Finite Group Databasebeta

← C2×#20284735 #28252109

Subgroups — C2×#20284735 #28252109

Order 13568.

2202 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811157C211yesmaximal, characteristic, complemented
2C2×C4×#11719945C211yesmaximal, characteristic, complemented
3#20284735C2116yesmaximal, direct product factor
4C2×#16810965C211yesmaximal, characteristic, complemented
5C2×#16810948C211yesmaximal, characteristic, complemented
6C2×#16810931C211yesmaximal, characteristic, complemented
7C2×#16810924C211yesmaximal, characteristic, complemented
8C2×#16810846C211yesmaximal, characteristic, complemented
9C2×#16810839C211yesmaximal, characteristic, complemented
10C2×#16810787C211yesmaximal, characteristic, complemented
11C2×#16810770C211yesmaximal, characteristic
12C2×C4×Dic212C211yesmaximal, characteristic, complemented
13C2×C4×#11719913C211yesmaximal, characteristic, complemented
14C2×C4×#11719913C211yesmaximal, characteristic, complemented
15C2×C4×D424C211yesmaximal, characteristic, complemented
16C2×C53×#431C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×Dic212C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×D424C2211yescharacteristic
22#16811157—24no—
23#16811157C2218yescomplemented
24C2×#13133211—21no—
25C2×#13133209C2211yescharacteristic
26C2×#13133205C2211yescharacteristic
27C2×#13133200—21no—
28C2×#13133196C2211yescharacteristic
29C2×#13133191C2211yescharacteristic
30C4×#11719945—24no—
31C4×#11719945C2218yescomplemented
32C2×C4×Dic106C2211yescharacteristic
33C2×C4×Dic106C2211yescharacteristic
34C2×C4×Dic106C2211yescharacteristic
35C2×C4×D212C2211yescharacteristic
36C2×C4×D212C2211yescharacteristic
37C2×C4×D212C2211yescharacteristic
38C2×C4×C22⋊D53—21no—
39C2×C4×C22⋊D53—21no—
40C2×C4×C22⋊D53—21no—
41C2×#13133176C2211yescharacteristic
42C2×#13133174—21no—
43C2×#13133174—21no—
44C2×C42×D53—21no—
45#16810965C2218yescomplemented
46#16810948C2218yescomplemented
47#16810931C2218yescomplemented
48#16810924C2218yescomplemented
49#16810846C2218yescomplemented
50#16810839C2218yescomplemented
51#16810787C2218yescomplemented
52#16810770C2218yes—
53C4×Dic212C2218yescomplemented
54C4×#11719913C2218yescomplemented
55C4×#11719913C2218yescomplemented
56C4×D424C2218yescomplemented
57C2×#13133151C2211yescharacteristic
58C2×#13133151C2211yescharacteristic
59C2×#13133149C2211yescharacteristic
60C2×#13133149C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133142C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133139C2211yescharacteristic
67C2×#13133139C2211yescharacteristic
68C2×#13133139C2211yescharacteristic
69C22×C42×C53C2211yescharacteristic
70C53×#431C2218yescomplemented
71C2×C4⋊C8×C53C2211yescharacteristic
72C2×C4⋊C8×C53C2211yescharacteristic
73C2×C22⋊C8×C53C2211yescharacteristic
74C2×C22⋊C8×C53C2211yescharacteristic
75C2×C4×C8×C53C2211yescharacteristic
76C2×C4×C8×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—24no—
79C2×#11719945—24no—
80C2×#11719945C2314yes—
81C22×Dic106C2311yescharacteristic
82C22×Dic106C2311yescharacteristic
83C22×D212C2311yescharacteristic
84C22×D212C2311yescharacteristic
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53—21no—
89C22×C4×D53—21no—
90C22×C4×D53—21no—
91C2×Dic212—24no—
92C2×Dic212C2314yes—
93C2×#11719913—24no—
94C2×#11719913—24no—
95C2×#11719913C2314yes—
96C2×#11719913C2314yes—
97C2×D424—24no—
98C2×D424C2314yes—
99#13133211—28no—
100#13133209—22no—
101#13133209C2314yes—
102#13133205—22no—
103#13133205C2314yes—
104#13133200—28no—
105#13133196—22no—
106#13133196C2314yes—
107#13133191—22no—
108#13133191C2314yes—
109C4×Dic106—22no—
110C4×Dic106—22no—
111C4×Dic106—22no—
112C4×Dic106C2314yes—
113C4×Dic106C2314yes—
114C4×Dic106C2314yes—
115C4×D212—22no—
116C4×D212—22no—
117C4×D212—22no—
118C4×D212C2314yes—
119C4×D212C2314yes—
120C4×D212C2314yes—
121C4×C22⋊D53—28no—
122C4×C22⋊D53—28no—
123C4×C22⋊D53—28no—
124#13133176—22no—
125#13133176C2314yes—
126#13133174—28no—
127#13133174—28no—
128C2×C4⋊Dic53C2311yescharacteristic
129C2×C4⋊Dic53C2311yescharacteristic
130C2×C4⋊Dic53C2311yescharacteristic
131C2×C4⋊Dic53C2311yescharacteristic
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×C22⋊Dic53—21no—
139C2×C22⋊Dic53—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×C4×Dic53—21no—
147C2×C4×Dic53—21no—
148C2×C4×Dic53—21no—
149C2×C4×Dic53—21no—
150C42×D53—28no—
151#13133151C2314yes—
152#13133151C2314yes—
153#13133149C2314yes—
154#13133149C2314yes—
155#13133142C2314yes—
156#13133142C2314yes—
157#13133142C2314yes—
158#13133142C2314yes—
159#13133139C2314yes—
160#13133139C2314yes—
161#13133139C2314yes—
162#13133139C2314yes—
163C23×C4×C53D411yescharacteristic
164C23×C4×C53D411yescharacteristic
165C23×C4×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170C2×C42×C53D411yescharacteristic
171C2×C42×C53D411yescharacteristic
172C2×C42×C53D414yes—
173C2×C42×C53C2311yescharacteristic
174C2×C42×C53C2311yescharacteristic
175C2×C42×C53C2314yes—
176C4⋊C8×C53C2314yes—
177C4⋊C8×C53C2314yes—
178C22⋊C8×C53C2314yes—
179C22⋊C8×C53C2314yes—
180C4×C8×C53C2314yes—
181C4×C8×C53C2314yes—
182C24×C53C2×D411yescharacteristic
183C23×D53—21no—
184C23×D53—21no—
185C22×C4×C53—24no—
186C22×C4×C53—22no—
187C22×C4×C53—22no—
188C22×C4×C53—42no—
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D412yes—
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2×D414yes—
195C22×C4×C53C2×D414yes—
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2412yes—
198C22×C4×C53C2411yescharacteristic
199C2×C22⋊D53—28no—
200C2×C22⋊D53—24no—
201C2×C22⋊D53—24no—
202C2×C22⋊D53—44no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209#11719945—216no—
210#11719945—28no—
211#11719945—28no—
212C2×D212—21no—
213C2×D212—22no—
214C2×D212—22no—
215C2×D212—22no—
216C2×D212—21no—
217C2×D212#4114yes—
218C2×D212C2412yes—
219C2×D212C2412yes—
220C2×C4×D53—28no—
221C2×C4×D53—24no—
222C2×C4×D53—24no—
223C2×C4×D53—24no—
224C2×C4×D53—24no—
225C2×C4×D53—44no—
226C2×C4×D53—44no—
227C2×C4×D53—44no—
228C2×Dic106—21no—
229C2×Dic106—22no—
230C2×Dic106—22no—
231C2×Dic106—22no—
232C2×Dic106—21no—
233C2×Dic106#4114yes—
234C2×Dic106C2412yes—
235C2×Dic106C2412yes—
236C2×C8×C53—22no—
237C2×C8×C53—22no—
238C2×C8×C53—22no—
239C2×C8×C53—22no—
240C2×C8×C53C2412yes—
241C2×C8×C53C2412yes—
242C2×C8×C53C2412yes—
243C2×C8×C53C2412yes—
244C42×C53C2×D414yes—
245C42×C53C2×D414yes—
246C42×C53C2×D412yes—
247C42×C53C2×D412yes—
248C42×C53C2412yes—
249C42×C53C2412yes—
250C22⋊Dic53—24no—
251C22⋊Dic53—24no—
252#11719921—24no—
253#11719921—24no—
254#11719921—24no—
255#11719921—24no—
256#11719921—24no—
257#11719921—24no—
258C4⋊Dic53—21no—
259C4⋊Dic53—21no—
260C4⋊Dic53—21no—
261C4⋊Dic53—21no—
262C4⋊Dic53C2412yes—
263C4⋊Dic53C2412yes—
264C4⋊Dic53C2412yes—
265C4⋊Dic53C2412yes—
266#11719919—24no—
267#11719919—24no—
268#11719919—24no—
269#11719919—24no—
270#11719919—24no—
271#11719919—24no—
272C4×Dic53—24no—
273C4×Dic53—24no—
274C4×Dic53—24no—
275C4×Dic53—24no—
276Dic212—28no—
277D424—28no—
278#11719913—28no—
279#11719913—28no—
280C23×C53—22no—
281C23×C53—22no—
282C23×C53—22no—
283C23×C53C22×D412yes—
284C23×C53C22×D411yescharacteristic
285C22×D53—24no—
286C22×D53—22no—
287C22×D53—22no—
288C22×D53—42no—
289C22×D53—42no—
290C22×D53—42no—
291C22×D53—42no—
292C22×D53—42no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—24no—
298C2×C4×C53—28no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—44no—
302C2×C4×C53#13514yes—
303C2×C4×C53C22×D412yes—
304C2×C4×C53C22×D412yes—
305C2×C4×C53C22×D412yes—
306C2×C4×C53C22×D412yes—
307C2×C4×C53C22×D411yescharacteristic
308C2×C4×C53C22×D412yes—
309C2×C4×C53C2×#4112yes—
310C2×C4×C53C2×#4112yes—
311C2×C4×C53C2511yescharacteristic
312C22⋊D53—216no—
313C22⋊D53—48no—
314C2×Dic53—24no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—42no—
325C2×Dic53—42no—
326D212—24no—
327D212—22no—
328D212—22no—
329D212—22no—
330D212—42no—
331D212C2×#4114yes—
332C4×D53—216no—
333C4×D53—48no—
334C4×D53—48no—
335C4×D53—48no—
336Dic106—24no—
337Dic106—22no—
338Dic106—22no—
339Dic106—22no—
340Dic106—42no—
341Dic106C2×#4114yes—
342C8×C53—22no—
343C8×C53—22no—
344C8×C53—22no—
345C8×C53—22no—
346C2×#3102—531nomaximal, Sylow
347C22×C53—22no—
348C22×C53—22no—
349C22×C53—22no—
350C22×C53—44no—
351C22×C53#52512yes—
352C22×C53C2×#13512yes—
353C22×C53#57512yes—
354C22×C53C23×D411yescharacteristic
355C2×D53—24no—
356C2×D53—48no—
357C2×D53—42no—
358C2×D53—42no—
359C2×D53—42no—
360C2×D53—42no—
361C2×D53—42no—
362C2×D53—84no—
363C4×C53—22no—
364C4×C53—22no—
365C4×C53—22no—
366C4×C53—22no—
367C4×C53#52512yes—
368C4×C53C2×#13514yes—
369C4×C53C22×#4111yescharacteristic
370C4×C53C22×#4111yescharacteristic
371Dic53—24no—
372Dic53—42no—
373Dic53—42no—
374Dic53—42no—
375Dic53—42no—
376Dic53—42no—
377C2×#529—531no—
378C2×C4×#41—531no—
379#3102—5316no—
380C2×#485—531no—
381C2×#482—531no—
382C2×#479—531no—
383C2×#478—531no—
384C2×#464—531no—
385C2×#463—531no—
386C2×#452—531no—
387C2×#449—531no—
388C2×C4×Q16—531no—
389C2×C4×SD16—531no—
390C2×C4×SD16—531no—
391C2×C4×D8—531no—
392C2×#431D5311yescharacteristic, complemented
393C2×C53—42no—
394C2×C53#310214yescomplemented
395C2×C53C2×#52511yescharacteristic
396C2×C53C22×#13511yescharacteristic
397C2×C53C2×#57511yescharacteristic
398D53—44no—
399D53—82no—
400C22×#41—531no—
401C22×Q16—531no—
402C22×SD16—531no—
403C22×SD16—531no—
404C22×D8—531no—
405#529—538no—
406#529—1064no—
407C2×#126—1061no—
408C2×#125—531no—
409C2×#124—531no—
410C2×#123—1061no—
411C2×C22⋊Q8—531no—
412C2×#121—531no—
413C4×#41—538no—
414C4×#41—1064no—
415C2×C4×Q8—531no—
416C2×C4×Q8—531no—
417C2×C4×Q8—531no—
418C2×C4×D4—531no—
419C2×C4×D4—531no—
420C2×C4×D4—531no—
421C2×C4×D4—1061no—
422C2×C4×D4—1061no—
423C2×C4×D4—1061no—
424C2×#117—531no—
425C2×#117—1061no—
426C2×#117—1061no—
427C22×C42—1061no—
428C22×C42C2×D5311yescharacteristic
429#485—538no—
430#482—538no—
431#479—538no—
432#478—538no—
433#464—538no—
434#463—538no—
435#452—538no—
436#449—538no—
437C4×Q16—538no—
438C4×SD16—538no—
439C4×SD16—538no—
440C4×D8—538no—
441#431C2×D5318yescomplemented
442C2×#107—531no—
443C2×#107—531no—
444C2×#106—531no—
445C2×#106—531no—
446C2×C4⋊C8C2×D5311yescharacteristic
447C2×C4⋊C8C2×D5311yescharacteristic
448C2×#103—531no—
449C2×#103—531no—
450C2×#103—531no—
451C2×#103—531no—
452C2×#102—531no—
453C2×#102—531no—
454C2×#102—531no—
455C2×#102—531no—
456C2×C22⋊C8C2×D5311yescharacteristic
457C2×C22⋊C8C2×D5311yescharacteristic
458C2×C4×C8C2×D5311yescharacteristic
459C2×C4×C8C2×D5311yescharacteristic
460C53C2×#310211yescharacteristic, complemented, Sylow
461C2×#41—534no—
462C2×#41—1064no—
463C2×#41—1064no—
464C2×#41—1062no—
465C22×Q8—531no—
466C22×Q8—531no—
467C22×D4—531no—
468C22×D4—531no—
469C22×D4—1061no—
470C22×D4—1061no—
471C23×C4—1061no—
472C23×C4—1061no—
473C23×C4—1061no—
474C23×C4—1061no—
475C23×C4D21211yescharacteristic
476C23×C4D21211yescharacteristic
477C23×C4C22×D5311yescharacteristic
478C2×Q16—534no—
479C2×Q16—1064no—
480C2×SD16—534no—
481C2×SD16—534no—
482C2×SD16—1064no—
483C2×SD16—1064no—
484C2×D8—534no—
485C2×D8—1064no—
486C22×C8C22×D5311yescharacteristic
487C22×C8C22×D5311yescharacteristic
488C22×C8C22×D5311yescharacteristic
489C22×C8C22×D5311yescharacteristic
490#126—1068no—
491#125—534no—
492#125—1062no—
493#124—534no—
494#124—1062no—
495#123—1068no—
496C22⋊Q8—534no—
497C22⋊Q8—1062no—
498#121—534no—
499#121—1062no—
500C4×Q8—534no—
501C4×Q8—534no—
502C4×Q8—534no—
503C4×Q8—1062no—
504C4×Q8—1062no—
505C4×Q8—1062no—
506C4×D4—534no—
507C4×D4—534no—
508C4×D4—534no—
509C4×D4—1068no—
510C4×D4—1068no—
511C4×D4—1068no—
512C4×D4—1062no—
513C4×D4—1062no—
514C4×D4—1062no—
515#117—534no—
516#117—1062no—
517#117—1068no—
518#117—1068no—
519C2×C4⋊C4—531no—
520C2×C4⋊C4—531no—
521C2×C4⋊C4—531no—
522C2×C4⋊C4—531no—
523C2×C4⋊C4—1061no—
524C2×C4⋊C4—1061no—
525C2×C4⋊C4—1061no—
526C2×C4⋊C4—1061no—
527C2×C4⋊C4—1061no—
528C2×C4⋊C4—1061no—
529C2×C22⋊C4—1061no—
530C2×C22⋊C4—1061no—
531C2×C22⋊C4—1061no—
532C2×C22⋊C4—1061no—
533C2×C22⋊C4—1061no—
534C2×C22⋊C4—1061no—
535C2×C22⋊C4—1061no—
536C2×C22⋊C4—1061no—
537C2×C42—1061no—
538C2×C42—1061no—
539C2×C42—1061no—
540C2×C42—1061no—
541C2×C42—1068no—
542C2×C42D21211yescharacteristic
543C2×C42D21214yes—
544C2×C42D21211yescharacteristic
545C2×C42C22×D5311yescharacteristic
546C2×C42C22×D5314yes—
547C2×C42C22×D5311yescharacteristic
548#107—534no—
549#107—534no—
550#106—534no—
551#106—534no—
552C4⋊C8C22×D5314yes—
553C4⋊C8C22×D5314yes—
554#103—534no—
555#103—534no—
556#103—534no—
557#103—534no—
558#102—534no—
559#102—534no—
560#102—534no—
561#102—534no—
562C22⋊C8C22×D5314yes—
563C22⋊C8C22×D5314yes—
564C4×C8C22×D5314yes—
565C4×C8C22×D5314yes—
566C24—1061no—
567C24—1061no—
568C24C2×D21211yescharacteristic
569#41—1068no—
570#41—1068no—
571#41—10616no—
572C2×Q8—534no—
573C2×Q8—532no—
574C2×Q8—532no—
575C2×Q8—1061no—
576C2×Q8—1061no—
577C2×Q8—1062no—
578C2×Q8—1062no—
579C2×Q8—1062no—
580C2×D4—534no—
581C2×D4—532no—
582C2×D4—532no—
583C2×D4—1068no—
584C2×D4—1064no—
585C2×D4—1064no—
586C2×D4—1061no—
587C2×D4—1061no—
588C2×D4—1062no—
589C2×D4—1062no—
590C2×D4—1062no—
591C2×D4—2124no—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—42no—
596C22×C4—1068no—
597C22×C4—1061no—
598C22×C4—1064no—
599C22×C4—1061no—
600C22×C4—1061no—
601C22×C4—1061no—
602C22×C4—1061no—
603C22×C4—1061no—
604C22×C4—1064no—
605C22×C4—1064no—
606C22×C4—1064no—
607C22×C4—2124no—
608C22×C4—2124no—
609C22×C4—2124no—
610C22×C4C2×D21211yescharacteristic
611C22×C4C2×D21211yescharacteristic
612C22×C4C2×D21212yes—
613C22×C4C2×D21211yescharacteristic
614C22×C4C2×D21211yescharacteristic
615C22×C4C2×D21214yes—
616C22×C4C2×D21214yes—
617C22×C4C2×D21211yescharacteristic
618C22×C4C23×D5312yes—
619C22×C4C23×D5311yescharacteristic
620Q16—1068no—
621SD16—1068no—
622SD16—1068no—
623D8—1068no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8C23×D5312yes—
629C2×C8C23×D5312yes—
630C2×C8C23×D5312yes—
631C2×C8C23×D5312yes—
632C4⋊C4—532no—
633C4⋊C4—532no—
634C4⋊C4—532no—
635C4⋊C4—532no—
636C4⋊C4—1061no—
637C4⋊C4—1061no—
638C4⋊C4—1061no—
639C4⋊C4—1061no—
640C4⋊C4—1064no—
641C4⋊C4—1064no—
642C4⋊C4—1064no—
643C4⋊C4—1064no—
644C4⋊C4—1064no—
645C4⋊C4—1064no—
646C22⋊C4—1064no—
647C22⋊C4—1064no—
648C22⋊C4—1064no—
649C22⋊C4—1064no—
650C22⋊C4—1064no—
651C22⋊C4—1064no—
652C22⋊C4—1064no—
653C22⋊C4—1064no—
654C42—1064no—
655C42—1064no—
656C42—1064no—
657C42—1064no—
658C42C2×D21214yes—
659C42C2×D21214yes—
660C42C2×D21212yes—
661C42C2×D21212yes—
662C42C23×D5312yes—
663C42C23×D5312yes—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—1064no—
668C23—1062no—
669C23—1062no—
670C23—2122no—
671C23—2122no—
672C23—2122no—
673C23—2122no—
674C23—2122no—
675C23C22×D21212yes—
676C23C22×D21211yescharacteristic
677Q8—534no—
678Q8—1064no—
679Q8—1062no—
680Q8—1062no—
681Q8—1062no—
682Q8—2122no—
683D4—534no—
684D4—10616no—
685D4—1064no—
686D4—1062no—
687D4—1062no—
688D4—1062no—
689D4—2128no—
690D4—2122no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—44no—
700C2×C4—10616no—
701C2×C4—1064no—
702C2×C4—1062no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—1062no—
707C2×C4—1062no—
708C2×C4—2128no—
709C2×C4—2122no—
710C2×C4—2122no—
711C2×C4—2122no—
712C2×C4—2122no—
713C2×C4—2122no—
714C2×C4—2128no—
715C2×C4—2128no—
716C2×C4#1313323914yes—
717C2×C4C22×D21212yes—
718C2×C4C22×D21212yes—
719C2×C4C22×D21212yes—
720C2×C4C22×D21212yes—
721C2×C4C22×D21211yescharacteristic
722C2×C4C22×D21212yes—
723C2×C4#41×D5312yes—
724C2×C4#41×D5312yes—
725C2×C4C24×D5311yescharacteristic
726C8—22no—
727C8—22no—
728C8—22no—
729C8—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—1064no—
735C22—4244no—
736C22—2122no—
737C22—2122no—
738C22—2122no—
739C22—2128no—
740C22—2122no—
741C22—2122no—
742C22#1681113512yes—
743C22C2×#1313323912yes—
744C22#1681142312yes—
745C22C23×D21211yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—1064no—
751C4—2122no—
752C4—2122no—
753C4—2122no—
754C4—2122no—
755C4—2122no—
756C4#1681113512yes—
757C4C2×#1313323914yes—
758C4C2×#41×D5311yescharacteristic
759C4C2×#41×D5311yescharacteristic
760C2—42no—
761C2—4242no—
762C2—2124no—
763C2#2028473514yesdirect product factor
764C2C2×#1681113511yescharacteristic
765C2C22×#1313323911yescharacteristic
766C2C2×#1681142311yescharacteristic
subgroupG/H
centerC22×C4C2×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#431C2
socleC23×C53C22×D4
prime radicalC2×#16810770C2
hypercenterC2×#431D53
hypocenterC53C2×#3102
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
1. C2×#16811157C2semidirect
2. C2×C4×#11719945C2semidirect
3. #20284735C2direct (N × H)
4. C2×#16810965C2semidirect
5. C2×#16810948C2semidirect
6. C2×#16810931C2semidirect
7. C2×#16810924C2semidirect
8. C2×#16810846C2semidirect
9. C2×#16810839C2semidirect
10. C2×#16810787C2semidirect
12. C2×C4×Dic212C2semidirect
13. C2×C4×#11719913C2semidirect
14. C2×C4×#11719913C2semidirect
15. C2×C4×D424C2semidirect
16. C2×C53×#431C2semidirect
23. #16811157C22semidirect
31. C4×#11719945C22semidirect
45. #16810965C22semidirect
46. #16810948C22semidirect
47. #16810931C22semidirect
48. #16810924C22semidirect
49. #16810846C22semidirect
50. #16810839C22semidirect
51. #16810787C22semidirect
53. C4×Dic212C22semidirect
54. C4×#11719913C22semidirect
55. C4×#11719913C22semidirect
56. C4×D424C22semidirect
70. C53×#431C22semidirect
392. C2×#431D53semidirect
394. C2×C53#3102semidirect
441. #431C2×D53semidirect
460. C53C2×#3102semidirect
763. C2#20284735direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111572
C2×C4×#117199452
#202847352
C2×#168109652
C2×#168109482
C2×#168109312
C2×#168109242
C2×#168108462
C2×#168108392
C2×#168107872
C2×#168107702
C2×C4×Dic2122
C2×C4×#117199132
C2×C4×D4242
C2×C53×#4312
C2×#310253