Finite Group Databasebeta

← C2×#20285811 #28255449

Subgroups — C2×#20285811 #28255449

Order 13568.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811244C211yesmaximal, characteristic, complemented
2C2×#16811192C211yesmaximal, characteristic, complemented
3#20285811C2116yesmaximal, direct product factor
4C2×#16811012C211yesmaximal, characteristic, complemented
5C2×#16811007C211yesmaximal, characteristic, complemented
6C2×#16810983C211yesmaximal, characteristic, complemented
7C2×#16810970C211yesmaximal, characteristic, complemented
8C2×#16810846C211yesmaximal, characteristic, complemented
9C2×#16810824C211yesmaximal, characteristic, complemented
10C2×#16810839C211yesmaximal, characteristic, complemented
11C2×#16810819C211yesmaximal, characteristic, complemented
12C2×#16810787C211yesmaximal, characteristic, complemented
13C2×#16810770C211yesmaximal, characteristic, complemented
14C2×#16810776C211yesmaximal, characteristic, complemented
15C2×#16810759C211yesmaximal, characteristic, complemented
16C2×C53×#433C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C23×D212C2211yescharacteristic
19C22×Dic212C2211yescharacteristic, complemented
20C22×#11719913C2211yescharacteristic
21C22×#11719913C2211yescharacteristic
22C22×#11719913C2211yescharacteristic, complemented
23C22×#11719913C2211yescharacteristic, complemented
24C22×D424C2211yescharacteristic
25C22×D424C2211yescharacteristic
26C22×D424C2211yescharacteristic, complemented
27#16811244—24no—
28#16811244C2218yescomplemented
29#16811192—24no—
30#16811192C2218yescomplemented
31C2×#13133217C2211yescharacteristic, complemented
32C2×#13133214C2211yescharacteristic
33C2×#13133214C2211yescharacteristic
34C2×#13133212—21no—
35C2×#13133205C2211yescharacteristic
36C2×#13133205C2211yescharacteristic
37C2×#13133205C2211yescharacteristic, complemented
38C2×#13133203—21no—
39C2×#13133199—21no—
40C2×#13133196C2211yescharacteristic
41C2×#13133195—21no—
42C2×#13133192—21no—
43C2×#13133192—21no—
44C2×#13133191C2211yescharacteristic
45C2×#13133187—21no—
46C2×#13133187—21no—
47C2×C4×Dic106C2211yescharacteristic, complemented
48C2×C4×D212C2211yescharacteristic, complemented
49#16811012C2218yescomplemented
50#16811007C2218yescomplemented
51#16810983C2218yescomplemented
52#16810970C2218yescomplemented
53#16810846C2218yescomplemented
54#16810839C2218yescomplemented
55#16810824C2218yescomplemented
56#16810819C2218yescomplemented
57#16810787C2218yescomplemented
58#16810776C2218yescomplemented
59#16810770C2218yescomplemented
60#16810759C2218yescomplemented
61C2×#13133142C2211yescharacteristic, complemented
62C2×#13133142C2211yescharacteristic, complemented
63C2×#13133139C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133139C2211yescharacteristic
67C2×#13133139C2211yescharacteristic, complemented
68C2×#13133139C2211yescharacteristic, complemented
69C2×#117×C53C2211yescharacteristic
70C53×#433C2218yescomplemented
71C2×C4⋊C8×C53C2211yescharacteristic, complemented
72C2×C4⋊C8×C53C2211yescharacteristic, complemented
73C2×C22⋊C8×C53C2211yescharacteristic
74C2×C22⋊C8×C53C2211yescharacteristic
75C2×#97×C53C2211yescharacteristic, complemented
76C2×C4×C8×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C2×#11719945—22no—
79C2×#11719945—42no—
80C2×#11719945—42no—
81C2×#11719945C2314yes—
82C22×Dic106—21no—
83C22×Dic106C2311yescharacteristic
84C22×Dic106C2311yescharacteristic
85C22×D212—21no—
86C22×D212—22no—
87C22×D212—21no—
88C22×D212—21no—
89C22×D212—21no—
90C22×D212—21no—
91C22×D212—42no—
92C22×D212—42no—
93C22×D212C2311yescharacteristic
94C22×D212C2311yescharacteristic
95C22×D212C2311yescharacteristic
96C22×D212C2311yescharacteristic
97C22×D212C2314yes—
98C22×C22⋊D53—21no—
99C22×C22⋊D53—21no—
100C22×C4×D53—21no—
101C22×C4×D53—21no—
102C2×Dic212—42no—
103C2×Dic212C2314yescomplemented
104C2×#11719913—42no—
105C2×#11719913—42no—
106C2×#11719913—42no—
107C2×#11719913—42no—
108C2×#11719913C2314yes—
109C2×#11719913C2314yes—
110C2×#11719913C2314yescomplemented
111C2×#11719913C2314yescomplemented
112C2×D424—42no—
113C2×D424—42no—
114C2×D424—42no—
115C2×D424C2314yes—
116C2×D424C2314yes—
117C2×D424C2314yescomplemented
118#13133217—22no—
119#13133217C2314yescomplemented
120#13133214—22no—
121#13133214—22no—
122#13133214C2314yes—
123#13133214C2314yes—
124#13133212—28no—
125#13133205—22no—
126#13133205—22no—
127#13133205—22no—
128#13133205C2314yes—
129#13133205C2314yes—
130#13133205C2314yescomplemented
131#13133203—28no—
132#13133199—28no—
133#13133196—22no—
134#13133196C2314yes—
135#13133195—28no—
136#13133192—28no—
137#13133192—28no—
138#13133191—22no—
139#13133191C2314yes—
140#13133187—28no—
141#13133187—28no—
142C4×Dic106—22no—
143C4×Dic106C2314yescomplemented
144C4×D212—22no—
145C4×D212C2314yescomplemented
146C2×C4⋊Dic53—21no—
147C2×C4⋊Dic53C2311yescharacteristic
148C2×C4⋊Dic53C2311yescharacteristic
149C2×#11719919—21no—
150C2×#11719919—21no—
151C2×C22⋊Dic53—21no—
152C2×#11719921—21no—
153C2×#11719921—21no—
154C2×#11719921—21no—
155C2×#11719921—21no—
156C2×#11719921—21no—
157C2×#11719921—21no—
158C2×#11719921—21no—
159C2×#11719921—21no—
160C2×C4×Dic53—21no—
161#13133142C2314yescomplemented
162#13133142C2314yescomplemented
163#13133139C2314yes—
164#13133139C2314yes—
165#13133139C2314yes—
166#13133139C2314yes—
167#13133139C2314yescomplemented
168#13133139C2314yescomplemented
169C23×C4×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172C22×C8×C53C2311yescharacteristic
173C22×C8×C53C2311yescharacteristic
174#117×C53D414yes—
175#117×C53C2314yes—
176C2×C4⋊C4×C53D411yescharacteristic
177C2×C4⋊C4×C53D411yescharacteristic
178C2×C22⋊C4×C53D411yescharacteristic
179C2×C22⋊C4×C53D411yescharacteristic
180C2×C42×C53C2311yescharacteristic
181C2×C42×C53C2311yescharacteristic
182C4⋊C8×C53C2314yescomplemented
183C4⋊C8×C53C2314yescomplemented
184C22⋊C8×C53C2314yes—
185C22⋊C8×C53C2314yes—
186#97×C53C2314yescomplemented
187C4×C8×C53C2314yescomplemented
188C24×C53C2×D411yescharacteristic
189C23×D53—21no—
190C23×D53—21no—
191C23×D53—21no—
192C23×D53—21no—
193C23×D53—24no—
194C23×D53—44no—
195C23×D53—82no—
196C23×D53—82no—
197C22×C4×C53—22no—
198C22×C4×C53—22no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D412yes—
205C22×C4×C53C2412yes—
206C22×C4×C53C2411yescharacteristic
207C2×C22⋊D53—24no—
208C2×C22⋊D53—24no—
209C2×C22⋊D53—44no—
210C2×C22⋊D53—82no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215#11719945—44no—
216#11719945—44no—
217#11719945—48no—
218C2×D212—22no—
219C2×D212—22no—
220C2×D212—22no—
221C2×D212—22no—
222C2×D212—22no—
223C2×D212—22no—
224C2×D212—22no—
225C2×D212—22no—
226C2×D212—21no—
227C2×D212—24no—
228C2×D212—21no—
229C2×D212—21no—
230C2×D212—21no—
231C2×D212—24no—
232C2×D212—24no—
233C2×D212—24no—
234C2×D212—24no—
235C2×D212—44no—
236C2×D212—44no—
237C2×D212—44no—
238C2×D212—48no—
239C2×D212—82no—
240C2×D212—82no—
241C2×D212—82no—
242C2×D212—82no—
243C2×D212C2412yes—
244C2×D212C2412yes—
245C2×D212C2412yes—
246C2×D212C2412yes—
247C2×C4×D53—24no—
248C2×C4×D53—24no—
249C2×C4×D53—44no—
250C2×C4×D53—82no—
251C2×Dic106—22no—
252C2×Dic106—22no—
253C2×Dic106—22no—
254C2×Dic106—22no—
255C2×Dic106—21no—
256C2×Dic106—21no—
257C2×Dic106—24no—
258C2×Dic106—82no—
259C2×Dic106C2412yes—
260C2×Dic106C2412yes—
261C2×C8×C53—22no—
262C2×C8×C53—22no—
263C2×C8×C53—22no—
264C2×C8×C53—22no—
265C2×C8×C53C2412yes—
266C2×C8×C53C2412yes—
267C2×C8×C53C2412yes—
268C2×C8×C53C2412yes—
269C4⋊C4×C53C2×D414yes—
270C4⋊C4×C53C2×D414yes—
271C22⋊C4×C53C2×D414yes—
272C22⋊C4×C53C2×D414yes—
273C42×C53C2×D412yes—
274C42×C53C2×D412yes—
275C42×C53C2412yes—
276C42×C53C2412yes—
277C22⋊Dic53—24no—
278#11719921—24no—
279#11719921—24no—
280#11719921—24no—
281#11719921—24no—
282#11719921—24no—
283#11719921—24no—
284#11719921—24no—
285#11719921—24no—
286C4⋊Dic53—24no—
287C4⋊Dic53—21no—
288C4⋊Dic53—21no—
289C4⋊Dic53C2412yes—
290C4⋊Dic53C2412yes—
291#11719919—24no—
292#11719919—24no—
293C4×Dic53—24no—
294Dic212—44no—
295D424—44no—
296D424—44no—
297D424—44no—
298#11719913—44no—
299#11719913—44no—
300#11719913—44no—
301#11719913—44no—
302C23×C53—22no—
303C23×C53—22no—
304C23×C53—22no—
305C23×C53C22×D412yes—
306C23×C53C22×D411yescharacteristic
307C22×D53—22no—
308C22×D53—22no—
309C22×D53—22no—
310C22×D53—22no—
311C22×D53—48no—
312C22×D53—42no—
313C22×D53—42no—
314C22×D53—42no—
315C22×D53—42no—
316C22×D53—42no—
317C22×D53—42no—
318C22×D53—42no—
319C22×D53—42no—
320C22×D53—42no—
321C22×D53—42no—
322C22×D53—42no—
323C22×D53—42no—
324C22×D53—84no—
325C22×D53—84no—
326C22×D53—816no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—24no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53C22×D412yes—
336C2×C4×C53C22×D412yes—
337C2×C4×C53C22×D412yes—
338C2×C4×C53C22×D412yes—
339C2×C4×C53C22×D412yes—
340C2×C4×C53C22×D411yescharacteristic
341C2×C4×C53H(5,𝔽2)12yes—
342C2×C4×C53H(5,𝔽2)12yes—
343C2×C4×C53C2511yescharacteristic
344C22⋊D53—48no—
345C22⋊D53—84no—
346C2×Dic53—22no—
347C2×Dic53—22no—
348C2×Dic53—22no—
349C2×Dic53—22no—
350C2×Dic53—42no—
351C2×Dic53—42no—
352C2×Dic53—42no—
353C2×Dic53—42no—
354D212—22no—
355D212—22no—
356D212—22no—
357D212—22no—
358D212—22no—
359D212—22no—
360D212—22no—
361D212—22no—
362D212—48no—
363D212—42no—
364D212—42no—
365D212—42no—
366D212—42no—
367D212—84no—
368D212—84no—
369D212—84no—
370D212—84no—
371C4×D53—48no—
372C4×D53—84no—
373Dic106—22no—
374Dic106—22no—
375Dic106—22no—
376Dic106—22no—
377Dic106—42no—
378Dic106—42no—
379Dic106—84no—
380C8×C53—22no—
381C8×C53—22no—
382C8×C53—22no—
383C8×C53—22no—
384C2×#3224—531nomaximal, Sylow
385C22×C53—22no—
386C22×C53—22no—
387C22×C53—22no—
388C22×C53—44no—
389C22×C53#53512yes—
390C22×C53#57612yes—
391C22×C53#57712yes—
392C22×C53C23×D411yescharacteristic
393C2×D53—42no—
394C2×D53—42no—
395C2×D53—42no—
396C2×D53—42no—
397C2×D53—42no—
398C2×D53—42no—
399C2×D53—42no—
400C2×D53—42no—
401C2×D53—42no—
402C2×D53—42no—
403C2×D53—42no—
404C2×D53—42no—
405C2×D53—816no—
406C2×D53—84no—
407C2×D53—84no—
408C2×D53—84no—
409C2×D53—84no—
410C4×C53—22no—
411C4×C53—22no—
412C4×C53—22no—
413C4×C53—22no—
414C4×C53—22no—
415C4×C53#53512yes—
416C4×C53C2×H(5,𝔽2)11yescharacteristic
417C4×C53C2×H(5,𝔽2)11yescharacteristic
418Dic53—42no—
419Dic53—42no—
420Dic53—42no—
421Dic53—42no—
422C2×#542—531no—
423C2×#535—531no—
424#3224—5316no—
425C2×#496—531no—
426C2×#495—531no—
427C2×#489—531no—
428C2×#486—531no—
429C2×#464—531no—
430C2×#460—531no—
431C2×#463—531no—
432C2×#459—531no—
433C2×#452—531no—
434C2×#449—531no—
435C2×#450—531no—
436C2×#447—531no—
437C2×#433D5311yescharacteristic, complemented
438C2×C53—42no—
439C2×C53#322414yescomplemented
440C2×C53C2×#53511yescharacteristic
441C2×C53C2×#57611yescharacteristic
442C2×C53C2×#57711yescharacteristic
443D53—82no—
444D53—82no—
445D53—82no—
446D53—82no—
447C22×#41—531no—
448C23×D4—531no—
449C22×Q16—531no—
450C22×SD16—531no—
451C22×SD16—531no—
452C22×SD16—531no—
453C22×SD16—531no—
454C22×D8—531no—
455C22×D8—531no—
456C22×D8—531no—
457#542—538no—
458#542—1064no—
459#535—538no—
460#535—1064no—
461C2×C4⋊Q8—531no—
462C2×#127—531no—
463C2×#127—531no—
464C2×#126—1061no—
465C2×#124—531no—
466C2×#124—531no—
467C2×#124—531no—
468C2×#124—1061no—
469C2×#123—1061no—
470C2×C22⋊Q8—531no—
471C2×C22⋊Q8—1061no—
472C2×#121—531no—
473C2×#121—1061no—
474C2×#121—1061no—
475C2×#120—1061no—
476C2×#120—1061no—
477C2×C4×Q8—531no—
478C2×C4×D4—531no—
479C2×#117C2×D5311yescharacteristic
480#496—538no—
481#495—538no—
482#489—538no—
483#486—538no—
484#464—538no—
485#463—538no—
486#460—538no—
487#459—538no—
488#452—538no—
489#450—538no—
490#449—538no—
491#447—538no—
492#433C2×D5318yescomplemented
493C2×C4⋊C8C2×D5311yescharacteristic, complemented
494C2×C4⋊C8C2×D5311yescharacteristic, complemented
495C2×#103—531no—
496C2×#103—531no—
497C2×#102—531no—
498C2×#102—531no—
499C2×#102—531no—
500C2×#102—531no—
501C2×#102—531no—
502C2×#102—531no—
503C2×C22⋊C8C2×D5311yescharacteristic
504C2×C22⋊C8C2×D5311yescharacteristic
505C2×#97C2×D5311yescharacteristic, complemented
506C2×C4×C8C2×D5311yescharacteristic, complemented
507C53C2×#322411yescharacteristic, complemented, Sylow
508C25—1061no—
509C2×#41—534no—
510C2×#41—1062no—
511C2×#41—2122no—
512C2×#41—2122no—
513C22×Q8—531no—
514C22×Q8—531no—
515C22×Q8—1061no—
516C22×D4—531no—
517C22×D4—531no—
518C22×D4—531no—
519C22×D4—531no—
520C22×D4—534no—
521C22×D4—1061no—
522C22×D4—1061no—
523C22×D4—1061no—
524C22×D4—1061no—
525C22×D4—1061no—
526C22×D4—1061no—
527C22×D4—1061no—
528C22×D4—1062no—
529C22×D4—2122no—
530C22×D4—2122no—
531C23×C4—1061no—
532C23×C4—1061no—
533C23×C4C22×D5311yescharacteristic
534C2×Q16—534no—
535C2×Q16—2122no—
536C2×SD16—534no—
537C2×SD16—534no—
538C2×SD16—534no—
539C2×SD16—534no—
540C2×SD16—2122no—
541C2×SD16—2122no—
542C2×SD16—2122no—
543C2×SD16—2122no—
544C2×D8—534no—
545C2×D8—534no—
546C2×D8—534no—
547C2×D8—2122no—
548C2×D8—2122no—
549C2×D8—2122no—
550C22×C8C22×D5311yescharacteristic
551C22×C8C22×D5311yescharacteristic
552C22×C8C22×D5311yescharacteristic
553C22×C8C22×D5311yescharacteristic
554C4⋊Q8—534no—
555C4⋊Q8—1062no—
556#127—534no—
557#127—534no—
558#127—1062no—
559#127—1062no—
560#126—1068no—
561#124—534no—
562#124—534no—
563#124—534no—
564#124—1068no—
565#124—1062no—
566#124—1062no—
567#124—1062no—
568#123—1068no—
569C22⋊Q8—534no—
570C22⋊Q8—1062no—
571C22⋊Q8—1068no—
572#121—534no—
573#121—1062no—
574#121—1068no—
575#121—1068no—
576#120—1068no—
577#120—1068no—
578C4×Q8—534no—
579C4×Q8—1062no—
580C4×D4—534no—
581C4×D4—1062no—
582#117D21214yes—
583#117C22×D5314yes—
584C2×C4⋊C4—531no—
585C2×C4⋊C4—531no—
586C2×C4⋊C4—1061no—
587C2×C4⋊C4—1061no—
588C2×C4⋊C4—1061no—
589C2×C4⋊C4D21211yescharacteristic
590C2×C4⋊C4D21211yescharacteristic
591C2×C22⋊C4—1061no—
592C2×C22⋊C4—1061no—
593C2×C22⋊C4—1061no—
594C2×C22⋊C4—1061no—
595C2×C22⋊C4—1061no—
596C2×C22⋊C4—1061no—
597C2×C22⋊C4—1061no—
598C2×C22⋊C4—1061no—
599C2×C22⋊C4—1061no—
600C2×C22⋊C4D21211yescharacteristic
601C2×C22⋊C4D21211yescharacteristic
602C2×C42—1061no—
603C2×C42C22×D5311yescharacteristic
604C2×C42C22×D5311yescharacteristic
605C4⋊C8C22×D5314yescomplemented
606C4⋊C8C22×D5314yescomplemented
607#103—534no—
608#103—534no—
609#102—534no—
610#102—534no—
611#102—534no—
612#102—534no—
613#102—534no—
614#102—534no—
615C22⋊C8C22×D5314yes—
616C22⋊C8C22×D5314yes—
617#97C22×D5314yescomplemented
618C4×C8C22×D5314yescomplemented
619C24—1064no—
620C24—1061no—
621C24—1061no—
622C24—1061no—
623C24—1061no—
624C24—4242no—
625C24—4242no—
626C24—2124no—
627C24C2×D21211yescharacteristic
628#41—2124no—
629#41—2124no—
630#41—2128no—
631C2×Q8—532no—
632C2×Q8—532no—
633C2×Q8—1064no—
634C2×Q8—1061no—
635C2×Q8—1061no—
636C2×Q8—1062no—
637C2×Q8—1062no—
638C2×Q8—1062no—
639C2×Q8—1062no—
640C2×Q8—4242no—
641C2×D4—532no—
642C2×D4—532no—
643C2×D4—532no—
644C2×D4—532no—
645C2×D4—1064no—
646C2×D4—1064no—
647C2×D4—1064no—
648C2×D4—1064no—
649C2×D4—1064no—
650C2×D4—1064no—
651C2×D4—1061no—
652C2×D4—1064no—
653C2×D4—1061no—
654C2×D4—1061no—
655C2×D4—1061no—
656C2×D4—1062no—
657C2×D4—1062no—
658C2×D4—1062no—
659C2×D4—1062no—
660C2×D4—1062no—
661C2×D4—1062no—
662C2×D4—1062no—
663C2×D4—1062no—
664C2×D4—4242no—
665C2×D4—4242no—
666C2×D4—4242no—
667C2×D4—4242no—
668C2×D4—4242no—
669C2×D4—2124no—
670C2×D4—2124no—
671C2×D4—2124no—
672C2×D4—2128no—
673C2×D4—2124no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—1061no—
677C22×C4—1061no—
678C22×C4—1061no—
679C22×C4—1061no—
680C22×C4—1064no—
681C22×C4—1064no—
682C22×C4—4242no—
683C22×C4—2124no—
684C22×C4C2×D21212yes—
685C22×C4C2×D21211yescharacteristic
686C22×C4C2×D21211yescharacteristic
687C22×C4C2×D21211yescharacteristic
688C22×C4C2×D21211yescharacteristic
689C22×C4C2×D21211yescharacteristic
690C22×C4C23×D5312yes—
691C22×C4C23×D5311yescharacteristic
692Q16—2124no—
693SD16—2124no—
694SD16—2124no—
695SD16—2124no—
696SD16—2124no—
697D8—2124no—
698D8—2124no—
699D8—2124no—
700C2×C8—22no—
701C2×C8—22no—
702C2×C8—22no—
703C2×C8—22no—
704C2×C8C23×D5312yes—
705C2×C8C23×D5312yes—
706C2×C8C23×D5312yes—
707C2×C8C23×D5312yes—
708C4⋊C4—532no—
709C4⋊C4—532no—
710C4⋊C4—1061no—
711C4⋊C4—1061no—
712C4⋊C4—1064no—
713C4⋊C4—1064no—
714C4⋊C4—1064no—
715C4⋊C4C2×D21214yes—
716C4⋊C4C2×D21214yes—
717C22⋊C4—1064no—
718C22⋊C4—1064no—
719C22⋊C4—1064no—
720C22⋊C4—1064no—
721C22⋊C4—1064no—
722C22⋊C4—1064no—
723C22⋊C4—1064no—
724C22⋊C4—1064no—
725C22⋊C4—1064no—
726C22⋊C4C2×D21214yes—
727C22⋊C4C2×D21214yes—
728C42—1064no—
729C42C2×D21212yes—
730C42C2×D21212yes—
731C42C23×D5312yes—
732C42C23×D5312yes—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—1062no—
737C23—1062no—
738C23—1062no—
739C23—1062no—
740C23—4244no—
741C23—4244no—
742C23—42416no—
743C23—2128no—
744C23—2122no—
745C23—2122no—
746C23—2122no—
747C23—2122no—
748C23—2122no—
749C23—2122no—
750C23—2122no—
751C23—2122no—
752C23—2122no—
753C23—2122no—
754C23—2122no—
755C23—2122no—
756C23C22×D21212yes—
757C23C22×D21211yescharacteristic
758Q8—1062no—
759Q8—1062no—
760Q8—1062no—
761Q8—1062no—
762Q8—4244no—
763Q8—2122no—
764Q8—2122no—
765D4—1062no—
766D4—1062no—
767D4—1062no—
768D4—1062no—
769D4—1062no—
770D4—1062no—
771D4—1062no—
772D4—1062no—
773D4—4244no—
774D4—4244no—
775D4—4244no—
776D4—4244no—
777D4—4244no—
778D4—2128no—
779D4—2128no—
780D4—2122no—
781D4—2122no—
782D4—2122no—
783D4—2122no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—1062no—
793C2×C4—1062no—
794C2×C4—1062no—
795C2×C4—1062no—
796C2×C4—4244no—
797C2×C4—2128no—
798C2×C4—2122no—
799C2×C4—2122no—
800C2×C4—2122no—
801C2×C4—2122no—
802C2×C4C22×D21212yes—
803C2×C4C22×D21212yes—
804C2×C4C22×D21212yes—
805C2×C4C22×D21212yes—
806C2×C4C22×D21212yes—
807C2×C4C22×D21211yescharacteristic
808C2×C4#1313326312yes—
809C2×C4#1313326312yes—
810C2×C4C24×D5311yescharacteristic
811C8—22no—
812C8—22no—
813C8—22no—
814C8—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—44no—
819C22—42416no—
820C22—4244no—
821C22—4244no—
822C22—4244no—
823C22—4244no—
824C22—2122no—
825C22—2122no—
826C22—2122no—
827C22—2122no—
828C22—2122no—
829C22—2122no—
830C22—2122no—
831C22—2122no—
832C22—2122no—
833C22—2122no—
834C22—2122no—
835C22—2122no—
836C22#1681119212yes—
837C22#1681142812yes—
838C22#1681143512yes—
839C22C23×D21211yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—22no—
844C4—22no—
845C4—2122no—
846C4—2122no—
847C4—2122no—
848C4—2122no—
849C4#1681119212yes—
850C4C2×#1313326311yescharacteristic
851C4C2×#1313326311yescharacteristic
852C2—42no—
853C2—4242no—
854C2—4242no—
855C2—4242no—
856C2—4242no—
857C2#2028581114yesdirect product factor
858C2C2×#1681119211yescharacteristic
859C2C2×#1681142811yescharacteristic
860C2C2×#1681143511yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#433C2
socleC23×C53C22×D4
hypercenterC2×#433D53
hypocenterC53C2×#3224
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#16811244C2semidirect
2. C2×#16811192C2semidirect
3. #20285811C2direct (N × H)
4. C2×#16811012C2semidirect
5. C2×#16811007C2semidirect
6. C2×#16810983C2semidirect
7. C2×#16810970C2semidirect
8. C2×#16810846C2semidirect
9. C2×#16810824C2semidirect
10. C2×#16810839C2semidirect
11. C2×#16810819C2semidirect
12. C2×#16810787C2semidirect
13. C2×#16810770C2semidirect
14. C2×#16810776C2semidirect
15. C2×#16810759C2semidirect
16. C2×C53×#433C2semidirect
19. C22×Dic212C22semidirect
22. C22×#11719913C22semidirect
23. C22×#11719913C22semidirect
26. C22×D424C22semidirect
28. #16811244C22semidirect
30. #16811192C22semidirect
31. C2×#13133217C22semidirect
37. C2×#13133205C22semidirect
47. C2×C4×Dic106C22semidirect
48. C2×C4×D212C22semidirect
49. #16811012C22semidirect
50. #16811007C22semidirect
51. #16810983C22semidirect
52. #16810970C22semidirect
53. #16810846C22semidirect
54. #16810839C22semidirect
55. #16810824C22semidirect
56. #16810819C22semidirect
57. #16810787C22semidirect
58. #16810776C22semidirect
59. #16810770C22semidirect
60. #16810759C22semidirect
61. C2×#13133142C22semidirect
62. C2×#13133142C22semidirect
67. C2×#13133139C22semidirect
68. C2×#13133139C22semidirect
70. C53×#433C22semidirect
71. C2×C4⋊C8×C53C22semidirect
72. C2×C4⋊C8×C53C22semidirect
75. C2×#97×C53C22semidirect
76. C2×C4×C8×C53C22semidirect
103. C2×Dic212C23semidirect
110. C2×#11719913C23semidirect
111. C2×#11719913C23semidirect
117. C2×D424C23semidirect
119. #13133217C23semidirect
130. #13133205C23semidirect
143. C4×Dic106C23semidirect
145. C4×D212C23semidirect
161. #13133142C23semidirect
162. #13133142C23semidirect
167. #13133139C23semidirect
168. #13133139C23semidirect
182. C4⋊C8×C53C23semidirect
183. C4⋊C8×C53C23semidirect
186. #97×C53C23semidirect
187. C4×C8×C53C23semidirect
437. C2×#433D53semidirect
439. C2×C53#3224semidirect
492. #433C2×D53semidirect
493. C2×C4⋊C8C2×D53semidirect
494. C2×C4⋊C8C2×D53semidirect
505. C2×#97C2×D53semidirect
506. C2×C4×C8C2×D53semidirect
507. C53C2×#3224semidirect
605. C4⋊C8C22×D53semidirect
606. C4⋊C8C22×D53semidirect
617. #97C22×D53semidirect
618. C4×C8C22×D53semidirect
857. C2#20285811direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112442
C2×#168111922
#202858112
C2×#168110122
C2×#168110072
C2×#168109832
C2×#168109702
C2×#168108462
C2×#168108242
C2×#168108392
C2×#168108192
C2×#168107872
C2×#168107702
C2×#168107762
C2×#168107592
C2×C53×#4332
C2×#322453