Finite Group Databasebeta

← C2×#20285430 #28254031

Subgroups — C2×#20285430 #28254031

Order 13568.

2234 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811177C211yesmaximal, characteristic, complemented
2C2×#16811170C211yesmaximal, characteristic
3#20285430C2116yesmaximal, direct product factor
4C2×#16811027C211yesmaximal, characteristic, complemented
5C2×#16810994C211yesmaximal, characteristic, complemented
6C2×#16810972C211yesmaximal, characteristic, complemented
7C2×#16810968C211yesmaximal, characteristic, complemented
8C2×#16810872C211yesmaximal, characteristic, complemented
9C2×#16810870C211yesmaximal, characteristic, complemented
10C2×#16810868C211yesmaximal, characteristic, complemented
11C2×#16810866C211yesmaximal, characteristic, complemented
12C2×#16810725C211yesmaximal, characteristic, complemented
13C2×#16810723C211yesmaximal, characteristic, complemented
14C2×#16810721C211yesmaximal, characteristic, complemented
15C2×#16810575C211yesmaximal, characteristic, complemented
16C2×C53×#440C211yesmaximal, characteristic, complemented
17C22×#11719945—21no—
18C22×#11719913C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21C22×#11719912C2211yescharacteristic
22C22×#11719912C2211yescharacteristic
23#16811177—24no—
24#16811177C2218yescomplemented
25#16811170—24no—
26#16811170C2218yes—
27C2×#13133216C2211yescharacteristic
28C2×#13133216C2211yescharacteristic
29C2×#13133215C2211yescharacteristic
30C2×#13133213C2211yescharacteristic
31C2×#13133207—21no—
32C2×#13133203—21no—
33C2×#13133197C2211yescharacteristic
34C2×#13133195—21no—
35C2×#13133193C2211yescharacteristic
36C2×#13133192C2211yescharacteristic
37C2×#13133190—21no—
38C2×#13133188C2211yescharacteristic
39C2×C4×Dic106—21no—
40C2×C4×Dic106C2211yescharacteristic
41C2×C4×D212C2211yescharacteristic
42C2×C4×C22⋊D53—21no—
43C2×#13133174—21no—
44C2×C42×D53C2211yescharacteristic
45#16811027C2218yescomplemented
46#16810994C2218yescomplemented
47#16810972C2218yescomplemented
48#16810968C2218yescomplemented
49#16810872C2218yescomplemented
50#16810870C2218yescomplemented
51#16810868C2218yescomplemented
52#16810866C2218yescomplemented
53#16810725C2218yescomplemented
54#16810723C2218yescomplemented
55#16810721C2218yescomplemented
56C2×#13133151C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58C2×#13133150C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65#16810575C2218yescomplemented
66C2×#13133128C2211yescharacteristic
67C2×C8×Dic53C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#440C2218yescomplemented
73C2×#107×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C2×#11719945—28no—
78C2×#11719945—48no—
79C22×Dic106—21no—
80C22×Dic106—21no—
81C22×Dic106C2311yescharacteristic
82C22×D212—21no—
83C22×D212C2311yescharacteristic
84C22×C22⋊D53—21no—
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53D411yescharacteristic
89C22×C4×D53D411yescharacteristic
90C22×C4×D53C2311yescharacteristic
91C2×#11719913—24no—
92C2×#11719913C2314yes—
93C2×#11719923—24no—
94C2×#11719923C2314yes—
95C2×#11719924—24no—
96C2×#11719924C2314yes—
97C2×#11719912—24no—
98C2×#11719912—24no—
99C2×#11719912C2314yes—
100C2×#11719912C2314yes—
101C22×#88322C2311yescharacteristic
102C22×#88322C2311yescharacteristic
103#13133216—22no—
104#13133216—22no—
105#13133216C2314yes—
106#13133216C2314yes—
107#13133215—22no—
108#13133215C2314yes—
109#13133213—22no—
110#13133213C2314yes—
111#13133207—28no—
112#13133203—28no—
113#13133197—22no—
114#13133197C2314yes—
115#13133195—28no—
116#13133193—22no—
117#13133193C2314yes—
118#13133192—22no—
119#13133192C2314yes—
120#13133190—28no—
121#13133188—22no—
122#13133188C2314yes—
123C4×Dic106—22no—
124C4×Dic106—28no—
125C4×Dic106C2314yes—
126C4×D212—22no—
127C4×D212C2314yes—
128C4×C22⋊D53—28no—
129#13133174—28no—
130C2×C4⋊Dic53—21no—
131C2×C4⋊Dic53C2311yescharacteristic
132C2×C4⋊Dic53C2311yescharacteristic
133C2×#11719919—21no—
134C2×#11719919—21no—
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×C4×Dic53—21no—
145C2×C4×Dic53D411yescharacteristic
146C2×C4×Dic53D411yescharacteristic
147C2×C4×Dic53C2311yescharacteristic
148C42×D53D414yes—
149C42×D53C2314yes—
150#13133151C2314yes—
151#13133150C2314yes—
152#13133150C2314yes—
153#13133142C2314yes—
154#13133141C2314yes—
155#13133140C2314yes—
156#13133139C2314yes—
157#13133138C2314yes—
158#13133137C2314yes—
159#13133128C2314yes—
160C8×Dic53C2314yes—
161C8×Dic53C2314yes—
162C22×Q8×C53C2311yescharacteristic
163C22×D4×C53C2311yescharacteristic
164C23×C4×C53—21no—
165C2×SD16×C53—24no—
166C2×SD16×C53C2314yes—
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C4×Q8×C53—22no—
170C4×Q8×C53C2314yes—
171C4×D4×C53—22no—
172C4×D4×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C22⋊C4×C53—21no—
177C2×C42×C53—21no—
178C2×C42×C53C2311yescharacteristic
179#107×C53C2314yes—
180#103×C53C2314yes—
181#102×C53C2314yes—
182#97×C53C2314yes—
183C24×C53—21no—
184C23×D53—21no—
185C23×D53C2×D411yescharacteristic
186C2×Q8×C53—21no—
187C2×Q8×C53—22no—
188C2×Q8×C53—22no—
189C2×Q8×C53C2412yes—
190C2×D4×C53—21no—
191C2×D4×C53—22no—
192C2×D4×C53—22no—
193C2×D4×C53C2412yes—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—24no—
198C22×C4×C53—44no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2411yescharacteristic
202C2×C22⋊D53—24no—
203C2×C22⋊D53—24no—
204C2×C22⋊D53—24no—
205C2×C22⋊D53—44no—
206C2×C22⋊D53—44no—
207C2×C22⋊D53—44no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213C22×Dic53C2×D411yescharacteristic
214#11719945—432no—
215C2×D212—22no—
216C2×D212—22no—
217C2×D212—24no—
218C2×D212—21no—
219C2×D212—44no—
220C2×D212C2412yes—
221C2×C4×D53—22no—
222C2×C4×D53—22no—
223C2×C4×D53—24no—
224C2×C4×D53—24no—
225C2×C4×D53—24no—
226C2×C4×D53—44no—
227C2×C4×D53C2×D412yes—
228C2×C4×D53C2×D414yes—
229C2×C4×D53C2×D414yes—
230C2×C4×D53C2412yes—
231C2×Dic106—22no—
232C2×Dic106—22no—
233C2×Dic106—21no—
234C2×Dic106—24no—
235C2×Dic106—24no—
236C2×Dic106—44no—
237C2×Dic106—44no—
238C2×Dic106C2412yes—
239SD16×C53—28no—
240C2×C8×C53—22no—
241C2×C8×C53#4114yescomplemented
242C2×C8×C53C2412yes—
243C2×C8×C53C2412yes—
244C4⋊C4×C53—24no—
245C4⋊C4×C53—21no—
246C4⋊C4×C53—21no—
247C4⋊C4×C53C2412yes—
248C4⋊C4×C53C2412yes—
249C22⋊C4×C53—24no—
250C42×C53—24no—
251C42×C53C2×D412yes—
252C42×C53C2412yes—
253C22⋊Dic53—24no—
254#11719924—28no—
255#11719923—28no—
256#11719921—24no—
257#11719921—24no—
258#11719921—24no—
259#11719921—24no—
260C4⋊Dic53—21no—
261C4⋊Dic53—21no—
262C4⋊Dic53—24no—
263C4⋊Dic53C2412yes—
264C4⋊Dic53C2412yes—
265#11719919—24no—
266#11719919—24no—
267#11719919—24no—
268#11719919—24no—
269#11719919—24no—
270#11719919—24no—
271C4×Dic53—24no—
272C4×Dic53C2×D412yes—
273C4×Dic53C2×D414yes—
274C4×Dic53C2×D414yes—
275C4×Dic53C2412yes—
276C2×#88322—22no—
277C2×#88322#4114yescomplemented
278C2×#88322C2412yes—
279C2×#88322C2412yes—
280#11719913—28no—
281#11719912—28no—
282#11719912—28no—
283C23×C53—22no—
284C23×C53—42no—
285C23×C53—42no—
286C23×C53—42no—
287C23×C53C22×D411yescharacteristic
288C22×D53—22no—
289C22×D53—22no—
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—42no—
293C22×D53—42no—
294C22×D53—42no—
295C22×D53C22×D412yes—
296Q8×C53—22no—
297Q8×C53—22no—
298Q8×C53—42no—
299D4×C53—22no—
300D4×C53—22no—
301D4×C53—42no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—48no—
308C2×C4×C53—42no—
309C2×C4×C53—42no—
310C2×C4×C53—42no—
311C2×C4×C53C22×D412yes—
312C2×C4×C53C22×D412yes—
313C2×C4×C53C22×D411yescharacteristic
314C2×C4×C53C2×#4112yes—
315C2×C4×C53C2×#4112yes—
316C2×C4×C53C2511yescharacteristic
317C22⋊D53—48no—
318C22⋊D53—48no—
319C22⋊D53—48no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—42no—
325C2×Dic53—42no—
326C2×Dic53—42no—
327C2×Dic53AGL(1,ℤ/8)14yes—
328C2×Dic53#13714yes—
329C2×Dic53C22×D412yes—
330C2×Dic53C22×D412yes—
331C2×Dic53C22×D412yes—
332D212—22no—
333D212—22no—
334D212—48no—
335D212—42no—
336C4×D53—24no—
337C4×D53—22no—
338C4×D53—22no—
339C4×D53—28no—
340C4×D53—28no—
341C4×D53—48no—
342Dic106—22no—
343Dic106—22no—
344Dic106—42no—
345Dic106—48no—
346Dic106—48no—
347C8×C53—22no—
348C8×C53C2×#4114yescomplemented
349#88322—22no—
350#88322C2×#4114yescomplemented
351C2×#3182—531nomaximal, Sylow
352C22×C53—42no—
353C22×C53—42no—
354C22×C53—42no—
355C22×C53—84no—
356C22×C53#53212yes—
357C22×C53C2×AGL(1,ℤ/8)12yes—
358C22×C53C2×#13712yes—
359C22×C53C23×D411yescharacteristic
360C2×D53—22no—
361C2×D53—22no—
362C2×D53—22no—
363C2×D53—44no—
364C2×D53—42no—
365C2×D53—42no—
366C2×D53—42no—
367C2×D53—84no—
368C4×C53—22no—
369C4×C53—22no—
370C4×C53—42no—
371C4×C53—42no—
372C4×C53—42no—
373C4×C53#53212yes—
374C4×C53C22×#4111yescharacteristic
375C4×C53C22×#4111yescharacteristic
376Dic53—22no—
377Dic53—42no—
378Dic53—42no—
379Dic53—42no—
380Dic53C2×AGL(1,ℤ/8)14yes—
381Dic53C2×#13714yes—
382C2×#533—531no—
383C2×#532—531no—
384#3182—5316no—
385C2×#500—531no—
386C2×#492—531no—
387C2×#487—531no—
388C2×#486—531no—
389C2×#468—531no—
390C2×#468—531no—
391C2×#468—531no—
392C2×#468—531no—
393C2×#440—531no—
394C2×#440—531no—
395C2×#440—531no—
396C2×#440D5311yescharacteristic, complemented
397C2×C4×M16—531no—
398C2×C53—82no—
399C2×C53#318214yescomplemented
400C2×C53C2×#53211yescharacteristic
401C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
402C2×C53C22×#13711yescharacteristic
403D53—42no—
404D53—82no—
405C22×#41—1061no—
406C22×SD16—531no—
407C22×SD16—531no—
408C22×SD16—531no—
409C22×SD16C2×D5311yescharacteristic
410C22×M16—531no—
411C22×M16—531no—
412#533—538no—
413#533—1064no—
414#532—538no—
415#532—1064no—
416C2×C4⋊Q8—531no—
417C2×C4⋊Q8—531no—
418C2×C4⋊Q8—531no—
419C2×#127—531no—
420C2×#125—1061no—
421C2×#124—1061no—
422C2×C22⋊Q8—531no—
423C2×C22⋊Q8—531no—
424C2×C22⋊Q8—1061no—
425C2×#121—531no—
426C2×#121—531no—
427C2×#121—1061no—
428C2×C4×Q8—531no—
429C2×C4×Q8—1061no—
430C2×C4×Q8C2×D5311yescharacteristic
431C2×C4×D4—531no—
432C2×C4×D4—1061no—
433C2×C4×D4C2×D5311yescharacteristic
434C2×#117—1061no—
435C22×C42—531no—
436#500—538no—
437#492—538no—
438#487—538no—
439#486—538no—
440#468—538no—
441#468—538no—
442#468—538no—
443#468—538no—
444#440—538no—
445#440—538no—
446#440—538no—
447#440C2×D5318yescomplemented
448C2×#107—531no—
449C2×#107—531no—
450C2×#107—531no—
451C2×#107C2×D5311yescharacteristic
452C2×#103—531no—
453C2×#103—531no—
454C2×#103—531no—
455C2×#103C2×D5311yescharacteristic
456C2×#102—531no—
457C2×#102—531no—
458C2×#102—531no—
459C2×#102C2×D5311yescharacteristic
460C4×M16—538no—
461C2×#97—531no—
462C2×#97C2×D5311yescharacteristic
463C2×C4×C8—531no—
464C2×C4×C8—531no—
465C53C2×#318211yescharacteristic, complemented, Sylow
466C2×#41—1068no—
467C2×#41—2128no—
468C22×Q8—531no—
469C22×Q8—1061no—
470C22×Q8—1061no—
471C22×Q8C22×D5311yescharacteristic
472C22×D4—531no—
473C22×D4—1061no—
474C22×D4—1061no—
475C22×D4—1061no—
476C22×D4—1061no—
477C22×D4C22×D5311yescharacteristic
478C23×C4—21no—
479C23×C4—531no—
480C23×C4—531no—
481C23×C4—531no—
482C23×C4—1061no—
483C2×SD16—24no—
484C2×SD16—534no—
485C2×SD16—534no—
486C2×SD16—534no—
487C2×SD16—1064no—
488C2×SD16—1064no—
489C2×SD16—1064no—
490C2×SD16C22×D5314yes—
491C2×M16—534no—
492C2×M16—534no—
493C2×M16—1064no—
494C2×M16—1064no—
495C22×C8—531no—
496C22×C8—531no—
497C22×C8C22×D5311yescharacteristic
498C22×C8C22×D5311yescharacteristic
499C4⋊Q8—534no—
500C4⋊Q8—534no—
501C4⋊Q8—534no—
502C4⋊Q8—1062no—
503C4⋊Q8—1062no—
504C4⋊Q8—1062no—
505#127—534no—
506#127—1062no—
507#125—1068no—
508#124—1068no—
509C22⋊Q8—534no—
510C22⋊Q8—534no—
511C22⋊Q8—1062no—
512C22⋊Q8—1068no—
513C22⋊Q8—1062no—
514#121—534no—
515#121—534no—
516#121—1068no—
517#121—1062no—
518#121—1062no—
519C4×Q8—22no—
520C4×Q8—534no—
521C4×Q8—1068no—
522C4×Q8—1062no—
523C4×Q8C22×D5314yes—
524C4×D4—22no—
525C4×D4—534no—
526C4×D4—1068no—
527C4×D4—1062no—
528C4×D4C22×D5314yes—
529#117—1068no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—531no—
532C2×C4⋊C4—531no—
533C2×C4⋊C4—1061no—
534C2×C4⋊C4—1061no—
535C2×C4⋊C4—1061no—
536C2×C4⋊C4—1061no—
537C2×C4⋊C4—1061no—
538C2×C4⋊C4—1061no—
539C2×C4⋊C4—1061no—
540C2×C4⋊C4C22×D5311yescharacteristic
541C2×C4⋊C4C22×D5311yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—1061no—
544C2×C22⋊C4—1061no—
545C2×C22⋊C4—1061no—
546C2×C22⋊C4—1061no—
547C2×C22⋊C4—1061no—
548C2×C42—21no—
549C2×C42—531no—
550C2×C42—531no—
551C2×C42—531no—
552C2×C42—534no—
553C2×C42—534no—
554C2×C42—1061no—
555C2×C42C22×D5311yescharacteristic
556#107—534no—
557#107—534no—
558#107—534no—
559#107C22×D5314yes—
560#103—534no—
561#103—534no—
562#103—534no—
563#103C22×D5314yes—
564#102—534no—
565#102—534no—
566#102—534no—
567#102C22×D5314yes—
568#97—534no—
569#97C22×D5314yes—
570C4×C8—534no—
571C4×C8—534no—
572C24—21no—
573C24—531no—
574C24—1061no—
575#41—21232no—
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—532no—
580C2×Q8—1064no—
581C2×Q8—1064no—
582C2×Q8—1061no—
583C2×Q8—1062no—
584C2×Q8—1062no—
585C2×Q8—2124no—
586C2×Q8—2124no—
587C2×Q8C23×D5312yes—
588C2×D4—21no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—532no—
592C2×D4—1064no—
593C2×D4—1064no—
594C2×D4—1064no—
595C2×D4—1064no—
596C2×D4—1061no—
597C2×D4—1062no—
598C2×D4—1062no—
599C2×D4—2124no—
600C2×D4—2124no—
601C2×D4—2124no—
602C2×D4—2124no—
603C2×D4C23×D5312yes—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—44no—
609C22×C4—531no—
610C22×C4—531no—
611C22×C4—531no—
612C22×C4—534no—
613C22×C4—532no—
614C22×C4—534no—
615C22×C4—532no—
616C22×C4—1064no—
617C22×C4—1064no—
618C22×C4—1062no—
619C22×C4—1062no—
620C22×C4—1061no—
621C22×C4—1061no—
622C22×C4—1061no—
623C22×C4—1064no—
624C22×C4—2124no—
625C22×C4D4×D5311yescharacteristic
626C22×C4D4×D5311yescharacteristic
627C22×C4C23×D5311yescharacteristic
628SD16—28no—
629SD16—1068no—
630SD16—1068no—
631SD16—1068no—
632M16—1068no—
633M16—1068no—
634C2×C8—22no—
635C2×C8—534no—
636C2×C8—532no—
637C2×C8—532no—
638C2×C8—1062no—
639C2×C8#1171994514yescomplemented
640C2×C8C23×D5312yes—
641C2×C8C23×D5312yes—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—532no—
646C4⋊C4—532no—
647C4⋊C4—1064no—
648C4⋊C4—1064no—
649C4⋊C4—1064no—
650C4⋊C4—1064no—
651C4⋊C4—1064no—
652C4⋊C4—1064no—
653C4⋊C4—1061no—
654C4⋊C4—1061no—
655C4⋊C4—1064no—
656C4⋊C4C23×D5312yes—
657C4⋊C4C23×D5312yes—
658C22⋊C4—24no—
659C22⋊C4—1064no—
660C22⋊C4—1064no—
661C22⋊C4—1064no—
662C22⋊C4—1064no—
663C22⋊C4—1064no—
664C42—24no—
665C42—534no—
666C42—534no—
667C42—532no—
668C42—532no—
669C42—1064no—
670C42D4×D5312yes—
671C42C23×D5312yes—
672C23—22no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—532no—
677C23—1062no—
678C23—1062no—
679C23—1062no—
680C23—1062no—
681C23—2122no—
682C23—2122no—
683C23—2122no—
684C23C2×D4×D5311yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—42no—
688Q8—1062no—
689Q8—1062no—
690Q8—2128no—
691Q8—2128no—
692Q8—2122no—
693D4—22no—
694D4—22no—
695D4—42no—
696D4—1062no—
697D4—1062no—
698D4—2128no—
699D4—2128no—
700D4—2128no—
701D4—2128no—
702D4—2122no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—48no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—534no—
713C2×C4—534no—
714C2×C4—532no—
715C2×C4—532no—
716C2×C4—532no—
717C2×C4—1068no—
718C2×C4—1068no—
719C2×C4—1062no—
720C2×C4—1064no—
721C2×C4—1062no—
722C2×C4—1062no—
723C2×C4—1062no—
724C2×C4—1062no—
725C2×C4—1062no—
726C2×C4—2128no—
727C2×C4—2122no—
728C2×C4—2122no—
729C2×C4—2122no—
730C2×C4C2×D4×D5312yes—
731C2×C4C2×D4×D5312yes—
732C2×C4C2×D4×D5311yescharacteristic
733C2×C4#41×D5312yes—
734C2×C4C2×#1171994512yes—
735C2×C4C24×D5311yescharacteristic
736C8—22no—
737C8—534no—
738C8—1062no—
739C8C2×#1171994514yescomplemented
740C22—42no—
741C22—42no—
742C22—42no—
743C22—84no—
744C22—1062no—
745C22—1062no—
746C22—1062no—
747C22—4244no—
748C22—2122no—
749C22—2122no—
750C22—2122no—
751C22—2124no—
752C22#1681117012yes—
753C22AGL(1,ℤ/8)×D5312yes—
754C22#137×D5312yes—
755C22C22×D4×D5311yescharacteristic
756C4—22no—
757C4—22no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—534no—
762C4—534no—
763C4—1062no—
764C4—2122no—
765C4—2122no—
766C4—2122no—
767C4#1681117012yes—
768C4C2×#41×D5311yescharacteristic
769C4C22×#1171994511yescharacteristic
770C2—82no—
771C2—4242no—
772C2—2122no—
773C2#2028543014yesdirect product factor
774C2C2×#1681117011yescharacteristic
775C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
776C2C2×#137×D5311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#440C2
socleC23×C53C22×D4
prime radicalC2×#16811170C2
hypercenterC2×#440D53
hypocenterC53C2×#3182
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#16811177C2semidirect
3. #20285430C2direct (N × H)
4. C2×#16811027C2semidirect
5. C2×#16810994C2semidirect
6. C2×#16810972C2semidirect
7. C2×#16810968C2semidirect
8. C2×#16810872C2semidirect
9. C2×#16810870C2semidirect
10. C2×#16810868C2semidirect
11. C2×#16810866C2semidirect
12. C2×#16810725C2semidirect
13. C2×#16810723C2semidirect
14. C2×#16810721C2semidirect
15. C2×#16810575C2semidirect
16. C2×C53×#440C2semidirect
24. #16811177C22semidirect
45. #16811027C22semidirect
46. #16810994C22semidirect
47. #16810972C22semidirect
48. #16810968C22semidirect
49. #16810872C22semidirect
50. #16810870C22semidirect
51. #16810868C22semidirect
52. #16810866C22semidirect
53. #16810725C22semidirect
54. #16810723C22semidirect
55. #16810721C22semidirect
65. #16810575C22semidirect
72. C53×#440C22semidirect
241. C2×C8×C53#41semidirect
277. C2×#88322#41semidirect
348. C8×C53C2×#41semidirect
350. #88322C2×#41semidirect
396. C2×#440D53semidirect
399. C2×C53#3182semidirect
447. #440C2×D53semidirect
465. C53C2×#3182semidirect
639. C2×C8#11719945semidirect
739. C8C2×#11719945semidirect
773. C2#20285430direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111772
C2×#168111702
#202854302
C2×#168110272
C2×#168109942
C2×#168109722
C2×#168109682
C2×#168108722
C2×#168108702
C2×#168108682
C2×#168108662
C2×#168107252
C2×#168107232
C2×#168107212
C2×#168105752
C2×C53×#4402
C2×#318253