Finite Group Databasebeta

← C2×#20284243 #28251005

Subgroups — C2×#20284243 #28251005

Order 13568.

2666 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133246C211yesmaximal, characteristic
2C22×Q16×D53C211yesmaximal, characteristic, complemented
3C2×#16811193C211yesmaximal, characteristic
4C2×#16811099C211yesmaximal, characteristic, complemented
5#20284243C2116yesmaximal, direct product factor
6C2×#16810844C211yesmaximal, characteristic, complemented
7C2×#16810843C211yesmaximal, characteristic, complemented
8C2×#16810842C211yesmaximal, characteristic, complemented
9C2×#16810834C211yesmaximal, characteristic, complemented
10C2×#16810833C211yesmaximal, characteristic, complemented
11C2×#16810832C211yesmaximal, characteristic, complemented
12C2×#16810831C211yesmaximal, characteristic, complemented
13C2×#16810648C211yesmaximal, characteristic, complemented
14C2×#16810630C211yesmaximal, characteristic, complemented
15C2×#16810616C211yesmaximal, characteristic
16C2×C53×#464C211yesmaximal, characteristic, complemented
17C22×#11719947C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×Q8×D53C2211yescharacteristic
20C2×#13133246—28no—
21C2×#13133246C2218yes—
22C22×Dic212C2211yescharacteristic
23C22×Dic212C2211yescharacteristic
24C22×#11719925C2211yescharacteristic
25C22×#11719925C2211yescharacteristic
26C22×#11719925C2211yescharacteristic
27C2×Q16×D53—28no—
28C2×Q16×D53C2218yescomplemented
29C22×#11719923C2211yescharacteristic
30C22×#11719912C2211yescharacteristic
31C22×C8×D53C2211yescharacteristic
32#16811193—24no—
33#16811193C2218yes—
34C2×#13133217C2211yescharacteristic
35C2×#13133215C2211yescharacteristic
36C2×#13133204C2211yescharacteristic
37C2×#13133199—21no—
38C2×#13133199—21no—
39C2×#13133194—21no—
40C2×#13133194—21no—
41#16811099—24no—
42#16811099C2218yescomplemented
43C2×Q8×Dic53C2211yescharacteristic
44C2×C4×Dic106—21no—
45C2×C4×Dic106C2211yescharacteristic
46C2×#13133182—21no—
47C2×#13133182C2211yescharacteristic
48C2×#13133175—21no—
49C2×#13133175C2211yescharacteristic
50C2×#13133174—21no—
51C2×#13133174C2211yescharacteristic
52#16810844C2218yescomplemented
53#16810843C2218yescomplemented
54#16810842C2218yescomplemented
55#16810834C2218yescomplemented
56#16810833C2218yescomplemented
57#16810832C2218yescomplemented
58#16810831C2218yescomplemented
59#16810648C2218yescomplemented
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63#16810630C2218yescomplemented
64#16810616C2218yes—
65C2×#13133142C2211yescharacteristic
66C2×#13133142C2211yescharacteristic
67C2×#13133141C2211yescharacteristic
68C2×#13133140C2211yescharacteristic
69C2×#13133140C2211yescharacteristic
70C2×#13133138C2211yescharacteristic
71C22×Q16×C53C2211yescharacteristic
72C22×SD16×C53C2211yescharacteristic
73C2×#124×C53C2211yescharacteristic
74C2×C4×Q8×C53C2211yescharacteristic
75C53×#464C2218yescomplemented
76C2×C4⋊C8×C53C2211yescharacteristic
77C2×#103×C53C2211yescharacteristic
78C2×#102×C53C2211yescharacteristic
79C2×#11719947—24no—
80C2×#11719947—22no—
81C2×#11719947—24no—
82C2×#11719947C2314yes—
83C22×Dic106—21no—
84C22×Dic106—21no—
85C22×Dic106C2311yescharacteristic
86C22×Dic106C2311yescharacteristic
87C22×Dic106C2311yescharacteristic
88C2×Q8×D53—22no—
89C2×Q8×D53—22no—
90C2×Q8×D53—24no—
91C2×Q8×D53—24no—
92C2×Q8×D53—24no—
93C2×Q8×D53D418yes—
94C2×Q8×D53C2314yes—
95C2×Q8×D53C2314yes—
96C22×C22⋊D53—21no—
97C23×Dic53—21no—
98C22×C4×D53—21no—
99C22×C4×D53—21no—
100C22×C4×D53C2311yescharacteristic
101#13133246—232no—
102C2×Dic212—24no—
103C2×Dic212—24no—
104C2×Dic212C2314yes—
105C2×Dic212C2314yes—
106C2×#11719925—24no—
107C2×#11719925—24no—
108C2×#11719925—24no—
109C2×#11719925C2314yes—
110C2×#11719925C2314yes—
111C2×#11719925C2314yes—
112Q16×D53—232no—
113C2×#11719923—24no—
114C2×#11719923C2314yes—
115C2×#11719912—24no—
116C2×#11719912C2314yes—
117C22×#88322C2311yescharacteristic
118C22×#88322C2311yescharacteristic
119C2×C8×D53—24no—
120C2×C8×D53C2314yes—
121#13133217—22no—
122#13133217C2314yes—
123#13133215—22no—
124#13133215C2314yes—
125#13133204—22no—
126#13133204C2314yes—
127#13133199—28no—
128#13133199—28no—
129#13133194—28no—
130#13133194—28no—
131Q8×Dic53—22no—
132Q8×Dic53C2314yes—
133C4×Dic106—22no—
134C4×Dic106—28no—
135C4×Dic106C2314yes—
136#13133182—28no—
137#13133182—22no—
138#13133182C2314yes—
139#13133175—28no—
140#13133175—22no—
141#13133175C2314yes—
142#13133174—28no—
143#13133174D414yes—
144#13133174C2314yes—
145C2×C4⋊Dic53—21no—
146C2×C4⋊Dic53—21no—
147C2×C4⋊Dic53—21no—
148C2×C4⋊Dic53C2311yescharacteristic
149C2×#11719919—21no—
150C2×#11719919—21no—
151C2×#11719919—21no—
152C2×#11719919—21no—
153C2×#11719919D411yescharacteristic
154C2×#11719919D411yescharacteristic
155C2×C22⋊Dic53—21no—
156C2×C22⋊Dic53—21no—
157C2×#11719921—21no—
158C2×#11719921D411yescharacteristic
159C2×#11719921D411yescharacteristic
160C2×C4×Dic53—21no—
161C2×C4×Dic53—21no—
162C2×C4×Dic53—21no—
163C2×C4×Dic53—21no—
164C2×C4×Dic53C2311yescharacteristic
165C4⋊#88322C2314yes—
166#13133146C2314yes—
167#13133146C2314yes—
168#13133142C2314yes—
169#13133142C2314yes—
170#13133141C2314yes—
171#13133140C2314yes—
172#13133140C2314yes—
173#13133138C2314yes—
174C22×Q8×C53C2311yescharacteristic
175C22×Q8×C53C2311yescharacteristic
176C22×D4×C53C2311yescharacteristic
177C2×Q16×C53—24no—
178C2×Q16×C53C2314yes—
179C2×SD16×C53—24no—
180C2×SD16×C53C2314yes—
181C22×C8×C53C2311yescharacteristic
182C22×C8×C53C2311yescharacteristic
183#124×C53—22no—
184#124×C53C2314yes—
185C4×Q8×C53—22no—
186C4×Q8×C53C2314yes—
187C2×C4⋊C4×C53—21no—
188C2×C4⋊C4×C53C2311yescharacteristic
189C2×C22⋊C4×C53—21no—
190C2×C22⋊C4×C53—21no—
191C2×C42×C53—21no—
192C2×C42×C53C2311yescharacteristic
193C4⋊C8×C53C2314yes—
194#103×C53C2314yes—
195#102×C53C2314yes—
196C24×C53—21no—
197C23×D53C2×D411yescharacteristic
198C2×Q8×C53—21no—
199C2×Q8×C53—21no—
200C2×Q8×C53—22no—
201C2×Q8×C53—22no—
202C2×Q8×C53—22no—
203C2×Q8×C53C2×D414yes—
204C2×Q8×C53C2412yes—
205C2×Q8×C53C2412yes—
206C2×D4×C53—22no—
207C2×D4×C53—21no—
208C2×D4×C53—22no—
209C2×D4×C53C2412yes—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53C2×D411yescharacteristic
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2411yescharacteristic
216C2×C22⋊D53—24no—
217C2×C22⋊D53—44no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—24no—
223C22×Dic53—44no—
224C22×Dic53C2×D411yescharacteristic
225C22×Dic53C2×D411yescharacteristic
226C22×Dic53C2×D411yescharacteristic
227Q8×D53—216no—
228Q8×D53—28no—
229Q8×D53—28no—
230Q8×D53—28no—
231Q8×D53—48no—
232Q8×D53C2×D4116yes—
233#11719947—28no—
234#11719947—28no—
235#11719947—48no—
236C2×C4×D53—28no—
237C2×C4×D53—24no—
238C2×C4×D53—24no—
239C2×C4×D53—44no—
240C2×C4×D53C2×D412yes—
241C2×C4×D53C2×D414yes—
242C2×C4×D53#4114yes—
243C2×C4×D53C2412yes—
244C2×Dic106—21no—
245C2×Dic106—22no—
246C2×Dic106—28no—
247C2×Dic106—24no—
248C2×Dic106—22no—
249C2×Dic106—22no—
250C2×Dic106—22no—
251C2×Dic106—22no—
252C2×Dic106—21no—
253C2×Dic106—21no—
254C2×Dic106—24no—
255C2×Dic106—44no—
256C2×Dic106C2×D414yes—
257C2×Dic106C2412yes—
258C2×Dic106C2412yes—
259C2×Dic106C2412yes—
260Q16×C53—28no—
261SD16×C53—28no—
262C2×C8×C53—22no—
263C2×C8×C53—22no—
264C2×C8×C53C2412yes—
265C2×C8×C53C2412yes—
266C4⋊C4×C53—24no—
267C4⋊C4×C53—21no—
268C4⋊C4×C53C2412yes—
269C22⋊C4×C53—24no—
270C22⋊C4×C53—24no—
271C42×C53—24no—
272C42×C53C2×D412yes—
273C42×C53C2412yes—
274C22⋊Dic53—24no—
275C22⋊Dic53—24no—
276#11719925—28no—
277#11719925—28no—
278#11719925—28no—
279#11719923—28no—
280#11719921—24no—
281#11719921C2×D414yes—
282#11719921C2×D414yes—
283C4⋊Dic53—24no—
284C4⋊Dic53—24no—
285C4⋊Dic53—21no—
286C4⋊Dic53—24no—
287C4⋊Dic53C2412yes—
288#11719919—24no—
289#11719919—24no—
290#11719919—24no—
291#11719919—24no—
292#11719919C2×D414yes—
293#11719919C2×D414yes—
294C4×Dic53—24no—
295C4×Dic53—24no—
296C4×Dic53—24no—
297C4×Dic53—24no—
298C4×Dic53C2×D412yes—
299C4×Dic53C2412yes—
300C2×#88322—22no—
301C2×#88322—22no—
302C2×#88322C2412yes—
303C2×#88322C2412yes—
304Dic212—28no—
305Dic212—28no—
306#11719912—28no—
307C8×D53—28no—
308C23×C53—22no—
309C23×C53—42no—
310C23×C53—42no—
311C23×C53—42no—
312C23×C53C22×D411yescharacteristic
313C22×D53—22no—
314C22×D53—22no—
315C22×D53#12114yes—
316C22×D53C22×D412yes—
317Q8×C53—24no—
318Q8×C53—22no—
319Q8×C53—22no—
320Q8×C53—22no—
321Q8×C53—42no—
322Q8×C53C22×D414yes—
323D4×C53—22no—
324D4×C53—22no—
325D4×C53—42no—
326C2×C4×C53—24no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—42no—
333C2×C4×C53—42no—
334C2×C4×C53C22×D412yes—
335C2×C4×C53C22×D412yes—
336C2×C4×C53C22×D411yescharacteristic
337C2×C4×C53C22×D412yes—
338C2×C4×C53C2×#4112yes—
339C2×C4×C53C2511yescharacteristic
340C22⋊D53—48no—
341C2×Dic53—24no—
342C2×Dic53—22no—
343C2×Dic53—22no—
344C2×Dic53—22no—
345C2×Dic53—22no—
346C2×Dic53—22no—
347C2×Dic53—22no—
348C2×Dic53—42no—
349C2×Dic53—42no—
350C2×Dic53—42no—
351C2×Dic53—48no—
352C2×Dic53#12114yes—
353C2×Dic53C22×D412yes—
354C2×Dic53C22×D412yes—
355C2×Dic53C22×D412yes—
356C4×D53—216no—
357C4×D53—48no—
358C4×D53#12118yes—
359C4×D53C22×D414yes—
360C4×D53C2×#4114yes—
361Dic106—24no—
362Dic106—22no—
363Dic106—216no—
364Dic106—22no—
365Dic106—22no—
366Dic106—22no—
367Dic106—22no—
368Dic106—42no—
369Dic106—42no—
370Dic106—48no—
371Dic106C22×D414yes—
372C8×C53—22no—
373C8×C53—22no—
374#88322—22no—
375#88322—22no—
376C2×#3044—531nomaximal, Sylow
377C22×C53—42no—
378C22×C53—42no—
379C22×C53—42no—
380C22×C53—84no—
381C22×C53C2×#12112yes—
382C22×C53#57812yes—
383C22×C53#57812yes—
384C22×C53C23×D411yescharacteristic
385C2×D53—28no—
386C2×D53—22no—
387C2×D53—22no—
388C2×D53C2×#12114yes—
389C4×C53—24no—
390C4×C53—22no—
391C4×C53—22no—
392C4×C53—42no—
393C4×C53—42no—
394C4×C53C2×#12112yes—
395C4×C53C23×D411yescharacteristic
396C4×C53C22×#4111yescharacteristic
397Dic53—24no—
398Dic53—22no—
399Dic53—22no—
400Dic53—42no—
401Dic53—42no—
402Dic53—42no—
403Dic53C2×#12114yes—
404C22×#137—531no—
405C23×Q16—531no—
406C2×#536—531no—
407C2×#519—531no—
408#3044—5316no—
409C2×#464—531no—
410C2×#464—531no—
411C2×#464—531no—
412C2×#464D5311yescharacteristic, complemented
413C2×#462—531no—
414C2×#462—531no—
415C2×#462—531no—
416C2×#462—531no—
417C2×#424—531no—
418C2×#419—531no—
419C2×#416—531no—
420C2×C53—82no—
421C2×C53#304414yescomplemented
422C2×C53C22×#12111yescharacteristic
423C2×C53C2×#57811yescharacteristic
424C2×C53C2×#57811yescharacteristic
425D53—24no—
426C22×#41—531no—
427C23×Q8—531no—
428C23×Q8—531no—
429C2×#137—538no—
430C2×#137—1068no—
431C22×Q16—531no—
432C22×Q16—531no—
433C22×Q16—531no—
434C22×Q16—538no—
435C22×Q16—531no—
436C22×Q16—531no—
437C22×Q16—1068no—
438C22×Q16C2×D5311yescharacteristic
439C22×SD16—531no—
440C22×SD16C2×D5311yescharacteristic
441C22×M16—531no—
442C23×C8—531no—
443#536—538no—
444#536—1064no—
445C2×C4⋊Q8—531no—
446C2×C4⋊Q8—531no—
447C2×#124—531no—
448C2×#124C2×D5311yescharacteristic
449C2×#123—1061no—
450C2×#123—1061no—
451C2×C22⋊Q8—1061no—
452C2×C22⋊Q8—1061no—
453#519—538no—
454#519—1064no—
455C2×C4×Q8—531no—
456C2×C4×Q8—531no—
457C2×C4×Q8—531no—
458C2×C4×Q8—1061no—
459C2×C4×Q8—1061no—
460C2×C4×Q8C2×D5311yescharacteristic
461C2×#117—531no—
462C2×#117—531no—
463C2×#117—1061no—
464C2×#117—1061no—
465#464—538no—
466#464—538no—
467#464—538no—
468#464C2×D5318yescomplemented
469#462—538no—
470#462—538no—
471#462—538no—
472#462—538no—
473#424—538no—
474C2×C4⋊C8—531no—
475C2×C4⋊C8—531no—
476C2×C4⋊C8—531no—
477C2×C4⋊C8C2×D5311yescharacteristic
478#419—538no—
479#416—538no—
480C2×#103—531no—
481C2×#103—531no—
482C2×#103—531no—
483C2×#103—531no—
484C2×#103—531no—
485C2×#103C2×D5311yescharacteristic
486C2×#102—531no—
487C2×#102C2×D5311yescharacteristic
488C53C2×#304411yescharacteristic, complemented, Sylow
489C2×#41—534no—
490C2×#41—1062no—
491C2×#41—1064no—
492C2×#41—1064no—
493C22×Q8—538no—
494C22×Q8—534no—
495C22×Q8—534no—
496C22×Q8—531no—
497C22×Q8—531no—
498C22×Q8—531no—
499C22×Q8—1061no—
500C22×Q8—1061no—
501C22×Q8—1062no—
502C22×Q8—1064no—
503C22×Q8—1062no—
504C22×Q8—1064no—
505C22×Q8—1064no—
506C22×Q8C22×D5311yescharacteristic
507C22×Q8C22×D5311yescharacteristic
508C22×D4—1061no—
509C22×D4C22×D5311yescharacteristic
510C23×C4—531no—
511C23×C4—1061no—
512C23×C4—1061no—
513C23×C4—1061no—
514#137—10632no—
515C2×Q16—24no—
516C2×Q16—534no—
517C2×Q16—534no—
518C2×Q16—534no—
519C2×Q16—534no—
520C2×Q16—534no—
521C2×Q16—1064no—
522C2×Q16—1064no—
523C2×Q16—10632no—
524C2×Q16—1064no—
525C2×Q16—1064no—
526C2×Q16—1064no—
527C2×Q16C22×D5314yes—
528C2×SD16—24no—
529C2×SD16—534no—
530C2×SD16—1064no—
531C2×SD16C22×D5314yes—
532C2×M16—534no—
533C2×M16—1064no—
534C22×C8—531no—
535C22×C8—531no—
536C22×C8—534no—
537C22×C8—1064no—
538C22×C8C22×D5311yescharacteristic
539C22×C8C22×D5311yescharacteristic
540C4⋊Q8—534no—
541C4⋊Q8—534no—
542C4⋊Q8—1062no—
543C4⋊Q8—1062no—
544#124—22no—
545#124—534no—
546#124—1062no—
547#124C22×D5314yes—
548#123—1068no—
549#123—1068no—
550C22⋊Q8—1068no—
551C22⋊Q8—1068no—
552C4×Q8—22no—
553C4×Q8—534no—
554C4×Q8—534no—
555C4×Q8—534no—
556C4×Q8—1068no—
557C4×Q8—1062no—
558C4×Q8—1062no—
559C4×Q8—1068no—
560C4×Q8—1062no—
561C4×Q8C22×D5314yes—
562#117—534no—
563#117—534no—
564#117—534no—
565#117—1068no—
566#117—1068no—
567#117—1062no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—531no—
570C2×C4⋊C4—531no—
571C2×C4⋊C4—531no—
572C2×C4⋊C4—1061no—
573C2×C4⋊C4—1061no—
574C2×C4⋊C4—1061no—
575C2×C4⋊C4—1061no—
576C2×C4⋊C4—1061no—
577C2×C4⋊C4—1061no—
578C2×C4⋊C4—1061no—
579C2×C4⋊C4C22×D5311yescharacteristic
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—531no—
583C2×C22⋊C4—531no—
584C2×C22⋊C4—1061no—
585C2×C22⋊C4—1061no—
586C2×C22⋊C4—1061no—
587C2×C42—21no—
588C2×C42—531no—
589C2×C42—1061no—
590C2×C42—1061no—
591C2×C42—1061no—
592C2×C42—1061no—
593C2×C42C22×D5311yescharacteristic
594C4⋊C8—534no—
595C4⋊C8—534no—
596C4⋊C8—534no—
597C4⋊C8C22×D5314yes—
598#103—534no—
599#103—534no—
600#103—534no—
601#103—534no—
602#103—534no—
603#103C22×D5314yes—
604#102—534no—
605#102C22×D5314yes—
606C24—21no—
607C24—531no—
608#41—1068no—
609#41—1068no—
610#41—2128no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—22no—
614C2×Q8—22no—
615C2×Q8—22no—
616C2×Q8—5316no—
617C2×Q8—534no—
618C2×Q8—532no—
619C2×Q8—532no—
620C2×Q8—532no—
621C2×Q8—1064no—
622C2×Q8—1068no—
623C2×Q8—1064no—
624C2×Q8—10616no—
625C2×Q8—1068no—
626C2×Q8—1068no—
627C2×Q8—1068no—
628C2×Q8—1061no—
629C2×Q8—1061no—
630C2×Q8—1061no—
631C2×Q8—1062no—
632C2×Q8—1062no—
633C2×Q8—1062no—
634C2×Q8—1062no—
635C2×Q8—1062no—
636C2×Q8—2124no—
637C2×Q8—2128no—
638C2×Q8D4×D5314yes—
639C2×Q8C23×D5312yes—
640C2×Q8C23×D5312yes—
641C2×D4—22no—
642C2×D4—21no—
643C2×D4—22no—
644C2×D4—1064no—
645C2×D4—2124no—
646C2×D4C23×D5312yes—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—531no—
651C22×C4—532no—
652C22×C4—534no—
653C22×C4—534no—
654C22×C4—532no—
655C22×C4—531no—
656C22×C4—531no—
657C22×C4—1064no—
658C22×C4—1068no—
659C22×C4—1064no—
660C22×C4—1064no—
661C22×C4—1061no—
662C22×C4—1061no—
663C22×C4—1061no—
664C22×C4—1061no—
665C22×C4—2124no—
666C22×C4—2124no—
667C22×C4D4×D5311yescharacteristic
668C22×C4D4×D5311yescharacteristic
669C22×C4C23×D5311yescharacteristic
670Q16—28no—
671Q16—1068no—
672Q16—1068no—
673Q16—1068no—
674Q16—1068no—
675Q16—1068no—
676SD16—28no—
677SD16—1068no—
678M16—1068no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—532no—
682C2×C8—532no—
683C2×C8—1068no—
684C2×C8—1062no—
685C2×C8—1062no—
686C2×C8C23×D5312yes—
687C2×C8C23×D5312yes—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—534no—
691C4⋊C4—534no—
692C4⋊C4—532no—
693C4⋊C4—1064no—
694C4⋊C4—1064no—
695C4⋊C4—1064no—
696C4⋊C4—1064no—
697C4⋊C4—1061no—
698C4⋊C4—1064no—
699C4⋊C4—1064no—
700C4⋊C4—1064no—
701C4⋊C4C23×D5312yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—534no—
705C22⋊C4—534no—
706C22⋊C4—1064no—
707C22⋊C4—1064no—
708C22⋊C4—1064no—
709C42—24no—
710C42—532no—
711C42—532no—
712C42—1064no—
713C42—1064no—
714C42—1064no—
715C42—1064no—
716C42D4×D5312yes—
717C42C23×D5312yes—
718C23—22no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—534no—
723C23—532no—
724C23—1062no—
725C23—1062no—
726C23C2×D4×D5311yescharacteristic
727Q8—24no—
728Q8—22no—
729Q8—22no—
730Q8—22no—
731Q8—42no—
732Q8—534no—
733Q8—10616no—
734Q8—1064no—
735Q8—1062no—
736Q8—1062no—
737Q8—1062no—
738Q8—1062no—
739Q8—1062no—
740Q8—2128no—
741Q8—2122no—
742Q8—2122no—
743Q8C2×D4×D5314yes—
744D4—22no—
745D4—22no—
746D4—42no—
747D4—2128no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—534no—
757C2×C4—532no—
758C2×C4—538no—
759C2×C4—534no—
760C2×C4—534no—
761C2×C4—532no—
762C2×C4—532no—
763C2×C4—10616no—
764C2×C4—1064no—
765C2×C4—1062no—
766C2×C4—1062no—
767C2×C4—1062no—
768C2×C4—1062no—
769C2×C4—1062no—
770C2×C4—1062no—
771C2×C4—2128no—
772C2×C4—2128no—
773C2×C4—2122no—
774C2×C4—2122no—
775C2×C4—2122no—
776C2×C4C2×D4×D5312yes—
777C2×C4C2×D4×D5312yes—
778C2×C4C2×D4×D5311yescharacteristic
779C2×C4C2×D4×D5312yes—
780C2×C4#41×D5312yes—
781C2×C4C24×D5311yescharacteristic
782C8—22no—
783C8—22no—
784C8—1062no—
785C8—1062no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—84no—
790C22—534no—
791C22—1068no—
792C22—1062no—
793C22—1062no—
794C22#121×D5312yes—
795C22#1681143712yes—
796C22#1681143912yes—
797C22C22×D4×D5311yescharacteristic
798C4—24no—
799C4—22no—
800C4—22no—
801C4—42no—
802C4—42no—
803C4—534no—
804C4—1064no—
805C4—1062no—
806C4—1062no—
807C4—2122no—
808C4—2122no—
809C4—2122no—
810C4#121×D5312yes—
811C4C22×D4×D5311yescharacteristic
812C4C2×#41×D5311yescharacteristic
813C2—82no—
814C2—1064no—
815C2#2028424314yesdirect product factor
816C2C2×#121×D5311yescharacteristic
817C2C2×#1681143711yescharacteristic
818C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#464C2
socleC23×C53C22×D4
prime radicalC22×#11719947C22
hypercenterC2×#464D53
hypocenterC53C2×#3044
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. C22×Q16×D53C2semidirect
4. C2×#16811099C2semidirect
5. #20284243C2direct (N × H)
6. C2×#16810844C2semidirect
7. C2×#16810843C2semidirect
8. C2×#16810842C2semidirect
9. C2×#16810834C2semidirect
10. C2×#16810833C2semidirect
11. C2×#16810832C2semidirect
12. C2×#16810831C2semidirect
13. C2×#16810648C2semidirect
14. C2×#16810630C2semidirect
16. C2×C53×#464C2semidirect
28. C2×Q16×D53C22semidirect
42. #16811099C22semidirect
52. #16810844C22semidirect
53. #16810843C22semidirect
54. #16810842C22semidirect
55. #16810834C22semidirect
56. #16810833C22semidirect
57. #16810832C22semidirect
58. #16810831C22semidirect
59. #16810648C22semidirect
63. #16810630C22semidirect
75. C53×#464C22semidirect
412. C2×#464D53semidirect
421. C2×C53#3044semidirect
468. #464C2×D53semidirect
488. C53C2×#3044semidirect
815. C2#20284243direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332462
C22×Q16×D532
C2×#168111932
C2×#168110992
#202842432
C2×#168108442
C2×#168108432
C2×#168108422
C2×#168108342
C2×#168108332
C2×#168108322
C2×#168108312
C2×#168106482
C2×#168106302
C2×#168106162
C2×C53×#4642
C2×#304453