Finite Group Databasebeta

← C2×#20287162 #28262630

Subgroups — C2×#20287162 #28262630

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×#16811278C211yesmaximal, characteristic
3#20287162C2116yesmaximal, direct product factor
4C2×#16811033C211yesmaximal, characteristic, complemented
5C2×#16810960C211yesmaximal, characteristic, complemented
6C2×#16810945C211yesmaximal, characteristic, complemented
7C2×#16810955C211yesmaximal, characteristic, complemented
8C2×#16810935C211yesmaximal, characteristic, complemented
9C2×#16810919C211yesmaximal, characteristic, complemented
10C2×#16810868C211yesmaximal, characteristic, complemented
11C2×#16810851C211yesmaximal, characteristic, complemented
12C2×#16810723C211yesmaximal, characteristic, complemented
13C2×#16810693C211yesmaximal, characteristic, complemented
14C2×#16810662C211yesmaximal, characteristic, complemented
15C2×#107×D53C211yesmaximal, characteristic, complemented
16C2×C53×#478C211yesmaximal, characteristic, complemented
17C22×#11719945—21no—
18C22×#11719923C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20C22×C8×D53C2211yescharacteristic
21#16811311—24no—
22#16811311C2218yescomplemented
23#16811278—24no—
24#16811278C2218yes—
25C2×#13133217C2211yescharacteristic
26C2×#13133212—21no—
27C2×#13133208—21no—
28C2×#13133202—21no—
29C2×#13133199—21no—
30C2×#13133199—21no—
31C2×#13133197C2211yescharacteristic
32C2×#13133197C2211yescharacteristic
33C2×#13133196—21no—
34C2×#13133188C2211yescharacteristic
35C2×#13133188C2211yescharacteristic
36C2×C4×Dic106C2211yescharacteristic
37C2×C4×D212C2211yescharacteristic
38C2×#13133175—21no—
39C2×#13133175C2211yescharacteristic
40C2×C4⋊C4×D53C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic
42C2×C4⋊C4×D53C2211yescharacteristic
43#16811033C2218yescomplemented
44#16810960C2218yescomplemented
45#16810955C2218yescomplemented
46#16810945C2218yescomplemented
47#16810935C2218yescomplemented
48#16810919C2218yescomplemented
49#16810868C2218yescomplemented
50#16810851C2218yescomplemented
51#16810723C2218yescomplemented
52#16810693C2218yescomplemented
53#16810662C2218yescomplemented
54C2×#13133151C2211yescharacteristic
55C2×#13133151C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58C2×#13133150C2211yescharacteristic
59#107×D53C2218yescomplemented
60C2×#13133148C2211yescharacteristic
61C2×#13133148C2211yescharacteristic
62C2×#13133142C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133128C2211yescharacteristic
69C2×#125×C53C2211yescharacteristic
70C2×C4×D4×C53C2211yescharacteristic
71C53×#478C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C2×#11719945—28no—
78C2×#11719945—48no—
79C22×Dic106—21no—
80C22×Dic106C2311yescharacteristic
81C22×D212D411yescharacteristic
82C22×C22⋊D53—21no—
83C22×C22⋊D53—21no—
84C22×C4×D53—21no—
85C22×C4×D53—21no—
86C22×C4×D53—21no—
87C22×C4×D53C2311yescharacteristic
88C22×C4×D53C2311yescharacteristic
89C2×#11719923—24no—
90C2×#11719923C2314yes—
91C2×#11719912—24no—
92C2×#11719912C2314yes—
93C22×#88322C2311yescharacteristic
94C22×#88322C2311yescharacteristic
95C2×C8×D53—24no—
96C2×C8×D53C2314yes—
97#13133217—22no—
98#13133217C2314yes—
99#13133212—28no—
100#13133208—28no—
101#13133202—28no—
102#13133199—28no—
103#13133199—28no—
104#13133197—22no—
105#13133197—22no—
106#13133197C2314yes—
107#13133197C2314yes—
108#13133196—28no—
109#13133188—22no—
110#13133188—22no—
111#13133188C2314yes—
112#13133188C2314yes—
113C4×Dic106—22no—
114C4×Dic106C2314yes—
115C4×D212D414yes—
116C4×D212C2314yes—
117#13133175—28no—
118#13133175—22no—
119#13133175C2314yes—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53D411yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C4⋊C4×D53—22no—
132C4⋊C4×D53—22no—
133C4⋊C4×D53—22no—
134C4⋊C4×D53C2314yes—
135C4⋊C4×D53C2314yes—
136C4⋊C4×D53C2314yes—
137C2×C22⋊Dic53—21no—
138C2×C22⋊Dic53—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#13133151C2314yes—
148#13133150C2314yes—
149#13133150C2314yes—
150#13133150C2314yes—
151#13133148C2314yes—
152#13133148C2314yes—
153#13133142C2314yes—
154#13133142C2314yes—
155#13133140C2314yes—
156#13133138C2314yes—
157#13133129C2314yes—
158#13133129C2314yes—
159#13133128C2314yes—
160C22×D4×C53C2311yescharacteristic
161C23×C4×C53—21no—
162C22×C8×C53C2311yescharacteristic
163C22×C8×C53C2311yescharacteristic
164#125×C53—22no—
165#125×C53C2314yes—
166C4×D4×C53—22no—
167C4×D4×C53C2314yes—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C22⋊C4×C53—21no—
174C2×C42×C53C2311yescharacteristic
175#107×C53C2314yes—
176#106×C53C2314yes—
177C4⋊C8×C53C2314yes—
178#102×C53C2314yes—
179#102×C53C2314yes—
180C24×C53—21no—
181C23×D53C2×D411yescharacteristic
182C23×D53C2×D411yescharacteristic
183C2×D4×C53—21no—
184C2×D4×C53—22no—
185C2×D4×C53—22no—
186C2×D4×C53C2412yes—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—24no—
191C22×C4×C53—44no—
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2411yescharacteristic
195C2×C22⋊D53—24no—
196C2×C22⋊D53—24no—
197C2×C22⋊D53—44no—
198C2×C22⋊D53—44no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53C2×D411yescharacteristic
204C22×Dic53C2×D411yescharacteristic
205#11719945—432no—
206C2×D212—24no—
207C2×D212C2×D414yes—
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—44no—
216C2×C4×D53—44no—
217C2×C4×D53—44no—
218C2×C4×D53C2×D412yes—
219C2×C4×D53C2×D412yes—
220C2×C4×D53C2412yes—
221C2×C4×D53C2412yes—
222C2×Dic106—22no—
223C2×Dic106—22no—
224C2×Dic106—21no—
225C2×Dic106—24no—
226C2×Dic106—44no—
227C2×Dic106C2412yes—
228C2×C8×C53—22no—
229C2×C8×C53—22no—
230C2×C8×C53C2412yes—
231C2×C8×C53C2412yes—
232C4⋊C4×C53—24no—
233C4⋊C4×C53—24no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53C2412yes—
238C4⋊C4×C53C2412yes—
239C4⋊C4×C53C2412yes—
240C22⋊C4×C53—24no—
241C42×C53C2×D412yes—
242C42×C53C2412yes—
243C22⋊Dic53—24no—
244C22⋊Dic53—24no—
245#11719923—28no—
246#11719921—24no—
247#11719921—24no—
248#11719921—24no—
249#11719921C2×D414yes—
250#11719921C2×D414yes—
251C4⋊Dic53—21no—
252C4⋊Dic53—21no—
253C4⋊Dic53—21no—
254C4⋊Dic53—24no—
255C4⋊Dic53—24no—
256C4⋊Dic53—24no—
257C4⋊Dic53C2×D414yes—
258C4⋊Dic53C2412yes—
259C4⋊Dic53C2412yes—
260C4⋊Dic53C2412yes—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264#11719919—24no—
265C4×Dic53—24no—
266C4×Dic53—24no—
267C2×#88322—22no—
268C2×#88322#4114yescomplemented
269C2×#88322C2412yes—
270C2×#88322C2412yes—
271#11719912—28no—
272C8×D53—28no—
273C23×C53—22no—
274C23×C53—42no—
275C23×C53—42no—
276C23×C53—42no—
277C23×C53C22×D411yescharacteristic
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—22no—
281C22×D53—22no—
282C22×D53—22no—
283C22×D53AGL(1,ℤ/8)14yes—
284C22×D53C22×D412yes—
285C22×D53C22×D412yes—
286D4×C53—22no—
287D4×C53—22no—
288D4×C53—42no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—48no—
295C2×C4×C53—42no—
296C2×C4×C53—42no—
297C2×C4×C53—42no—
298C2×C4×C53C22×D412yes—
299C2×C4×C53C22×D412yes—
300C2×C4×C53C22×D411yescharacteristic
301C2×C4×C53C2×#4112yes—
302C2×C4×C532−1+412yes—
303C2×C4×C53C2511yescharacteristic
304C22⋊D53—48no—
305C22⋊D53—48no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53C22×D412yes—
317C2×Dic53C22×D412yes—
318D212—28no—
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—
328Dic106—22no—
329Dic106—22no—
330Dic106—48no—
331Dic106—42no—
332C8×C53—22no—
333C8×C53—22no—
334#88322—22no—
335#88322C2×#4114yescomplemented
336C2×#3343—531nomaximal, Sylow
337C22×C53—42no—
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—84no—
341C22×C53#54712yes—
342C22×C53C2×AGL(1,ℤ/8)12yes—
343C22×C53#57812yes—
344C22×C53C23×D411yescharacteristic
345C2×D53—28no—
346C2×D53—22no—
347C2×D53—22no—
348C2×D53—22no—
349C2×D53—22no—
350C2×D53—22no—
351C2×D53—44no—
352C2×D53C2×AGL(1,ℤ/8)14yes—
353C4×C53—22no—
354C4×C53—22no—
355C4×C53—42no—
356C4×C53—42no—
357C4×C53—42no—
358C4×C53#54712yes—
359C4×C53C22×#4111yescharacteristic
360C4×C53C2×2−1+411yescharacteristic
361Dic53—22no—
362Dic53—22no—
363Dic53—42no—
364Dic53—42no—
365Dic53—42no—
366Dic53—42no—
367C2×#552—531no—
368C2×#547—531no—
369#3343—5316no—
370C2×#501—531no—
371C2×#484—531no—
372C2×#482—531no—
373C2×#483—531no—
374C2×#480—531no—
375C2×#477—531no—
376C2×#478D5311yescharacteristic, complemented
377C2×#468—531no—
378C2×#465—531no—
379C2×#440—531no—
380C2×#435—531no—
381C2×#428—531no—
382C22×#107—531no—
383C2×C53—82no—
384C2×C53#334314yescomplemented
385C2×C53C2×#54711yescharacteristic
386C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
387C2×C53C2×#57811yescharacteristic
388D53—24no—
389D53—42no—
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⋊Q8—531no—
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×D4C2×D5311yescharacteristic
413C2×#117—531no—
414C2×#117—1061no—
415C22×C4⋊C4—531no—
416C22×C4⋊C4—531no—
417C22×C4⋊C4—531no—
418#501—538no—
419#484—538no—
420#483—538no—
421#482—538no—
422#480—538no—
423#478C2×D5318yescomplemented
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—531no—
435C2×#107—538no—
436C2×#107C2×D5311yescharacteristic
437C2×#106—531no—
438C2×#106—531no—
439C2×#106C2×D5311yescharacteristic
440C2×C4⋊C8C2×D5311yescharacteristic
441C2×#103—531no—
442C2×#103—531no—
443C2×#103—531no—
444C2×#102—531no—
445C2×#102C2×D5311yescharacteristic
446C2×#102C2×D5311yescharacteristic
447C2×C22⋊C8—531no—
448C2×C22⋊C8—531no—
449C2×#97—531no—
450C53C2×#334311yescharacteristic, complemented, Sylow
451C2×#41—1068no—
452C2×#41—2128no—
453C22×Q8—531no—
454C22×Q8—1061no—
455C22×D4—531no—
456C22×D4—1061no—
457C22×D4—1061no—
458C22×D4C22×D5311yescharacteristic
459C23×C4—21no—
460C23×C4—531no—
461C23×C4—531no—
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—534no—
476C4⋊Q8—1062no—
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—22no—
496C4×D4—534no—
497C4×D4—534no—
498C4×D4C22×D5314yes—
499#117—534no—
500#117—1068no—
501#117—1062no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—531no—
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⋊C4—1061no—
521C2×C4⋊C4C22×D5311yescharacteristic
522C2×C4⋊C4C22×D5311yescharacteristic
523C2×C4⋊C4C22×D5311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—531no—
526C2×C22⋊C4—531no—
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#107—534no—
540#107C22×D5314yes—
541#106—534no—
542#106—534no—
543#106C22×D5314yes—
544C4⋊C8C22×D5314yes—
545#103—534no—
546#103—534no—
547#103—534no—
548#102—534no—
549#102C22×D5314yes—
550#102C22×D5314yes—
551C22⋊C8—534no—
552C22⋊C8—534no—
553#97—534no—
554C24—21no—
555C24—531no—
556C24—531no—
557#41—21232no—
558C2×Q8—532no—
559C2×Q8—1061no—
560C2×Q8—1064no—
561C2×Q8—1062no—
562C2×Q8—1062no—
563C2×Q8—2124no—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—534no—
568C2×D4—1064no—
569C2×D4—1064no—
570C2×D4—1064no—
571C2×D4—2124no—
572C2×D4—2124no—
573C2×D4C23×D5312yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—44no—
579C22×C4—531no—
580C22×C4—531no—
581C22×C4—532no—
582C22×C4—532no—
583C22×C4—532no—
584C22×C4—532no—
585C22×C4—1064no—
586C22×C4—1064no—
587C22×C4—1064no—
588C22×C4—1062no—
589C22×C4—1062no—
590C22×C4—1062no—
591C22×C4—1062no—
592C22×C4—1061no—
593C22×C4—1061no—
594C22×C4—1061no—
595C22×C4—1061no—
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—22no—
606C2×C8—534no—
607C2×C8—532no—
608C2×C8—532no—
609C2×C8—1068no—
610C2×C8—1062no—
611C2×C8C23×D5312yes—
612C2×C8C23×D5312yes—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—534no—
619C4⋊C4—532no—
620C4⋊C4—532no—
621C4⋊C4—532no—
622C4⋊C4—1064no—
623C4⋊C4—1064no—
624C4⋊C4—1064no—
625C4⋊C4—1064no—
626C4⋊C4—1064no—
627C4⋊C4—1061no—
628C4⋊C4—1061no—
629C4⋊C4—1061no—
630C4⋊C4—1064no—
631C4⋊C4—1064no—
632C4⋊C4C23×D5312yes—
633C4⋊C4C23×D5312yes—
634C4⋊C4C23×D5312yes—
635C22⋊C4—24no—
636C22⋊C4—534no—
637C22⋊C4—534no—
638C22⋊C4—1064no—
639C22⋊C4—1064no—
640C22⋊C4—1064no—
641C22⋊C4—1064no—
642C22⋊C4—1064no—
643C42—1064no—
644C42—1064no—
645C42D4×D5312yes—
646C42C23×D5312yes—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—534no—
652C23—532no—
653C23—532no—
654C23—1062no—
655C23—1062no—
656C23—1062no—
657C23—1062no—
658C23—1062no—
659C23C2×D4×D5311yescharacteristic
660Q8—1062no—
661Q8—1062no—
662Q8—2128no—
663Q8—2122no—
664D4—22no—
665D4—22no—
666D4—42no—
667D4—1068no—
668D4—2128no—
669D4—2128no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—48no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—532no—
680C2×C4—532no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—1064no—
684C2×C4—1064no—
685C2×C4—1062no—
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—2122no—
697C2×C4—2122no—
698C2×C4—2122no—
699C2×C4—2122no—
700C2×C4C2×D4×D5312yes—
701C2×C4C2×D4×D5312yes—
702C2×C4C2×D4×D5311yescharacteristic
703C2×C4#41×D5312yes—
704C2×C4#1313326512yes—
705C2×C4C24×D5311yescharacteristic
706C8—22no—
707C8—22no—
708C8—534no—
709C8—1062no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—534no—
715C22—1062no—
716C22—1068no—
717C22—1062no—
718C22—1062no—
719C22—1062no—
720C22—1062no—
721C22—2124no—
722C22#1681127512yes—
723C22AGL(1,ℤ/8)×D5312yes—
724C22#1681143712yes—
725C22C22×D4×D5311yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—1062no—
732C4—1062no—
733C4—2122no—
734C4—2122no—
735C4—2122no—
736C4—2122no—
737C4#1681127512yes—
738C4C2×#41×D5311yescharacteristic
739C4C2×#1313326511yescharacteristic
740C2—82no—
741C2—1064no—
742C2—2122no—
743C2#2028716214yesdirect product factor
744C2C2×#1681127511yescharacteristic
745C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
746C2C2×#1681143711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#478C2
socleC23×C53C22×D4
prime radicalC2×#16811278C2
hypercenterC2×#478D53
hypocenterC53C2×#3343
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#16811311C2semidirect
3. #20287162C2direct (N × H)
4. C2×#16811033C2semidirect
5. C2×#16810960C2semidirect
6. C2×#16810945C2semidirect
7. C2×#16810955C2semidirect
8. C2×#16810935C2semidirect
9. C2×#16810919C2semidirect
10. C2×#16810868C2semidirect
11. C2×#16810851C2semidirect
12. C2×#16810723C2semidirect
13. C2×#16810693C2semidirect
14. C2×#16810662C2semidirect
15. C2×#107×D53C2semidirect
16. C2×C53×#478C2semidirect
22. #16811311C22semidirect
43. #16811033C22semidirect
44. #16810960C22semidirect
45. #16810955C22semidirect
46. #16810945C22semidirect
47. #16810935C22semidirect
48. #16810919C22semidirect
49. #16810868C22semidirect
50. #16810851C22semidirect
51. #16810723C22semidirect
52. #16810693C22semidirect
53. #16810662C22semidirect
59. #107×D53C22semidirect
71. C53×#478C22semidirect
268. C2×#88322#41semidirect
335. #88322C2×#41semidirect
376. C2×#478D53semidirect
384. C2×C53#3343semidirect
423. #478C2×D53semidirect
450. C53C2×#3343semidirect
743. C2#20287162direct (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×#168112782
#202871622
C2×#168110332
C2×#168109602
C2×#168109452
C2×#168109552
C2×#168109352
C2×#168109192
C2×#168108682
C2×#168108512
C2×#168107232
C2×#168106932
C2×#168106622
C2×#107×D532
C2×C53×#4782
C2×#334353