Finite Group Databasebeta

← C2×#20287154 #28262622

Subgroups — C2×#20287154 #28262622

Order 13568.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811311C211yesmaximal, characteristic, complemented
2C2×#16811276C211yesmaximal, characteristic
3#20287154C2116yesmaximal, direct product factor
4C2×#16810960C211yesmaximal, characteristic, complemented
5C2×#16810949C211yesmaximal, characteristic, complemented
6C2×#16810955C211yesmaximal, characteristic, complemented
7C2×#16810938C211yesmaximal, characteristic, complemented
8C2×#16810915C211yesmaximal, characteristic, complemented
9C2×#16810920C211yesmaximal, characteristic, complemented
10C2×#16810870C211yesmaximal, characteristic, complemented
11C2×#16810853C211yesmaximal, characteristic, complemented
12C2×#16810725C211yesmaximal, characteristic, complemented
13C2×#16810696C211yesmaximal, characteristic, complemented
14C2×#16810662C211yesmaximal, characteristic, complemented
15C2×#107×D53C211yesmaximal, characteristic, complemented
16C2×C53×#501C211yesmaximal, characteristic, complemented
17C22×#11719949—21no—
18C22×#11719913C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20C22×C8×D53C2211yescharacteristic
21#16811311—24no—
22#16811311C2218yescomplemented
23#16811276—24no—
24#16811276C2218yes—
25C2×#13133212—21no—
26C2×#13133208—21no—
27C2×#13133202—21no—
28C2×#13133202—21no—
29C2×#13133202—21no—
30C2×#13133197C2211yescharacteristic
31C2×#13133197C2211yescharacteristic
32C2×#13133193—21no—
33C2×#13133192C2211yescharacteristic
34C2×#13133192C2211yescharacteristic
35C2×C4×Dic106C2211yescharacteristic
36C2×C4×D212C2211yescharacteristic
37C2×C4×D212C2211yescharacteristic
38C2×#13133175—21no—
39C2×#13133175C2211yescharacteristic
40C2×C4⋊C4×D53C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic
42C2×C4⋊C4×D53C2211yescharacteristic
43#16810960C2218yescomplemented
44#16810955C2218yescomplemented
45#16810949C2218yescomplemented
46#16810938C2218yescomplemented
47#16810920C2218yescomplemented
48#16810915C2218yescomplemented
49#16810870C2218yescomplemented
50#16810853C2218yescomplemented
51#16810725C2218yescomplemented
52#16810696C2218yescomplemented
53#16810662C2218yescomplemented
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58#107×D53C2218yescomplemented
59C2×#13133148C2211yescharacteristic
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C2×C4⋊Q8×C53C2211yescharacteristic
70C2×#125×C53C2211yescharacteristic
71C53×#501C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#107×C53C2211yescharacteristic
74C2×#106×C53C2211yescharacteristic
75C2×#106×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C2×#11719949—28no—
78C2×#11719949—48no—
79C22×Dic106C2311yescharacteristic
80C22×D212—21no—
81C22×D212—21no—
82C22×D212D411yescharacteristic
83C22×D212C2311yescharacteristic
84C22×C4×D53—21no—
85C22×C4×D53—21no—
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53C2311yescharacteristic
89C22×C4×D53C2311yescharacteristic
90C2×#11719913—24no—
91C2×#11719913C2314yes—
92C2×#11719912—24no—
93C2×#11719912C2314yes—
94C22×#88322C2311yescharacteristic
95C22×#88322C2311yescharacteristic
96C2×C8×D53—24no—
97C2×C8×D53C2314yes—
98#13133212—28no—
99#13133208—28no—
100#13133202—28no—
101#13133202—28no—
102#13133202—28no—
103#13133197—22no—
104#13133197—22no—
105#13133197C2314yes—
106#13133197C2314yes—
107#13133193—28no—
108#13133192—22no—
109#13133192—22no—
110#13133192C2314yes—
111#13133192C2314yes—
112C4×Dic106—22no—
113C4×Dic106C2314yes—
114C4×D212—22no—
115C4×D212D414yes—
116C4×D212C2314yes—
117C4×D212C2314yes—
118#13133175—28no—
119#13133175—22no—
120#13133175C2314yes—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53D411yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C4⋊C4×D53—22no—
131C4⋊C4×D53—22no—
132C4⋊C4×D53—22no—
133C4⋊C4×D53C2314yes—
134C4⋊C4×D53C2314yes—
135C4⋊C4×D53C2314yes—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921D411yescharacteristic
143C2×#11719921D411yescharacteristic
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146#13133151C2314yes—
147#13133150C2314yes—
148#13133150C2314yes—
149#13133150C2314yes—
150#13133148C2314yes—
151C4⋊#88322C2314yes—
152#13133142C2314yes—
153#13133140C2314yes—
154#13133140C2314yes—
155#13133139C2314yes—
156#13133137C2314yes—
157#13133137C2314yes—
158#13133129C2314yes—
159#13133129C2314yes—
160C22×Q8×C53—21no—
161C22×C8×C53C2311yescharacteristic
162C22×C8×C53C2311yescharacteristic
163C4⋊Q8×C53—22no—
164C4⋊Q8×C53C2314yes—
165#125×C53—22no—
166#125×C53C2314yes—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C42×C53C2311yescharacteristic
175#107×C53C2314yes—
176#107×C53C2314yes—
177#106×C53C2314yes—
178#106×C53C2314yes—
179#97×C53C2314yes—
180C23×D53—21no—
181C23×D53C2×D411yescharacteristic
182C23×D53C2×D411yescharacteristic
183C2×Q8×C53—24no—
184C2×Q8×C53—44no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2411yescharacteristic
192C22×Dic53—21no—
193C22×Dic53—21no—
194C22×Dic53—21no—
195C22×Dic53C2×D411yescharacteristic
196C22×Dic53C2×D411yescharacteristic
197#11719949—432no—
198C2×D212—24no—
199C2×D212—22no—
200C2×D212—22no—
201C2×D212—24no—
202C2×D212—24no—
203C2×D212—21no—
204C2×D212—44no—
205C2×D212—44no—
206C2×D212C2×D414yes—
207C2×D212C2412yes—
208C2×C4×D53—22no—
209C2×C4×D53—22no—
210C2×C4×D53—22no—
211C2×C4×D53—22no—
212C2×C4×D53—24no—
213C2×C4×D53—24no—
214C2×C4×D53—24no—
215C2×C4×D53—24no—
216C2×C4×D53—44no—
217C2×C4×D53—44no—
218C2×C4×D53—44no—
219C2×C4×D53—44no—
220C2×C4×D53C2×D412yes—
221C2×C4×D53C2×D412yes—
222C2×C4×D53C2412yes—
223C2×C4×D53C2412yes—
224C2×Dic106—22no—
225C2×Dic106—22no—
226C2×Dic106—21no—
227C2×Dic106C2412yes—
228C2×C8×C53—22no—
229C2×C8×C53#4114yescomplemented
230C2×C8×C53C2412yes—
231C2×C8×C53C2412yes—
232C4⋊C4×C53—24no—
233C4⋊C4×C53—24no—
234C4⋊C4×C53—24no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53—21no—
238C4⋊C4×C53—21no—
239C4⋊C4×C53C2412yes—
240C4⋊C4×C53C2412yes—
241C4⋊C4×C53C2412yes—
242C4⋊C4×C53C2412yes—
243C42×C53C2×D412yes—
244C42×C53C2412yes—
245#11719921—24no—
246#11719921—24no—
247#11719921—24no—
248#11719921—24no—
249#11719921—24no—
250#11719921—24no—
251#11719921C2×D414yes—
252#11719921C2×D414yes—
253C4⋊Dic53—21no—
254C4⋊Dic53—21no—
255C4⋊Dic53—24no—
256C4⋊Dic53—24no—
257C4⋊Dic53C2×D414yes—
258C4⋊Dic53C2412yes—
259C4⋊Dic53C2412yes—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264C4×Dic53—24no—
265C4×Dic53—24no—
266C2×#88322—22no—
267C2×#88322—22no—
268C2×#88322C2412yes—
269C2×#88322C2412yes—
270#11719913—28no—
271#11719912—28no—
272C8×D53—28no—
273C23×C53C22×D411yescharacteristic
274C22×D53—22no—
275C22×D53—22no—
276C22×D53—22no—
277C22×D53—22no—
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—42no—
281C22×D53—42no—
282C22×D53—42no—
283C22×D53AGL(1,ℤ/8)14yes—
284C22×D53C22×D412yes—
285C22×D53C22×D412yes—
286Q8×C53—48no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—42no—
294C2×C4×C53—42no—
295C2×C4×C53—42no—
296C2×C4×C53—42no—
297C2×C4×C53C22×D412yes—
298C2×C4×C53C22×D412yes—
299C2×C4×C53C22×D411yescharacteristic
300C2×C4×C53C2×#4112yes—
301C2×C4×C532−1+412yes—
302C2×C4×C53C2511yescharacteristic
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—42no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53C22×D412yes—
312C2×Dic53C22×D412yes—
313D212—28no—
314D212—22no—
315D212—22no—
316D212—48no—
317D212—48no—
318D212—42no—
319C4×D53—24no—
320C4×D53—24no—
321C4×D53—22no—
322C4×D53—22no—
323C4×D53—22no—
324C4×D53—22no—
325C4×D53—48no—
326C4×D53—48no—
327C4×D53—48no—
328C4×D53—48no—
329Dic106—22no—
330Dic106—22no—
331Dic106—42no—
332C8×C53—22no—
333C8×C53C2×#4114yescomplemented
334#88322—22no—
335#88322—22no—
336C2×#3343—531nomaximal, Sylow
337C22×C53#54712yes—
338C22×C53C2×AGL(1,ℤ/8)12yes—
339C22×C53#57812yes—
340C22×C53C23×D411yescharacteristic
341C2×D53—28no—
342C2×D53—22no—
343C2×D53—22no—
344C2×D53—22no—
345C2×D53—22no—
346C2×D53—22no—
347C2×D53—44no—
348C2×D53—42no—
349C2×D53—42no—
350C2×D53—42no—
351C2×D53—84no—
352C2×D53C2×AGL(1,ℤ/8)14yes—
353C4×C53—22no—
354C4×C53—22no—
355C4×C53—42no—
356C4×C53—42no—
357C4×C53—42no—
358C4×C53—42no—
359C4×C53#54712yes—
360C4×C53C22×#4111yescharacteristic
361C4×C53C2×2−1+411yescharacteristic
362Dic53—22no—
363Dic53—22no—
364Dic53—42no—
365Dic53—42no—
366Dic53—42no—
367C2×#552—531no—
368C2×#547—531no—
369#3343—5316no—
370C2×#501D5311yescharacteristic, complemented
371C2×#484—531no—
372C2×#482—531no—
373C2×#483—531no—
374C2×#480—531no—
375C2×#477—531no—
376C2×#478—531no—
377C2×#468—531no—
378C2×#465—531no—
379C2×#440—531no—
380C2×#435—531no—
381C2×#428—531no—
382C22×#107—531no—
383C2×C53#334314yescomplemented
384C2×C53C2×#54711yescharacteristic
385C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
386C2×C53C2×#57811yescharacteristic
387D53—24no—
388D53—42no—
389D53—82no—
390C22×#41—1061no—
391C22×SD16—531no—
392C22×M16—531no—
393C23×C8—531no—
394#552—538no—
395#552—1064no—
396#547—538no—
397#547—1064no—
398C2×C4⋊Q8C2×D5311yescharacteristic
399C2×#126—1061no—
400C2×#125—1061no—
401C2×#125C2×D5311yescharacteristic
402C2×#123—1061no—
403C2×#123—1061no—
404C2×#123—1061no—
405C2×C22⋊Q8—531no—
406C2×C22⋊Q8—531no—
407C2×C22⋊Q8—1061no—
408C2×#121—531no—
409C2×#121—531no—
410C2×C4×Q8—531no—
411C2×C4×D4—531no—
412C2×C4×D4—531no—
413C2×#117—531no—
414C2×#117—1061no—
415C22×C4⋊C4—531no—
416C22×C4⋊C4—531no—
417C22×C4⋊C4—531no—
418#501C2×D5318yescomplemented
419#484—538no—
420#483—538no—
421#482—538no—
422#480—538no—
423#478—538no—
424#477—538no—
425#468—538no—
426#465—538no—
427#440—538no—
428#435—538no—
429#428—538no—
430C2×#107—531no—
431C2×#107—531no—
432C2×#107—531no—
433C2×#107—531no—
434C2×#107—538no—
435C2×#107C2×D5311yescharacteristic
436C2×#107C2×D5311yescharacteristic
437C2×#106—531no—
438C2×#106C2×D5311yescharacteristic
439C2×#106C2×D5311yescharacteristic
440C2×C4⋊C8—531no—
441C2×#103—531no—
442C2×#103—531no—
443C2×#103—531no—
444C2×#102—531no—
445C2×#102—531no—
446C2×#102—531no—
447C2×C22⋊C8—531no—
448C2×C22⋊C8—531no—
449C2×#97C2×D5311yescharacteristic
450C53C2×#334311yescharacteristic, complemented, Sylow
451C2×#41—1068no—
452C2×#41—2128no—
453C22×Q8—21no—
454C22×Q8—531no—
455C22×D4—531no—
456C22×D4—531no—
457C22×D4—1061no—
458C22×D4—1061no—
459C23×C4—531no—
460C23×C4—531no—
461C23×C4—1061no—
462C23×C4—1061no—
463C23×C4—1061no—
464C23×C4—1061no—
465C2×SD16—534no—
466C2×SD16—1064no—
467C2×M16—534no—
468C2×M16—1064no—
469C22×C8—531no—
470C22×C8—531no—
471C22×C8—534no—
472C22×C8—1064no—
473C22×C8C22×D5311yescharacteristic
474C22×C8C22×D5311yescharacteristic
475C4⋊Q8—22no—
476C4⋊Q8C22×D5314yes—
477#126—1068no—
478#125—22no—
479#125—1068no—
480#125C22×D5314yes—
481#123—1068no—
482#123—1068no—
483#123—1068no—
484C22⋊Q8—534no—
485C22⋊Q8—534no—
486C22⋊Q8—1062no—
487C22⋊Q8—1062no—
488C22⋊Q8—1068no—
489#121—534no—
490#121—534no—
491#121—1062no—
492#121—1062no—
493C4×Q8—534no—
494C4×Q8—1062no—
495C4×D4—534no—
496C4×D4—534no—
497C4×D4—534no—
498C4×D4—1062no—
499#117—534no—
500#117—1068no—
501#117—1062no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—531no—
506C2×C4⋊C4—531no—
507C2×C4⋊C4—531no—
508C2×C4⋊C4—534no—
509C2×C4⋊C4—534no—
510C2×C4⋊C4—534no—
511C2×C4⋊C4—1062no—
512C2×C4⋊C4—1062no—
513C2×C4⋊C4—1062no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4C22×D5311yescharacteristic
521C2×C4⋊C4C22×D5311yescharacteristic
522C2×C4⋊C4C22×D5311yescharacteristic
523C2×C4⋊C4C22×D5311yescharacteristic
524C2×C22⋊C4—531no—
525C2×C22⋊C4—531no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4—1061no—
528C2×C22⋊C4—1061no—
529C2×C22⋊C4—1061no—
530C2×C22⋊C4—1061no—
531C2×C22⋊C4—1061no—
532C2×C42—1061no—
533C2×C42—1061no—
534C2×C42C22×D5311yescharacteristic
535#107—534no—
536#107—534no—
537#107—534no—
538#107—534no—
539#107C22×D5314yes—
540#107C22×D5314yes—
541#106—534no—
542#106C22×D5314yes—
543#106C22×D5314yes—
544C4⋊C8—534no—
545#103—534no—
546#103—534no—
547#103—534no—
548#102—534no—
549#102—534no—
550#102—534no—
551C22⋊C8—534no—
552C22⋊C8—534no—
553#97C22×D5314yes—
554C24—531no—
555C24—531no—
556C24—1061no—
557#41—21232no—
558C2×Q8—24no—
559C2×Q8—44no—
560C2×Q8—532no—
561C2×Q8—1061no—
562C2×Q8—1062no—
563C2×Q8—1062no—
564C2×D4—534no—
565C2×D4—532no—
566C2×D4—1064no—
567C2×D4—1064no—
568C2×D4—1064no—
569C2×D4—1061no—
570C2×D4—1062no—
571C2×D4—1062no—
572C2×D4—2124no—
573C2×D4—2124no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—531no—
579C22×C4—531no—
580C22×C4—532no—
581C22×C4—532no—
582C22×C4—532no—
583C22×C4—532no—
584C22×C4—1064no—
585C22×C4—1064no—
586C22×C4—1064no—
587C22×C4—1062no—
588C22×C4—1062no—
589C22×C4—1062no—
590C22×C4—1062no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—1061no—
594C22×C4—1064no—
595C22×C4—2124no—
596C22×C4—2124no—
597C22×C4—2124no—
598C22×C4—2124no—
599C22×C4D4×D5311yescharacteristic
600C22×C4D4×D5311yescharacteristic
601C22×C4C23×D5311yescharacteristic
602SD16—1068no—
603M16—1068no—
604C2×C8—22no—
605C2×C8—532no—
606C2×C8—532no—
607C2×C8—1062no—
608C2×C8—1062no—
609C2×C8—1068no—
610C2×C8#1171994914yescomplemented
611C2×C8C23×D5312yes—
612C2×C8C23×D5312yes—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—534no—
621C4⋊C4—532no—
622C4⋊C4—532no—
623C4⋊C4—1064no—
624C4⋊C4—1064no—
625C4⋊C4—1064no—
626C4⋊C4—1064no—
627C4⋊C4—1064no—
628C4⋊C4—1061no—
629C4⋊C4—1061no—
630C4⋊C4—1064no—
631C4⋊C4C23×D5312yes—
632C4⋊C4C23×D5312yes—
633C4⋊C4C23×D5312yes—
634C4⋊C4C23×D5312yes—
635C22⋊C4—534no—
636C22⋊C4—534no—
637C22⋊C4—1064no—
638C22⋊C4—1064no—
639C22⋊C4—1064no—
640C22⋊C4—1064no—
641C22⋊C4—1064no—
642C22⋊C4—1064no—
643C42—1064no—
644C42—1064no—
645C42D4×D5312yes—
646C42C23×D5312yes—
647C23—534no—
648C23—532no—
649C23—532no—
650C23—1062no—
651C23—1062no—
652C23—1062no—
653C23—1062no—
654C23—1062no—
655C23—1062no—
656C23—2122no—
657C23—2122no—
658C23—2122no—
659C23C2×D4×D5311yescharacteristic
660Q8—48no—
661Q8—1062no—
662Q8—1062no—
663Q8—2122no—
664D4—1068no—
665D4—1062no—
666D4—1062no—
667D4—2128no—
668D4—2128no—
669D4—2122no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—532no—
681C2×C4—532no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1064no—
685C2×C4—1064no—
686C2×C4—1062no—
687C2×C4—1062no—
688C2×C4—1062no—
689C2×C4—1062no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—2128no—
694C2×C4—2128no—
695C2×C4—2128no—
696C2×C4—2128no—
697C2×C4—2122no—
698C2×C4—2122no—
699C2×C4—2122no—
700C2×C4C2×D4×D5312yes—
701C2×C4C2×D4×D5312yes—
702C2×C4C2×D4×D5311yescharacteristic
703C2×C4C2×#1171994912yes—
704C2×C4#1313326512yes—
705C2×C4C24×D5311yescharacteristic
706C8—22no—
707C8—1062no—
708C8—1062no—
709C8C2×#1171994914yescomplemented
710C22—534no—
711C22—1062no—
712C22—1068no—
713C22—1062no—
714C22—1062no—
715C22—1062no—
716C22—1062no—
717C22—4244no—
718C22—2122no—
719C22—2122no—
720C22—2122no—
721C22—2124no—
722C22#1681127612yes—
723C22AGL(1,ℤ/8)×D5312yes—
724C22#1681143912yes—
725C22C22×D4×D5311yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—42no—
732C4—1062no—
733C4—1062no—
734C4—2122no—
735C4—2122no—
736C4—2122no—
737C4#1681127612yes—
738C4C22×#1171994911yescharacteristic
739C4C2×#1313326511yescharacteristic
740C2—1064no—
741C2—4242no—
742C2—2122no—
743C2#2028715414yesdirect product factor
744C2C2×#1681127611yescharacteristic
745C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
746C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#501C2
socleC23×C53C22×D4
prime radicalC2×#16811276C2
hypercenterC2×#501D53
hypocenterC53C2×#3343
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#16811311C2semidirect
3. #20287154C2direct (N × H)
4. C2×#16810960C2semidirect
5. C2×#16810949C2semidirect
6. C2×#16810955C2semidirect
7. C2×#16810938C2semidirect
8. C2×#16810915C2semidirect
9. C2×#16810920C2semidirect
10. C2×#16810870C2semidirect
11. C2×#16810853C2semidirect
12. C2×#16810725C2semidirect
13. C2×#16810696C2semidirect
14. C2×#16810662C2semidirect
15. C2×#107×D53C2semidirect
16. C2×C53×#501C2semidirect
22. #16811311C22semidirect
43. #16810960C22semidirect
44. #16810955C22semidirect
45. #16810949C22semidirect
46. #16810938C22semidirect
47. #16810920C22semidirect
48. #16810915C22semidirect
49. #16810870C22semidirect
50. #16810853C22semidirect
51. #16810725C22semidirect
52. #16810696C22semidirect
53. #16810662C22semidirect
58. #107×D53C22semidirect
71. C53×#501C22semidirect
229. C2×C8×C53#41semidirect
333. C8×C53C2×#41semidirect
370. C2×#501D53semidirect
383. C2×C53#3343semidirect
418. #501C2×D53semidirect
450. C53C2×#3343semidirect
610. C2×C8#11719949semidirect
709. C8C2×#11719949semidirect
743. C2#20287154direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113112
C2×#168112762
#202871542
C2×#168109602
C2×#168109492
C2×#168109552
C2×#168109382
C2×#168109152
C2×#168109202
C2×#168108702
C2×#168108532
C2×#168107252
C2×#168106962
C2×#168106622
C2×#107×D532
C2×C53×#5012
C2×#334353