Finite Group Databasebeta

← C2×#20287430 #28263764

Subgroups — C2×#20287430 #28263764

Order 13568.

2070 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811342C211yesmaximal, characteristic, complemented
2C2×#16811288C211yesmaximal, characteristic, complemented
3#20287430C2116yesmaximal, direct product factor
4C2×#16810981C211yesmaximal, characteristic, complemented
5C2×#16810972C211yesmaximal, characteristic, complemented
6C2×#16810916C211yesmaximal, characteristic, complemented
7C2×#16810915C211yesmaximal, characteristic, complemented
8C2×#16810901C211yesmaximal, characteristic, complemented
9C2×#16810837C211yesmaximal, characteristic
10C2×#16810835C211yesmaximal, characteristic
11C2×#16810827C211yesmaximal, characteristic, complemented
12C2×#16810751C211yesmaximal, characteristic, complemented
13C2×#16810726C211yesmaximal, characteristic, complemented
14C2×#16810725C211yesmaximal, characteristic, complemented
15C2×#16810703C211yesmaximal, characteristic
16C2×C53×#489C211yesmaximal, characteristic, complemented
17C22×Q8×D53—21no—
18C22×#11719913C2211yescharacteristic
19C22×#11719924C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21#16811342—24no—
22#16811342C2218yescomplemented
23#16811288—24no—
24#16811288C2218yescomplemented
25C2×#13133216C2211yescharacteristic
26C2×#13133216C2211yescharacteristic
27C2×#13133215C2211yescharacteristic
28C2×#13133210—21no—
29C2×#13133210—21no—
30C2×#13133204C2211yescharacteristic
31C2×#13133195—21no—
32C2×#13133195—21no—
33C2×#13133194—21no—
34C2×#13133193—21no—
35C2×Q8×Dic53C2211yescharacteristic
36C2×C4×Dic106C2211yescharacteristic
37C2×C4×Dic106C2211yescharacteristic
38C2×C4×D212C2211yescharacteristic
39C2×D4×Dic53C2211yescharacteristic
40C2×#13133179C2211yescharacteristic
41C2×#13133179C2211yescharacteristic
42C2×#13133173—21no—
43#16810981C2218yescomplemented
44#16810972C2218yescomplemented
45#16810916C2218yescomplemented
46#16810915C2218yescomplemented
47#16810901C2218yescomplemented
48#16810837C2218yes—
49#16810835C2218yes—
50#16810827C2218yescomplemented
51#16810751C2218yescomplemented
52#16810726C2218yescomplemented
53#16810725C2218yescomplemented
54#16810703C2218yes—
55C2×#13133151C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58C2×C4⋊#88322C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133146C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133138C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×C4⋊Q8×C53C2211yescharacteristic
70C2×#124×C53C2211yescharacteristic
71C53×#489C2218yescomplemented
72C2×#103×C53C2211yescharacteristic
73C2×#103×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—21no—
79C22×Dic106D411yescharacteristic
80C22×Dic106C2311yescharacteristic
81C2×Q8×D53—28no—
82C2×Q8×D53—48no—
83C22×D212C2311yescharacteristic
84C23×Dic53—21no—
85C22×C4×D53—21no—
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C2×#11719913—24no—
89C2×#11719913C2314yes—
90C2×#11719924—24no—
91C2×#11719924C2314yes—
92C2×#11719922—24no—
93C2×#11719922C2314yes—
94C22×#88322C2311yescharacteristic
95C22×#88322C2311yescharacteristic
96#13133216—22no—
97#13133216—22no—
98#13133216C2314yes—
99#13133216C2314yes—
100#13133215—22no—
101#13133215C2314yes—
102#13133210—28no—
103#13133210—28no—
104#13133204—22no—
105#13133204C2314yes—
106#13133195—28no—
107#13133195—28no—
108#13133194—28no—
109#13133193—28no—
110Q8×Dic53—22no—
111Q8×Dic53C2314yes—
112C4×Dic106—22no—
113C4×Dic106D414yes—
114C4×Dic106C2314yes—
115C4×Dic106C2314yes—
116C4×D212—22no—
117C4×D212C2314yes—
118D4×Dic53—22no—
119D4×Dic53C2314yes—
120#13133179—22no—
121#13133179—22no—
122#13133179C2314yes—
123#13133179C2314yes—
124#13133173—28no—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53D411yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919D411yescharacteristic
135C2×#11719919D411yescharacteristic
136C2×C22⋊Dic53—21no—
137C2×C22⋊Dic53—21no—
138C2×C22⋊Dic53—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53C2311yescharacteristic
145C2×C4×Dic53C2311yescharacteristic
146#13133151C2314yes—
147#13133150C2314yes—
148#13133150C2314yes—
149C4⋊#88322C2314yes—
150#13133146C2314yes—
151#13133146C2314yes—
152#13133142C2314yes—
153#13133141C2314yes—
154#13133140C2314yes—
155#13133140C2314yes—
156#13133139C2314yes—
157#13133138C2314yes—
158#13133127C2314yes—
159C8×Dic53C2314yes—
160C22×Q8×C53—21no—
161C22×Q8×C53C2311yescharacteristic
162C22×D4×C53C2311yescharacteristic
163C22×C8×C53C2311yescharacteristic
164C22×C8×C53C2311yescharacteristic
165C4⋊Q8×C53—22no—
166C4⋊Q8×C53C2314yes—
167#124×C53—22no—
168#124×C53C2314yes—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C22⋊C4×C53—21no—
173C2×C22⋊C4×C53—21no—
174C2×C42×C53C2311yescharacteristic
175#103×C53C2314yes—
176#103×C53C2314yes—
177#102×C53C2314yes—
178#102×C53C2314yes—
179#97×C53C2314yes—
180C24×C53—21no—
181C23×D53—21no—
182C2×Q8×C53—21no—
183C2×Q8×C53—24no—
184C2×Q8×C53—22no—
185C2×Q8×C53—22no—
186C2×Q8×C53—44no—
187C2×Q8×C53C2412yes—
188C2×D4×C53—21no—
189C2×D4×C53—22no—
190C2×D4×C53—22no—
191C2×D4×C53C2412yes—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2411yescharacteristic
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—24no—
202C22×Dic53—44no—
203C22×Dic53C2×D411yescharacteristic
204C22×Dic53C2×D411yescharacteristic
205C22×Dic53C2×D411yescharacteristic
206C22×Dic53C2×D411yescharacteristic
207Q8×D53—432no—
208C2×D212—21no—
209C2×D212—22no—
210C2×D212#4114yes—
211C2×D212C2412yes—
212C2×C4×D53—24no—
213C2×C4×D53—24no—
214C2×C4×D53—24no—
215C2×C4×D53—44no—
216C2×C4×D53—44no—
217C2×C4×D53—44no—
218C2×Dic106—24no—
219C2×Dic106—22no—
220C2×Dic106—22no—
221C2×Dic106—21no—
222C2×Dic106—24no—
223C2×Dic106—24no—
224C2×Dic106—44no—
225C2×Dic106—44no—
226C2×Dic106C2×D414yes—
227C2×Dic106C2412yes—
228C2×C8×C53—22no—
229C2×C8×C53—22no—
230C2×C8×C53C2412yes—
231C2×C8×C53C2412yes—
232C4⋊C4×C53—24no—
233C4⋊C4×C53—21no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53C2412yes—
236C4⋊C4×C53C2412yes—
237C22⋊C4×C53—24no—
238C22⋊C4×C53—24no—
239C42×C53C2×D412yes—
240C42×C53C2412yes—
241C22⋊Dic53—24no—
242C22⋊Dic53—24no—
243C22⋊Dic53—24no—
244#11719924—28no—
245#11719922—28no—
246#11719921—24no—
247#11719921—24no—
248#11719921—24no—
249C4⋊Dic53—21no—
250C4⋊Dic53—21no—
251C4⋊Dic53—24no—
252C4⋊Dic53C2×D414yes—
253C4⋊Dic53C2412yes—
254C4⋊Dic53C2412yes—
255#11719919—24no—
256#11719919—24no—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919C2×D414yes—
261#11719919C2×D414yes—
262C4×Dic53—24no—
263C4×Dic53—24no—
264C4×Dic53C2×D412yes—
265C4×Dic53C2×D412yes—
266C4×Dic53C2412yes—
267C4×Dic53C2412yes—
268C2×#88322—22no—
269C2×#88322—22no—
270C2×#88322C2412yes—
271C2×#88322C2412yes—
272#11719913—28no—
273C23×C53—22no—
274C23×C53—42no—
275C23×C53—42no—
276C23×C53—42no—
277C23×C53C22×D411yescharacteristic
278C22×D53—24no—
279C22×D53—22no—
280C22×D53—42no—
281C22×D53—42no—
282Q8×C53—22no—
283Q8×C53—22no—
284Q8×C53—48no—
285Q8×C53—42no—
286D4×C53—22no—
287D4×C53—22no—
288D4×C53—42no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—42no—
295C2×C4×C53—42no—
296C2×C4×C53—42no—
297C2×C4×C53C22×D412yes—
298C2×C4×C53C22×D412yes—
299C2×C4×C53C22×D411yescharacteristic
300C2×C4×C53C2×#4112yes—
301C2×C4×C532−1+412yes—
302C2×C4×C53C2511yescharacteristic
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53—42no—
312C2×Dic53—48no—
313C2×Dic53AGL(1,ℤ/8)14yes—
314C2×Dic53C22×D412yes—
315C2×Dic53C22×D412yes—
316C2×Dic53C22×D412yes—
317C2×Dic53C22×D412yes—
318D212—24no—
319D212—22no—
320D212C2×#4114yes—
321C4×D53—48no—
322C4×D53—48no—
323C4×D53—48no—
324Dic106—28no—
325Dic106—22no—
326Dic106—22no—
327Dic106—48no—
328Dic106—42no—
329Dic106—48no—
330C8×C53—22no—
331C8×C53—22no—
332#88322—22no—
333#88322—22no—
334C2×#3367—531nomaximal, Sylow
335C22×C53—42no—
336C22×C53—42no—
337C22×C53—42no—
338C22×C53—84no—
339C22×C53#54812yes—
340C22×C53C2×AGL(1,ℤ/8)12yes—
341C22×C53#57812yes—
342C22×C53C23×D411yescharacteristic
343C2×D53—24no—
344C2×D53—48no—
345C2×D53—42no—
346C2×D53—42no—
347C4×C53—22no—
348C4×C53—22no—
349C4×C53—42no—
350C4×C53—42no—
351C4×C53—42no—
352C4×C53#54812yes—
353C4×C53C22×#4111yescharacteristic
354C4×C53C2×2−1+411yescharacteristic
355Dic53—22no—
356Dic53—22no—
357Dic53—22no—
358Dic53—42no—
359Dic53—42no—
360Dic53—42no—
361Dic53C2×AGL(1,ℤ/8)14yes—
362C2×#556—531no—
363C2×D4×Q8—531no—
364#3367—5316no—
365C2×#489—531no—
366C2×#489D5311yescharacteristic, complemented
367C2×#487—531no—
368C2×#477—531no—
369C2×#477—531no—
370C2×#474—531no—
371C2×#463—531no—
372C2×#463—531no—
373C2×#461—531no—
374C2×#446—531no—
375C2×#440—531no—
376C2×#440—531no—
377C2×C4×D8—531no—
378C2×C53—82no—
379C2×C53#336714yescomplemented
380C2×C53C2×#54811yescharacteristic
381C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
382C2×C53C2×#57811yescharacteristic
383D53—44no—
384C23×Q8—1061no—
385C22×SD16—531no—
386C22×SD16—531no—
387C22×D8—531no—
388#556—538no—
389#556—1064no—
390D4×Q8—538no—
391D4×Q8—1064no—
392C2×C4⋊Q8—531no—
393C2×C4⋊Q8—531no—
394C2×C4⋊Q8—531no—
395C2×C4⋊Q8C2×D5311yescharacteristic
396C2×#126—1061no—
397C2×#126—1061no—
398C2×#124—531no—
399C2×#124C2×D5311yescharacteristic
400C2×C22⋊Q8—1061no—
401C2×C22⋊Q8—1061no—
402C2×C22⋊Q8—1061no—
403C2×C22⋊Q8—1061no—
404C2×C4×Q8—531no—
405C2×C4×Q8—531no—
406C2×C4×Q8—531no—
407C2×C4×D4—531no—
408C2×C4×D4—531no—
409C2×C4×D4—531no—
410C2×C4×D4—531no—
411C2×#117—1061no—
412#489—538no—
413#489C2×D5318yescomplemented
414#487—538no—
415#477—538no—
416#477—538no—
417#474—538no—
418#463—538no—
419#463—538no—
420#461—538no—
421#446—538no—
422#440—538no—
423#440—538no—
424C4×D8—538no—
425C2×#107—531no—
426C2×#107—531no—
427C2×#107—531no—
428C2×C4⋊C8—531no—
429C2×C4⋊C8—531no—
430C2×C4⋊C8—531no—
431C2×#103—531no—
432C2×#103—531no—
433C2×#103—531no—
434C2×#103—531no—
435C2×#103C2×D5311yescharacteristic
436C2×#103C2×D5311yescharacteristic
437C2×#102—531no—
438C2×#102—531no—
439C2×#102C2×D5311yescharacteristic
440C2×#102C2×D5311yescharacteristic
441C2×#97—531no—
442C2×#97C2×D5311yescharacteristic
443C2×C4×C8—531no—
444C53C2×#336711yescharacteristic, complemented, Sylow
445C22×Q8—21no—
446C22×Q8—531no—
447C22×Q8—531no—
448C22×Q8—1061no—
449C22×Q8—1061no—
450C22×Q8—1068no—
451C22×Q8—2128no—
452C22×Q8C22×D5311yescharacteristic
453C22×D4—531no—
454C22×D4C22×D5311yescharacteristic
455C23×C4—1061no—
456C23×C4—1061no—
457C23×C4—1061no—
458C23×C4—1061no—
459C2×SD16—534no—
460C2×SD16—534no—
461C2×SD16—1064no—
462C2×SD16—1064no—
463C2×D8—534no—
464C2×D8—1064no—
465C22×C8—531no—
466C22×C8—531no—
467C22×C8C22×D5311yescharacteristic
468C22×C8C22×D5311yescharacteristic
469C4⋊Q8—22no—
470C4⋊Q8—534no—
471C4⋊Q8—534no—
472C4⋊Q8—534no—
473C4⋊Q8—1062no—
474C4⋊Q8—1062no—
475C4⋊Q8—1062no—
476C4⋊Q8C22×D5314yes—
477#126—1068no—
478#126—1068no—
479#124—22no—
480#124—534no—
481#124—1062no—
482#124C22×D5314yes—
483C22⋊Q8—1068no—
484C22⋊Q8—1068no—
485C22⋊Q8—1068no—
486C22⋊Q8—1068no—
487C4×Q8—534no—
488C4×Q8—534no—
489C4×Q8—534no—
490C4×Q8—534no—
491C4×Q8—1062no—
492C4×Q8—1062no—
493C4×D4—534no—
494C4×D4—534no—
495C4×D4—534no—
496C4×D4—534no—
497C4×D4—1062no—
498C4×D4—1062no—
499C4×D4—1062no—
500C4×D4—1062no—
501#117—1068no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—531no—
504C2×C4⋊C4—531no—
505C2×C4⋊C4—531no—
506C2×C4⋊C4—531no—
507C2×C4⋊C4—531no—
508C2×C4⋊C4—1061no—
509C2×C4⋊C4—1061no—
510C2×C4⋊C4—1061no—
511C2×C4⋊C4—1061no—
512C2×C4⋊C4—1061no—
513C2×C4⋊C4—1061no—
514C2×C4⋊C4C22×D5311yescharacteristic
515C2×C4⋊C4C22×D5311yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—1061no—
519C2×C22⋊C4—1061no—
520C2×C22⋊C4—1061no—
521C2×C22⋊C4—1061no—
522C2×C22⋊C4—1061no—
523C2×C22⋊C4—1061no—
524C2×C42—531no—
525C2×C42—531no—
526C2×C42—1061no—
527C2×C42—1061no—
528C2×C42C22×D5311yescharacteristic
529#107—534no—
530#107—534no—
531#107—534no—
532C4⋊C8—534no—
533C4⋊C8—534no—
534C4⋊C8—534no—
535#103—534no—
536#103—534no—
537#103—534no—
538#103—534no—
539#103C22×D5314yes—
540#103C22×D5314yes—
541#102—534no—
542#102—534no—
543#102C22×D5314yes—
544#102C22×D5314yes—
545#97—534no—
546#97C22×D5314yes—
547C4×C8—534no—
548C24—21no—
549C24—1061no—
550C2×Q8—21no—
551C2×Q8—24no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—44no—
555C2×Q8—534no—
556C2×Q8—532no—
557C2×Q8—1064no—
558C2×Q8—1064no—
559C2×Q8—1064no—
560C2×Q8—1061no—
561C2×Q8—1062no—
562C2×Q8—1062no—
563C2×Q8—2124no—
564C2×Q8—2124no—
565C2×Q8—21232no—
566C2×Q8C23×D5312yes—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—534no—
571C2×D4—532no—
572C2×D4—1061no—
573C2×D4—1062no—
574C2×D4C23×D5312yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—531no—
579C22×C4—531no—
580C22×C4—531no—
581C22×C4—531no—
582C22×C4—1064no—
583C22×C4—1064no—
584C22×C4—1064no—
585C22×C4—1061no—
586C22×C4—1061no—
587C22×C4—1061no—
588C22×C4—1064no—
589C22×C4—2124no—
590C22×C4—2124no—
591C22×C4—2124no—
592C22×C4—2124no—
593C22×C4D4×D5311yescharacteristic
594C22×C4D4×D5311yescharacteristic
595C22×C4C23×D5311yescharacteristic
596SD16—1068no—
597SD16—1068no—
598D8—1068no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—532no—
602C2×C8—532no—
603C2×C8—1062no—
604C2×C8—1062no—
605C2×C8C23×D5312yes—
606C2×C8C23×D5312yes—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—534no—
611C4⋊C4—534no—
612C4⋊C4—534no—
613C4⋊C4—532no—
614C4⋊C4—532no—
615C4⋊C4—1064no—
616C4⋊C4—1064no—
617C4⋊C4—1064no—
618C4⋊C4—1064no—
619C4⋊C4—1064no—
620C4⋊C4—1061no—
621C4⋊C4—1061no—
622C4⋊C4—1064no—
623C4⋊C4C23×D5312yes—
624C4⋊C4C23×D5312yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—1064no—
628C22⋊C4—1064no—
629C22⋊C4—1064no—
630C22⋊C4—1064no—
631C22⋊C4—1064no—
632C22⋊C4—1064no—
633C42—532no—
634C42—532no—
635C42—532no—
636C42—532no—
637C42—1064no—
638C42—1064no—
639C42D4×D5312yes—
640C42C23×D5312yes—
641C23—22no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—1064no—
646C23—1062no—
647C23—2122no—
648C23—2122no—
649C23C2×D4×D5311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—48no—
653Q8—42no—
654Q8—1068no—
655Q8—1062no—
656Q8—1062no—
657Q8—2128no—
658Q8—2128no—
659Q8—2122no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—534no—
664D4—1064no—
665D4—1062no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—534no—
675C2×C4—532no—
676C2×C4—532no—
677C2×C4—532no—
678C2×C4—532no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—2128no—
686C2×C4—2128no—
687C2×C4—2128no—
688C2×C4—2128no—
689C2×C4—2122no—
690C2×C4—2122no—
691C2×C4—2122no—
692C2×C4C2×D4×D5312yes—
693C2×C4C2×D4×D5312yes—
694C2×C4C2×D4×D5311yescharacteristic
695C2×C4#41×D5312yes—
696C2×C4#1313326412yes—
697C2×C4C24×D5311yescharacteristic
698C8—22no—
699C8—22no—
700C8—1062no—
701C8—1062no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—84no—
706C22—1064no—
707C22—2122no—
708C22—2128no—
709C22—2122no—
710C22#1681128112yes—
711C22AGL(1,ℤ/8)×D5312yes—
712C22#1681143912yes—
713C22C22×D4×D5311yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—534no—
720C4—1062no—
721C4—1062no—
722C4—1062no—
723C4—2122no—
724C4—2122no—
725C4—2122no—
726C4#1681128112yes—
727C4C2×#41×D5311yescharacteristic
728C4C2×#1313326411yescharacteristic
729C2—82no—
730C2—2124no—
731C2#2028743014yesdirect product factor
732C2C2×#1681128111yescharacteristic
733C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
734C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#489C2
socleC23×C53C22×D4
prime radicalC22×#11719922C22
hypercenterC2×#489D53
hypocenterC53C2×#3367
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#16811342C2semidirect
2. C2×#16811288C2semidirect
3. #20287430C2direct (N × H)
4. C2×#16810981C2semidirect
5. C2×#16810972C2semidirect
6. C2×#16810916C2semidirect
7. C2×#16810915C2semidirect
8. C2×#16810901C2semidirect
11. C2×#16810827C2semidirect
12. C2×#16810751C2semidirect
13. C2×#16810726C2semidirect
14. C2×#16810725C2semidirect
16. C2×C53×#489C2semidirect
22. #16811342C22semidirect
24. #16811288C22semidirect
43. #16810981C22semidirect
44. #16810972C22semidirect
45. #16810916C22semidirect
46. #16810915C22semidirect
47. #16810901C22semidirect
50. #16810827C22semidirect
51. #16810751C22semidirect
52. #16810726C22semidirect
53. #16810725C22semidirect
71. C53×#489C22semidirect
366. C2×#489D53semidirect
379. C2×C53#3367semidirect
413. #489C2×D53semidirect
444. C53C2×#3367semidirect
731. C2#20287430direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113422
C2×#168112882
#202874302
C2×#168109812
C2×#168109722
C2×#168109162
C2×#168109152
C2×#168109012
C2×#168108372
C2×#168108352
C2×#168108272
C2×#168107512
C2×#168107262
C2×#168107252
C2×#168107032
C2×C53×#4892
C2×#336753