Finite Group Databasebeta

← C2×#20285568 #28254746

Subgroups — C2×#20285568 #28254746

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×#16811203C211yesmaximal, characteristic, complemented
2C2×#16811189C211yesmaximal, characteristic, complemented
3#20285568C2116yesmaximal, direct product factor
4C2×#16810940C211yesmaximal, characteristic, complemented
5C2×#16810962C211yesmaximal, characteristic, complemented
6C2×#16810950C211yesmaximal, characteristic, complemented
7C2×#16810938C211yesmaximal, characteristic, complemented
8C2×#16810876C211yesmaximal, characteristic, complemented
9C2×#16810857C211yesmaximal, characteristic, complemented
10C2×#16810854C211yesmaximal, characteristic, complemented
11C2×#16810771C211yesmaximal, characteristic, complemented
12C2×#16810767C211yesmaximal, characteristic, complemented
13C2×#16810772C211yesmaximal, characteristic, complemented
14C2×#16810758C211yesmaximal, characteristic, complemented
15C2×#16810591C211yesmaximal, characteristic, complemented
16C2×C53×#468C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic, complemented
18C22×#11719945C2211yescharacteristic
19C22×D4×D53C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21C22×D424C2211yescharacteristic
22C22×#11719922C2211yescharacteristic
23C23×#88322C2211yescharacteristic, complemented
24#16811203—24no—
25#16811203C2218yescomplemented
26#16811189—24no—
27#16811189C2218yescomplemented
28C2×#13133213—21no—
29C2×#13133203—21no—
30C2×#13133195—21no—
31C2×#13133193C2211yescharacteristic
32C2×#13133192—21no—
33C2×#13133192C2211yescharacteristic
34C2×#13133192C2211yescharacteristic
35C2×#13133191C2211yescharacteristic
36C2×#13133191C2211yescharacteristic, complemented
37C2×#13133190—21no—
38C2×#13133190—21no—
39C2×#13133188C2211yescharacteristic
40C2×#13133187—21no—
41C2×#13133185—21no—
42C2×#13133175C2211yescharacteristic
43C2×C4⋊C4×D53C2211yescharacteristic, complemented
44#16810962C2218yescomplemented
45#16810950C2218yescomplemented
46#16810940C2218yescomplemented
47#16810938C2218yescomplemented
48#16810876C2218yescomplemented
49#16810857C2218yescomplemented
50#16810854C2218yescomplemented
51#16810772C2218yescomplemented
52#16810771C2218yescomplemented
53#16810767C2218yescomplemented
54#16810758C2218yescomplemented
55C2×#13133150C2211yescharacteristic, complemented
56C2×#13133149C2211yescharacteristic, complemented
57C2×#13133148C2211yescharacteristic, complemented
58C2×#13133141C2211yescharacteristic, complemented
59C2×#13133139C2211yescharacteristic
60C2×#13133139C2211yescharacteristic, complemented
61C2×#13133138C2211yescharacteristic
62C2×#13133137C2211yescharacteristic
63C2×#13133137C2211yescharacteristic, complemented
64#16810591C2218yescomplemented
65C2×#13133129C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic, complemented
68C2×#13133129C2211yescharacteristic, complemented
69C22×SD16×C53C2211yescharacteristic
70C22×M16×C53C2211yescharacteristic, complemented
71C2×C22⋊Q8×C53C2211yescharacteristic, complemented
72C2×#121×C53C2211yescharacteristic
73C53×#468C2218yescomplemented
74C2×#107×C53C2211yescharacteristic, complemented
75C2×#103×C53C2211yescharacteristic, complemented
76C2×#102×C53C2211yescharacteristic
77C24×D53—21no—
78C2×#11719949—22no—
79C2×#11719949—42no—
80C2×#11719949—42no—
81C2×#11719949C2314yescomplemented
82C2×#11719945—42no—
83C2×#11719945—42no—
84C2×#11719945D414yes—
85C2×#11719945C2314yes—
86C22×Dic106D411yescharacteristic
87C22×D212—21no—
88C22×D212—21no—
89C22×D212—21no—
90C22×D212D411yescharacteristic
91C22×D212C2311yescharacteristic
92C22×D212C2311yescharacteristic
93C22×C22⋊D53—21no—
94C22×C22⋊D53—21no—
95C22×C22⋊D53—21no—
96C22×C22⋊D53—21no—
97C22×C22⋊D53D411yescharacteristic
98C22×C22⋊D53D411yescharacteristic
99C2×D4×D53—22no—
100C2×D4×D53—42no—
101C2×D4×D53—42no—
102C2×D4×D53C2314yes—
103C22×C4×D53—21no—
104C22×C4×D53—21no—
105C22×C4×D53C2311yescharacteristic
106C22×C4×D53C2311yescharacteristic
107C2×#11719924—42no—
108C2×#11719924C2314yes—
109C2×D424—42no—
110C2×D424C2314yes—
111C2×#11719922—42no—
112C2×#11719922C2314yes—
113C22×#88322—42no—
114C22×#88322C2311yescharacteristic
115C22×#88322C2311yescharacteristic
116C22×#88322C2314yescomplemented
117#13133213—28no—
118#13133203—28no—
119#13133195—28no—
120#13133193—22no—
121#13133193C2314yes—
122#13133192—28no—
123#13133192—22no—
124#13133192—22no—
125#13133192C2314yes—
126#13133192C2314yes—
127#13133191—22no—
128#13133191—22no—
129#13133191C2314yes—
130#13133191C2314yescomplemented
131#13133190—28no—
132#13133190—28no—
133#13133188—22no—
134#13133188C2314yes—
135#13133187—28no—
136#13133185—28no—
137#13133175—22no—
138#13133175C2314yes—
139C2×C4⋊Dic53C2311yescharacteristic
140C2×C4⋊Dic53C2311yescharacteristic
141C2×#11719919—21no—
142C2×#11719919—21no—
143C4⋊C4×D53—22no—
144C4⋊C4×D53C2314yescomplemented
145C2×C22⋊Dic53—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×#11719921—21no—
152C2×C4×Dic53—21no—
153#13133150C2314yescomplemented
154#13133149C2314yescomplemented
155#13133148C2314yescomplemented
156#13133141C2314yescomplemented
157#13133139C2314yes—
158#13133139C2314yescomplemented
159#13133138C2314yes—
160#13133137C2314yes—
161#13133137C2314yescomplemented
162#13133129C2314yes—
163#13133129C2314yes—
164#13133129C2314yescomplemented
165#13133129C2314yescomplemented
166C22×Q8×C53C2311yescharacteristic
167C22×D4×C53—21no—
168C22×D4×C53C2311yescharacteristic
169C23×C4×C53C2311yescharacteristic
170C2×SD16×C53—42no—
171C2×SD16×C53C2314yes—
172C2×M16×C53—42no—
173C2×M16×C53C2314yescomplemented
174C22×C8×C53C2311yescharacteristic
175C22×C8×C53C2311yescharacteristic
176C22⋊Q8×C53—22no—
177C22⋊Q8×C53C2314yescomplemented
178#121×C53—22no—
179#121×C53C2314yes—
180C2×C4⋊C4×C53—21no—
181C2×C4⋊C4×C53C2311yescharacteristic
182C2×C4⋊C4×C53C2311yescharacteristic
183C2×C22⋊C4×C53—21no—
184C2×C22⋊C4×C53—21no—
185#107×C53C2314yescomplemented
186#103×C53C2314yescomplemented
187#102×C53C2314yes—
188C24×C53—21no—
189C24×C53C2×D411yescharacteristic
190C23×D53—21no—
191C23×D53—21no—
192C23×D53—24no—
193C23×D53—44no—
194C23×D53—82no—
195C23×D53—82no—
196C23×D53C2×D411yescharacteristic
197C23×D53C2×D411yescharacteristic
198C2×Q8×C53—21no—
199C2×Q8×C53—22no—
200C2×Q8×C53—22no—
201C2×Q8×C53C2412yes—
202C2×D4×C53—24no—
203C2×D4×C53—21no—
204C2×D4×C53—22no—
205C2×D4×C53—22no—
206C2×D4×C53—82no—
207C2×D4×C53C2412yes—
208C22×C4×C53—22no—
209C22×C4×C53—22no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53C2×D411yescharacteristic
214C22×C4×C53C2×D412yes—
215C22×C4×C53C2412yes—
216C22×C4×C53C2411yescharacteristic
217C2×C22⋊D53—24no—
218C2×C22⋊D53—24no—
219C2×C22⋊D53—24no—
220C2×C22⋊D53—24no—
221C2×C22⋊D53—42no—
222C2×C22⋊D53—42no—
223C2×C22⋊D53—44no—
224C2×C22⋊D53—82no—
225C2×C22⋊D53—82no—
226C2×C22⋊D53—82no—
227C2×C22⋊D53C2×D414yes—
228C2×C22⋊D53C2×D414yes—
229C22×Dic53—21no—
230C22×Dic53—21no—
231C22×Dic53C2×D411yescharacteristic
232C22×Dic53C2×D411yescharacteristic
233#11719949—44no—
234#11719949—44no—
235#11719949—48no—
236D4×D53—44no—
237D4×D53—44no—
238D4×D53—48no—
239#11719945—48no—
240#11719945—44no—
241#11719945—44no—
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—42no—
252C2×D212—44no—
253C2×D212—82no—
254C2×D212—82no—
255C2×D212C2×D414yes—
256C2×D212C2412yes—
257C2×D212C2412yes—
258C2×C4×D53—22no—
259C2×C4×D53—22no—
260C2×C4×D53—22no—
261C2×C4×D53—22no—
262C2×C4×D53—24no—
263C2×C4×D53—24no—
264C2×C4×D53—44no—
265C2×C4×D53—82no—
266C2×C4×D53C2×D412yes—
267C2×C4×D53C2×D412yes—
268C2×C4×D53C2412yes—
269C2×C4×D53C2412yes—
270C2×Dic106—42no—
271C2×Dic106C2×D414yes—
272SD16×C53—44no—
273M16×C53—44no—
274C2×C8×C53—22no—
275C2×C8×C53—22no—
276C2×C8×C53C2412yes—
277C2×C8×C53C2412yes—
278C4⋊C4×C53—24no—
279C4⋊C4×C53—21no—
280C4⋊C4×C53—21no—
281C4⋊C4×C53C2412yes—
282C4⋊C4×C53C2412yes—
283C22⋊C4×C53—24no—
284C22⋊C4×C53—24no—
285C22⋊Dic53—24no—
286#11719924—44no—
287#11719922—44no—
288#11719921—24no—
289#11719921—24no—
290#11719921—24no—
291#11719921—24no—
292#11719921—24no—
293#11719921—24no—
294C4⋊Dic53—21no—
295C4⋊Dic53—21no—
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—
306D424—44no—
307C23×C53—22no—
308C23×C53—22no—
309C23×C53—22no—
310C23×C53—22no—
311C23×C53—42no—
312C23×C53—42no—
313C23×C53—42no—
314C23×C53C22×D412yes—
315C23×C53C22×D411yescharacteristic
316C22×D53—22no—
317C22×D53—22no—
318C22×D53—22no—
319C22×D53—22no—
320C22×D53—22no—
321C22×D53—22no—
322C22×D53—22no—
323C22×D53—22no—
324C22×D53—48no—
325C22×D53—42no—
326C22×D53—42no—
327C22×D53—42no—
328C22×D53—42no—
329C22×D53—42no—
330C22×D53—42no—
331C22×D53—84no—
332C22×D53—84no—
333C22×D53—816no—
334C22×D53C22×D412yes—
335C22×D53C22×D412yes—
336Q8×C53—22no—
337Q8×C53—22no—
338Q8×C53—42no—
339D4×C53—22no—
340D4×C53—22no—
341D4×C53—42no—
342D4×C53—84no—
343C2×C4×C53—22no—
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×C53—42no—
353C2×C4×C53C22×D412yes—
354C2×C4×C53C22×D411yescharacteristic
355C2×C4×C53H(5,𝔽2)12yes—
356C2×C4×C53H(5,𝔽2)12yes—
357C2×C4×C53C2511yescharacteristic
358C22⋊D53—44no—
359C22⋊D53—44no—
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—42no—
369C2×Dic53—42no—
370C2×Dic53C22×D412yes—
371C2×Dic53C22×D412yes—
372D212—22no—
373D212—22no—
374D212—22no—
375D212—22no—
376D212—44no—
377D212—48no—
378D212—42no—
379D212—42no—
380D212—84no—
381D212—84no—
382C4×D53—24no—
383C4×D53—24no—
384C4×D53—22no—
385C4×D53—22no—
386C4×D53—22no—
387C4×D53—22no—
388C4×D53—48no—
389C4×D53—84no—
390Dic106—44no—
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—84no—
404C22×C53#53412yes—
405C22×C53#57612yes—
406C22×C53#57712yes—
407C22×C53C23×D411yescharacteristic
408C2×D53—22no—
409C2×D53—22no—
410C2×D53—22no—
411C2×D53—22no—
412C2×D53—22no—
413C2×D53—22no—
414C2×D53—44no—
415C2×D53—44no—
416C2×D53—42no—
417C2×D53—42no—
418C2×D53—42no—
419C2×D53—42no—
420C2×D53—42no—
421C2×D53—42no—
422C2×D53—816no—
423C2×D53—84no—
424C2×D53—84no—
425C4×C53—22no—
426C4×C53—42no—
427C4×C53—42no—
428C4×C53—42no—
429C4×C53#53412yes—
430C4×C53C2×H(5,𝔽2)11yescharacteristic
431C4×C53C2×H(5,𝔽2)11yescharacteristic
432Dic53—22no—
433Dic53—22no—
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×#469—531no—
444C2×#468D5311yescharacteristic, complemented
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#319814yescomplemented
455C2×C53C2×#53411yescharacteristic
456C2×C53C2×#57611yescharacteristic
457C2×C53C2×#57711yescharacteristic
458D53—42no—
459D53—42no—
460D53—82no—
461D53—82no—
462C22×#41—531no—
463C22×#41—531no—
464C23×D4—531no—
465C22×SD16—531no—
466C22×SD16C2×D5311yescharacteristic
467C22×D8—531no—
468C22×D8—531no—
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—1061no—
479C2×C22⋊Q8C2×D5311yescharacteristic, complemented
480C2×#121—531no—
481C2×#121—531no—
482C2×#121—531no—
483C2×#121—531no—
484C2×#121—531no—
485C2×#121—1061no—
486C2×#121—1061no—
487C2×#121—1061no—
488C2×#121C2×D5311yescharacteristic
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#469—538no—
498#468C2×D5318yescomplemented
499#466—538no—
500#465—538no—
501#450—538no—
502#449—538no—
503#449—538no—
504#447—538no—
505C2×#107—531no—
506C2×#107C2×D5311yescharacteristic, complemented
507C2×#106—531no—
508C2×#106—531no—
509C2×#103—531no—
510C2×#103C2×D5311yescharacteristic, complemented
511C2×#102—531no—
512C2×#102—531no—
513C2×#102—531no—
514C2×#102—531no—
515C2×#102—531no—
516C2×#102C2×D5311yescharacteristic
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×Q8C22×D5311yescharacteristic
534C22×D4—21no—
535C22×D4—531no—
536C22×D4—531no—
537C22×D4—534no—
538C22×D4—531no—
539C22×D4—531no—
540C22×D4—531no—
541C22×D4—1061no—
542C22×D4—1061no—
543C22×D4—1061no—
544C22×D4—1062no—
545C22×D4—1061no—
546C22×D4—1061no—
547C22×D4—1061no—
548C22×D4—1061no—
549C22×D4—2122no—
550C22×D4—2122no—
551C22×D4C22×D5311yescharacteristic
552C23×C4—531no—
553C23×C4—531no—
554C23×C4—1061no—
555C23×C4—1061no—
556C23×C4C22×D5311yescharacteristic
557C2×SD16—42no—
558C2×SD16—534no—
559C2×SD16—2122no—
560C2×SD16C22×D5314yes—
561C2×D8—534no—
562C2×D8—534no—
563C2×D8—2122no—
564C2×D8—2122no—
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—22no—
576C22⋊Q8—534no—
577C22⋊Q8—1068no—
578C22⋊Q8—1062no—
579C22⋊Q8C22×D5314yescomplemented
580#121—22no—
581#121—534no—
582#121—534no—
583#121—534no—
584#121—534no—
585#121—534no—
586#121—1068no—
587#121—1068no—
588#121—1062no—
589#121—1062no—
590#121—1068no—
591#121—1062no—
592#121—1062no—
593#121—1062no—
594#121C22×D5314yes—
595#120—1068no—
596#120—1068no—
597#117—534no—
598#117—1062no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—531no—
601C2×C4⋊C4—531no—
602C2×C4⋊C4—534no—
603C2×C4⋊C4—1062no—
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#107C22×D5314yescomplemented
620#106—534no—
621#106—534no—
622#103—534no—
623#103C22×D5314yescomplemented
624#102—534no—
625#102—534no—
626#102—534no—
627#102—534no—
628#102—534no—
629#102C22×D5314yes—
630C22⋊C8—534no—
631C22⋊C8—534no—
632C22⋊C8—534no—
633C22⋊C8—534no—
634C24—21no—
635C24—531no—
636C24—531no—
637C24—1064no—
638C24—1061no—
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—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—534no—
654C2×Q8—2122no—
655C2×Q8C23×D5312yes—
656C2×D4—24no—
657C2×D4—21no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—82no—
661C2×D4—534no—
662C2×D4—534no—
663C2×D4—534no—
664C2×D4—532no—
665C2×D4—532no—
666C2×D4—1064no—
667C2×D4—1064no—
668C2×D4—1064no—
669C2×D4—1064no—
670C2×D4—1064no—
671C2×D4—1064no—
672C2×D4—1064no—
673C2×D4—1061no—
674C2×D4—1061no—
675C2×D4—1062no—
676C2×D4—1062no—
677C2×D4—1062no—
678C2×D4—1062no—
679C2×D4—4242no—
680C2×D4—4242no—
681C2×D4—4242no—
682C2×D4—4242no—
683C2×D4—4242no—
684C2×D4—2122no—
685C2×D4—2124no—
686C2×D4—2124no—
687C2×D4—2124no—
688C2×D4—2128no—
689C2×D4—2122no—
690C2×D4—2122no—
691C2×D4—2124no—
692C2×D4C23×D5312yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—531no—
699C22×C4—531no—
700C22×C4—532no—
701C22×C4—532no—
702C22×C4—532no—
703C22×C4—532no—
704C22×C4—1064no—
705C22×C4—1064no—
706C22×C4—1062no—
707C22×C4—1062no—
708C22×C4—1062no—
709C22×C4—1062no—
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—44no—
719SD16—2124no—
720D8—2124no—
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—24no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—532no—
736C4⋊C4—532no—
737C4⋊C4—1064no—
738C4⋊C4—1064no—
739C4⋊C4—1061no—
740C4⋊C4—1061no—
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—42no—
758C23—42no—
759C23—42no—
760C23—532no—
761C23—532no—
762C23—1062no—
763C23—1062no—
764C23—1062no—
765C23—1062no—
766C23—1062no—
767C23—1062no—
768C23—1062no—
769C23—1062no—
770C23—4244no—
771C23—4244no—
772C23—42416no—
773C23—2128no—
774C23—2122no—
775C23—2122no—
776C23—2122no—
777C23—2122no—
778C23—2122no—
779C23—2122no—
780C23C2×D4×D5312yes—
781C23C2×D4×D5311yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—42no—
785Q8—2124no—
786D4—22no—
787D4—22no—
788D4—42no—
789D4—84no—
790D4—1062no—
791D4—1062no—
792D4—1062no—
793D4—1062no—
794D4—4244no—
795D4—4244no—
796D4—4244no—
797D4—4244no—
798D4—4244no—
799D4—2124no—
800D4—2128no—
801D4—2124no—
802D4—2124no—
803D4—2128no—
804D4—2122no—
805D4—2122no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—532no—
817C2×C4—532no—
818C2×C4—1062no—
819C2×C4—1062no—
820C2×C4—1064no—
821C2×C4—1064no—
822C2×C4—1062no—
823C2×C4—1062no—
824C2×C4—1062no—
825C2×C4—1062no—
826C2×C4—1062no—
827C2×C4—1062no—
828C2×C4—4244no—
829C2×C4—2128no—
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—84no—
849C22—1062no—
850C22—1062no—
851C22—1062no—
852C22—1062no—
853C22—1062no—
854C22—1062no—
855C22—42416no—
856C22—4244no—
857C22—4244no—
858C22—2122no—
859C22—2122no—
860C22—2122no—
861C22—2122no—
862C22—2122no—
863C22—2122no—
864C22—2124no—
865C22—2124no—
866C22#1681118112yes—
867C22#1681142712yes—
868C22#1681143212yes—
869C22C22×D4×D5311yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—1062no—
875C4—1062no—
876C4—2122no—
877C4—2122no—
878C4#1681118112yes—
879C4C2×#1313326211yescharacteristic
880C4C2×#1313326311yescharacteristic
881C2—42no—
882C2—82no—
883C2—4242no—
884C2—4242no—
885C2—2122no—
886C2—2122no—
887C2#2028556814yesdirect product factor
888C2C2×#1681118111yescharacteristic
889C2C2×#1681142711yescharacteristic
890C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#468C2
socleC23×C53C22×D4
hypercenterC2×#468D53
hypocenterC53C2×#3198
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#16811203C2semidirect
2. C2×#16811189C2semidirect
3. #20285568C2direct (N × H)
4. C2×#16810940C2semidirect
5. C2×#16810962C2semidirect
6. C2×#16810950C2semidirect
7. C2×#16810938C2semidirect
8. C2×#16810876C2semidirect
9. C2×#16810857C2semidirect
10. C2×#16810854C2semidirect
11. C2×#16810771C2semidirect
12. C2×#16810767C2semidirect
13. C2×#16810772C2semidirect
14. C2×#16810758C2semidirect
15. C2×#16810591C2semidirect
16. C2×C53×#468C2semidirect
17. C22×#11719949C22semidirect
23. C23×#88322C22semidirect
25. #16811203C22semidirect
27. #16811189C22semidirect
36. C2×#13133191C22semidirect
43. C2×C4⋊C4×D53C22semidirect
44. #16810962C22semidirect
45. #16810950C22semidirect
46. #16810940C22semidirect
47. #16810938C22semidirect
48. #16810876C22semidirect
49. #16810857C22semidirect
50. #16810854C22semidirect
51. #16810772C22semidirect
52. #16810771C22semidirect
53. #16810767C22semidirect
54. #16810758C22semidirect
55. C2×#13133150C22semidirect
56. C2×#13133149C22semidirect
57. C2×#13133148C22semidirect
58. C2×#13133141C22semidirect
60. C2×#13133139C22semidirect
63. C2×#13133137C22semidirect
64. #16810591C22semidirect
67. C2×#13133129C22semidirect
68. C2×#13133129C22semidirect
70. C22×M16×C53C22semidirect
71. C2×C22⋊Q8×C53C22semidirect
73. C53×#468C22semidirect
74. C2×#107×C53C22semidirect
75. C2×#103×C53C22semidirect
81. C2×#11719949C23semidirect
116. C22×#88322C23semidirect
130. #13133191C23semidirect
144. C4⋊C4×D53C23semidirect
153. #13133150C23semidirect
154. #13133149C23semidirect
155. #13133148C23semidirect
156. #13133141C23semidirect
158. #13133139C23semidirect
161. #13133137C23semidirect
164. #13133129C23semidirect
165. #13133129C23semidirect
173. C2×M16×C53C23semidirect
177. C22⋊Q8×C53C23semidirect
185. #107×C53C23semidirect
186. #103×C53C23semidirect
444. C2×#468D53semidirect
454. C2×C53#3198semidirect
469. C22×M16C2×D53semidirect
479. C2×C22⋊Q8C2×D53semidirect
498. #468C2×D53semidirect
506. C2×#107C2×D53semidirect
510. C2×#103C2×D53semidirect
522. C53C2×#3198semidirect
566. C2×M16C22×D53semidirect
579. C22⋊Q8C22×D53semidirect
619. #107C22×D53semidirect
623. #103C22×D53semidirect
887. C2#20285568direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112032
C2×#168111892
#202855682
C2×#168109402
C2×#168109622
C2×#168109502
C2×#168109382
C2×#168108762
C2×#168108572
C2×#168108542
C2×#168107712
C2×#168107672
C2×#168107722
C2×#168107582
C2×#168105912
C2×C53×#4682
C2×#319853