Finite Group Databasebeta

← C2×#20284961 #28252390

Subgroups — C2×#20284961 #28252390

Order 13568.

2210 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811233C211yesmaximal, characteristic, complemented
2C2×#16811098C211yesmaximal, characteristic
3#20284961C2116yesmaximal, direct product factor
4C2×#16810965C211yesmaximal, characteristic, complemented
5C2×#16810961C211yesmaximal, characteristic, complemented
6C2×#16810925C211yesmaximal, characteristic, complemented
7C2×#16810921C211yesmaximal, characteristic, complemented
8C2×#16810826C211yesmaximal, characteristic, complemented
9C2×#16810826C211yesmaximal, characteristic, complemented
10C2×#16810774C211yesmaximal, characteristic
11C2×#16810724C211yesmaximal, characteristic, complemented
12C2×#16810720C211yesmaximal, characteristic, complemented
13C2×#16810714C211yesmaximal, characteristic, complemented
14C2×SD16×Dic53C211yesmaximal, characteristic, complemented
15C2×#16810681C211yesmaximal, characteristic, complemented
16C2×C53×#450C211yesmaximal, characteristic
17C22×#11719923C2211yescharacteristic
18C22×#11719923C2211yescharacteristic
19#16811233—24no—
20#16811233C2218yescomplemented
21C2×#13133215C2211yescharacteristic, complemented
22C2×#13133210—21no—
23C2×#13133210—21no—
24C2×#13133208—21no—
25C2×#13133208C2211yescharacteristic, complemented
26C2×#13133207—21no—
27C2×#13133196C2211yescharacteristic
28#16811098—24no—
29#16811098C2218yes—
30C2×Q8×Dic53C2211yescharacteristic, complemented
31C2×#13133182C2211yescharacteristic, complemented
32C2×D4×Dic53—21no—
33C2×D4×Dic53—21no—
34C2×D4×Dic53C2211yescharacteristic
35C2×D4×Dic53C2211yescharacteristic
36C2×D4×Dic53C2211yescharacteristic
37C2×D4×Dic53C2211yescharacteristic
38C2×#13133176C2211yescharacteristic
39C2×#13133176C2211yescharacteristic
40C22×C22⋊Dic53—21no—
41C22×C22⋊Dic53—21no—
42#16810965C2218yescomplemented
43#16810961C2218yescomplemented
44#16810925C2218yescomplemented
45#16810921C2218yescomplemented
46#16810826C2218yescomplemented
47#16810826C2218yescomplemented
48#16810774C2218yes—
49#16810724C2218yescomplemented
50#16810720C2218yescomplemented
51#16810714C2218yescomplemented
52SD16×Dic53C2218yescomplemented
53#16810681C2218yescomplemented
54C2×#13133151C2211yescharacteristic, complemented
55C2×#13133150C2211yescharacteristic, complemented
56C2×#13133149C2211yescharacteristic, complemented
57C2×#13133148C2211yescharacteristic, complemented
58C2×#13133146C2211yescharacteristic, complemented
59C2×#13133146C2211yescharacteristic, complemented
60C2×#13133142C2211yescharacteristic, complemented
61C2×#13133142C2211yescharacteristic, complemented
62C2×#13133141C2211yescharacteristic, complemented
63C2×#13133141C2211yescharacteristic, complemented
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133127C2211yescharacteristic, complemented
68C2×C8×Dic53C2211yescharacteristic, complemented
69C23×D4×C53C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic
71C22×SD16×C53C2211yescharacteristic
72C2×C22⋊Q8×C53C2211yescharacteristic
73C53×#450C2218yes—
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C22×Dic106C2311yescharacteristic
78C23×Dic53—21no—
79C23×Dic53—21no—
80C23×Dic53—21no—
81C23×Dic53—21no—
82C2×#11719923—24no—
83C2×#11719923—24no—
84C2×#11719923C2314yes—
85C2×#11719923C2314yes—
86C22×#88322C2311yescharacteristic
87C22×#88322C2311yescharacteristic
88#13133215—22no—
89#13133215C2314yescomplemented
90#13133210—28no—
91#13133210—28no—
92#13133208—28no—
93#13133208—22no—
94#13133208C2314yescomplemented
95#13133207—28no—
96#13133196—22no—
97#13133196C2314yes—
98Q8×Dic53—22no—
99Q8×Dic53C2314yescomplemented
100#13133182—22no—
101#13133182C2314yescomplemented
102D4×Dic53—28no—
103D4×Dic53—28no—
104D4×Dic53—22no—
105D4×Dic53—22no—
106D4×Dic53—22no—
107D4×Dic53—22no—
108D4×Dic53C2314yes—
109D4×Dic53C2314yes—
110D4×Dic53C2314yes—
111D4×Dic53C2314yes—
112#13133176—22no—
113#13133176D414yes—
114#13133176C2314yes—
115#13133176C2314yes—
116C2×C4⋊Dic53—21no—
117C2×C4⋊Dic53—21no—
118C2×C4⋊Dic53D411yescharacteristic
119C2×C4⋊Dic53D411yescharacteristic
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×C22⋊Dic53—28no—
129C2×C22⋊Dic53—28no—
130C2×C22⋊Dic53—21no—
131C2×C22⋊Dic53—21no—
132C2×C22⋊Dic53—21no—
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53D411yescharacteristic
137C2×C22⋊Dic53D411yescharacteristic
138C2×C4×Dic53—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53C2311yescharacteristic
142C2×C4×Dic53C2311yescharacteristic
143#13133151C2314yescomplemented
144#13133150C2314yescomplemented
145#13133149C2314yescomplemented
146#13133148C2314yescomplemented
147#13133146C2314yescomplemented
148#13133146C2314yescomplemented
149#13133142C2314yescomplemented
150#13133142C2314yescomplemented
151#13133141C2314yescomplemented
152#13133141C2314yescomplemented
153#13133138C2314yes—
154#13133138C2314yes—
155C22⋊#88322C2314yes—
156#13133127C2314yescomplemented
157C8×Dic53C2314yescomplemented
158C25×C53—21no—
159C22×Q8×C53C2311yescharacteristic
160C22×D4×C53—24no—
161C22×D4×C53—24no—
162C22×D4×C53—21no—
163C22×D4×C53—22no—
164C22×D4×C53C2314yes—
165C22×D4×C53C2311yescharacteristic
166C22×D4×C53C2311yescharacteristic
167C23×C4×C53C2311yescharacteristic
168C2×SD16×C53—24no—
169C2×SD16×C53—24no—
170C2×SD16×C53C2314yes—
171C2×SD16×C53C2314yes—
172C22×C8×C53C2311yescharacteristic
173C22×C8×C53C2311yescharacteristic
174C22⋊Q8×C53—22no—
175C22⋊Q8×C53C2314yes—
176C2×C4⋊C4×C53—21no—
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C22⋊C4×C53—21no—
179#102×C53C2314yes—
180#102×C53C2314yes—
181C22⋊C8×C53C2314yes—
182C24×C53—28no—
183C24×C53—21no—
184C24×C53—21no—
185C24×C53—24no—
186C24×C53—82no—
187C24×C53—82no—
188C24×C53C2×D411yescharacteristic
189C2×Q8×C53—21no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53C2412yes—
193C2×D4×C53—28no—
194C2×D4×C53—216no—
195C2×D4×C53—28no—
196C2×D4×C53—28no—
197C2×D4×C53—24no—
198C2×D4×C53—21no—
199C2×D4×C53—21no—
200C2×D4×C53—22no—
201C2×D4×C53—22no—
202C2×D4×C53#4114yes—
203C2×D4×C53#4114yes—
204C2×D4×C53C2412yes—
205C2×D4×C53C2412yes—
206C22×C4×C53—22no—
207C22×C4×C53—22no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53C2×D411yescharacteristic
211C22×C4×C53C2×D412yes—
212C22×C4×C53C2412yes—
213C22×C4×C53C2411yescharacteristic
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—24no—
219C22×Dic53—24no—
220C22×Dic53—24no—
221C22×Dic53—24no—
222C22×Dic53—82no—
223C22×Dic53—82no—
224C22×Dic53—82no—
225C22×Dic53—82no—
226C22×Dic53C2×D411yescharacteristic
227C22×Dic53C2×D411yescharacteristic
228C22×Dic53C2×D411yescharacteristic
229C22×Dic53C2×D411yescharacteristic
230C2×Dic106—22no—
231C2×Dic106—22no—
232C2×Dic106—21no—
233C2×Dic106C2412yes—
234SD16×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⋊Dic53—24no—
245C22⋊Dic53—24no—
246C22⋊Dic53—24no—
247C22⋊Dic53—24no—
248C22⋊Dic53—24no—
249C22⋊Dic53—24no—
250C22⋊Dic53C2×D414yes—
251C22⋊Dic53C2×D414yes—
252#11719923—28no—
253#11719923—28no—
254C4⋊Dic53—21no—
255C4⋊Dic53—21no—
256C4⋊Dic53—21no—
257C4⋊Dic53—24no—
258C4⋊Dic53—24no—
259C4⋊Dic53C2×D414yes—
260C4⋊Dic53C2×D414yes—
261C4⋊Dic53C2412yes—
262C4⋊Dic53C2412yes—
263C4⋊Dic53C2412yes—
264#11719919—24no—
265#11719919—24no—
266#11719919—24no—
267#11719919—24no—
268#11719919—24no—
269C4×Dic53—24no—
270C4×Dic53—24no—
271C4×Dic53—24no—
272C4×Dic53C2×D412yes—
273C4×Dic53C2×D412yes—
274C4×Dic53C2412yes—
275C4×Dic53C2412yes—
276C2×#88322—22no—
277C2×#88322—22no—
278C2×#88322C2412yes—
279C2×#88322C2412yes—
280C23×C53—216no—
281C23×C53—22no—
282C23×C53—24no—
283C23×C53—24no—
284C23×C53—22no—
285C23×C53—22no—
286C23×C53—22no—
287C23×C53—22no—
288C23×C53—42no—
289C23×C53—42no—
290C23×C53—42no—
291C23×C53—42no—
292C23×C53—84no—
293C23×C53—84no—
294C23×C53—816no—
295C23×C53C22×D412yes—
296C23×C53C22×D411yescharacteristic
297Q8×C53—22no—
298Q8×C53—22no—
299Q8×C53—42no—
300D4×C53—216no—
301D4×C53—24no—
302D4×C53—24no—
303D4×C53—22no—
304D4×C53—22no—
305D4×C53C2×#4114yes—
306D4×C53C2×#4114yes—
307C2×C4×C53—22no—
308C2×C4×C53—24no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53C22×D412yes—
316C2×C4×C53C22×D411yescharacteristic
317C2×C4×C53C2×#4112yes—
318C2×C4×C53C2×#4112yes—
319C2×C4×C53C2511yescharacteristic
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53—84no—
333C2×Dic53—84no—
334C2×Dic53—84no—
335C2×Dic53—84no—
336C2×Dic53C22×D412yes—
337C2×Dic53C22×D412yes—
338C2×Dic53C22×D412yes—
339C2×Dic53C22×D412yes—
340Dic106—22no—
341Dic106—22no—
342Dic106—42no—
343C8×C53—22no—
344C8×C53—22no—
345#88322—22no—
346#88322—22no—
347C2×#3123—531nomaximal, Sylow
348C22×C53—22no—
349C22×C53—24no—
350C22×C53—24no—
351C22×C53—22no—
352C22×C53—22no—
353C22×C53—44no—
354C22×C53—48no—
355C22×C53—48no—
356C22×C53—42no—
357C22×C53—42no—
358C22×C53—42no—
359C22×C53—42no—
360C22×C53—816no—
361C22×C53#52512yes—
362C22×C53#57712yes—
363C22×C53#57712yes—
364C22×C53C23×D411yescharacteristic
365C4×C53—22no—
366C4×C53—42no—
367C4×C53—42no—
368C4×C53#52512yes—
369C4×C53C22×#4111yescharacteristic
370C4×C53C22×#4111yescharacteristic
371Dic53—22no—
372Dic53—22no—
373Dic53—22no—
374Dic53—22no—
375Dic53—42no—
376Dic53—42no—
377Dic53—42no—
378Dic53—42no—
379C2×#541—531no—
380C2×#518—531no—
381#3123—5316no—
382C2×#485—531no—
383C2×#485—531no—
384C2×#478—531no—
385C2×#478—531no—
386C2×#461—531no—
387C2×#461—531no—
388C2×#450—531no—
389C2×#450D5311yescharacteristic
390C2×#440—531no—
391C2×#440—531no—
392C2×C4×SD16—531no—
393C2×C4×SD16—531no—
394C2×#433—531no—
395C2×C53—42no—
396C2×C53—44no—
397C2×C53—44no—
398C2×C53#312314yescomplemented
399C2×C53C2×#52511yescharacteristic
400C2×C53C2×#57711yescharacteristic
401C2×C53C2×#57711yescharacteristic
402C23×D4C2×D5311yescharacteristic
403C22×SD16—531no—
404C22×SD16—531no—
405C22×SD16C2×D5311yescharacteristic
406C22×SD16C2×D5311yescharacteristic
407#541—538no—
408#541—1064no—
409C2×C4⋊Q8—531no—
410C2×#126—1061no—
411C2×#126—1061no—
412C2×#125—531no—
413C2×#125—1061no—
414C2×#125—1061no—
415C2×C22⋊Q8—531no—
416C2×C22⋊Q8C2×D5311yescharacteristic
417#518—538no—
418#518—1064no—
419C2×C4×Q8—531no—
420C2×C4×Q8—531no—
421C2×C4×D4—531no—
422C2×C4×D4—531no—
423C2×C4×D4—531no—
424C2×C4×D4—531no—
425C2×C4×D4—1061no—
426C2×C4×D4—1061no—
427C2×#117—531no—
428C2×#117—531no—
429C22×C22⋊C4—1061no—
430C22×C22⋊C4—1061no—
431#485—538no—
432#485—538no—
433#478—538no—
434#478—538no—
435#461—538no—
436#461—538no—
437#450—538no—
438#450C2×D5318yes—
439#440—538no—
440#440—538no—
441C4×SD16—538no—
442C4×SD16—538no—
443#433—538no—
444C2×#107—531no—
445C2×#107—531no—
446C2×#106—531no—
447C2×#106—531no—
448C2×C4⋊C8—531no—
449C2×C4⋊C8—531no—
450C2×#103—531no—
451C2×#103—531no—
452C2×#103—531no—
453C2×#103—531no—
454C2×#102—531no—
455C2×#102—531no—
456C2×#102C2×D5311yescharacteristic
457C2×#102C2×D5311yescharacteristic
458C2×C22⋊C8—531no—
459C2×C22⋊C8C2×D5311yescharacteristic
460C2×#97—531no—
461C2×C4×C8—531no—
462C53C2×#312311yescharacteristic, complemented, Sylow
463C25—21no—
464C22×Q8—531no—
465C22×Q8C22×D5311yescharacteristic
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—21no—
469C22×D4—22no—
470C22×D4C22×D5314yes—
471C22×D4C22×D5311yescharacteristic
472C22×D4C22×D5311yescharacteristic
473C23×C4—1061no—
474C23×C4—1061no—
475C23×C4—1061no—
476C23×C4—1061no—
477C23×C4C22×D5311yescharacteristic
478C2×SD16—24no—
479C2×SD16—24no—
480C2×SD16—534no—
481C2×SD16—534no—
482C2×SD16—1064no—
483C2×SD16—1064no—
484C2×SD16C22×D5314yes—
485C2×SD16C22×D5314yes—
486C22×C8—531no—
487C22×C8—531no—
488C22×C8C22×D5311yescharacteristic
489C22×C8C22×D5311yescharacteristic
490C4⋊Q8—534no—
491C4⋊Q8—1062no—
492#126—1068no—
493#126—1068no—
494#125—534no—
495#125—1062no—
496#125—1068no—
497#125—1068no—
498C22⋊Q8—22no—
499C22⋊Q8—534no—
500C22⋊Q8—1062no—
501C22⋊Q8C22×D5314yes—
502C4×Q8—534no—
503C4×Q8—534no—
504C4×Q8—1062no—
505C4×Q8—1062no—
506C4×D4—534no—
507C4×D4—534no—
508C4×D4—534no—
509C4×D4—534no—
510C4×D4—1062no—
511C4×D4—1062no—
512C4×D4—1062no—
513C4×D4—1062no—
514C4×D4—1068no—
515C4×D4—1068no—
516#117—534no—
517#117—534no—
518#117—534no—
519#117—1062no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—531no—
522C2×C4⋊C4—531no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—531no—
525C2×C4⋊C4—531no—
526C2×C4⋊C4—1061no—
527C2×C4⋊C4—1061no—
528C2×C4⋊C4—1061no—
529C2×C4⋊C4—1061no—
530C2×C4⋊C4—1061no—
531C2×C4⋊C4—1061no—
532C2×C4⋊C4—1061no—
533C2×C4⋊C4C22×D5311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—531no—
536C2×C22⋊C4—531no—
537C2×C22⋊C4—1068no—
538C2×C22⋊C4—1068no—
539C2×C22⋊C4—1061no—
540C2×C22⋊C4—1061no—
541C2×C22⋊C4—1061no—
542C2×C22⋊C4—1061no—
543C2×C22⋊C4—1061no—
544C2×C22⋊C4—1061no—
545C2×C42—531no—
546C2×C42—531no—
547C2×C42—1061no—
548C2×C42—1061no—
549C2×C42—1061no—
550#107—534no—
551#107—534no—
552#106—534no—
553#106—534no—
554C4⋊C8—534no—
555C4⋊C8—534no—
556#103—534no—
557#103—534no—
558#103—534no—
559#103—534no—
560#102—534no—
561#102—534no—
562#102C22×D5314yes—
563#102C22×D5314yes—
564C22⋊C8—534no—
565C22⋊C8C22×D5314yes—
566#97—534no—
567C4×C8—534no—
568C24—28no—
569C24—21no—
570C24—21no—
571C24—24no—
572C24—82no—
573C24—82no—
574C24D4×D5311yescharacteristic
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—532no—
579C2×Q8—1061no—
580C2×Q8—1062no—
581C2×Q8—1062no—
582C2×Q8C23×D5312yes—
583C2×D4—28no—
584C2×D4—216no—
585C2×D4—28no—
586C2×D4—28no—
587C2×D4—24no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4#1171994714yes—
593C2×D4#1171994714yes—
594C2×D4C23×D5312yes—
595C2×D4C23×D5312yes—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—531no—
601C22×C4—531no—
602C22×C4—531no—
603C22×C4—531no—
604C22×C4—1064no—
605C22×C4—1064no—
606C22×C4—1064no—
607C22×C4—1064no—
608C22×C4—1061no—
609C22×C4—1061no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4—4242no—
613C22×C4—4242no—
614C22×C4—4242no—
615C22×C4—4242no—
616C22×C4D4×D5312yes—
617C22×C4D4×D5311yescharacteristic
618C22×C4C23×D5312yes—
619C22×C4C23×D5311yescharacteristic
620SD16—28no—
621SD16—28no—
622SD16—1068no—
623SD16—1068no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—532no—
627C2×C8—532no—
628C2×C8—1062no—
629C2×C8—1062no—
630C2×C8C23×D5312yes—
631C2×C8C23×D5312yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—534no—
635C4⋊C4—534no—
636C4⋊C4—532no—
637C4⋊C4—532no—
638C4⋊C4—532no—
639C4⋊C4—1064no—
640C4⋊C4—1064no—
641C4⋊C4—1064no—
642C4⋊C4—1064no—
643C4⋊C4—1064no—
644C4⋊C4—1064no—
645C4⋊C4—1061no—
646C4⋊C4—1061no—
647C4⋊C4—1061no—
648C4⋊C4—1064no—
649C4⋊C4C23×D5312yes—
650C22⋊C4—24no—
651C22⋊C4—534no—
652C22⋊C4—534no—
653C22⋊C4—1064no—
654C22⋊C4—1064no—
655C22⋊C4—1064no—
656C22⋊C4—1064no—
657C22⋊C4—1064no—
658C22⋊C4—1064no—
659C42—532no—
660C42—532no—
661C42—532no—
662C42—532no—
663C42—1064no—
664C42—1064no—
665C42—1064no—
666C23—216no—
667C23—22no—
668C23—24no—
669C23—24no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—84no—
679C23—84no—
680C23—816no—
681C23C2×D4×D5312yes—
682C23C2×D4×D5311yescharacteristic
683Q8—22no—
684Q8—22no—
685Q8—42no—
686Q8—1062no—
687Q8—1062no—
688Q8—2122no—
689D4—216no—
690D4—24no—
691D4—24no—
692D4—22no—
693D4—22no—
694D4C2×#1171994714yes—
695D4C2×#1171994714yes—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—532no—
705C2×C4—532no—
706C2×C4—532no—
707C2×C4—532no—
708C2×C4—1062no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—1062no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—4244no—
717C2×C4—4244no—
718C2×C4—4244no—
719C2×C4—4244no—
720C2×C4—2122no—
721C2×C4—2122no—
722C2×C4—2122no—
723C2×C4—2122no—
724C2×C4C2×D4×D5312yes—
725C2×C4C2×D4×D5311yescharacteristic
726C2×C4C2×#1171994712yes—
727C2×C4C2×#1171994712yes—
728C2×C4C24×D5311yescharacteristic
729C8—22no—
730C8—22no—
731C8—1062no—
732C8—1062no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—24no—
737C22—24no—
738C22—44no—
739C22—48no—
740C22—48no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—816no—
746C22#1681112912yes—
747C22#1681142912yes—
748C22#1681143312yes—
749C22C22×D4×D5311yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—1062no—
754C4—1062no—
755C4—1062no—
756C4—1062no—
757C4—2122no—
758C4—2122no—
759C4—2122no—
760C4—2122no—
761C4#1681112912yes—
762C4C22×#1171994711yescharacteristic
763C4C22×#1171994711yescharacteristic
764C2—42no—
765C2—44no—
766C2—44no—
767C2#2028496114yesdirect product factor
768C2C2×#1681112911yescharacteristic
769C2C2×#1681142911yescharacteristic
770C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#450C2
socleC23×C53C22×D4
prime radicalC23×D4×C53C22
hypercenterC2×#450D53
hypocenterC53C2×#3123
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×#16811233C2semidirect
3. #20284961C2direct (N × H)
4. C2×#16810965C2semidirect
5. C2×#16810961C2semidirect
6. C2×#16810925C2semidirect
7. C2×#16810921C2semidirect
8. C2×#16810826C2semidirect
9. C2×#16810826C2semidirect
11. C2×#16810724C2semidirect
12. C2×#16810720C2semidirect
13. C2×#16810714C2semidirect
14. C2×SD16×Dic53C2semidirect
15. C2×#16810681C2semidirect
20. #16811233C22semidirect
21. C2×#13133215C22semidirect
25. C2×#13133208C22semidirect
30. C2×Q8×Dic53C22semidirect
31. C2×#13133182C22semidirect
42. #16810965C22semidirect
43. #16810961C22semidirect
44. #16810925C22semidirect
45. #16810921C22semidirect
46. #16810826C22semidirect
47. #16810826C22semidirect
49. #16810724C22semidirect
50. #16810720C22semidirect
51. #16810714C22semidirect
52. SD16×Dic53C22semidirect
53. #16810681C22semidirect
54. C2×#13133151C22semidirect
55. C2×#13133150C22semidirect
56. C2×#13133149C22semidirect
57. C2×#13133148C22semidirect
58. C2×#13133146C22semidirect
59. C2×#13133146C22semidirect
60. C2×#13133142C22semidirect
61. C2×#13133142C22semidirect
62. C2×#13133141C22semidirect
63. C2×#13133141C22semidirect
67. C2×#13133127C22semidirect
68. C2×C8×Dic53C22semidirect
89. #13133215C23semidirect
94. #13133208C23semidirect
99. Q8×Dic53C23semidirect
101. #13133182C23semidirect
143. #13133151C23semidirect
144. #13133150C23semidirect
145. #13133149C23semidirect
146. #13133148C23semidirect
147. #13133146C23semidirect
148. #13133146C23semidirect
149. #13133142C23semidirect
150. #13133142C23semidirect
151. #13133141C23semidirect
152. #13133141C23semidirect
156. #13133127C23semidirect
157. C8×Dic53C23semidirect
398. C2×C53#3123semidirect
462. C53C2×#3123semidirect
767. C2#20284961direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112332
C2×#168110982
#202849612
C2×#168109652
C2×#168109612
C2×#168109252
C2×#168109212
C2×#168108262
C2×#168107742
C2×#168107242
C2×#168107202
C2×#168107142
C2×SD16×Dic532
C2×#168106812
C2×C53×#4502
C2×#312353