Finite Group Databasebeta

← C2×#20285562 #28254740

Subgroups — C2×#20285562 #28254740

Order 13568.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811202C211yesmaximal, characteristic, complemented
2C2×#16811189C211yesmaximal, characteristic, complemented
3#20285562C2116yesmaximal, direct product factor
4C2×#16810943C211yesmaximal, characteristic, complemented
5C2×#16810967C211yesmaximal, characteristic, complemented
6C2×#16810945C211yesmaximal, characteristic, complemented
7C2×#16810935C211yesmaximal, characteristic, complemented
8C2×#16810869C211yesmaximal, characteristic, complemented
9C2×#16810857C211yesmaximal, characteristic, complemented
10C2×#16810850C211yesmaximal, characteristic, complemented
11C2×#16810769C211yesmaximal, characteristic, complemented
12C2×#16810765C211yesmaximal, characteristic, complemented
13C2×#16810775C211yesmaximal, characteristic, complemented
14C2×#16810755C211yesmaximal, characteristic, complemented
15C2×#16810591C211yesmaximal, characteristic, complemented
16C2×C53×#469C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×#11719947C2211yescharacteristic, complemented
19C22×D4×D53C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×#11719923C2211yescharacteristic
22C22×#11719922C2211yescharacteristic
23C23×#88322C2211yescharacteristic, complemented
24#16811202—24no—
25#16811202C2218yescomplemented
26#16811189—24no—
27#16811189C2218yescomplemented
28C2×#13133213—21no—
29C2×#13133203—21no—
30C2×#13133197C2211yescharacteristic
31C2×#13133196C2211yescharacteristic, complemented
32C2×#13133194—21no—
33C2×#13133192C2211yescharacteristic
34C2×#13133191C2211yescharacteristic
35C2×#13133190—21no—
36C2×#13133189—21no—
37C2×#13133188—21no—
38C2×#13133188C2211yescharacteristic
39C2×#13133188C2211yescharacteristic
40C2×#13133187—21no—
41C2×#13133185—21no—
42C2×#13133175C2211yescharacteristic
43C2×C4⋊C4×D53C2211yescharacteristic, complemented
44#16810967C2218yescomplemented
45#16810945C2218yescomplemented
46#16810943C2218yescomplemented
47#16810935C2218yescomplemented
48#16810869C2218yescomplemented
49#16810857C2218yescomplemented
50#16810850C2218yescomplemented
51#16810775C2218yescomplemented
52#16810769C2218yescomplemented
53#16810765C2218yescomplemented
54#16810755C2218yescomplemented
55C2×#13133151C2211yescharacteristic, complemented
56C2×#13133150C2211yescharacteristic, complemented
57C2×#13133148C2211yescharacteristic, complemented
58C2×#13133142C2211yescharacteristic, complemented
59C2×#13133140C2211yescharacteristic, complemented
60C2×#13133139C2211yescharacteristic
61C2×#13133138C2211yescharacteristic
62C2×#13133138C2211yescharacteristic, complemented
63C2×#13133137C2211yescharacteristic
64#16810591C2218yescomplemented
65C2×#13133129C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic, complemented
68C2×#13133129C2211yescharacteristic, complemented
69C22×D8×C53C2211yescharacteristic
70C22×M16×C53C2211yescharacteristic, complemented
71C2×#121×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic, complemented
73C53×#469C2218yescomplemented
74C2×#106×C53C2211yescharacteristic, complemented
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C2×#11719945—42no—
79C2×#11719945—42no—
80C2×#11719945D414yes—
81C2×#11719945C2314yes—
82C2×#11719947—22no—
83C2×#11719947—42no—
84C2×#11719947—42no—
85C2×#11719947C2314yescomplemented
86C22×Dic106D411yescharacteristic
87C22×Dic106C2311yescharacteristic
88C22×D212—21no—
89C22×D212D411yescharacteristic
90C22×D212C2311yescharacteristic
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C22×C22⋊D53—21no—
94C22×C22⋊D53—21no—
95C22×C22⋊D53—21no—
96C22×C22⋊D53D411yescharacteristic
97C22×C22⋊D53D411yescharacteristic
98C2×D4×D53—22no—
99C2×D4×D53—42no—
100C2×D4×D53—42no—
101C2×D4×D53C2314yes—
102C23×Dic53—21no—
103C22×C4×D53—21no—
104C22×C4×D53C2311yescharacteristic
105C22×C4×D53C2311yescharacteristic
106C2×#11719913—42no—
107C2×#11719913C2314yes—
108C2×#11719923—42no—
109C2×#11719923C2314yes—
110C2×#11719922—42no—
111C2×#11719922C2314yes—
112C22×#88322—42no—
113C22×#88322C2311yescharacteristic
114C22×#88322C2311yescharacteristic
115C22×#88322C2314yescomplemented
116#13133213—28no—
117#13133203—28no—
118#13133197—22no—
119#13133197C2314yes—
120#13133196—22no—
121#13133196C2314yescomplemented
122#13133194—28no—
123#13133192—22no—
124#13133192C2314yes—
125#13133191—22no—
126#13133191C2314yes—
127#13133190—28no—
128#13133189—28no—
129#13133188—28no—
130#13133188—22no—
131#13133188—22no—
132#13133188C2314yes—
133#13133188C2314yes—
134#13133187—28no—
135#13133185—28no—
136#13133175—22no—
137#13133175C2314yes—
138C2×C4⋊Dic53—21no—
139C2×C4⋊Dic53C2311yescharacteristic
140C2×C4⋊Dic53C2311yescharacteristic
141C2×#11719919—21no—
142C2×#11719919—21no—
143C4⋊C4×D53—22no—
144C4⋊C4×D53C2314yescomplemented
145C2×C22⋊Dic53—21no—
146C2×C22⋊Dic53—21no—
147C2×C22⋊Dic53—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×#11719921—21no—
152C2×C4×Dic53—21no—
153#13133151C2314yescomplemented
154#13133150C2314yescomplemented
155#13133148C2314yescomplemented
156#13133142C2314yescomplemented
157#13133140C2314yescomplemented
158#13133139C2314yes—
159#13133138C2314yes—
160#13133138C2314yescomplemented
161#13133137C2314yes—
162#13133129C2314yes—
163#13133129C2314yes—
164#13133129C2314yescomplemented
165#13133129C2314yescomplemented
166C22×D4×C53—21no—
167C22×D4×C53—21no—
168C22×D4×C53C2311yescharacteristic
169C22×D4×C53C2311yescharacteristic
170C23×C4×C53C2311yescharacteristic
171C2×D8×C53—42no—
172C2×D8×C53C2314yes—
173C2×M16×C53—42no—
174C2×M16×C53C2314yescomplemented
175C22×C8×C53C2311yescharacteristic
176C22×C8×C53C2311yescharacteristic
177#121×C53—22no—
178#121×C53—22no—
179#121×C53C2314yes—
180#121×C53C2314yescomplemented
181C2×C4⋊C4×C53C2311yescharacteristic
182C2×C4⋊C4×C53C2311yescharacteristic
183C2×C22⋊C4×C53—21no—
184C2×C22⋊C4×C53—21no—
185#106×C53C2314yescomplemented
186#102×C53C2314yes—
187#102×C53C2314yescomplemented
188C24×C53—21no—
189C24×C53—21no—
190C24×C53C2×D411yescharacteristic
191C23×D53—21no—
192C23×D53—24no—
193C23×D53—44no—
194C23×D53—82no—
195C23×D53—82no—
196C23×D53C2×D411yescharacteristic
197C23×D53C2×D411yescharacteristic
198C2×D4×C53—24no—
199C2×D4×C53—24no—
200C2×D4×C53—21no—
201C2×D4×C53—21no—
202C2×D4×C53—22no—
203C2×D4×C53—22no—
204C2×D4×C53—22no—
205C2×D4×C53—22no—
206C2×D4×C53—82no—
207C2×D4×C53—82no—
208C2×D4×C53C2412yes—
209C2×D4×C53C2412yes—
210C22×C4×C53—22no—
211C22×C4×C53—22no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D412yes—
216C22×C4×C53C2412yes—
217C22×C4×C53C2411yescharacteristic
218C2×C22⋊D53—24no—
219C2×C22⋊D53—24no—
220C2×C22⋊D53—24no—
221C2×C22⋊D53—24no—
222C2×C22⋊D53—24no—
223C2×C22⋊D53—42no—
224C2×C22⋊D53—42no—
225C2×C22⋊D53—44no—
226C2×C22⋊D53—44no—
227C2×C22⋊D53—82no—
228C2×C22⋊D53—82no—
229C2×C22⋊D53—82no—
230C2×C22⋊D53C2×D414yes—
231C2×C22⋊D53C2×D414yes—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—24no—
236C22×Dic53—44no—
237C22×Dic53C2×D411yescharacteristic
238C22×Dic53C2×D411yescharacteristic
239#11719947—44no—
240#11719947—44no—
241#11719947—48no—
242D4×D53—44no—
243D4×D53—44no—
244D4×D53—48no—
245#11719945—48no—
246#11719945—44no—
247#11719945—44no—
248C2×D212—22no—
249C2×D212—22no—
250C2×D212—21no—
251C2×D212—24no—
252C2×D212—42no—
253C2×D212—82no—
254C2×D212C2×D414yes—
255C2×D212C2412yes—
256C2×C4×D53—22no—
257C2×C4×D53—22no—
258C2×C4×D53—22no—
259C2×C4×D53—22no—
260C2×C4×D53—24no—
261C2×C4×D53—82no—
262C2×C4×D53C2×D412yes—
263C2×C4×D53C2×D412yes—
264C2×C4×D53C2412yes—
265C2×C4×D53C2412yes—
266C2×Dic106—22no—
267C2×Dic106—22no—
268C2×Dic106—21no—
269C2×Dic106—42no—
270C2×Dic106C2×D414yes—
271C2×Dic106C2412yes—
272D8×C53—44no—
273M16×C53—44no—
274C2×C8×C53—22no—
275C2×C8×C53—22no—
276C2×C8×C53C2412yes—
277C2×C8×C53C2412yes—
278C4⋊C4×C53—21no—
279C4⋊C4×C53—21no—
280C4⋊C4×C53C2412yes—
281C4⋊C4×C53C2412yes—
282C22⋊C4×C53—24no—
283C22⋊C4×C53—24no—
284C22⋊Dic53—24no—
285C22⋊Dic53—24no—
286C22⋊Dic53—24no—
287#11719923—44no—
288#11719922—44no—
289#11719921—24no—
290#11719921—24no—
291#11719921—24no—
292#11719921—24no—
293C4⋊Dic53—21no—
294C4⋊Dic53—21no—
295C4⋊Dic53—24no—
296C4⋊Dic53C2412yes—
297C4⋊Dic53C2412yes—
298#11719919—24no—
299#11719919—24no—
300C4×Dic53—24no—
301C2×#88322—22no—
302C2×#88322—22no—
303C2×#88322—44no—
304C2×#88322C2412yes—
305C2×#88322C2412yes—
306#11719913—44no—
307C23×C53—22no—
308C23×C53—22no—
309C23×C53—22no—
310C23×C53—22no—
311C23×C53—22no—
312C23×C53—42no—
313C23×C53—42no—
314C23×C53—42no—
315C23×C53—42no—
316C23×C53—42no—
317C23×C53—42no—
318C23×C53C22×D412yes—
319C23×C53C22×D411yescharacteristic
320C22×D53—22no—
321C22×D53—22no—
322C22×D53—22no—
323C22×D53—22no—
324C22×D53—22no—
325C22×D53—22no—
326C22×D53—22no—
327C22×D53—48no—
328C22×D53—42no—
329C22×D53—42no—
330C22×D53—42no—
331C22×D53—84no—
332C22×D53—84no—
333C22×D53—816no—
334C22×D53C22×D412yes—
335C22×D53C22×D412yes—
336D4×C53—22no—
337D4×C53—22no—
338D4×C53—22no—
339D4×C53—22no—
340D4×C53—42no—
341D4×C53—42no—
342D4×C53—84no—
343D4×C53—84no—
344C2×C4×C53—22no—
345C2×C4×C53—24no—
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×D411yescharacteristic
354C2×C4×C53H(5,𝔽2)12yes—
355C2×C4×C53H(5,𝔽2)12yes—
356C2×C4×C53C2511yescharacteristic
357C22⋊D53—44no—
358C22⋊D53—44no—
359C22⋊D53—48no—
360C22⋊D53—48no—
361C22⋊D53—84no—
362C22⋊D53—84no—
363C22⋊D53—84no—
364C2×Dic53—22no—
365C2×Dic53—22no—
366C2×Dic53—22no—
367C2×Dic53—22no—
368C2×Dic53—22no—
369C2×Dic53—48no—
370C2×Dic53—42no—
371C2×Dic53—42no—
372C2×Dic53—42no—
373C2×Dic53C22×D412yes—
374C2×Dic53C22×D412yes—
375D212—22no—
376D212—22no—
377D212—44no—
378D212—42no—
379D212—84no—
380C4×D53—24no—
381C4×D53—24no—
382C4×D53—22no—
383C4×D53—22no—
384C4×D53—22no—
385C4×D53—22no—
386C4×D53—84no—
387Dic106—22no—
388Dic106—22no—
389Dic106—44no—
390Dic106—42no—
391C8×C53—22no—
392C8×C53—22no—
393#88322—22no—
394#88322—22no—
395C2×#3198—531nomaximal, Sylow
396C22×C53—22no—
397C22×C53—22no—
398C22×C53—22no—
399C22×C53—44no—
400C22×C53—42no—
401C22×C53—42no—
402C22×C53—42no—
403C22×C53—42no—
404C22×C53—42no—
405C22×C53—42no—
406C22×C53—84no—
407C22×C53—84no—
408C22×C53#53412yes—
409C22×C53#57612yes—
410C22×C53#57712yes—
411C22×C53C23×D411yescharacteristic
412C2×D53—22no—
413C2×D53—22no—
414C2×D53—22no—
415C2×D53—22no—
416C2×D53—22no—
417C2×D53—22no—
418C2×D53—44no—
419C2×D53—44no—
420C2×D53—42no—
421C2×D53—42no—
422C2×D53—42no—
423C2×D53—816no—
424C2×D53—84no—
425C4×C53—22no—
426C4×C53—42no—
427C4×C53—42no—
428C4×C53#53412yes—
429C4×C53C2×H(5,𝔽2)11yescharacteristic
430C4×C53C2×H(5,𝔽2)11yescharacteristic
431Dic53—22no—
432Dic53—22no—
433Dic53—42no—
434Dic53—42no—
435Dic53—42no—
436C2×#537—531no—
437C2×#535—531no—
438#3198—5316no—
439C2×#481—531no—
440C2×#485—531no—
441C2×#482—531no—
442C2×#480—531no—
443C2×#469D5311yescharacteristic, complemented
444C2×#468—531no—
445C2×#466—531no—
446C2×#465—531no—
447C2×#449—531no—
448C2×#449—531no—
449C2×#450—531no—
450C2×#447—531no—
451C2×#408—531no—
452C2×C53—42no—
453C2×C53—82no—
454C2×C53—82no—
455C2×C53#319814yescomplemented
456C2×C53C2×#53411yescharacteristic
457C2×C53C2×#57611yescharacteristic
458C2×C53C2×#57711yescharacteristic
459D53—42no—
460D53—42no—
461D53—82no—
462C22×#41—531no—
463C22×#41—531no—
464C23×D4—531no—
465C22×SD16—531no—
466C22×SD16—531no—
467C22×D8—531no—
468C22×D8C2×D5311yescharacteristic
469C22×M16C2×D5311yescharacteristic, complemented
470C23×C8—531no—
471#537—538no—
472#537—1064no—
473#535—538no—
474#535—1064no—
475C2×#127—1061no—
476C2×#124—1061no—
477C2×C22⋊Q8—531no—
478C2×C22⋊Q8—531no—
479C2×C22⋊Q8—1061no—
480C2×#121—531no—
481C2×#121—531no—
482C2×#121—531no—
483C2×#121—531no—
484C2×#121—1061no—
485C2×#121—1061no—
486C2×#121—1061no—
487C2×#121C2×D5311yescharacteristic
488C2×#121C2×D5311yescharacteristic, complemented
489C2×#120—1061no—
490C2×#120—1061no—
491C2×#117—531no—
492C22×C4⋊C4—531no—
493#485—538no—
494#482—538no—
495#481—538no—
496#480—538no—
497#469C2×D5318yescomplemented
498#468—538no—
499#466—538no—
500#465—538no—
501#450—538no—
502#449—538no—
503#449—538no—
504#447—538no—
505C2×#107—531no—
506C2×#107—531no—
507C2×#106—531no—
508C2×#106C2×D5311yescharacteristic, complemented
509C2×#103—531no—
510C2×#103—531no—
511C2×#102—531no—
512C2×#102—531no—
513C2×#102—531no—
514C2×#102—531no—
515C2×#102C2×D5311yescharacteristic
516C2×#102C2×D5311yescharacteristic, complemented
517#408—538no—
518C2×C22⋊C8—531no—
519C2×C22⋊C8—531no—
520C2×C22⋊C8—531no—
521C2×C22⋊C8—531no—
522C53C2×#319811yescharacteristic, complemented, Sylow
523C25—1061no—
524C2×#41—534no—
525C2×#41—534no—
526C2×#41—534no—
527C2×#41—1062no—
528C2×#41—2122no—
529C2×#41—2122no—
530C2×#41—2122no—
531C2×#41—2122no—
532C22×Q8—531no—
533C22×Q8—531no—
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—531no—
537C22×D4—531no—
538C22×D4—534no—
539C22×D4—531no—
540C22×D4—531no—
541C22×D4—1061no—
542C22×D4—1062no—
543C22×D4—1061no—
544C22×D4—1061no—
545C22×D4—1061no—
546C22×D4—1061no—
547C22×D4—1061no—
548C22×D4—2122no—
549C22×D4—2122no—
550C22×D4C22×D5311yescharacteristic
551C22×D4C22×D5311yescharacteristic
552C23×C4—531no—
553C23×C4—531no—
554C23×C4—1061no—
555C23×C4—1061no—
556C23×C4C22×D5311yescharacteristic
557C2×SD16—534no—
558C2×SD16—534no—
559C2×SD16—2122no—
560C2×SD16—2122no—
561C2×D8—42no—
562C2×D8—534no—
563C2×D8—2122no—
564C2×D8C22×D5314yes—
565C2×M16—42no—
566C2×M16C22×D5314yescomplemented
567C22×C8—531no—
568C22×C8—531no—
569C22×C8—534no—
570C22×C8—2122no—
571C22×C8C22×D5311yescharacteristic
572C22×C8C22×D5311yescharacteristic
573#127—1068no—
574#124—1068no—
575C22⋊Q8—534no—
576C22⋊Q8—534no—
577C22⋊Q8—1068no—
578C22⋊Q8—1062no—
579C22⋊Q8—1062no—
580#121—22no—
581#121—22no—
582#121—534no—
583#121—534no—
584#121—534no—
585#121—534no—
586#121—1068no—
587#121—1062no—
588#121—1062no—
589#121—1062no—
590#121—1068no—
591#121—1068no—
592#121—1062no—
593#121C22×D5314yes—
594#121C22×D5314yescomplemented
595#120—1068no—
596#120—1068no—
597#117—534no—
598#117—1062no—
599C2×C4⋊C4—531no—
600C2×C4⋊C4—531no—
601C2×C4⋊C4—534no—
602C2×C4⋊C4—1062no—
603C2×C4⋊C4—1061no—
604C2×C4⋊C4—1061no—
605C2×C4⋊C4—1061no—
606C2×C4⋊C4C22×D5311yescharacteristic
607C2×C4⋊C4C22×D5311yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—1061no—
611C2×C22⋊C4—1061no—
612C2×C22⋊C4—1061no—
613C2×C22⋊C4—1061no—
614C2×C22⋊C4—1061no—
615C2×C22⋊C4—1061no—
616C2×C22⋊C4—1061no—
617C2×C42—1061no—
618#107—534no—
619#107—534no—
620#106—534no—
621#106C22×D5314yescomplemented
622#103—534no—
623#103—534no—
624#102—534no—
625#102—534no—
626#102—534no—
627#102—534no—
628#102C22×D5314yes—
629#102C22×D5314yescomplemented
630C22⋊C8—534no—
631C22⋊C8—534no—
632C22⋊C8—534no—
633C22⋊C8—534no—
634C24—21no—
635C24—21no—
636C24—531no—
637C24—531no—
638C24—1064no—
639C24—1061no—
640C24—4242no—
641C24—4242no—
642C24—2124no—
643C24D4×D5311yescharacteristic
644#41—2128no—
645#41—2124no—
646#41—2124no—
647#41—2124no—
648#41—2124no—
649#41—2128no—
650C2×Q8—534no—
651C2×Q8—532no—
652C2×Q8—1061no—
653C2×Q8—1062no—
654C2×Q8—1062no—
655C2×Q8—2122no—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—22no—
664C2×D4—82no—
665C2×D4—82no—
666C2×D4—534no—
667C2×D4—534no—
668C2×D4—534no—
669C2×D4—532no—
670C2×D4—1064no—
671C2×D4—1064no—
672C2×D4—1064no—
673C2×D4—1064no—
674C2×D4—1064no—
675C2×D4—1064no—
676C2×D4—1061no—
677C2×D4—1062no—
678C2×D4—1062no—
679C2×D4—4242no—
680C2×D4—4242no—
681C2×D4—4242no—
682C2×D4—4242no—
683C2×D4—2122no—
684C2×D4—2124no—
685C2×D4—2124no—
686C2×D4—2128no—
687C2×D4—2122no—
688C2×D4—2122no—
689C2×D4—2124no—
690C2×D4—2124no—
691C2×D4C23×D5312yes—
692C2×D4C23×D5312yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—531no—
698C22×C4—531no—
699C22×C4—532no—
700C22×C4—532no—
701C22×C4—532no—
702C22×C4—532no—
703C22×C4—1064no—
704C22×C4—1064no—
705C22×C4—1062no—
706C22×C4—1062no—
707C22×C4—1062no—
708C22×C4—1062no—
709C22×C4—1061no—
710C22×C4—1061no—
711C22×C4—1061no—
712C22×C4—4242no—
713C22×C4—2124no—
714C22×C4D4×D5312yes—
715C22×C4D4×D5311yescharacteristic
716C22×C4C23×D5312yes—
717C22×C4C23×D5311yescharacteristic
718SD16—2124no—
719SD16—2124no—
720D8—44no—
721D8—2124no—
722M16—44no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—532no—
726C2×C8—532no—
727C2×C8—1062no—
728C2×C8—1062no—
729C2×C8—2124no—
730C2×C8C23×D5312yes—
731C2×C8C23×D5312yes—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—532no—
735C4⋊C4—532no—
736C4⋊C4—1064no—
737C4⋊C4—1064no—
738C4⋊C4—1061no—
739C4⋊C4—1061no—
740C4⋊C4—1064no—
741C4⋊C4C23×D5312yes—
742C4⋊C4C23×D5312yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—1064no—
746C22⋊C4—1064no—
747C22⋊C4—1064no—
748C22⋊C4—1064no—
749C22⋊C4—1064no—
750C22⋊C4—1064no—
751C22⋊C4—1064no—
752C42—1064no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—532no—
765C23—532no—
766C23—1062no—
767C23—1062no—
768C23—1062no—
769C23—1062no—
770C23—1062no—
771C23—1062no—
772C23—1062no—
773C23—4244no—
774C23—4244no—
775C23—42416no—
776C23—2128no—
777C23—2122no—
778C23—2122no—
779C23—2122no—
780C23C2×D4×D5312yes—
781C23C2×D4×D5311yescharacteristic
782Q8—1062no—
783Q8—1062no—
784Q8—2124no—
785Q8—2122no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—42no—
791D4—42no—
792D4—84no—
793D4—84no—
794D4—1062no—
795D4—1062no—
796D4—4244no—
797D4—4244no—
798D4—4244no—
799D4—4244no—
800D4—2124no—
801D4—2124no—
802D4—2124no—
803D4—2128no—
804D4—2128no—
805D4—2122no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—532no—
815C2×C4—532no—
816C2×C4—1062no—
817C2×C4—1062no—
818C2×C4—1064no—
819C2×C4—1064no—
820C2×C4—1062no—
821C2×C4—1062no—
822C2×C4—1062no—
823C2×C4—1062no—
824C2×C4—1062no—
825C2×C4—1062no—
826C2×C4—1062no—
827C2×C4—4244no—
828C2×C4—2128no—
829C2×C4—2122no—
830C2×C4—2122no—
831C2×C4—2122no—
832C2×C4C2×D4×D5312yes—
833C2×C4C2×D4×D5311yescharacteristic
834C2×C4#1313326212yes—
835C2×C4#1313326312yes—
836C2×C4C24×D5311yescharacteristic
837C8—22no—
838C8—22no—
839C8—1062no—
840C8—1062no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—84no—
852C22—84no—
853C22—1062no—
854C22—1062no—
855C22—1062no—
856C22—1062no—
857C22—1062no—
858C22—1062no—
859C22—42416no—
860C22—4244no—
861C22—2122no—
862C22—2122no—
863C22—2122no—
864C22—2124no—
865C22—2124no—
866C22#1681118112yes—
867C22#1681142712yes—
868C22#1681143312yes—
869C22C22×D4×D5311yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—1062no—
874C4—1062no—
875C4—2122no—
876C4—2122no—
877C4—2122no—
878C4#1681118112yes—
879C4C2×#1313326211yescharacteristic
880C4C2×#1313326311yescharacteristic
881C2—42no—
882C2—82no—
883C2—82no—
884C2—4242no—
885C2—2122no—
886C2—2122no—
887C2#2028556214yesdirect product factor
888C2C2×#1681118111yescharacteristic
889C2C2×#1681142711yescharacteristic
890C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#469C2
socleC23×C53C22×D4
hypercenterC2×#469D53
hypocenterC53C2×#3198
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#16811202C2semidirect
2. C2×#16811189C2semidirect
3. #20285562C2direct (N × H)
4. C2×#16810943C2semidirect
5. C2×#16810967C2semidirect
6. C2×#16810945C2semidirect
7. C2×#16810935C2semidirect
8. C2×#16810869C2semidirect
9. C2×#16810857C2semidirect
10. C2×#16810850C2semidirect
11. C2×#16810769C2semidirect
12. C2×#16810765C2semidirect
13. C2×#16810775C2semidirect
14. C2×#16810755C2semidirect
15. C2×#16810591C2semidirect
16. C2×C53×#469C2semidirect
18. C22×#11719947C22semidirect
23. C23×#88322C22semidirect
25. #16811202C22semidirect
27. #16811189C22semidirect
31. C2×#13133196C22semidirect
43. C2×C4⋊C4×D53C22semidirect
44. #16810967C22semidirect
45. #16810945C22semidirect
46. #16810943C22semidirect
47. #16810935C22semidirect
48. #16810869C22semidirect
49. #16810857C22semidirect
50. #16810850C22semidirect
51. #16810775C22semidirect
52. #16810769C22semidirect
53. #16810765C22semidirect
54. #16810755C22semidirect
55. C2×#13133151C22semidirect
56. C2×#13133150C22semidirect
57. C2×#13133148C22semidirect
58. C2×#13133142C22semidirect
59. C2×#13133140C22semidirect
62. C2×#13133138C22semidirect
64. #16810591C22semidirect
67. C2×#13133129C22semidirect
68. C2×#13133129C22semidirect
70. C22×M16×C53C22semidirect
72. C2×#121×C53C22semidirect
73. C53×#469C22semidirect
74. C2×#106×C53C22semidirect
76. C2×#102×C53C22semidirect
85. C2×#11719947C23semidirect
115. C22×#88322C23semidirect
121. #13133196C23semidirect
144. C4⋊C4×D53C23semidirect
153. #13133151C23semidirect
154. #13133150C23semidirect
155. #13133148C23semidirect
156. #13133142C23semidirect
157. #13133140C23semidirect
160. #13133138C23semidirect
164. #13133129C23semidirect
165. #13133129C23semidirect
174. C2×M16×C53C23semidirect
180. #121×C53C23semidirect
185. #106×C53C23semidirect
187. #102×C53C23semidirect
443. C2×#469D53semidirect
455. C2×C53#3198semidirect
469. C22×M16C2×D53semidirect
488. C2×#121C2×D53semidirect
497. #469C2×D53semidirect
508. C2×#106C2×D53semidirect
516. C2×#102C2×D53semidirect
522. C53C2×#3198semidirect
566. C2×M16C22×D53semidirect
594. #121C22×D53semidirect
621. #106C22×D53semidirect
629. #102C22×D53semidirect
887. C2#20285562direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112022
C2×#168111892
#202855622
C2×#168109432
C2×#168109672
C2×#168109452
C2×#168109352
C2×#168108692
C2×#168108572
C2×#168108502
C2×#168107692
C2×#168107652
C2×#168107752
C2×#168107552
C2×#168105912
C2×C53×#4692
C2×#319853