Finite Group Databasebeta

← C2×#20284234 #28250995

Subgroups — C2×#20284234 #28250995

Order 13568.

2858 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133249C211yesmaximal, characteristic, complemented
2C22×SD16×D53C211yesmaximal, characteristic, complemented
3C2×#16811191C211yesmaximal, characteristic
4C2×#16811099C211yesmaximal, characteristic, complemented
5#20284234C2116yesmaximal, direct product factor
6C2×#16810848C211yesmaximal, characteristic, complemented
7C2×#16810847C211yesmaximal, characteristic, complemented
8C2×#16810842C211yesmaximal, characteristic, complemented
9C2×#16810824C211yesmaximal, characteristic, complemented
10C2×#16810823C211yesmaximal, characteristic, complemented
11C2×#16810822C211yesmaximal, characteristic, complemented
12C2×#16810821C211yesmaximal, characteristic, complemented
13C2×#16810648C211yesmaximal, characteristic, complemented
14C2×#16810626C211yesmaximal, characteristic, complemented
15C2×#16810618C211yesmaximal, characteristic, complemented
16C2×C53×#464C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×D4×D53C2211yescharacteristic
20C2×#13133249—28no—
21C2×#13133249C2218yescomplemented
22C22×#11719925C2211yescharacteristic, complemented
23C22×#11719913C2211yescharacteristic
24C22×#11719913C2211yescharacteristic, complemented
25C22×#11719923C2211yescharacteristic
26C22×#11719924C2211yescharacteristic
27C22×#11719924C2211yescharacteristic, complemented
28C2×SD16×D53—28no—
29C2×SD16×D53C2218yescomplemented
30C22×#11719912C2211yescharacteristic
31C22×C8×D53C2211yescharacteristic
32#16811191—24no—
33#16811191C2218yes—
34C2×#13133214C2211yescharacteristic
35C2×#13133213C2211yescharacteristic
36C2×#13133206C2211yescharacteristic
37C2×#13133190—21no—
38C2×#13133190—21no—
39C2×#13133187—21no—
40C2×#13133187—21no—
41#16811099—24no—
42#16811099C2218yescomplemented
43C2×Q8×Dic53C2211yescharacteristic, complemented
44C2×C4×Dic106—21no—
45C2×C4×Dic106C2211yescharacteristic, complemented
46C2×#13133182—21no—
47C2×#13133182C2211yescharacteristic, complemented
48C2×#13133175—21no—
49C2×#13133175C2211yescharacteristic
50C2×#13133174—21no—
51C2×#13133174C2211yescharacteristic
52#16810848C2218yescomplemented
53#16810847C2218yescomplemented
54#16810842C2218yescomplemented
55#16810824C2218yescomplemented
56#16810823C2218yescomplemented
57#16810822C2218yescomplemented
58#16810821C2218yescomplemented
59#16810648C2218yescomplemented
60C2×C4⋊#88322C2211yescharacteristic, complemented
61C2×#13133146C2211yescharacteristic, complemented
62C2×#13133146C2211yescharacteristic, complemented
63#16810626C2218yescomplemented
64#16810618C2218yescomplemented
65C2×#13133141C2211yescharacteristic, complemented
66C2×#13133139C2211yescharacteristic
67C2×#13133139C2211yescharacteristic, complemented
68C2×#13133138C2211yescharacteristic
69C2×#13133137C2211yescharacteristic
70C2×#13133137C2211yescharacteristic, complemented
71C22×Q16×C53C2211yescharacteristic, complemented
72C22×SD16×C53C2211yescharacteristic
73C2×#124×C53C2211yescharacteristic
74C2×C4×Q8×C53C2211yescharacteristic, complemented
75C53×#464C2218yescomplemented
76C2×C4⋊C8×C53C2211yescharacteristic, complemented
77C2×#103×C53C2211yescharacteristic, complemented
78C2×#102×C53C2211yescharacteristic
79C24×D53—21no—
80C2×#11719949—22no—
81C2×#11719949—24no—
82C2×#11719949—24no—
83C2×#11719949C2314yes—
84C22×Dic106—21no—
85C22×Dic106C2311yescharacteristic
86C2×Q8×D53—22no—
87C2×Q8×D53—24no—
88C2×Q8×D53D418yescomplemented
89C2×Q8×D53C2314yes—
90C22×D212—21no—
91C22×D212—21no—
92C22×D212—21no—
93C22×D212C2311yescharacteristic
94C22×D212C2311yescharacteristic
95C22×C22⋊D53—21no—
96C22×C22⋊D53—21no—
97C22×C22⋊D53—21no—
98C2×D4×D53—24no—
99C2×D4×D53—22no—
100C2×D4×D53—24no—
101C2×D4×D53C2314yes—
102C22×C4×D53—21no—
103C22×C4×D53—21no—
104C22×C4×D53C2311yescharacteristic
105#13133249—232no—
106C2×#11719925—24no—
107C2×#11719925C2314yescomplemented
108C2×#11719913—24no—
109C2×#11719913—24no—
110C2×#11719913C2314yes—
111C2×#11719913C2314yescomplemented
112C2×#11719923—24no—
113C2×#11719923C2314yes—
114C2×#11719924—24no—
115C2×#11719924—24no—
116C2×#11719924C2314yes—
117C2×#11719924C2314yescomplemented
118SD16×D53—232no—
119C2×#11719912—24no—
120C2×#11719912C2314yes—
121C22×#88322C2311yescharacteristic
122C22×#88322C2311yescharacteristic
123C2×C8×D53—24no—
124C2×C8×D53C2314yes—
125#13133214—22no—
126#13133214C2314yes—
127#13133213—22no—
128#13133213C2314yes—
129#13133206—22no—
130#13133206C2314yes—
131#13133190—28no—
132#13133190—28no—
133#13133187—28no—
134#13133187—28no—
135Q8×Dic53—22no—
136Q8×Dic53C2314yescomplemented
137C4×Dic106—22no—
138C4×Dic106—28no—
139C4×Dic106C2314yescomplemented
140#13133182—28no—
141#13133182—22no—
142#13133182C2314yescomplemented
143#13133175—28no—
144#13133175—22no—
145#13133175C2314yes—
146#13133174—28no—
147#13133174D414yes—
148#13133174C2314yes—
149C2×C4⋊Dic53—21no—
150C2×C4⋊Dic53C2311yescharacteristic
151C2×#11719919—21no—
152C2×#11719919—21no—
153C2×#11719919D411yescharacteristic
154C2×#11719919D411yescharacteristic
155C2×#11719921—21no—
156C2×#11719921—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⋊#88322C2314yescomplemented
166#13133146C2314yescomplemented
167#13133146C2314yescomplemented
168#13133141C2314yescomplemented
169#13133139C2314yes—
170#13133139C2314yescomplemented
171#13133138C2314yes—
172#13133137C2314yes—
173#13133137C2314yescomplemented
174C22×Q8×C53C2311yescharacteristic
175C22×Q8×C53C2311yescharacteristic
176C22×D4×C53C2311yescharacteristic
177C2×Q16×C53—24no—
178C2×Q16×C53C2314yescomplemented
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×C53C2314yescomplemented
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×C53C2314yescomplemented
194#103×C53C2314yescomplemented
195#102×C53C2314yes—
196C24×C53—21no—
197C23×D53—21no—
198C23×D53—21no—
199C23×D53—24no—
200C23×D53—44no—
201C23×D53—82no—
202C23×D53—82no—
203C23×D53C2×D411yescharacteristic
204C2×Q8×C53—21no—
205C2×Q8×C53—21no—
206C2×Q8×C53—22no—
207C2×Q8×C53—22no—
208C2×Q8×C53—22no—
209C2×Q8×C53C2×D414yes—
210C2×Q8×C53C2412yes—
211C2×Q8×C53C2412yes—
212C2×D4×C53—22no—
213C2×D4×C53—21no—
214C2×D4×C53—22no—
215C2×D4×C53C2412yes—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53C2×D411yescharacteristic
220C22×C4×C53C2×D411yescharacteristic
221C22×C4×C53C2411yescharacteristic
222C2×C22⋊D53—24no—
223C2×C22⋊D53—24no—
224C2×C22⋊D53—24no—
225C2×C22⋊D53—44no—
226C2×C22⋊D53—82no—
227C2×C22⋊D53—82no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230C22×Dic53C2×D411yescharacteristic
231C22×Dic53C2×D411yescharacteristic
232C22×Dic53C2×D411yescharacteristic
233#11719949—28no—
234#11719949—28no—
235#11719949—48no—
236Q8×D53—216no—
237Q8×D53—28no—
238Q8×D53C2×D4116yescomplemented
239D4×D53—28no—
240D4×D53—28no—
241D4×D53—48no—
242C2×D212—22no—
243C2×D212—22no—
244C2×D212—22no—
245C2×D212—22no—
246C2×D212—24no—
247C2×D212—21no—
248C2×D212—21no—
249C2×D212—24no—
250C2×D212—24no—
251C2×D212—44no—
252C2×D212—82no—
253C2×D212—82no—
254C2×D212C2412yes—
255C2×D212C2412yes—
256C2×C4×D53—28no—
257C2×C4×D53—24no—
258C2×C4×D53—24no—
259C2×C4×D53—44no—
260C2×C4×D53C2×D412yes—
261C2×C4×D53C2×D414yes—
262C2×C4×D53#4114yes—
263C2×C4×D53C2412yes—
264C2×Dic106—21no—
265C2×Dic106—22no—
266C2×Dic106—28no—
267C2×Dic106—24no—
268C2×Dic106C2×D414yes—
269C2×Dic106C2412yes—
270Q16×C53—28no—
271SD16×C53—28no—
272C2×C8×C53—22no—
273C2×C8×C53—22no—
274C2×C8×C53C2412yes—
275C2×C8×C53C2412yes—
276C4⋊C4×C53—24no—
277C4⋊C4×C53—21no—
278C4⋊C4×C53C2412yes—
279C22⋊C4×C53—24no—
280C22⋊C4×C53—24no—
281C42×C53—24no—
282C42×C53C2×D412yes—
283C42×C53C2412yes—
284#11719925—28no—
285#11719924—28no—
286#11719924—28no—
287#11719923—28no—
288#11719921—24no—
289#11719921—24no—
290#11719921—24no—
291#11719921C2×D414yes—
292#11719921C2×D414yes—
293C4⋊Dic53—21no—
294C4⋊Dic53—24no—
295C4⋊Dic53C2412yes—
296#11719919—24no—
297#11719919—24no—
298#11719919C2×D414yes—
299#11719919C2×D414yes—
300C4×Dic53—24no—
301C4×Dic53—24no—
302C4×Dic53—24no—
303C4×Dic53—24no—
304C4×Dic53C2×D412yes—
305C4×Dic53C2412yes—
306C2×#88322—22no—
307C2×#88322—22no—
308C2×#88322C2412yes—
309C2×#88322C2412yes—
310#11719913—28no—
311#11719913—28no—
312#11719912—28no—
313C8×D53—28no—
314C23×C53—22no—
315C23×C53—42no—
316C23×C53—42no—
317C23×C53—42no—
318C23×C53C22×D411yescharacteristic
319C22×D53—22no—
320C22×D53—22no—
321C22×D53—22no—
322C22×D53—22no—
323C22×D53—42no—
324C22×D53—42no—
325C22×D53—42no—
326C22×D53—42no—
327C22×D53—42no—
328C22×D53—42no—
329C22×D53—48no—
330C22×D53—84no—
331C22×D53—84no—
332C22×D53—816no—
333C22×D53#12114yes—
334C22×D53C22×D412yes—
335Q8×C53—24no—
336Q8×C53—22no—
337Q8×C53—22no—
338Q8×C53—22no—
339Q8×C53—42no—
340Q8×C53C22×D414yes—
341D4×C53—22no—
342D4×C53—22no—
343D4×C53—42no—
344C2×C4×C53—24no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—42no—
351C2×C4×C53—42no—
352C2×C4×C53C22×D412yes—
353C2×C4×C53C22×D412yes—
354C2×C4×C53C22×D411yescharacteristic
355C2×C4×C53C22×D412yes—
356C2×C4×C53C2×#4112yes—
357C2×C4×C53C2511yescharacteristic
358C22⋊D53—48no—
359C22⋊D53—84no—
360C22⋊D53—84no—
361C2×Dic53—24no—
362C2×Dic53—22no—
363C2×Dic53—22no—
364C2×Dic53—22no—
365C2×Dic53—22no—
366C2×Dic53—42no—
367C2×Dic53#12114yes—
368C2×Dic53C22×D412yes—
369C2×Dic53C22×D412yes—
370C2×Dic53C22×D412yes—
371D212—22no—
372D212—22no—
373D212—22no—
374D212—22no—
375D212—48no—
376D212—42no—
377D212—42no—
378D212—84no—
379D212—84no—
380C4×D53—216no—
381C4×D53—48no—
382C4×D53#12118yes—
383C4×D53C22×D414yes—
384C4×D53C2×#4114yes—
385Dic106—24no—
386Dic106—22no—
387Dic106—216no—
388Dic106C22×D414yes—
389C8×C53—22no—
390C8×C53—22no—
391#88322—22no—
392#88322—22no—
393C2×#3043—531nomaximal, Sylow
394C22×C53—42no—
395C22×C53—42no—
396C22×C53—42no—
397C22×C53—84no—
398C22×C53C2×#12112yes—
399C22×C53#57712yes—
400C22×C53#57712yes—
401C22×C53C23×D411yescharacteristic
402C2×D53—28no—
403C2×D53—22no—
404C2×D53—22no—
405C2×D53—42no—
406C2×D53—42no—
407C2×D53—42no—
408C2×D53—42no—
409C2×D53—42no—
410C2×D53—42no—
411C2×D53—816no—
412C2×D53—84no—
413C2×D53—84no—
414C2×D53C2×#12114yes—
415C4×C53—24no—
416C4×C53—22no—
417C4×C53—22no—
418C4×C53—42no—
419C4×C53—42no—
420C4×C53C2×#12112yes—
421C4×C53C23×D411yescharacteristic
422C4×C53C22×#4111yescharacteristic
423Dic53—24no—
424Dic53—22no—
425Dic53—22no—
426Dic53—42no—
427Dic53C2×#12114yes—
428C22×#137—531no—
429C23×SD16—531no—
430C2×#535—531no—
431C2×#519—531no—
432#3043—5316no—
433C2×#464—531no—
434C2×#464—531no—
435C2×#464—531no—
436C2×#464D5311yescharacteristic, complemented
437C2×#460—531no—
438C2×#460—531no—
439C2×#460—531no—
440C2×#460—531no—
441C2×#424—531no—
442C2×#418—531no—
443C2×#416—531no—
444C2×C53—82no—
445C2×C53#304314yescomplemented
446C2×C53C22×#12111yescharacteristic
447C2×C53C2×#57711yescharacteristic
448C2×C53C2×#57711yescharacteristic
449D53—24no—
450D53—82no—
451D53—82no—
452C22×#41—531no—
453C23×Q8—531no—
454C23×D4—531no—
455C2×#137—538no—
456C2×#137—1068no—
457C22×Q16—531no—
458C22×Q16C2×D5311yescharacteristic, complemented
459C22×SD16—531no—
460C22×SD16—531no—
461C22×SD16—531no—
462C22×SD16—538no—
463C22×SD16—531no—
464C22×SD16—531no—
465C22×SD16—1068no—
466C22×SD16C2×D5311yescharacteristic
467C22×M16—531no—
468C23×C8—531no—
469#535—538no—
470#535—1064no—
471C2×#127—531no—
472C2×#127—531no—
473C2×#124—531no—
474C2×#124C2×D5311yescharacteristic
475C2×#121—1061no—
476C2×#121—1061no—
477C2×#120—1061no—
478C2×#120—1061no—
479#519—538no—
480#519—1064no—
481C2×C4×Q8—531no—
482C2×C4×Q8—531no—
483C2×C4×Q8—531no—
484C2×C4×Q8—1061no—
485C2×C4×Q8—1061no—
486C2×C4×Q8C2×D5311yescharacteristic, complemented
487C2×#117—531no—
488C2×#117—531no—
489C2×#117—1061no—
490C2×#117—1061no—
491#464—538no—
492#464—538no—
493#464—538no—
494#464C2×D5318yescomplemented
495#460—538no—
496#460—538no—
497#460—538no—
498#460—538no—
499#424—538no—
500C2×C4⋊C8—531no—
501C2×C4⋊C8—531no—
502C2×C4⋊C8—531no—
503C2×C4⋊C8C2×D5311yescharacteristic, complemented
504#418—538no—
505#416—538no—
506C2×#103—531no—
507C2×#103C2×D5311yescharacteristic, complemented
508C2×#102—531no—
509C2×#102—531no—
510C2×#102—531no—
511C2×#102—531no—
512C2×#102—531no—
513C2×#102C2×D5311yescharacteristic
514C53C2×#304311yescharacteristic, complemented, Sylow
515C25—1061no—
516C2×#41—534no—
517C2×#41—1062no—
518C2×#41—1064no—
519C2×#41—1064no—
520C22×Q8—538no—
521C22×Q8—534no—
522C22×Q8—531no—
523C22×Q8—1061no—
524C22×Q8—1062no—
525C22×Q8—1064no—
526C22×Q8C22×D5311yescharacteristic
527C22×Q8C22×D5311yescharacteristic
528C22×D4—534no—
529C22×D4—531no—
530C22×D4—531no—
531C22×D4—1061no—
532C22×D4—1064no—
533C22×D4—1064no—
534C22×D4—1062no—
535C22×D4—1061no—
536C22×D4—1061no—
537C22×D4—1061no—
538C22×D4—1061no—
539C22×D4—1061no—
540C22×D4C22×D5311yescharacteristic
541C23×C4—531no—
542C23×C4—1061no—
543C23×C4—1061no—
544#137—10632no—
545C2×Q16—24no—
546C2×Q16—534no—
547C2×Q16—1064no—
548C2×Q16C22×D5314yescomplemented
549C2×SD16—24no—
550C2×SD16—534no—
551C2×SD16—534no—
552C2×SD16—534no—
553C2×SD16—534no—
554C2×SD16—534no—
555C2×SD16—1064no—
556C2×SD16—1064no—
557C2×SD16—10632no—
558C2×SD16—1064no—
559C2×SD16—1064no—
560C2×SD16—1064no—
561C2×SD16C22×D5314yes—
562C2×M16—534no—
563C2×M16—1064no—
564C22×C8—531no—
565C22×C8—531no—
566C22×C8—534no—
567C22×C8—1064no—
568C22×C8C22×D5311yescharacteristic
569C22×C8C22×D5311yescharacteristic
570#127—534no—
571#127—534no—
572#127—1062no—
573#127—1062no—
574#124—22no—
575#124—534no—
576#124—1062no—
577#124C22×D5314yes—
578#121—1068no—
579#121—1068no—
580#120—1068no—
581#120—1068no—
582C4×Q8—22no—
583C4×Q8—534no—
584C4×Q8—534no—
585C4×Q8—534no—
586C4×Q8—1068no—
587C4×Q8—1062no—
588C4×Q8—1062no—
589C4×Q8—1068no—
590C4×Q8—1062no—
591C4×Q8C22×D5314yescomplemented
592#117—534no—
593#117—534no—
594#117—534no—
595#117—1068no—
596#117—1068no—
597#117—1062no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—531no—
600C2×C4⋊C4—531no—
601C2×C4⋊C4—531no—
602C2×C4⋊C4—1061no—
603C2×C4⋊C4—1061no—
604C2×C4⋊C4—1061no—
605C2×C4⋊C4C22×D5311yescharacteristic
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—531no—
609C2×C22⋊C4—531no—
610C2×C22⋊C4—1061no—
611C2×C22⋊C4—1061no—
612C2×C22⋊C4—1061no—
613C2×C42—21no—
614C2×C42—531no—
615C2×C42—1061no—
616C2×C42—1061no—
617C2×C42—1061no—
618C2×C42—1061no—
619C2×C42C22×D5311yescharacteristic
620C4⋊C8—534no—
621C4⋊C8—534no—
622C4⋊C8—534no—
623C4⋊C8C22×D5314yescomplemented
624#103—534no—
625#103C22×D5314yescomplemented
626#102—534no—
627#102—534no—
628#102—534no—
629#102—534no—
630#102—534no—
631#102C22×D5314yes—
632C24—21no—
633C24—531no—
634C24—1064no—
635C24—1061no—
636C24—1061no—
637C24—4242no—
638C24—4242no—
639C24—2124no—
640#41—1068no—
641#41—1068no—
642#41—2128no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8—22no—
648C2×Q8—5316no—
649C2×Q8—534no—
650C2×Q8—532no—
651C2×Q8—1064no—
652C2×Q8—1068no—
653C2×Q8—10616no—
654C2×Q8—1068no—
655C2×Q8—1061no—
656C2×Q8—1062no—
657C2×Q8D4×D5314yes—
658C2×Q8C23×D5312yes—
659C2×Q8C23×D5312yes—
660C2×D4—22no—
661C2×D4—21no—
662C2×D4—22no—
663C2×D4—532no—
664C2×D4—532no—
665C2×D4—1064no—
666C2×D4—1068no—
667C2×D4—1068no—
668C2×D4—1064no—
669C2×D4—1064no—
670C2×D4—1064no—
671C2×D4—1062no—
672C2×D4—1062no—
673C2×D4—1064no—
674C2×D4—1064no—
675C2×D4—1061no—
676C2×D4—1061no—
677C2×D4—1062no—
678C2×D4—1062no—
679C2×D4—4242no—
680C2×D4—4242no—
681C2×D4—4242no—
682C2×D4—4242no—
683C2×D4—2124no—
684C2×D4—2128no—
685C2×D4—2124no—
686C2×D4C23×D5312yes—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—531no—
691C22×C4—532no—
692C22×C4—534no—
693C22×C4—534no—
694C22×C4—532no—
695C22×C4—531no—
696C22×C4—531no—
697C22×C4—1064no—
698C22×C4—1064no—
699C22×C4—1068no—
700C22×C4—1061no—
701C22×C4—1061no—
702C22×C4—2124no—
703C22×C4D4×D5311yescharacteristic
704C22×C4D4×D5311yescharacteristic
705C22×C4C23×D5311yescharacteristic
706Q16—28no—
707Q16—1068no—
708SD16—28no—
709SD16—1068no—
710SD16—1068no—
711SD16—1068no—
712SD16—1068no—
713SD16—1068no—
714M16—1068no—
715C2×C8—22no—
716C2×C8—22no—
717C2×C8—532no—
718C2×C8—532no—
719C2×C8—1068no—
720C2×C8—1062no—
721C2×C8—1062no—
722C2×C8C23×D5312yes—
723C2×C8C23×D5312yes—
724C4⋊C4—24no—
725C4⋊C4—21no—
726C4⋊C4—534no—
727C4⋊C4—534no—
728C4⋊C4—532no—
729C4⋊C4—1064no—
730C4⋊C4—1064no—
731C4⋊C4—1061no—
732C4⋊C4—1064no—
733C4⋊C4C23×D5312yes—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—534no—
737C22⋊C4—534no—
738C22⋊C4—1064no—
739C22⋊C4—1064no—
740C22⋊C4—1064no—
741C42—24no—
742C42—532no—
743C42—532no—
744C42—1064no—
745C42—1064no—
746C42—1064no—
747C42—1064no—
748C42D4×D5312yes—
749C42C23×D5312yes—
750C23—22no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—534no—
755C23—532no—
756C23—1062no—
757C23—1062no—
758C23—1062no—
759C23—1062no—
760C23—4244no—
761C23—4244no—
762C23—42416no—
763C23—2128no—
764C23—2122no—
765C23—2122no—
766C23—2122no—
767C23—2122no—
768C23—2122no—
769C23—2122no—
770C23C2×D4×D5311yescharacteristic
771Q8—24no—
772Q8—22no—
773Q8—22no—
774Q8—22no—
775Q8—42no—
776Q8—534no—
777Q8—10616no—
778Q8—1064no—
779Q8—1062no—
780Q8C2×D4×D5314yes—
781D4—22no—
782D4—22no—
783D4—42no—
784D4—1062no—
785D4—1062no—
786D4—1062no—
787D4—1062no—
788D4—4244no—
789D4—4244no—
790D4—4244no—
791D4—4244no—
792D4—2128no—
793D4—2128no—
794D4—2122no—
795D4—2122no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—534no—
805C2×C4—532no—
806C2×C4—538no—
807C2×C4—534no—
808C2×C4—534no—
809C2×C4—532no—
810C2×C4—532no—
811C2×C4—10616no—
812C2×C4—1064no—
813C2×C4—1062no—
814C2×C4—1062no—
815C2×C4—1062no—
816C2×C4—1062no—
817C2×C4—2128no—
818C2×C4—2122no—
819C2×C4C2×D4×D5312yes—
820C2×C4C2×D4×D5312yes—
821C2×C4C2×D4×D5311yescharacteristic
822C2×C4C2×D4×D5312yes—
823C2×C4#41×D5312yes—
824C2×C4C24×D5311yescharacteristic
825C8—22no—
826C8—22no—
827C8—1062no—
828C8—1062no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—84no—
833C22—534no—
834C22—1068no—
835C22—1062no—
836C22—1062no—
837C22—42416no—
838C22—4244no—
839C22—4244no—
840C22—2122no—
841C22—2122no—
842C22—2122no—
843C22—2122no—
844C22—2122no—
845C22—2122no—
846C22#121×D5312yes—
847C22#1681143012yes—
848C22#1681143212yes—
849C22C22×D4×D5311yescharacteristic
850C4—24no—
851C4—22no—
852C4—22no—
853C4—42no—
854C4—42no—
855C4—534no—
856C4—1064no—
857C4—1062no—
858C4—1062no—
859C4—2122no—
860C4#121×D5312yes—
861C4C22×D4×D5311yescharacteristic
862C4C2×#41×D5311yescharacteristic
863C2—82no—
864C2—1064no—
865C2—4242no—
866C2—4242no—
867C2#2028423414yesdirect product factor
868C2C2×#121×D5311yescharacteristic
869C2C2×#1681143011yescharacteristic
870C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#464C2
socleC23×C53C22×D4
prime radicalC2×#16811191C2
hypercenterC2×#464D53
hypocenterC53C2×#3043
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
1. C22×#13133249C2semidirect
2. C22×SD16×D53C2semidirect
4. C2×#16811099C2semidirect
5. #20284234C2direct (N × H)
6. C2×#16810848C2semidirect
7. C2×#16810847C2semidirect
8. C2×#16810842C2semidirect
9. C2×#16810824C2semidirect
10. C2×#16810823C2semidirect
11. C2×#16810822C2semidirect
12. C2×#16810821C2semidirect
13. C2×#16810648C2semidirect
14. C2×#16810626C2semidirect
15. C2×#16810618C2semidirect
16. C2×C53×#464C2semidirect
21. C2×#13133249C22semidirect
22. C22×#11719925C22semidirect
24. C22×#11719913C22semidirect
27. C22×#11719924C22semidirect
29. C2×SD16×D53C22semidirect
42. #16811099C22semidirect
43. C2×Q8×Dic53C22semidirect
45. C2×C4×Dic106C22semidirect
47. C2×#13133182C22semidirect
52. #16810848C22semidirect
53. #16810847C22semidirect
54. #16810842C22semidirect
55. #16810824C22semidirect
56. #16810823C22semidirect
57. #16810822C22semidirect
58. #16810821C22semidirect
59. #16810648C22semidirect
60. C2×C4⋊#88322C22semidirect
61. C2×#13133146C22semidirect
62. C2×#13133146C22semidirect
63. #16810626C22semidirect
64. #16810618C22semidirect
65. C2×#13133141C22semidirect
67. C2×#13133139C22semidirect
70. C2×#13133137C22semidirect
71. C22×Q16×C53C22semidirect
74. C2×C4×Q8×C53C22semidirect
75. C53×#464C22semidirect
76. C2×C4⋊C8×C53C22semidirect
77. C2×#103×C53C22semidirect
88. C2×Q8×D53D4semidirect
107. C2×#11719925C23semidirect
111. C2×#11719913C23semidirect
117. C2×#11719924C23semidirect
136. Q8×Dic53C23semidirect
139. C4×Dic106C23semidirect
142. #13133182C23semidirect
165. C4⋊#88322C23semidirect
166. #13133146C23semidirect
167. #13133146C23semidirect
168. #13133141C23semidirect
170. #13133139C23semidirect
173. #13133137C23semidirect
178. C2×Q16×C53C23semidirect
186. C4×Q8×C53C23semidirect
193. C4⋊C8×C53C23semidirect
194. #103×C53C23semidirect
238. Q8×D53C2×D4semidirect
436. C2×#464D53semidirect
445. C2×C53#3043semidirect
458. C22×Q16C2×D53semidirect
486. C2×C4×Q8C2×D53semidirect
494. #464C2×D53semidirect
503. C2×C4⋊C8C2×D53semidirect
507. C2×#103C2×D53semidirect
514. C53C2×#3043semidirect
548. C2×Q16C22×D53semidirect
591. C4×Q8C22×D53semidirect
623. C4⋊C8C22×D53semidirect
625. #103C22×D53semidirect
867. C2#20284234direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332492
C22×SD16×D532
C2×#168111912
C2×#168110992
#202842342
C2×#168108482
C2×#168108472
C2×#168108422
C2×#168108242
C2×#168108232
C2×#168108222
C2×#168108212
C2×#168106482
C2×#168106262
C2×#168106182
C2×C53×#4642
C2×#304353