Finite Group Databasebeta

← C2×#20286700 #28260660

Subgroups — C2×#20286700 #28260660

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×#16811282C211yesmaximal, characteristic, complemented
2#20286700C2116yesmaximal, direct product factor
3C2×#16810985C211yesmaximal, characteristic, complemented
4C2×#16810958C211yesmaximal, characteristic, complemented
5C2×#16810936C211yesmaximal, characteristic, complemented
6C2×#16810915C211yesmaximal, characteristic, complemented
7C2×#16810867C211yesmaximal, characteristic, complemented
8C2×#16810857C211yesmaximal, characteristic, complemented
9C2×#16810838C211yesmaximal, characteristic, complemented
10C2×#16810766C211yesmaximal, characteristic, complemented
11C2×#16810761C211yesmaximal, characteristic, complemented
12C2×#16810723C211yesmaximal, characteristic, complemented
13C2×#16810695C211yesmaximal, characteristic, complemented
14C2×#16810622C211yesmaximal, characteristic, complemented
15C22×#13133140C211yesmaximal, characteristic, complemented
16C2×C53×#547C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C23×Dic106C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719923C2211yescharacteristic
21C22×#11719922C2211yescharacteristic
22C22×#11719917C2211yescharacteristic
23C23×#88322C2211yescharacteristic
24#16811282—24no—
25#16811282C2218yescomplemented
26C2×#13133205C2211yescharacteristic
27C2×#13133203—21no—
28C2×#13133196C2211yescharacteristic
29C2×#13133195—21no—
30C2×#13133191C2211yescharacteristic
31C2×#13133189—21no—
32C2×C4×Dic106C2211yescharacteristic
33C2×#13133177—21no—
34#16810985C2218yescomplemented
35#16810958C2218yescomplemented
36#16810936C2218yescomplemented
37#16810915C2218yescomplemented
38#16810867C2218yescomplemented
39#16810857C2218yescomplemented
40#16810838C2218yescomplemented
41#16810766C2218yescomplemented
42#16810761C2218yescomplemented
43#16810723C2218yescomplemented
44#16810695C2218yescomplemented
45C2×#13133150C2211yescharacteristic
46C2×#13133150C2211yescharacteristic
47C2×#13133150C2211yescharacteristic
48C2×C4⋊#88322C2211yescharacteristic
49#16810622C2218yescomplemented
50C2×#13133140C2211yescharacteristic
51C2×#13133140C2211yescharacteristic
52C2×#13133140C2211yescharacteristic
53C2×#13133140C2211yescharacteristic
54C2×#13133140C2211yescharacteristic
55C2×#13133140C2211yescharacteristic
56C2×#13133140C2218yescomplemented
57C2×#13133138C2211yescharacteristic
58C2×#13133137C2211yescharacteristic
59C2×#13133137C2211yescharacteristic
60C2×#13133137C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×C22⋊#88322C2211yescharacteristic
63C2×#13133128C2211yescharacteristic
64C22×#41×C53—21no—
65C53×#547—24no—
66C53×#547C2218yescomplemented
67C2×C4⋊Q8×C53C2211yescharacteristic
68C2×#123×C53—21no—
69C2×#123×C53—21no—
70C2×C22⋊Q8×C53—21no—
71C2×#121×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C2×C4×D4×C53C2211yescharacteristic
74C2×C4×D4×C53C2211yescharacteristic
75C22×C4⋊C4×C53C2211yescharacteristic
76C22×C4⋊C4×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—24no—
79C2×#11719945—42no—
80C2×#11719945C2314yes—
81C22×Dic106—24no—
82C22×Dic106—22no—
83C22×Dic106—21no—
84C22×Dic106—42no—
85C22×Dic106C2311yescharacteristic
86C22×Dic106C2314yes—
87C22×Dic106C2311yescharacteristic
88C22×D212C2311yescharacteristic
89C22×C22⋊D53—21no—
90C22×C22⋊D53—21no—
91C23×Dic53—21no—
92C22×C4×D53—21no—
93C2×#11719923—24no—
94C2×#11719923—42no—
95C2×#11719923C2314yes—
96C2×#11719923C2314yes—
97C2×#11719922—42no—
98C2×#11719922C2314yes—
99C2×#11719917—42no—
100C2×#11719917C2314yes—
101C22×#88322—42no—
102C22×#88322C2311yescharacteristic
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105C22×#88322C2311yescharacteristic
106C22×#88322C2314yes—
107#13133205—22no—
108#13133205C2314yes—
109#13133203—28no—
110#13133196—22no—
111#13133196C2314yes—
112#13133195—28no—
113#13133191—22no—
114#13133191C2314yes—
115#13133189—28no—
116C4×Dic106—22no—
117C4×Dic106C2314yes—
118#13133177—28no—
119C2×C4⋊Dic53C2311yescharacteristic
120C2×#11719919—21no—
121C2×#11719919—21no—
122C2×C22⋊Dic53—21no—
123C2×#11719921—21no—
124C2×#11719921—21no—
125C2×#11719921—21no—
126C2×C4×Dic53—21no—
127#13133150C2314yes—
128#13133150C2314yes—
129#13133150C2314yes—
130C4⋊#88322C2314yes—
131#13133140C2314yes—
132#13133140C2314yes—
133#13133140C2314yes—
134#13133140C2314yes—
135#13133140C2314yes—
136#13133140C2314yes—
137#13133138C2314yes—
138#13133137C2314yes—
139#13133137C2314yes—
140#13133137C2314yes—
141C22⋊#88322C2314yes—
142C22⋊#88322C2314yes—
143#13133128C2314yes—
144C2×#41×C53—28no—
145C2×#41×C53—48no—
146C22×Q8×C53—21no—
147C22×D4×C53—21no—
148C22×D4×C53—21no—
149C22×D4×C53D411yescharacteristic
150C22×D4×C53C2311yescharacteristic
151C23×C4×C53—21no—
152C23×C4×C53—21no—
153C23×C4×C53—21no—
154C23×C4×C53C2311yescharacteristic
155C23×C4×C53C2311yescharacteristic
156C4⋊Q8×C53—22no—
157C4⋊Q8×C53C2314yes—
158#123×C53—28no—
159#123×C53—28no—
160C22⋊Q8×C53—28no—
161#121×C53—22no—
162#121×C53—22no—
163#121×C53C2314yes—
164#121×C53C2314yes—
165C4×D4×C53—22no—
166C4×D4×C53D414yes—
167C4×D4×C53C2314yes—
168C4×D4×C53C2314yes—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53—22no—
172C2×C4⋊C4×C53—22no—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53D411yescharacteristic
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C4⋊C4×C53C2314yes—
179C2×C4⋊C4×C53C2314yes—
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53—21no—
182C2×C22⋊C4×C53—21no—
183C2×C22⋊C4×C53D411yescharacteristic
184C2×C22⋊C4×C53D411yescharacteristic
185C2×C42×C53C2311yescharacteristic
186C24×C53—21no—
187C24×C53C2×D411yescharacteristic
188C24×C53C2×D411yescharacteristic
189C23×D53—21no—
190#41×C53—432no—
191C2×Q8×C53—24no—
192C2×Q8×C53—44no—
193C2×D4×C53—24no—
194C2×D4×C53—24no—
195C2×D4×C53—24no—
196C2×D4×C53—21no—
197C2×D4×C53—22no—
198C2×D4×C53—22no—
199C2×D4×C53—44no—
200C2×D4×C53—44no—
201C2×D4×C53C2×D414yes—
202C2×D4×C53C2412yes—
203C22×C4×C53—22no—
204C22×C4×C53—22no—
205C22×C4×C53—22no—
206C22×C4×C53—22no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—24no—
211C22×C4×C53—24no—
212C22×C4×C53—24no—
213C22×C4×C53—44no—
214C22×C4×C53—44no—
215C22×C4×C53—44no—
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2×D411yescharacteristic
219C22×C4×C53C2×D411yescharacteristic
220C22×C4×C53C2×D412yes—
221C22×C4×C53C2×D412yes—
222C22×C4×C53C2412yes—
223C22×C4×C53C2412yes—
224C22×C4×C53C2411yescharacteristic
225C2×C22⋊D53—24no—
226C2×C22⋊D53—24no—
227C2×C22⋊D53—44no—
228C2×C22⋊D53—44no—
229C22×Dic53—21no—
230C22×Dic53—21no—
231C22×Dic53—21no—
232C22×Dic53—24no—
233C22×Dic53—44no—
234#11719945—28no—
235#11719945—44no—
236#11719945—48no—
237C2×D212—22no—
238C2×D212—22no—
239C2×D212—21no—
240C2×D212C2412yes—
241C2×C4×D53—24no—
242C2×C4×D53—44no—
243C2×Dic106—21no—
244C2×Dic106—22no—
245C2×Dic106—22no—
246C2×Dic106—22no—
247C2×Dic106—28no—
248C2×Dic106—24no—
249C2×Dic106—21no—
250C2×Dic106—44no—
251C2×Dic106—48no—
252C2×Dic106—44no—
253C2×Dic106#4114yescomplemented
254C2×Dic106C2412yes—
255C2×Dic106C2412yes—
256C4⋊C4×C53—21no—
257C4⋊C4×C53—21no—
258C4⋊C4×C53—21no—
259C4⋊C4×C53—24no—
260C4⋊C4×C53—24no—
261C4⋊C4×C53—24no—
262C4⋊C4×C53C2×D414yes—
263C4⋊C4×C53C2412yes—
264C4⋊C4×C53C2412yes—
265C4⋊C4×C53C2412yes—
266C22⋊C4×C53—24no—
267C22⋊C4×C53—24no—
268C22⋊C4×C53—24no—
269C22⋊C4×C53C2×D414yes—
270C22⋊C4×C53C2×D414yes—
271C42×C53C2×D412yes—
272C42×C53C2412yes—
273C22⋊Dic53—24no—
274#11719923—28no—
275#11719923—44no—
276#11719922—44no—
277#11719921—24no—
278#11719921—24no—
279#11719921—24no—
280C4⋊Dic53—21no—
281C4⋊Dic53C2412yes—
282#11719919—24no—
283#11719919—24no—
284C4×Dic53—24no—
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—48no—
313D4×C53—28no—
314D4×C53—22no—
315D4×C53—22no—
316D4×C53—48no—
317D4×C53—48no—
318D4×C53—42no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—24no—
324C2×C4×C53—24no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—48no—
333C2×C4×C53—48no—
334C2×C4×C53—42no—
335C2×C4×C53—42no—
336C2×C4×C53—42no—
337C2×C4×C53—48no—
338C2×C4×C53C22×D412yes—
339C2×C4×C53C22×D412yes—
340C2×C4×C53C22×D412yes—
341C2×C4×C53C22×D412yes—
342C2×C4×C53C22×D411yescharacteristic
343C2×C4×C53C2×#4112yes—
344C2×C4×C53H(5,𝔽2)12yes—
345C2×C4×C53C2511yescharacteristic
346C22⋊D53—48no—
347C22⋊D53—48no—
348C2×Dic53—24no—
349C2×Dic53—22no—
350C2×Dic53—22no—
351C2×Dic53—22no—
352C2×Dic53—48no—
353C2×Dic53—42no—
354C2×Dic53—42no—
355D212—22no—
356D212—22no—
357D212—42no—
358C4×D53—48no—
359Dic106—24no—
360Dic106—22no—
361Dic106—22no—
362Dic106—22no—
363Dic106—48no—
364Dic106—42no—
365Dic106C2×#4114yescomplemented
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—22no—
394C4×C53—22no—
395C4×C53—42no—
396C4×C53—42no—
397C4×C53—42no—
398C4×C53#54612yes—
399C4×C53C22×#4111yescharacteristic
400C4×C53C2×H(5,𝔽2)11yescharacteristic
401Dic53—24no—
402Dic53—42no—
403Dic53—42no—
404C2×#548—531no—
405C2×#547D5311yescharacteristic, complemented
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—21no—
429C22×#41—531no—
430C23×Q8—531no—
431C22×SD16—531no—
432C22×SD16—531no—
433C22×D8—531no—
434C22×M16—531no—
435C23×C8—531no—
436#548—538no—
437#548—1064no—
438#547—24no—
439#547C2×D5318yescomplemented
440C2×C4⋊Q8C2×D5311yescharacteristic
441C2×#124—531no—
442C2×#124—1061no—
443C2×#123—21no—
444C2×#123—21no—
445C2×C22⋊Q8—21no—
446C2×C22⋊Q8—531no—
447C2×C22⋊Q8—1061no—
448C2×#121—531no—
449C2×#121—1061no—
450C2×#121C2×D5311yescharacteristic
451C2×#121C2×D5311yescharacteristic
452C2×C4×Q8—531no—
453C2×C4×D4—1061no—
454C2×C4×D4C2×D5311yescharacteristic
455C2×C4×D4C2×D5311yescharacteristic
456C22×C4⋊C4C2×D5311yescharacteristic
457C22×C4⋊C4C2×D5311yescharacteristic
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—28no—
490C2×#41—48no—
491C2×#41—534no—
492C2×#41—1064no—
493C2×#41—1062no—
494C2×#41—2122no—
495C22×Q8—21no—
496C22×Q8—531no—
497C22×Q8—531no—
498C22×Q8—534no—
499C22×Q8—1064no—
500C22×Q8—1061no—
501C22×Q8—1062no—
502C22×Q8—2122no—
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—21no—
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—22no—
532C4⋊Q8C22×D5314yes—
533#124—534no—
534#124—1068no—
535#124—1062no—
536#123—28no—
537#123—28no—
538C22⋊Q8—28no—
539C22⋊Q8—534no—
540C22⋊Q8—1062no—
541C22⋊Q8—1068no—
542#121—22no—
543#121—22no—
544#121—534no—
545#121—1068no—
546#121—1062no—
547#121C22×D5314yes—
548#121C22×D5314yes—
549C4×Q8—534no—
550C4×Q8—1062no—
551C4×D4—22no—
552C4×D4—1068no—
553C4×D4C22⋊D5314yes—
554C4×D4C22×D5314yes—
555C4×D4C22×D5314yes—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—531no—
562C2×C4⋊C4—1061no—
563C2×C4⋊C4—1061no—
564C2×C4⋊C4C22⋊D5311yescharacteristic
565C2×C4⋊C4C22×D5311yescharacteristic
566C2×C4⋊C4C22×D5311yescharacteristic
567C2×C4⋊C4C22×D5311yescharacteristic
568C2×C4⋊C4C22×D5314yes—
569C2×C4⋊C4C22×D5314yes—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4—1061no—
575C2×C22⋊C4—1061no—
576C2×C22⋊C4—1061no—
577C2×C22⋊C4C22⋊D5311yescharacteristic
578C2×C22⋊C4C22⋊D5311yescharacteristic
579C2×C42—1061no—
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—432no—
603#41—1068no—
604#41—2124no—
605#41—2128no—
606C2×Q8—24no—
607C2×Q8—44no—
608C2×Q8—534no—
609C2×Q8—532no—
610C2×Q8—532no—
611C2×Q8—1068no—
612C2×Q8—1061no—
613C2×Q8—1064no—
614C2×Q8—1061no—
615C2×Q8—1062no—
616C2×Q8—1062no—
617C2×Q8—1062no—
618C2×Q8—2124no—
619C2×Q8—2124no—
620C2×Q8—2128no—
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—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—24no—
649C22×C4—44no—
650C22×C4—44no—
651C22×C4—44no—
652C22×C4—1061no—
653C22×C4—1064no—
654C22×C4—1061no—
655C22×C4—1061no—
656C22×C4—1064no—
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—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—532no—
688C4⋊C4—1061no—
689C4⋊C4—1064no—
690C4⋊C4—1064no—
691C4⋊C4C2×C22⋊D5314yes—
692C4⋊C4C23×D5312yes—
693C4⋊C4C23×D5312yes—
694C4⋊C4C23×D5312yes—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—1064no—
699C22⋊C4—1064no—
700C22⋊C4—1064no—
701C22⋊C4—1064no—
702C22⋊C4C2×C22⋊D5314yes—
703C22⋊C4C2×C22⋊D5314yes—
704C42—1064no—
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#1313324314yes—
721C23C22×C22⋊D5312yes—
722C23C22×C22⋊D5312yes—
723C23C22×C22⋊D5311yescharacteristic
724Q8—48no—
725Q8—534no—
726Q8—1062no—
727Q8—1064no—
728Q8—1062no—
729Q8—1062no—
730Q8—2128no—
731Q8—2122no—
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—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—48no—
757C2×C4—48no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—48no—
762C2×C4—1062no—
763C2×C4—1064no—
764C2×C4—1062no—
765C2×C4—1062no—
766C2×C4—2128no—
767C2×C4—2128no—
768C2×C4—2122no—
769C2×C4—2122no—
770C2×C4C22×C22⋊D5312yes—
771C2×C4C22×C22⋊D5312yes—
772C2×C4C22×C22⋊D5312yes—
773C2×C4C22×C22⋊D5312yes—
774C2×C4C22×C22⋊D5311yescharacteristic
775C2×C4#41×D5312yes—
776C2×C4#1313326312yes—
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#1681126112yes—
798C22C2×#1313324314yes—
799C22C2×#1313324312yes—
800C22#1681143812yes—
801C22C23×C22⋊D5311yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—1064no—
810C4—2122no—
811C4—2122no—
812C4#1681126112yes—
813C4C2×#41×D5311yescharacteristic
814C4C2×#1313326311yescharacteristic
815C2—24no—
816C2—42no—
817C2—82no—
818C2—4242no—
819C2#2028670014yesdirect product factor
820C2C2×#1681126111yescharacteristic
821C2C22×#1313324311yescharacteristic
822C2C2×#1681143811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#547C2
socleC23×C53C22×D4
hypercenterC2×#547D53
hypocenterC53C2×#3308
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#16811282C2semidirect
2. #20286700C2direct (N × H)
3. C2×#16810985C2semidirect
4. C2×#16810958C2semidirect
5. C2×#16810936C2semidirect
6. C2×#16810915C2semidirect
7. C2×#16810867C2semidirect
8. C2×#16810857C2semidirect
9. C2×#16810838C2semidirect
10. C2×#16810766C2semidirect
11. C2×#16810761C2semidirect
12. C2×#16810723C2semidirect
13. C2×#16810695C2semidirect
14. C2×#16810622C2semidirect
15. C22×#13133140C2semidirect
16. C2×C53×#547C2semidirect
25. #16811282C22semidirect
34. #16810985C22semidirect
35. #16810958C22semidirect
36. #16810936C22semidirect
37. #16810915C22semidirect
38. #16810867C22semidirect
39. #16810857C22semidirect
40. #16810838C22semidirect
41. #16810766C22semidirect
42. #16810761C22semidirect
43. #16810723C22semidirect
44. #16810695C22semidirect
49. #16810622C22semidirect
56. C2×#13133140C22semidirect
66. C53×#547C22semidirect
253. C2×Dic106#41semidirect
365. Dic106C2×#41semidirect
405. C2×#547D53semidirect
423. C2×C53#3308semidirect
439. #547C2×D53semidirect
488. C53C2×#3308semidirect
819. C2#20286700direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112822
#202867002
C2×#168109852
C2×#168109582
C2×#168109362
C2×#168109152
C2×#168108672
C2×#168108572
C2×#168108382
C2×#168107662
C2×#168107612
C2×#168107232
C2×#168106952
C2×#168106222
C22×#131331402
C2×C53×#5472
C2×#330853