Finite Group Databasebeta

← C2×#20284169 #28250911

Subgroups — C2×#20284169 #28250911

Order 13568.

2874 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133240C211yesmaximal, characteristic, complemented
2C22×#13133238C211yesmaximal, characteristic, complemented
3C2×#16811172C211yesmaximal, characteristic, complemented
4C2×C4×#11719949C211yesmaximal, characteristic, complemented
5#20284169C2116yesmaximal, direct product factor
6C2×#16810845C211yesmaximal, characteristic, complemented
7C2×#16810831C211yesmaximal, characteristic, complemented
8C2×#16810821C211yesmaximal, characteristic, complemented
9C2×#16810839C211yesmaximal, characteristic, complemented
10C2×#16810835C211yesmaximal, characteristic, complemented
11C2×#16810827C211yesmaximal, characteristic, complemented
12C2×#16810817C211yesmaximal, characteristic, complemented
13C2×C4⋊C8×D53C211yesmaximal, characteristic, complemented
14C2×#16810618C211yesmaximal, characteristic, complemented
15C2×#16810616C211yesmaximal, characteristic, complemented
16C2×C53×#464C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719949C2211yescharacteristic
19C22×#11719947C2211yescharacteristic
20C2×#13133240—28no—
21C2×#13133240C2218yescomplemented
22C2×#13133238—28no—
23C2×#13133238C2218yescomplemented
24C22×#11719925C2211yescharacteristic
25C22×#11719913C2211yescharacteristic
26C22×#11719924C2211yescharacteristic
27C22×#11719924C2211yescharacteristic
28C22×D424C2211yescharacteristic
29C22×#11719922C2211yescharacteristic
30C22×C8×D53C2211yescharacteristic
31C22×C8×D53C2211yescharacteristic
32#16811172—24no—
33#16811172C2218yescomplemented
34C2×#13133215C2211yescharacteristic
35C2×#13133213C2211yescharacteristic
36C2×#13133205C2211yescharacteristic
37C2×#13133190—21no—
38C2×#13133190—21no—
39C4×#11719949—24no—
40C4×#11719949C2218yescomplemented
41C2×Q8×Dic53C2211yescharacteristic
42C2×C4×D212—21no—
43C2×C4×D212C2211yescharacteristic
44C2×#13133179—21no—
45C2×#13133179C2211yescharacteristic
46C2×#13133177—21no—
47C2×#13133177—21no—
48C2×#13133175—21no—
49C2×#13133175C2211yescharacteristic
50C2×C42×D53—21no—
51C2×C42×D53C2211yescharacteristic
52#16810845C2218yescomplemented
53#16810839C2218yescomplemented
54#16810835C2218yescomplemented
55#16810831C2218yescomplemented
56#16810827C2218yescomplemented
57#16810821C2218yescomplemented
58#16810817C2218yescomplemented
59C2×C4⋊#88322C2211yescharacteristic
60C2×#13133146C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C4⋊C8×D53C2218yescomplemented
63#16810618C2218yescomplemented
64#16810616C2218yescomplemented
65C2×#13133142C2211yescharacteristic
66C2×#13133141C2211yescharacteristic
67C2×#13133140C2211yescharacteristic
68C2×#13133139C2211yescharacteristic
69C2×#13133138C2211yescharacteristic
70C2×#13133137C2211yescharacteristic
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×#11719949—22no—
80C2×#11719949—22no—
81C2×#11719949—24no—
82C2×#11719949—24no—
83C2×#11719949—24no—
84C2×#11719949D418yescomplemented
85C2×#11719949C2314yes—
86C2×#11719949C2314yes—
87C2×#11719947—24no—
88C2×#11719947—22no—
89C2×#11719947—24no—
90C2×#11719947C2314yes—
91C22×Dic106C2311yescharacteristic
92C22×D212—21no—
93C22×D212—21no—
94C22×D212C2311yescharacteristic
95C22×D212C2311yescharacteristic
96C22×C22⋊D53—21no—
97C22×C22⋊D53—21no—
98C22×C22⋊D53—21no—
99C23×Dic53—21no—
100C22×C4×D53—21no—
101C22×C4×D53—21no—
102C22×C4×D53—21no—
103C22×C4×D53—21no—
104C22×C4×D53D411yescharacteristic
105C22×C4×D53D411yescharacteristic
106C22×C4×D53C2311yescharacteristic
107#13133240—232no—
108#13133238—232no—
109C2×#11719925—24no—
110C2×#11719925C2314yes—
111C2×#11719913—24no—
112C2×#11719913C2314yes—
113C2×#11719924—24no—
114C2×#11719924—24no—
115C2×#11719924C2314yes—
116C2×#11719924C2314yes—
117C2×D424—24no—
118C2×D424C2314yes—
119C2×#11719922—24no—
120C2×#11719922C2314yes—
121C22×#88322C2311yescharacteristic
122C22×#88322C2311yescharacteristic
123C2×C8×D53—24no—
124C2×C8×D53—24no—
125C2×C8×D53C2314yes—
126C2×C8×D53C2314yes—
127#13133215—22no—
128#13133215C2314yes—
129#13133213—22no—
130#13133213C2314yes—
131#13133205—22no—
132#13133205C2314yes—
133#13133190—28no—
134#13133190—28no—
135Q8×Dic53—22no—
136Q8×Dic53C2314yes—
137C4×D212—22no—
138C4×D212—28no—
139C4×D212C2314yes—
140#13133179—22no—
141#13133179—28no—
142#13133179C2314yes—
143#13133177—28no—
144#13133177—28no—
145#13133175—28no—
146#13133175—22no—
147#13133175C2314yes—
148C2×C4⋊Dic53—21no—
149C2×C4⋊Dic53C2311yescharacteristic
150C2×#11719919—21no—
151C2×#11719919—21no—
152C2×#11719921—21no—
153C2×#11719921—21no—
154C2×#11719921—21no—
155C2×#11719921—21no—
156C2×#11719921—21no—
157C2×C4×Dic53—21no—
158C2×C4×Dic53—21no—
159C2×C4×Dic53D411yescharacteristic
160C2×C4×Dic53D411yescharacteristic
161C2×C4×Dic53C2311yescharacteristic
162C42×D53—28no—
163C42×D53D414yes—
164C42×D53C2314yes—
165C4⋊#88322C2314yes—
166#13133146C2314yes—
167#13133146C2314yes—
168#13133142C2314yes—
169#13133141C2314yes—
170#13133140C2314yes—
171#13133139C2314yes—
172#13133138C2314yes—
173#13133137C2314yes—
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×D53—21no—
198C23×D53—21no—
199C23×D53C2×D411yescharacteristic
200C2×Q8×C53—21no—
201C2×Q8×C53—21no—
202C2×Q8×C53—22no—
203C2×Q8×C53—22no—
204C2×Q8×C53—22no—
205C2×Q8×C53C2×D414yes—
206C2×Q8×C53C2412yes—
207C2×Q8×C53C2412yes—
208C2×D4×C53—22no—
209C2×D4×C53—21no—
210C2×D4×C53—22no—
211C2×D4×C53C2412yes—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2411yescharacteristic
218C2×C22⋊D53—24no—
219C2×C22⋊D53—24no—
220C2×C22⋊D53—24no—
221C2×C22⋊D53—44no—
222C2×C22⋊D53—44no—
223C2×C22⋊D53—44no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—24no—
227C22×Dic53—44no—
228C22×Dic53C2×D411yescharacteristic
229C22×Dic53C2×D411yescharacteristic
230C22×Dic53C2×D411yescharacteristic
231#11719949—216no—
232#11719949—28no—
233#11719949—28no—
234#11719949—28no—
235#11719949—48no—
236#11719949C2×D4116yescomplemented
237#11719947—28no—
238#11719947—28no—
239#11719947—48no—
240C2×D212—28no—
241C2×D212—24no—
242C2×D212—21no—
243C2×D212—22no—
244C2×D212—22no—
245C2×D212—22no—
246C2×D212—24no—
247C2×D212—21no—
248C2×D212—44no—
249C2×D212C2×D414yes—
250C2×D212C2412yes—
251C2×D212C2412yes—
252C2×C4×D53—28no—
253C2×C4×D53—24no—
254C2×C4×D53—24no—
255C2×C4×D53—24no—
256C2×C4×D53—24no—
257C2×C4×D53—24no—
258C2×C4×D53—42no—
259C2×C4×D53—44no—
260C2×C4×D53—44no—
261C2×C4×D53—44no—
262C2×C4×D53C2×D414yes—
263C2×C4×D53C2×D414yes—
264C2×C4×D53C2×D412yes—
265C2×C4×D53C2×D414yes—
266C2×C4×D53#4114yes—
267C2×C4×D53C2412yes—
268C2×Dic106—22no—
269C2×Dic106—22no—
270C2×Dic106—21no—
271C2×Dic106C2412yes—
272Q16×C53—28no—
273SD16×C53—28no—
274C2×C8×C53—22no—
275C2×C8×C53—22no—
276C2×C8×C53C2412yes—
277C2×C8×C53C2412yes—
278C4⋊C4×C53—24no—
279C4⋊C4×C53—21no—
280C4⋊C4×C53C2412yes—
281C22⋊C4×C53—24no—
282C22⋊C4×C53—24no—
283C42×C53—24no—
284C42×C53C2×D412yes—
285C42×C53C2412yes—
286#11719925—28no—
287#11719924—28no—
288#11719924—28no—
289#11719922—28no—
290#11719921—24no—
291#11719921—24no—
292#11719921—24no—
293#11719921—24no—
294#11719921—24no—
295C4⋊Dic53—21no—
296C4⋊Dic53—24no—
297C4⋊Dic53C2412yes—
298#11719919—24no—
299#11719919—24no—
300C4×Dic53—24no—
301C4×Dic53—24no—
302C4×Dic53C2×D414yes—
303C4×Dic53C2×D412yes—
304C4×Dic53C2×D414yes—
305C4×Dic53C2412yes—
306C2×#88322—22no—
307C2×#88322—22no—
308C2×#88322C2412yes—
309C2×#88322C2412yes—
310D424—28no—
311#11719913—28no—
312C8×D53—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—24no—
322C22×D53—22no—
323C22×D53—22no—
324C22×D53—42no—
325C22×D53—42no—
326C22×D53—42no—
327C22×D53—42no—
328C22×D53—42no—
329C22×D53#12114yes—
330C22×D53C22×D412yes—
331Q8×C53—24no—
332Q8×C53—22no—
333Q8×C53—22no—
334Q8×C53—22no—
335Q8×C53—42no—
336Q8×C53C22×D414yes—
337D4×C53—22no—
338D4×C53—22no—
339D4×C53—42no—
340C2×C4×C53—24no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—42no—
347C2×C4×C53—42no—
348C2×C4×C53C22×D412yes—
349C2×C4×C53C22×D412yes—
350C2×C4×C53C22×D411yescharacteristic
351C2×C4×C53C22×D412yes—
352C2×C4×C53C2×#4112yes—
353C2×C4×C53C2511yescharacteristic
354C22⋊D53—48no—
355C22⋊D53—48no—
356C22⋊D53—48no—
357C2×Dic53—22no—
358C2×Dic53—22no—
359C2×Dic53—22no—
360C2×Dic53—42no—
361C2×Dic53—42no—
362C2×Dic53—48no—
363C2×Dic53#12114yes—
364C2×Dic53#13514yescomplemented
365C2×Dic53C22×D412yes—
366C2×Dic53C22×D412yes—
367C2×Dic53C22×D412yes—
368D212—216no—
369D212—24no—
370D212—22no—
371D212—22no—
372D212—22no—
373D212—48no—
374D212—42no—
375D212C22×D414yes—
376C4×D53—216no—
377C4×D53—28no—
378C4×D53—44no—
379C4×D53—48no—
380C4×D53—48no—
381C4×D53—48no—
382C4×D53#12118yes—
383C4×D53C22×D414yes—
384C4×D53C2×#4114yes—
385Dic106—22no—
386Dic106—22no—
387Dic106—42no—
388C8×C53—22no—
389C8×C53—22no—
390#88322—22no—
391#88322—22no—
392C2×#3035—531nomaximal, Sylow
393C22×C53—42no—
394C22×C53—42no—
395C22×C53—42no—
396C22×C53—84no—
397C22×C53C2×#12112yes—
398C22×C53C2×#13512yes—
399C22×C53#57512yes—
400C22×C53C23×D411yescharacteristic
401C2×D53—28no—
402C2×D53—22no—
403C2×D53—22no—
404C2×D53—24no—
405C2×D53—48no—
406C2×D53—42no—
407C2×D53—42no—
408C2×D53—42no—
409C2×D53—42no—
410C2×D53—42no—
411C2×D53—84no—
412C2×D53C2×#12114yes—
413C4×C53—24no—
414C4×C53—22no—
415C4×C53—22no—
416C4×C53—42no—
417C4×C53—42no—
418C4×C53C2×#12112yes—
419C4×C53C23×D411yescharacteristic
420C4×C53C22×#4111yescharacteristic
421Dic53—22no—
422Dic53—42no—
423Dic53—42no—
424Dic53C2×#12114yes—
425Dic53C2×#13514yescomplemented
426C22×#135—531no—
427C22×#135—531no—
428C2×#532—531no—
429C2×C4×#41—531no—
430#3035—5316no—
431C2×#464—531no—
432C2×#464D5311yescharacteristic, complemented
433C2×#462—531no—
434C2×#460—531no—
435C2×#463—531no—
436C2×#463—531no—
437C2×#461—531no—
438C2×#459—531no—
439C22×C4⋊C8—531no—
440C2×#416—531no—
441C2×#416—531no—
442C2×C53—82no—
443C2×C53#303514yescomplemented
444C2×C53C22×#12111yescharacteristic
445C2×C53C22×#13511yescharacteristic
446C2×C53C2×#57511yescharacteristic
447D53—24no—
448D53—44no—
449D53—82no—
450C22×#41—531no—
451C22×#41—531no—
452C22×#41—531no—
453C2×#135—538no—
454C2×#135—538no—
455C2×#135—1068no—
456C2×#135—1068no—
457C22×Q16—531no—
458C22×Q16C2×D5311yescharacteristic
459C22×SD16—531no—
460C22×SD16—531no—
461C22×SD16—531no—
462C22×SD16C2×D5311yescharacteristic
463C22×D8—531no—
464C22×D8—531no—
465C23×C8—531no—
466C23×C8—531no—
467#532—538no—
468#532—1064no—
469C2×C4⋊Q8—531no—
470C2×#127—531no—
471C2×#124—531no—
472C2×#124C2×D5311yescharacteristic
473C2×#121—1061no—
474C2×#121—1061no—
475C4×#41—538no—
476C4×#41—1064no—
477C2×C4×Q8—531no—
478C2×C4×Q8C2×D5311yescharacteristic
479C2×C4×D4—531no—
480C2×C4×D4—531no—
481C2×C4×D4—1061no—
482C2×C4×D4—1061no—
483C2×C4×D4—1061no—
484C2×C4×D4—1061no—
485C2×#117—531no—
486C2×#117—1061no—
487C22×C42—531no—
488C22×C42—1061no—
489#464—538no—
490#464C2×D5318yescomplemented
491#463—538no—
492#463—538no—
493#462—538no—
494#461—538no—
495#460—538no—
496#459—538no—
497C2×C4⋊C8—531no—
498C2×C4⋊C8—531no—
499C2×C4⋊C8—531no—
500C2×C4⋊C8—538no—
501C2×C4⋊C8C2×D5311yescharacteristic
502#416—538no—
503#416—538no—
504C2×#103—531no—
505C2×#103—531no—
506C2×#103—531no—
507C2×#103C2×D5311yescharacteristic
508C2×#102—531no—
509C2×#102—531no—
510C2×#102—531no—
511C2×#102C2×D5311yescharacteristic
512C53C2×#303511yescharacteristic, complemented, Sylow
513C2×#41—538no—
514C2×#41—534no—
515C2×#41—534no—
516C2×#41—534no—
517C2×#41—1062no—
518C2×#41—1062no—
519C2×#41—1064no—
520C2×#41—1062no—
521C2×#41—1064no—
522C2×#41—1064no—
523C2×#41—1064no—
524C2×#41—1064no—
525C22×Q8—531no—
526C22×Q8C22×D5311yescharacteristic
527C22×Q8C22×D5311yescharacteristic
528C22×D4—531no—
529C22×D4—531no—
530C22×D4—1061no—
531C22×D4—1061no—
532C22×D4—1061no—
533C22×D4—1061no—
534C22×D4—1061no—
535C22×D4C22×D5311yescharacteristic
536C23×C4—531no—
537C23×C4—531no—
538C23×C4—531no—
539C23×C4—1061no—
540C23×C4—1061no—
541C23×C4—1061no—
542C23×C4—1061no—
543C23×C4—1061no—
544#135—10632no—
545#135—10632no—
546C2×Q16—24no—
547C2×Q16—534no—
548C2×Q16—1064no—
549C2×Q16C22×D5314yes—
550C2×SD16—24no—
551C2×SD16—534no—
552C2×SD16—534no—
553C2×SD16—534no—
554C2×SD16—1064no—
555C2×SD16—1064no—
556C2×SD16—1064no—
557C2×SD16C22×D5314yes—
558C2×D8—534no—
559C2×D8—534no—
560C2×D8—1064no—
561C2×D8—1064no—
562C22×C8—531no—
563C22×C8—531no—
564C22×C8—534no—
565C22×C8—534no—
566C22×C8—1064no—
567C22×C8—1064no—
568C22×C8C22×D5311yescharacteristic
569C22×C8C22×D5311yescharacteristic
570C4⋊Q8—534no—
571C4⋊Q8—1062no—
572#127—534no—
573#127—1062no—
574#124—22no—
575#124—534no—
576#124—1062no—
577#124C22×D5314yes—
578#121—1068no—
579#121—1068no—
580C4×Q8—22no—
581C4×Q8—534no—
582C4×Q8—1062no—
583C4×Q8C22×D5314yes—
584C4×D4—534no—
585C4×D4—534no—
586C4×D4—1068no—
587C4×D4—1068no—
588C4×D4—1068no—
589C4×D4—1062no—
590C4×D4—1068no—
591C4×D4—1062no—
592#117—534no—
593#117—1068no—
594#117—1062no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—531no—
597C2×C4⋊C4—1061no—
598C2×C4⋊C4—1061no—
599C2×C4⋊C4—1061no—
600C2×C4⋊C4C22×D5311yescharacteristic
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—1061no—
604C2×C22⋊C4—1061no—
605C2×C22⋊C4—1061no—
606C2×C22⋊C4—1061no—
607C2×C22⋊C4—1061no—
608C2×C42—21no—
609C2×C42—531no—
610C2×C42—531no—
611C2×C42—531no—
612C2×C42—534no—
613C2×C42—534no—
614C2×C42—1068no—
615C2×C42—1061no—
616C2×C42—1061no—
617C2×C42C22×D5311yescharacteristic
618C4⋊C8—534no—
619C4⋊C8—534no—
620C4⋊C8—534no—
621C4⋊C8C22×D5314yes—
622#103—534no—
623#103—534no—
624#103—534no—
625#103C22×D5314yes—
626#102—534no—
627#102—534no—
628#102—534no—
629#102C22×D5314yes—
630C24—21no—
631C24—531no—
632C24—1061no—
633C24—1061no—
634#41—5316no—
635#41—10616no—
636#41—1068no—
637#41—1068no—
638#41—1068no—
639#41—1068no—
640#41—1068no—
641#41—2128no—
642#41—2128no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8—22no—
648C2×Q8—532no—
649C2×Q8—1061no—
650C2×Q8—1062no—
651C2×Q8—1062no—
652C2×Q8D4×D5314yes—
653C2×Q8C23×D5312yes—
654C2×Q8C23×D5312yes—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—534no—
659C2×D4—532no—
660C2×D4—532no—
661C2×D4—1064no—
662C2×D4—1068no—
663C2×D4—1064no—
664C2×D4—1064no—
665C2×D4—1064no—
666C2×D4—1064no—
667C2×D4—1061no—
668C2×D4—1062no—
669C2×D4—1061no—
670C2×D4—1062no—
671C2×D4—1062no—
672C2×D4—2124no—
673C2×D4—2124no—
674C2×D4—2124no—
675C2×D4—2124no—
676C2×D4C23×D5312yes—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—531no—
681C22×C4—531no—
682C22×C4—532no—
683C22×C4—534no—
684C22×C4—534no—
685C22×C4—532no—
686C22×C4—531no—
687C22×C4—534no—
688C22×C4—534no—
689C22×C4—1064no—
690C22×C4—1064no—
691C22×C4—1068no—
692C22×C4—1064no—
693C22×C4—1064no—
694C22×C4—1064no—
695C22×C4—1061no—
696C22×C4—1061no—
697C22×C4—1064no—
698C22×C4—2122no—
699C22×C4—2124no—
700C22×C4—2124no—
701C22×C4—2124no—
702C22×C4—2124no—
703C22×C4D4×D5311yescharacteristic
704C22×C4D4×D5311yescharacteristic
705C22×C4C23×D5311yescharacteristic
706Q16—28no—
707Q16—1068no—
708SD16—28no—
709SD16—1068no—
710SD16—1068no—
711SD16—1068no—
712D8—1068no—
713D8—1068no—
714C2×C8—22no—
715C2×C8—22no—
716C2×C8—532no—
717C2×C8—532no—
718C2×C8—1068no—
719C2×C8—1068no—
720C2×C8—1062no—
721C2×C8—1062no—
722C2×C8C23×D5312yes—
723C2×C8C23×D5312yes—
724C4⋊C4—24no—
725C4⋊C4—21no—
726C4⋊C4—532no—
727C4⋊C4—1064no—
728C4⋊C4—1064no—
729C4⋊C4—1064no—
730C4⋊C4—1061no—
731C4⋊C4C23×D5312yes—
732C22⋊C4—24no—
733C22⋊C4—24no—
734C22⋊C4—1064no—
735C22⋊C4—1064no—
736C22⋊C4—1064no—
737C22⋊C4—1064no—
738C22⋊C4—1064no—
739C42—24no—
740C42—534no—
741C42—534no—
742C42—532no—
743C42—532no—
744C42—1064no—
745C42—1064no—
746C42D4×D5312yes—
747C42C23×D5312yes—
748C23—22no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—534no—
753C23—532no—
754C23—1062no—
755C23—1062no—
756C23—1064no—
757C23—1062no—
758C23—1062no—
759C23—2122no—
760C23—2122no—
761C23—2122no—
762C23—2122no—
763C23—2122no—
764C23C2×D4×D5311yescharacteristic
765Q8—24no—
766Q8—22no—
767Q8—22no—
768Q8—22no—
769Q8—42no—
770Q8—1062no—
771Q8—1062no—
772Q8—2122no—
773Q8C2×D4×D5314yes—
774D4—22no—
775D4—22no—
776D4—42no—
777D4—534no—
778D4—10616no—
779D4—1064no—
780D4—1062no—
781D4—1062no—
782D4—1062no—
783D4—2128no—
784D4—2128no—
785D4—2128no—
786D4—2128no—
787D4—2122no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—534no—
797C2×C4—534no—
798C2×C4—532no—
799C2×C4—532no—
800C2×C4—538no—
801C2×C4—534no—
802C2×C4—534no—
803C2×C4—532no—
804C2×C4—1068no—
805C2×C4—10616no—
806C2×C4—1062no—
807C2×C4—1062no—
808C2×C4—1062no—
809C2×C4—2124no—
810C2×C4—2128no—
811C2×C4—2128no—
812C2×C4—2128no—
813C2×C4—2128no—
814C2×C4—2122no—
815C2×C4—2122no—
816C2×C4C2×D4×D5312yes—
817C2×C4C2×D4×D5312yes—
818C2×C4C2×D4×D5311yescharacteristic
819C2×C4C2×D4×D5312yes—
820C2×C4#41×D5312yes—
821C2×C4C24×D5311yescharacteristic
822C8—22no—
823C8—22no—
824C8—1062no—
825C8—1062no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—84no—
830C22—534no—
831C22—1068no—
832C22—1062no—
833C22—1062no—
834C22—1064no—
835C22—4244no—
836C22—2122no—
837C22—2122no—
838C22—2122no—
839C22—2128no—
840C22—2122no—
841C22—2122no—
842C22#121×D5312yes—
843C22#135×D5312yes—
844C22#1681142212yes—
845C22C22×D4×D5311yescharacteristic
846C4—22no—
847C4—22no—
848C4—24no—
849C4—42no—
850C4—42no—
851C4—534no—
852C4—534no—
853C4—1062no—
854C4—2122no—
855C4—2122no—
856C4#121×D5312yes—
857C4C22×D4×D5311yescharacteristic
858C4C2×#41×D5311yescharacteristic
859C2—82no—
860C2—1064no—
861C2—4242no—
862C2—2124no—
863C2#2028416914yesdirect product factor
864C2C2×#121×D5311yescharacteristic
865C2C2×#135×D5311yescharacteristic
866C2C2×#1681142211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#464C2
socleC23×C53C22×D4
hypercenterC2×#464D53
hypocenterC53C2×#3035
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×#13133240C2semidirect
2. C22×#13133238C2semidirect
3. C2×#16811172C2semidirect
4. C2×C4×#11719949C2semidirect
5. #20284169C2direct (N × H)
6. C2×#16810845C2semidirect
7. C2×#16810831C2semidirect
8. C2×#16810821C2semidirect
9. C2×#16810839C2semidirect
10. C2×#16810835C2semidirect
11. C2×#16810827C2semidirect
12. C2×#16810817C2semidirect
13. C2×C4⋊C8×D53C2semidirect
14. C2×#16810618C2semidirect
15. C2×#16810616C2semidirect
16. C2×C53×#464C2semidirect
21. C2×#13133240C22semidirect
23. C2×#13133238C22semidirect
33. #16811172C22semidirect
40. C4×#11719949C22semidirect
52. #16810845C22semidirect
53. #16810839C22semidirect
54. #16810835C22semidirect
55. #16810831C22semidirect
56. #16810827C22semidirect
57. #16810821C22semidirect
58. #16810817C22semidirect
62. C4⋊C8×D53C22semidirect
63. #16810618C22semidirect
64. #16810616C22semidirect
75. C53×#464C22semidirect
84. C2×#11719949D4semidirect
236. #11719949C2×D4semidirect
364. C2×Dic53#135semidirect
425. Dic53C2×#135semidirect
432. C2×#464D53semidirect
443. C2×C53#3035semidirect
490. #464C2×D53semidirect
512. C53C2×#3035semidirect
863. C2#20284169direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332402
C22×#131332382
C2×#168111722
C2×C4×#117199492
#202841692
C2×#168108452
C2×#168108312
C2×#168108212
C2×#168108392
C2×#168108352
C2×#168108272
C2×#168108172
C2×C4⋊C8×D532
C2×#168106182
C2×#168106162
C2×C53×#4642
C2×#303553