Finite Group Databasebeta

← C2×#20285475 #28254621

Subgroups — C2×#20285475 #28254621

Order 13568.

2718 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811133C211yesmaximal, characteristic, complemented
2C2×#121×D53C211yesmaximal, characteristic, complemented
3#20285475C2116yesmaximal, direct product factor
4C2×#16810960C211yesmaximal, characteristic, complemented
5C2×#16810940C211yesmaximal, characteristic, complemented
6C2×#16810950C211yesmaximal, characteristic, complemented
7C2×#16810946C211yesmaximal, characteristic, complemented
8C2×#16810857C211yesmaximal, characteristic, complemented
9C2×#16810852C211yesmaximal, characteristic, complemented
10C2×#16810850C211yesmaximal, characteristic, complemented
11C2×#16810769C211yesmaximal, characteristic, complemented
12C2×#16810765C211yesmaximal, characteristic, complemented
13C2×#16810775C211yesmaximal, characteristic, complemented
14C2×#16810755C211yesmaximal, characteristic, complemented
15C22×#13133129C211yesmaximal, characteristic, complemented
16C2×C53×#466C211yesmaximal, characteristic, complemented
17C22×#11719947C2211yescharacteristic, complemented
18C22×D4×D53—21no—
19C22×D4×D53C2211yescharacteristic
20C23×C4×D53C2211yescharacteristic
21C22×#11719913C2211yescharacteristic, complemented
22C22×#11719923C2211yescharacteristic, complemented
23C22×#11719922C2211yescharacteristic, complemented
24C23×#88322C2211yescharacteristic, complemented
25#16811133—24no—
26#16811133C2218yescomplemented
27C2×#13133199—21no—
28C2×#13133197C2211yescharacteristic
29C2×#13133196C2211yescharacteristic, complemented
30C2×#13133192C2211yescharacteristic
31C2×#13133191C2211yescharacteristic
32C2×#13133190—21no—
33C2×#13133189—21no—
34C2×#13133188C2211yescharacteristic
35C2×#13133188C2211yescharacteristic
36#121×D53—24no—
37#121×D53C2218yescomplemented
38C2×#13133185—21no—
39C2×D4×Dic53—21no—
40C2×#13133177—21no—
41C2×#13133175C2211yescharacteristic, complemented
42C2×C4⋊C4×D53C2211yescharacteristic
43C2×C22⋊C4×D53—21no—
44#16810960C2218yescomplemented
45#16810950C2218yescomplemented
46#16810946C2218yescomplemented
47#16810940C2218yescomplemented
48#16810857C2218yescomplemented
49#16810852C2218yescomplemented
50#16810850C2218yescomplemented
51#16810775C2218yescomplemented
52#16810769C2218yescomplemented
53#16810765C2218yescomplemented
54#16810755C2218yescomplemented
55C2×#13133150C2211yescharacteristic, complemented
56C2×#13133149C2211yescharacteristic, complemented
57C2×#13133148C2211yescharacteristic, complemented
58C2×#13133142C2211yescharacteristic, complemented
59C2×#13133140C2211yescharacteristic, complemented
60C2×#13133139C2211yescharacteristic, complemented
61C2×#13133138C2211yescharacteristic, complemented
62C2×#13133138C2211yescharacteristic, complemented
63C2×#13133137C2211yescharacteristic, complemented
64C2×#13133129C2211yescharacteristic
65C2×#13133129C2211yescharacteristic
66C2×#13133129C2211yescharacteristic, complemented
67C2×#13133129C2211yescharacteristic, complemented
68C2×#13133129C2218yescomplemented
69C22×D8×C53C2211yescharacteristic, complemented
70C23×C8×C53C2211yescharacteristic, complemented
71C2×#121×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic, complemented
73C53×#466C2218yescomplemented
74C2×#107×C53C2211yescharacteristic, complemented
75C2×#102×C53C2211yescharacteristic, complemented
76C2×#102×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C24×D53D411yescharacteristic
79C2×#11719947—22no—
80C2×#11719947—42no—
81C2×#11719947—42no—
82C2×#11719947C2314yescomplemented
83C22×Dic106C2311yescharacteristic
84C22×D212—21no—
85C22×D212C2311yescharacteristic
86C22×C22⋊D53—21no—
87C22×C22⋊D53—21no—
88C22×C22⋊D53—21no—
89C22×C22⋊D53—21no—
90C22×C22⋊D53—21no—
91C2×D4×D53—28no—
92C2×D4×D53—22no—
93C2×D4×D53—42no—
94C2×D4×D53—42no—
95C2×D4×D53—48no—
96C2×D4×D53C2314yes—
97C23×Dic53—21no—
98C23×Dic53D411yescharacteristic
99C22×C4×D53—21no—
100C22×C4×D53—42no—
101C22×C4×D53—42no—
102C22×C4×D53D411yescharacteristic
103C22×C4×D53D414yes—
104C22×C4×D53D411yescharacteristic
105C22×C4×D53C2311yescharacteristic
106C22×C4×D53C2311yescharacteristic
107C22×C4×D53C2314yes—
108C2×#11719913—42no—
109C2×#11719913C2314yescomplemented
110C2×#11719923—42no—
111C2×#11719923C2314yescomplemented
112C2×#11719922—42no—
113C2×#11719922C2314yescomplemented
114C22×#88322—42no—
115C22×#88322C2311yescharacteristic
116C22×#88322C2311yescharacteristic
117C22×#88322C2314yescomplemented
118#13133199—28no—
119#13133197—22no—
120#13133197C2314yes—
121#13133196—22no—
122#13133196C2314yescomplemented
123#13133192—22no—
124#13133192C2314yes—
125#13133191—22no—
126#13133191C2314yes—
127#13133190—28no—
128#13133189—28no—
129#13133188—22no—
130#13133188—22no—
131#13133188C2314yes—
132#13133188C2314yes—
133#13133185—28no—
134D4×Dic53—28no—
135#13133177—28no—
136#13133175—22no—
137#13133175C2314yescomplemented
138C2×C4⋊Dic53—21no—
139C2×C4⋊Dic53C2311yescharacteristic
140C2×C4⋊Dic53C2311yescharacteristic
141C2×#11719919—21no—
142C2×#11719919—21no—
143C4⋊C4×D53—22no—
144C4⋊C4×D53C2314yes—
145C2×C22⋊Dic53—21no—
146C2×C22⋊Dic53—21no—
147C2×C22⋊Dic53—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×#11719921—21no—
152C22⋊C4×D53—28no—
153C2×C4×Dic53—21no—
154#13133150C2314yescomplemented
155#13133149C2314yescomplemented
156#13133148C2314yescomplemented
157#13133142C2314yescomplemented
158#13133140C2314yescomplemented
159#13133139C2314yescomplemented
160#13133138C2314yescomplemented
161#13133138C2314yescomplemented
162#13133137C2314yescomplemented
163#13133129C2314yes—
164#13133129C2314yes—
165#13133129C2314yescomplemented
166#13133129C2314yescomplemented
167C22×D4×C53—21no—
168C22×D4×C53—21no—
169C22×D4×C53C2311yescharacteristic
170C22×D4×C53C2311yescharacteristic
171C23×C4×C53C2311yescharacteristic
172C2×D8×C53—42no—
173C2×D8×C53C2314yescomplemented
174C22×C8×C53—42no—
175C22×C8×C53C2311yescharacteristic
176C22×C8×C53C2311yescharacteristic
177C22×C8×C53C2314yescomplemented
178#121×C53—22no—
179#121×C53—22no—
180#121×C53C2314yes—
181#121×C53C2314yescomplemented
182C2×C4⋊C4×C53C2311yescharacteristic
183C2×C4⋊C4×C53C2311yescharacteristic
184C2×C22⋊C4×C53—21no—
185C2×C22⋊C4×C53—21no—
186#107×C53C2314yescomplemented
187#102×C53C2314yescomplemented
188#102×C53C2314yescomplemented
189C24×C53—21no—
190C24×C53—21no—
191C24×C53C2×D411yescharacteristic
192C23×D53—24no—
193C23×D53—24no—
194C23×D53—21no—
195C23×D53—24no—
196C23×D53—42no—
197C23×D53—44no—
198C23×D53—44no—
199C23×D53—44no—
200C23×D53C2×D411yescharacteristic
201C23×D53C2×D414yes—
202C23×D53C2×D411yescharacteristic
203C2×D4×C53—24no—
204C2×D4×C53—24no—
205C2×D4×C53—21no—
206C2×D4×C53—21no—
207C2×D4×C53—22no—
208C2×D4×C53—22no—
209C2×D4×C53—22no—
210C2×D4×C53—22no—
211C2×D4×C53—44no—
212C2×D4×C53—44no—
213C2×D4×C53C2412yes—
214C2×D4×C53C2412yes—
215C22×C4×C53—22no—
216C22×C4×C53—22no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53C2×D411yescharacteristic
220C22×C4×C53C2×D412yes—
221C22×C4×C53C2412yes—
222C22×C4×C53C2411yescharacteristic
223C2×C22⋊D53—24no—
224C2×C22⋊D53—24no—
225C2×C22⋊D53—24no—
226C2×C22⋊D53—24no—
227C2×C22⋊D53—24no—
228C2×C22⋊D53—44no—
229C2×C22⋊D53—44no—
230C2×C22⋊D53—44no—
231C2×C22⋊D53—44no—
232C2×C22⋊D53—44no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—24no—
237C22×Dic53—42no—
238C22×Dic53—44no—
239C22×Dic53C2×D411yescharacteristic
240C22×Dic53C2×D411yescharacteristic
241C22×Dic53C2×D414yes—
242#11719947—44no—
243#11719947—44no—
244#11719947—48no—
245D4×D53—44no—
246D4×D53—44no—
247D4×D53—48no—
248D4×D53—432no—
249C2×D212—22no—
250C2×D212—22no—
251C2×D212—24no—
252C2×D212—21no—
253C2×D212—44no—
254C2×D212C2412yes—
255C2×C4×D53—22no—
256C2×C4×D53—22no—
257C2×C4×D53—22no—
258C2×C4×D53—22no—
259C2×C4×D53—24no—
260C2×C4×D53—48no—
261C2×C4×D53—44no—
262C2×C4×D53—44no—
263C2×C4×D53—42no—
264C2×C4×D53—42no—
265C2×C4×D53—44no—
266C2×C4×D53C2×D412yes—
267C2×C4×D53C2×D412yes—
268C2×C4×D53C2×D414yes—
269C2×C4×D53C2×D414yes—
270C2×C4×D53C2412yes—
271C2×C4×D53C2412yes—
272C2×Dic106—22no—
273C2×Dic106—22no—
274C2×Dic106—21no—
275C2×Dic106C2412yes—
276D8×C53—44no—
277C2×C8×C53—22no—
278C2×C8×C53—22no—
279C2×C8×C53—44no—
280C2×C8×C53C2412yes—
281C2×C8×C53C2412yes—
282C4⋊C4×C53—21no—
283C4⋊C4×C53—21no—
284C4⋊C4×C53C2412yes—
285C4⋊C4×C53C2412yes—
286C22⋊C4×C53—24no—
287C22⋊C4×C53—24no—
288C22⋊Dic53—24no—
289C22⋊Dic53—24no—
290C22⋊Dic53—24no—
291#11719923—44no—
292#11719922—44no—
293#11719921—24no—
294#11719921—24no—
295#11719921—24no—
296#11719921—24no—
297C4⋊Dic53—21no—
298C4⋊Dic53—21no—
299C4⋊Dic53—24no—
300C4⋊Dic53C2412yes—
301C4⋊Dic53C2412yes—
302#11719919—24no—
303#11719919—24no—
304C4×Dic53—24no—
305C2×#88322—22no—
306C2×#88322—22no—
307C2×#88322—44no—
308C2×#88322C2412yes—
309C2×#88322C2412yes—
310#11719913—44no—
311C23×C53—22no—
312C23×C53—22no—
313C23×C53—22no—
314C23×C53—22no—
315C23×C53—42no—
316C23×C53—42no—
317C23×C53—42no—
318C23×C53—42no—
319C23×C53—42no—
320C23×C53—42no—
321C23×C53AGL(1,ℤ/8)14yes—
322C23×C53C22×D412yes—
323C23×C53C22×D411yescharacteristic
324C22×D53—22no—
325C22×D53—22no—
326C22×D53—22no—
327C22×D53—22no—
328C22×D53—22no—
329C22×D53—28no—
330C22×D53—28no—
331C22×D53—22no—
332C22×D53—44no—
333C22×D53—416no—
334C22×D53—48no—
335C22×D53—48no—
336C22×D53—42no—
337C22×D53—42no—
338C22×D53—42no—
339C22×D53—48no—
340C22×D53—816no—
341C22×D53#13514yes—
342C22×D53C22×D412yes—
343C22×D53C22×D412yes—
344D4×C53—22no—
345D4×C53—22no—
346D4×C53—22no—
347D4×C53—22no—
348D4×C53—48no—
349D4×C53—48no—
350D4×C53—42no—
351D4×C53—42no—
352C2×C4×C53—22no—
353C2×C4×C53—24no—
354C2×C4×C53—22no—
355C2×C4×C53—22no—
356C2×C4×C53—22no—
357C2×C4×C53—22no—
358C2×C4×C53—42no—
359C2×C4×C53—42no—
360C2×C4×C53C22×D412yes—
361C2×C4×C53C22×D411yescharacteristic
362C2×C4×C53H(5,𝔽2)12yes—
363C2×C4×C53H(5,𝔽2)12yes—
364C2×C4×C53C2511yescharacteristic
365C22⋊D53—48no—
366C22⋊D53—48no—
367C22⋊D53—48no—
368C22⋊D53—48no—
369C22⋊D53—48no—
370C2×Dic53—22no—
371C2×Dic53—22no—
372C2×Dic53—22no—
373C2×Dic53—22no—
374C2×Dic53—22no—
375C2×Dic53—44no—
376C2×Dic53—48no—
377C2×Dic53—42no—
378C2×Dic53—42no—
379C2×Dic53—42no—
380C2×Dic53C22×D412yes—
381C2×Dic53C22×D412yes—
382D212—22no—
383D212—22no—
384D212—48no—
385D212—42no—
386C4×D53—24no—
387C4×D53—24no—
388C4×D53—22no—
389C4×D53—22no—
390C4×D53—22no—
391C4×D53—22no—
392C4×D53—44no—
393C4×D53—44no—
394C4×D53—48no—
395Dic106—22no—
396Dic106—22no—
397Dic106—42no—
398C8×C53—22no—
399C8×C53—22no—
400#88322—22no—
401#88322—22no—
402C2×#3188—531nomaximal, Sylow
403C22×C53—28no—
404C22×C53—22no—
405C22×C53—22no—
406C22×C53—42no—
407C22×C53—42no—
408C22×C53—42no—
409C22×C53—42no—
410C22×C53—42no—
411C22×C53—42no—
412C22×C53—84no—
413C22×C53—84no—
414C22×C53#53412yes—
415C22×C53C2×#13512yes—
416C22×C53C2×AGL(1,ℤ/8)14yes—
417C22×C53C2×AGL(1,ℤ/8)12yes—
418C22×C53C23×D411yescharacteristic
419C2×D53—28no—
420C2×D53—22no—
421C2×D53—22no—
422C2×D53—22no—
423C2×D53—22no—
424C2×D53—22no—
425C2×D53—416no—
426C2×D53—44no—
427C2×D53—42no—
428C2×D53—42no—
429C2×D53—42no—
430C2×D53—816no—
431C2×D53—84no—
432C2×D53C2×#13514yes—
433C4×C53—22no—
434C4×C53—42no—
435C4×C53—42no—
436C4×C53#53412yes—
437C4×C53C2×H(5,𝔽2)11yescharacteristic
438C4×C53C2×H(5,𝔽2)11yescharacteristic
439Dic53—22no—
440Dic53—22no—
441Dic53—42no—
442Dic53—42no—
443Dic53—42no—
444C2×#525—531no—
445C22×#121—531no—
446#3188—5316no—
447C2×#484—531no—
448C2×#481—531no—
449C2×#482—531no—
450C2×#482—531no—
451C2×#466—531no—
452C2×#466D5311yescharacteristic, complemented
453C2×#465—531no—
454C2×#465—531no—
455C2×#449—531no—
456C2×#449—531no—
457C2×#450—531no—
458C2×#447—531no—
459C22×C22⋊C8—531no—
460C2×C53—24no—
461C2×C53—82no—
462C2×C53—82no—
463C2×C53#318814yescomplemented
464C2×C53C2×#53411yescharacteristic
465C2×C53C22×#13511yescharacteristic
466C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
467D53—24no—
468D53—42no—
469D53—82no—
470C22×#41—531no—
471C23×D4—531no—
472C23×D4—1061no—
473C24×C4—531no—
474C22×SD16—531no—
475C22×SD16—531no—
476C22×D8—531no—
477C22×D8C2×D5311yescharacteristic, complemented
478C23×C8—531no—
479C23×C8C2×D5311yescharacteristic, complemented
480#525—538no—
481#525—1064no—
482C2×#123—1061no—
483C2×C22⋊Q8—531no—
484C2×C22⋊Q8—531no—
485C2×#121—531no—
486C2×#121—531no—
487C2×#121—531no—
488C2×#121—538no—
489C2×#121—531no—
490C2×#121—1061no—
491C2×#121—1064no—
492C2×#121—1061no—
493C2×#121C2×D5311yescharacteristic
494C2×#121C2×D5311yescharacteristic, complemented
495C2×#120—1061no—
496C2×C4×D4—1061no—
497C2×C4×D4—1061no—
498C2×#117—531no—
499C22×C4⋊C4—531no—
500C22×C22⋊C4—1061no—
501#484—538no—
502#482—538no—
503#482—538no—
504#481—538no—
505#466—538no—
506#466C2×D5318yescomplemented
507#465—538no—
508#465—538no—
509#450—538no—
510#449—538no—
511#449—538no—
512#447—538no—
513C2×#107—531no—
514C2×#107C2×D5311yescharacteristic, complemented
515C2×#106—531no—
516C2×#106—531no—
517C2×#103—531no—
518C2×#103—531no—
519C2×#102—531no—
520C2×#102—531no—
521C2×#102—531no—
522C2×#102—531no—
523C2×#102C2×D5311yescharacteristic, complemented
524C2×#102C2×D5311yescharacteristic, complemented
525C2×C22⋊C8—531no—
526C2×C22⋊C8—531no—
527C2×C22⋊C8—531no—
528C2×C22⋊C8—531no—
529C2×C22⋊C8—538no—
530C53C2×#318811yescharacteristic, complemented, Sylow
531C25—531no—
532C25—1061no—
533C2×#41—534no—
534C2×#41—1062no—
535C2×#41—2122no—
536C2×#41—2122no—
537C22×Q8—531no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—534no—
541C22×D4—531no—
542C22×D4—1061no—
543C22×D4—1062no—
544C22×D4—1061no—
545C22×D4—1068no—
546C22×D4—1061no—
547C22×D4—1061no—
548C22×D4—1061no—
549C22×D4—1061no—
550C22×D4—2122no—
551C22×D4—2122no—
552C22×D4—2128no—
553C22×D4C22×D5311yescharacteristic
554C22×D4C22×D5311yescharacteristic
555C23×C4—531no—
556C23×C4—531no—
557C23×C4—531no—
558C23×C4—531no—
559C23×C4—531no—
560C23×C4—534no—
561C23×C4—534no—
562C23×C4—1061no—
563C23×C4—1061no—
564C23×C4—2122no—
565C23×C4—2122no—
566C23×C4C22×D5311yescharacteristic
567C2×SD16—534no—
568C2×SD16—534no—
569C2×SD16—2122no—
570C2×SD16—2122no—
571C2×D8—42no—
572C2×D8—534no—
573C2×D8—2122no—
574C2×D8C22×D5314yescomplemented
575C22×C8—42no—
576C22×C8—531no—
577C22×C8—531no—
578C22×C8—534no—
579C22×C8—2122no—
580C22×C8C22×D5311yescharacteristic
581C22×C8C22×D5311yescharacteristic
582C22×C8C22×D5314yescomplemented
583#123—1068no—
584C22⋊Q8—534no—
585C22⋊Q8—534no—
586C22⋊Q8—1062no—
587C22⋊Q8—1062no—
588#121—22no—
589#121—22no—
590#121—534no—
591#121—534no—
592#121—534no—
593#121—534no—
594#121—1068no—
595#121—1062no—
596#121—1062no—
597#121—1068no—
598#121—1062no—
599#121—1062no—
600#121C22×D5314yes—
601#121C22×D5314yescomplemented
602#120—1068no—
603C4×D4—1068no—
604C4×D4—1068no—
605#117—534no—
606#117—1062no—
607C2×C4⋊C4—531no—
608C2×C4⋊C4—531no—
609C2×C4⋊C4—534no—
610C2×C4⋊C4—1062no—
611C2×C4⋊C4—1061no—
612C2×C4⋊C4—1061no—
613C2×C4⋊C4—1061no—
614C2×C4⋊C4C22×D5311yescharacteristic
615C2×C4⋊C4C22×D5311yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—1068no—
619C2×C22⋊C4—1061no—
620C2×C22⋊C4—1061no—
621C2×C22⋊C4—1061no—
622C2×C22⋊C4—1061no—
623C2×C22⋊C4—1061no—
624C2×C22⋊C4—1061no—
625C2×C22⋊C4—1061no—
626C2×C42—1061no—
627#107—534no—
628#107C22×D5314yescomplemented
629#106—534no—
630#106—534no—
631#103—534no—
632#103—534no—
633#102—534no—
634#102—534no—
635#102—534no—
636#102—534no—
637#102C22×D5314yescomplemented
638#102C22×D5314yescomplemented
639C22⋊C8—534no—
640C22⋊C8—534no—
641C22⋊C8—534no—
642C22⋊C8—534no—
643C24—21no—
644C24—21no—
645C24—531no—
646C24—531no—
647C24—534no—
648C24—1064no—
649C24—1064no—
650C24—1064no—
651C24—1061no—
652C24—2122no—
653C24—2124no—
654C24—2124no—
655C24—2124no—
656C24D4×D5311yescharacteristic
657#41—2124no—
658#41—2124no—
659#41—2128no—
660C2×Q8—532no—
661C2×Q8—1061no—
662C2×Q8—1062no—
663C2×Q8—1062no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—532no—
675C2×D4—1064no—
676C2×D4—1064no—
677C2×D4—1064no—
678C2×D4—1064no—
679C2×D4—1064no—
680C2×D4—1064no—
681C2×D4—1061no—
682C2×D4—1062no—
683C2×D4—1062no—
684C2×D4—2124no—
685C2×D4—2124no—
686C2×D4—2124no—
687C2×D4—2128no—
688C2×D4—2124no—
689C2×D4—21232no—
690C2×D4—2124no—
691C2×D4—2124no—
692C2×D4—2124no—
693C2×D4—2124no—
694C2×D4C23×D5312yes—
695C2×D4C23×D5312yes—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—531no—
701C22×C4—531no—
702C22×C4—534no—
703C22×C4—532no—
704C22×C4—532no—
705C22×C4—532no—
706C22×C4—532no—
707C22×C4—534no—
708C22×C4—534no—
709C22×C4—1064no—
710C22×C4—1064no—
711C22×C4—1062no—
712C22×C4—1062no—
713C22×C4—1062no—
714C22×C4—1062no—
715C22×C4—1061no—
716C22×C4—1061no—
717C22×C4—1061no—
718C22×C4—2128no—
719C22×C4—2124no—
720C22×C4—2124no—
721C22×C4—2122no—
722C22×C4—2122no—
723C22×C4—2124no—
724C22×C4—2122no—
725C22×C4—2124no—
726C22×C4D4×D5312yes—
727C22×C4D4×D5311yescharacteristic
728C22×C4C23×D5312yes—
729C22×C4C23×D5311yescharacteristic
730SD16—2124no—
731SD16—2124no—
732D8—44no—
733D8—2124no—
734C2×C8—22no—
735C2×C8—22no—
736C2×C8—44no—
737C2×C8—532no—
738C2×C8—532no—
739C2×C8—1062no—
740C2×C8—1062no—
741C2×C8—2124no—
742C2×C8C23×D5312yes—
743C2×C8C23×D5312yes—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—532no—
747C4⋊C4—532no—
748C4⋊C4—1064no—
749C4⋊C4—1064no—
750C4⋊C4—1061no—
751C4⋊C4—1061no—
752C4⋊C4—1064no—
753C4⋊C4C23×D5312yes—
754C4⋊C4C23×D5312yes—
755C22⋊C4—24no—
756C22⋊C4—24no—
757C22⋊C4—1064no—
758C22⋊C4—1064no—
759C22⋊C4—1064no—
760C22⋊C4—1064no—
761C22⋊C4—1064no—
762C22⋊C4—1064no—
763C22⋊C4—1064no—
764C42—1064no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—534no—
776C23—532no—
777C23—532no—
778C23—1068no—
779C23—1062no—
780C23—1062no—
781C23—1062no—
782C23—1068no—
783C23—1062no—
784C23—1062no—
785C23—1062no—
786C23—42416no—
787C23—2124no—
788C23—21216no—
789C23—2128no—
790C23—2128no—
791C23—2128no—
792C23—2122no—
793C23—2122no—
794C23—2122no—
795C23#1313324114yes—
796C23C2×D4×D5312yes—
797C23C2×D4×D5311yescharacteristic
798Q8—1062no—
799Q8—1062no—
800Q8—2122no—
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—48no—
806D4—48no—
807D4—42no—
808D4—42no—
809D4—1062no—
810D4—1062no—
811D4—2128no—
812D4—2128no—
813D4—2128no—
814D4—2128no—
815D4—2128no—
816D4—2128no—
817D4—2122no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—532no—
827C2×C4—532no—
828C2×C4—1062no—
829C2×C4—1062no—
830C2×C4—1064no—
831C2×C4—1064no—
832C2×C4—1062no—
833C2×C4—1062no—
834C2×C4—1062no—
835C2×C4—1062no—
836C2×C4—1062no—
837C2×C4—1062no—
838C2×C4—1062no—
839C2×C4—2124no—
840C2×C4—2124no—
841C2×C4—2128no—
842C2×C4—2124no—
843C2×C4—2128no—
844C2×C4—2122no—
845C2×C4—2122no—
846C2×C4—2122no—
847C2×C4C2×D4×D5312yes—
848C2×C4C2×D4×D5311yescharacteristic
849C2×C4#1313326212yes—
850C2×C4#1313326312yes—
851C2×C4C24×D5311yescharacteristic
852C8—22no—
853C8—22no—
854C8—1062no—
855C8—1062no—
856C22—22no—
857C22—28no—
858C22—22no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—84no—
866C22—84no—
867C22—534no—
868C22—1062no—
869C22—1068no—
870C22—1062no—
871C22—1062no—
872C22—1062no—
873C22—1062no—
874C22—42416no—
875C22—4244no—
876C22—21216no—
877C22—2122no—
878C22—2122no—
879C22—2122no—
880C22—2124no—
881C22#1681118112yes—
882C22#135×D5312yes—
883C22C2×#1313324114yes—
884C22C2×#1313324112yes—
885C22C22×D4×D5311yescharacteristic
886C4—22no—
887C4—42no—
888C4—42no—
889C4—1062no—
890C4—1062no—
891C4—2122no—
892C4—2122no—
893C4—2122no—
894C4#1681118112yes—
895C4C2×#1313326211yescharacteristic
896C4C2×#1313326311yescharacteristic
897C2—24no—
898C2—82no—
899C2—82no—
900C2—1064no—
901C2—4242no—
902C2—2122no—
903C2#2028547514yesdirect product factor
904C2C2×#1681118111yescharacteristic
905C2C2×#135×D5311yescharacteristic
906C2C22×#1313324111yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#466C2
socleC23×C53C22×D4
hypercenterC2×#466D53
hypocenterC53C2×#3188
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#16811133C2semidirect
2. C2×#121×D53C2semidirect
3. #20285475C2direct (N × H)
4. C2×#16810960C2semidirect
5. C2×#16810940C2semidirect
6. C2×#16810950C2semidirect
7. C2×#16810946C2semidirect
8. C2×#16810857C2semidirect
9. C2×#16810852C2semidirect
10. C2×#16810850C2semidirect
11. C2×#16810769C2semidirect
12. C2×#16810765C2semidirect
13. C2×#16810775C2semidirect
14. C2×#16810755C2semidirect
15. C22×#13133129C2semidirect
16. C2×C53×#466C2semidirect
17. C22×#11719947C22semidirect
21. C22×#11719913C22semidirect
22. C22×#11719923C22semidirect
23. C22×#11719922C22semidirect
24. C23×#88322C22semidirect
26. #16811133C22semidirect
29. C2×#13133196C22semidirect
37. #121×D53C22semidirect
41. C2×#13133175C22semidirect
44. #16810960C22semidirect
45. #16810950C22semidirect
46. #16810946C22semidirect
47. #16810940C22semidirect
48. #16810857C22semidirect
49. #16810852C22semidirect
50. #16810850C22semidirect
51. #16810775C22semidirect
52. #16810769C22semidirect
53. #16810765C22semidirect
54. #16810755C22semidirect
55. C2×#13133150C22semidirect
56. C2×#13133149C22semidirect
57. C2×#13133148C22semidirect
58. C2×#13133142C22semidirect
59. C2×#13133140C22semidirect
60. C2×#13133139C22semidirect
61. C2×#13133138C22semidirect
62. C2×#13133138C22semidirect
63. C2×#13133137C22semidirect
66. C2×#13133129C22semidirect
67. C2×#13133129C22semidirect
68. C2×#13133129C22semidirect
69. C22×D8×C53C22semidirect
70. C23×C8×C53C22semidirect
72. C2×#121×C53C22semidirect
73. C53×#466C22semidirect
74. C2×#107×C53C22semidirect
75. C2×#102×C53C22semidirect
76. C2×#102×C53C22semidirect
82. C2×#11719947C23semidirect
109. C2×#11719913C23semidirect
111. C2×#11719923C23semidirect
113. C2×#11719922C23semidirect
117. C22×#88322C23semidirect
122. #13133196C23semidirect
137. #13133175C23semidirect
154. #13133150C23semidirect
155. #13133149C23semidirect
156. #13133148C23semidirect
157. #13133142C23semidirect
158. #13133140C23semidirect
159. #13133139C23semidirect
160. #13133138C23semidirect
161. #13133138C23semidirect
162. #13133137C23semidirect
165. #13133129C23semidirect
166. #13133129C23semidirect
173. C2×D8×C53C23semidirect
177. C22×C8×C53C23semidirect
181. #121×C53C23semidirect
186. #107×C53C23semidirect
187. #102×C53C23semidirect
188. #102×C53C23semidirect
452. C2×#466D53semidirect
463. C2×C53#3188semidirect
477. C22×D8C2×D53semidirect
479. C23×C8C2×D53semidirect
494. C2×#121C2×D53semidirect
506. #466C2×D53semidirect
514. C2×#107C2×D53semidirect
523. C2×#102C2×D53semidirect
524. C2×#102C2×D53semidirect
530. C53C2×#3188semidirect
574. C2×D8C22×D53semidirect
582. C22×C8C22×D53semidirect
601. #121C22×D53semidirect
628. #107C22×D53semidirect
637. #102C22×D53semidirect
638. #102C22×D53semidirect
903. C2#20285475direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111332
C2×#121×D532
#202854752
C2×#168109602
C2×#168109402
C2×#168109502
C2×#168109462
C2×#168108572
C2×#168108522
C2×#168108502
C2×#168107692
C2×#168107652
C2×#168107752
C2×#168107552
C22×#131331292
C2×C53×#4662
C2×#318853