Finite Group Databasebeta

← C2×#20287789 #28265107

Subgroups — C2×#20287789 #28265107

Order 13568.

1938 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811347C211yesmaximal, characteristic, complemented
2C2×#16811345C211yesmaximal, characteristic, complemented
3#20287789C2116yesmaximal, direct product factor
4C2×#16811016C211yesmaximal, characteristic, complemented
5C2×#16811015C211yesmaximal, characteristic, complemented
6C2×#16811008C211yesmaximal, characteristic
7C2×#16810848C211yesmaximal, characteristic, complemented
8C2×#16810847C211yesmaximal, characteristic, complemented
9C2×#16810831C211yesmaximal, characteristic, complemented
10C2×#16810841C211yesmaximal, characteristic
11C2×#16810839C211yesmaximal, characteristic
12C2×#16810752C211yesmaximal, characteristic, complemented
13C2×#16810726C211yesmaximal, characteristic, complemented
14C2×#16810721C211yesmaximal, characteristic, complemented
15C2×#16810715C211yesmaximal, characteristic, complemented
16C2×C53×#462C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21C22×#11719924C2211yescharacteristic
22C22×#11719924C2211yescharacteristic
23C22×D424C2211yescharacteristic
24#16811347—24no—
25#16811347C2218yescomplemented
26#16811345—24no—
27#16811345C2218yescomplemented
28C2×#13133215C2211yescharacteristic
29C2×#13133212—21no—
30C2×#13133212—21no—
31C2×#13133212—21no—
32C2×#13133211—21no—
33C2×#13133206C2211yescharacteristic
34C2×#13133206C2211yescharacteristic
35C2×#13133206C2211yescharacteristic
36C2×#13133205C2211yescharacteristic
37C2×#13133197—21no—
38C2×#13133195—21no—
39C2×Q8×Dic53C2211yescharacteristic
40C2×Q8×Dic53C2211yescharacteristic
41C2×C4×Dic106C2211yescharacteristic
42C2×#13133182C2211yescharacteristic
43C2×C4×D212C2211yescharacteristic
44C2×#13133179C2211yescharacteristic
45C2×#13133175—21no—
46C2×#13133174—21no—
47#16811016C2218yescomplemented
48#16811015C2218yescomplemented
49#16811008C2218yes—
50#16810848C2218yescomplemented
51#16810847C2218yescomplemented
52#16810841C2218yes—
53#16810839C2218yes—
54#16810831C2218yescomplemented
55#16810752C2218yescomplemented
56#16810726C2218yescomplemented
57#16810721C2218yescomplemented
58#16810715C2218yescomplemented
59C2×#13133150C2211yescharacteristic
60C2×#13133146C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133142C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133128C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×Q16×C53C2211yescharacteristic
70C22×Q16×C53C2211yescharacteristic
71C2×C4⋊Q8×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic
73C53×#462C2218yescomplemented
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C22×Dic106D411yescharacteristic
78C22×Dic106C2311yescharacteristic
79C22×D212C2311yescharacteristic
80C22×D212C2311yescharacteristic
81C22×C4×D53—21no—
82C22×C4×D53—21no—
83C2×#11719925—24no—
84C2×#11719925—42no—
85C2×#11719925C2314yes—
86C2×#11719925C2314yes—
87C2×#11719913—42no—
88C2×#11719913C2314yes—
89C2×#11719924—24no—
90C2×#11719924—24no—
91C2×#11719924—42no—
92C2×#11719924C2314yes—
93C2×#11719924C2314yes—
94C2×#11719924C2314yes—
95C2×D424—42no—
96C2×D424C2314yes—
97C22×#88322C2311yescharacteristic
98C22×#88322C2311yescharacteristic
99#13133215—22no—
100#13133215C2314yes—
101#13133212—28no—
102#13133212—28no—
103#13133212—28no—
104#13133211—28no—
105#13133206—22no—
106#13133206—22no—
107#13133206—22no—
108#13133206C2314yes—
109#13133206C2314yes—
110#13133206C2314yes—
111#13133205—22no—
112#13133205C2314yes—
113#13133197—28no—
114#13133195—28no—
115Q8×Dic53—22no—
116Q8×Dic53—22no—
117Q8×Dic53C2314yes—
118Q8×Dic53C2314yes—
119C4×Dic106D414yes—
120C4×Dic106C2314yes—
121#13133182—22no—
122#13133182C2314yes—
123C4×D212—22no—
124C4×D212C2314yes—
125#13133179—22no—
126#13133179C2314yes—
127#13133175—28no—
128#13133174—28no—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53—21no—
131C2×C4⋊Dic53D411yescharacteristic
132C2×C4⋊Dic53C2311yescharacteristic
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919D411yescharacteristic
137C2×#11719919D411yescharacteristic
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×C4×Dic53—21no—
149C2×C4×Dic53—21no—
150C2×C4×Dic53—21no—
151C2×C4×Dic53C2311yescharacteristic
152C2×C4×Dic53C2311yescharacteristic
153#13133150C2314yes—
154#13133146C2314yes—
155#13133146C2314yes—
156#13133142C2314yes—
157#13133141C2314yes—
158#13133139C2314yes—
159#13133137C2314yes—
160#13133128C2314yes—
161#13133127C2314yes—
162C8×Dic53C2314yes—
163C22×Q8×C53C2311yescharacteristic
164C22×Q8×C53C2311yescharacteristic
165C22×Q8×C53C2311yescharacteristic
166C2×Q16×C53—42no—
167C2×Q16×C53—42no—
168C2×Q16×C53C2314yes—
169C2×Q16×C53C2314yes—
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172C4⋊Q8×C53—22no—
173C4⋊Q8×C53C2314yes—
174C4×Q8×C53—22no—
175C4×Q8×C53C2314yes—
176C2×C4⋊C4×C53—21no—
177C2×C4⋊C4×C53—21no—
178C2×C4⋊C4×C53—21no—
179C2×C4⋊C4×C53C2311yescharacteristic
180C2×C42×C53—21no—
181C2×C42×C53C2311yescharacteristic
182C4⋊C8×C53C2314yes—
183#103×C53C2314yes—
184#103×C53C2314yes—
185C23×D53—21no—
186C23×D53—21no—
187C2×Q8×C53—21no—
188C2×Q8×C53—21no—
189C2×Q8×C53—21no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53—22no—
193C2×Q8×C53—22no—
194C2×Q8×C53—22no—
195C2×Q8×C53—22no—
196C2×Q8×C53C2412yes—
197C2×Q8×C53C2412yes—
198C2×Q8×C53C2412yes—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2411yescharacteristic
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53C2×D411yescharacteristic
209C22×Dic53C2×D411yescharacteristic
210C22×Dic53C2×D411yescharacteristic
211C22×Dic53C2×D411yescharacteristic
212C2×D212—22no—
213C2×D212—22no—
214C2×D212—22no—
215C2×D212—22no—
216C2×D212—21no—
217C2×D212—21no—
218C2×D212C2412yes—
219C2×D212C2412yes—
220C2×C4×D53—24no—
221C2×C4×D53—24no—
222C2×C4×D53—44no—
223C2×C4×D53—44no—
224C2×Dic106—22no—
225C2×Dic106—22no—
226C2×Dic106—21no—
227C2×Dic106—42no—
228C2×Dic106C2×D414yes—
229C2×Dic106C2412yes—
230Q16×C53—44no—
231Q16×C53—44no—
232C2×C8×C53—22no—
233C2×C8×C53—22no—
234C2×C8×C53C2412yes—
235C2×C8×C53C2412yes—
236C4⋊C4×C53—24no—
237C4⋊C4×C53—24no—
238C4⋊C4×C53—24no—
239C4⋊C4×C53—21no—
240C4⋊C4×C53C2412yes—
241C42×C53—24no—
242C42×C53C2×D412yes—
243C42×C53C2412yes—
244#11719925—28no—
245#11719925—44no—
246#11719924—28no—
247#11719924—28no—
248#11719924—44no—
249#11719921—24no—
250#11719921—24no—
251#11719921—24no—
252#11719921—24no—
253#11719921—24no—
254#11719921—24no—
255#11719921—24no—
256#11719921—24no—
257#11719921—24no—
258#11719921—24no—
259C4⋊Dic53—21no—
260C4⋊Dic53—24no—
261C4⋊Dic53—24no—
262C4⋊Dic53C2×D414yes—
263C4⋊Dic53C2412yes—
264#11719919—24no—
265#11719919—24no—
266#11719919—24no—
267#11719919C2×D414yes—
268#11719919C2×D414yes—
269C4×Dic53—24no—
270C4×Dic53—24no—
271C4×Dic53—24no—
272C4×Dic53C2×D412yes—
273C4×Dic53C2×D412yes—
274C4×Dic53C2412yes—
275C4×Dic53C2412yes—
276C2×#88322—22no—
277C2×#88322#4114yes—
278C2×#88322C2412yes—
279C2×#88322C2412yes—
280D424—44no—
281#11719913—44no—
282C23×C53C22×D411yescharacteristic
283C22×D53—22no—
284C22×D53—22no—
285C22×D53—42no—
286C22×D53—42no—
287C22×D53—42no—
288C22×D53—42no—
289C22×D53—42no—
290C22×D53—42no—
291Q8×C53—22no—
292Q8×C53—22no—
293Q8×C53—22no—
294Q8×C53—22no—
295Q8×C53—22no—
296Q8×C53—22no—
297Q8×C53—42no—
298Q8×C53—42no—
299Q8×C53—42no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—42no—
307C2×C4×C53—42no—
308C2×C4×C53—42no—
309C2×C4×C53—42no—
310C2×C4×C53C22×D412yes—
311C2×C4×C53C22×D412yes—
312C2×C4×C53C22×D411yescharacteristic
313C2×C4×C53C2×#4112yes—
314C2×C4×C53H(5,𝔽2)12yes—
315C2×C4×C53C2511yescharacteristic
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53C22×D412yes—
325C2×Dic53C22×D412yes—
326C2×Dic53C22×D412yes—
327C2×Dic53C22×D412yes—
328D212—22no—
329D212—22no—
330D212—22no—
331D212—22no—
332D212—42no—
333D212—42no—
334C4×D53—48no—
335C4×D53—48no—
336Dic106—22no—
337Dic106—22no—
338Dic106—44no—
339Dic106—42no—
340C8×C53—22no—
341C8×C53—22no—
342#88322—22no—
343#88322C2×#4114yes—
344C2×#3402—531nomaximal, Sylow
345C22×C53#55012yes—
346C22×C53#57512yes—
347C22×C53#57812yes—
348C22×C53C23×D411yescharacteristic
349C2×D53—42no—
350C2×D53—42no—
351C2×D53—42no—
352C2×D53—42no—
353C2×D53—42no—
354C2×D53—42no—
355C2×D53—84no—
356C2×D53—84no—
357C4×C53—22no—
358C4×C53—22no—
359C4×C53—42no—
360C4×C53—42no—
361C4×C53—42no—
362C4×C53—42no—
363C4×C53#55012yes—
364C4×C53C22×#4111yescharacteristic
365C4×C53C2×H(5,𝔽2)11yescharacteristic
366Dic53—22no—
367Dic53—22no—
368Dic53—22no—
369Dic53—22no—
370Dic53—42no—
371Dic53—42no—
372C2×#556—531no—
373C2×#556—531no—
374#3402—5316no—
375C2×#497—531no—
376C2×#497—531no—
377C2×#495—531no—
378C2×#464—531no—
379C2×#464—531no—
380C2×#462—531no—
381C2×#462D5311yescharacteristic, complemented
382C2×#463—531no—
383C2×#463—531no—
384C2×#446—531no—
385C2×#440—531no—
386C2×#440—531no—
387C2×C4×Q16—531no—
388C2×C53#340214yescomplemented
389C2×C53C2×#55011yescharacteristic
390C2×C53C2×#57511yescharacteristic
391C2×C53C2×#57811yescharacteristic
392D53—82no—
393D53—82no—
394C22×Q16—531no—
395C22×Q16—531no—
396C22×Q16C2×D5311yescharacteristic
397C22×Q16C2×D5311yescharacteristic
398C22×SD16—531no—
399C22×SD16—531no—
400C22×SD16—531no—
401C22×SD16—531no—
402C22×D8—531no—
403#556—538no—
404#556—538no—
405#556—1064no—
406#556—1064no—
407C2×C4⋊Q8—531no—
408C2×C4⋊Q8C2×D5311yescharacteristic
409C2×#126—1061no—
410C2×#126—1061no—
411C2×#126—1061no—
412C2×#126—1061no—
413C2×#124—531no—
414C2×#124—531no—
415C2×#124—531no—
416C2×#124—531no—
417C2×C22⋊Q8—1061no—
418C2×C22⋊Q8—1061no—
419C2×C4×Q8—531no—
420C2×C4×Q8—531no—
421C2×C4×Q8—531no—
422C2×C4×Q8—531no—
423C2×C4×Q8C2×D5311yescharacteristic
424C2×C4×D4—531no—
425C2×C4×D4—531no—
426C2×#117—1061no—
427C2×#117—1061no—
428#497—538no—
429#497—538no—
430#495—538no—
431#464—538no—
432#464—538no—
433#463—538no—
434#463—538no—
435#462—538no—
436#462C2×D5318yescomplemented
437#446—538no—
438#440—538no—
439#440—538no—
440C4×Q16—538no—
441C2×#107—531no—
442C2×C4⋊C8—531no—
443C2×C4⋊C8—531no—
444C2×C4⋊C8C2×D5311yescharacteristic
445C2×#103—531no—
446C2×#103—531no—
447C2×#103C2×D5311yescharacteristic
448C2×#103C2×D5311yescharacteristic
449C2×#102—531no—
450C2×#102—531no—
451C2×#97—531no—
452C2×#97—531no—
453C2×C4×C8—531no—
454C53C2×#340211yescharacteristic, complemented, Sylow
455C22×Q8—531no—
456C22×Q8—531no—
457C22×Q8C22×D5311yescharacteristic
458C22×Q8C22×D5311yescharacteristic
459C22×Q8C22×D5311yescharacteristic
460C22×D4—531no—
461C22×D4—531no—
462C23×C4—1061no—
463C23×C4—1061no—
464C2×Q16—42no—
465C2×Q16—42no—
466C2×Q16—534no—
467C2×Q16—534no—
468C2×Q16—1064no—
469C2×Q16—2122no—
470C2×Q16C22×D5314yes—
471C2×Q16C22×D5314yes—
472C2×SD16—534no—
473C2×SD16—534no—
474C2×SD16—534no—
475C2×SD16—534no—
476C2×SD16—1064no—
477C2×SD16—1064no—
478C2×SD16—2122no—
479C2×SD16—2122no—
480C2×D8—534no—
481C2×D8—2122no—
482C22×C8—531no—
483C22×C8—531no—
484C22×C8C22×D5311yescharacteristic
485C22×C8C22×D5311yescharacteristic
486C4⋊Q8—22no—
487C4⋊Q8—534no—
488C4⋊Q8—1062no—
489C4⋊Q8C22×D5314yes—
490#126—1068no—
491#126—1068no—
492#126—1068no—
493#126—1068no—
494#124—534no—
495#124—534no—
496#124—534no—
497#124—534no—
498#124—1062no—
499#124—1062no—
500#124—1062no—
501#124—1062no—
502C22⋊Q8—1068no—
503C22⋊Q8—1068no—
504C4×Q8—22no—
505C4×Q8—534no—
506C4×Q8—534no—
507C4×Q8—534no—
508C4×Q8—534no—
509C4×Q8—534no—
510C4×Q8—1062no—
511C4×Q8—1062no—
512C4×Q8—1062no—
513C4×Q8C22×D5314yes—
514C4×D4—534no—
515C4×D4—534no—
516C4×D4—1062no—
517C4×D4—1062no—
518#117—1068no—
519#117—1068no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—531no—
525C2×C4⋊C4—531no—
526C2×C4⋊C4—531no—
527C2×C4⋊C4—1061no—
528C2×C4⋊C4—1061no—
529C2×C4⋊C4—1061no—
530C2×C4⋊C4—1061no—
531C2×C4⋊C4—1061no—
532C2×C4⋊C4C22×D5311yescharacteristic
533C2×C22⋊C4—1061no—
534C2×C22⋊C4—1061no—
535C2×C22⋊C4—1061no—
536C2×C22⋊C4—1061no—
537C2×C22⋊C4—1061no—
538C2×C22⋊C4—1061no—
539C2×C22⋊C4—1061no—
540C2×C22⋊C4—1061no—
541C2×C22⋊C4—1061no—
542C2×C22⋊C4—1061no—
543C2×C42—21no—
544C2×C42—531no—
545C2×C42—531no—
546C2×C42—1061no—
547C2×C42—1061no—
548C2×C42—1061no—
549C2×C42C22×D5311yescharacteristic
550#107—534no—
551C4⋊C8—534no—
552C4⋊C8—534no—
553C4⋊C8C22×D5314yes—
554#103—534no—
555#103—534no—
556#103C22×D5314yes—
557#103C22×D5314yes—
558#102—534no—
559#102—534no—
560#97—534no—
561#97—534no—
562C4×C8—534no—
563C24—1061no—
564C24—1061no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—534no—
575C2×Q8—532no—
576C2×Q8—1061no—
577C2×Q8—1062no—
578C2×Q8—1062no—
579C2×Q8—2122no—
580C2×Q8C23×D5312yes—
581C2×Q8C23×D5312yes—
582C2×Q8C23×D5312yes—
583C2×D4—532no—
584C2×D4—532no—
585C2×D4—1061no—
586C2×D4—1061no—
587C2×D4—1062no—
588C2×D4—1062no—
589C2×D4—1062no—
590C2×D4—1062no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—531no—
596C22×C4—531no—
597C22×C4—531no—
598C22×C4—531no—
599C22×C4—1064no—
600C22×C4—1061no—
601C22×C4—1061no—
602C22×C4—1064no—
603C22×C4—2124no—
604C22×C4—2124no—
605C22×C4D4×D5311yescharacteristic
606C22×C4D4×D5311yescharacteristic
607C22×C4C23×D5311yescharacteristic
608Q16—44no—
609Q16—44no—
610Q16—1068no—
611Q16—2124no—
612SD16—1068no—
613SD16—1068no—
614SD16—2124no—
615SD16—2124no—
616D8—2124no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—534no—
620C2×C8—532no—
621C2×C8—532no—
622C2×C8—1062no—
623C2×C8C23×D5312yes—
624C2×C8C23×D5312yes—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—21no—
629C4⋊C4—534no—
630C4⋊C4—534no—
631C4⋊C4—534no—
632C4⋊C4—532no—
633C4⋊C4—1064no—
634C4⋊C4—1064no—
635C4⋊C4—1064no—
636C4⋊C4—1064no—
637C4⋊C4—1064no—
638C4⋊C4—1061no—
639C4⋊C4C23×D5312yes—
640C22⋊C4—1064no—
641C22⋊C4—1064no—
642C22⋊C4—1064no—
643C22⋊C4—1064no—
644C22⋊C4—1064no—
645C22⋊C4—1064no—
646C22⋊C4—1064no—
647C22⋊C4—1064no—
648C22⋊C4—1064no—
649C22⋊C4—1064no—
650C42—24no—
651C42—532no—
652C42—532no—
653C42—532no—
654C42—532no—
655C42—1064no—
656C42—1064no—
657C42—1064no—
658C42D4×D5312yes—
659C42C23×D5312yes—
660C23—1062no—
661C23—1062no—
662C23—2122no—
663C23—2122no—
664C23—2122no—
665C23—2122no—
666C23—2122no—
667C23—2122no—
668C23C2×D4×D5311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—22no—
674Q8—22no—
675Q8—42no—
676Q8—42no—
677Q8—42no—
678Q8—1062no—
679Q8—1062no—
680Q8—2124no—
681Q8—2122no—
682D4—1062no—
683D4—1062no—
684D4—1062no—
685D4—1062no—
686D4—2122no—
687D4—2122no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—532no—
699C2×C4—532no—
700C2×C4—532no—
701C2×C4—532no—
702C2×C4—1062no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—1062no—
707C2×C4—1062no—
708C2×C4—2128no—
709C2×C4—2128no—
710C2×C4—2122no—
711C2×C4—2122no—
712C2×C4C2×D4×D5312yes—
713C2×C4C2×D4×D5312yes—
714C2×C4C2×D4×D5311yescharacteristic
715C2×C4#41×D5312yes—
716C2×C4#1313326212yes—
717C2×C4C24×D5311yescharacteristic
718C8—22no—
719C8—22no—
720C8—534no—
721C8—1062no—
722C22—4244no—
723C22—4244no—
724C22—2122no—
725C22—2122no—
726C22—2122no—
727C22—2122no—
728C22—2122no—
729C22—2122no—
730C22#1681129112yes—
731C22#1681142212yes—
732C22#1681143612yes—
733C22C22×D4×D5311yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—1062no—
741C4—1062no—
742C4—1062no—
743C4—1062no—
744C4—2122no—
745C4—2122no—
746C4#1681129112yes—
747C4C2×#41×D5311yescharacteristic
748C4C2×#1313326211yescharacteristic
749C2—4242no—
750C2—4242no—
751C2#2028778914yesdirect product factor
752C2C2×#1681129111yescharacteristic
753C2C2×#1681142211yescharacteristic
754C2C2×#1681143611yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#462C2
socleC23×C53C22×D4
prime radicalC22×D424C22
hypercenterC2×#462D53
hypocenterC53C2×#3402
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C2×#16811347C2semidirect
2. C2×#16811345C2semidirect
3. #20287789C2direct (N × H)
4. C2×#16811016C2semidirect
5. C2×#16811015C2semidirect
7. C2×#16810848C2semidirect
8. C2×#16810847C2semidirect
9. C2×#16810831C2semidirect
12. C2×#16810752C2semidirect
13. C2×#16810726C2semidirect
14. C2×#16810721C2semidirect
15. C2×#16810715C2semidirect
16. C2×C53×#462C2semidirect
25. #16811347C22semidirect
27. #16811345C22semidirect
47. #16811016C22semidirect
48. #16811015C22semidirect
50. #16810848C22semidirect
51. #16810847C22semidirect
54. #16810831C22semidirect
55. #16810752C22semidirect
56. #16810726C22semidirect
57. #16810721C22semidirect
58. #16810715C22semidirect
73. C53×#462C22semidirect
381. C2×#462D53semidirect
388. C2×C53#3402semidirect
436. #462C2×D53semidirect
454. C53C2×#3402semidirect
751. C2#20287789direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113472
C2×#168113452
#202877892
C2×#168110162
C2×#168110152
C2×#168110082
C2×#168108482
C2×#168108472
C2×#168108312
C2×#168108412
C2×#168108392
C2×#168107522
C2×#168107262
C2×#168107212
C2×#168107152
C2×C53×#4622
C2×#340253