Finite Group Databasebeta

← C2×#20285574 #28254752

Subgroups — C2×#20285574 #28254752

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×#16811204C211yesmaximal, characteristic, complemented
2C2×#16811189C211yesmaximal, characteristic, complemented
3#20285574C2116yesmaximal, direct product factor
4C2×#16810941C211yesmaximal, characteristic, complemented
5C2×#16810966C211yesmaximal, characteristic, complemented
6C2×#16810950C211yesmaximal, characteristic, complemented
7C2×#16810875C211yesmaximal, characteristic, complemented
8C2×#16810870C211yesmaximal, characteristic, complemented
9C2×#16810860C211yesmaximal, characteristic, complemented
10C2×#16810851C211yesmaximal, characteristic, complemented
11C2×#16810770C211yesmaximal, characteristic, complemented
12C2×#16810766C211yesmaximal, characteristic, complemented
13C2×#16810775C211yesmaximal, characteristic, complemented
14C2×#16810758C211yesmaximal, characteristic, complemented
15C2×#16810588C211yesmaximal, characteristic, complemented
16C2×C53×#480C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×#11719945C2211yescharacteristic, complemented
19C22×D4×D53C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×#11719923C2211yescharacteristic
22C22×D424C2211yescharacteristic
23C22×#11719922C2211yescharacteristic
24C22×#11719912C2211yescharacteristic, complemented
25C22×C8×D53C2211yescharacteristic, complemented
26#16811204—24no—
27#16811204C2218yescomplemented
28#16811189—24no—
29#16811189C2218yescomplemented
30C2×#13133213—21no—
31C2×#13133203—21no—
32C2×#13133197—21no—
33C2×#13133197C2211yescharacteristic
34C2×#13133197C2211yescharacteristic, complemented
35C2×#13133192—21no—
36C2×#13133192C2211yescharacteristic
37C2×#13133192C2211yescharacteristic
38C2×#13133192C2211yescharacteristic, complemented
39C2×#13133191—21no—
40C2×#13133191—21no—
41C2×#13133191C2211yescharacteristic
42C2×#13133188C2211yescharacteristic
43C2×#13133187—21no—
44C2×#13133185—21no—
45C2×#13133175C2211yescharacteristic
46#16810966C2218yescomplemented
47#16810950C2218yescomplemented
48#16810941C2218yescomplemented
49#16810875C2218yescomplemented
50#16810870C2218yescomplemented
51#16810860C2218yescomplemented
52#16810851C2218yescomplemented
53#16810775C2218yescomplemented
54#16810770C2218yescomplemented
55#16810766C2218yescomplemented
56#16810758C2218yescomplemented
57C2×#13133148C2211yescharacteristic, complemented
58C2×#13133148C2211yescharacteristic, complemented
59C2×#13133142C2211yescharacteristic, complemented
60C2×#13133140C2211yescharacteristic, complemented
61C2×#13133139C2211yescharacteristic, complemented
62C2×#13133137C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic, complemented
65#16810588C2218yescomplemented
66C2×C22⋊#88322C2211yescharacteristic, complemented
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C2×#121×C53C2211yescharacteristic
70C22×C4⋊C4×C53C2211yescharacteristic, complemented
71C53×#480C2218yescomplemented
72C2×#107×C53C2211yescharacteristic, complemented
73C2×#107×C53C2211yescharacteristic, complemented
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C2×#11719945—22no—
79C2×#11719945—42no—
80C2×#11719945—42no—
81C2×#11719945—42no—
82C2×#11719945—42no—
83C2×#11719945D414yes—
84C2×#11719945C2314yes—
85C2×#11719945C2314yescomplemented
86C22×Dic106D411yescharacteristic
87C22×Dic106C2311yescharacteristic
88C22×D212—21no—
89C22×D212—21no—
90C22×D212—21no—
91C22×D212D411yescharacteristic
92C22×D212C2311yescharacteristic
93C22×D212C2311yescharacteristic
94C22×C22⋊D53—21no—
95C22×C22⋊D53—21no—
96C22×C22⋊D53—21no—
97C22×C22⋊D53—21no—
98C22×C22⋊D53D411yescharacteristic
99C22×C22⋊D53D411yescharacteristic
100C2×D4×D53—22no—
101C2×D4×D53—42no—
102C2×D4×D53—42no—
103C2×D4×D53C2314yes—
104C22×C4×D53—21no—
105C22×C4×D53C2311yescharacteristic
106C22×C4×D53C2311yescharacteristic
107C2×#11719913—42no—
108C2×#11719913C2314yes—
109C2×#11719923—42no—
110C2×#11719923C2314yes—
111C2×D424—42no—
112C2×D424C2314yes—
113C2×#11719922—42no—
114C2×#11719922C2314yes—
115C2×#11719912—42no—
116C2×#11719912C2314yescomplemented
117C22×#88322C2311yescharacteristic
118C22×#88322C2311yescharacteristic
119C2×C8×D53—42no—
120C2×C8×D53C2314yescomplemented
121#13133213—28no—
122#13133203—28no—
123#13133197—22no—
124#13133197—22no—
125#13133197—28no—
126#13133197C2314yes—
127#13133197C2314yescomplemented
128#13133192—28no—
129#13133192—22no—
130#13133192—22no—
131#13133192—22no—
132#13133192C2314yes—
133#13133192C2314yes—
134#13133192C2314yescomplemented
135#13133191—22no—
136#13133191—28no—
137#13133191—28no—
138#13133191C2314yes—
139#13133188—22no—
140#13133188C2314yes—
141#13133187—28no—
142#13133185—28no—
143#13133175—22no—
144#13133175C2314yes—
145C2×C4⋊Dic53—21no—
146C2×C4⋊Dic53—21no—
147C2×C4⋊Dic53C2311yescharacteristic
148C2×C22⋊Dic53—21no—
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×#11719921—21no—
152C2×#11719921—21no—
153C2×#11719921—21no—
154C2×#11719921—21no—
155C2×#11719921—21no—
156C2×C4×Dic53—21no—
157#13133148C2314yescomplemented
158#13133148C2314yescomplemented
159#13133142C2314yescomplemented
160#13133140C2314yescomplemented
161#13133139C2314yescomplemented
162#13133137C2314yes—
163#13133137C2314yes—
164#13133137C2314yescomplemented
165C22⋊#88322C2314yescomplemented
166#13133129C2314yes—
167#13133129C2314yes—
168C22×D4×C53—21no—
169C22×D4×C53C2311yescharacteristic
170C23×C4×C53—21no—
171C23×C4×C53C2311yescharacteristic
172C22×C8×C53C2311yescharacteristic
173C22×C8×C53C2311yescharacteristic
174#121×C53—22no—
175#121×C53C2314yes—
176C2×C4⋊C4×C53—21no—
177C2×C4⋊C4×C53—22no—
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C4⋊C4×C53C2311yescharacteristic
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C4⋊C4×C53C2314yescomplemented
182C2×C22⋊C4×C53—21no—
183#107×C53C2314yescomplemented
184#107×C53C2314yescomplemented
185#102×C53C2314yes—
186#102×C53C2314yes—
187C22⋊C8×C53C2314yescomplemented
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×D4×C53—24no—
199C2×D4×C53—21no—
200C2×D4×C53—22no—
201C2×D4×C53—22no—
202C2×D4×C53—82no—
203C2×D4×C53C2412yes—
204C22×C4×C53—22no—
205C22×C4×C53—22no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—24no—
210C22×C4×C53—82no—
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2×D412yes—
213C22×C4×C53C2412yes—
214C22×C4×C53C2411yescharacteristic
215C2×C22⋊D53—24no—
216C2×C22⋊D53—24no—
217C2×C22⋊D53—24no—
218C2×C22⋊D53—24no—
219C2×C22⋊D53—42no—
220C2×C22⋊D53—42no—
221C2×C22⋊D53—44no—
222C2×C22⋊D53—44no—
223C2×C22⋊D53—82no—
224C2×C22⋊D53—82no—
225C2×C22⋊D53C2×D414yes—
226C2×C22⋊D53C2×D414yes—
227C22×Dic53—21no—
228C22×Dic53—21no—
229C22×Dic53C2×D411yescharacteristic
230C22×Dic53C2×D411yescharacteristic
231D4×D53—44no—
232D4×D53—44no—
233D4×D53—48no—
234#11719945—44no—
235#11719945—44no—
236#11719945—48no—
237#11719945—44no—
238#11719945—44no—
239#11719945—48no—
240C2×D212—22no—
241C2×D212—22no—
242C2×D212—22no—
243C2×D212—22no—
244C2×D212—21no—
245C2×D212—21no—
246C2×D212—24no—
247C2×D212—24no—
248C2×D212—24no—
249C2×D212—42no—
250C2×D212—82no—
251C2×D212—82no—
252C2×D212—82no—
253C2×D212C2×D414yes—
254C2×D212C2412yes—
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—44no—
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—
272C2×C8×C53—22no—
273C2×C8×C53—22no—
274C2×C8×C53C2412yes—
275C2×C8×C53C2412yes—
276C4⋊C4×C53—21no—
277C4⋊C4×C53—21no—
278C4⋊C4×C53—24no—
279C4⋊C4×C53—21no—
280C4⋊C4×C53C2412yes—
281C4⋊C4×C53C2412yes—
282C4⋊C4×C53C2412yes—
283C22⋊C4×C53—24no—
284C22⋊Dic53—24no—
285#11719923—44no—
286#11719922—44no—
287#11719921—24no—
288#11719921—24no—
289#11719921—24no—
290#11719921—24no—
291#11719921—24no—
292#11719921—24no—
293#11719921—24no—
294C4⋊Dic53—21no—
295C4⋊Dic53—24no—
296C4⋊Dic53—24no—
297C4⋊Dic53C2412yes—
298C4×Dic53—24no—
299C2×#88322—22no—
300C2×#88322—22no—
301C2×#88322C2412yes—
302C2×#88322C2412yes—
303D424—44no—
304#11719913—44no—
305#11719912—44no—
306C8×D53—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—
336D4×C53—22no—
337D4×C53—22no—
338D4×C53—42no—
339D4×C53—84no—
340C2×C4×C53—22no—
341C2×C4×C53—24no—
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—84no—
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—48no—
359C22⋊D53—48no—
360C22⋊D53—84no—
361C22⋊D53—84no—
362C2×Dic53—22no—
363C2×Dic53—22no—
364C2×Dic53—22no—
365C2×Dic53—22no—
366C2×Dic53—42no—
367C2×Dic53—42no—
368C2×Dic53C22×D412yes—
369C2×Dic53C22×D412yes—
370D212—22no—
371D212—22no—
372D212—22no—
373D212—22no—
374D212—44no—
375D212—42no—
376D212—42no—
377D212—84no—
378D212—84no—
379D212—84no—
380C4×D53—24no—
381C4×D53—24no—
382C4×D53—22no—
383C4×D53—22no—
384C4×D53—22no—
385C4×D53—22no—
386C4×D53—48no—
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—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×#480D5311yescharacteristic, complemented
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—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×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—531no—
479C2×C22⋊Q8—1061no—
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⋊C4C2×D5311yescharacteristic, complemented
493#485—538no—
494#482—538no—
495#481—538no—
496#480C2×D5318yescomplemented
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×#107C2×D5311yescharacteristic, complemented
506C2×#107C2×D5311yescharacteristic, complemented
507C2×#106—531no—
508C2×#106—531no—
509C2×#103—531no—
510C2×#103—531no—
511C2×#102—531no—
512C2×#102—531no—
513C2×#102—531no—
514C2×#102—531no—
515C2×#102C2×D5311yescharacteristic
516C2×#102C2×D5311yescharacteristic
517#408—538no—
518C2×C22⋊C8—531no—
519C2×C22⋊C8—531no—
520C2×C22⋊C8—531no—
521C2×C22⋊C8C2×D5311yescharacteristic, complemented
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—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—21no—
553C23×C4—531no—
554C23×C4—531no—
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—534no—
576C22⋊Q8—534no—
577C22⋊Q8—1062no—
578C22⋊Q8—1062no—
579C22⋊Q8—1068no—
580#121—22no—
581#121—534no—
582#121—534no—
583#121—534no—
584#121—534no—
585#121—534no—
586#121—1062no—
587#121—1062no—
588#121—1062no—
589#121—1068no—
590#121—1068no—
591#121—1068no—
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—22no—
601C2×C4⋊C4—531no—
602C2×C4⋊C4—1061no—
603C2×C4⋊C4—1061no—
604C2×C4⋊C4C22×D5311yescharacteristic
605C2×C4⋊C4C22×D5311yescharacteristic
606C2×C4⋊C4C22×D5311yescharacteristic
607C2×C4⋊C4C22×D5314yescomplemented
608C2×C22⋊C4—21no—
609C2×C22⋊C4—1061no—
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#107C22×D5314yescomplemented
619#107C22×D5314yescomplemented
620#106—534no—
621#106—534no—
622#103—534no—
623#103—534no—
624#102—534no—
625#102—534no—
626#102—534no—
627#102—534no—
628#102C22×D5314yes—
629#102C22×D5314yes—
630C22⋊C8—534no—
631C22⋊C8—534no—
632C22⋊C8—534no—
633C22⋊C8C22×D5314yescomplemented
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—534no—
651C2×Q8—532no—
652C2×Q8—1061no—
653C2×Q8—1062no—
654C2×Q8—1062no—
655C2×Q8—2122no—
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—2128no—
688C2×D4—2122no—
689C2×D4—2122no—
690C2×D4—2124no—
691C2×D4—2124no—
692C2×D4C23×D5312yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—82no—
700C22×C4—531no—
701C22×C4—531no—
702C22×C4—532no—
703C22×C4—532no—
704C22×C4—532no—
705C22×C4—532no—
706C22×C4—1062no—
707C22×C4—1062no—
708C22×C4—1062no—
709C22×C4—1062no—
710C22×C4—1061no—
711C22×C4—1061no—
712C22×C4—1064no—
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—21no—
733C4⋊C4—21no—
734C4⋊C4—24no—
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—1064no—
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—1062no—
783Q8—1062no—
784Q8—2124no—
785Q8—2122no—
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—2124no—
801D4—2124no—
802D4—2128no—
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—84no—
817C2×C4—532no—
818C2×C4—532no—
819C2×C4—1062no—
820C2×C4—1062no—
821C2×C4—1064no—
822C2×C4—1064no—
823C2×C4—1062no—
824C2×C4—1062no—
825C2×C4—1062no—
826C2×C4—1062no—
827C2×C4—1062no—
828C2×C4—1062no—
829C2×C4—2128no—
830C2×C4—2122no—
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—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#1681118412yes—
867C22#1681142412yes—
868C22#1681143212yes—
869C22C22×D4×D5311yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—1062no—
875C4—1062no—
876C4—2122no—
877C4—2122no—
878C4#1681118412yes—
879C4C2×#1313326311yescharacteristic
880C4C2×#1313326311yescharacteristic
881C2—42no—
882C2—82no—
883C2—4242no—
884C2—4242no—
885C2—2122no—
886C2—2122no—
887C2#2028557414yesdirect product factor
888C2C2×#1681118411yescharacteristic
889C2C2×#1681142411yescharacteristic
890C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#480C2
socleC23×C53C22×D4
hypercenterC2×#480D53
hypocenterC53C2×#3198
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#16811204C2semidirect
2. C2×#16811189C2semidirect
3. #20285574C2direct (N × H)
4. C2×#16810941C2semidirect
5. C2×#16810966C2semidirect
6. C2×#16810950C2semidirect
7. C2×#16810875C2semidirect
8. C2×#16810870C2semidirect
9. C2×#16810860C2semidirect
10. C2×#16810851C2semidirect
11. C2×#16810770C2semidirect
12. C2×#16810766C2semidirect
13. C2×#16810775C2semidirect
14. C2×#16810758C2semidirect
15. C2×#16810588C2semidirect
16. C2×C53×#480C2semidirect
18. C22×#11719945C22semidirect
24. C22×#11719912C22semidirect
25. C22×C8×D53C22semidirect
27. #16811204C22semidirect
29. #16811189C22semidirect
34. C2×#13133197C22semidirect
38. C2×#13133192C22semidirect
46. #16810966C22semidirect
47. #16810950C22semidirect
48. #16810941C22semidirect
49. #16810875C22semidirect
50. #16810870C22semidirect
51. #16810860C22semidirect
52. #16810851C22semidirect
53. #16810775C22semidirect
54. #16810770C22semidirect
55. #16810766C22semidirect
56. #16810758C22semidirect
57. C2×#13133148C22semidirect
58. C2×#13133148C22semidirect
59. C2×#13133142C22semidirect
60. C2×#13133140C22semidirect
61. C2×#13133139C22semidirect
64. C2×#13133137C22semidirect
65. #16810588C22semidirect
66. C2×C22⋊#88322C22semidirect
70. C22×C4⋊C4×C53C22semidirect
71. C53×#480C22semidirect
72. C2×#107×C53C22semidirect
73. C2×#107×C53C22semidirect
76. C2×C22⋊C8×C53C22semidirect
85. C2×#11719945C23semidirect
116. C2×#11719912C23semidirect
120. C2×C8×D53C23semidirect
127. #13133197C23semidirect
134. #13133192C23semidirect
157. #13133148C23semidirect
158. #13133148C23semidirect
159. #13133142C23semidirect
160. #13133140C23semidirect
161. #13133139C23semidirect
164. #13133137C23semidirect
165. C22⋊#88322C23semidirect
181. C2×C4⋊C4×C53C23semidirect
183. #107×C53C23semidirect
184. #107×C53C23semidirect
187. C22⋊C8×C53C23semidirect
442. C2×#480D53semidirect
454. C2×C53#3198semidirect
492. C22×C4⋊C4C2×D53semidirect
496. #480C2×D53semidirect
505. C2×#107C2×D53semidirect
506. C2×#107C2×D53semidirect
521. C2×C22⋊C8C2×D53semidirect
522. C53C2×#3198semidirect
607. C2×C4⋊C4C22×D53semidirect
618. #107C22×D53semidirect
619. #107C22×D53semidirect
633. C22⋊C8C22×D53semidirect
887. C2#20285574direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112042
C2×#168111892
#202855742
C2×#168109412
C2×#168109662
C2×#168109502
C2×#168108752
C2×#168108702
C2×#168108602
C2×#168108512
C2×#168107702
C2×#168107662
C2×#168107752
C2×#168107582
C2×#168105882
C2×C53×#4802
C2×#319853