Finite Group Databasebeta

← C2×#20285609 #28254791

Subgroups — C2×#20285609 #28254791

Order 13568.

2122 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811199C211yesmaximal, characteristic
2C2×#16811196C211yesmaximal, characteristic
3#20285609C2116yesmaximal, direct product factor
4C2×#16810967C211yesmaximal, characteristic, complemented
5C2×#16810966C211yesmaximal, characteristic, complemented
6C2×#16810964C211yesmaximal, characteristic, complemented
7C2×#16810882C211yesmaximal, characteristic, complemented
8C2×#16810880C211yesmaximal, characteristic, complemented
9C2×#16810865C211yesmaximal, characteristic, complemented
10C2×#16810863C211yesmaximal, characteristic, complemented
11C2×#16810781C211yesmaximal, characteristic, complemented
12C2×#16810780C211yesmaximal, characteristic, complemented
13C2×#16810780C211yesmaximal, characteristic, complemented
14C2×#16810778C211yesmaximal, characteristic, complemented
15C2×#16810588C211yesmaximal, characteristic
16C2×C53×#485C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C23×Dic106C2211yescharacteristic
19C22×Q8×D53C2211yescharacteristic
20C22×Dic212C2211yescharacteristic
21C22×Dic212C2211yescharacteristic
22C22×#11719925C2211yescharacteristic
23C22×#11719925C2211yescharacteristic
24C22×#11719912C2211yescharacteristic
25C22×C8×D53C2211yescharacteristic
26#16811199—24no—
27#16811199C2218yes—
28#16811196—24no—
29#16811196C2218yes—
30C2×#13133217—21no—
31C2×#13133216—21no—
32C2×#13133205—21no—
33C2×#13133203—21no—
34C2×#13133202—21no—
35C2×#13133201—21no—
36C2×#13133201—21no—
37C2×#13133199—21no—
38C2×#13133197C2211yescharacteristic
39C2×#13133197C2211yescharacteristic
40C2×#13133197C2211yescharacteristic
41C2×#13133197C2211yescharacteristic
42C2×#13133197C2211yescharacteristic
43C2×#13133196C2211yescharacteristic
44C2×#13133193C2211yescharacteristic
45C2×#13133175C2211yescharacteristic
46#16810967C2218yescomplemented
47#16810966C2218yescomplemented
48#16810964C2218yescomplemented
49#16810882C2218yescomplemented
50#16810880C2218yescomplemented
51#16810865C2218yescomplemented
52#16810863C2218yescomplemented
53#16810781C2218yescomplemented
54#16810780C2218yescomplemented
55#16810780C2218yescomplemented
56#16810778C2218yescomplemented
57C2×#13133150C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65#16810588C2218yes—
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C2×C22⋊Q8×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C53×#485C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719945—42no—
78C2×#11719945—42no—
79C2×#11719945D414yes—
80C2×#11719945C2314yes—
81C22×Dic106—21no—
82C22×Dic106—22no—
83C22×Dic106—21no—
84C22×Dic106—42no—
85C22×Dic106—42no—
86C22×Dic106D411yescharacteristic
87C22×Dic106C2311yescharacteristic
88C22×Dic106C2311yescharacteristic
89C22×Dic106C2311yescharacteristic
90C22×Dic106C2314yes—
91C2×Q8×D53—22no—
92C2×Q8×D53—42no—
93C2×Q8×D53—42no—
94C2×Q8×D53C2314yes—
95C22×D212D411yescharacteristic
96C22×C22⋊D53D411yescharacteristic
97C22×C22⋊D53D411yescharacteristic
98C23×Dic53—21no—
99C22×C4×D53—21no—
100C22×C4×D53C2311yescharacteristic
101C22×C4×D53C2311yescharacteristic
102C2×Dic212—42no—
103C2×Dic212—42no—
104C2×Dic212C2314yes—
105C2×Dic212C2314yes—
106C2×#11719925—42no—
107C2×#11719925—42no—
108C2×#11719925C2314yes—
109C2×#11719925C2314yes—
110C2×#11719912—42no—
111C2×#11719912C2314yes—
112C22×#88322C2311yescharacteristic
113C22×#88322C2311yescharacteristic
114C2×C8×D53—42no—
115C2×C8×D53C2314yes—
116#13133217—28no—
117#13133216—28no—
118#13133205—28no—
119#13133203—28no—
120#13133202—28no—
121#13133201—28no—
122#13133201—28no—
123#13133199—28no—
124#13133197—22no—
125#13133197—22no—
126#13133197—22no—
127#13133197—22no—
128#13133197—22no—
129#13133197C2314yes—
130#13133197C2314yes—
131#13133197C2314yes—
132#13133197C2314yes—
133#13133197C2314yes—
134#13133196—22no—
135#13133196C2314yes—
136#13133193—22no—
137#13133193C2314yes—
138#13133175—22no—
139#13133175C2314yes—
140C2×C4⋊Dic53—21no—
141C2×C4⋊Dic53—21no—
142C2×C4⋊Dic53—21no—
143C2×C4⋊Dic53—21no—
144C2×C4⋊Dic53—21no—
145C2×C4⋊Dic53C2311yescharacteristic
146C2×#11719919—21no—
147C2×#11719919—21no—
148C2×C22⋊Dic53—21no—
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×#11719921—21no—
152C2×#11719921—21no—
153C2×#11719921—21no—
154C2×#11719921—21no—
155C2×#11719921—21no—
156C2×C4×Dic53—21no—
157#13133150C2314yes—
158#13133148C2314yes—
159#13133142C2314yes—
160#13133142C2314yes—
161#13133140C2314yes—
162#13133140C2314yes—
163#13133140C2314yes—
164#13133140C2314yes—
165C22⋊#88322C2314yes—
166#13133129C2314yes—
167#13133129C2314yes—
168C22×Q8×C53C2311yescharacteristic
169C23×C4×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172C22⋊Q8×C53—22no—
173C22⋊Q8×C53C2314yes—
174#117×C53—22no—
175#117×C53C2314yes—
176C2×C4⋊C4×C53—21no—
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C4⋊C4×C53C2311yescharacteristic
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53—21no—
182C2×C42×C53—21no—
183#107×C53C2314yes—
184#106×C53C2314yes—
185#103×C53C2314yes—
186#103×C53C2314yes—
187C22⋊C8×C53C2314yes—
188C24×C53C2×D411yescharacteristic
189C23×D53C2×D411yescharacteristic
190C23×D53C2×D411yescharacteristic
191C2×Q8×C53—21no—
192C2×Q8×C53—22no—
193C2×Q8×C53—22no—
194C2×Q8×C53C2412yes—
195C22×C4×C53—22no—
196C22×C4×C53—22no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D412yes—
203C22×C4×C53C2412yes—
204C22×C4×C53C2411yescharacteristic
205C2×C22⋊D53—42no—
206C2×C22⋊D53—42no—
207C2×C22⋊D53C2×D414yes—
208C2×C22⋊D53C2×D414yes—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—24no—
214C22×Dic53—44no—
215C22×Dic53C2×D411yescharacteristic
216C22×Dic53C2×D411yescharacteristic
217Q8×D53—44no—
218Q8×D53—44no—
219Q8×D53—48no—
220#11719945—48no—
221#11719945—44no—
222#11719945—44no—
223C2×D212—42no—
224C2×D212C2×D414yes—
225C2×C4×D53—22no—
226C2×C4×D53—22no—
227C2×C4×D53—22no—
228C2×C4×D53—22no—
229C2×C4×D53—24no—
230C2×C4×D53—44no—
231C2×C4×D53C2×D412yes—
232C2×C4×D53C2×D412yes—
233C2×C4×D53C2412yes—
234C2×C4×D53C2412yes—
235C2×Dic106—22no—
236C2×Dic106—22no—
237C2×Dic106—22no—
238C2×Dic106—22no—
239C2×Dic106—22no—
240C2×Dic106—22no—
241C2×Dic106—21no—
242C2×Dic106—21no—
243C2×Dic106—21no—
244C2×Dic106—24no—
245C2×Dic106—24no—
246C2×Dic106—44no—
247C2×Dic106—44no—
248C2×Dic106—42no—
249C2×Dic106—44no—
250C2×Dic106—44no—
251C2×Dic106—48no—
252C2×Dic106C2×D414yes—
253C2×Dic106C2412yes—
254C2×Dic106C2412yes—
255C2×Dic106C2412yes—
256C2×C8×C53—22no—
257C2×C8×C53—22no—
258C2×C8×C53C2412yes—
259C2×C8×C53C2412yes—
260C4⋊C4×C53—24no—
261C4⋊C4×C53—21no—
262C4⋊C4×C53—21no—
263C4⋊C4×C53—21no—
264C4⋊C4×C53C2412yes—
265C4⋊C4×C53C2412yes—
266C4⋊C4×C53C2412yes—
267C22⋊C4×C53—24no—
268C22⋊C4×C53—24no—
269C42×C53—24no—
270C22⋊Dic53—24no—
271#11719925—44no—
272#11719925—44no—
273#11719921—24no—
274#11719921—24no—
275#11719921—24no—
276#11719921—24no—
277#11719921—24no—
278#11719921—24no—
279#11719921—24no—
280C4⋊Dic53—21no—
281C4⋊Dic53—24no—
282C4⋊Dic53—24no—
283C4⋊Dic53—24no—
284C4⋊Dic53—24no—
285C4⋊Dic53—24no—
286C4⋊Dic53C2412yes—
287#11719919—24no—
288#11719919—24no—
289C4×Dic53—24no—
290C2×#88322—22no—
291C2×#88322—22no—
292C2×#88322C2412yes—
293C2×#88322C2412yes—
294Dic212—44no—
295Dic212—44no—
296#11719912—44no—
297C8×D53—44no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53—22no—
301C23×C53C22×D412yes—
302C23×C53C22×D411yescharacteristic
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—22no—
306C22×D53—22no—
307C22×D53—22no—
308C22×D53—22no—
309C22×D53C22×D412yes—
310C22×D53C22×D412yes—
311Q8×C53—22no—
312Q8×C53—22no—
313Q8×C53—42no—
314C2×C4×C53—22no—
315C2×C4×C53—24no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—42no—
323C2×C4×C53—42no—
324C2×C4×C53—42no—
325C2×C4×C53—42no—
326C2×C4×C53C22×D412yes—
327C2×C4×C53C22×D411yescharacteristic
328C2×C4×C53H(5,𝔽2)12yes—
329C2×C4×C53H(5,𝔽2)12yes—
330C2×C4×C53C2511yescharacteristic
331C22⋊D53—44no—
332C22⋊D53—44no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—48no—
340C2×Dic53—42no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344C2×Dic53C22×D412yes—
345C2×Dic53C22×D412yes—
346D212—44no—
347C4×D53—24no—
348C4×D53—24no—
349C4×D53—22no—
350C4×D53—22no—
351C4×D53—22no—
352C4×D53—22no—
353C4×D53—48no—
354Dic106—22no—
355Dic106—22no—
356Dic106—22no—
357Dic106—22no—
358Dic106—22no—
359Dic106—22no—
360Dic106—44no—
361Dic106—48no—
362Dic106—48no—
363Dic106—42no—
364Dic106—42no—
365Dic106—42no—
366C8×C53—22no—
367C8×C53—22no—
368#88322—22no—
369#88322—22no—
370C2×#3202—531nomaximal, Sylow
371C22×C53—22no—
372C22×C53—22no—
373C22×C53—22no—
374C22×C53—44no—
375C22×C53#53412yes—
376C22×C53#57812yes—
377C22×C53#57812yes—
378C22×C53C23×D411yescharacteristic
379C2×D53—22no—
380C2×D53—22no—
381C2×D53—22no—
382C2×D53—22no—
383C2×D53—22no—
384C2×D53—22no—
385C2×D53—44no—
386C2×D53—44no—
387C4×C53—22no—
388C4×C53—42no—
389C4×C53—42no—
390C4×C53—42no—
391C4×C53—42no—
392C4×C53#53412yes—
393C4×C53C2×H(5,𝔽2)11yescharacteristic
394C4×C53C2×H(5,𝔽2)11yescharacteristic
395Dic53—22no—
396Dic53—22no—
397Dic53—42no—
398Dic53—42no—
399Dic53—42no—
400Dic53—42no—
401C2×#536—531no—
402C2×#536—531no—
403#3202—5316no—
404C2×#485—531no—
405C2×#485—531no—
406C2×#485—531no—
407C2×#485D5311yescharacteristic, complemented
408C2×#470—531no—
409C2×#470—531no—
410C2×#467—531no—
411C2×#467—531no—
412C2×#451—531no—
413C2×#451—531no—
414C2×#451—531no—
415C2×#451—531no—
416C2×#408—531no—
417C2×C53—42no—
418C2×C53#320214yescomplemented
419C2×C53C2×#53411yescharacteristic
420C2×C53C2×#57811yescharacteristic
421C2×C53C2×#57811yescharacteristic
422D53—42no—
423D53—42no—
424C22×#41—531no—
425C23×Q8—531no—
426C23×Q8—531no—
427C22×Q16—531no—
428C22×Q16—531no—
429C22×Q16—531no—
430C22×Q16—531no—
431C22×M16—531no—
432C23×C8—531no—
433#536—538no—
434#536—538no—
435#536—1064no—
436#536—1064no—
437C2×C4⋊Q8—1061no—
438C2×C4⋊Q8—1061no—
439C2×#124—1061no—
440C2×#124—1061no—
441C2×#123—1061no—
442C2×#123—1061no—
443C2×#123—1061no—
444C2×#123—1061no—
445C2×C22⋊Q8—531no—
446C2×C22⋊Q8—531no—
447C2×C22⋊Q8—531no—
448C2×C22⋊Q8—531no—
449C2×C22⋊Q8—531no—
450C2×C22⋊Q8—531no—
451C2×C22⋊Q8—531no—
452C2×C22⋊Q8C2×D5311yescharacteristic
453C2×#117—531no—
454C2×#117C2×D5311yescharacteristic
455#485—538no—
456#485—538no—
457#485—538no—
458#485C2×D5318yescomplemented
459#470—538no—
460#470—538no—
461#467—538no—
462#467—538no—
463#451—538no—
464#451—538no—
465#451—538no—
466#451—538no—
467C2×#107—531no—
468C2×#107C2×D5311yescharacteristic
469C2×#106—531no—
470C2×#106C2×D5311yescharacteristic
471C2×#103—531no—
472C2×#103—531no—
473C2×#103—531no—
474C2×#103—531no—
475C2×#103—531no—
476C2×#103—531no—
477C2×#103C2×D5311yescharacteristic
478C2×#103C2×D5311yescharacteristic
479#408—538no—
480C2×C22⋊C8—531no—
481C2×C22⋊C8—531no—
482C2×C22⋊C8—531no—
483C2×C22⋊C8C2×D5311yescharacteristic
484C53C2×#320211yescharacteristic, complemented, Sylow
485C2×#41—534no—
486C2×#41—534no—
487C2×#41—2122no—
488C2×#41—2122no—
489C22×Q8—531no—
490C22×Q8—534no—
491C22×Q8—531no—
492C22×Q8—531no—
493C22×Q8—531no—
494C22×Q8—534no—
495C22×Q8—1061no—
496C22×Q8—1062no—
497C22×Q8—1061no—
498C22×Q8—1062no—
499C22×Q8—2122no—
500C22×Q8—2122no—
501C22×Q8—2122no—
502C22×Q8—2122no—
503C22×Q8C22×D5311yescharacteristic
504C22×D4—531no—
505C22×D4—531no—
506C22×D4—531no—
507C23×C4—531no—
508C23×C4—531no—
509C23×C4—1061no—
510C23×C4—1061no—
511C23×C4C22×D5311yescharacteristic
512C2×Q16—534no—
513C2×Q16—534no—
514C2×Q16—534no—
515C2×Q16—534no—
516C2×Q16—2122no—
517C2×Q16—2122no—
518C2×Q16—2122no—
519C2×Q16—2122no—
520C2×M16—534no—
521C2×M16—2122no—
522C22×C8—531no—
523C22×C8—531no—
524C22×C8—534no—
525C22×C8—2122no—
526C22×C8C22×D5311yescharacteristic
527C22×C8C22×D5311yescharacteristic
528C4⋊Q8—1068no—
529C4⋊Q8—1068no—
530#124—1068no—
531#124—1068no—
532#123—1068no—
533#123—1068no—
534#123—1068no—
535#123—1068no—
536C22⋊Q8—22no—
537C22⋊Q8—534no—
538C22⋊Q8—534no—
539C22⋊Q8—534no—
540C22⋊Q8—534no—
541C22⋊Q8—534no—
542C22⋊Q8—534no—
543C22⋊Q8—534no—
544C22⋊Q8—1062no—
545C22⋊Q8—1062no—
546C22⋊Q8—1062no—
547C22⋊Q8—1062no—
548C22⋊Q8—1062no—
549C22⋊Q8—1062no—
550C22⋊Q8—1062no—
551C22⋊Q8C22×D5314yes—
552#117—22no—
553#117—534no—
554#117—1062no—
555#117C22×D5314yes—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—531no—
558C2×C4⋊C4—1061no—
559C2×C4⋊C4—1061no—
560C2×C4⋊C4—1061no—
561C2×C4⋊C4—1061no—
562C2×C4⋊C4—1061no—
563C2×C4⋊C4—1061no—
564C2×C4⋊C4—1061no—
565C2×C4⋊C4C22×D5311yescharacteristic
566C2×C4⋊C4C22×D5311yescharacteristic
567C2×C4⋊C4C22×D5311yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—1061no—
571C2×C22⋊C4—1061no—
572C2×C22⋊C4—1061no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4—1061no—
575C2×C22⋊C4—1061no—
576C2×C22⋊C4—1061no—
577C2×C22⋊C4—1061no—
578C2×C42—21no—
579C2×C42—1061no—
580#107—534no—
581#107C22×D5314yes—
582#106—534no—
583#106C22×D5314yes—
584#103—534no—
585#103—534no—
586#103—534no—
587#103—534no—
588#103—534no—
589#103—534no—
590#103C22×D5314yes—
591#103C22×D5314yes—
592C22⋊C8—534no—
593C22⋊C8—534no—
594C22⋊C8—534no—
595C22⋊C8C22×D5314yes—
596C24—531no—
597C24—531no—
598C24D4×D5311yescharacteristic
599#41—2128no—
600#41—2124no—
601#41—2124no—
602C2×Q8—21no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—534no—
606C2×Q8—532no—
607C2×Q8—532no—
608C2×Q8—532no—
609C2×Q8—1064no—
610C2×Q8—1061no—
611C2×Q8—1061no—
612C2×Q8—1061no—
613C2×Q8—1064no—
614C2×Q8—1062no—
615C2×Q8—1062no—
616C2×Q8—1062no—
617C2×Q8—1062no—
618C2×Q8—1062no—
619C2×Q8—1062no—
620C2×Q8—2122no—
621C2×Q8—2124no—
622C2×Q8—2124no—
623C2×Q8—2124no—
624C2×Q8—2128no—
625C2×Q8—2124no—
626C2×Q8—2124no—
627C2×Q8—2124no—
628C2×Q8—2128no—
629C2×Q8C23×D5312yes—
630C2×D4—534no—
631C2×D4—534no—
632C2×D4—534no—
633C2×D4—2122no—
634C2×D4—2122no—
635C2×D4—2122no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—531no—
643C22×C4—531no—
644C22×C4—532no—
645C22×C4—532no—
646C22×C4—532no—
647C22×C4—532no—
648C22×C4—1064no—
649C22×C4—1062no—
650C22×C4—1062no—
651C22×C4—1062no—
652C22×C4—1062no—
653C22×C4—1064no—
654C22×C4—1061no—
655C22×C4—1061no—
656C22×C4—1061no—
657C22×C4—1061no—
658C22×C4—2124no—
659C22×C4—2124no—
660C22×C4D4×D5312yes—
661C22×C4D4×D5311yescharacteristic
662C22×C4C23×D5312yes—
663C22×C4C23×D5311yescharacteristic
664Q16—2124no—
665Q16—2124no—
666Q16—2124no—
667Q16—2124no—
668M16—2124no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—532no—
672C2×C8—532no—
673C2×C8—1062no—
674C2×C8—1062no—
675C2×C8—2124no—
676C2×C8C23×D5312yes—
677C2×C8C23×D5312yes—
678C4⋊C4—24no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—532no—
683C4⋊C4—1064no—
684C4⋊C4—1064no—
685C4⋊C4—1064no—
686C4⋊C4—1064no—
687C4⋊C4—1064no—
688C4⋊C4—1064no—
689C4⋊C4—1061no—
690C4⋊C4—1064no—
691C4⋊C4C23×D5312yes—
692C4⋊C4C23×D5312yes—
693C4⋊C4C23×D5312yes—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—1064no—
697C22⋊C4—1064no—
698C22⋊C4—1064no—
699C22⋊C4—1064no—
700C22⋊C4—1064no—
701C22⋊C4—1064no—
702C22⋊C4—1064no—
703C22⋊C4—1064no—
704C42—24no—
705C42—1064no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—532no—
710C23—532no—
711C23—1062no—
712C23—1062no—
713C23—1062no—
714C23—1062no—
715C23—1062no—
716C23—1062no—
717C23C2×D4×D5312yes—
718C23C2×D4×D5311yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—42no—
722Q8—1062no—
723Q8—1062no—
724Q8—1062no—
725Q8—1062no—
726Q8—1062no—
727Q8—1062no—
728Q8—2124no—
729Q8—2128no—
730Q8—2128no—
731Q8—2122no—
732Q8—2122no—
733Q8—2122no—
734D4—2124no—
735D4—2124no—
736D4—2124no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—532no—
750C2×C4—532no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1064no—
754C2×C4—1064no—
755C2×C4—1062no—
756C2×C4—1062no—
757C2×C4—1062no—
758C2×C4—1062no—
759C2×C4—1062no—
760C2×C4—1062no—
761C2×C4—1062no—
762C2×C4—1062no—
763C2×C4—2128no—
764C2×C4—2128no—
765C2×C4—2122no—
766C2×C4—2122no—
767C2×C4—2122no—
768C2×C4—2122no—
769C2×C4C2×D4×D5312yes—
770C2×C4C2×D4×D5311yescharacteristic
771C2×C4#1313326312yes—
772C2×C4#1313326312yes—
773C2×C4C24×D5311yescharacteristic
774C8—22no—
775C8—22no—
776C8—1062no—
777C8—1062no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—44no—
782C22—1062no—
783C22—1062no—
784C22—1062no—
785C22—1062no—
786C22—1062no—
787C22—1062no—
788C22—2124no—
789C22—2124no—
790C22#1681118412yes—
791C22#1681143712yes—
792C22#1681143912yes—
793C22C22×D4×D5311yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—1062no—
800C4—1062no—
801C4—2122no—
802C4—2122no—
803C4—2122no—
804C4—2122no—
805C4#1681118412yes—
806C4C2×#1313326311yescharacteristic
807C4C2×#1313326311yescharacteristic
808C2—42no—
809C2—2122no—
810C2—2122no—
811C2#2028560914yesdirect product factor
812C2C2×#1681118411yescharacteristic
813C2C2×#1681143711yescharacteristic
814C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#485C2
socleC23×C53C22×D4
prime radicalC22×#11719945C22
hypercenterC2×#485D53
hypocenterC53C2×#3202
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. #20285609C2direct (N × H)
4. C2×#16810967C2semidirect
5. C2×#16810966C2semidirect
6. C2×#16810964C2semidirect
7. C2×#16810882C2semidirect
8. C2×#16810880C2semidirect
9. C2×#16810865C2semidirect
10. C2×#16810863C2semidirect
11. C2×#16810781C2semidirect
12. C2×#16810780C2semidirect
13. C2×#16810780C2semidirect
14. C2×#16810778C2semidirect
16. C2×C53×#485C2semidirect
46. #16810967C22semidirect
47. #16810966C22semidirect
48. #16810964C22semidirect
49. #16810882C22semidirect
50. #16810880C22semidirect
51. #16810865C22semidirect
52. #16810863C22semidirect
53. #16810781C22semidirect
54. #16810780C22semidirect
55. #16810780C22semidirect
56. #16810778C22semidirect
71. C53×#485C22semidirect
407. C2×#485D53semidirect
418. C2×C53#3202semidirect
458. #485C2×D53semidirect
484. C53C2×#3202semidirect
811. C2#20285609direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111992
C2×#168111962
#202856092
C2×#168109672
C2×#168109662
C2×#168109642
C2×#168108822
C2×#168108802
C2×#168108652
C2×#168108632
C2×#168107812
C2×#168107802
C2×#168107782
C2×#168105882
C2×C53×#4852
C2×#320253