Finite Group Databasebeta

← C2×#20286584 #28260480

Subgroups — C2×#20286584 #28260480

Order 13568.

2158 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811331C211yesmaximal, characteristic
2C2×Q8×C22⋊D53C211yesmaximal, characteristic
3#20286584C2116yesmaximal, direct product factor
4C2×#16810972C211yesmaximal, characteristic, complemented
5C2×#16810959C211yesmaximal, characteristic, complemented
6C2×#16810957C211yesmaximal, characteristic, complemented
7C2×#16810916C211yesmaximal, characteristic, complemented
8C2×#16810862C211yesmaximal, characteristic, complemented
9C2×#16810861C211yesmaximal, characteristic, complemented
10C2×#16810831C211yesmaximal, characteristic, complemented
11C2×#16810777C211yesmaximal, characteristic, complemented
12C2×Q16×Dic53C211yesmaximal, characteristic, complemented
13C2×#16810686C211yesmaximal, characteristic
14C22×#13133141C211yesmaximal, characteristic, complemented
15C2×#103×D53C211yesmaximal, characteristic, complemented
16C2×C53×#451C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C23×#88322C2211yescharacteristic
20C22×C8×D53C2211yescharacteristic
21#16811331—24no—
22#16811331C2218yes—
23Q8×C22⋊D53—24no—
24Q8×C22⋊D53C2218yes—
25C2×#13133216C2211yescharacteristic
26C2×#13133215—21no—
27C2×#13133215C2211yescharacteristic
28C2×#13133207—21no—
29C2×#13133197—21no—
30C2×#13133196—21no—
31C2×#13133196C2211yescharacteristic
32C2×#13133194—21no—
33C2×#13133193—21no—
34C2×#13133193C2211yescharacteristic
35C2×#13133193C2211yescharacteristic
36C2×Q8×Dic53C2211yescharacteristic
37C2×Q8×Dic53C2211yescharacteristic
38C2×C4×C22⋊D53—21no—
39C2×C4×C22⋊D53C2211yescharacteristic
40C2×#13133177—21no—
41C22×C4⋊Dic53C2211yescharacteristic
42C2×C4⋊C4×D53C2211yescharacteristic
43#16810972C2218yescomplemented
44#16810959C2218yescomplemented
45#16810957C2218yescomplemented
46#16810916C2218yescomplemented
47#16810862C2218yescomplemented
48#16810861C2218yescomplemented
49#16810831C2218yescomplemented
50#16810777C2218yescomplemented
51Q16×Dic53C2218yescomplemented
52#16810686C2218yes—
53C2×#13133151C2211yescharacteristic
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57C2×#13133142C2211yescharacteristic
58C2×#13133142C2211yescharacteristic
59C2×#13133141C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133141C2218yescomplemented
65C2×#13133140C2211yescharacteristic
66#103×D53C2218yescomplemented
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C23×Q8×C53C2211yescharacteristic
70C22×Q16×C53C2211yescharacteristic
71C22×Q16×C53C2211yescharacteristic
72C2×C22⋊Q8×C53C2211yescharacteristic
73C53×#451C2218yescomplemented
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—21no—
79C22×Dic106C2311yescharacteristic
80C2×Q8×D53—22no—
81C2×Q8×D53—24no—
82C2×Q8×D53—42no—
83C2×Q8×D53C2314yes—
84C22×C22⋊D53D411yescharacteristic
85C23×Dic53—21no—
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53C2311yescharacteristic
89C2×#11719925—42no—
90C2×#11719925C2314yes—
91C22×#88322—42no—
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94C22×#88322C2314yes—
95C2×C8×D53—42no—
96C2×C8×D53C2314yes—
97#13133216—22no—
98#13133216C2314yes—
99#13133215—28no—
100#13133215—22no—
101#13133215C2314yes—
102#13133207—28no—
103#13133197—28no—
104#13133196—28no—
105#13133196—22no—
106#13133196C2314yes—
107#13133194—28no—
108#13133193—28no—
109#13133193—22no—
110#13133193—22no—
111#13133193C2314yes—
112#13133193C2314yes—
113Q8×Dic53—22no—
114Q8×Dic53—22no—
115Q8×Dic53C2314yes—
116Q8×Dic53C2314yes—
117C4×C22⋊D53—28no—
118C4×C22⋊D53D414yes—
119C4×C22⋊D53C2314yes—
120#13133177—28no—
121C2×C4⋊Dic53—22no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2314yes—
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919D411yescharacteristic
137C4⋊C4×D53—22no—
138C4⋊C4×D53C2314yes—
139C2×C22⋊Dic53—21no—
140C2×C22⋊Dic53D411yescharacteristic
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921D411yescharacteristic
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53C2311yescharacteristic
147#13133151C2314yes—
148#13133151C2314yes—
149#13133150C2314yes—
150#13133146C2314yes—
151#13133142C2314yes—
152#13133142C2314yes—
153#13133141C2314yes—
154#13133141C2314yes—
155#13133141C2314yes—
156#13133141C2314yes—
157#13133141C2314yes—
158#13133140C2314yes—
159#13133129C2314yes—
160C8×Dic53C2314yes—
161C22×Q8×C53—22no—
162C22×Q8×C53—21no—
163C22×Q8×C53—24no—
164C22×Q8×C53—42no—
165C22×Q8×C53C2311yescharacteristic
166C22×Q8×C53C2311yescharacteristic
167C22×Q8×C53C2314yes—
168C22×Q8×C53C2311yescharacteristic
169C23×C4×C53—21no—
170C23×C4×C53C2311yescharacteristic
171C2×Q16×C53—24no—
172C2×Q16×C53—42no—
173C2×Q16×C53C2314yes—
174C2×Q16×C53C2314yes—
175C22×C8×C53C2311yescharacteristic
176C22×C8×C53C2311yescharacteristic
177C22⋊Q8×C53—22no—
178C22⋊Q8×C53C2314yes—
179C2×C4⋊C4×C53—21no—
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C22⋊C4×C53—21no—
182#103×C53C2314yes—
183#103×C53C2314yes—
184C22⋊C8×C53C2314yes—
185C24×C53C2×D411yescharacteristic
186C23×D53C2×D411yescharacteristic
187C2×Q8×C53—21no—
188C2×Q8×C53—21no—
189C2×Q8×C53—24no—
190C2×Q8×C53—21no—
191C2×Q8×C53—22no—
192C2×Q8×C53—28no—
193C2×Q8×C53—22no—
194C2×Q8×C53—22no—
195C2×Q8×C53—22no—
196C2×Q8×C53—22no—
197C2×Q8×C53—44no—
198C2×Q8×C53—44no—
199C2×Q8×C53—48no—
200C2×Q8×C53#4114yes—
201C2×Q8×C53C2412yes—
202C2×Q8×C53C2412yes—
203C2×Q8×C53C2412yes—
204C22×C4×C53—21no—
205C22×C4×C53—22no—
206C22×C4×C53—22no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—24no—
211C22×C4×C53—44no—
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2×D412yes—
214C22×C4×C53C2412yes—
215C22×C4×C53C2411yescharacteristic
216C2×C22⋊D53Q1618yescomplemented
217C2×C22⋊D53C2×D414yes—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—24no—
223C22×Dic53—82no—
224C22×Dic53C2×D411yescharacteristic
225C22×Dic53C2×D411yescharacteristic
226C22×Dic53C2×D411yescharacteristic
227Q8×D53—28no—
228Q8×D53—44no—
229Q8×D53—48no—
230C2×C4×D53—22no—
231C2×C4×D53—22no—
232C2×C4×D53—24no—
233C2×C4×D53—24no—
234C2×C4×D53—44no—
235C2×C4×D53—82no—
236C2×C4×D53C2×D412yes—
237C2×C4×D53C2412yes—
238C2×Dic106—22no—
239C2×Dic106—22no—
240C2×Dic106—21no—
241C2×Dic106—24no—
242C2×Dic106—24no—
243C2×Dic106—44no—
244C2×Dic106—82no—
245C2×Dic106C2412yes—
246Q16×C53—28no—
247Q16×C53—44no—
248C2×C8×C53—22no—
249C2×C8×C53—22no—
250C2×C8×C53C2412yes—
251C2×C8×C53C2412yes—
252C4⋊C4×C53—24no—
253C4⋊C4×C53—21no—
254C4⋊C4×C53C2412yes—
255C22⋊C4×C53—24no—
256C22⋊Dic53—24no—
257C22⋊Dic53C2×D414yes—
258#11719925—44no—
259#11719921—24no—
260#11719921—24no—
261#11719921C2×D414yes—
262C4⋊Dic53—21no—
263C4⋊Dic53—21no—
264C4⋊Dic53—24no—
265C4⋊Dic53—21no—
266C4⋊Dic53—24no—
267C4⋊Dic53—24no—
268C4⋊Dic53C2412yes—
269C4⋊Dic53C2412yes—
270C4⋊Dic53C2412yes—
271#11719919—24no—
272#11719919—24no—
273#11719919—24no—
274#11719919—24no—
275#11719919—24no—
276#11719919—24no—
277#11719919—24no—
278#11719919C2×D414yes—
279C4×Dic53—24no—
280C4×Dic53—24no—
281C4×Dic53C2×D412yes—
282C4×Dic53C2412yes—
283C2×#88322—22no—
284C2×#88322—22no—
285C2×#88322—44no—
286C2×#88322C2412yes—
287C2×#88322C2412yes—
288C8×D53—44no—
289C23×C53—22no—
290C23×C53—22no—
291C23×C53C2×Q1614yes—
292C23×C53C22×D412yes—
293C23×C53C22×D411yescharacteristic
294C22×D53—22no—
295C22×D53—22no—
296C22×D53C2×Q1614yes—
297C22×D53C22×D412yes—
298Q8×C53—24no—
299Q8×C53—22no—
300Q8×C53—22no—
301Q8×C53—22no—
302Q8×C53—22no—
303Q8×C53—22no—
304Q8×C53—48no—
305Q8×C53—42no—
306Q8×C53—42no—
307Q8×C53C2×#4114yes—
308C2×C4×C53—24no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—24no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—48no—
318C2×C4×C53—42no—
319C2×C4×C53—42no—
320C2×C4×C53—42no—
321C2×C4×C53C22×D412yes—
322C2×C4×C53C22×D411yescharacteristic
323C2×C4×C53C2×#4112yes—
324C2×C4×C53H(5,𝔽2)12yes—
325C2×C4×C53C2511yescharacteristic
326C22⋊D53C2×Q16116yescomplemented
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337C2×Dic53—84no—
338C2×Dic53C2×Q1614yes—
339C2×Dic53C22×D412yes—
340C2×Dic53C22×D412yes—
341C2×Dic53C22×D412yes—
342C4×D53—24no—
343C4×D53—22no—
344C4×D53—22no—
345C4×D53—48no—
346C4×D53—84no—
347Dic106—22no—
348Dic106—22no—
349Dic106—48no—
350Dic106—42no—
351Dic106—84no—
352C8×C53—22no—
353C8×C53—22no—
354#88322—22no—
355#88322—22no—
356C2×#3299—531nomaximal, Sylow
357C22×C53—22no—
358C22×C53—28no—
359C22×C53—22no—
360C22×C53#54612yes—
361C22×C53C22×Q1614yes—
362C22×C53C22×Q1612yes—
363C22×C53#57712yes—
364C22×C53C23×D411yescharacteristic
365C2×D53—22no—
366C2×D53—28no—
367C2×D53—22no—
368C2×D53C22×Q1614yes—
369C4×C53—24no—
370C4×C53—22no—
371C4×C53—42no—
372C4×C53—42no—
373C4×C53—42no—
374C4×C53#54612yes—
375C4×C53C22×#4111yescharacteristic
376C4×C53C2×H(5,𝔽2)11yescharacteristic
377Dic53—22no—
378Dic53—22no—
379Dic53—42no—
380Dic53—42no—
381Dic53—42no—
382Dic53—42no—
383Dic53C22×Q1614yes—
384C2×#554—531no—
385C2×D4×Q8—531no—
386#3299—5316no—
387C2×#487—531no—
388C2×#484—531no—
389C2×#484—531no—
390C2×#477—531no—
391C2×#467—531no—
392C2×#467—531no—
393C2×#462—531no—
394C2×#451—531no—
395C2×#451D5311yescharacteristic, complemented
396C2×C4×Q16—531no—
397C2×C8×D4—531no—
398C22×#103—531no—
399C22×#103—531no—
400C2×C53—24no—
401C2×C53#329914yescomplemented
402C2×C53C2×#54611yescharacteristic
403C2×C53C23×Q1611yescharacteristic
404C2×C53C2×#57711yescharacteristic
405D53—24no—
406C23×Q8—531no—
407C23×Q8C2×D5311yescharacteristic
408C22×Q16—531no—
409C22×Q16C2×D5311yescharacteristic
410C22×Q16C2×D5311yescharacteristic
411C23×C8—531no—
412C23×C8—531no—
413#554—538no—
414#554—1064no—
415D4×Q8—538no—
416D4×Q8—1064no—
417C2×C4⋊Q8—531no—
418C2×C4⋊Q8—531no—
419C2×C4⋊Q8—1061no—
420C2×#125—1061no—
421C2×C22⋊Q8—531no—
422C2×C22⋊Q8—531no—
423C2×C22⋊Q8—531no—
424C2×C22⋊Q8—1061no—
425C2×C22⋊Q8—1061no—
426C2×C22⋊Q8—1061no—
427C2×C22⋊Q8—1061no—
428C2×C22⋊Q8C2×D5311yescharacteristic
429C2×C4×Q8—531no—
430C2×C4×Q8—531no—
431C2×C4×D4—531no—
432C2×C4×D4—1061no—
433C2×C4×D4—1061no—
434C22×C4⋊C4—531no—
435C22×C4⋊C4—531no—
436#487—538no—
437#484—538no—
438#484—538no—
439#477—538no—
440#467—538no—
441#467—538no—
442#462—538no—
443#451—538no—
444#451C2×D5318yescomplemented
445C4×Q16—538no—
446C8×D4—538no—
447C2×#107—531no—
448C2×#107—531no—
449C2×#107—531no—
450C2×C4⋊C8—531no—
451C2×#103—531no—
452C2×#103—531no—
453C2×#103—531no—
454C2×#103—531no—
455C2×#103—538no—
456C2×#103—531no—
457C2×#103—531no—
458C2×#103—531no—
459C2×#103—531no—
460C2×#103—538no—
461C2×#103C2×D5311yescharacteristic
462C2×#103C2×D5311yescharacteristic
463C2×C22⋊C8—531no—
464C2×C22⋊C8C2×D5311yescharacteristic
465C2×C4×C8—531no—
466C53C2×#329911yescharacteristic, complemented, Sylow
467C22×Q8—21no—
468C22×Q8—22no—
469C22×Q8—24no—
470C22×Q8—42no—
471C22×Q8—534no—
472C22×Q8—531no—
473C22×Q8—1061no—
474C22×Q8—1061no—
475C22×Q8—1062no—
476C22×Q8—1064no—
477C22×Q8—2122no—
478C22×Q8C22×D5311yescharacteristic
479C22×Q8C22×D5311yescharacteristic
480C22×Q8C22×D5314yes—
481C22×Q8C22×D5311yescharacteristic
482C22×D4—531no—
483C23×C4—21no—
484C23×C4—531no—
485C23×C4—1061no—
486C23×C4—1061no—
487C23×C4—1061no—
488C23×C4C22×D5311yescharacteristic
489C2×Q16—24no—
490C2×Q16—42no—
491C2×Q16—534no—
492C2×Q16—2122no—
493C2×Q16C22×D5314yes—
494C2×Q16C22×D5314yes—
495C22×C8—531no—
496C22×C8—531no—
497C22×C8—534no—
498C22×C8—534no—
499C22×C8—2122no—
500C22×C8—2122no—
501C22×C8C22×D5311yescharacteristic
502C22×C8C22×D5311yescharacteristic
503C4⋊Q8—534no—
504C4⋊Q8—534no—
505C4⋊Q8—1062no—
506C4⋊Q8—1062no—
507C4⋊Q8—1068no—
508#125—1068no—
509C22⋊Q8—22no—
510C22⋊Q8—534no—
511C22⋊Q8—534no—
512C22⋊Q8—534no—
513C22⋊Q8—1068no—
514C22⋊Q8—1068no—
515C22⋊Q8—1068no—
516C22⋊Q8—1068no—
517C22⋊Q8—1062no—
518C22⋊Q8—1062no—
519C22⋊Q8—1062no—
520C22⋊Q8C22×D5314yes—
521C4×Q8—534no—
522C4×Q8—534no—
523C4×Q8—1062no—
524C4×Q8—1062no—
525C4×D4—534no—
526C4×D4—534no—
527C4×D4—1068no—
528C4×D4—1068no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—531no—
531C2×C4⋊C4—531no—
532C2×C4⋊C4—531no—
533C2×C4⋊C4—534no—
534C2×C4⋊C4—531no—
535C2×C4⋊C4—534no—
536C2×C4⋊C4—1062no—
537C2×C4⋊C4—1061no—
538C2×C4⋊C4—1061no—
539C2×C4⋊C4—1061no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4—1061no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4—1061no—
544C2×C4⋊C4—1061no—
545C2×C4⋊C4—1061no—
546C2×C4⋊C4—1062no—
547C2×C4⋊C4—1061no—
548C2×C4⋊C4C22×D5311yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—531no—
551C2×C22⋊C4—531no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4—1061no—
555C2×C42—531no—
556C2×C42—1061no—
557C2×C42—1061no—
558#107—534no—
559#107—534no—
560#107—534no—
561C4⋊C8—534no—
562#103—534no—
563#103—534no—
564#103—534no—
565#103—534no—
566#103—534no—
567#103—534no—
568#103—534no—
569#103—534no—
570#103C22×D5314yes—
571#103C22×D5314yes—
572C22⋊C8—534no—
573C22⋊C8C22×D5314yes—
574C4×C8—534no—
575C24—531no—
576C24D4×D5311yescharacteristic
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—24no—
580C2×Q8—21no—
581C2×Q8—22no—
582C2×Q8—28no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—22no—
586C2×Q8—22no—
587C2×Q8—44no—
588C2×Q8—44no—
589C2×Q8—48no—
590C2×Q8—532no—
591C2×Q8—1064no—
592C2×Q8—1064no—
593C2×Q8—1061no—
594C2×Q8—1068no—
595C2×Q8—1062no—
596C2×Q8—1062no—
597C2×Q8—4242no—
598C2×Q8—2124no—
599C2×Q8—2124no—
600C2×Q8—2128no—
601C2×Q8#1171994714yes—
602C2×Q8C23×D5312yes—
603C2×Q8C23×D5312yes—
604C2×Q8C23×D5312yes—
605C2×D4—538no—
606C2×D4—534no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—24no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—44no—
615C22×C4—531no—
616C22×C4—531no—
617C22×C4—531no—
618C22×C4—532no—
619C22×C4—532no—
620C22×C4—1064no—
621C22×C4—1064no—
622C22×C4—1062no—
623C22×C4—1062no—
624C22×C4—1064no—
625C22×C4—1061no—
626C22×C4—1061no—
627C22×C4—1061no—
628C22×C4—1061no—
629C22×C4—4242no—
630C22×C4—4242no—
631C22×C4—2124no—
632C22×C4D4×D5312yes—
633C22×C4D4×D5311yescharacteristic
634C22×C4C23×D5312yes—
635C22×C4C23×D5311yescharacteristic
636Q16—28no—
637Q16—44no—
638Q16—2124no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—532no—
642C2×C8—532no—
643C2×C8—1062no—
644C2×C8—1062no—
645C2×C8—2124no—
646C2×C8—2124no—
647C2×C8C23×D5312yes—
648C2×C8C23×D5312yes—
649C4⋊C4—24no—
650C4⋊C4—21no—
651C4⋊C4—534no—
652C4⋊C4—532no—
653C4⋊C4—532no—
654C4⋊C4—532no—
655C4⋊C4—1064no—
656C4⋊C4—1064no—
657C4⋊C4—1064no—
658C4⋊C4—1064no—
659C4⋊C4—1064no—
660C4⋊C4—1064no—
661C4⋊C4—1064no—
662C4⋊C4—1064no—
663C4⋊C4—1061no—
664C4⋊C4—1064no—
665C4⋊C4—1061no—
666C4⋊C4—1061no—
667C4⋊C4—1064no—
668C4⋊C4C23×D5312yes—
669C22⋊C4—24no—
670C22⋊C4—534no—
671C22⋊C4—534no—
672C22⋊C4—1064no—
673C22⋊C4—1064no—
674C22⋊C4—1064no—
675C42—532no—
676C42—532no—
677C42—1064no—
678C42—1064no—
679C23—22no—
680C23—22no—
681C23—534no—
682C23—532no—
683C23—1062no—
684C23—1062no—
685C23Q16×D5314yes—
686C23C2×D4×D5312yes—
687C23C2×D4×D5311yescharacteristic
688Q8—22no—
689Q8—24no—
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8—22no—
694Q8—48no—
695Q8—42no—
696Q8—42no—
697Q8—1062no—
698Q8—1062no—
699Q8—4244no—
700Q8—2128no—
701Q8—2122no—
702Q8C2×#1171994714yes—
703D4—5316no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—48no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—534no—
718C2×C4—532no—
719C2×C4—532no—
720C2×C4—532no—
721C2×C4—1062no—
722C2×C4—1062no—
723C2×C4—1062no—
724C2×C4—1062no—
725C2×C4—1064no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—4244no—
731C2×C4—4244no—
732C2×C4—2128no—
733C2×C4—2122no—
734C2×C4—2122no—
735C2×C4—2122no—
736C2×C4—2122no—
737C2×C4C2×D4×D5312yes—
738C2×C4C2×D4×D5311yescharacteristic
739C2×C4C2×#1171994712yes—
740C2×C4#1313326212yes—
741C2×C4C24×D5311yescharacteristic
742C8—22no—
743C8—22no—
744C8—1062no—
745C8—1062no—
746C22—28no—
747C22—22no—
748C22—22no—
749C22—534no—
750C22—1068no—
751C22—1062no—
752C22—1062no—
753C22#1681126012yes—
754C22C2×Q16×D5314yes—
755C22C2×Q16×D5312yes—
756C22#1681143212yes—
757C22C22×D4×D5311yescharacteristic
758C4—22no—
759C4—24no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—534no—
764C4—1062no—
765C4—1062no—
766C4—2122no—
767C4—2122no—
768C4—2122no—
769C4—2122no—
770C4#1681126012yes—
771C4C22×#1171994711yescharacteristic
772C4C2×#1313326211yescharacteristic
773C2—24no—
774C2—1064no—
775C2#2028658414yesdirect product factor
776C2C2×#1681126011yescharacteristic
777C2C22×Q16×D5311yescharacteristic
778C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#451C2
socleC23×C53C22×D4
prime radicalC22×C22⋊D53D4
hypercenterC2×#451D53
hypocenterC53C2×#3299
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
3. #20286584C2direct (N × H)
4. C2×#16810972C2semidirect
5. C2×#16810959C2semidirect
6. C2×#16810957C2semidirect
7. C2×#16810916C2semidirect
8. C2×#16810862C2semidirect
9. C2×#16810861C2semidirect
10. C2×#16810831C2semidirect
11. C2×#16810777C2semidirect
12. C2×Q16×Dic53C2semidirect
14. C22×#13133141C2semidirect
15. C2×#103×D53C2semidirect
16. C2×C53×#451C2semidirect
43. #16810972C22semidirect
44. #16810959C22semidirect
45. #16810957C22semidirect
46. #16810916C22semidirect
47. #16810862C22semidirect
48. #16810861C22semidirect
49. #16810831C22semidirect
50. #16810777C22semidirect
51. Q16×Dic53C22semidirect
64. C2×#13133141C22semidirect
66. #103×D53C22semidirect
73. C53×#451C22semidirect
216. C2×C22⋊D53Q16semidirect
326. C22⋊D53C2×Q16semidirect
395. C2×#451D53semidirect
401. C2×C53#3299semidirect
444. #451C2×D53semidirect
466. C53C2×#3299semidirect
775. C2#20286584direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113312
C2×Q8×C22⋊D532
#202865842
C2×#168109722
C2×#168109592
C2×#168109572
C2×#168109162
C2×#168108622
C2×#168108612
C2×#168108312
C2×#168107772
C2×Q16×Dic532
C2×#168106862
C22×#131331412
C2×#103×D532
C2×C53×#4512
C2×#329953