Finite Group Databasebeta

← C2×#20286723 #28260796

Subgroups — C2×#20286723 #28260796

Order 13568.

2242 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811319C211yesmaximal, characteristic, complemented
2C2×#16811294C211yesmaximal, characteristic, complemented
3#20286723C2116yesmaximal, direct product factor
4C2×#16810988C211yesmaximal, characteristic, complemented
5C2×#16810948C211yesmaximal, characteristic, complemented
6C2×#16810937C211yesmaximal, characteristic, complemented
7C2×#16810931C211yesmaximal, characteristic, complemented
8C2×#16810876C211yesmaximal, characteristic, complemented
9C2×#16810859C211yesmaximal, characteristic, complemented
10C2×#16810819C211yesmaximal, characteristic, complemented
11C2×#16810770C211yesmaximal, characteristic, complemented
12C2×#16810770C211yesmaximal, characteristic, complemented
13C2×#16810725C211yesmaximal, characteristic, complemented
14C2×#16810625C211yesmaximal, characteristic, complemented
15C2×#16810620C211yesmaximal, characteristic, complemented
16C2×C53×#435C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×#11719945C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×D424C2211yescharacteristic
21C22×D424C2211yescharacteristic
22#16811319—24no—
23#16811319C2218yescomplemented
24#16811294—24no—
25#16811294C2218yescomplemented
26C2×#13133214C2211yescharacteristic
27C2×#13133213—21no—
28C2×#13133212—21no—
29C2×#13133209C2211yescharacteristic
30C2×#13133199—21no—
31C2×#13133191C2211yescharacteristic
32C2×#13133191C2211yescharacteristic
33C2×#13133191C2211yescharacteristic
34C2×#13133191C2211yescharacteristic
35C2×#13133190—21no—
36C2×#13133190—21no—
37C2×#13133189—21no—
38C2×C4×Dic106C2211yescharacteristic
39C2×C4×D212C2211yescharacteristic
40C2×#13133179—21no—
41C2×#13133177—21no—
42C2×#13133176C2211yescharacteristic
43C22×C4⋊Dic53C2211yescharacteristic
44#16810988C2218yescomplemented
45#16810948C2218yescomplemented
46#16810937C2218yescomplemented
47#16810931C2218yescomplemented
48#16810876C2218yescomplemented
49#16810859C2218yescomplemented
50#16810819C2218yescomplemented
51#16810770C2218yescomplemented
52#16810770C2218yescomplemented
53#16810725C2218yescomplemented
54C2×#13133151C2211yescharacteristic
55C2×#13133151C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57#16810625C2218yescomplemented
58#16810620C2218yescomplemented
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133139C2211yescharacteristic
67C2×#13133139C2211yescharacteristic
68C2×#13133139C2211yescharacteristic
69C22×M16×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#435C2218yescomplemented
73C2×C4⋊C8×C53C2211yescharacteristic
74C2×C22⋊C8×C53C2211yescharacteristic
75C2×C22⋊C8×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—22no—
79C2×#11719945—24no—
80C2×#11719945—24no—
81C2×#11719945—42no—
82C2×#11719945—42no—
83C2×#11719945C2314yes—
84C2×#11719945C2314yes—
85C22×Dic106C2311yescharacteristic
86C22×D212—21no—
87C22×D212—21no—
88C22×D212C2311yescharacteristic
89C22×D212C2311yescharacteristic
90C22×D212C2311yescharacteristic
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C22×C22⋊D53—21no—
94C22×C22⋊D53—21no—
95C22×C22⋊D53—21no—
96C22×C22⋊D53—21no—
97C23×Dic53—21no—
98C22×C4×D53—21no—
99C22×C4×D53—21no—
100C22×C4×D53—21no—
101C2×#11719913—24no—
102C2×#11719913C2314yes—
103C2×D424—42no—
104C2×D424—42no—
105C2×D424C2314yes—
106C2×D424C2314yes—
107#13133214—22no—
108#13133214C2314yes—
109#13133213—28no—
110#13133212—28no—
111#13133209—22no—
112#13133209C2314yes—
113#13133199—28no—
114#13133191—22no—
115#13133191—22no—
116#13133191—22no—
117#13133191—22no—
118#13133191C2314yes—
119#13133191C2314yes—
120#13133191C2314yes—
121#13133191C2314yes—
122#13133190—28no—
123#13133190—28no—
124#13133189—28no—
125C4×Dic106—22no—
126C4×Dic106C2314yes—
127C4×D212—22no—
128C4×D212C2314yes—
129#13133179—28no—
130#13133177—28no—
131#13133176—22no—
132#13133176C2314yes—
133C2×C4⋊Dic53—22no—
134C2×C4⋊Dic53—21no—
135C2×C4⋊Dic53C2314yes—
136C2×C4⋊Dic53C2311yescharacteristic
137C2×C4⋊Dic53C2311yescharacteristic
138C2×C4⋊Dic53C2311yescharacteristic
139C2×C4⋊Dic53C2311yescharacteristic
140C2×#11719919—21no—
141C2×#11719919—21no—
142C2×#11719919—21no—
143C2×C22⋊Dic53—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×C4×Dic53—21no—
150C2×C4×Dic53—21no—
151#13133151C2314yes—
152#13133151C2314yes—
153#13133149C2314yes—
154#13133142C2314yes—
155#13133142C2314yes—
156#13133142C2314yes—
157#13133139C2314yes—
158#13133139C2314yes—
159#13133139C2314yes—
160#13133139C2314yes—
161#13133139C2314yes—
162#13133139C2314yes—
163#13133139C2314yes—
164C22×D4×C53D411yescharacteristic
165C23×C4×C53C2311yescharacteristic
166C23×C4×C53C2311yescharacteristic
167C2×M16×C53—42no—
168C2×M16×C53C2314yes—
169C22×C8×C53—42no—
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172C22×C8×C53C2311yescharacteristic
173C22×C8×C53C2311yescharacteristic
174C22×C8×C53C2314yes—
175C4×D4×C53D414yes—
176C4×D4×C53C2314yes—
177C2×C4⋊C4×C53D411yescharacteristic
178C2×C22⋊C4×C53D411yescharacteristic
179C2×C22⋊C4×C53D411yescharacteristic
180C2×C42×C53C2311yescharacteristic
181C4⋊C8×C53C2314yes—
182C22⋊C8×C53C2314yes—
183C22⋊C8×C53C2314yes—
184#97×C53C2314yes—
185C24×C53C2×D411yescharacteristic
186C24×C53C2×D411yescharacteristic
187C23×D53—21no—
188C23×D53—21no—
189C23×D53—21no—
190C2×D4×C53—42no—
191C2×D4×C53C2×D414yes—
192C22×C4×C53—22no—
193C22×C4×C53—22no—
194C22×C4×C53—22no—
195C22×C4×C53—22no—
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D412yes—
201C22×C4×C53C2×D412yes—
202C22×C4×C53C2412yes—
203C22×C4×C53C2412yes—
204C22×C4×C53C2411yescharacteristic
205C2×C22⋊D53—24no—
206C2×C22⋊D53—24no—
207C2×C22⋊D53—24no—
208C2×C22⋊D53—24no—
209C2×C22⋊D53—24no—
210C2×C22⋊D53—24no—
211C2×C22⋊D53—44no—
212C2×C22⋊D53—44no—
213C2×C22⋊D53—44no—
214C2×C22⋊D53—82no—
215C2×C22⋊D53—82no—
216C2×C22⋊D53—82no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—24no—
223C22×Dic53—82no—
224#11719945—28no—
225#11719945—28no—
226#11719945—44no—
227#11719945—44no—
228#11719945—48no—
229#11719945—48no—
230C2×D212—22no—
231C2×D212—22no—
232C2×D212—22no—
233C2×D212—22no—
234C2×D212—22no—
235C2×D212—22no—
236C2×D212—24no—
237C2×D212—21no—
238C2×D212—21no—
239C2×D212—21no—
240C2×D212—24no—
241C2×D212—44no—
242C2×D212—82no—
243C2×D212C2412yes—
244C2×D212C2412yes—
245C2×D212C2412yes—
246C2×C4×D53—24no—
247C2×C4×D53—24no—
248C2×C4×D53—24no—
249C2×C4×D53—44no—
250C2×C4×D53—44no—
251C2×C4×D53—82no—
252C2×Dic106—21no—
253C2×Dic106—22no—
254C2×Dic106#4114yes—
255C2×Dic106C2412yes—
256M16×C53—44no—
257C2×C8×C53—22no—
258C2×C8×C53—22no—
259C2×C8×C53—22no—
260C2×C8×C53—22no—
261C2×C8×C53—44no—
262C2×C8×C53C2412yes—
263C2×C8×C53C2412yes—
264C2×C8×C53C2412yes—
265C2×C8×C53C2412yes—
266C4⋊C4×C53C2×D414yes—
267C22⋊C4×C53C2×D414yes—
268C22⋊C4×C53C2×D414yes—
269C42×C53C2×D412yes—
270C42×C53C2412yes—
271C22⋊Dic53—24no—
272#11719921—24no—
273#11719921—24no—
274#11719921—24no—
275#11719921—24no—
276#11719921—24no—
277C4⋊Dic53—21no—
278C4⋊Dic53—21no—
279C4⋊Dic53—24no—
280C4⋊Dic53—21no—
281C4⋊Dic53—21no—
282C4⋊Dic53C2412yes—
283C4⋊Dic53C2412yes—
284C4⋊Dic53C2412yes—
285C4⋊Dic53C2412yes—
286#11719919—24no—
287#11719919—24no—
288#11719919—24no—
289C4×Dic53—24no—
290C4×Dic53—24no—
291D424—44no—
292D424—44no—
293#11719913—28no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53C22×D412yes—
301C23×C53C22×D412yes—
302C23×C53C22×D411yescharacteristic
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—22no—
306C22×D53—42no—
307C22×D53—42no—
308C22×D53—42no—
309C22×D53—42no—
310C22×D53—42no—
311C22×D53—42no—
312C22×D53—42no—
313C22×D53—42no—
314C22×D53—42no—
315D4×C53—44no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—24no—
321C2×C4×C53—24no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53C22×D412yes—
327C2×C4×C53C22×D412yes—
328C2×C4×C53C22×D412yes—
329C2×C4×C53C22×D412yes—
330C2×C4×C53C22×D411yescharacteristic
331C2×C4×C53C2×#4112yes—
332C2×C4×C53H(5,𝔽2)12yes—
333C2×C4×C53C2511yescharacteristic
334C22⋊D53—48no—
335C22⋊D53—48no—
336C22⋊D53—48no—
337C22⋊D53—84no—
338C22⋊D53—84no—
339C22⋊D53—84no—
340C2×Dic53—24no—
341C2×Dic53—22no—
342C2×Dic53—22no—
343C2×Dic53—22no—
344C2×Dic53—22no—
345C2×Dic53—22no—
346C2×Dic53—42no—
347C2×Dic53—42no—
348C2×Dic53—42no—
349C2×Dic53—42no—
350C2×Dic53—84no—
351D212—22no—
352D212—22no—
353D212—22no—
354D212—22no—
355D212—22no—
356D212—22no—
357D212—48no—
358D212—42no—
359D212—42no—
360D212—42no—
361D212—84no—
362C4×D53—48no—
363C4×D53—48no—
364C4×D53—84no—
365Dic106—24no—
366Dic106—22no—
367Dic106C2×#4114yes—
368C8×C53—22no—
369C8×C53—22no—
370C8×C53—22no—
371C8×C53—22no—
372C2×#3309—531nomaximal, Sylow
373C22×C53—22no—
374C22×C53—22no—
375C22×C53—22no—
376C22×C53—22no—
377C22×C53—22no—
378C22×C53—22no—
379C22×C53—44no—
380C22×C53—44no—
381C22×C53#54612yes—
382C22×C53#57512yes—
383C22×C53#57612yes—
384C22×C53C23×D411yescharacteristic
385C2×D53—42no—
386C2×D53—42no—
387C2×D53—42no—
388C2×D53—42no—
389C2×D53—42no—
390C2×D53—42no—
391C2×D53—42no—
392C2×D53—42no—
393C2×D53—42no—
394C2×D53—84no—
395C2×D53—84no—
396C2×D53—84no—
397C4×C53—22no—
398C4×C53—22no—
399C4×C53—22no—
400C4×C53—22no—
401C4×C53#54612yes—
402C4×C53C22×#4111yescharacteristic
403C4×C53C2×H(5,𝔽2)11yescharacteristic
404Dic53—24no—
405Dic53—42no—
406Dic53—42no—
407Dic53—42no—
408Dic53—42no—
409C2×#553—531no—
410C2×#550—531no—
411#3309—5316no—
412C2×#490—531no—
413C2×#482—531no—
414C2×#480—531no—
415C2×#479—531no—
416C2×#469—531no—
417C2×#466—531no—
418C2×#459—531no—
419C2×#449—531no—
420C2×#449—531no—
421C2×#440—531no—
422C2×#435D5311yescharacteristic, complemented
423C2×#417—531no—
424C2×#416—531no—
425C2×C53—42no—
426C2×C53—42no—
427C2×C53#330914yescomplemented
428C2×C53C2×#54611yescharacteristic
429C2×C53C2×#57511yescharacteristic
430C2×C53C2×#57611yescharacteristic
431D53—82no—
432D53—82no—
433D53—82no—
434C22×#41—531no—
435C22×#41—531no—
436C22×SD16—531no—
437C22×D8—531no—
438C22×D8—531no—
439C22×M16C2×D5311yescharacteristic
440C23×C8C2×D5311yescharacteristic
441#553—538no—
442#553—1064no—
443#550—538no—
444#550—1064no—
445C2×#127—531no—
446C2×#127—1061no—
447C2×#126—1061no—
448C2×#125—531no—
449C2×#123—1061no—
450C2×#121—531no—
451C2×#121—531no—
452C2×#121—531no—
453C2×#121—531no—
454C2×#121—1061no—
455C2×#121—1061no—
456C2×#121—1061no—
457C2×C4×Q8—531no—
458C2×C4×D4—531no—
459C2×C4×D4—1061no—
460C2×C4×D4—1061no—
461C2×C4×D4C2×D5311yescharacteristic
462C2×#117—531no—
463C22×C4⋊C4—531no—
464#490—538no—
465#482—538no—
466#480—538no—
467#479—538no—
468#469—538no—
469#466—538no—
470#459—538no—
471#449—538no—
472#449—538no—
473#440—538no—
474#435C2×D5318yescomplemented
475C2×#107—531no—
476C2×#107—531no—
477C2×#106—531no—
478C2×C4⋊C8C2×D5311yescharacteristic
479#417—538no—
480#416—538no—
481C2×#103—531no—
482C2×#103—531no—
483C2×#103—531no—
484C2×#102—531no—
485C2×#102—531no—
486C2×#102—531no—
487C2×#102—531no—
488C2×#102—531no—
489C2×#102—531no—
490C2×#102—531no—
491C2×C22⋊C8C2×D5311yescharacteristic
492C2×C22⋊C8C2×D5311yescharacteristic
493C2×#97C2×D5311yescharacteristic
494C53C2×#330911yescharacteristic, complemented, Sylow
495C2×#41—534no—
496C2×#41—534no—
497C2×#41—1064no—
498C2×#41—1064no—
499C2×#41—1062no—
500C2×#41—1062no—
501C2×#41—2122no—
502C2×#41—2122no—
503C22×Q8—531no—
504C22×D4—531no—
505C22×D4—531no—
506C22×D4—531no—
507C22×D4—1061no—
508C22×D4—1061no—
509C22×D4—1061no—
510C22×D4—1061no—
511C22×D4—1061no—
512C22×D4—1061no—
513C22×D4—1061no—
514C22×D4—1061no—
515C22×D4D21211yescharacteristic
516C23×C4—1061no—
517C23×C4—1061no—
518C23×C4—1061no—
519C23×C4—1061no—
520C23×C4C22×D5311yescharacteristic
521C23×C4C22×D5311yescharacteristic
522C2×SD16—534no—
523C2×SD16—1064no—
524C2×D8—534no—
525C2×D8—534no—
526C2×D8—2122no—
527C2×D8—2122no—
528C2×M16—42no—
529C2×M16C22×D5314yes—
530C22×C8—42no—
531C22×C8C22×D5311yescharacteristic
532C22×C8C22×D5311yescharacteristic
533C22×C8C22×D5311yescharacteristic
534C22×C8C22×D5311yescharacteristic
535C22×C8C22×D5314yes—
536#127—534no—
537#127—1068no—
538#127—1062no—
539#126—1068no—
540#125—534no—
541#125—1062no—
542#123—1068no—
543#121—534no—
544#121—534no—
545#121—534no—
546#121—534no—
547#121—1068no—
548#121—1062no—
549#121—1062no—
550#121—1062no—
551#121—1062no—
552#121—1068no—
553#121—1068no—
554C4×Q8—534no—
555C4×Q8—1062no—
556C4×D4—534no—
557C4×D4—1068no—
558C4×D4—1068no—
559C4×D4—1062no—
560C4×D4D21214yes—
561C4×D4C22×D5314yes—
562#117—534no—
563#117—1062no—
564C2×C4⋊C4—531no—
565C2×C4⋊C4—531no—
566C2×C4⋊C4—534no—
567C2×C4⋊C4—531no—
568C2×C4⋊C4—531no—
569C2×C4⋊C4—1061no—
570C2×C4⋊C4—1062no—
571C2×C4⋊C4—1061no—
572C2×C4⋊C4—1061no—
573C2×C4⋊C4—1061no—
574C2×C4⋊C4D21211yescharacteristic
575C2×C22⋊C4—1061no—
576C2×C22⋊C4—1061no—
577C2×C22⋊C4—1061no—
578C2×C22⋊C4—1061no—
579C2×C22⋊C4—1061no—
580C2×C22⋊C4—1061no—
581C2×C22⋊C4D21211yescharacteristic
582C2×C22⋊C4D21211yescharacteristic
583C2×C42—1061no—
584C2×C42—1061no—
585C2×C42C22×D5311yescharacteristic
586#107—534no—
587#107—534no—
588#106—534no—
589C4⋊C8C22×D5314yes—
590#103—534no—
591#103—534no—
592#103—534no—
593#102—534no—
594#102—534no—
595#102—534no—
596#102—534no—
597#102—534no—
598#102—534no—
599#102—534no—
600C22⋊C8C22×D5314yes—
601C22⋊C8C22×D5314yes—
602#97C22×D5314yes—
603C24—1061no—
604C24—1061no—
605C24—1061no—
606C24C2×D21211yescharacteristic
607C24C2×D21211yescharacteristic
608#41—1068no—
609#41—1068no—
610#41—2124no—
611#41—2124no—
612#41—2128no—
613#41—2128no—
614C2×Q8—534no—
615C2×Q8—532no—
616C2×Q8—1061no—
617C2×Q8—1062no—
618C2×D4—42no—
619C2×D4—532no—
620C2×D4—532no—
621C2×D4—532no—
622C2×D4—1064no—
623C2×D4—1064no—
624C2×D4—1064no—
625C2×D4—1064no—
626C2×D4—1064no—
627C2×D4—1064no—
628C2×D4—1064no—
629C2×D4—1061no—
630C2×D4—1064no—
631C2×D4—1061no—
632C2×D4—1061no—
633C2×D4—1062no—
634C2×D4—1062no—
635C2×D4—1062no—
636C2×D4—1062no—
637C2×D4—1062no—
638C2×D4—1062no—
639C2×D4—4242no—
640C2×D4—4242no—
641C2×D4—4242no—
642C2×D4—4242no—
643C2×D4—2124no—
644C2×D4—2124no—
645C2×D4—2124no—
646C2×D4—2124no—
647C2×D4C2×D21214yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—1061no—
653C22×C4—1064no—
654C22×C4—1061no—
655C22×C4—1061no—
656C22×C4—1061no—
657C22×C4—1061no—
658C22×C4—1064no—
659C22×C4—1064no—
660C22×C4—1064no—
661C22×C4—4242no—
662C22×C4—4242no—
663C22×C4—2124no—
664C22×C4—2124no—
665C22×C4C2×D21212yes—
666C22×C4C2×D21212yes—
667C22×C4C2×D21211yescharacteristic
668C22×C4C2×D21211yescharacteristic
669C22×C4C2×D21211yescharacteristic
670C22×C4C2×D21211yescharacteristic
671C22×C4C23×D5312yes—
672C22×C4C23×D5312yes—
673C22×C4C23×D5311yescharacteristic
674SD16—1068no—
675D8—2124no—
676D8—2124no—
677M16—44no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—44no—
683C2×C8C23×D5312yes—
684C2×C8C23×D5312yes—
685C2×C8C23×D5312yes—
686C2×C8C23×D5312yes—
687C4⋊C4—532no—
688C4⋊C4—532no—
689C4⋊C4—532no—
690C4⋊C4—532no—
691C4⋊C4—1061no—
692C4⋊C4—1061no—
693C4⋊C4—1064no—
694C4⋊C4—1061no—
695C4⋊C4—1061no—
696C4⋊C4—1064no—
697C4⋊C4—1064no—
698C4⋊C4—1064no—
699C4⋊C4C2×D21214yes—
700C22⋊C4—1064no—
701C22⋊C4—1064no—
702C22⋊C4—1064no—
703C22⋊C4—1064no—
704C22⋊C4—1064no—
705C22⋊C4—1064no—
706C22⋊C4C2×D21214yes—
707C22⋊C4C2×D21214yes—
708C42—1064no—
709C42—1064no—
710C42C2×D21212yes—
711C42C23×D5312yes—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—1062no—
719C23—1062no—
720C23—1062no—
721C23—2122no—
722C23—2122no—
723C23—2122no—
724C23—2122no—
725C23—2122no—
726C23—2122no—
727C23—2122no—
728C23—2122no—
729C23—2122no—
730C23C22×D21212yes—
731C23C22×D21212yes—
732C23C22×D21211yescharacteristic
733Q8—534no—
734Q8—1064no—
735Q8—1062no—
736D4—44no—
737D4—1062no—
738D4—1062no—
739D4—1062no—
740D4—1062no—
741D4—1062no—
742D4—1062no—
743D4—4244no—
744D4—4244no—
745D4—4244no—
746D4—4244no—
747D4—2128no—
748D4—2128no—
749D4—2128no—
750D4—2128no—
751D4—2122no—
752D4—2122no—
753D4—2122no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—1064no—
765C2×C4—1062no—
766C2×C4—1062no—
767C2×C4—1062no—
768C2×C4—1062no—
769C2×C4—1062no—
770C2×C4—4244no—
771C2×C4—4244no—
772C2×C4—2128no—
773C2×C4—2128no—
774C2×C4—2122no—
775C2×C4—2122no—
776C2×C4—2122no—
777C2×C4—2122no—
778C2×C4C22×D21212yes—
779C2×C4C22×D21212yes—
780C2×C4C22×D21212yes—
781C2×C4C22×D21212yes—
782C2×C4C22×D21211yescharacteristic
783C2×C4#41×D5312yes—
784C2×C4#1313326212yes—
785C2×C4C24×D5311yescharacteristic
786C8—22no—
787C8—22no—
788C8—22no—
789C8—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—44no—
798C22—4244no—
799C22—4244no—
800C22—4244no—
801C22—2122no—
802C22—2122no—
803C22—2122no—
804C22—2122no—
805C22—2122no—
806C22—2122no—
807C22—2122no—
808C22—2122no—
809C22—2122no—
810C22#1681126812yes—
811C22#1681142312yes—
812C22#1681142812yes—
813C22C23×D21211yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—1064no—
819C4—2122no—
820C4—2122no—
821C4—2122no—
822C4—2122no—
823C4#1681126812yes—
824C4C2×#41×D5311yescharacteristic
825C4C2×#1313326211yescharacteristic
826C2—42no—
827C2—42no—
828C2—4242no—
829C2—4242no—
830C2—4242no—
831C2#2028672314yesdirect product factor
832C2C2×#1681126811yescharacteristic
833C2C2×#1681142311yescharacteristic
834C2C2×#1681142811yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#435C2
socleC23×C53C22×D4
hypercenterC2×#435D53
hypocenterC53C2×#3309
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16811319C2semidirect
2. C2×#16811294C2semidirect
3. #20286723C2direct (N × H)
4. C2×#16810988C2semidirect
5. C2×#16810948C2semidirect
6. C2×#16810937C2semidirect
7. C2×#16810931C2semidirect
8. C2×#16810876C2semidirect
9. C2×#16810859C2semidirect
10. C2×#16810819C2semidirect
11. C2×#16810770C2semidirect
12. C2×#16810770C2semidirect
13. C2×#16810725C2semidirect
14. C2×#16810625C2semidirect
15. C2×#16810620C2semidirect
16. C2×C53×#435C2semidirect
23. #16811319C22semidirect
25. #16811294C22semidirect
44. #16810988C22semidirect
45. #16810948C22semidirect
46. #16810937C22semidirect
47. #16810931C22semidirect
48. #16810876C22semidirect
49. #16810859C22semidirect
50. #16810819C22semidirect
51. #16810770C22semidirect
52. #16810770C22semidirect
53. #16810725C22semidirect
57. #16810625C22semidirect
58. #16810620C22semidirect
72. C53×#435C22semidirect
422. C2×#435D53semidirect
427. C2×C53#3309semidirect
474. #435C2×D53semidirect
494. C53C2×#3309semidirect
831. C2#20286723direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113192
C2×#168112942
#202867232
C2×#168109882
C2×#168109482
C2×#168109372
C2×#168109312
C2×#168108762
C2×#168108592
C2×#168108192
C2×#168107702
C2×#168107252
C2×#168106252
C2×#168106202
C2×C53×#4352
C2×#330953