Finite Group Databasebeta

← C2×#20287436 #28263770

Subgroups — C2×#20287436 #28263770

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×#16811345C211yesmaximal, characteristic, complemented
2C2×#16811288C211yesmaximal, characteristic, complemented
3#20287436C2116yesmaximal, direct product factor
4C2×#16810985C211yesmaximal, characteristic, complemented
5C2×#16810984C211yesmaximal, characteristic, complemented
6C2×#16810972C211yesmaximal, characteristic, complemented
7C2×#16810917C211yesmaximal, characteristic, complemented
8C2×#16810902C211yesmaximal, characteristic, complemented
9C2×#16810841C211yesmaximal, characteristic
10C2×#16810839C211yesmaximal, characteristic
11C2×#16810827C211yesmaximal, characteristic, complemented
12C2×#16810752C211yesmaximal, characteristic, complemented
13C2×#16810722C211yesmaximal, characteristic, complemented
14C2×#16810721C211yesmaximal, characteristic, complemented
15C2×#16810705C211yesmaximal, characteristic
16C2×C53×#477C211yesmaximal, characteristic, complemented
17C22×Q8×D53—21no—
18C22×#11719913C2211yescharacteristic
19C22×#11719924C2211yescharacteristic
20C22×D424C2211yescharacteristic
21#16811345—24no—
22#16811345C2218yescomplemented
23#16811288—24no—
24#16811288C2218yescomplemented
25C2×#13133216C2211yescharacteristic
26C2×#13133216C2211yescharacteristic
27C2×#13133215C2211yescharacteristic
28C2×#13133212—21no—
29C2×#13133211—21no—
30C2×#13133206C2211yescharacteristic
31C2×#13133205C2211yescharacteristic
32C2×#13133195—21no—
33C2×#13133195—21no—
34C2×#13133195—21no—
35C2×#13133193—21no—
36C2×C4×Dic106C2211yescharacteristic
37C2×#13133182C2211yescharacteristic
38C2×C4×D212C2211yescharacteristic
39C2×#13133179C2211yescharacteristic
40C2×#13133179C2211yescharacteristic
41C2×#13133179C2211yescharacteristic
42C2×#13133174—21no—
43#16810985C2218yescomplemented
44#16810984C2218yescomplemented
45#16810972C2218yescomplemented
46#16810917C2218yescomplemented
47#16810902C2218yescomplemented
48#16810841C2218yes—
49#16810839C2218yes—
50#16810827C2218yescomplemented
51#16810752C2218yescomplemented
52#16810722C2218yescomplemented
53#16810721C2218yescomplemented
54#16810705C2218yes—
55C2×#13133150C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57C2×#13133146C2211yescharacteristic
58C2×#13133142C2211yescharacteristic
59C2×#13133141C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133128C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×C4⋊Q8×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C53×#477C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#107×C53C2211yescharacteristic
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—21no—
79C22×Dic106D411yescharacteristic
80C22×Dic106C2311yescharacteristic
81C2×Q8×D53—28no—
82C2×Q8×D53—48no—
83C22×D212C2311yescharacteristic
84C22×D212C2311yescharacteristic
85C22×C4×D53—21no—
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53—21no—
89C2×#11719913—24no—
90C2×#11719913C2314yes—
91C2×#11719924—24no—
92C2×#11719924C2314yes—
93C2×D424—24no—
94C2×D424C2314yes—
95C22×#88322C2311yescharacteristic
96C22×#88322C2311yescharacteristic
97#13133216—22no—
98#13133216—22no—
99#13133216C2314yes—
100#13133216C2314yes—
101#13133215—22no—
102#13133215C2314yes—
103#13133212—28no—
104#13133211—28no—
105#13133206—22no—
106#13133206C2314yes—
107#13133205—22no—
108#13133205C2314yes—
109#13133195—28no—
110#13133195—28no—
111#13133195—28no—
112#13133193—28no—
113C4×Dic106D414yes—
114C4×Dic106C2314yes—
115#13133182—22no—
116#13133182C2314yes—
117C4×D212—22no—
118C4×D212C2314yes—
119#13133179—22no—
120#13133179—22no—
121#13133179—22no—
122#13133179C2314yes—
123#13133179C2314yes—
124#13133179C2314yes—
125#13133174—28no—
126C2×C4⋊Dic53D411yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919D411yescharacteristic
134C2×#11719919D411yescharacteristic
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53C2311yescharacteristic
145C2×C4×Dic53C2311yescharacteristic
146#13133150C2314yes—
147#13133146C2314yes—
148#13133146C2314yes—
149#13133142C2314yes—
150#13133141C2314yes—
151#13133140C2314yes—
152#13133140C2314yes—
153#13133139C2314yes—
154#13133137C2314yes—
155#13133137C2314yes—
156#13133137C2314yes—
157#13133128C2314yes—
158#13133127C2314yes—
159C8×Dic53C2314yes—
160C22×Q8×C53—21no—
161C22×Q8×C53C2311yescharacteristic
162C22×C8×C53C2311yescharacteristic
163C22×C8×C53C2311yescharacteristic
164C4⋊Q8×C53—22no—
165C4⋊Q8×C53C2314yes—
166C4×Q8×C53—22no—
167C4×Q8×C53C2314yes—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C42×C53—21no—
174C2×C42×C53C2311yescharacteristic
175#107×C53C2314yes—
176#107×C53C2314yes—
177C4⋊C8×C53C2314yes—
178#103×C53C2314yes—
179#103×C53C2314yes—
180C23×D53—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—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2411yescharacteristic
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53C2×D411yescharacteristic
198C22×Dic53C2×D411yescharacteristic
199C22×Dic53C2×D411yescharacteristic
200C22×Dic53C2×D411yescharacteristic
201Q8×D53—432no—
202C2×D212—21no—
203C2×D212—22no—
204C2×D212—22no—
205C2×D212—22no—
206C2×D212—21no—
207C2×D212#4114yes—
208C2×D212C2412yes—
209C2×D212C2412yes—
210C2×C4×D53—24no—
211C2×C4×D53—24no—
212C2×C4×D53—24no—
213C2×C4×D53—24no—
214C2×C4×D53—44no—
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—24no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53C2412yes—
238C4⋊C4×C53C2412yes—
239C4⋊C4×C53C2412yes—
240C42×C53—24no—
241C42×C53C2×D412yes—
242C42×C53C2412yes—
243#11719924—28no—
244#11719921—24no—
245#11719921—24no—
246#11719921—24no—
247#11719921—24no—
248#11719921—24no—
249#11719921—24no—
250#11719921—24no—
251#11719921—24no—
252C4⋊Dic53—21no—
253C4⋊Dic53C2×D414yes—
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×Dic53C2×D412yes—
264C4×Dic53C2×D412yes—
265C4×Dic53C2412yes—
266C4×Dic53C2412yes—
267C2×#88322—22no—
268C2×#88322—22no—
269C2×#88322C2412yes—
270C2×#88322C2412yes—
271D424—28no—
272#11719913—28no—
273C23×C53C22×D411yescharacteristic
274C22×D53—24no—
275C22×D53—22no—
276C22×D53—22no—
277C22×D53—42no—
278C22×D53—42no—
279C22×D53—42no—
280C22×D53—42no—
281C22×D53—42no—
282Q8×C53—22no—
283Q8×C53—22no—
284Q8×C53—48no—
285Q8×C53—42no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—42no—
293C2×C4×C53—42no—
294C2×C4×C53—42no—
295C2×C4×C53—42no—
296C2×C4×C53C22×D412yes—
297C2×C4×C53C22×D412yes—
298C2×C4×C53C22×D411yescharacteristic
299C2×C4×C53C2×#4112yes—
300C2×C4×C532−1+412yes—
301C2×C4×C53C2511yescharacteristic
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—42no—
308C2×Dic53—42no—
309C2×Dic53AGL(1,ℤ/8)14yes—
310C2×Dic53C22×D412yes—
311C2×Dic53C22×D412yes—
312C2×Dic53C22×D412yes—
313C2×Dic53C22×D412yes—
314D212—24no—
315D212—22no—
316D212—22no—
317D212—22no—
318D212—42no—
319D212C2×#4114yes—
320C4×D53—48no—
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#54812yes—
336C22×C53C2×AGL(1,ℤ/8)12yes—
337C22×C53#57812yes—
338C22×C53C23×D411yescharacteristic
339C2×D53—24no—
340C2×D53—48no—
341C2×D53—42no—
342C2×D53—42no—
343C2×D53—42no—
344C2×D53—42no—
345C2×D53—42no—
346C2×D53—84no—
347C4×C53—22no—
348C4×C53—22no—
349C4×C53—42no—
350C4×C53—42no—
351C4×C53—42no—
352C4×C53—42no—
353C4×C53#54812yes—
354C4×C53C22×#4111yescharacteristic
355C4×C53C2×2−1+411yescharacteristic
356Dic53—22no—
357Dic53—22no—
358Dic53—22no—
359Dic53—42no—
360Dic53—42no—
361Dic53C2×AGL(1,ℤ/8)14yes—
362C2×#556—531no—
363C2×D4×Q8—531no—
364#3367—5316no—
365C2×#489—531no—
366C2×#489—531no—
367C2×#487—531no—
368C2×#477—531no—
369C2×#477D5311yescharacteristic, complemented
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#336714yescomplemented
379C2×C53C2×#54811yescharacteristic
380C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
381C2×C53C2×#57811yescharacteristic
382D53—44no—
383D53—82no—
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×#124—531no—
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×Q8C2×D5311yescharacteristic
407C2×C4×D4—531no—
408C2×C4×D4—531no—
409C2×C4×D4—531no—
410C2×C4×D4—531no—
411C2×#117—1061no—
412#489—538no—
413#489—538no—
414#487—538no—
415#477—538no—
416#477C2×D5318yescomplemented
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×#107C2×D5311yescharacteristic
427C2×#107C2×D5311yescharacteristic
428C2×C4⋊C8—531no—
429C2×C4⋊C8—531no—
430C2×C4⋊C8C2×D5311yescharacteristic
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×#102—531no—
440C2×#102—531no—
441C2×#97—531no—
442C2×#97—531no—
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×D4—531no—
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—534no—
480#124—534no—
481#124—1062no—
482#124—1062no—
483C22⋊Q8—1068no—
484C22⋊Q8—1068no—
485C22⋊Q8—1068no—
486C22⋊Q8—1068no—
487C4×Q8—22no—
488C4×Q8—534no—
489C4×Q8—534no—
490C4×Q8—534no—
491C4×Q8—1062no—
492C4×Q8C22×D5314yes—
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—21no—
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⋊C4C22×D5311yescharacteristic
514C2×C4⋊C4C22×D5311yescharacteristic
515C2×C4⋊C4C22×D5311yescharacteristic
516C2×C22⋊C4—1061no—
517C2×C22⋊C4—1061no—
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—21no—
525C2×C42—531no—
526C2×C42—531no—
527C2×C42—1061no—
528C2×C42C22×D5311yescharacteristic
529#107—534no—
530#107C22×D5314yes—
531#107C22×D5314yes—
532C4⋊C8—534no—
533C4⋊C8—534no—
534C4⋊C8C22×D5314yes—
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#102—534no—
544#102—534no—
545#97—534no—
546#97—534no—
547C4×C8—534no—
548C24—1061no—
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—534no—
568C2×D4—532no—
569C2×D4—532no—
570C2×D4—1061no—
571C2×D4—1061no—
572C2×D4—1062no—
573C2×D4—1062no—
574C2×D4—1062no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—531no—
580C22×C4—531no—
581C22×C4—531no—
582C22×C4—531no—
583C22×C4—1064no—
584C22×C4—1064no—
585C22×C4—1064no—
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—24no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—534no—
613C4⋊C4—534no—
614C4⋊C4—534no—
615C4⋊C4—532no—
616C4⋊C4—1064no—
617C4⋊C4—1064no—
618C4⋊C4—1064no—
619C4⋊C4—1064no—
620C4⋊C4—1064no—
621C4⋊C4—1061no—
622C4⋊C4C23×D5312yes—
623C4⋊C4C23×D5312yes—
624C4⋊C4C23×D5312yes—
625C22⋊C4—1064no—
626C22⋊C4—1064no—
627C22⋊C4—1064no—
628C22⋊C4—1064no—
629C22⋊C4—1064no—
630C22⋊C4—1064no—
631C22⋊C4—1064no—
632C22⋊C4—1064no—
633C42—24no—
634C42—532no—
635C42—532no—
636C42—532no—
637C42—532no—
638C42—1064no—
639C42D4×D5312yes—
640C42C23×D5312yes—
641C23—1064no—
642C23—1062no—
643C23—1062no—
644C23—2122no—
645C23—2122no—
646C23—2122no—
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—534no—
661D4—1064no—
662D4—1062no—
663D4—1062no—
664D4—1062no—
665D4—2122no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—534no—
677C2×C4—532no—
678C2×C4—532no—
679C2×C4—532no—
680C2×C4—532no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—1062no—
686C2×C4—2128no—
687C2×C4—2128no—
688C2×C4—2128no—
689C2×C4—2128no—
690C2×C4—2122no—
691C2×C4—2122no—
692C2×C4C2×D4×D5312yes—
693C2×C4C2×D4×D5312yes—
694C2×C4C2×D4×D5311yescharacteristic
695C2×C4#41×D5312yes—
696C2×C4#1313326512yes—
697C2×C4C24×D5311yescharacteristic
698C8—22no—
699C8—22no—
700C8—1062no—
701C8—1062no—
702C22—1064no—
703C22—4244no—
704C22—2122no—
705C22—2122no—
706C22—2122no—
707C22—2122no—
708C22—2122no—
709C22—2128no—
710C22#1681128312yes—
711C22AGL(1,ℤ/8)×D5312yes—
712C22#1681143612yes—
713C22C22×D4×D5311yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—534no—
721C4—1062no—
722C4—1062no—
723C4—1062no—
724C4—2122no—
725C4—2122no—
726C4#1681128312yes—
727C4C2×#41×D5311yescharacteristic
728C4C2×#1313326511yescharacteristic
729C2—4242no—
730C2—2124no—
731C2#2028743614yesdirect product factor
732C2C2×#1681128311yescharacteristic
733C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
734C2C2×#1681143611yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#477C2
socleC23×C53C22×D4
prime radicalC22×D424C22
hypercenterC2×#477D53
hypocenterC53C2×#3367
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#16811345C2semidirect
2. C2×#16811288C2semidirect
3. #20287436C2direct (N × H)
4. C2×#16810985C2semidirect
5. C2×#16810984C2semidirect
6. C2×#16810972C2semidirect
7. C2×#16810917C2semidirect
8. C2×#16810902C2semidirect
11. C2×#16810827C2semidirect
12. C2×#16810752C2semidirect
13. C2×#16810722C2semidirect
14. C2×#16810721C2semidirect
16. C2×C53×#477C2semidirect
22. #16811345C22semidirect
24. #16811288C22semidirect
43. #16810985C22semidirect
44. #16810984C22semidirect
45. #16810972C22semidirect
46. #16810917C22semidirect
47. #16810902C22semidirect
50. #16810827C22semidirect
51. #16810752C22semidirect
52. #16810722C22semidirect
53. #16810721C22semidirect
71. C53×#477C22semidirect
369. C2×#477D53semidirect
378. C2×C53#3367semidirect
416. #477C2×D53semidirect
444. C53C2×#3367semidirect
731. C2#20287436direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113452
C2×#168112882
#202874362
C2×#168109852
C2×#168109842
C2×#168109722
C2×#168109172
C2×#168109022
C2×#168108412
C2×#168108392
C2×#168108272
C2×#168107522
C2×#168107222
C2×#168107212
C2×#168107052
C2×C53×#4772
C2×#336753