8×C53C2211yescharacteristic
74C2×C22⋊C8×C53C2211yescharacteristic
75C2×C22⋊C8×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—24no—
79C2×#11719945—42no—
80C2×#11719945C2314yes—
81C22×Dic106—24no—
82C22×Dic106—22no—
83C22×Dic106—21no—
84C22×Dic106—21no—
85C22×Dic106—42no—
86C22×Dic106C2311yescharacteristic
87C22×Dic106C2311yescharacteristic
88C22×Dic106C2314yes—
89C22×Dic106C2311yescharacteristic
90C22×D212C2311yescharacteristic
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C23×Dic53—21no—
94C22×C4×D53—21no—
95C2×Dic212—24no—
96C2×Dic212—42no—
97C2×Dic212C2314yes—
98C2×Dic212C2314yes—
99C2×#11719913—42no—
100C2×#11719913C2314yes—
101#13133217—22no—
102#13133217C2314yes—
103#13133210—28no—
104#13133210—28no—
105#13133205—22no—
106#13133205C2314yes—
107#13133204—28no—
108#13133203—28no—
109#13133196—22no—
110#13133196—22no—
111#13133196—22no—
112#13133196C2314yes—
113#13133196C2314yes—
114#13133196C2314yes—
115#13133195—28no—
116#13133191—22no—
117#13133191C2314yes—
118#13133189—28no—
119C4×Dic106—22no—
120C4×Dic106—22no—
121C4×Dic106C2314yes—
122C4×Dic106C2314yes—
123#13133182—28no—
124#13133177—28no—
125#13133176—22no—
126#13133176—22no—
127#13133176C2314yes—
128#13133176C2314yes—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53C2311yescharacteristic
131C2×C4⋊Dic53C2311yescharacteristic
132C2×C4⋊Dic53C2311yescharacteristic
133C2×C4⋊Dic53C2311yescharacteristic
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×C22⋊Dic53—21no—
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×C22⋊Dic53—21no—
143C2×C22⋊Dic53—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×C4×Dic53—21no—
148C2×C4×Dic53—21no—
149C2×C4×Dic53—21no—
150C2×C4×Dic53—21no—
151#13133151C2314yes—
152#13133151C2314yes—
153#13133149C2314yes—
154#13133142C2314yes—
155#13133142C2314yes—
156#13133142C2314yes—
157#13133142C2314yes—
158#13133142C2314yes—
159#13133142C2314yes—
160#13133142C2314yes—
161#13133139C2314yes—
162#13133139C2314yes—
163#13133139C2314yes—
164C22×D4×C53D411yescharacteristic
165C23×C4×C53C2311yescharacteristic
166C23×C4×C53C2311yescharacteristic
167C2×M16×C53—42no—
168C2×M16×C53C2314yes—
169C22×C8×C53—42no—
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172C22×C8×C53C2311yescharacteristic
173C22×C8×C53C2311yescharacteristic
174C22×C8×C53C2314yes—
175C4×D4×C53D414yes—
176C4×D4×C53C2314yes—
177C2×C4⋊C4×C53D411yescharacteristic
178C2×C22⋊C4×C53D411yescharacteristic
179C2×C22⋊C4×C53D411yescharacteristic
180C2×C42×C53C2311yescharacteristic
181C4⋊C8×C53C2314yes—
182C22⋊C8×C53C2314yes—
183C22⋊C8×C53C2314yes—
184#97×C53C2314yes—
185C24×C53C2×D411yescharacteristic
186C24×C53C2×D411yescharacteristic
187C23×D53—21no—
188C2×D4×C53—42no—
189C2×D4×C53C2×D414yes—
190C22×C4×C53—22no—
191C22×C4×C53—22no—
192C22×C4×C53—22no—
193C22×C4×C53—22no—
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D412yes—
199C22×C4×C53C2×D412yes—
200C22×C4×C53C2412yes—
201C22×C4×C53C2412yes—
202C22×C4×C53C2411yescharacteristic
203C2×C22⋊D53—24no—
204C2×C22⋊D53—24no—
205C2×C22⋊D53—44no—
206C2×C22⋊D53—44no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—24no—
215C22×Dic53—44no—
216#11719945—28no—
217#11719945—44no—
218#11719945—48no—
219C2×D212—22no—
220C2×D212—22no—
221C2×D212—21no—
222C2×D212C2412yes—
223C2×C4×D53—24no—
224C2×C4×D53—44no—
225C2×Dic106—21no—
226C2×Dic106—22no—
227C2×Dic106—22no—
228C2×Dic106—22no—
229C2×Dic106—22no—
230C2×Dic106—22no—
231C2×Dic106—28no—
232C2×Dic106—24no—
233C2×Dic106—21no—
234C2×Dic106—24no—
235C2×Dic106—21no—
236C2×Dic106—44no—
237C2×Dic106—48no—
238C2×Dic106—44no—
239C2×Dic106—44no—
240C2×Dic106#4114yes—
241C2×Dic106C2412yes—
242C2×Dic106C2412yes—
243C2×Dic106C2412yes—
244M16×C53—44no—
245C2×C8×C53—22no—
246C2×C8×C53—22no—
247C2×C8×C53—22no—
248C2×C8×C53—22no—
249C2×C8×C53—44no—
250C2×C8×C53C2412yes—
251C2×C8×C53C2412yes—
252C2×C8×C53C2412yes—
253C2×C8×C53C2412yes—
254C4⋊C4×C53C2×D414yes—
255C22⋊C4×C53C2×D414yes—
256C22⋊C4×C53C2×D414yes—
257C42×C53C2×D412yes—
258C42×C53C2412yes—
259C22⋊Dic53—24no—
260C22⋊Dic53—24no—
261C22⋊Dic53—24no—
262C22⋊Dic53—24no—
263C22⋊Dic53—24no—
264#11719921—24no—
265#11719921—24no—
266#11719921—24no—
267C4⋊Dic53—24no—
268C4⋊Dic53—21no—
269C4⋊Dic53—21no—
270C4⋊Dic53—21no—
271C4⋊Dic53—21no—
272C4⋊Dic53C2412yes—
273C4⋊Dic53C2412yes—
274C4⋊Dic53C2412yes—
275C4⋊Dic53C2412yes—
276#11719919—24no—
277#11719919—24no—
278#11719919—24no—
279#11719919—24no—
280#11719919—24no—
281C4×Dic53—24no—
282C4×Dic53—24no—
283C4×Dic53—24no—
284C4×Dic53—24no—
285Dic212—28no—
286Dic212—44no—
287#11719913—44no—
288C23×C53—22no—
289C23×C53—22no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53C22×D412yes—
295C23×C53C22×D412yes—
296C23×C53C22×D411yescharacteristic
297C22×D53—22no—
298C22×D53—42no—
299C22×D53—42no—
300C22×D53—42no—
301D4×C53—44no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—24no—
307C2×C4×C53—24no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53C22×D412yes—
313C2×C4×C53C22×D412yes—
314C2×C4×C53C22×D412yes—
315C2×C4×C53C22×D412yes—
316C2×C4×C53C22×D411yescharacteristic
317C2×C4×C53C2×#4112yes—
318C2×C4×C53H(5,𝔽2)12yes—
319C2×C4×C53C2511yescharacteristic
320C22⋊D53—48no—
321C22⋊D53—48no—
322C2×Dic53—24no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—48no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337D212—22no—
338D212—22no—
339D212—42no—
340C4×D53—48no—
341Dic106—24no—
342Dic106—22no—
343Dic106—22no—
344Dic106—22no—
345Dic106—22no—
346Dic106—22no—
347Dic106—48no—
348Dic106—48no—
349Dic106—42no—
350Dic106—42no—
351Dic106C2×#4114yes—
352C8×C53—22no—
353C8×C53—22no—
354C8×C53—22no—
355C8×C53—22no—
356C2×#3313—531nomaximal, Sylow
357C22×C53—22no—
358C22×C53—22no—
359C22×C53—22no—
360C22×C53—22no—
361C22×C53—22no—
362C22×C53—22no—
363C22×C53—44no—
364C22×C53—44no—
365C22×C53#54612yes—
366C22×C53#57512yes—
367C22×C53#57812yes—
368C22×C53C23×D411yescharacteristic
369C2×D53—42no—
370C2×D53—42no—
371C2×D53—42no—
372C2×D53—84no—
373C4×C53—22no—
374C4×C53—22no—
375C4×C53—22no—
376C4×C53—22no—
377C4×C53#54612yes—
378C4×C53C22×#4111yescharacteristic
379C4×C53C2×H(5,𝔽2)11yescharacteristic
380Dic53—24no—
381Dic53—42no—
382Dic53—42no—
383Dic53—42no—
384Dic53—42no—
385Dic53—42no—
386Dic53—42no—
387C2×#556—531no—
388C2×#548—531no—
389#3313—5316no—
390C2×#489—531no—
391C2×#485—531no—
392C2×#482—531no—
393C2×#477—531no—
394C2×#468—531no—
395C2×#467—531no—
396C2×#464—531no—
397C2×#452—531no—
398C2×#451—531no—
399C2×#441—531no—
400C2×#435D5311yescharacteristic, complemented
401C2×#419—531no—
402C2×#416—531no—
403C2×C53—42no—
404C2×C53—42no—
405C2×C53#331314yescomplemented
406C2×C53C2×#54611yescharacteristic
407C2×C53C2×#57511yescharacteristic
408C2×C53C2×#57811yescharacteristic
409D53—82no—
410C22×#41—531no—
411C23×Q8—531no—
412C22×Q16—531no—
413C22×Q16—531no—
414C22×SD16—531no—
415C22×M16C2×D5311yescharacteristic
416C23×C8C2×D5311yescharacteristic
417#556—538no—
418#556—1064no—
419#548—538no—
420#548—1064no—
421C2×C4⋊Q8—531no—
422C2×#126—1061no—
423C2×#126—1061no—
424C2×#124—531no—
425C2×#124—1061no—
426C2×#124—1061no—
427C2×C22⋊Q8—531no—
428C2×C22⋊Q8—531no—
429C2×C22⋊Q8—531no—
430C2×C22⋊Q8—1061no—
431C2×#121—531no—
432C2×#121—1061no—
433C2×C4×Q8—531no—
434C2×C4×Q8—531no—
435C2×C4×Q8—1061no—
436C2×C4×D4—1061no—
437C2×C4×D4C2×D5311yescharacteristic
438C2×#117—531no—
439C2×#117—531no—
440#489—538no—
441#485—538no—
442#482—538no—
443#477—538no—
444#468—538no—
445#467—538no—
446#464—538no—
447#452—538no—
448#451—538no—
449#441—538no—
450#435C2×D5318yescomplemented
451C2×#107—531no—
452C2×#107—531no—
453C2×#106—531no—
454C2×C4⋊C8C2×D5311yescharacteristic
455#419—538no—
456#416—538no—
457C2×#103—531no—
458C2×#103—531no—
459C2×#103—531no—
460C2×#103—531no—
461C2×#103—531no—
462C2×#103—531no—
463C2×#103—531no—
464C2×#102—531no—
465C2×#102—531no—
466C2×#102—531no—
467C2×C22⋊C8C2×D5311yescharacteristic
468C2×C22⋊C8C2×D5311yescharacteristic
469C2×#97C2×D5311yescharacteristic
470C53C2×#331311yescharacteristic, complemented, Sylow
471C2×#41—534no—
472C2×#41—1064no—
473C2×#41—1062no—
474C2×#41—2122no—
475C22×Q8—531no—
476C22×Q8—531no—
477C22×Q8—531no—
478C22×Q8—534no—
479C22×Q8—1064no—
480C22×Q8—1061no—
481C22×Q8—1061no—
482C22×Q8—1062no—
483C22×Q8—2122no—
484C22×D4—531no—
485C22×D4—1061no—
486C22×D4—1061no—
487C22×D4D21211yescharacteristic
488C23×C4—1061no—
489C23×C4—1061no—
490C23×C4C22×D5311yescharacteristic
491C23×C4C22×D5311yescharacteristic
492C2×Q16—534no—
493C2×Q16—534no—
494C2×Q16—1064no—
495C2×Q16—2122no—
496C2×SD16—534no—
497C2×SD16—2122no—
498C2×M16—42no—
499C2×M16C22×D5314yes—
500C22×C8—42no—
501C22×C8C22×D5311yescharacteristic
502C22×C8C22×D5311yescharacteristic
503C22×C8C22×D5311yescharacteristic
504C22×C8C22×D5311yescharacteristic
505C22×C8C22×D5314yes—
506C4⋊Q8—534no—
507C4⋊Q8—1062no—
508#126—1068no—
509#126—1068no—
510#124—534no—
511#124—1068no—
512#124—1068no—
513#124—1062no—
514C22⋊Q8—534no—
515C22⋊Q8—534no—
516C22⋊Q8—534no—
517C22⋊Q8—1062no—
518C22⋊Q8—1062no—
519C22⋊Q8—1062no—
520C22⋊Q8—1068no—
521#121—534no—
522#121—1068no—
523#121—1062no—
524C4×Q8—534no—
525C4×Q8—534no—
526C4×Q8—1068no—
527C4×Q8—1062no—
528C4×Q8—1062no—
529C4×D4—1068no—
530C4×D4D21214yes—
531C4×D4C22×D5314yes—
532#117—534no—
533#117—534no—
534#117—1062no—
535#117—1062no—
536C2×C4⋊C4—531no—
537C2×C4⋊C4—531no—
538C2×C4⋊C4—531no—
539C2×C4⋊C4—531no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4—1061no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4—1061no—
544C2×C4⋊C4—1061no—
545C2×C4⋊C4—1061no—
546C2×C4⋊C4D21211yescharacteristic
547C2×C22⋊C4—1061no—
548C2×C22⋊C4—1061no—
549C2×C22⋊C4—1061no—
550C2×C22⋊C4—1061no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4—1061no—
555C2×C22⋊C4D21211yescharacteristic
556C2×C22⋊C4D21211yescharacteristic
557C2×C42—1061no—
558C2×C42—1061no—
559C2×C42—1061no—
560C2×C42—1061no—
561C2×C42C22×D5311yescharacteristic
562#107—534no—
563#107—534no—
564#106—534no—
565C4⋊C8C22×D5314yes—
566#103—534no—
567#103—534no—
568#103—534no—
569#103—534no—
570#103—534no—
571#103—534no—
572#103—534no—
573#102—534no—
574#102—534no—
575#102—534no—
576C22⋊C8C22×D5314yes—
577C22⋊C8C22×D5314yes—
578#97C22×D5314yes—
579C24—1061no—
580C24C2×D21211yescharacteristic
581C24C2×D21211yescharacteristic
582#41—1068no—
583#41—2124no—
584#41—2128no—
585C2×Q8—534no—
586C2×Q8—532no—
587C2×Q8—532no—
588C2×Q8—532no—
589C2×Q8—1068no—
590C2×Q8—1061no—
591C2×Q8—1061no—
592C2×Q8—1064no—
593C2×Q8—1064no—
594C2×Q8—1061no—
595C2×Q8—1062no—
596C2×Q8—1062no—
597C2×Q8—1062no—
598C2×Q8—1062no—
599C2×Q8—1062no—
600C2×Q8—2124no—
601C2×Q8—2124no—
602C2×Q8—2128no—
603C2×Q8—2124no—
604C2×D4—42no—
605C2×D4—532no—
606C2×D4—1064no—
607C2×D4—1064no—
608C2×D4—1061no—
609C2×D4—1062no—
610C2×D4—1062no—
611C2×D4—2124no—
612C2×D4—2124no—
613C2×D4C2×D21214yes—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—1061no—
619C22×C4—1064no—
620C22×C4—1061no—
621C22×C4—1061no—
622C22×C4—1061no—
623C22×C4—1061no—
624C22×C4—1061no—
625C22×C4—1061no—
626C22×C4—1064no—
627C22×C4—2124no—
628C22×C4—2124no—
629C22×C4C2×D21212yes—
630C22×C4C2×D21212yes—
631C22×C4C2×D21211yescharacteristic
632C22×C4C2×D21211yescharacteristic
633C22×C4C2×D21211yescharacteristic
634C22×C4C2×D21211yescharacteristic
635C22×C4C23×D5312yes—
636C22×C4C23×D5312yes—
637C22×C4C23×D5311yescharacteristic
638Q16—1068no—
639Q16—2124no—
640SD16—2124no—
641M16—44no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—44no—
647C2×C8C23×D5312yes—
648C2×C8C23×D5312yes—
649C2×C8C23×D5312yes—
650C2×C8C23×D5312yes—
651C4⋊C4—532no—
652C4⋊C4—532no—
653C4⋊C4—532no—
654C4⋊C4—532no—
655C4⋊C4—1061no—
656C4⋊C4—1061no—
657C4⋊C4—1061no—
658C4⋊C4—1061no—
659C4⋊C4—1064no—
660C4⋊C4—1064no—
661C4⋊C4—1064no—
662C4⋊C4—1064no—
663C4⋊C4—1064no—
664C4⋊C4—1064no—
665C4⋊C4C2×D21214yes—
666C22⋊C4—1064no—
667C22⋊C4—1064no—
668C22⋊C4—1064no—
669C22⋊C4—1064no—
670C22⋊C4—1064no—
671C22⋊C4—1064no—
672C22⋊C4—1064no—
673C22⋊C4—1064no—
674C22⋊C4C2×D21214yes—
675C22⋊C4C2×D21214yes—
676C42—1064no—
677C42—1064no—
678C42—1064no—
679C42—1064no—
680C42C2×D21212yes—
681C42C23×D5312yes—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—1062no—
689C23—2122no—
690C23—2122no—
691C23—2122no—
692C23C22×D21212yes—
693C23C22×D21212yes—
694C23C22×D21211yescharacteristic
695Q8—534no—
696Q8—1064no—
697Q8—1062no—
698Q8—1062no—
699Q8—1062no—
700Q8—1062no—
701Q8—1062no—
702Q8—2128no—
703Q8—2128no—
704Q8—2122no—
705Q8—2122no—
706D4—44no—
707D4—1062no—
708D4—1062no—
709D4—2128no—
710D4—2128no—
711D4—2122no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—1064no—
723C2×C4—1062no—
724C2×C4—1062no—
725C2×C4—1062no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—2128no—
731C2×C4—2128no—
732C2×C4—2122no—
733C2×C4—2122no—
734C2×C4—2122no—
735C2×C4—2122no—
736C2×C4—2122no—
737C2×C4—2122no—
738C2×C4C22×D21212yes—
739C2×C4C22×D21212yes—
740C2×C4C22×D21212yes—
741C2×C4C22×D21212yes—
742C2×C4C22×D21211yescharacteristic
743C2×C4#41×D5312yes—
744C2×C4#1313326212yes—
745C2×C4C24×D5311yescharacteristic
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—4244no—
759C22—2122no—
760C22—2122no—
761C22—2122no—
762C22#1681126812yes—
763C22#1681142312yes—
764C22#1681144012yes—
765C22C23×D21211yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—1064no—
771C4—2122no—
772C4—2122no—
773C4—2122no—
774C4—2122no—
775C4—2122no—
776C4—2122no—
777C4#1681126812yes—
778C4C2×#41×D5311yescharacteristic
779C4C2×#1313326211yescharacteristic
780C2—42no—
781C2—42no—
782C2—4242no—
783C2#2028678314yesdirect product factor
784C2C2×#1681126811yescharacteristic
785C2C2×#1681142311yescharacteristic
786C2C2×#1681144011yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#435C2
socleC23×C53C22×D4
prime radicalC2×#16811282C2
hypercenterC2×#435D53
hypocenterC53C2×#3313
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16811343C2semidirect
3. #20286783C2direct (N × H)
4. C2×#16810983C2semidirect
5. C2×#16810965C2semidirect
6. C2×#16810948C2semidirect
7. C2×#16810919C2semidirect
8. C2×#16810869C2semidirect
9. C2×#16810864C2semidirect
10. C2×#16810846C2semidirect
11. C2×#16810787C2semidirect
12. C2×#16810781C2semidirect
13. C2×#16810731C2semidirect
14. C2×#16810633C2semidirect
15. C2×#16810620C2semidirect
16. C2×C53×#435C2semidirect
23. #16811343C22semidirect
44. #16810983C22semidirect
45. #16810965C22semidirect
46. #16810948C22semidirect
47. #16810919C22semidirect
48. #16810869C22semidirect
49. #16810864C22semidirect
50. #16810846C22semidirect
51. #16810787C22semidirect
52. #16810781C22semidirect
53. #16810731C22semidirect
57. #16810633C22semidirect
58. #16810620C22semidirect
72. C53×#435C22semidirect
400. C2×#435D53semidirect
405. C2×C53#3313semidirect
450. #435C2×D53semidirect
470. C53C2×#3313semidirect
783. C2#20286783direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113432
C2×#168112822
#202867832
C2×#168109832
C2×#168109652
C2×#168109482
C2×#168109192
C2×#168108692
C2×#168108642
C2×#168108462
C2×#168107872
C2×#168107812
C2×#168107312
C2×#168106332
C2×#168106202
C2×C53×#4352
C2×#331353