Finite Group Databasebeta

← C2×#20287698 #28264996

Subgroups — C2×#20287698 #28264996

Order 13568.

1958 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×#16811345C211yesmaximal, characteristic, complemented
2C2×#16811342C211yesmaximal, characteristic, complemented
3#20287698C2116yesmaximal, direct product factor
4C2×#16811005C211yesmaximal, characteristic
5C2×#16811004C211yesmaximal, characteristic
6C2×#16811001C211yesmaximal, characteristic, complemented
7C2×#16810847C211yesmaximal, characteristic, complemented
8C2×#16810846C211yesmaximal, characteristic, complemented
9C2×#16810844C211yesmaximal, characteristic, complemented
10C2×#16810827C211yesmaximal, characteristic, complemented
11C2×#16810826C211yesmaximal, characteristic, complemented
12C2×#16810747C211yesmaximal, characteristic, complemented
13C2×C4×#11719925C211yesmaximal, characteristic, complemented
14C2×#16810715C211yesmaximal, characteristic, complemented
15C2×#16810703C211yesmaximal, characteristic
16C2×C53×#464C211yesmaximal, characteristic, complemented
17C22×Dic212C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×#11719923C2211yescharacteristic
22C22×#11719924C2211yescharacteristic
23C22×#11719922C2211yescharacteristic
24#16811345—24no—
25#16811345C2218yescomplemented
26#16811342—24no—
27#16811342C2218yescomplemented
28C2×#13133215C2211yescharacteristic
29C2×#13133215C2211yescharacteristic
30C2×#13133212—21no—
31C2×#13133211—21no—
32C2×#13133210—21no—
33C2×#13133210—21no—
34C2×#13133206C2211yescharacteristic
35C2×#13133205C2211yescharacteristic
36C2×#13133204C2211yescharacteristic
37C2×#13133195—21no—
38C2×#13133194—21no—
39C2×Q8×Dic53C2211yescharacteristic
40C2×C4×Dic106C2211yescharacteristic
41C2×C4×Dic106C2211yescharacteristic
42C2×#13133182C2211yescharacteristic
43C2×D4×Dic53C2211yescharacteristic
44C2×#13133179C2211yescharacteristic
45C2×#13133174—21no—
46C2×#13133173—21no—
47#16811005C2218yes—
48#16811004C2218yes—
49#16811001C2218yescomplemented
50#16810847C2218yescomplemented
51#16810846C2218yescomplemented
52#16810844C2218yescomplemented
53#16810827C2218yescomplemented
54#16810826C2218yescomplemented
55#16810747C2218yescomplemented
56C4×#11719925C2218yescomplemented
57#16810715C2218yescomplemented
58#16810703C2218yes—
59C2×#13133150C2211yescharacteristic
60C2×#13133146C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133142C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×C4×#88322C2211yescharacteristic
67C2×C8×Dic53C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×Q16×C53C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic
71C2×#124×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic
73C53×#464C2218yescomplemented
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C22×Dic106D411yescharacteristic
78C22×Dic106C2311yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×D212C2311yescharacteristic
81C23×Dic53—21no—
82C22×C4×D53—21no—
83C2×Dic212—42no—
84C2×Dic212C2314yes—
85C2×#11719925—24no—
86C2×#11719925—24no—
87C2×#11719925C2314yes—
88C2×#11719925C2314yes—
89C2×#11719913—42no—
90C2×#11719913C2314yes—
91C2×#11719923—42no—
92C2×#11719923C2314yes—
93C2×#11719924—42no—
94C2×#11719924C2314yes—
95C2×#11719922—24no—
96C2×#11719922C2314yes—
97C22×#88322C2311yescharacteristic
98C22×#88322C2311yescharacteristic
99#13133215—22no—
100#13133215—22no—
101#13133215C2314yes—
102#13133215C2314yes—
103#13133212—28no—
104#13133211—28no—
105#13133210—28no—
106#13133210—28no—
107#13133206—22no—
108#13133206C2314yes—
109#13133205—22no—
110#13133205C2314yes—
111#13133204—22no—
112#13133204C2314yes—
113#13133195—28no—
114#13133194—28no—
115Q8×Dic53—22no—
116Q8×Dic53C2314yes—
117C4×Dic106—22no—
118C4×Dic106D414yes—
119C4×Dic106C2314yes—
120C4×Dic106C2314yes—
121#13133182—22no—
122#13133182C2314yes—
123D4×Dic53—22no—
124D4×Dic53C2314yes—
125#13133179—22no—
126#13133179C2314yes—
127#13133174—28no—
128#13133173—28no—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53D411yescharacteristic
131C2×C4⋊Dic53C2311yescharacteristic
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919D411yescharacteristic
139C2×#11719919D411yescharacteristic
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×C22⋊Dic53—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#13133140C2314yes—
159#13133139C2314yes—
160C4×#88322C2314yes—
161C8×Dic53C2314yes—
162C8×Dic53C2314yes—
163C22×Q8×C53C2311yescharacteristic
164C22×Q8×C53C2311yescharacteristic
165C22×D4×C53C2311yescharacteristic
166C2×Q16×C53—42no—
167C2×Q16×C53C2314yes—
168C2×SD16×C53—42no—
169C2×SD16×C53C2314yes—
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172#124×C53—22no—
173#124×C53C2314yes—
174C4×Q8×C53—22no—
175C4×Q8×C53C2314yes—
176C2×C4⋊C4×C53—21no—
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53—21no—
180C2×C42×C53—21no—
181C2×C42×C53C2311yescharacteristic
182C4⋊C8×C53C2314yes—
183#103×C53C2314yes—
184#102×C53C2314yes—
185C24×C53—21no—
186C23×D53—21no—
187C2×Q8×C53—21no—
188C2×Q8×C53—21no—
189C2×Q8×C53—22no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53—22no—
193C2×Q8×C53C2412yes—
194C2×Q8×C53C2412yes—
195C2×D4×C53—21no—
196C2×D4×C53—22no—
197C2×D4×C53—22no—
198C2×D4×C53C2412yes—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2411yescharacteristic
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—24no—
209C22×Dic53—44no—
210C22×Dic53C2×D411yescharacteristic
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213C22×Dic53C2×D411yescharacteristic
214C2×D212—22no—
215C2×D212—22no—
216C2×D212—21no—
217C2×D212C2412yes—
218C2×C4×D53—24no—
219C2×C4×D53—44no—
220C2×Dic106—24no—
221C2×Dic106—22no—
222C2×Dic106—22no—
223C2×Dic106—22no—
224C2×Dic106—22no—
225C2×Dic106—21no—
226C2×Dic106—21no—
227C2×Dic106C2×D414yes—
228C2×Dic106C2412yes—
229C2×Dic106C2412yes—
230Q16×C53—44no—
231SD16×C53—44no—
232C2×C8×C53—22no—
233C2×C8×C53—22no—
234C2×C8×C53C2412yes—
235C2×C8×C53C2412yes—
236C4⋊C4×C53—24no—
237C4⋊C4×C53—21no—
238C4⋊C4×C53C2412yes—
239C22⋊C4×C53—24no—
240C22⋊C4×C53—24no—
241C42×C53—24no—
242C42×C53C2×D412yes—
243C42×C53C2412yes—
244C22⋊Dic53—24no—
245C22⋊Dic53—24no—
246C22⋊Dic53—24no—
247#11719925—28no—
248#11719925—28no—
249#11719924—44no—
250#11719923—44no—
251#11719922—28no—
252#11719921—24no—
253#11719921—24no—
254#11719921—24no—
255#11719921—24no—
256#11719921—24no—
257C4⋊Dic53—21no—
258C4⋊Dic53—24no—
259C4⋊Dic53C2×D414yes—
260C4⋊Dic53C2412yes—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
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—
280Dic212—44no—
281#11719913—44no—
282C23×C53—22no—
283C23×C53—42no—
284C23×C53—42no—
285C23×C53—42no—
286C23×C53C22×D411yescharacteristic
287C22×D53—22no—
288C22×D53—42no—
289C22×D53—42no—
290C22×D53—42no—
291Q8×C53—22no—
292Q8×C53—22no—
293Q8×C53—22no—
294Q8×C53—22no—
295Q8×C53—42no—
296Q8×C53—42no—
297D4×C53—22no—
298D4×C53—22no—
299D4×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—42no—
306C2×C4×C53—42no—
307C2×C4×C53—42no—
308C2×C4×C53C22×D412yes—
309C2×C4×C53C22×D412yes—
310C2×C4×C53C22×D411yescharacteristic
311C2×C4×C53C2×#4112yes—
312C2×C4×C53H(5,𝔽2)12yes—
313C2×C4×C53C2511yescharacteristic
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—48no—
324C2×Dic53#13514yes—
325C2×Dic53C22×D412yes—
326C2×Dic53C22×D412yes—
327C2×Dic53C22×D412yes—
328C2×Dic53C22×D412yes—
329D212—22no—
330D212—22no—
331D212—42no—
332C4×D53—48no—
333Dic106—28no—
334Dic106—22no—
335Dic106—22no—
336Dic106—22no—
337Dic106—22no—
338Dic106—42no—
339Dic106—42no—
340C8×C53—22no—
341C8×C53—22no—
342#88322—22no—
343#88322C2×#4114yes—
344C2×#3393—531nomaximal, Sylow
345C22×C53—42no—
346C22×C53—42no—
347C22×C53—42no—
348C22×C53—84no—
349C22×C53#55012yes—
350C22×C53C2×#13512yes—
351C22×C53#57812yes—
352C22×C53C23×D411yescharacteristic
353C2×D53—42no—
354C2×D53—42no—
355C2×D53—42no—
356C2×D53—84no—
357C4×C53—22no—
358C4×C53—22no—
359C4×C53—42no—
360C4×C53—42no—
361C4×C53—42no—
362C4×C53#55012yes—
363C4×C53C22×#4111yescharacteristic
364C4×C53C2×H(5,𝔽2)11yescharacteristic
365Dic53—22no—
366Dic53—22no—
367Dic53—22no—
368Dic53—42no—
369Dic53—42no—
370Dic53—42no—
371Dic53C2×#13514yes—
372C2×#556—531no—
373C2×#556—531no—
374#3393—5316no—
375C2×#495—531no—
376C2×#495—531no—
377C2×#494—531no—
378C2×#464—531no—
379C2×#464—531no—
380C2×#464—531no—
381C2×#464D5311yescharacteristic, complemented
382C2×#461—531no—
383C2×#461—531no—
384C2×C8×Q8—531no—
385C2×C4×Q16—531no—
386C2×C4×Q16—531no—
387C2×C4×D8—531no—
388C2×C53—82no—
389C2×C53#339314yescomplemented
390C2×C53C2×#55011yescharacteristic
391C2×C53C22×#13511yescharacteristic
392C2×C53C2×#57811yescharacteristic
393D53—82no—
394C22×Q16—531no—
395C22×Q16—531no—
396C22×Q16—531no—
397C22×Q16C2×D5311yescharacteristic
398C22×SD16—531no—
399C22×SD16—531no—
400C22×SD16—531no—
401C22×SD16C2×D5311yescharacteristic
402C22×D8—531no—
403#556—538no—
404#556—538no—
405#556—1064no—
406#556—1064no—
407C2×C4⋊Q8—531no—
408C2×C4⋊Q8—531no—
409C2×#126—1061no—
410C2×#126—1061no—
411C2×#126—1061no—
412C2×#126—1061no—
413C2×#124—531no—
414C2×#124—531no—
415C2×#124—531no—
416C2×#124C2×D5311yescharacteristic
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#495—538no—
429#495—538no—
430#494—538no—
431#464—538no—
432#464—538no—
433#464—538no—
434#464C2×D5318yescomplemented
435#461—538no—
436#461—538no—
437C8×Q8—538no—
438C4×Q16—538no—
439C4×Q16—538no—
440C4×D8—538no—
441C2×#107—531no—
442C2×C4⋊C8—531no—
443C2×C4⋊C8—531no—
444C2×C4⋊C8C2×D5311yescharacteristic
445C2×#103—531no—
446C2×#103—531no—
447C2×#103—531no—
448C2×#103C2×D5311yescharacteristic
449C2×#102—531no—
450C2×#102C2×D5311yescharacteristic
451C2×C4×C8—531no—
452C2×C4×C8—531no—
453C2×C4×C8—531no—
454C53C2×#339311yescharacteristic, complemented, Sylow
455C22×Q8—531no—
456C22×Q8—531no—
457C22×Q8—531no—
458C22×Q8C22×D5311yescharacteristic
459C22×Q8C22×D5311yescharacteristic
460C22×D4—531no—
461C22×D4C22×D5311yescharacteristic
462C23×C4—1061no—
463C23×C4—1061no—
464C2×Q16—42no—
465C2×Q16—534no—
466C2×Q16—534no—
467C2×Q16—534no—
468C2×Q16—1064no—
469C2×Q16—1064no—
470C2×Q16—2122no—
471C2×Q16C22×D5314yes—
472C2×SD16—42no—
473C2×SD16—534no—
474C2×SD16—534no—
475C2×SD16—534no—
476C2×SD16—2122no—
477C2×SD16—2122no—
478C2×SD16—2122no—
479C2×SD16C22×D5314yes—
480C2×D8—534no—
481C2×D8—1064no—
482C22×C8—531no—
483C22×C8—531no—
484C22×C8C22×D5311yescharacteristic
485C22×C8C22×D5311yescharacteristic
486C4⋊Q8—534no—
487C4⋊Q8—534no—
488C4⋊Q8—1062no—
489C4⋊Q8—1062no—
490#126—1068no—
491#126—1068no—
492#126—1068no—
493#126—1068no—
494#124—22no—
495#124—534no—
496#124—534no—
497#124—534no—
498#124—1062no—
499#124—1062no—
500#124—1062no—
501#124C22×D5314yes—
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—531no—
522C2×C4⋊C4—531no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—531no—
525C2×C4⋊C4—1061no—
526C2×C4⋊C4—1061no—
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—21no—
534C2×C22⋊C4—21no—
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#103—534no—
557#103C22×D5314yes—
558#102—534no—
559#102C22×D5314yes—
560C4×C8—534no—
561C4×C8—534no—
562C4×C8—534no—
563C24—21no—
564C24—1061no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—534no—
572C2×Q8—532no—
573C2×Q8—532no—
574C2×Q8—1064no—
575C2×Q8—1061no—
576C2×Q8—1061no—
577C2×Q8—1062no—
578C2×Q8—1062no—
579C2×Q8—1062no—
580C2×Q8—1062no—
581C2×Q8C23×D5312yes—
582C2×Q8C23×D5312yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—532no—
587C2×D4—1061no—
588C2×D4—1062no—
589C2×D4—1062no—
590C2×D4C23×D5312yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—531no—
595C22×C4—531no—
596C22×C4—531no—
597C22×C4—531no—
598C22×C4—1064no—
599C22×C4—1064no—
600C22×C4—1061no—
601C22×C4—1061no—
602C22×C4—1061no—
603C22×C4—2124no—
604C22×C4—2124no—
605C22×C4D4×D5311yescharacteristic
606C22×C4D4×D5311yescharacteristic
607C22×C4C23×D5311yescharacteristic
608Q16—44no—
609Q16—1068no—
610Q16—1068no—
611Q16—2124no—
612SD16—44no—
613SD16—2124no—
614SD16—2124no—
615SD16—2124no—
616D8—1068no—
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—21no—
627C4⋊C4—534no—
628C4⋊C4—534no—
629C4⋊C4—534no—
630C4⋊C4—532no—
631C4⋊C4—1064no—
632C4⋊C4—1064no—
633C4⋊C4—1064no—
634C4⋊C4—1064no—
635C4⋊C4—1064no—
636C4⋊C4—1064no—
637C4⋊C4—1061no—
638C4⋊C4—1064no—
639C4⋊C4C23×D5312yes—
640C22⋊C4—24no—
641C22⋊C4—24no—
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—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—1062no—
665C23—2122no—
666C23—2122no—
667C23—2122no—
668C23C2×D4×D5311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—42no—
674Q8—42no—
675Q8—1068no—
676Q8—1062no—
677Q8—1062no—
678Q8—1062no—
679Q8—1062no—
680Q8—2122no—
681Q8—2122no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—1062no—
686D4—1062no—
687D4—2122no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—534no—
697C2×C4—532no—
698C2×C4—532no—
699C2×C4—532no—
700C2×C4—532no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—1062no—
707C2×C4—2128no—
708C2×C4—2128no—
709C2×C4—2122no—
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—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—4244no—
727C22—2122no—
728C22—2122no—
729C22—2122no—
730C22#1681129112yes—
731C22#135×D5312yes—
732C22#1681143912yes—
733C22C22×D4×D5311yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—534no—
740C4—1062no—
741C4—1062no—
742C4—1062no—
743C4—2122no—
744C4—2122no—
745C4—2122no—
746C4#1681129112yes—
747C4C2×#41×D5311yescharacteristic
748C4C2×#1313326211yescharacteristic
749C2—82no—
750C2—4242no—
751C2#2028769814yesdirect product factor
752C2C2×#1681129111yescharacteristic
753C2C2×#135×D5311yescharacteristic
754C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#464C2
socleC23×C53C22×D4
prime radicalC22×#11719922C22
hypercenterC2×#464D53
hypocenterC53C2×#3393
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#16811345C2semidirect
2. C2×#16811342C2semidirect
3. #20287698C2direct (N × H)
6. C2×#16811001C2semidirect
7. C2×#16810847C2semidirect
8. C2×#16810846C2semidirect
9. C2×#16810844C2semidirect
10. C2×#16810827C2semidirect
11. C2×#16810826C2semidirect
12. C2×#16810747C2semidirect
13. C2×C4×#11719925C2semidirect
14. C2×#16810715C2semidirect
16. C2×C53×#464C2semidirect
25. #16811345C22semidirect
27. #16811342C22semidirect
49. #16811001C22semidirect
50. #16810847C22semidirect
51. #16810846C22semidirect
52. #16810844C22semidirect
53. #16810827C22semidirect
54. #16810826C22semidirect
55. #16810747C22semidirect
56. C4×#11719925C22semidirect
57. #16810715C22semidirect
73. C53×#464C22semidirect
381. C2×#464D53semidirect
389. C2×C53#3393semidirect
434. #464C2×D53semidirect
454. C53C2×#3393semidirect
751. C2#20287698direct (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×#168113422
#202876982
C2×#168110052
C2×#168110042
C2×#168110012
C2×#168108472
C2×#168108462
C2×#168108442
C2×#168108272
C2×#168108262
C2×#168107472
C2×C4×#117199252
C2×#168107152
C2×#168107032
C2×C53×#4642
C2×#339353