Finite Group Databasebeta

← C2×#20285573 #28254751

Subgroups — C2×#20285573 #28254751

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×#16811192C211yesmaximal, characteristic, complemented
3#20285573C2116yesmaximal, direct product factor
4C2×#16810943C211yesmaximal, characteristic, complemented
5C2×#16810947C211yesmaximal, characteristic, complemented
6C2×#16810938C211yesmaximal, characteristic, complemented
7C2×#16810877C211yesmaximal, characteristic, complemented
8C2×#16810872C211yesmaximal, characteristic, complemented
9C2×#16810860C211yesmaximal, characteristic, complemented
10C2×#16810855C211yesmaximal, characteristic, complemented
11C2×#16810771C211yesmaximal, characteristic, complemented
12C2×#16810771C211yesmaximal, characteristic, complemented
13C2×#16810773C211yesmaximal, characteristic, complemented
14C2×#16810759C211yesmaximal, characteristic, complemented
15C2×#16810588C211yesmaximal, characteristic, complemented
16C2×C53×#485C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic, complemented
18C22×#11719945C2211yescharacteristic
19C23×D212C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21C22×#11719924C2211yescharacteristic
22C22×D424C2211yescharacteristic
23C22×D424C2211yescharacteristic
24C22×#11719912C2211yescharacteristic, complemented
25C22×C8×D53C2211yescharacteristic, complemented
26#16811203—24no—
27#16811203C2218yescomplemented
28#16811192—24no—
29#16811192C2218yescomplemented
30C2×#13133214—21no—
31C2×#13133205—21no—
32C2×#13133195—21no—
33C2×#13133193C2211yescharacteristic, complemented
34C2×#13133192—21no—
35C2×#13133192C2211yescharacteristic
36C2×#13133192C2211yescharacteristic
37C2×#13133192C2211yescharacteristic
38C2×#13133192C2211yescharacteristic
39C2×#13133192C2211yescharacteristic, complemented
40C2×#13133191C2211yescharacteristic
41C2×#13133190—21no—
42C2×#13133190—21no—
43C2×#13133187—21no—
44C2×#13133187—21no—
45C2×C4⋊C4×D53C2211yescharacteristic, complemented
46#16810947C2218yescomplemented
47#16810943C2218yescomplemented
48#16810938C2218yescomplemented
49#16810877C2218yescomplemented
50#16810872C2218yescomplemented
51#16810860C2218yescomplemented
52#16810855C2218yescomplemented
53#16810773C2218yescomplemented
54#16810771C2218yescomplemented
55#16810771C2218yescomplemented
56#16810759C2218yescomplemented
57C2×#13133150C2211yescharacteristic, complemented
58C2×#13133148C2211yescharacteristic, complemented
59C2×#13133139C2211yescharacteristic
60C2×#13133139C2211yescharacteristic
61C2×#13133137C2211yescharacteristic
62C2×#13133137C2211yescharacteristic
63C2×#13133137C2211yescharacteristic, complemented
64C2×#13133137C2211yescharacteristic, complemented
65#16810588C2218yescomplemented
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic, complemented
68C2×#13133129C2211yescharacteristic, complemented
69C2×C22⋊Q8×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C53×#485C2218yescomplemented
72C2×#107×C53C2211yescharacteristic, complemented
73C2×#106×C53C2211yescharacteristic, complemented
74C2×#103×C53C2211yescharacteristic, complemented
75C2×#103×C53C2211yescharacteristic, complemented
76C2×C22⋊C8×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—22no—
90C22×D212—21no—
91C22×D212—21no—
92C22×D212—21no—
93C22×D212—21no—
94C22×D212—21no—
95C22×D212—42no—
96C22×D212—42no—
97C22×D212D411yescharacteristic
98C22×D212C2311yescharacteristic
99C22×D212C2311yescharacteristic
100C22×D212C2311yescharacteristic
101C22×D212C2314yes—
102C22×C22⋊D53—21no—
103C22×C22⋊D53D411yescharacteristic
104C22×C22⋊D53D411yescharacteristic
105C22×C4×D53—21no—
106C22×C4×D53—21no—
107C22×C4×D53C2311yescharacteristic
108C22×C4×D53C2311yescharacteristic
109C2×#11719924—42no—
110C2×#11719924—42no—
111C2×#11719924C2314yes—
112C2×#11719924C2314yes—
113C2×D424—42no—
114C2×D424—42no—
115C2×D424C2314yes—
116C2×D424C2314yes—
117C2×#11719912—42no—
118C2×#11719912C2314yescomplemented
119C22×#88322C2311yescharacteristic
120C22×#88322C2311yescharacteristic
121C2×C8×D53—42no—
122C2×C8×D53C2314yescomplemented
123#13133214—28no—
124#13133205—28no—
125#13133195—28no—
126#13133193—22no—
127#13133193C2314yescomplemented
128#13133192—28no—
129#13133192—22no—
130#13133192—22no—
131#13133192—22no—
132#13133192—22no—
133#13133192—22no—
134#13133192C2314yes—
135#13133192C2314yes—
136#13133192C2314yes—
137#13133192C2314yes—
138#13133192C2314yescomplemented
139#13133191—22no—
140#13133191C2314yes—
141#13133190—28no—
142#13133190—28no—
143#13133187—28no—
144#13133187—28no—
145C2×C4⋊Dic53C2311yescharacteristic
146C2×#11719919—21no—
147C2×#11719919—21no—
148C4⋊C4×D53—22no—
149C4⋊C4×D53C2314yescomplemented
150C2×#11719921—21no—
151C2×#11719921—21no—
152C2×#11719921—21no—
153C2×#11719921—21no—
154C2×#11719921—21no—
155C2×#11719921—21no—
156C2×#11719921—21no—
157#13133150C2314yescomplemented
158#13133148C2314yescomplemented
159#13133139C2314yes—
160#13133139C2314yes—
161#13133137C2314yes—
162#13133137C2314yes—
163#13133137C2314yescomplemented
164#13133137C2314yescomplemented
165C22⋊#88322C2314yes—
166#13133129C2314yescomplemented
167#13133129C2314yescomplemented
168C22×Q8×C53C2311yescharacteristic
169C23×C4×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172C22⋊Q8×C53—22no—
173C22⋊Q8×C53C2314yes—
174#117×C53—22no—
175#117×C53C2314yes—
176C2×C4⋊C4×C53—21no—
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C4⋊C4×C53C2311yescharacteristic
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53—21no—
182C2×C42×C53—21no—
183#107×C53C2314yescomplemented
184#106×C53C2314yescomplemented
185#103×C53C2314yescomplemented
186#103×C53C2314yescomplemented
187C22⋊C8×C53C2314yes—
188C24×C53C2×D411yescharacteristic
189C23×D53—21no—
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—
202C22×C4×C53—22no—
203C22×C4×C53—22no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53C2×D412yes—
210C22×C4×C53C2412yes—
211C22×C4×C53C2411yescharacteristic
212C2×C22⋊D53—24no—
213C2×C22⋊D53—42no—
214C2×C22⋊D53—42no—
215C2×C22⋊D53—82no—
216C2×C22⋊D53C2×D414yes—
217C2×C22⋊D53C2×D414yes—
218C22×Dic53—21no—
219C22×Dic53C2×D411yescharacteristic
220C22×Dic53C2×D411yescharacteristic
221#11719949—44no—
222#11719949—44no—
223#11719949—48no—
224#11719945—48no—
225#11719945—44no—
226#11719945—44no—
227C2×D212—22no—
228C2×D212—22no—
229C2×D212—22no—
230C2×D212—22no—
231C2×D212—22no—
232C2×D212—22no—
233C2×D212—24no—
234C2×D212—21no—
235C2×D212—21no—
236C2×D212—21no—
237C2×D212—24no—
238C2×D212—24no—
239C2×D212—24no—
240C2×D212—24no—
241C2×D212—24no—
242C2×D212—24no—
243C2×D212—44no—
244C2×D212—44no—
245C2×D212—42no—
246C2×D212—44no—
247C2×D212—48no—
248C2×D212—44no—
249C2×D212—82no—
250C2×D212—82no—
251C2×D212—82no—
252C2×D212—82no—
253C2×D212—82no—
254C2×D212C2×D414yes—
255C2×D212C2412yes—
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—
272C2×C8×C53—22no—
273C2×C8×C53—22no—
274C2×C8×C53C2412yes—
275C2×C8×C53C2412yes—
276C4⋊C4×C53—24no—
277C4⋊C4×C53—21no—
278C4⋊C4×C53—21no—
279C4⋊C4×C53—21no—
280C4⋊C4×C53C2412yes—
281C4⋊C4×C53C2412yes—
282C4⋊C4×C53C2412yes—
283C22⋊C4×C53—24no—
284C22⋊C4×C53—24no—
285C42×C53—24no—
286#11719924—44no—
287#11719924—44no—
288#11719921—24no—
289#11719921—24no—
290#11719921—24no—
291#11719921—24no—
292#11719921—24no—
293#11719921—24no—
294#11719921—24no—
295C4⋊Dic53—21no—
296C4⋊Dic53C2412yes—
297#11719919—24no—
298#11719919—24no—
299C2×#88322—22no—
300C2×#88322—22no—
301C2×#88322C2412yes—
302C2×#88322C2412yes—
303D424—44no—
304D424—44no—
305#11719912—44no—
306C8×D53—44no—
307C23×C53—22no—
308C23×C53—22no—
309C23×C53—22no—
310C23×C53C22×D412yes—
311C23×C53C22×D411yescharacteristic
312C22×D53—22no—
313C22×D53—22no—
314C22×D53—22no—
315C22×D53—22no—
316C22×D53—22no—
317C22×D53—22no—
318C22×D53—22no—
319C22×D53—22no—
320C22×D53—22no—
321C22×D53—48no—
322C22×D53—42no—
323C22×D53—42no—
324C22×D53—42no—
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—
339C2×C4×C53—22no—
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—22no—
347C2×C4×C53—42no—
348C2×C4×C53—42no—
349C2×C4×C53—42no—
350C2×C4×C53—42no—
351C2×C4×C53C22×D412yes—
352C2×C4×C53C22×D411yescharacteristic
353C2×C4×C53H(5,𝔽2)12yes—
354C2×C4×C53H(5,𝔽2)12yes—
355C2×C4×C53C2511yescharacteristic
356C22⋊D53—44no—
357C22⋊D53—44no—
358C22⋊D53—84no—
359C2×Dic53—22no—
360C2×Dic53—22no—
361C2×Dic53—22no—
362C2×Dic53—42no—
363C2×Dic53C22×D412yes—
364C2×Dic53C22×D412yes—
365D212—22no—
366D212—22no—
367D212—22no—
368D212—22no—
369D212—22no—
370D212—22no—
371D212—44no—
372D212—48no—
373D212—48no—
374D212—42no—
375D212—42no—
376D212—42no—
377D212—84no—
378D212—84no—
379D212—84no—
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#53412yes—
401C22×C53#57612yes—
402C22×C53#57712yes—
403C22×C53C23×D411yescharacteristic
404C2×D53—22no—
405C2×D53—22no—
406C2×D53—22no—
407C2×D53—22no—
408C2×D53—22no—
409C2×D53—22no—
410C2×D53—44no—
411C2×D53—44no—
412C2×D53—42no—
413C2×D53—42no—
414C2×D53—42no—
415C2×D53—42no—
416C2×D53—42no—
417C2×D53—42no—
418C2×D53—42no—
419C2×D53—42no—
420C2×D53—42no—
421C2×D53—816no—
422C2×D53—84no—
423C2×D53—84no—
424C2×D53—84no—
425C4×C53—22no—
426C4×C53—42no—
427C4×C53—42no—
428C4×C53—42no—
429C4×C53—42no—
430C4×C53#53412yes—
431C4×C53C2×H(5,𝔽2)11yescharacteristic
432C4×C53C2×H(5,𝔽2)11yescharacteristic
433Dic53—22no—
434Dic53—22no—
435Dic53—42no—
436C2×#537—531no—
437C2×#535—531no—
438#3198—5316no—
439C2×#481—531no—
440C2×#485D5311yescharacteristic, complemented
441C2×#482—531no—
442C2×#480—531no—
443C2×#469—531no—
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#319814yescomplemented
454C2×C53C2×#53411yescharacteristic
455C2×C53C2×#57611yescharacteristic
456C2×C53C2×#57711yescharacteristic
457D53—42no—
458D53—42no—
459D53—82no—
460D53—82no—
461D53—82no—
462C22×#41—531no—
463C22×#41—531no—
464C23×D4—531no—
465C22×SD16—531no—
466C22×SD16—531no—
467C22×D8—531no—
468C22×D8—531no—
469C22×M16—531no—
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
480C2×#121—531no—
481C2×#121—531no—
482C2×#121—531no—
483C2×#121—531no—
484C2×#121—531no—
485C2×#121—531no—
486C2×#121—1061no—
487C2×#121—1061no—
488C2×#121—1061no—
489C2×#120—1061no—
490C2×#120—1061no—
491C2×#117C2×D5311yescharacteristic
492C22×C4⋊C4—531no—
493#485C2×D5318yescomplemented
494#482—538no—
495#481—538no—
496#480—538no—
497#469—538no—
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×#107C2×D5311yescharacteristic, complemented
507C2×#106—531no—
508C2×#106C2×D5311yescharacteristic, complemented
509C2×#103C2×D5311yescharacteristic, complemented
510C2×#103C2×D5311yescharacteristic, complemented
511C2×#102—531no—
512C2×#102—531no—
513C2×#102—531no—
514C2×#102—531no—
515C2×#102—531no—
516C2×#102—531no—
517#408—538no—
518C2×C22⋊C8—531no—
519C2×C22⋊C8—531no—
520C2×C22⋊C8—531no—
521C2×C22⋊C8C2×D5311yescharacteristic
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—531no—
535C22×D4—531no—
536C22×D4—531no—
537C22×D4—531no—
538C22×D4—531no—
539C22×D4—531no—
540C22×D4—534no—
541C22×D4—1061no—
542C22×D4—1061no—
543C22×D4—1061no—
544C22×D4—1061no—
545C22×D4—1061no—
546C22×D4—1061no—
547C22×D4—1061no—
548C22×D4—1061no—
549C22×D4—1062no—
550C22×D4—2122no—
551C22×D4—2122no—
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—534no—
562C2×D8—534no—
563C2×D8—2122no—
564C2×D8—2122no—
565C2×M16—534no—
566C2×M16—2122no—
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×D5314yes—
580#121—534no—
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—1062no—
591#121—1062no—
592#121—1062no—
593#121—1068no—
594#121—1062no—
595#120—1068no—
596#120—1068no—
597#117—22no—
598#117C22×D5314yes—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—531no—
601C2×C4⋊C4—534no—
602C2×C4⋊C4—1062no—
603C2×C4⋊C4—1061no—
604C2×C4⋊C4—1061no—
605C2×C4⋊C4C22×D5311yescharacteristic
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—21no—
618#107—534no—
619#107C22×D5314yescomplemented
620#106—534no—
621#106C22×D5314yescomplemented
622#103C22×D5314yescomplemented
623#103C22×D5314yescomplemented
624#102—534no—
625#102—534no—
626#102—534no—
627#102—534no—
628#102—534no—
629#102—534no—
630C22⋊C8—534no—
631C22⋊C8—534no—
632C22⋊C8—534no—
633C22⋊C8C22×D5314yes—
634C24—531no—
635C24—531no—
636C24—1064no—
637C24—1061no—
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—534no—
657C2×D4—534no—
658C2×D4—534no—
659C2×D4—532no—
660C2×D4—532no—
661C2×D4—532no—
662C2×D4—1064no—
663C2×D4—1064no—
664C2×D4—1064no—
665C2×D4—1064no—
666C2×D4—1064no—
667C2×D4—1064no—
668C2×D4—1064no—
669C2×D4—1061no—
670C2×D4—1061no—
671C2×D4—1061no—
672C2×D4—1064no—
673C2×D4—1062no—
674C2×D4—1062no—
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—4242no—
685C2×D4—2124no—
686C2×D4—2124no—
687C2×D4—2122no—
688C2×D4—2124no—
689C2×D4—2128no—
690C2×D4—2124no—
691C2×D4—2122no—
692C2×D4—2122no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—531no—
700C22×C4—531no—
701C22×C4—532no—
702C22×C4—532no—
703C22×C4—532no—
704C22×C4—532no—
705C22×C4—1064no—
706C22×C4—1064no—
707C22×C4—1062no—
708C22×C4—1062no—
709C22×C4—1062no—
710C22×C4—1062no—
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—2124no—
721D8—2124no—
722M16—2124no—
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—21no—
736C4⋊C4—532no—
737C4⋊C4—1064no—
738C4⋊C4—1064no—
739C4⋊C4—1061no—
740C4⋊C4C23×D5312yes—
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—24no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—532no—
757C23—532no—
758C23—1062no—
759C23—1062no—
760C23—1062no—
761C23—1062no—
762C23—1062no—
763C23—1062no—
764C23—1062no—
765C23—1062no—
766C23—1062no—
767C23—4244no—
768C23—4244no—
769C23—42416no—
770C23—2128no—
771C23—2122no—
772C23—2122no—
773C23—2122no—
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—1062no—
787D4—1062no—
788D4—1062no—
789D4—1062no—
790D4—1062no—
791D4—1062no—
792D4—4244no—
793D4—4244no—
794D4—4244no—
795D4—4244no—
796D4—4244no—
797D4—4244no—
798D4—2124no—
799D4—2128no—
800D4—2128no—
801D4—2124no—
802D4—2124no—
803D4—2122no—
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—22no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—532no—
819C2×C4—532no—
820C2×C4—1062no—
821C2×C4—1062no—
822C2×C4—1064no—
823C2×C4—1064no—
824C2×C4—1062no—
825C2×C4—1062no—
826C2×C4—1062no—
827C2×C4—1062no—
828C2×C4—1062no—
829C2×C4—4244no—
830C2×C4—2128no—
831C2×C4—2122no—
832C2×C4C2×D4×D5312yes—
833C2×C4C2×D4×D5311yescharacteristic
834C2×C4#1313326312yes—
835C2×C4#1313326312yes—
836C2×C4C24×D5311yescharacteristic
837C8—22no—
838C8—22no—
839C8—1062no—
840C8—1062no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—1062no—
846C22—1062no—
847C22—1062no—
848C22—1062no—
849C22—1062no—
850C22—1062no—
851C22—42416no—
852C22—4244no—
853C22—4244no—
854C22—4244no—
855C22—2122no—
856C22—2122no—
857C22—2122no—
858C22—2122no—
859C22—2122no—
860C22—2122no—
861C22—2122no—
862C22—2122no—
863C22—2122no—
864C22—2124no—
865C22—2124no—
866C22#1681118412yes—
867C22#1681142512yes—
868C22#1681143212yes—
869C22C22×D4×D5311yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—1062no—
876C4—1062no—
877C4—2122no—
878C4#1681118412yes—
879C4C2×#1313326311yescharacteristic
880C4C2×#1313326311yescharacteristic
881C2—42no—
882C2—4242no—
883C2—4242no—
884C2—4242no—
885C2—2122no—
886C2—2122no—
887C2#2028557314yesdirect product factor
888C2C2×#1681118411yescharacteristic
889C2C2×#1681142511yescharacteristic
890C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#485C2
socleC23×C53C22×D4
hypercenterC2×#485D53
hypocenterC53C2×#3198
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#16811203C2semidirect
2. C2×#16811192C2semidirect
3. #20285573C2direct (N × H)
4. C2×#16810943C2semidirect
5. C2×#16810947C2semidirect
6. C2×#16810938C2semidirect
7. C2×#16810877C2semidirect
8. C2×#16810872C2semidirect
9. C2×#16810860C2semidirect
10. C2×#16810855C2semidirect
11. C2×#16810771C2semidirect
12. C2×#16810771C2semidirect
13. C2×#16810773C2semidirect
14. C2×#16810759C2semidirect
15. C2×#16810588C2semidirect
16. C2×C53×#485C2semidirect
17. C22×#11719949C22semidirect
24. C22×#11719912C22semidirect
25. C22×C8×D53C22semidirect
27. #16811203C22semidirect
29. #16811192C22semidirect
33. C2×#13133193C22semidirect
39. C2×#13133192C22semidirect
45. C2×C4⋊C4×D53C22semidirect
46. #16810947C22semidirect
47. #16810943C22semidirect
48. #16810938C22semidirect
49. #16810877C22semidirect
50. #16810872C22semidirect
51. #16810860C22semidirect
52. #16810855C22semidirect
53. #16810773C22semidirect
54. #16810771C22semidirect
55. #16810771C22semidirect
56. #16810759C22semidirect
57. C2×#13133150C22semidirect
58. C2×#13133148C22semidirect
63. C2×#13133137C22semidirect
64. C2×#13133137C22semidirect
65. #16810588C22semidirect
67. C2×#13133129C22semidirect
68. C2×#13133129C22semidirect
71. C53×#485C22semidirect
72. C2×#107×C53C22semidirect
73. C2×#106×C53C22semidirect
74. C2×#103×C53C22semidirect
75. C2×#103×C53C22semidirect
81. C2×#11719949C23semidirect
118. C2×#11719912C23semidirect
122. C2×C8×D53C23semidirect
127. #13133193C23semidirect
138. #13133192C23semidirect
149. C4⋊C4×D53C23semidirect
157. #13133150C23semidirect
158. #13133148C23semidirect
163. #13133137C23semidirect
164. #13133137C23semidirect
166. #13133129C23semidirect
167. #13133129C23semidirect
183. #107×C53C23semidirect
184. #106×C53C23semidirect
185. #103×C53C23semidirect
186. #103×C53C23semidirect
440. C2×#485D53semidirect
453. C2×C53#3198semidirect
493. #485C2×D53semidirect
506. C2×#107C2×D53semidirect
508. C2×#106C2×D53semidirect
509. C2×#103C2×D53semidirect
510. C2×#103C2×D53semidirect
522. C53C2×#3198semidirect
619. #107C22×D53semidirect
621. #106C22×D53semidirect
622. #103C22×D53semidirect
623. #103C22×D53semidirect
887. C2#20285573direct (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×#168111922
#202855732
C2×#168109432
C2×#168109472
C2×#168109382
C2×#168108772
C2×#168108722
C2×#168108602
C2×#168108552
C2×#168107712
C2×#168107732
C2×#168107592
C2×#168105882
C2×C53×#4852
C2×#319853