Finite Group Databasebeta

← C2×#20286706 #28260666

Subgroups — C2×#20286706 #28260666

Order 13568.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811277C211yesmaximal, characteristic, complemented
2#20286706C2116yesmaximal, direct product factor
3C2×#16810982C211yesmaximal, characteristic, complemented
4C2×#16810956C211yesmaximal, characteristic, complemented
5C2×#16810934C211yesmaximal, characteristic, complemented
6C2×#16810918C211yesmaximal, characteristic, complemented
7C2×#16810871C211yesmaximal, characteristic, complemented
8C2×#16810857C211yesmaximal, characteristic, complemented
9C2×#16810835C211yesmaximal, characteristic, complemented
10C2×#16810768C211yesmaximal, characteristic, complemented
11C2×#16810762C211yesmaximal, characteristic, complemented
12C2×#16810721C211yesmaximal, characteristic, complemented
13C2×#16810695C211yesmaximal, characteristic, complemented
14C2×#16810624C211yesmaximal, characteristic, complemented
15C22×#13133141C211yesmaximal, characteristic, complemented
16C2×C53×#548C211yesmaximal, characteristic, complemented
17C22×#11719947—21no—
18C22×#11719924C2211yescharacteristic
19C22×#11719924C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21C22×#11719917C2211yescharacteristic
22C23×#88322C2211yescharacteristic
23#16811277—24no—
24#16811277C2218yescomplemented
25C2×#13133217C2211yescharacteristic
26C2×#13133201—21no—
27C2×#13133201—21no—
28C2×#13133197—21no—
29C2×#13133191C2211yescharacteristic
30C2×#13133191C2211yescharacteristic
31C2×C4×D212C2211yescharacteristic
32C22×C4⋊Dic53C2211yescharacteristic
33C22×C4⋊Dic53C2211yescharacteristic
34#16810982C2218yescomplemented
35#16810956C2218yescomplemented
36#16810934C2218yescomplemented
37#16810918C2218yescomplemented
38#16810871C2218yescomplemented
39#16810857C2218yescomplemented
40#16810835C2218yescomplemented
41#16810768C2218yescomplemented
42#16810762C2218yescomplemented
43#16810721C2218yescomplemented
44#16810695C2218yescomplemented
45C2×#13133150C2211yescharacteristic
46C2×#13133150C2211yescharacteristic
47C2×#13133150C2211yescharacteristic
48C2×C4⋊#88322C2211yescharacteristic
49#16810624C2218yescomplemented
50C2×#13133141C2211yescharacteristic
51C2×#13133141C2211yescharacteristic
52C2×#13133141C2211yescharacteristic
53C2×#13133141C2211yescharacteristic
54C2×#13133141C2211yescharacteristic
55C2×#13133141C2211yescharacteristic
56C2×#13133141C2218yescomplemented
57C2×#13133138C2211yescharacteristic
58C2×#13133138C2211yescharacteristic
59C2×#13133138C2211yescharacteristic
60C2×#13133137C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×C22⋊#88322C2211yescharacteristic
63C2×#13133128C2211yescharacteristic
64C22×#41×C53C2211yescharacteristic
65C23×Q8×C53C2211yescharacteristic
66C53×#548—24no—
67C53×#548C2218yescomplemented
68C2×#124×C53—21no—
69C2×#124×C53C2211yescharacteristic
70C2×C22⋊Q8×C53—21no—
71C2×C22⋊Q8×C53C2211yescharacteristic
72C2×#121×C53—21no—
73C2×#121×C53C2211yescharacteristic
74C2×C4×Q8×C53C2211yescharacteristic
75C2×C4×D4×C53—21no—
76C2×C4×D4×C53C2211yescharacteristic
77C2×#11719947—28no—
78C2×#11719947—48no—
79C22×Dic106—21no—
80C22×D212C2311yescharacteristic
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C23×Dic53—21no—
84C23×Dic53—21no—
85C22×C4×D53—21no—
86C2×#11719924—24no—
87C2×#11719924—42no—
88C2×#11719924C2314yes—
89C2×#11719924C2314yes—
90C2×#11719922—42no—
91C2×#11719922C2314yes—
92C2×#11719917—42no—
93C2×#11719917C2314yes—
94C22×#88322—42no—
95C22×#88322C2311yescharacteristic
96C22×#88322C2311yescharacteristic
97C22×#88322C2311yescharacteristic
98C22×#88322C2311yescharacteristic
99C22×#88322C2314yes—
100#13133217—22no—
101#13133217C2314yes—
102#13133201—28no—
103#13133201—28no—
104#13133197—28no—
105#13133191—22no—
106#13133191—22no—
107#13133191C2314yes—
108#13133191C2314yes—
109C4×D212—22no—
110C4×D212C2314yes—
111C2×C4⋊Dic53—22no—
112C2×C4⋊Dic53—22no—
113C2×C4⋊Dic53—21no—
114C2×C4⋊Dic53—21no—
115C2×C4⋊Dic53—21no—
116C2×C4⋊Dic53C2314yes—
117C2×C4⋊Dic53C2314yes—
118C2×C4⋊Dic53C2311yescharacteristic
119C2×C4⋊Dic53C2311yescharacteristic
120C2×C4⋊Dic53C2311yescharacteristic
121C2×#11719921—21no—
122C2×#11719921—21no—
123C2×#11719921—21no—
124#13133150C2314yes—
125#13133150C2314yes—
126#13133150C2314yes—
127C4⋊#88322C2314yes—
128#13133141C2314yes—
129#13133141C2314yes—
130#13133141C2314yes—
131#13133141C2314yes—
132#13133141C2314yes—
133#13133141C2314yes—
134#13133138C2314yes—
135#13133138C2314yes—
136#13133138C2314yes—
137#13133137C2314yes—
138C22⋊#88322C2314yes—
139C22⋊#88322C2314yes—
140#13133128C2314yes—
141C2×#41×C53—22no—
142C2×#41×C53—24no—
143C2×#41×C53—42no—
144C2×#41×C53C2314yes—
145C22×Q8×C53—21no—
146C22×Q8×C53—22no—
147C22×Q8×C53—24no—
148C22×Q8×C53—42no—
149C22×Q8×C53C2311yescharacteristic
150C22×Q8×C53C2314yes—
151C22×Q8×C53C2311yescharacteristic
152C22×D4×C53—21no—
153C22×D4×C53—21no—
154C22×D4×C53D411yescharacteristic
155C22×D4×C53C2311yescharacteristic
156C23×C4×C53—21no—
157C23×C4×C53—21no—
158C23×C4×C53C2311yescharacteristic
159C23×C4×C53C2311yescharacteristic
160#124×C53—28no—
161#124×C53—22no—
162#124×C53C2314yes—
163C22⋊Q8×C53—28no—
164C22⋊Q8×C53—22no—
165C22⋊Q8×C53C2314yes—
166#121×C53—28no—
167#121×C53—22no—
168#121×C53C2314yes—
169C4×Q8×C53—22no—
170C4×Q8×C53C2314yes—
171C4×D4×C53—28no—
172C4×D4×C53D414yes—
173C4×D4×C53C2314yes—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53—21no—
176C2×C4⋊C4×C53D411yescharacteristic
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53—21no—
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53—21no—
182C2×C22⋊C4×C53D411yescharacteristic
183C2×C22⋊C4×C53D411yescharacteristic
184C2×C42×C53—21no—
185C2×C42×C53C2311yescharacteristic
186C24×C53—21no—
187C24×C53C2×D411yescharacteristic
188C24×C53C2×D411yescharacteristic
189C23×D53—21no—
190#41×C53—28no—
191#41×C53—44no—
192#41×C53—48no—
193C2×Q8×C53—21no—
194C2×Q8×C53—24no—
195C2×Q8×C53—21no—
196C2×Q8×C53—22no—
197C2×Q8×C53—28no—
198C2×Q8×C53—22no—
199C2×Q8×C53—22no—
200C2×Q8×C53—44no—
201C2×Q8×C53—44no—
202C2×Q8×C53—48no—
203C2×Q8×C53#4114yescomplemented
204C2×Q8×C53C2412yes—
205C2×Q8×C53C2412yes—
206C2×D4×C53—24no—
207C2×D4×C53—24no—
208C2×D4×C53—24no—
209C2×D4×C53—21no—
210C2×D4×C53—22no—
211C2×D4×C53—22no—
212C2×D4×C53—44no—
213C2×D4×C53—44no—
214C2×D4×C53C2×D414yes—
215C2×D4×C53C2412yes—
216C22×C4×C53—21no—
217C22×C4×C53—22no—
218C22×C4×C53—22no—
219C22×C4×C53—22no—
220C22×C4×C53—22no—
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53—24no—
224C22×C4×C53—24no—
225C22×C4×C53—44no—
226C22×C4×C53—44no—
227C22×C4×C53C2×D411yescharacteristic
228C22×C4×C53C2×D411yescharacteristic
229C22×C4×C53C2×D411yescharacteristic
230C22×C4×C53C2×D411yescharacteristic
231C22×C4×C53C2×D412yes—
232C22×C4×C53C2×D412yes—
233C22×C4×C53C2412yes—
234C22×C4×C53C2412yes—
235C22×C4×C53C2411yescharacteristic
236C2×C22⋊D53—24no—
237C2×C22⋊D53—24no—
238C2×C22⋊D53—44no—
239C2×C22⋊D53—44no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53—24no—
244C22×Dic53—24no—
245C22×Dic53—44no—
246C22×Dic53—44no—
247#11719947—432no—
248C2×D212—22no—
249C2×D212—22no—
250C2×D212—21no—
251C2×D212C2412yes—
252C2×C4×D53—24no—
253C2×C4×D53—44no—
254C2×Dic106—24no—
255C2×Dic106—44no—
256C4⋊C4×C53—24no—
257C4⋊C4×C53—24no—
258C4⋊C4×C53—21no—
259C4⋊C4×C53C2×D414yes—
260C4⋊C4×C53C2412yes—
261C22⋊C4×C53—24no—
262C22⋊C4×C53—24no—
263C22⋊C4×C53—24no—
264C22⋊C4×C53—24no—
265C22⋊C4×C53C2×D414yes—
266C22⋊C4×C53C2×D414yes—
267C42×C53—24no—
268C42×C53C2×D412yes—
269C42×C53C2412yes—
270#11719924—28no—
271#11719924—44no—
272#11719922—44no—
273#11719921—24no—
274#11719921—24no—
275#11719921—24no—
276C4⋊Dic53—21no—
277C4⋊Dic53—21no—
278C4⋊Dic53—21no—
279C4⋊Dic53—24no—
280C4⋊Dic53—24no—
281C4⋊Dic53—24no—
282C4⋊Dic53C2412yes—
283C4⋊Dic53C2412yes—
284C4⋊Dic53C2412yes—
285#11719917—44no—
286C2×#88322—22no—
287C2×#88322—22no—
288C2×#88322—22no—
289C2×#88322—22no—
290C2×#88322—44no—
291C2×#88322C2412yes—
292C2×#88322C2412yes—
293C2×#88322C2412yes—
294C2×#88322C2412yes—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53—22no—
301C23×C53—42no—
302C23×C53—42no—
303C23×C53—42no—
304C23×C53AGL(1,ℤ/8)14yes—
305C23×C53C22×D412yes—
306C23×C53C22×D412yes—
307C23×C53C22×D411yescharacteristic
308C22×D53—22no—
309C22×D53—42no—
310C22×D53—42no—
311C22×D53—42no—
312Q8×C53—24no—
313Q8×C53—22no—
314Q8×C53—22no—
315Q8×C53—22no—
316Q8×C53—48no—
317Q8×C53—42no—
318Q8×C53C2×#4114yescomplemented
319D4×C53—28no—
320D4×C53—22no—
321D4×C53—22no—
322D4×C53—48no—
323D4×C53—48no—
324D4×C53—42no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—24no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—24no—
332C2×C4×C53—24no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—48no—
340C2×C4×C53—48no—
341C2×C4×C53—42no—
342C2×C4×C53—42no—
343C2×C4×C53C22×D412yes—
344C2×C4×C53C22×D412yes—
345C2×C4×C53C22×D412yes—
346C2×C4×C53C22×D412yes—
347C2×C4×C53C22×D411yescharacteristic
348C2×C4×C53C2×#4112yes—
349C2×C4×C53H(5,𝔽2)12yes—
350C2×C4×C53C2511yescharacteristic
351C22⋊D53—48no—
352C22⋊D53—48no—
353C2×Dic53—22no—
354C2×Dic53—22no—
355C2×Dic53—22no—
356C2×Dic53—48no—
357C2×Dic53—42no—
358C2×Dic53—42no—
359C2×Dic53—42no—
360C2×Dic53—48no—
361D212—22no—
362D212—22no—
363D212—42no—
364C4×D53—48no—
365Dic106—48no—
366#88322—22no—
367#88322—22no—
368#88322—22no—
369#88322—22no—
370C2×#3308—531nomaximal, Sylow
371C22×C53—22no—
372C22×C53—28no—
373C22×C53—22no—
374C22×C53—22no—
375C22×C53—22no—
376C22×C53—22no—
377C22×C53—44no—
378C22×C53—42no—
379C22×C53—42no—
380C22×C53—42no—
381C22×C53—84no—
382C22×C53#54612yes—
383C22×C53C2×AGL(1,ℤ/8)14yes—
384C22×C53C2×AGL(1,ℤ/8)12yes—
385C22×C53#57812yes—
386C22×C53C23×D411yescharacteristic
387C2×D53—42no—
388C2×D53—42no—
389C2×D53—42no—
390C2×D53—84no—
391C4×C53—22no—
392C4×C53—22no—
393C4×C53—24no—
394C4×C53—22no—
395C4×C53—22no—
396C4×C53—42no—
397C4×C53—42no—
398C4×C53#54612yes—
399C4×C53C22×#4111yescharacteristic
400C4×C53C2×H(5,𝔽2)11yescharacteristic
401Dic53—42no—
402Dic53—42no—
403Dic53—42no—
404C2×#548D5311yescharacteristic, complemented
405C2×#547—531no—
406#3308—5316no—
407C2×#489—531no—
408C2×#484—531no—
409C2×#480—531no—
410C2×#477—531no—
411C2×#468—531no—
412C2×#466—531no—
413C2×#463—531no—
414C2×#449—531no—
415C2×#448—531no—
416C2×#440—531no—
417C2×#435—531no—
418C2×#417—531no—
419C22×#103—531no—
420C2×C53—24no—
421C2×C53—42no—
422C2×C53—82no—
423C2×C53#330814yescomplemented
424C2×C53C2×#54611yescharacteristic
425C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
426C2×C53C2×#57811yescharacteristic
427D53—82no—
428C22×#41—1061no—
429C22×#41C2×D5311yescharacteristic
430C23×Q8C2×D5311yescharacteristic
431C22×SD16—531no—
432C22×SD16—531no—
433C22×D8—531no—
434C22×M16—531no—
435C23×C8—531no—
436#548—24no—
437#548C2×D5318yescomplemented
438#547—538no—
439#547—1064no—
440C2×C4⋊Q8—531no—
441C2×#124—21no—
442C2×#124C2×D5311yescharacteristic
443C2×#123—1061no—
444C2×#123—1061no—
445C2×C22⋊Q8—21no—
446C2×C22⋊Q8—1061no—
447C2×C22⋊Q8C2×D5311yescharacteristic
448C2×#121—21no—
449C2×#121—531no—
450C2×#121—531no—
451C2×#121C2×D5311yescharacteristic
452C2×C4×Q8C2×D5311yescharacteristic
453C2×C4×D4—21no—
454C2×C4×D4—531no—
455C2×C4×D4C2×D5311yescharacteristic
456C22×C4⋊C4—531no—
457C22×C4⋊C4—531no—
458#489—538no—
459#484—538no—
460#480—538no—
461#477—538no—
462#468—538no—
463#466—538no—
464#463—538no—
465#449—538no—
466#448—538no—
467#440—538no—
468#435—538no—
469C2×#107—531no—
470C2×#107—531no—
471C2×#107—531no—
472C2×C4⋊C8—531no—
473#417—538no—
474C2×#103—531no—
475C2×#103—531no—
476C2×#103—531no—
477C2×#103—531no—
478C2×#103—531no—
479C2×#103—531no—
480C2×#103—538no—
481C2×#102—531no—
482C2×#102—531no—
483C2×#102—531no—
484C2×#102—531no—
485C2×C22⋊C8—531no—
486C2×C22⋊C8—531no—
487C2×#97—531no—
488C53C2×#330811yescharacteristic, complemented, Sylow
489C2×#41—22no—
490C2×#41—24no—
491C2×#41—42no—
492C2×#41—1068no—
493C2×#41—2128no—
494C2×#41C22×D5314yes—
495C22×Q8—21no—
496C22×Q8—22no—
497C22×Q8—24no—
498C22×Q8—42no—
499C22×Q8—1061no—
500C22×Q8C22×D5311yescharacteristic
501C22×Q8C22×D5314yes—
502C22×Q8C22×D5311yescharacteristic
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—531no—
506C22×D4—1061no—
507C22×D4—1061no—
508C22×D4C22⋊D5311yescharacteristic
509C22×D4C22×D5311yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—1061no—
513C23×C4—1061no—
514C23×C4—1061no—
515C23×C4C22×D5311yescharacteristic
516C23×C4C22×D5311yescharacteristic
517C2×SD16—534no—
518C2×SD16—534no—
519C2×SD16—1064no—
520C2×SD16—2122no—
521C2×D8—534no—
522C2×D8—2122no—
523C2×M16—534no—
524C2×M16—2122no—
525C22×C8—531no—
526C22×C8—531no—
527C22×C8—531no—
528C22×C8—531no—
529C22×C8—534no—
530C22×C8—2122no—
531C4⋊Q8—534no—
532C4⋊Q8—1062no—
533#124—28no—
534#124—22no—
535#124C22×D5314yes—
536#123—1068no—
537#123—1068no—
538C22⋊Q8—22no—
539C22⋊Q8—28no—
540C22⋊Q8—1068no—
541C22⋊Q8C22×D5314yes—
542#121—28no—
543#121—22no—
544#121—534no—
545#121—534no—
546#121—1062no—
547#121—1062no—
548#121C22×D5314yes—
549C4×Q8—22no—
550C4×Q8C22×D5314yes—
551C4×D4—28no—
552C4×D4—534no—
553C4×D4—1062no—
554C4×D4C22⋊D5314yes—
555C4×D4C22×D5314yes—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—531no—
559C2×C4⋊C4—531no—
560C2×C4⋊C4—531no—
561C2×C4⋊C4—534no—
562C2×C4⋊C4—534no—
563C2×C4⋊C4—1061no—
564C2×C4⋊C4—1061no—
565C2×C4⋊C4—1062no—
566C2×C4⋊C4—1062no—
567C2×C4⋊C4—1061no—
568C2×C4⋊C4C22⋊D5311yescharacteristic
569C2×C4⋊C4C22×D5311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—1061no—
575C2×C22⋊C4—1061no—
576C2×C22⋊C4—1061no—
577C2×C22⋊C4C22⋊D5311yescharacteristic
578C2×C22⋊C4C22⋊D5311yescharacteristic
579C2×C42—21no—
580C2×C42C22×D5311yescharacteristic
581#107—534no—
582#107—534no—
583#107—534no—
584C4⋊C8—534no—
585#103—534no—
586#103—534no—
587#103—534no—
588#103—534no—
589#103—534no—
590#103—534no—
591#102—534no—
592#102—534no—
593#102—534no—
594#102—534no—
595C22⋊C8—534no—
596C22⋊C8—534no—
597#97—534no—
598C24—21no—
599C24—1061no—
600C24C2×C22⋊D5311yescharacteristic
601C24C2×C22⋊D5311yescharacteristic
602#41—28no—
603#41—44no—
604#41—48no—
605#41—21232no—
606C2×Q8—21no—
607C2×Q8—24no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—28no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—44no—
614C2×Q8—44no—
615C2×Q8—48no—
616C2×Q8—1064no—
617C2×Q8—2124no—
618C2×Q8#1171994714yescomplemented
619C2×Q8C23×D5312yes—
620C2×Q8C23×D5312yes—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—532no—
630C2×D4—1064no—
631C2×D4—1064no—
632C2×D4—1061no—
633C2×D4—1062no—
634C2×D4—1062no—
635C2×D4—2124no—
636C2×D4—2124no—
637C2×D4C2×C22⋊D5314yes—
638C2×D4C23×D5312yes—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—24no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—1064no—
651C22×C4—1064no—
652C22×C4—1061no—
653C22×C4—1061no—
654C22×C4—1061no—
655C22×C4—1064no—
656C22×C4—2124no—
657C22×C4—2124no—
658C22×C4—2124no—
659C22×C4C2×C22⋊D5312yes—
660C22×C4C2×C22⋊D5312yes—
661C22×C4C2×C22⋊D5311yescharacteristic
662C22×C4C2×C22⋊D5311yescharacteristic
663C22×C4C2×C22⋊D5311yescharacteristic
664C22×C4C2×C22⋊D5311yescharacteristic
665C22×C4C23×D5312yes—
666C22×C4C23×D5312yes—
667C22×C4C23×D5311yescharacteristic
668SD16—1068no—
669SD16—2124no—
670D8—2124no—
671M16—2124no—
672C2×C8—532no—
673C2×C8—532no—
674C2×C8—532no—
675C2×C8—532no—
676C2×C8—1062no—
677C2×C8—1062no—
678C2×C8—1062no—
679C2×C8—1062no—
680C2×C8—2124no—
681C4⋊C4—24no—
682C4⋊C4—24no—
683C4⋊C4—21no—
684C4⋊C4—532no—
685C4⋊C4—532no—
686C4⋊C4—532no—
687C4⋊C4—1061no—
688C4⋊C4—1061no—
689C4⋊C4—1061no—
690C4⋊C4—1064no—
691C4⋊C4—1064no—
692C4⋊C4—1064no—
693C4⋊C4C2×C22⋊D5314yes—
694C4⋊C4C23×D5312yes—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—1064no—
700C22⋊C4—1064no—
701C22⋊C4—1064no—
702C22⋊C4C2×C22⋊D5314yes—
703C22⋊C4C2×C22⋊D5314yes—
704C42—24no—
705C42C2×C22⋊D5312yes—
706C42C23×D5312yes—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—1062no—
717C23—2122no—
718C23—2122no—
719C23—2122no—
720C23#1313324214yes—
721C23C22×C22⋊D5312yes—
722C23C22×C22⋊D5312yes—
723C23C22×C22⋊D5311yescharacteristic
724Q8—24no—
725Q8—22no—
726Q8—22no—
727Q8—22no—
728Q8—48no—
729Q8—42no—
730Q8—2128no—
731Q8C2×#1171994714yescomplemented
732D4—28no—
733D4—22no—
734D4—22no—
735D4—48no—
736D4—48no—
737D4—42no—
738D4—1062no—
739D4—1062no—
740D4—2128no—
741D4—2128no—
742D4—2122no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—48no—
758C2×C4—48no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—1062no—
762C2×C4—1062no—
763C2×C4—1062no—
764C2×C4—2128no—
765C2×C4—2128no—
766C2×C4—2122no—
767C2×C4—2122no—
768C2×C4—2122no—
769C2×C4—2128no—
770C2×C4C22×C22⋊D5312yes—
771C2×C4C22×C22⋊D5312yes—
772C2×C4C22×C22⋊D5312yes—
773C2×C4C22×C22⋊D5312yes—
774C2×C4C22×C22⋊D5311yescharacteristic
775C2×C4C2×#1171994712yes—
776C2×C4#1313326212yes—
777C2×C4C24×D5311yescharacteristic
778C8—1062no—
779C8—1062no—
780C8—1062no—
781C8—1062no—
782C22—22no—
783C22—22no—
784C22—28no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—44no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—84no—
793C22—4244no—
794C22—2122no—
795C22—2122no—
796C22—2122no—
797C22#1681126712yes—
798C22C2×#1313324214yes—
799C22C2×#1313324212yes—
800C22#1681143812yes—
801C22C23×C22⋊D5311yescharacteristic
802C4—22no—
803C4—22no—
804C4—24no—
805C4—22no—
806C4—22no—
807C4—42no—
808C4—42no—
809C4—2122no—
810C4—2122no—
811C4—2122no—
812C4#1681126712yes—
813C4C22×#1171994711yescharacteristic
814C4C2×#1313326211yescharacteristic
815C2—24no—
816C2—42no—
817C2—82no—
818C2—4242no—
819C2#2028670614yesdirect product factor
820C2C2×#1681126711yescharacteristic
821C2C22×#1313324211yescharacteristic
822C2C2×#1681143811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#548C2
socleC23×C53C22×D4
hypercenterC2×#548D53
hypocenterC53C2×#3308
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#16811277C2semidirect
2. #20286706C2direct (N × H)
3. C2×#16810982C2semidirect
4. C2×#16810956C2semidirect
5. C2×#16810934C2semidirect
6. C2×#16810918C2semidirect
7. C2×#16810871C2semidirect
8. C2×#16810857C2semidirect
9. C2×#16810835C2semidirect
10. C2×#16810768C2semidirect
11. C2×#16810762C2semidirect
12. C2×#16810721C2semidirect
13. C2×#16810695C2semidirect
14. C2×#16810624C2semidirect
15. C22×#13133141C2semidirect
16. C2×C53×#548C2semidirect
24. #16811277C22semidirect
34. #16810982C22semidirect
35. #16810956C22semidirect
36. #16810934C22semidirect
37. #16810918C22semidirect
38. #16810871C22semidirect
39. #16810857C22semidirect
40. #16810835C22semidirect
41. #16810768C22semidirect
42. #16810762C22semidirect
43. #16810721C22semidirect
44. #16810695C22semidirect
49. #16810624C22semidirect
56. C2×#13133141C22semidirect
67. C53×#548C22semidirect
203. C2×Q8×C53#41semidirect
318. Q8×C53C2×#41semidirect
404. C2×#548D53semidirect
423. C2×C53#3308semidirect
437. #548C2×D53semidirect
488. C53C2×#3308semidirect
618. C2×Q8#11719947semidirect
731. Q8C2×#11719947semidirect
819. C2#20286706direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112772
#202867062
C2×#168109822
C2×#168109562
C2×#168109342
C2×#168109182
C2×#168108712
C2×#168108572
C2×#168108352
C2×#168107682
C2×#168107622
C2×#168107212
C2×#168106952
C2×#168106242
C22×#131331412
C2×C53×#5482
C2×#330853