Finite Group Databasebeta

← C2×#20284794 #28252174

Subgroups — C2×#20284794 #28252174

Order 13568.

2170 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811152C211yesmaximal, characteristic
2C2×C4×Q8×D53C211yesmaximal, characteristic, complemented
3#20284794C2116yesmaximal, direct product factor
4C2×#16810952C211yesmaximal, characteristic, complemented
5C2×#16810935C211yesmaximal, characteristic
6C2×#16810931C211yesmaximal, characteristic, complemented
7C2×#16810930C211yesmaximal, characteristic, complemented
8C2×#16810842C211yesmaximal, characteristic, complemented
9C2×#16810777C211yesmaximal, characteristic, complemented
10C2×#16810760C211yesmaximal, characteristic
11C2×Q16×Dic53C211yesmaximal, characteristic, complemented
12C2×#16810715C211yesmaximal, characteristic, complemented
13C2×#16810714C211yesmaximal, characteristic, complemented
14C2×SD16×Dic53C211yesmaximal, characteristic, complemented
15C2×#16810675C211yesmaximal, characteristic, complemented
16C2×C53×#464C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20#16811152—24no—
21#16811152C2218yes—
22C2×#13133210—21no—
23C2×#13133209C2211yescharacteristic
24C2×#13133199—21no—
25C2×#13133193C2211yescharacteristic
26C2×#13133188C2211yescharacteristic
27C2×Q8×Dic53C2211yescharacteristic
28C2×Q8×Dic53C2211yescharacteristic
29C2×C4×Dic106—21no—
30C2×C4×Dic106C2211yescharacteristic
31C2×#13133182—21no—
32C2×#13133182C2211yescharacteristic
33C4×Q8×D53—24no—
34C4×Q8×D53C2218yescomplemented
35C2×D4×Dic53C2211yescharacteristic
36C2×#13133177—21no—
37C2×#13133173—21no—
38C2×C4⋊C4×D53—21no—
39C2×C4⋊C4×D53C2211yescharacteristic
40C2×C42×D53—21no—
41C2×C42×D53C2211yescharacteristic
42#16810952C2218yescomplemented
43#16810935C2218yes—
44#16810931C2218yescomplemented
45#16810930C2218yescomplemented
46#16810842C2218yescomplemented
47#16810777C2218yescomplemented
48#16810760C2218yes—
49Q16×Dic53C2218yescomplemented
50#16810715C2218yescomplemented
51#16810714C2218yescomplemented
52SD16×Dic53C2218yescomplemented
53#16810675C2218yescomplemented
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×C4⋊#88322C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133129C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×C8×Dic53C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×Q16×C53C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic
71C2×#124×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic
73C53×#464C2218yescomplemented
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C2×Q8×D53—24no—
80C2×Q8×D53—22no—
81C2×Q8×D53—24no—
82C2×Q8×D53C2314yes—
83C22×C22⋊D53—21no—
84C23×Dic53—21no—
85C22×C4×D53—21no—
86C22×C4×D53—21no—
87C22×C4×D53D411yescharacteristic
88C22×C4×D53D411yescharacteristic
89C22×C4×D53C2311yescharacteristic
90C2×#11719925—24no—
91C2×#11719925C2314yes—
92C2×#11719923—24no—
93C2×#11719923C2314yes—
94C22×#88322C2311yescharacteristic
95C22×#88322C2311yescharacteristic
96#13133210—28no—
97#13133209—22no—
98#13133209C2314yes—
99#13133199—28no—
100#13133193—22no—
101#13133193C2314yes—
102#13133188—22no—
103#13133188C2314yes—
104Q8×Dic53—22no—
105Q8×Dic53—22no—
106Q8×Dic53C2314yes—
107Q8×Dic53C2314yes—
108C4×Dic106—22no—
109C4×Dic106—28no—
110C4×Dic106C2314yes—
111#13133182—22no—
112#13133182—28no—
113#13133182C2314yes—
114D4×Dic53—22no—
115D4×Dic53C2314yes—
116#13133177—28no—
117#13133173—28no—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53C2311yescharacteristic
121C2×C4⋊Dic53C2311yescharacteristic
122C2×C4⋊Dic53C2311yescharacteristic
123C2×#11719919—21no—
124C2×#11719919—21no—
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C4⋊C4×D53—28no—
130C4⋊C4×D53—22no—
131C4⋊C4×D53C2314yes—
132C2×C22⋊Dic53—21no—
133C2×C22⋊Dic53—21no—
134C2×#11719921—21no—
135C2×C4×Dic53—21no—
136C2×C4×Dic53—21no—
137C2×C4×Dic53—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53D411yescharacteristic
140C2×C4×Dic53D411yescharacteristic
141C2×C4×Dic53C2311yescharacteristic
142C42×D53—28no—
143C42×D53D414yes—
144C42×D53C2314yes—
145#13133151C2314yes—
146#13133150C2314yes—
147#13133149C2314yes—
148#13133148C2314yes—
149C4⋊#88322C2314yes—
150#13133142C2314yes—
151#13133142C2314yes—
152#13133141C2314yes—
153#13133141C2314yes—
154#13133141C2314yes—
155#13133138C2314yes—
156#13133129C2314yes—
157#13133129C2314yes—
158C8×Dic53C2314yes—
159C8×Dic53C2314yes—
160C22×Q8×C53C2311yescharacteristic
161C22×Q8×C53C2311yescharacteristic
162C22×D4×C53C2311yescharacteristic
163C2×Q16×C53—24no—
164C2×Q16×C53C2314yes—
165C2×SD16×C53—24no—
166C2×SD16×C53C2314yes—
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169#124×C53—22no—
170#124×C53C2314yes—
171C4×Q8×C53—22no—
172C4×Q8×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53—21no—
177C2×C42×C53—21no—
178C2×C42×C53C2311yescharacteristic
179C4⋊C8×C53C2314yes—
180#103×C53C2314yes—
181#102×C53C2314yes—
182C24×C53—21no—
183C23×D53C2×D411yescharacteristic
184C2×Q8×C53—21no—
185C2×Q8×C53—21no—
186C2×Q8×C53—22no—
187C2×Q8×C53—22no—
188C2×Q8×C53—22no—
189C2×Q8×C53#4114yes—
190C2×Q8×C53C2412yes—
191C2×Q8×C53C2412yes—
192C2×D4×C53—21no—
193C2×D4×C53—22no—
194C2×D4×C53—22no—
195C2×D4×C53C2412yes—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2411yescharacteristic
202C2×C22⋊D53—24no—
203C2×C22⋊D53—44no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—24no—
209C22×Dic53—44no—
210C22×Dic53C2×D411yescharacteristic
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213Q8×D53—216no—
214Q8×D53—28no—
215Q8×D53—28no—
216C2×C4×D53—28no—
217C2×C4×D53—24no—
218C2×C4×D53—24no—
219C2×C4×D53—22no—
220C2×C4×D53—22no—
221C2×C4×D53—24no—
222C2×C4×D53—24no—
223C2×C4×D53—44no—
224C2×C4×D53C2×D414yes—
225C2×C4×D53C2×D412yes—
226C2×C4×D53C2×D414yes—
227C2×C4×D53C2412yes—
228C2×Dic106—28no—
229C2×Dic106—21no—
230C2×Dic106—22no—
231C2×Dic106—24no—
232C2×Dic106#4114yes—
233C2×Dic106C2412yes—
234Q16×C53—28no—
235SD16×C53—28no—
236C2×C8×C53—22no—
237C2×C8×C53—22no—
238C2×C8×C53C2412yes—
239C2×C8×C53C2412yes—
240C4⋊C4×C53—24no—
241C4⋊C4×C53—21no—
242C4⋊C4×C53C2412yes—
243C22⋊C4×C53—24no—
244C22⋊C4×C53—24no—
245C42×C53—24no—
246C42×C53C2×D412yes—
247C42×C53C2412yes—
248C22⋊Dic53—24no—
249C22⋊Dic53—24no—
250#11719925—28no—
251#11719923—28no—
252#11719921—24no—
253C4⋊Dic53—21no—
254C4⋊Dic53—21no—
255C4⋊Dic53—21no—
256C4⋊Dic53—24no—
257C4⋊Dic53—24no—
258C4⋊Dic53C2412yes—
259C4⋊Dic53C2412yes—
260C4⋊Dic53C2412yes—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264#11719919—24no—
265#11719919—24no—
266#11719919—24no—
267C4×Dic53—24no—
268C4×Dic53—24no—
269C4×Dic53—24no—
270C4×Dic53—24no—
271C4×Dic53C2×D412yes—
272C4×Dic53C2×D414yes—
273C4×Dic53C2×D414yes—
274C4×Dic53C2412yes—
275C2×#88322—22no—
276C2×#88322—22no—
277C2×#88322C2412yes—
278C2×#88322C2412yes—
279C23×C53—22no—
280C23×C53—42no—
281C23×C53—42no—
282C23×C53—42no—
283C23×C53C22×D411yescharacteristic
284C22×D53—22no—
285C22×D53—22no—
286C22×D53#13514yes—
287C22×D53C22×D412yes—
288Q8×C53—24no—
289Q8×C53—22no—
290Q8×C53—22no—
291Q8×C53—22no—
292Q8×C53—42no—
293Q8×C53C2×#4114yes—
294D4×C53—22no—
295D4×C53—22no—
296D4×C53—42no—
297C2×C4×C53—24no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—42no—
304C2×C4×C53—42no—
305C2×C4×C53C22×D412yes—
306C2×C4×C53C22×D412yes—
307C2×C4×C53C22×D411yescharacteristic
308C2×C4×C53C2×#4112yes—
309C2×C4×C53C2×#4112yes—
310C2×C4×C53C2511yescharacteristic
311C22⋊D53—48no—
312C2×Dic53—22no—
313C2×Dic53—24no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—42no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53—48no—
323C2×Dic53#13714yes—
324C2×Dic53C22×D412yes—
325C2×Dic53C22×D412yes—
326C2×Dic53C22×D412yes—
327C4×D53—216no—
328C4×D53—28no—
329C4×D53—24no—
330C4×D53—22no—
331C4×D53—22no—
332C4×D53—28no—
333C4×D53—48no—
334Dic106—216no—
335Dic106—24no—
336Dic106—22no—
337Dic106C2×#4114yes—
338C8×C53—22no—
339C8×C53—22no—
340#88322—22no—
341#88322—22no—
342C2×#3108—531nomaximal, Sylow
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—42no—
346C22×C53—84no—
347C22×C53#52512yes—
348C22×C53C2×#13512yes—
349C22×C53C2×#13712yes—
350C22×C53C23×D411yescharacteristic
351C2×D53—28no—
352C2×D53—22no—
353C2×D53—22no—
354C2×D53C2×#13514yes—
355C4×C53—24no—
356C4×C53—22no—
357C4×C53—22no—
358C4×C53—42no—
359C4×C53—42no—
360C4×C53#52512yes—
361C4×C53C22×#4111yescharacteristic
362C4×C53C22×#4111yescharacteristic
363Dic53—22no—
364Dic53—24no—
365Dic53—22no—
366Dic53—42no—
367Dic53—42no—
368Dic53—42no—
369Dic53C2×#13714yes—
370C2×#529—531no—
371C22×C4×Q8—531no—
372#3108—5316no—
373C2×#483—531no—
374C2×#480—531no—
375C2×#479—531no—
376C2×#479—531no—
377C2×#464—531no—
378C2×#464D5311yescharacteristic, complemented
379C2×#451—531no—
380C2×#448—531no—
381C2×C4×Q16—531no—
382C2×C4×Q16—531no—
383C2×C4×SD16—531no—
384C2×C4×SD16—531no—
385C2×#431—531no—
386C2×C53—82no—
387C2×C53#310814yescomplemented
388C2×C53C2×#52511yescharacteristic
389C2×C53C22×#13511yescharacteristic
390C2×C53C22×#13711yescharacteristic
391D53—24no—
392C23×Q8—531no—
393C22×Q16—531no—
394C22×Q16C2×D5311yescharacteristic
395C22×SD16—531no—
396C22×SD16C2×D5311yescharacteristic
397#529—538no—
398#529—1064no—
399C2×#126—1061no—
400C2×#125—531no—
401C2×#124C2×D5311yescharacteristic
402C2×#123—1061no—
403C2×C22⋊Q8—531no—
404C2×#121—531no—
405C2×C4×Q8—531no—
406C2×C4×Q8—531no—
407C2×C4×Q8—538no—
408C2×C4×Q8—531no—
409C2×C4×Q8—531no—
410C2×C4×Q8—1061no—
411C2×C4×Q8—1061no—
412C2×C4×Q8—1064no—
413C2×C4×Q8C2×D5311yescharacteristic
414C2×C4×D4—531no—
415C2×C4×D4—1061no—
416C2×#117—1061no—
417C22×C4⋊C4—531no—
418C22×C4⋊C4—1061no—
419C22×C42—531no—
420C22×C42—1061no—
421#483—538no—
422#480—538no—
423#479—538no—
424#479—538no—
425#464—538no—
426#464C2×D5318yescomplemented
427#451—538no—
428#448—538no—
429C4×Q16—538no—
430C4×Q16—538no—
431C4×SD16—538no—
432C4×SD16—538no—
433#431—538no—
434C2×#107—531no—
435C2×#107—531no—
436C2×#106—531no—
437C2×#106—531no—
438C2×C4⋊C8—531no—
439C2×C4⋊C8C2×D5311yescharacteristic
440C2×#103—531no—
441C2×#103—531no—
442C2×#103—531no—
443C2×#103—531no—
444C2×#103—531no—
445C2×#103C2×D5311yescharacteristic
446C2×#102—531no—
447C2×#102C2×D5311yescharacteristic
448C2×C22⋊C8—531no—
449C2×C22⋊C8—531no—
450C2×C4×C8—531no—
451C2×C4×C8—531no—
452C53C2×#310811yescharacteristic, complemented, Sylow
453C22×Q8—534no—
454C22×Q8—531no—
455C22×Q8—1061no—
456C22×Q8—1062no—
457C22×Q8—1064no—
458C22×Q8—1064no—
459C22×Q8C22×D5311yescharacteristic
460C22×Q8C22×D5311yescharacteristic
461C22×D4—1061no—
462C22×D4C22×D5311yescharacteristic
463C23×C4—531no—
464C23×C4—531no—
465C23×C4—531no—
466C23×C4—1061no—
467C23×C4—1061no—
468C23×C4—1061no—
469C2×Q16—24no—
470C2×Q16—534no—
471C2×Q16—1064no—
472C2×Q16C22×D5314yes—
473C2×SD16—24no—
474C2×SD16—534no—
475C2×SD16—1064no—
476C2×SD16C22×D5314yes—
477C22×C8—531no—
478C22×C8—531no—
479C22×C8C22×D5311yescharacteristic
480C22×C8C22×D5311yescharacteristic
481#126—1068no—
482#125—534no—
483#125—1062no—
484#124—22no—
485#124C22×D5314yes—
486#123—1068no—
487C22⋊Q8—534no—
488C22⋊Q8—1062no—
489#121—534no—
490#121—1062no—
491C4×Q8—22no—
492C4×Q8—534no—
493C4×Q8—534no—
494C4×Q8—534no—
495C4×Q8—534no—
496C4×Q8—1068no—
497C4×Q8—1068no—
498C4×Q8—1062no—
499C4×Q8—1062no—
500C4×Q8—1062no—
501C4×Q8—1062no—
502C4×Q8C22×D5314yes—
503C4×D4—534no—
504C4×D4—1062no—
505C4×D4—1068no—
506#117—1068no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—531no—
509C2×C4⋊C4—531no—
510C2×C4⋊C4—531no—
511C2×C4⋊C4—534no—
512C2×C4⋊C4—1062no—
513C2×C4⋊C4—1068no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4—1061no—
521C2×C4⋊C4—1061no—
522C2×C4⋊C4C22×D5311yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4—1061no—
528C2×C42—21no—
529C2×C42—531no—
530C2×C42—531no—
531C2×C42—531no—
532C2×C42—534no—
533C2×C42—534no—
534C2×C42—1068no—
535C2×C42—1061no—
536C2×C42—1061no—
537C2×C42—1061no—
538C2×C42—1061no—
539C2×C42C22×D5311yescharacteristic
540#107—534no—
541#107—534no—
542#106—534no—
543#106—534no—
544C4⋊C8—534no—
545C4⋊C8C22×D5314yes—
546#103—534no—
547#103—534no—
548#103—534no—
549#103—534no—
550#103—534no—
551#103C22×D5314yes—
552#102—534no—
553#102C22×D5314yes—
554C22⋊C8—534no—
555C22⋊C8—534no—
556C4×C8—534no—
557C4×C8—534no—
558C24—21no—
559C24—531no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—534no—
566C2×Q8—532no—
567C2×Q8—1064no—
568C2×Q8—1068no—
569C2×Q8—1068no—
570C2×Q8—10616no—
571C2×Q8—1068no—
572C2×Q8—1061no—
573C2×Q8—1062no—
574C2×Q8#1171994714yes—
575C2×Q8C23×D5312yes—
576C2×Q8C23×D5312yes—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—1064no—
581C2×D4—2124no—
582C2×D4C23×D5312yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—531no—
587C22×C4—531no—
588C22×C4—531no—
589C22×C4—534no—
590C22×C4—534no—
591C22×C4—532no—
592C22×C4—532no—
593C22×C4—1064no—
594C22×C4—1064no—
595C22×C4—1064no—
596C22×C4—1068no—
597C22×C4—1064no—
598C22×C4—1064no—
599C22×C4—1061no—
600C22×C4—1062no—
601C22×C4—1062no—
602C22×C4—1061no—
603C22×C4—1061no—
604C22×C4—1061no—
605C22×C4—2124no—
606C22×C4—2124no—
607C22×C4D4×D5311yescharacteristic
608C22×C4D4×D5311yescharacteristic
609C22×C4C23×D5311yescharacteristic
610Q16—28no—
611Q16—1068no—
612SD16—28no—
613SD16—1068no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—532no—
617C2×C8—532no—
618C2×C8—1062no—
619C2×C8—1062no—
620C2×C8C23×D5312yes—
621C2×C8C23×D5312yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—532no—
625C4⋊C4—532no—
626C4⋊C4—532no—
627C4⋊C4—1064no—
628C4⋊C4—1064no—
629C4⋊C4—1064no—
630C4⋊C4—1064no—
631C4⋊C4—1064no—
632C4⋊C4—1061no—
633C4⋊C4—1061no—
634C4⋊C4—1061no—
635C4⋊C4—1064no—
636C4⋊C4—1064no—
637C4⋊C4—1064no—
638C4⋊C4C23×D5312yes—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—1064no—
642C22⋊C4—1064no—
643C22⋊C4—1064no—
644C42—24no—
645C42—534no—
646C42—532no—
647C42—534no—
648C42—532no—
649C42—1064no—
650C42—1064no—
651C42—1064no—
652C42—1064no—
653C42D4×D5312yes—
654C42C23×D5312yes—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—534no—
660C23—532no—
661C23—1062no—
662C23—1062no—
663C23C2×D4×D5311yescharacteristic
664Q8—24no—
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—534no—
670Q8—10616no—
671Q8—1064no—
672Q8—1062no—
673Q8C2×#1171994714yes—
674D4—22no—
675D4—22no—
676D4—42no—
677D4—2128no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—534no—
687C2×C4—532no—
688C2×C4—532no—
689C2×C4—532no—
690C2×C4—1068no—
691C2×C4—1068no—
692C2×C4—10616no—
693C2×C4—1062no—
694C2×C4—1064no—
695C2×C4—1062no—
696C2×C4—1062no—
697C2×C4—1064no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—2128no—
704C2×C4—2128no—
705C2×C4—2122no—
706C2×C4—2122no—
707C2×C4—2122no—
708C2×C4C2×D4×D5312yes—
709C2×C4C2×D4×D5312yes—
710C2×C4C2×D4×D5311yescharacteristic
711C2×C4#41×D5312yes—
712C2×C4C2×#1171994712yes—
713C2×C4C24×D5311yescharacteristic
714C8—22no—
715C8—22no—
716C8—1062no—
717C8—1062no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—84no—
722C22—534no—
723C22—1068no—
724C22—1062no—
725C22—1062no—
726C22#1681113312yes—
727C22#135×D5312yes—
728C22#137×D5312yes—
729C22C22×D4×D5311yescharacteristic
730C4—22no—
731C4—22no—
732C4—24no—
733C4—42no—
734C4—42no—
735C4—534no—
736C4—1062no—
737C4—1062no—
738C4—1064no—
739C4—2122no—
740C4—2122no—
741C4—2122no—
742C4#1681113312yes—
743C4C2×#41×D5311yescharacteristic
744C4C22×#1171994711yescharacteristic
745C2—82no—
746C2—1064no—
747C2#2028479414yesdirect product factor
748C2C2×#1681113311yescharacteristic
749C2C2×#135×D5311yescharacteristic
750C2C2×#137×D5311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#464C2
socleC23×C53C22×D4
prime radicalC2×#13133188C22
hypercenterC2×#464D53
hypocenterC53C2×#3108
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D53C2semidirect
3. #20284794C2direct (N × H)
4. C2×#16810952C2semidirect
6. C2×#16810931C2semidirect
7. C2×#16810930C2semidirect
8. C2×#16810842C2semidirect
9. C2×#16810777C2semidirect
11. C2×Q16×Dic53C2semidirect
12. C2×#16810715C2semidirect
13. C2×#16810714C2semidirect
14. C2×SD16×Dic53C2semidirect
15. C2×#16810675C2semidirect
16. C2×C53×#464C2semidirect
34. C4×Q8×D53C22semidirect
42. #16810952C22semidirect
44. #16810931C22semidirect
45. #16810930C22semidirect
46. #16810842C22semidirect
47. #16810777C22semidirect
49. Q16×Dic53C22semidirect
50. #16810715C22semidirect
51. #16810714C22semidirect
52. SD16×Dic53C22semidirect
53. #16810675C22semidirect
73. C53×#464C22semidirect
378. C2×#464D53semidirect
387. C2×C53#3108semidirect
426. #464C2×D53semidirect
452. C53C2×#3108semidirect
747. C2#20284794direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111522
C2×C4×Q8×D532
#202847942
C2×#168109522
C2×#168109352
C2×#168109312
C2×#168109302
C2×#168108422
C2×#168107772
C2×#168107602
C2×Q16×Dic532
C2×#168107152
C2×#168107142
C2×SD16×Dic532
C2×#168106752
C2×C53×#4642
C2×#310853