Finite Group Databasebeta

← C2×#20284793 #28252173

Subgroups — C2×#20284793 #28252173

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×#16811155C211yesmaximal, characteristic
2C2×C4×Q8×D53C211yesmaximal, characteristic, complemented
3#20284793C2116yesmaximal, direct product factor
4C2×#16810955C211yesmaximal, characteristic, complemented
5C2×#16810935C211yesmaximal, characteristic
6C2×#16810933C211yesmaximal, characteristic, complemented
7C2×#16810932C211yesmaximal, characteristic, complemented
8C2×#16810844C211yesmaximal, characteristic, complemented
9C2×#16810843C211yesmaximal, characteristic, complemented
10C2×#16810780C211yesmaximal, characteristic, complemented
11C2×#16810760C211yesmaximal, characteristic
12C2×C4×Dic212C211yesmaximal, characteristic, complemented
13C2×C4×#11719925C211yesmaximal, characteristic, complemented
14C2×C4×#11719923C211yesmaximal, characteristic, complemented
15C2×#16810674C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C53C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18C22×Dic212C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719923C2211yescharacteristic
21#16811155—24no—
22#16811155C2218yes—
23C2×#13133210—21no—
24C2×#13133208C2211yescharacteristic
25C2×#13133204C2211yescharacteristic
26C2×#13133199—21no—
27C2×#13133197C2211yescharacteristic
28C2×#13133188C2211yescharacteristic
29C2×Q8×Dic53C2211yescharacteristic
30C2×C4×Dic106—21no—
31C2×C4×Dic106C2211yescharacteristic
32C2×C4×Dic106C2211yescharacteristic
33C2×#13133182—21no—
34C2×#13133182C2211yescharacteristic
35C4×Q8×D53—24no—
36C4×Q8×D53C2218yescomplemented
37C2×C4×C22⋊D53—21no—
38C2×#13133176—21no—
39C2×C4⋊C4×D53—21no—
40C2×C4⋊C4×D53C2211yescharacteristic
41C2×C42×D53—21no—
42C2×C42×D53C2211yescharacteristic
43#16810955C2218yescomplemented
44#16810935C2218yes—
45#16810933C2218yescomplemented
46#16810932C2218yescomplemented
47#16810844C2218yescomplemented
48#16810843C2218yescomplemented
49#16810780C2218yescomplemented
50#16810760C2218yes—
51C4×Dic212C2218yescomplemented
52C4×#11719925C2218yescomplemented
53C4×#11719923C2218yescomplemented
54#16810674C2218yescomplemented
55C2×#13133151C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C4×#88322C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C4×SD16×C53C2218yescomplemented
73C2×#106×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C4×C8×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C22×Dic106C2311yescharacteristic
80C2×Q8×D53—24no—
81C2×Q8×D53—22no—
82C2×Q8×D53—24no—
83C2×Q8×D53C2314yes—
84C22×C22⋊D53—21no—
85C22×C4×D53—21no—
86C22×C4×D53—21no—
87C22×C4×D53D411yescharacteristic
88C22×C4×D53D411yescharacteristic
89C22×C4×D53C2311yescharacteristic
90C2×Dic212—24no—
91C2×Dic212C2314yes—
92C2×#11719925—24no—
93C2×#11719925C2314yes—
94C2×#11719923—24no—
95C2×#11719923C2314yes—
96C22×#88322C2311yescharacteristic
97C22×#88322C2311yescharacteristic
98#13133210—28no—
99#13133208—22no—
100#13133208C2314yes—
101#13133204—22no—
102#13133204C2314yes—
103#13133199—28no—
104#13133197—22no—
105#13133197C2314yes—
106#13133188—22no—
107#13133188C2314yes—
108Q8×Dic53—22no—
109Q8×Dic53C2314yes—
110C4×Dic106—22no—
111C4×Dic106—22no—
112C4×Dic106—28no—
113C4×Dic106C2314yes—
114C4×Dic106C2314yes—
115#13133182—22no—
116#13133182—28no—
117#13133182C2314yes—
118C4×C22⋊D53—28no—
119#13133176—28no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C4⋊C4×D53—28no—
131C4⋊C4×D53—22no—
132C4⋊C4×D53C2314yes—
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53—21no—
136C2×#11719921—21no—
137C2×C4×Dic53—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53D411yescharacteristic
142C2×C4×Dic53D411yescharacteristic
143C2×C4×Dic53C2311yescharacteristic
144C42×D53—28no—
145C42×D53D414yes—
146C42×D53C2314yes—
147#13133151C2314yes—
148#13133150C2314yes—
149#13133148C2314yes—
150#13133146C2314yes—
151#13133146C2314yes—
152#13133142C2314yes—
153#13133142C2314yes—
154#13133141C2314yes—
155#13133140C2314yes—
156#13133140C2314yes—
157#13133138C2314yes—
158#13133129C2314yes—
159#13133129C2314yes—
160C4×#88322C2314yes—
161C22×Q8×C53C2311yescharacteristic
162C22×D4×C53C2311yescharacteristic
163C23×C4×C53—21no—
164C2×SD16×C53—24no—
165C2×SD16×C53C2314yes—
166C22×C8×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C4×Q8×C53—22no—
169C4×Q8×C53C2314yes—
170C4×D4×C53—22no—
171C4×D4×C53C2314yes—
172C2×C4⋊C4×C53—21no—
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C42×C53—21no—
177C2×C42×C53C2311yescharacteristic
178#106×C53C2314yes—
179#103×C53C2314yes—
180#102×C53C2314yes—
181C4×C8×C53C2314yes—
182C24×C53—21no—
183C23×D53C2×D411yescharacteristic
184C2×Q8×C53—21no—
185C2×Q8×C53—22no—
186C2×Q8×C53#4114yes—
187C2×Q8×C53C2412yes—
188C2×D4×C53—21no—
189C2×D4×C53—22no—
190C2×D4×C53—22no—
191C2×D4×C53C2412yes—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—24no—
196C22×C4×C53—44no—
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2411yescharacteristic
200C2×C22⋊D53—24no—
201C2×C22⋊D53—44no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C22×Dic53C2×D411yescharacteristic
209Q8×D53—216no—
210Q8×D53—28no—
211Q8×D53—28no—
212C2×C4×D53—28no—
213C2×C4×D53—24no—
214C2×C4×D53—24no—
215C2×C4×D53—24no—
216C2×C4×D53—22no—
217C2×C4×D53—22no—
218C2×C4×D53—24no—
219C2×C4×D53—44no—
220C2×C4×D53C2×D414yes—
221C2×C4×D53C2×D412yes—
222C2×C4×D53C2×D414yes—
223C2×C4×D53C2412yes—
224C2×Dic106—28no—
225C2×Dic106—21no—
226C2×Dic106—22no—
227C2×Dic106—24no—
228C2×Dic106—22no—
229C2×Dic106—22no—
230C2×Dic106—21no—
231C2×Dic106#4114yes—
232C2×Dic106C2412yes—
233C2×Dic106C2412yes—
234SD16×C53—28no—
235C2×C8×C53—22no—
236C2×C8×C53—22no—
237C2×C8×C53C2412yes—
238C2×C8×C53C2412yes—
239C4⋊C4×C53—24no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53—21no—
242C4⋊C4×C53C2412yes—
243C4⋊C4×C53C2412yes—
244C22⋊C4×C53—24no—
245C42×C53—24no—
246C42×C53C2×D412yes—
247C42×C53C2412yes—
248C22⋊Dic53—24no—
249C22⋊Dic53—24no—
250C22⋊Dic53—24no—
251#11719925—28no—
252#11719923—28no—
253#11719921—24no—
254C4⋊Dic53—21no—
255C4⋊Dic53—21no—
256C4⋊Dic53—24no—
257C4⋊Dic53—24no—
258C4⋊Dic53—24no—
259C4⋊Dic53C2412yes—
260C4⋊Dic53C2412yes—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264#11719919—24no—
265#11719919—24no—
266C4×Dic53—24no—
267C4×Dic53—24no—
268C4×Dic53—24no—
269C4×Dic53—24no—
270C4×Dic53C2×D412yes—
271C4×Dic53C2×D414yes—
272C4×Dic53C2×D414yes—
273C4×Dic53C2412yes—
274C2×#88322—22no—
275C2×#88322—22no—
276C2×#88322C2412yes—
277C2×#88322C2412yes—
278Dic212—28no—
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×C53C2×#4114yes—
291D4×C53—22no—
292D4×C53—22no—
293D4×C53—42no—
294C2×C4×C53—24no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53—48no—
302C2×C4×C53#13714yes—
303C2×C4×C53C22×D412yes—
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53C22×D412yes—
306C2×C4×C53C2×#4112yes—
307C2×C4×C53C2×#4112yes—
308C2×C4×C53C2511yescharacteristic
309C22⋊D53—48no—
310C2×Dic53—22no—
311C2×Dic53—24no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—42no—
321C2×Dic53C22×D412yes—
322C2×Dic53C22×D412yes—
323C2×Dic53C22×D412yes—
324C4×D53—216no—
325C4×D53—28no—
326C4×D53—24no—
327C4×D53—28no—
328C4×D53—22no—
329C4×D53—22no—
330C4×D53—48no—
331Dic106—216no—
332Dic106—24no—
333Dic106—22no—
334Dic106—22no—
335Dic106—22no—
336Dic106—42no—
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—42no—
358C4×C53—42no—
359C4×C53#52512yes—
360C4×C53C2×#13714yes—
361C4×C53C22×#4111yescharacteristic
362C4×C53C22×#4111yescharacteristic
363Dic53—22no—
364Dic53—24no—
365Dic53—22no—
366Dic53—22no—
367Dic53—42no—
368Dic53—42no—
369Dic53—42no—
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×#464—531no—
379C2×#451—531no—
380C2×#448—531no—
381C2×C4×Q16—531no—
382C2×C4×Q16—531no—
383C2×C4×SD16—531no—
384C2×C4×SD16D5311yescharacteristic, complemented
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×Q16—531no—
395C22×SD16—531no—
396C22×SD16C2×D5311yescharacteristic
397#529—538no—
398#529—1064no—
399C2×#126—1061no—
400C2×#125—531no—
401C2×#124—531no—
402C2×#123—1061no—
403C2×C22⋊Q8—531no—
404C2×#121—531no—
405C2×C4×Q8—531no—
406C2×C4×Q8—538no—
407C2×C4×Q8—531no—
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—1061no—
415C2×C4×D4C2×D5311yescharacteristic
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#464—538no—
427#451—538no—
428#448—538no—
429C4×Q16—538no—
430C4×Q16—538no—
431C4×SD16—538no—
432C4×SD16C2×D5318yescomplemented
433#431—538no—
434C2×#107—531no—
435C2×#107—531no—
436C2×#106—531no—
437C2×#106C2×D5311yescharacteristic
438C2×C4⋊C8—531no—
439C2×C4⋊C8—531no—
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×C8C2×D5311yescharacteristic
452C53C2×#310811yescharacteristic, complemented, Sylow
453C22×Q8—534no—
454C22×Q8—531no—
455C22×Q8—531no—
456C22×Q8—1061no—
457C22×Q8—1062no—
458C22×Q8—1064no—
459C22×Q8—1064no—
460C22×Q8C22×D5311yescharacteristic
461C22×D4—1061no—
462C22×D4C22×D5311yescharacteristic
463C23×C4—21no—
464C23×C4—531no—
465C23×C4—531no—
466C23×C4—531no—
467C23×C4—1061no—
468C23×C4—1061no—
469C2×Q16—534no—
470C2×Q16—534no—
471C2×Q16—1064no—
472C2×Q16—1064no—
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—534no—
485#124—1062no—
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—1062no—
498C4×Q8—1068no—
499C4×Q8—1062no—
500C4×Q8—1062no—
501C4×Q8—1062no—
502C4×Q8C22×D5314yes—
503C4×D4—22no—
504C4×D4—1068no—
505C4×D4C22×D5314yes—
506#117—1068no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—531no—
509C2×C4⋊C4—531no—
510C2×C4⋊C4—534no—
511C2×C4⋊C4—1062no—
512C2×C4⋊C4—1068no—
513C2×C4⋊C4—1061no—
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⋊C4C22×D5311yescharacteristic
522C2×C4⋊C4C22×D5311yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—1061no—
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#106C22×D5314yes—
544C4⋊C8—534no—
545C4⋊C8—534no—
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×C8C22×D5314yes—
558C24—21no—
559C24—531no—
560C2×Q8—21no—
561C2×Q8—22no—
562C2×Q8—534no—
563C2×Q8—532no—
564C2×Q8—532no—
565C2×Q8—1064no—
566C2×Q8—1068no—
567C2×Q8—1068no—
568C2×Q8—10616no—
569C2×Q8—1068no—
570C2×Q8—1061no—
571C2×Q8—1061no—
572C2×Q8—1062no—
573C2×Q8—1062no—
574C2×Q8—1062no—
575C2×Q8#1171994514yes—
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—24no—
587C22×C4—44no—
588C22×C4—531no—
589C22×C4—531no—
590C22×C4—531no—
591C22×C4—534no—
592C22×C4—534no—
593C22×C4—532no—
594C22×C4—532no—
595C22×C4—1064no—
596C22×C4—1064no—
597C22×C4—1068no—
598C22×C4—1064no—
599C22×C4—1061no—
600C22×C4—1064no—
601C22×C4—1062no—
602C22×C4—1062no—
603C22×C4—1061no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4—2124no—
607C22×C4D4×D5311yescharacteristic
608C22×C4D4×D5311yescharacteristic
609C22×C4C23×D5311yescharacteristic
610Q16—1068no—
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—21no—
625C4⋊C4—532no—
626C4⋊C4—532no—
627C4⋊C4—1064no—
628C4⋊C4—1064no—
629C4⋊C4—1064no—
630C4⋊C4—1064no—
631C4⋊C4—1064no—
632C4⋊C4—1064no—
633C4⋊C4—1061no—
634C4⋊C4—1061no—
635C4⋊C4—1064no—
636C4⋊C4—1064no—
637C4⋊C4C23×D5312yes—
638C4⋊C4C23×D5312yes—
639C22⋊C4—24no—
640C22⋊C4—1064no—
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—534no—
667Q8—10616no—
668Q8—1064no—
669Q8—1062no—
670Q8—1062no—
671Q8—1062no—
672Q8—2122no—
673Q8C2×#1171994514yes—
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—42no—
684C2×C4—42no—
685C2×C4—48no—
686C2×C4—532no—
687C2×C4—532no—
688C2×C4—532no—
689C2×C4—1068no—
690C2×C4—10616no—
691C2×C4—1062no—
692C2×C4—1064no—
693C2×C4—1062no—
694C2×C4—1062no—
695C2×C4—1062no—
696C2×C4—1064no—
697C2×C4—1068no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—2128no—
704C2×C4—2122no—
705C2×C4—2122no—
706C2×C4—2122no—
707C2×C4#1313324614yes—
708C2×C4C2×D4×D5312yes—
709C2×C4C2×D4×D5311yescharacteristic
710C2×C4C2×D4×D5312yes—
711C2×C4#41×D5312yes—
712C2×C4C2×#1171994512yes—
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#1681113212yes—
727C22#135×D5312yes—
728C22C2×#1313324612yes—
729C22C22×D4×D5311yescharacteristic
730C4—22no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—1062no—
735C4—1062no—
736C4—1062no—
737C4—1064no—
738C4—2122no—
739C4—2122no—
740C4—2122no—
741C4#1681113212yes—
742C4C2×#1313324614yes—
743C4C2×#41×D5311yescharacteristic
744C4C22×#1171994511yescharacteristic
745C2—82no—
746C2—1064no—
747C2#2028479314yesdirect product factor
748C2C2×#1681113211yescharacteristic
749C2C2×#135×D5311yescharacteristic
750C2C22×#1313324611yescharacteristic
subgroupG/H
centerC22×C4D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C4×SD16×C53C2
socleC23×C53C22×D4
prime radicalC2×#13133188C22
hypercenterC2×C4×SD16D53
hypocenterC53C2×#3108
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D53C2semidirect
3. #20284793C2direct (N × H)
4. C2×#16810955C2semidirect
6. C2×#16810933C2semidirect
7. C2×#16810932C2semidirect
8. C2×#16810844C2semidirect
9. C2×#16810843C2semidirect
10. C2×#16810780C2semidirect
12. C2×C4×Dic212C2semidirect
13. C2×C4×#11719925C2semidirect
14. C2×C4×#11719923C2semidirect
15. C2×#16810674C2semidirect
16. C2×C4×SD16×C53C2semidirect
36. C4×Q8×D53C22semidirect
43. #16810955C22semidirect
45. #16810933C22semidirect
46. #16810932C22semidirect
47. #16810844C22semidirect
48. #16810843C22semidirect
49. #16810780C22semidirect
51. C4×Dic212C22semidirect
52. C4×#11719925C22semidirect
53. C4×#11719923C22semidirect
54. #16810674C22semidirect
72. C4×SD16×C53C22semidirect
384. C2×C4×SD16D53semidirect
387. C2×C53#3108semidirect
432. C4×SD16C2×D53semidirect
452. C53C2×#3108semidirect
747. C2#20284793direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111552
C2×C4×Q8×D532
#202847932
C2×#168109552
C2×#168109352
C2×#168109332
C2×#168109322
C2×#168108442
C2×#168108432
C2×#168107802
C2×#168107602
C2×C4×Dic2122
C2×C4×#117199252
C2×C4×#117199232
C2×#168106742
C2×C4×SD16×C532
C2×#310853