Finite Group Databasebeta

← C2×#20285398 #28253976

Subgroups — C2×#20285398 #28253976

Order 13568.

2034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811244C211yesmaximal, characteristic, complemented
2C2×#16811228C211yesmaximal, characteristic, complemented
3#20285398C2116yesmaximal, direct product factor
4C2×#16811032C211yesmaximal, characteristic, complemented
5C2×#16811012C211yesmaximal, characteristic, complemented
6C2×#16810978C211yesmaximal, characteristic, complemented
7C2×#16810970C211yesmaximal, characteristic, complemented
8C2×#16810876C211yesmaximal, characteristic, complemented
9C2×#16810869C211yesmaximal, characteristic, complemented
10C2×#16810859C211yesmaximal, characteristic, complemented
11C2×#16810852C211yesmaximal, characteristic, complemented
12C2×#16810736C211yesmaximal, characteristic, complemented
13C2×#16810725C211yesmaximal, characteristic, complemented
14C2×C4×#11719913C211yesmaximal, characteristic, complemented
15C2×C4×D424C211yesmaximal, characteristic, complemented
16C2×C53×#405C211yesmaximal, characteristic, complemented
17C22×#11719913C2211yescharacteristic
18C22×#11719913C2211yescharacteristic
19C22×D424C2211yescharacteristic
20C22×D424C2211yescharacteristic
21#16811244—24no—
22#16811244C2218yescomplemented
23#16811228—24no—
24#16811228C2218yescomplemented
25C2×#13133217C2211yescharacteristic
26C2×#13133214C2211yescharacteristic
27C2×#13133212—21no—
28C2×#13133209C2211yescharacteristic
29C2×#13133205C2211yescharacteristic
30C2×#13133203—21no—
31C2×#13133202—21no—
32C2×#13133202—21no—
33C2×#13133199—21no—
34C2×#13133196C2211yescharacteristic
35C2×#13133195—21no—
36C2×#13133191C2211yescharacteristic
37C2×#13133191C2211yescharacteristic
38C2×#13133191C2211yescharacteristic
39C2×#13133190—21no—
40C2×#13133190—21no—
41C2×C4×Dic106C2211yescharacteristic
42C2×C4×D212C2211yescharacteristic
43C2×C4×D212C2211yescharacteristic
44C2×C4×D212C2211yescharacteristic
45#16811032C2218yescomplemented
46#16811012C2218yescomplemented
47#16810978C2218yescomplemented
48#16810970C2218yescomplemented
49#16810876C2218yescomplemented
50#16810869C2218yescomplemented
51#16810859C2218yescomplemented
52#16810852C2218yescomplemented
53#16810736C2218yescomplemented
54#16810725C2218yescomplemented
55C4×#11719913C2218yescomplemented
56C4×D424C2218yescomplemented
57C2×#13133151C2211yescharacteristic
58C2×#13133151C2211yescharacteristic
59C2×#13133149C2211yescharacteristic
60C2×#13133149C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133142C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133139C2211yescharacteristic
67C2×#13133139C2211yescharacteristic
68C2×#13133139C2211yescharacteristic
69C22×M16×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C2×#117×C53C2211yescharacteristic
72C53×#405C2218yescomplemented
73C2×#97×C53C2211yescharacteristic
74C2×#97×C53C2211yescharacteristic
75C2×C4×C8×C53C2211yescharacteristic
76C2×C4×C8×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C22×D212—21no—
80C22×D212—21no—
81C22×D212C2311yescharacteristic
82C22×D212C2311yescharacteristic
83C22×D212C2311yescharacteristic
84C22×C22⋊D53—21no—
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53—21no—
89C22×C4×D53—21no—
90C2×#11719913—24no—
91C2×#11719913—24no—
92C2×#11719913C2314yes—
93C2×#11719913C2314yes—
94C2×D424—24no—
95C2×D424—24no—
96C2×D424C2314yes—
97C2×D424C2314yes—
98#13133217—22no—
99#13133217C2314yes—
100#13133214—22no—
101#13133214C2314yes—
102#13133212—28no—
103#13133209—22no—
104#13133209C2314yes—
105#13133205—22no—
106#13133205C2314yes—
107#13133203—28no—
108#13133202—28no—
109#13133202—28no—
110#13133199—28no—
111#13133196—22no—
112#13133196C2314yes—
113#13133195—28no—
114#13133191—22no—
115#13133191—22no—
116#13133191—22no—
117#13133191C2314yes—
118#13133191C2314yes—
119#13133191C2314yes—
120#13133190—28no—
121#13133190—28no—
122C4×Dic106—22no—
123C4×Dic106C2314yes—
124C4×D212—22no—
125C4×D212—22no—
126C4×D212—22no—
127C4×D212C2314yes—
128C4×D212C2314yes—
129C4×D212C2314yes—
130C2×C4⋊Dic53—21no—
131C2×C4⋊Dic53C2311yescharacteristic
132C2×C4⋊Dic53C2311yescharacteristic
133C2×C4⋊Dic53C2311yescharacteristic
134C2×C4⋊Dic53C2311yescharacteristic
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×C22⋊Dic53—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—
149#13133151C2314yes—
150#13133151C2314yes—
151#13133149C2314yes—
152#13133149C2314yes—
153#13133142C2314yes—
154#13133142C2314yes—
155#13133139C2314yes—
156#13133139C2314yes—
157#13133139C2314yes—
158#13133139C2314yes—
159#13133139C2314yes—
160#13133139C2314yes—
161C23×C4×C53C2311yescharacteristic
162C2×M16×C53—24no—
163C2×M16×C53C2314yes—
164C22×C8×C53—24no—
165C22×C8×C53C2314yes—
166C22×C8×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170#117×C53D414yes—
171#117×C53C2314yes—
172C2×C4⋊C4×C53D411yescharacteristic
173C2×C4⋊C4×C53D411yescharacteristic
174C2×C22⋊C4×C53D411yescharacteristic
175C2×C22⋊C4×C53D411yescharacteristic
176C2×C42×C53C2311yescharacteristic
177C2×C42×C53C2311yescharacteristic
178#97×C53C2314yes—
179#97×C53C2314yes—
180C4×C8×C53C2314yes—
181C4×C8×C53C2314yes—
182C24×C53C2×D411yescharacteristic
183C23×D53—21no—
184C23×D53—21no—
185C23×D53—21no—
186C22×C4×C53—22no—
187C22×C4×C53—22no—
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D412yes—
194C22×C4×C53C2412yes—
195C22×C4×C53C2411yescharacteristic
196C2×C22⋊D53—24no—
197C2×C22⋊D53—24no—
198C2×C22⋊D53—24no—
199C2×C22⋊D53—82no—
200C2×C22⋊D53—82no—
201C2×C22⋊D53—82no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C2×D212—22no—
208C2×D212—22no—
209C2×D212—22no—
210C2×D212—22no—
211C2×D212—22no—
212C2×D212—22no—
213C2×D212—21no—
214C2×D212—21no—
215C2×D212—21no—
216C2×D212—24no—
217C2×D212—24no—
218C2×D212—82no—
219C2×D212—82no—
220C2×D212C2412yes—
221C2×D212C2412yes—
222C2×D212C2412yes—
223C2×C4×D53—24no—
224C2×C4×D53—24no—
225C2×C4×D53—24no—
226C2×C4×D53—82no—
227C2×C4×D53—82no—
228C2×C4×D53—82no—
229C2×Dic106—22no—
230C2×Dic106—22no—
231C2×Dic106—21no—
232C2×Dic106—24no—
233C2×Dic106—82no—
234C2×Dic106C2412yes—
235M16×C53—28no—
236C2×C8×C53—22no—
237C2×C8×C53—22no—
238C2×C8×C53—28no—
239C2×C8×C53#4114yes—
240C2×C8×C53#4114yes—
241C2×C8×C53C2412yes—
242C2×C8×C53C2412yes—
243C2×C8×C53C2412yes—
244C2×C8×C53C2412yes—
245C4⋊C4×C53C2×D414yes—
246C4⋊C4×C53C2×D414yes—
247C22⋊C4×C53C2×D414yes—
248C22⋊C4×C53C2×D414yes—
249C42×C53C2×D412yes—
250C42×C53C2×D412yes—
251C42×C53C2412yes—
252C42×C53C2412yes—
253C22⋊Dic53—24no—
254#11719921—24no—
255#11719921—24no—
256#11719921—24no—
257#11719921—24no—
258#11719921—24no—
259#11719921—24no—
260#11719921—24no—
261#11719921—24no—
262C4⋊Dic53—24no—
263C4⋊Dic53—21no—
264C4⋊Dic53—21no—
265C4⋊Dic53—21no—
266C4⋊Dic53—21no—
267C4⋊Dic53C2412yes—
268C4⋊Dic53C2412yes—
269C4⋊Dic53C2412yes—
270C4⋊Dic53C2412yes—
271#11719919—24no—
272#11719919—24no—
273#11719919—24no—
274#11719919—24no—
275C4×Dic53—24no—
276D424—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—22no—
286C22×D53—22no—
287C22×D53—22no—
288C22×D53—42no—
289C22×D53—42no—
290C22×D53—42no—
291C22×D53—42no—
292C22×D53—42no—
293C22×D53—42no—
294C22×D53—42no—
295C22×D53—42no—
296C22×D53—42no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—24no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53C22×D412yes—
306C2×C4×C53C22×D412yes—
307C2×C4×C53C22×D412yes—
308C2×C4×C53C22×D412yes—
309C2×C4×C53C22×D412yes—
310C2×C4×C53C22×D411yescharacteristic
311C2×C4×C53C2×#4112yes—
312C2×C4×C53C2×#4112yes—
313C2×C4×C53C2511yescharacteristic
314C22⋊D53—84no—
315C22⋊D53—84no—
316C22⋊D53—84no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—42no—
325C2×Dic53—42no—
326C2×Dic53—42no—
327D212—22no—
328D212—22no—
329D212—22no—
330D212—22no—
331D212—22no—
332D212—22no—
333D212—42no—
334D212—42no—
335D212—42no—
336D212—84no—
337D212—84no—
338C4×D53—84no—
339C4×D53—84no—
340C4×D53—84no—
341Dic106—22no—
342Dic106—22no—
343Dic106—42no—
344Dic106—84no—
345C8×C53—22no—
346C8×C53—22no—
347C8×C53C2×#4114yes—
348C8×C53C2×#4114yes—
349C2×#3179—531nomaximal, Sylow
350C22×C53—22no—
351C22×C53—22no—
352C22×C53—22no—
353C22×C53—44no—
354C22×C53#53212yes—
355C22×C53#57612yes—
356C22×C53#57712yes—
357C22×C53C23×D411yescharacteristic
358C2×D53—42no—
359C2×D53—42no—
360C2×D53—42no—
361C2×D53—42no—
362C2×D53—42no—
363C2×D53—42no—
364C2×D53—42no—
365C2×D53—42no—
366C2×D53—42no—
367C2×D53—84no—
368C2×D53—84no—
369C2×D53—84no—
370C4×C53—22no—
371C4×C53—22no—
372C4×C53—22no—
373C4×C53—22no—
374C4×C53—22no—
375C4×C53#53212yes—
376C4×C53C22×#4111yescharacteristic
377C4×C53C22×#4111yescharacteristic
378Dic53—42no—
379Dic53—42no—
380Dic53—42no—
381Dic53—42no—
382Dic53—42no—
383C2×#542—531no—
384C2×#540—531no—
385#3179—5316no—
386C2×#501—531no—
387C2×#496—531no—
388C2×#488—531no—
389C2×#486—531no—
390C2×#469—531no—
391C2×#468—531no—
392C2×#466—531no—
393C2×#465—531no—
394C2×#442—531no—
395C2×#440—531no—
396C2×C4×SD16—531no—
397C2×C4×D8—531no—
398C2×#405D5311yescharacteristic, complemented
399C2×C53—42no—
400C2×C53#317914yescomplemented
401C2×C53C2×#53211yescharacteristic
402C2×C53C2×#57611yescharacteristic
403C2×C53C2×#57711yescharacteristic
404D53—82no—
405D53—82no—
406D53—82no—
407C22×SD16—531no—
408C22×SD16—531no—
409C22×D8—531no—
410C22×D8—531no—
411C22×M16C2×D5311yescharacteristic
412C23×C8C2×D5311yescharacteristic
413#542—538no—
414#542—1064no—
415#540—538no—
416#540—1064no—
417C2×C4⋊Q8—531no—
418C2×#127—531no—
419C2×#126—1061no—
420C2×#125—531no—
421C2×#124—531no—
422C2×#124—1061no—
423C2×#123—1061no—
424C2×#123—1061no—
425C2×#123—1061no—
426C2×C22⋊Q8—531no—
427C2×C22⋊Q8—1061no—
428C2×#121—531no—
429C2×#121—531no—
430C2×#121—531no—
431C2×#121—1061no—
432C2×#121—1061no—
433C2×C4×Q8—531no—
434C2×C4×D4—531no—
435C2×C4×D4—531no—
436C2×C4×D4—531no—
437C2×#117C2×D5311yescharacteristic
438#501—538no—
439#496—538no—
440#488—538no—
441#486—538no—
442#469—538no—
443#468—538no—
444#466—538no—
445#465—538no—
446#442—538no—
447#440—538no—
448C4×SD16—538no—
449C4×D8—538no—
450C2×#107—531no—
451C2×#107—531no—
452C2×#106—531no—
453C2×#106—531no—
454C2×#103—531no—
455C2×#103—531no—
456C2×#102—531no—
457C2×#102—531no—
458C2×#102—531no—
459C2×#102—531no—
460C2×#102—531no—
461C2×#102—531no—
462#405C2×D5318yescomplemented
463C2×#97C2×D5311yescharacteristic
464C2×#97C2×D5311yescharacteristic
465C2×C4×C8C2×D5311yescharacteristic
466C2×C4×C8C2×D5311yescharacteristic
467C53C2×#317911yescharacteristic, complemented, Sylow
468C22×Q8—531no—
469C22×Q8—1061no—
470C22×D4—531no—
471C22×D4—531no—
472C22×D4—531no—
473C22×D4—1061no—
474C22×D4—1061no—
475C22×D4—1061no—
476C22×D4—1061no—
477C22×D4—1061no—
478C23×C4—1061no—
479C23×C4—1061no—
480C23×C4—1061no—
481C23×C4C22×D5311yescharacteristic
482C2×SD16—534no—
483C2×SD16—534no—
484C2×SD16—1064no—
485C2×SD16—1064no—
486C2×D8—534no—
487C2×D8—534no—
488C2×D8—1064no—
489C2×D8—1064no—
490C2×M16—24no—
491C2×M16C22×D5314yes—
492C22×C8—24no—
493C22×C8C22×D5311yescharacteristic
494C22×C8C22×D5314yes—
495C22×C8C22×D5311yescharacteristic
496C22×C8C22×D5311yescharacteristic
497C22×C8C22×D5311yescharacteristic
498C4⋊Q8—534no—
499C4⋊Q8—1062no—
500#127—534no—
501#127—1062no—
502#126—1068no—
503#125—534no—
504#125—1062no—
505#124—534no—
506#124—1068no—
507#124—1062no—
508#123—1068no—
509#123—1068no—
510#123—1068no—
511C22⋊Q8—534no—
512C22⋊Q8—1062no—
513C22⋊Q8—1068no—
514#121—534no—
515#121—534no—
516#121—534no—
517#121—1062no—
518#121—1062no—
519#121—1062no—
520#121—1068no—
521#121—1068no—
522C4×Q8—534no—
523C4×Q8—1062no—
524C4×D4—534no—
525C4×D4—534no—
526C4×D4—534no—
527C4×D4—1062no—
528C4×D4—1062no—
529C4×D4—1062no—
530#117D21214yes—
531#117C22×D5314yes—
532C2×C4⋊C4—531no—
533C2×C4⋊C4—531no—
534C2×C4⋊C4—531no—
535C2×C4⋊C4—531no—
536C2×C4⋊C4—1061no—
537C2×C4⋊C4—1061no—
538C2×C4⋊C4—1061no—
539C2×C4⋊C4—1061no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4D21211yescharacteristic
542C2×C4⋊C4D21211yescharacteristic
543C2×C22⋊C4—1061no—
544C2×C22⋊C4—1061no—
545C2×C22⋊C4—1061no—
546C2×C22⋊C4—1061no—
547C2×C22⋊C4—1061no—
548C2×C22⋊C4—1061no—
549C2×C22⋊C4—1061no—
550C2×C22⋊C4—1061no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4D21211yescharacteristic
553C2×C22⋊C4D21211yescharacteristic
554C2×C42—1061no—
555C2×C42C22×D5311yescharacteristic
556C2×C42C22×D5311yescharacteristic
557#107—534no—
558#107—534no—
559#106—534no—
560#106—534no—
561#103—534no—
562#103—534no—
563#102—534no—
564#102—534no—
565#102—534no—
566#102—534no—
567#102—534no—
568#102—534no—
569#97C22×D5314yes—
570#97C22×D5314yes—
571C4×C8C22×D5314yes—
572C4×C8C22×D5314yes—
573C24—1061no—
574C24—1061no—
575C24—1061no—
576C24C2×D21211yescharacteristic
577C2×Q8—532no—
578C2×Q8—1064no—
579C2×Q8—1061no—
580C2×Q8—1062no—
581C2×Q8—1062no—
582C2×Q8—4242no—
583C2×D4—532no—
584C2×D4—532no—
585C2×D4—532no—
586C2×D4—1064no—
587C2×D4—1064no—
588C2×D4—1064no—
589C2×D4—1064no—
590C2×D4—1064no—
591C2×D4—1061no—
592C2×D4—1061no—
593C2×D4—1061no—
594C2×D4—1062no—
595C2×D4—1062no—
596C2×D4—1062no—
597C2×D4—1062no—
598C2×D4—1062no—
599C2×D4—1062no—
600C2×D4—4242no—
601C2×D4—4242no—
602C2×D4—4242no—
603C2×D4—4242no—
604C2×D4—4242no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—1061no—
608C22×C4—1061no—
609C22×C4—1061no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4—1064no—
613C22×C4—1064no—
614C22×C4—1064no—
615C22×C4—4242no—
616C22×C4—4242no—
617C22×C4—4242no—
618C22×C4C2×D21212yes—
619C22×C4C2×D21211yescharacteristic
620C22×C4C2×D21211yescharacteristic
621C22×C4C2×D21211yescharacteristic
622C22×C4C2×D21211yescharacteristic
623C22×C4C2×D21211yescharacteristic
624C22×C4C23×D5312yes—
625C22×C4C23×D5311yescharacteristic
626SD16—1068no—
627SD16—1068no—
628D8—1068no—
629D8—1068no—
630M16—28no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—28no—
634C2×C8#1171994514yes—
635C2×C8#1171994514yes—
636C2×C8C23×D5312yes—
637C2×C8C23×D5312yes—
638C2×C8C23×D5312yes—
639C2×C8C23×D5312yes—
640C4⋊C4—532no—
641C4⋊C4—532no—
642C4⋊C4—532no—
643C4⋊C4—532no—
644C4⋊C4—1061no—
645C4⋊C4—1061no—
646C4⋊C4—1061no—
647C4⋊C4—1061no—
648C4⋊C4—1064no—
649C4⋊C4—1064no—
650C4⋊C4—1064no—
651C4⋊C4—1064no—
652C4⋊C4—1064no—
653C4⋊C4C2×D21214yes—
654C4⋊C4C2×D21214yes—
655C22⋊C4—1064no—
656C22⋊C4—1064no—
657C22⋊C4—1064no—
658C22⋊C4—1064no—
659C22⋊C4—1064no—
660C22⋊C4—1064no—
661C22⋊C4—1064no—
662C22⋊C4—1064no—
663C22⋊C4—1064no—
664C22⋊C4C2×D21214yes—
665C22⋊C4C2×D21214yes—
666C42—1064no—
667C42C2×D21212yes—
668C42C2×D21212yes—
669C42C23×D5312yes—
670C42C23×D5312yes—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—1062no—
675C23—1062no—
676C23—1062no—
677C23—2122no—
678C23—2122no—
679C23—2122no—
680C23—2122no—
681C23—2122no—
682C23—2122no—
683C23—2122no—
684C23—2122no—
685C23—2122no—
686C23C22×D21212yes—
687C23C22×D21211yescharacteristic
688Q8—1062no—
689Q8—1062no—
690Q8—4244no—
691Q8—2122no—
692D4—1062no—
693D4—1062no—
694D4—1062no—
695D4—1062no—
696D4—1062no—
697D4—1062no—
698D4—4244no—
699D4—4244no—
700D4—4244no—
701D4—4244no—
702D4—4244no—
703D4—2122no—
704D4—2122no—
705D4—2122no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—1062no—
717C2×C4—1062no—
718C2×C4—1062no—
719C2×C4—4244no—
720C2×C4—4244no—
721C2×C4—4244no—
722C2×C4—2122no—
723C2×C4—2122no—
724C2×C4—2122no—
725C2×C4—2122no—
726C2×C4—2122no—
727C2×C4C22×D21212yes—
728C2×C4C22×D21212yes—
729C2×C4C22×D21212yes—
730C2×C4C22×D21212yes—
731C2×C4C22×D21212yes—
732C2×C4C22×D21211yescharacteristic
733C2×C4C2×#1171994512yes—
734C2×C4C2×#1171994512yes—
735C2×C4C24×D5311yescharacteristic
736C8—22no—
737C8—22no—
738C8C2×#1171994514yes—
739C8C2×#1171994514yes—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—4244no—
745C22—4244no—
746C22—4244no—
747C22—2122no—
748C22—2122no—
749C22—2122no—
750C22—2122no—
751C22—2122no—
752C22—2122no—
753C22—2122no—
754C22—2122no—
755C22—2122no—
756C22#1681117312yes—
757C22#1681142812yes—
758C22#1681143512yes—
759C22C23×D21211yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—2122no—
766C4—2122no—
767C4—2122no—
768C4—2122no—
769C4—2122no—
770C4#1681117312yes—
771C4C22×#1171994511yescharacteristic
772C4C22×#1171994511yescharacteristic
773C2—42no—
774C2—4242no—
775C2—4242no—
776C2—4242no—
777C2#2028539814yesdirect product factor
778C2C2×#1681117311yescharacteristic
779C2C2×#1681142811yescharacteristic
780C2C2×#1681143511yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#405C2
socleC23×C53C22×D4
hypercenterC2×#405D53
hypocenterC53C2×#3179
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
1. C2×#16811244C2semidirect
2. C2×#16811228C2semidirect
3. #20285398C2direct (N × H)
4. C2×#16811032C2semidirect
5. C2×#16811012C2semidirect
6. C2×#16810978C2semidirect
7. C2×#16810970C2semidirect
8. C2×#16810876C2semidirect
9. C2×#16810869C2semidirect
10. C2×#16810859C2semidirect
11. C2×#16810852C2semidirect
12. C2×#16810736C2semidirect
13. C2×#16810725C2semidirect
14. C2×C4×#11719913C2semidirect
15. C2×C4×D424C2semidirect
16. C2×C53×#405C2semidirect
22. #16811244C22semidirect
24. #16811228C22semidirect
45. #16811032C22semidirect
46. #16811012C22semidirect
47. #16810978C22semidirect
48. #16810970C22semidirect
49. #16810876C22semidirect
50. #16810869C22semidirect
51. #16810859C22semidirect
52. #16810852C22semidirect
53. #16810736C22semidirect
54. #16810725C22semidirect
55. C4×#11719913C22semidirect
56. C4×D424C22semidirect
72. C53×#405C22semidirect
398. C2×#405D53semidirect
400. C2×C53#3179semidirect
462. #405C2×D53semidirect
467. C53C2×#3179semidirect
777. C2#20285398direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112442
C2×#168112282
#202853982
C2×#168110322
C2×#168110122
C2×#168109782
C2×#168109702
C2×#168108762
C2×#168108692
C2×#168108592
C2×#168108522
C2×#168107362
C2×#168107252
C2×C4×#117199132
C2×C4×D4242
C2×C53×#4052
C2×#317953