Finite Group Databasebeta

← C2×#20285608 #28254790

Subgroups — C2×#20285608 #28254790

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×#16811197C211yesmaximal, characteristic
2C2×#16811196C211yesmaximal, characteristic
3#20285608C2116yesmaximal, direct product factor
4C2×#16810965C211yesmaximal, characteristic, complemented
5C2×#16810963C211yesmaximal, characteristic, complemented
6C2×#16810962C211yesmaximal, characteristic, complemented
7C2×#16810961C211yesmaximal, characteristic, complemented
8C2×#16810880C211yesmaximal, characteristic, complemented
9C2×#16810878C211yesmaximal, characteristic, complemented
10C2×#16810863C211yesmaximal, characteristic, complemented
11C2×#16810861C211yesmaximal, characteristic, complemented
12C2×#16810779C211yesmaximal, characteristic, complemented
13C2×#16810777C211yesmaximal, characteristic, complemented
14C2×#16810777C211yesmaximal, characteristic, complemented
15C2×#16810588C211yesmaximal, characteristic
16C2×C53×#451C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719925C2211yescharacteristic
21C22×#11719912C2211yescharacteristic
22C22×C8×D53C2211yescharacteristic
23#16811197—24no—
24#16811197C2218yes—
25#16811196—24no—
26#16811196C2218yes—
27C2×#13133216—21no—
28C2×#13133215—21no—
29C2×#13133206—21no—
30C2×#13133203—21no—
31C2×#13133202—21no—
32C2×#13133200—21no—
33C2×#13133200—21no—
34C2×#13133199—21no—
35C2×#13133197C2211yescharacteristic
36C2×#13133196C2211yescharacteristic
37C2×#13133193C2211yescharacteristic
38C2×#13133193C2211yescharacteristic
39C2×#13133193C2211yescharacteristic
40C2×#13133193C2211yescharacteristic
41C2×#13133193C2211yescharacteristic
42C2×#13133176C2211yescharacteristic
43C2×#13133175C2211yescharacteristic
44#16810965C2218yescomplemented
45#16810963C2218yescomplemented
46#16810962C2218yescomplemented
47#16810961C2218yescomplemented
48#16810880C2218yescomplemented
49#16810878C2218yescomplemented
50#16810863C2218yescomplemented
51#16810861C2218yescomplemented
52#16810779C2218yescomplemented
53#16810777C2218yescomplemented
54#16810777C2218yescomplemented
55C2×#13133151C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133149C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133141C2211yescharacteristic
65#16810588C2218yes—
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
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
77C2×#11719945—42no—
78C2×#11719945—42no—
79C2×#11719945D414yes—
80C2×#11719945C2314yes—
81C22×Dic106—21no—
82C22×Dic106D411yescharacteristic
83C22×Dic106C2311yescharacteristic
84C2×Q8×D53—22no—
85C2×Q8×D53—42no—
86C2×Q8×D53—42no—
87C2×Q8×D53C2314yes—
88C22×D212D411yescharacteristic
89C22×C22⋊D53D411yescharacteristic
90C22×C22⋊D53D411yescharacteristic
91C22×C4×D53—21no—
92C22×C4×D53C2311yescharacteristic
93C22×C4×D53C2311yescharacteristic
94C2×#11719925—42no—
95C2×#11719925—42no—
96C2×#11719925C2314yes—
97C2×#11719925C2314yes—
98C2×#11719912—42no—
99C2×#11719912C2314yes—
100C22×#88322C2311yescharacteristic
101C22×#88322C2311yescharacteristic
102C2×C8×D53—42no—
103C2×C8×D53C2314yes—
104#13133216—28no—
105#13133215—28no—
106#13133206—28no—
107#13133203—28no—
108#13133202—28no—
109#13133200—28no—
110#13133200—28no—
111#13133199—28no—
112#13133197—22no—
113#13133197C2314yes—
114#13133196—22no—
115#13133196C2314yes—
116#13133193—22no—
117#13133193—22no—
118#13133193—22no—
119#13133193—22no—
120#13133193—22no—
121#13133193C2314yes—
122#13133193C2314yes—
123#13133193C2314yes—
124#13133193C2314yes—
125#13133193C2314yes—
126#13133176—22no—
127#13133176C2314yes—
128#13133175—22no—
129#13133175C2314yes—
130C2×C4⋊Dic53—21no—
131C2×C4⋊Dic53C2311yescharacteristic
132C2×C4⋊Dic53C2311yescharacteristic
133C2×C4⋊Dic53C2311yescharacteristic
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×C4×Dic53—21no—
150C2×C4×Dic53—21no—
151#13133151C2314yes—
152#13133150C2314yes—
153#13133149C2314yes—
154#13133148C2314yes—
155#13133142C2314yes—
156#13133142C2314yes—
157#13133141C2314yes—
158#13133141C2314yes—
159#13133141C2314yes—
160#13133141C2314yes—
161C22⋊#88322C2314yes—
162#13133129C2314yes—
163#13133129C2314yes—
164C22×Q8×C53—21no—
165C22×Q8×C53—22no—
166C22×Q8×C53—42no—
167C22×Q8×C53—42no—
168C22×Q8×C53C2311yescharacteristic
169C22×Q8×C53C2311yescharacteristic
170C22×Q8×C53C2311yescharacteristic
171C22×Q8×C53C2314yes—
172C23×C4×C53—21no—
173C23×C4×C53C2311yescharacteristic
174C2×Q16×C53—42no—
175C2×Q16×C53—42no—
176C2×Q16×C53C2314yes—
177C2×Q16×C53C2314yes—
178C22×C8×C53C2311yescharacteristic
179C22×C8×C53C2311yescharacteristic
180C22⋊Q8×C53—22no—
181C22⋊Q8×C53C2314yes—
182C2×C4⋊C4×C53—21no—
183C2×C4⋊C4×C53C2311yescharacteristic
184C2×C22⋊C4×C53—21no—
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—21no—
193C2×Q8×C53—21no—
194C2×Q8×C53—24no—
195C2×Q8×C53—22no—
196C2×Q8×C53—22no—
197C2×Q8×C53—22no—
198C2×Q8×C53—22no—
199C2×Q8×C53—22no—
200C2×Q8×C53—22no—
201C2×Q8×C53—44no—
202C2×Q8×C53—44no—
203C2×Q8×C53—44no—
204C2×Q8×C53—48no—
205C2×Q8×C53C2412yes—
206C2×Q8×C53C2412yes—
207C2×Q8×C53C2412yes—
208C22×C4×C53—22no—
209C22×C4×C53—22no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—24no—
215C22×C4×C53—44no—
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D412yes—
218C22×C4×C53C2412yes—
219C22×C4×C53C2411yescharacteristic
220C2×C22⋊D53—42no—
221C2×C22⋊D53—42no—
222C2×C22⋊D53C2×D414yes—
223C2×C22⋊D53C2×D414yes—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53C2×D411yescharacteristic
229C22×Dic53C2×D411yescharacteristic
230Q8×D53—44no—
231Q8×D53—44no—
232Q8×D53—48no—
233#11719945—48no—
234#11719945—44no—
235#11719945—44no—
236C2×D212—42no—
237C2×D212C2×D414yes—
238C2×C4×D53—22no—
239C2×C4×D53—22no—
240C2×C4×D53—22no—
241C2×C4×D53—22no—
242C2×C4×D53—24no—
243C2×C4×D53—44no—
244C2×C4×D53C2×D412yes—
245C2×C4×D53C2×D412yes—
246C2×C4×D53C2412yes—
247C2×C4×D53C2412yes—
248C2×Dic106—22no—
249C2×Dic106—22no—
250C2×Dic106—21no—
251C2×Dic106—24no—
252C2×Dic106—42no—
253C2×Dic106—44no—
254C2×Dic106C2×D414yes—
255C2×Dic106C2412yes—
256Q16×C53—44no—
257Q16×C53—44no—
258C2×C8×C53—22no—
259C2×C8×C53—22no—
260C2×C8×C53C2412yes—
261C2×C8×C53C2412yes—
262C4⋊C4×C53—24no—
263C4⋊C4×C53—21no—
264C4⋊C4×C53C2412yes—
265C22⋊C4×C53—24no—
266C22⋊Dic53—24no—
267C22⋊Dic53—24no—
268#11719925—44no—
269#11719925—44no—
270#11719921—24no—
271#11719921—24no—
272#11719921—24no—
273#11719921—24no—
274#11719921—24no—
275#11719921—24no—
276#11719921—24no—
277C4⋊Dic53—21no—
278C4⋊Dic53—21no—
279C4⋊Dic53—21no—
280C4⋊Dic53—24no—
281C4⋊Dic53C2412yes—
282C4⋊Dic53C2412yes—
283C4⋊Dic53C2412yes—
284#11719919—24no—
285#11719919—24no—
286#11719919—24no—
287#11719919—24no—
288#11719919—24no—
289#11719919—24no—
290C4×Dic53—24no—
291C4×Dic53—24no—
292C2×#88322—22no—
293C2×#88322—22no—
294C2×#88322C2412yes—
295C2×#88322C2412yes—
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—22no—
314Q8×C53—22no—
315Q8×C53—22no—
316Q8×C53—22no—
317Q8×C53—48no—
318Q8×C53—42no—
319Q8×C53—42no—
320Q8×C53—42no—
321C2×C4×C53—22no—
322C2×C4×C53—24no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—48no—
330C2×C4×C53—42no—
331C2×C4×C53—42no—
332C2×C4×C53—42no—
333C2×C4×C53—42no—
334C2×C4×C53C22×D412yes—
335C2×C4×C53C22×D411yescharacteristic
336C2×C4×C53H(5,𝔽2)12yes—
337C2×C4×C53H(5,𝔽2)12yes—
338C2×C4×C53C2511yescharacteristic
339C22⋊D53—44no—
340C22⋊D53—44no—
341C2×Dic53—22no—
342C2×Dic53—22no—
343C2×Dic53—22no—
344C2×Dic53—22no—
345C2×Dic53—22no—
346C2×Dic53—22no—
347C2×Dic53—42no—
348C2×Dic53—42no—
349C2×Dic53—42no—
350C2×Dic53—42no—
351C2×Dic53C22×D412yes—
352C2×Dic53C22×D412yes—
353D212—44no—
354C4×D53—24no—
355C4×D53—24no—
356C4×D53—22no—
357C4×D53—22no—
358C4×D53—22no—
359C4×D53—22no—
360C4×D53—48no—
361Dic106—22no—
362Dic106—22no—
363Dic106—44no—
364Dic106—48no—
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×#485—531no—
408C2×#470—531no—
409C2×#470—531no—
410C2×#467—531no—
411C2×#467—531no—
412C2×#451—531no—
413C2×#451—531no—
414C2×#451—531no—
415C2×#451D5311yescharacteristic, complemented
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×Q8C2×D5311yescharacteristic
427C22×Q16—531no—
428C22×Q16—531no—
429C22×Q16C2×D5311yescharacteristic
430C22×Q16C2×D5311yescharacteristic
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×#117—531no—
455#485—538no—
456#485—538no—
457#485—538no—
458#485—538no—
459#470—538no—
460#470—538no—
461#467—538no—
462#467—538no—
463#451—538no—
464#451—538no—
465#451—538no—
466#451C2×D5318yescomplemented
467C2×#107—531no—
468C2×#107—531no—
469C2×#106—531no—
470C2×#106—531no—
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—21no—
490C22×Q8—22no—
491C22×Q8—42no—
492C22×Q8—42no—
493C22×Q8—531no—
494C22×Q8—534no—
495C22×Q8—531no—
496C22×Q8—1061no—
497C22×Q8—1062no—
498C22×Q8—2122no—
499C22×Q8—2122no—
500C22×Q8C22×D5311yescharacteristic
501C22×Q8C22×D5311yescharacteristic
502C22×Q8C22×D5311yescharacteristic
503C22×Q8C22×D5314yes—
504C22×D4—531no—
505C22×D4—531no—
506C22×D4—531no—
507C23×C4—21no—
508C23×C4—531no—
509C23×C4—531no—
510C23×C4—1061no—
511C23×C4C22×D5311yescharacteristic
512C2×Q16—42no—
513C2×Q16—42no—
514C2×Q16—534no—
515C2×Q16—534no—
516C2×Q16—2122no—
517C2×Q16—2122no—
518C2×Q16C22×D5314yes—
519C2×Q16C22×D5314yes—
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—534no—
553#117—534no—
554#117—1062no—
555#117—1062no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—531no—
558C2×C4⋊C4—531no—
559C2×C4⋊C4—531no—
560C2×C4⋊C4—1061no—
561C2×C4⋊C4—1061no—
562C2×C4⋊C4—1061no—
563C2×C4⋊C4—1061no—
564C2×C4⋊C4—1061no—
565C2×C4⋊C4—1061no—
566C2×C4⋊C4—1061no—
567C2×C4⋊C4C22×D5311yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—1061no—
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—1061no—
579C2×C42—1061no—
580#107—534no—
581#107—534no—
582#106—534no—
583#106—534no—
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—21no—
604C2×Q8—21no—
605C2×Q8—24no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—44no—
613C2×Q8—44no—
614C2×Q8—44no—
615C2×Q8—48no—
616C2×Q8—534no—
617C2×Q8—532no—
618C2×Q8—1064no—
619C2×Q8—1061no—
620C2×Q8—1062no—
621C2×Q8—1062no—
622C2×Q8—2122no—
623C2×Q8—2124no—
624C2×Q8—2124no—
625C2×Q8—2124no—
626C2×Q8—2128no—
627C2×Q8C23×D5312yes—
628C2×Q8C23×D5312yes—
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—24no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—44no—
644C22×C4—531no—
645C22×C4—531no—
646C22×C4—532no—
647C22×C4—532no—
648C22×C4—532no—
649C22×C4—532no—
650C22×C4—1064no—
651C22×C4—1062no—
652C22×C4—1062no—
653C22×C4—1062no—
654C22×C4—1062no—
655C22×C4—1061no—
656C22×C4—1061no—
657C22×C4—1061no—
658C22×C4—1061no—
659C22×C4—2124no—
660C22×C4D4×D5312yes—
661C22×C4D4×D5311yescharacteristic
662C22×C4C23×D5312yes—
663C22×C4C23×D5311yescharacteristic
664Q16—44no—
665Q16—44no—
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—532no—
681C4⋊C4—532no—
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—1061no—
691C4⋊C4—1061no—
692C4⋊C4—1064no—
693C4⋊C4C23×D5312yes—
694C22⋊C4—24no—
695C22⋊C4—1064no—
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—1064no—
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—22no—
722Q8—22no—
723Q8—22no—
724Q8—22no—
725Q8—48no—
726Q8—42no—
727Q8—42no—
728Q8—42no—
729Q8—1062no—
730Q8—1062no—
731Q8—2124no—
732Q8—2128no—
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—48no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—532no—
751C2×C4—532no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—1064no—
755C2×C4—1064no—
756C2×C4—1062no—
757C2×C4—1062no—
758C2×C4—1062no—
759C2×C4—1062no—
760C2×C4—1062no—
761C2×C4—1062no—
762C2×C4—1062no—
763C2×C4—1062no—
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#1313326212yes—
772C2×C4#1313326212yes—
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#1681118312yes—
791C22#1681143612yes—
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#1681118312yes—
806C4C2×#1313326211yescharacteristic
807C4C2×#1313326211yescharacteristic
808C2—42no—
809C2—2122no—
810C2—2122no—
811C2#2028560814yesdirect product factor
812C2C2×#1681118311yescharacteristic
813C2C2×#1681143611yescharacteristic
814C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#451C2
socleC23×C53C22×D4
prime radicalC22×#11719945C22
hypercenterC2×#451D53
hypocenterC53C2×#3202
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. #20285608C2direct (N × H)
4. C2×#16810965C2semidirect
5. C2×#16810963C2semidirect
6. C2×#16810962C2semidirect
7. C2×#16810961C2semidirect
8. C2×#16810880C2semidirect
9. C2×#16810878C2semidirect
10. C2×#16810863C2semidirect
11. C2×#16810861C2semidirect
12. C2×#16810779C2semidirect
13. C2×#16810777C2semidirect
14. C2×#16810777C2semidirect
16. C2×C53×#451C2semidirect
44. #16810965C22semidirect
45. #16810963C22semidirect
46. #16810962C22semidirect
47. #16810961C22semidirect
48. #16810880C22semidirect
49. #16810878C22semidirect
50. #16810863C22semidirect
51. #16810861C22semidirect
52. #16810779C22semidirect
53. #16810777C22semidirect
54. #16810777C22semidirect
73. C53×#451C22semidirect
415. C2×#451D53semidirect
418. C2×C53#3202semidirect
466. #451C2×D53semidirect
484. C53C2×#3202semidirect
811. C2#20285608direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111972
C2×#168111962
#202856082
C2×#168109652
C2×#168109632
C2×#168109622
C2×#168109612
C2×#168108802
C2×#168108782
C2×#168108632
C2×#168108612
C2×#168107792
C2×#168107772
C2×#168105882
C2×C53×#4512
C2×#320253