Finite Group Databasebeta

← C2×#20286589 #28260485

Subgroups — C2×#20286589 #28260485

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×#16811328C211yesmaximal, characteristic
2C2×#16811286C211yesmaximal, characteristic
3#20286589C2116yesmaximal, direct product factor
4C2×#16810972C211yesmaximal, characteristic, complemented
5C2×#16810960C211yesmaximal, characteristic, complemented
6C2×#16810917C211yesmaximal, characteristic, complemented
7C2×#16810865C211yesmaximal, characteristic, complemented
8C2×#16810862C211yesmaximal, characteristic, complemented
9C2×#16810832C211yesmaximal, characteristic, complemented
10C2×#16810781C211yesmaximal, characteristic, complemented
11C2×#16810780C211yesmaximal, characteristic, complemented
12C2×#16810717C211yesmaximal, characteristic, complemented
13C2×#16810686C211yesmaximal, characteristic
14C22×#13133140C211yesmaximal, characteristic, complemented
15C2×#103×D53C211yesmaximal, characteristic, complemented
16C2×C53×#484C211yesmaximal, characteristic, complemented
17C23×Dic106C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×Dic212C2211yescharacteristic
20C22×Dic212C2211yescharacteristic
21C22×#11719925C2211yescharacteristic
22C23×#88322C2211yescharacteristic
23C22×C8×D53C2211yescharacteristic
24#16811328—24no—
25#16811328C2218yes—
26#16811286—24no—
27#16811286C2218yes—
28C2×#13133216—21no—
29C2×#13133216C2211yescharacteristic
30C2×#13133215C2211yescharacteristic
31C2×#13133207—21no—
32C2×#13133197C2211yescharacteristic
33C2×#13133197C2211yescharacteristic
34C2×#13133196—21no—
35C2×#13133196C2211yescharacteristic
36C2×#13133195—21no—
37C2×#13133195—21no—
38C2×#13133194—21no—
39C2×#13133182C2211yescharacteristic
40C2×#13133182C2211yescharacteristic
41C2×C4×C22⋊D53—21no—
42C2×C4×C22⋊D53C2211yescharacteristic
43C2×#13133177—21no—
44C2×C4⋊C4×D53C2211yescharacteristic
45#16810972C2218yescomplemented
46#16810960C2218yescomplemented
47#16810917C2218yescomplemented
48#16810865C2218yescomplemented
49#16810862C2218yescomplemented
50#16810832C2218yescomplemented
51#16810781C2218yescomplemented
52#16810780C2218yescomplemented
53#16810717C2218yescomplemented
54#16810686C2218yes—
55C2×#13133150C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57C2×#13133142C2211yescharacteristic
58C2×#13133142C2211yescharacteristic
59C2×#13133141C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133140C2218yescomplemented
66#103×D53C2218yescomplemented
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×C22⋊Q8×C53C2211yescharacteristic
70C22×C4⋊C4×C53C2211yescharacteristic
71C53×#484C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#107×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C22×Dic106—24no—
78C22×Dic106—22no—
79C22×Dic106—21no—
80C22×Dic106—21no—
81C22×Dic106—21no—
82C22×Dic106—42no—
83C22×Dic106C2311yescharacteristic
84C22×Dic106C2311yescharacteristic
85C22×Dic106C2314yes—
86C22×Dic106C2311yescharacteristic
87C2×Q8×D53—22no—
88C2×Q8×D53—24no—
89C2×Q8×D53—42no—
90C2×Q8×D53C2314yes—
91C22×C22⋊D53D411yescharacteristic
92C23×Dic53—21no—
93C22×C4×D53—21no—
94C22×C4×D53—21no—
95C22×C4×D53C2311yescharacteristic
96C2×Dic212—24no—
97C2×Dic212—42no—
98C2×Dic212C2314yes—
99C2×Dic212C2314yes—
100C2×#11719925—42no—
101C2×#11719925C2314yes—
102C22×#88322—42no—
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105C22×#88322C2314yes—
106C2×C8×D53—42no—
107C2×C8×D53C2314yes—
108#13133216—28no—
109#13133216—22no—
110#13133216C2314yes—
111#13133215—22no—
112#13133215C2314yes—
113#13133207—28no—
114#13133197—22no—
115#13133197—22no—
116#13133197C2314yes—
117#13133197C2314yes—
118#13133196—28no—
119#13133196—22no—
120#13133196C2314yes—
121#13133195—28no—
122#13133195—28no—
123#13133194—28no—
124#13133182—22no—
125#13133182—22no—
126#13133182C2314yes—
127#13133182C2314yes—
128C4×C22⋊D53—28no—
129C4×C22⋊D53D414yes—
130C4×C22⋊D53C2314yes—
131#13133177—28no—
132C2×C4⋊Dic53—21no—
133C2×C4⋊Dic53—21no—
134C2×C4⋊Dic53C2311yescharacteristic
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×#11719919—21no—
141C2×#11719919—21no—
142C2×#11719919D411yescharacteristic
143C4⋊C4×D53—22no—
144C4⋊C4×D53C2314yes—
145C2×C22⋊Dic53—21no—
146C2×C22⋊Dic53D411yescharacteristic
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921D411yescharacteristic
150C2×C4×Dic53—21no—
151C2×C4×Dic53—21no—
152C2×C4×Dic53C2311yescharacteristic
153#13133150C2314yes—
154#13133146C2314yes—
155#13133142C2314yes—
156#13133142C2314yes—
157#13133141C2314yes—
158#13133140C2314yes—
159#13133140C2314yes—
160#13133140C2314yes—
161#13133140C2314yes—
162#13133140C2314yes—
163#13133129C2314yes—
164C8×Dic53C2314yes—
165C22×Q8×C53C2311yescharacteristic
166C23×C4×C53—21no—
167C23×C4×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170C22⋊Q8×C53—22no—
171C22⋊Q8×C53C2314yes—
172C2×C4⋊C4×C53—22no—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C4⋊C4×C53C2314yes—
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C22⋊C4×C53—21no—
180#107×C53C2314yes—
181#107×C53C2314yes—
182#103×C53C2314yes—
183#103×C53C2314yes—
184C22⋊C8×C53C2314yes—
185C24×C53C2×D411yescharacteristic
186C23×D53C2×D411yescharacteristic
187C2×Q8×C53—21no—
188C2×Q8×C53—22no—
189C2×Q8×C53—22no—
190C2×Q8×C53C2412yes—
191C22×C4×C53—22no—
192C22×C4×C53—22no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—24no—
198C22×C4×C53—82no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D412yes—
201C22×C4×C53C2412yes—
202C22×C4×C53C2411yescharacteristic
203C2×C22⋊D53Q1618yescomplemented
204C2×C22⋊D53C2×D414yes—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—24no—
210C22×Dic53—44no—
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213C22×Dic53C2×D411yescharacteristic
214Q8×D53—28no—
215Q8×D53—44no—
216Q8×D53—48no—
217C2×C4×D53—22no—
218C2×C4×D53—22no—
219C2×C4×D53—24no—
220C2×C4×D53—24no—
221C2×C4×D53—44no—
222C2×C4×D53—82no—
223C2×C4×D53C2×D412yes—
224C2×C4×D53C2412yes—
225C2×Dic106—21no—
226C2×Dic106—22no—
227C2×Dic106—22no—
228C2×Dic106—22no—
229C2×Dic106—22no—
230C2×Dic106—22no—
231C2×Dic106—28no—
232C2×Dic106—21no—
233C2×Dic106—24no—
234C2×Dic106—21no—
235C2×Dic106—24no—
236C2×Dic106—24no—
237C2×Dic106—44no—
238C2×Dic106—48no—
239C2×Dic106—44no—
240C2×Dic106—44no—
241C2×Dic106—82no—
242C2×Dic106#4114yes—
243C2×Dic106C2412yes—
244C2×Dic106C2412yes—
245C2×Dic106C2412yes—
246C2×C8×C53—22no—
247C2×C8×C53—22no—
248C2×C8×C53C2412yes—
249C2×C8×C53C2412yes—
250C4⋊C4×C53—21no—
251C4⋊C4×C53—24no—
252C4⋊C4×C53—21no—
253C4⋊C4×C53—24no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53C2412yes—
256C4⋊C4×C53C2412yes—
257C4⋊C4×C53C2412yes—
258C22⋊C4×C53—24no—
259C22⋊Dic53—24no—
260C22⋊Dic53C2×D414yes—
261#11719925—44no—
262#11719921—24no—
263#11719921—24no—
264#11719921C2×D414yes—
265C4⋊Dic53—21no—
266C4⋊Dic53—24no—
267C4⋊Dic53—24no—
268C4⋊Dic53C2412yes—
269#11719919—24no—
270#11719919—24no—
271#11719919—24no—
272#11719919—24no—
273#11719919—24no—
274#11719919—24no—
275#11719919—24no—
276#11719919C2×D414yes—
277C4×Dic53—24no—
278C4×Dic53—24no—
279C4×Dic53C2×D412yes—
280C4×Dic53C2412yes—
281C2×#88322—22no—
282C2×#88322—22no—
283C2×#88322—44no—
284C2×#88322C2412yes—
285C2×#88322C2412yes—
286Dic212—28no—
287Dic212—44no—
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—22no—
299Q8×C53—22no—
300Q8×C53—42no—
301C2×C4×C53—22no—
302C2×C4×C53—24no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—42no—
310C2×C4×C53—42no—
311C2×C4×C53—42no—
312C2×C4×C53—42no—
313C2×C4×C53—84no—
314C2×C4×C53C22×D412yes—
315C2×C4×C53C22×D411yescharacteristic
316C2×C4×C53C2×#4112yes—
317C2×C4×C53H(5,𝔽2)12yes—
318C2×C4×C53C2511yescharacteristic
319C22⋊D53C2×Q16116yescomplemented
320C2×Dic53—24no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—48no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53C2×Q1614yes—
332C2×Dic53C22×D412yes—
333C2×Dic53C22×D412yes—
334C2×Dic53C22×D412yes—
335C4×D53—24no—
336C4×D53—22no—
337C4×D53—22no—
338C4×D53—48no—
339C4×D53—84no—
340Dic106—24no—
341Dic106—22no—
342Dic106—22no—
343Dic106—22no—
344Dic106—22no—
345Dic106—22no—
346Dic106—48no—
347Dic106—48no—
348Dic106—42no—
349Dic106—42no—
350Dic106—84no—
351Dic106C2×#4114yes—
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—22no—
370C4×C53—42no—
371C4×C53—42no—
372C4×C53—42no—
373C4×C53—42no—
374C4×C53#54612yes—
375C4×C53C22×#4111yescharacteristic
376C4×C53C2×H(5,𝔽2)11yescharacteristic
377Dic53—24no—
378Dic53—22no—
379Dic53—22no—
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×#484D5311yescharacteristic, complemented
390C2×#477—531no—
391C2×#467—531no—
392C2×#467—531no—
393C2×#462—531no—
394C2×#451—531no—
395C2×#451—531no—
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×Q8—531no—
408C22×Q16—531no—
409C22×Q16—531no—
410C22×Q16—531no—
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⋊C4C2×D5311yescharacteristic
436#487—538no—
437#484—538no—
438#484C2×D5318yescomplemented
439#477—538no—
440#467—538no—
441#467—538no—
442#462—538no—
443#451—538no—
444#451—538no—
445C4×Q16—538no—
446C8×D4—538no—
447C2×#107—531no—
448C2×#107C2×D5311yescharacteristic
449C2×#107C2×D5311yescharacteristic
450C2×C4⋊C8—531no—
451C2×#103—531no—
452C2×#103—531no—
453C2×#103—531no—
454C2×#103—531no—
455C2×#103—531no—
456C2×#103—531no—
457C2×#103—531no—
458C2×#103—538no—
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—534no—
468C22×Q8—531no—
469C22×Q8—531no—
470C22×Q8—531no—
471C22×Q8—534no—
472C22×Q8—1061no—
473C22×Q8—1061no—
474C22×Q8—1064no—
475C22×Q8—1062no—
476C22×Q8—1061no—
477C22×Q8—1062no—
478C22×Q8—1064no—
479C22×Q8—2122no—
480C22×Q8—2122no—
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—534no—
490C2×Q16—534no—
491C2×Q16—534no—
492C2×Q16—1064no—
493C2×Q16—2122no—
494C2×Q16—2122no—
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—22no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—531no—
533C2×C4⋊C4—531no—
534C2×C4⋊C4—534no—
535C2×C4⋊C4—1062no—
536C2×C4⋊C4—1061no—
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⋊C4C22×D5311yescharacteristic
546C2×C4⋊C4C22×D5311yescharacteristic
547C2×C4⋊C4C22×D5314yes—
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#107C22×D5314yes—
560#107C22×D5314yes—
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—22no—
579C2×Q8—22no—
580C2×Q8—534no—
581C2×Q8—532no—
582C2×Q8—532no—
583C2×Q8—532no—
584C2×Q8—1064no—
585C2×Q8—1064no—
586C2×Q8—1068no—
587C2×Q8—1061no—
588C2×Q8—1061no—
589C2×Q8—1064no—
590C2×Q8—1061no—
591C2×Q8—1062no—
592C2×Q8—1068no—
593C2×Q8—1062no—
594C2×Q8—1062no—
595C2×Q8—1062no—
596C2×Q8—1062no—
597C2×Q8—4242no—
598C2×Q8—2124no—
599C2×Q8—2124no—
600C2×Q8—2128no—
601C2×Q8—2124no—
602C2×Q8—2124no—
603C2×Q8—2128no—
604C2×Q8C23×D5312yes—
605C2×D4—538no—
606C2×D4—534no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—24no—
614C22×C4—82no—
615C22×C4—531no—
616C22×C4—531no—
617C22×C4—531no—
618C22×C4—532no—
619C22×C4—532no—
620C22×C4—1064no—
621C22×C4—1064no—
622C22×C4—1061no—
623C22×C4—1062no—
624C22×C4—1062no—
625C22×C4—1064no—
626C22×C4—1061no—
627C22×C4—1061no—
628C22×C4—1061no—
629C22×C4—4242no—
630C22×C4—2124no—
631C22×C4—2124no—
632C22×C4D4×D5312yes—
633C22×C4D4×D5311yescharacteristic
634C22×C4C23×D5312yes—
635C22×C4C23×D5311yescharacteristic
636Q16—1068no—
637Q16—2124no—
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—21no—
650C4⋊C4—24no—
651C4⋊C4—21no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—534no—
655C4⋊C4—532no—
656C4⋊C4—1064no—
657C4⋊C4—1064no—
658C4⋊C4—1064no—
659C4⋊C4—1064no—
660C4⋊C4—1064no—
661C4⋊C4—1064no—
662C4⋊C4—1064no—
663C4⋊C4—1064no—
664C4⋊C4—1061no—
665C4⋊C4—1064no—
666C4⋊C4C23×D5312yes—
667C4⋊C4C23×D5312yes—
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—22no—
690Q8—42no—
691Q8—534no—
692Q8—1064no—
693Q8—1062no—
694Q8—1062no—
695Q8—1062no—
696Q8—1062no—
697Q8—1062no—
698Q8—4244no—
699Q8—2128no—
700Q8—2128no—
701Q8—2122no—
702Q8—2122no—
703D4—5316no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—84no—
717C2×C4—534no—
718C2×C4—532no—
719C2×C4—532no—
720C2×C4—532no—
721C2×C4—1062no—
722C2×C4—1064no—
723C2×C4—1062no—
724C2×C4—1062no—
725C2×C4—1064no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—4244no—
732C2×C4—2128no—
733C2×C4—2128no—
734C2×C4—2122no—
735C2×C4—2122no—
736C2×C4—2122no—
737C2×C4C2×D4×D5312yes—
738C2×C4C2×D4×D5311yescharacteristic
739C2×C4#41×D5312yes—
740C2×C4#1313326312yes—
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#1681126512yes—
754C22C2×Q16×D5314yes—
755C22C2×Q16×D5312yes—
756C22#1681143312yes—
757C22C22×D4×D5311yescharacteristic
758C4—22no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—534no—
764C4—1062no—
765C4—1064no—
766C4—1062no—
767C4—2122no—
768C4—2122no—
769C4—2122no—
770C4#1681126512yes—
771C4C2×#41×D5311yescharacteristic
772C4C2×#1313326311yescharacteristic
773C2—24no—
774C2—1064no—
775C2#2028658914yesdirect product factor
776C2C2×#1681126511yescharacteristic
777C2C22×Q16×D5311yescharacteristic
778C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#484C2
socleC23×C53C22×D4
prime radicalC22×C22⋊D53D4
hypercenterC2×#484D53
hypocenterC53C2×#3299
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. #20286589C2direct (N × H)
4. C2×#16810972C2semidirect
5. C2×#16810960C2semidirect
6. C2×#16810917C2semidirect
7. C2×#16810865C2semidirect
8. C2×#16810862C2semidirect
9. C2×#16810832C2semidirect
10. C2×#16810781C2semidirect
11. C2×#16810780C2semidirect
12. C2×#16810717C2semidirect
14. C22×#13133140C2semidirect
15. C2×#103×D53C2semidirect
16. C2×C53×#484C2semidirect
45. #16810972C22semidirect
46. #16810960C22semidirect
47. #16810917C22semidirect
48. #16810865C22semidirect
49. #16810862C22semidirect
50. #16810832C22semidirect
51. #16810781C22semidirect
52. #16810780C22semidirect
53. #16810717C22semidirect
65. C2×#13133140C22semidirect
66. #103×D53C22semidirect
71. C53×#484C22semidirect
203. C2×C22⋊D53Q16semidirect
319. C22⋊D53C2×Q16semidirect
389. C2×#484D53semidirect
401. C2×C53#3299semidirect
438. #484C2×D53semidirect
466. C53C2×#3299semidirect
775. C2#20286589direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113282
C2×#168112862
#202865892
C2×#168109722
C2×#168109602
C2×#168109172
C2×#168108652
C2×#168108622
C2×#168108322
C2×#168107812
C2×#168107802
C2×#168107172
C2×#168106862
C22×#131331402
C2×#103×D532
C2×C53×#4842
C2×#329953