Finite Group Databasebeta

← C2×#20278580 #27552256

Subgroups — C2×#20278580 #27552256

Order 13568.

3094 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
1C22×#13133207C211yesmaximal, characteristic, complemented
2C22×#13133177C211yesmaximal, characteristic
3#20278580C2116yesmaximal, direct product factor
4C2×#16810559C211yesmaximal, characteristic, complemented
5C2×#16810558C211yesmaximal, characteristic, complemented
6C2×#16810547C211yesmaximal, characteristic, complemented
7C2×#16810523C211yesmaximal, characteristic
8C2×#16810523C211yesmaximal, characteristic
9C2×#16810518C211yesmaximal, characteristic, complemented
10C2×#16810518C211yesmaximal, characteristic, complemented
11C2×#16810495C211yesmaximal, characteristic, complemented
12C2×#16810494C211yesmaximal, characteristic, complemented
13C2×#16810481C211yesmaximal, characteristic, complemented
14C2×#16810480C211yesmaximal, characteristic, complemented
15C2×#16810474C211yesmaximal, characteristic, complemented
16C2×C53×#396C211yesmaximal, characteristic, complemented
17C23×C22⋊D53C2211yescharacteristic
18C24×Dic53C2211yescharacteristic
19C23×C4×D53C2211yescharacteristic
20C2×#13133207—28no—
21C2×#13133207C2218yescomplemented
22C2×#13133177—28no—
23C2×#13133177C2218yes—
24C22×C4⋊Dic53C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×#11719919C2211yescharacteristic
29C22×#11719919C2211yescharacteristic
30C22×#11719919C2211yescharacteristic
31C22×#11719919C2211yescharacteristic
32C22×#11719919C2211yescharacteristic
33C22×#11719919C2211yescharacteristic
34C22×C22⋊Dic53C2211yescharacteristic
35C22×C22⋊Dic53C2211yescharacteristic
36C22×#11719921C2211yescharacteristic
37C22×#11719921C2211yescharacteristic
38C22×#11719921C2211yescharacteristic
39C22×#11719921C2211yescharacteristic
40C22×#11719921C2211yescharacteristic
41C22×C4×Dic53C2211yescharacteristic
42C22×C4×Dic53C2211yescharacteristic
43C22×C4×Dic53C2211yescharacteristic
44#16810559C2218yescomplemented
45#16810558C2218yescomplemented
46#16810547C2218yescomplemented
47#16810523C2218yes—
48#16810523C2218yes—
49#16810518C2218yescomplemented
50#16810518C2218yescomplemented
51#16810495C2218yescomplemented
52#16810494C2218yescomplemented
53#16810481C2218yescomplemented
54#16810480C2218yescomplemented
55#16810474C2218yescomplemented
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60C2×#13133124C2211yescharacteristic
61C22×C4⋊C4×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×C4⋊C4×C53C2211yescharacteristic
64C22×C22⋊C4×C53C2211yescharacteristic
65C22×C22⋊C4×C53C2211yescharacteristic
66C22×C22⋊C4×C53C2211yescharacteristic
67C53×#396C2218yescomplemented
68C2×#95×C53C2211yescharacteristic
69C24×D53C2311yescharacteristic
70C22×C22⋊D53—24no—
71C22×C22⋊D53—24no—
72C22×C22⋊D53Q818yes—
73C22×C22⋊D53C2314yes—
74C23×Dic53—24no—
75C23×Dic53—24no—
76C23×Dic53—42no—
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2314yes—
81C23×Dic53C2311yescharacteristic
82C23×Dic53C2311yescharacteristic
83C23×Dic53C2311yescharacteristic
84C23×Dic53C2311yescharacteristic
85C22×C4×D53—24no—
86C22×C4×D53—24no—
87C22×C4×D53—42no—
88C22×C4×D53C2314yes—
89#13133207—232no—
90#13133177—232no—
91C2×C4⋊Dic53—24no—
92C2×C4⋊Dic53C2314yes—
93C2×#11719919—24no—
94C2×#11719919—24no—
95C2×#11719919—24no—
96C2×#11719919—24no—
97C2×#11719919—24no—
98C2×#11719919—24no—
99C2×#11719919—42no—
100C2×#11719919—42no—
101C2×#11719919D418yes—
102C2×#11719919C2314yes—
103C2×#11719919C2314yes—
104C2×#11719919C2314yes—
105C2×#11719919C2314yes—
106C2×#11719919C2314yes—
107C2×#11719919C2314yes—
108C2×#11719919C2314yes—
109C2×#11719919C2314yes—
110C2×#11719919C2314yes—
111C2×C22⋊Dic53—24no—
112C2×C22⋊Dic53—42no—
113C2×C22⋊Dic53C2314yes—
114C2×C22⋊Dic53C2314yes—
115C2×#11719921—24no—
116C2×#11719921—24no—
117C2×#11719921—42no—
118C2×#11719921—42no—
119C2×#11719921—42no—
120C2×#11719921C2314yes—
121C2×#11719921C2314yes—
122C2×#11719921C2314yes—
123C2×#11719921C2314yes—
124C2×#11719921C2314yes—
125C2×C4×Dic53—24no—
126C2×C4×Dic53—24no—
127C2×C4×Dic53—24no—
128C2×C4×Dic53C2314yes—
129C2×C4×Dic53C2314yes—
130C2×C4×Dic53C2314yes—
131#13133124C2314yes—
132#13133124C2314yes—
133#13133124C2314yes—
134#13133124C2314yes—
135#13133124C2314yes—
136C25×C53C2311yescharacteristic
137C23×C4×C53C2311yescharacteristic
138C23×C4×C53C2311yescharacteristic
139C23×C4×C53C2311yescharacteristic
140C23×C4×C53C2311yescharacteristic
141C23×C4×C53C2311yescharacteristic
142C23×C4×C53C2311yescharacteristic
143C2×C4⋊C4×C53—24no—
144C2×C4⋊C4×C53—42no—
145C2×C4⋊C4×C53—42no—
146C2×C4⋊C4×C53C2314yes—
147C2×C4⋊C4×C53C2314yes—
148C2×C4⋊C4×C53C2314yes—
149C2×C22⋊C4×C53—24no—
150C2×C22⋊C4×C53—42no—
151C2×C22⋊C4×C53—42no—
152C2×C22⋊C4×C53C2314yes—
153C2×C22⋊C4×C53C2314yes—
154C2×C22⋊C4×C53C2314yes—
155#95×C53C2314yes—
156C24×C53—22no—
157C24×C53—22no—
158C24×C53—22no—
159C24×C53—22no—
160C24×C53—22no—
161C24×C53—22no—
162C24×C53C2×Q814yes—
163C24×C53C2412yes—
164C24×C53C2411yescharacteristic
165C23×D53—22no—
166C23×D53—22no—
167C23×D53—22no—
168C23×D53—22no—
169C23×D53—22no—
170C23×D53—22no—
171C23×D53C2×Q814yes—
172C23×D53C2412yes—
173C22×C4×C53—22no—
174C22×C4×C53—22no—
175C22×C4×C53—22no—
176C22×C4×C53—22no—
177C22×C4×C53—22no—
178C22×C4×C53—22no—
179C22×C4×C53—22no—
180C22×C4×C53—22no—
181C22×C4×C53—22no—
182C22×C4×C53—22no—
183C22×C4×C53—22no—
184C22×C4×C53—22no—
185C22×C4×C53—22no—
186C22×C4×C53—22no—
187C22×C4×C53—22no—
188C22×C4×C53—22no—
189C22×C4×C53—22no—
190C22×C4×C53C2×D414yes—
191C22×C4×C53C2412yes—
192C22×C4×C53C2412yes—
193C22×C4×C53C2412yes—
194C22×C4×C53C2412yes—
195C22×C4×C53C2412yes—
196C22×C4×C53C2412yes—
197C2×C22⋊D53—232no—
198C2×C22⋊D53—28no—
199C2×C22⋊D53—28no—
200C2×C22⋊D53C2×Q8116yes—
201C22×Dic53—22no—
202C22×Dic53—22no—
203C22×Dic53—22no—
204C22×Dic53—22no—
205C22×Dic53—22no—
206C22×Dic53—22no—
207C22×Dic53—22no—
208C22×Dic53—22no—
209C22×Dic53—22no—
210C22×Dic53—22no—
211C22×Dic53—22no—
212C22×Dic53—22no—
213C22×Dic53—22no—
214C22×Dic53—22no—
215C22×Dic53—22no—
216C22×Dic53—28no—
217C22×Dic53—28no—
218C22×Dic53—44no—
219C22×Dic53—416no—
220C22×Dic53C2×D414yes—
221C22×Dic53C2×D414yes—
222C22×Dic53C2×Q814yes—
223C22×Dic53#4114yes—
224C22×Dic53#4114yes—
225C22×Dic53#4114yes—
226C22×Dic53C2412yes—
227C22×Dic53C2412yes—
228C22×Dic53C2412yes—
229C22×Dic53C2412yes—
230C22×Dic53C2412yes—
231C22×Dic53C2412yes—
232C22×Dic53C2412yes—
233C2×C4×D53—28no—
234C2×C4×D53—28no—
235C2×C4×D53—44no—
236C2×C4×D53—416no—
237C4⋊C4×C53—28no—
238C4⋊C4×C53—44no—
239C4⋊C4×C53—44no—
240C22⋊C4×C53—28no—
241C22⋊C4×C53—44no—
242C22⋊C4×C53—44no—
243C22⋊Dic53—28no—
244C22⋊Dic53—44no—
245#11719921—28no—
246#11719921—28no—
247#11719921—44no—
248#11719921—44no—
249#11719921—44no—
250C4⋊Dic53—28no—
251#11719919—28no—
252#11719919—28no—
253#11719919—28no—
254#11719919—28no—
255#11719919—28no—
256#11719919—28no—
257#11719919—44no—
258#11719919—44no—
259#11719919C2×D4116yes—
260C4×Dic53—28no—
261C4×Dic53—28no—
262C4×Dic53—28no—
263C23×C53—28no—
264C23×C53—28no—
265C23×C53—28no—
266C23×C53—22no—
267C23×C53—22no—
268C23×C53—22no—
269C23×C53—22no—
270C23×C53—22no—
271C23×C53—22no—
272C23×C53—44no—
273C23×C53—44no—
274C23×C53—44no—
275C23×C53—44no—
276C23×C53C22×D412yes—
277C23×C53C22×Q814yes—
278C23×C53C22×Q812yes—
279C23×C53C2×#4112yes—
280C23×C53C2×#4112yes—
281C23×C53C2×#4112yes—
282C23×C53H(5,𝔽2)12yes—
283C23×C53H(5,𝔽2)12yes—
284C23×C53C2511yescharacteristic
285C22×D53—28no—
286C22×D53—28no—
287C22×D53—28no—
288C22×D53—22no—
289C22×D53—22no—
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—22no—
293C22×D53—22no—
294C22×D53—44no—
295C22×D53—44no—
296C22×D53—44no—
297C22×D53—44no—
298C22×D53C22×Q814yes—
299C2×C4×C53—28no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
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—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—44no—
318C2×C4×C53—44no—
319C2×C4×C53—44no—
320C2×C4×C53—44no—
321C2×C4×C53—44no—
322C2×C4×C53C22×D414yes—
323C22⋊D53—232no—
324C2×Dic53—28no—
325C2×Dic53—28no—
326C2×Dic53—28no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—416no—
343C2×Dic53—44no—
344C2×Dic53—44no—
345C2×Dic53—44no—
346C2×Dic53C22⋊Q8116yes—
347C2×Dic53C22×D414yes—
348C2×Dic53C22×D414yes—
349C2×Dic53C22×Q814yes—
350C2×Dic53C2×#4114yes—
351C2×Dic53C2×#4114yes—
352C2×Dic53C2×#4114yes—
353C4×D53—416no—
354C2×#2454—531nomaximal, Sylow
355C22×C53—24no—
356C22×C53—24no—
357C22×C53—24no—
358C22×C53—42no—
359C22×C53—42no—
360C22×C53—42no—
361C22×C53—42no—
362C22×C53—416no—
363C22×C53C2×C22⋊Q814yes—
364C22×C53#52914yes—
365C22×C53#54014yes—
366C22×C53#54614yes—
367C22×C53#55014yes—
368C22×C53#55414yes—
369C22×C53#55414yes—
370C22×C53C23×D411yescharacteristic
371C22×C53C23×Q811yescharacteristic
372C22×C53C22×#4111yescharacteristic
373C22×C53C22×#4111yescharacteristic
374C22×C53C22×#4111yescharacteristic
375C22×C53C2×H(5,𝔽2)11yescharacteristic
376C22×C53C2×H(5,𝔽2)11yescharacteristic
377C2×D53—24no—
378C2×D53—24no—
379C2×D53—24no—
380C2×D53—42no—
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—42no—
384C2×D53—416no—
385C4×C53—24no—
386C4×C53—42no—
387C4×C53—42no—
388C4×C53—42no—
389C4×C53—42no—
390C4×C53—42no—
391Dic53—24no—
392Dic53—24no—
393Dic53—24no—
394Dic53—42no—
395Dic53—42no—
396Dic53—42no—
397Dic53C2×C22⋊Q818yes—
398C22×#125—531no—
399C22×C4×D4—531no—
400#2454—5316no—
401C2×#399—531no—
402C2×#399—531no—
403C2×#396—531no—
404C2×#396D5311yescharacteristic, complemented
405C2×#390—531no—
406C2×#390—531no—
407C2×#389—531no—
408C2×#389—531no—
409C2×#385—531no—
410C2×#385—531no—
411C2×#380—531no—
412C2×#380—531no—
413C2×C4×C4⋊C4—531no—
414C2×C53—44no—
415C2×C53#245418yescomplemented
416C2×C53C22×C22⋊Q811yescharacteristic
417C2×C53C2×#52911yescharacteristic
418C2×C53C2×#54011yescharacteristic
419C2×C53C2×#54611yescharacteristic
420C2×C53C2×#55011yescharacteristic
421C2×C53C2×#55411yescharacteristic
422C2×C53C2×#55411yescharacteristic
423D53—44no—
424C23×D4—531no—
425C24×C4—531no—
426C24×C4—531no—
427C2×#125—538no—
428C2×#125—1068no—
429C2×C4×D4—538no—
430C2×C4×D4—1068no—
431C22×C4⋊C4—531no—
432C22×C4⋊C4—531no—
433C22×C4⋊C4—531no—
434C22×C4⋊C4—531no—
435C22×C4⋊C4—531no—
436C22×C4⋊C4—531no—
437C22×C4⋊C4—531no—
438C22×C4⋊C4—531no—
439C22×C4⋊C4—531no—
440C22×C4⋊C4—531no—
441C22×C4⋊C4C2×D5311yescharacteristic
442C22×C4⋊C4C2×D5311yescharacteristic
443C22×C4⋊C4C2×D5311yescharacteristic
444C22×C22⋊C4—531no—
445C22×C22⋊C4—531no—
446C22×C22⋊C4—531no—
447C22×C22⋊C4—531no—
448C22×C22⋊C4—531no—
449C22×C22⋊C4—531no—
450C22×C22⋊C4—531no—
451C22×C22⋊C4C2×D5311yescharacteristic
452C22×C22⋊C4C2×D5311yescharacteristic
453C22×C22⋊C4C2×D5311yescharacteristic
454C22×C42—531no—
455C22×C42—531no—
456C22×C42—531no—
457#399—538no—
458#399—538no—
459#396—538no—
460#396C2×D5318yescomplemented
461#390—538no—
462#390—538no—
463#389—538no—
464#389—538no—
465#385—538no—
466#385—538no—
467#380—538no—
468#380—538no—
469C4×C4⋊C4—538no—
470C2×#95—531no—
471C2×#95—531no—
472C2×#95—531no—
473C2×#95—531no—
474C2×#95—531no—
475C2×#95C2×D5311yescharacteristic
476C53C2×#245411yescharacteristic, complemented, Sylow
477C25—531no—
478C25C22×D5311yescharacteristic
479C22×D4—538no—
480C22×D4—534no—
481C22×D4—1064no—
482C22×D4—1064no—
483C23×C4—531no—
484C23×C4—531no—
485C23×C4—531no—
486C23×C4—531no—
487C23×C4—531no—
488C23×C4—531no—
489C23×C4—531no—
490C23×C4—534no—
491C23×C4—534no—
492C23×C4—1064no—
493C23×C4—1064no—
494C23×C4—1064no—
495C23×C4—1064no—
496C23×C4—2122no—
497C23×C4—2122no—
498C23×C4C22×D5311yescharacteristic
499C23×C4C22×D5311yescharacteristic
500C23×C4C22×D5311yescharacteristic
501C23×C4C22×D5311yescharacteristic
502C23×C4C22×D5311yescharacteristic
503C23×C4C22×D5311yescharacteristic
504#125—10632no—
505C4×D4—10632no—
506C2×C4⋊C4—24no—
507C2×C4⋊C4—42no—
508C2×C4⋊C4—42no—
509C2×C4⋊C4—538no—
510C2×C4⋊C4—534no—
511C2×C4⋊C4—534no—
512C2×C4⋊C4—534no—
513C2×C4⋊C4—534no—
514C2×C4⋊C4—534no—
515C2×C4⋊C4—534no—
516C2×C4⋊C4—534no—
517C2×C4⋊C4—534no—
518C2×C4⋊C4—534no—
519C2×C4⋊C4—534no—
520C2×C4⋊C4—1064no—
521C2×C4⋊C4—1064no—
522C2×C4⋊C4—1064no—
523C2×C4⋊C4—1064no—
524C2×C4⋊C4—1064no—
525C2×C4⋊C4—1064no—
526C2×C4⋊C4—1064no—
527C2×C4⋊C4—2122no—
528C2×C4⋊C4—2122no—
529C2×C4⋊C4C22×D5314yes—
530C2×C4⋊C4C22×D5314yes—
531C2×C4⋊C4C22×D5314yes—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—534no—
536C2×C22⋊C4—534no—
537C2×C22⋊C4—534no—
538C2×C22⋊C4—534no—
539C2×C22⋊C4—534no—
540C2×C22⋊C4—534no—
541C2×C22⋊C4—534no—
542C2×C22⋊C4—1064no—
543C2×C22⋊C4—1064no—
544C2×C22⋊C4—1064no—
545C2×C22⋊C4—2122no—
546C2×C22⋊C4—2122no—
547C2×C22⋊C4—2122no—
548C2×C22⋊C4—2122no—
549C2×C22⋊C4C22×D5314yes—
550C2×C22⋊C4C22×D5314yes—
551C2×C22⋊C4C22×D5314yes—
552C2×C42—534no—
553C2×C42—534no—
554C2×C42—534no—
555C2×C42—1064no—
556C2×C42—1064no—
557C2×C42—1064no—
558#95—534no—
559#95—534no—
560#95—534no—
561#95—534no—
562#95—534no—
563#95C22×D5314yes—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—534no—
571C24—532no—
572C24—1062no—
573C24—1062no—
574C24—1062no—
575C24—1062no—
576C24—1062no—
577C24—1062no—
578C24Q8×D5314yes—
579C24C23×D5312yes—
580C24C23×D5311yescharacteristic
581C2×D4—5316no—
582C2×D4—1068no—
583C2×D4—10632no—
584C2×D4—1068no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—534no—
603C22×C4—534no—
604C22×C4—534no—
605C22×C4—532no—
606C22×C4—534no—
607C22×C4—534no—
608C22×C4—534no—
609C22×C4—532no—
610C22×C4—532no—
611C22×C4—532no—
612C22×C4—532no—
613C22×C4—532no—
614C22×C4—532no—
615C22×C4—1068no—
616C22×C4—1068no—
617C22×C4—1068no—
618C22×C4—1062no—
619C22×C4—1062no—
620C22×C4—1062no—
621C22×C4—1062no—
622C22×C4—1062no—
623C22×C4—1062no—
624C22×C4—1062no—
625C22×C4—1062no—
626C22×C4—1062no—
627C22×C4—1062no—
628C22×C4—1062no—
629C22×C4—1062no—
630C22×C4—1062no—
631C22×C4—1062no—
632C22×C4—1062no—
633C22×C4—1068no—
634C22×C4—2124no—
635C22×C4—21216no—
636C22×C4—2124no—
637C22×C4—21216no—
638C22×C4D4×D5314yes—
639C22×C4C23×D5312yes—
640C22×C4C23×D5312yes—
641C22×C4C23×D5312yes—
642C22×C4C23×D5312yes—
643C22×C4C23×D5312yes—
644C22×C4C23×D5312yes—
645C4⋊C4—28no—
646C4⋊C4—44no—
647C4⋊C4—44no—
648C4⋊C4—5316no—
649C4⋊C4—1068no—
650C4⋊C4—1068no—
651C4⋊C4—1068no—
652C4⋊C4—1068no—
653C4⋊C4—1068no—
654C4⋊C4—1068no—
655C4⋊C4—1068no—
656C4⋊C4—2124no—
657C4⋊C4—2124no—
658C22⋊C4—28no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—1068no—
662C22⋊C4—1068no—
663C22⋊C4—1068no—
664C22⋊C4—2124no—
665C22⋊C4—2124no—
666C22⋊C4—2124no—
667C22⋊C4—2124no—
668C42—1068no—
669C42—1068no—
670C42—1068no—
671C23—28no—
672C23—28no—
673C23—28no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—534no—
685C23—1068no—
686C23—1068no—
687C23—1068no—
688C23—1062no—
689C23—1062no—
690C23—1062no—
691C23—1062no—
692C23—1062no—
693C23—1062no—
694C23—2124no—
695C23—2124no—
696C23—2124no—
697C23—2124no—
698C23C2×D4×D5312yes—
699C23C2×Q8×D5314yes—
700C23C2×Q8×D5312yes—
701C23#41×D5312yes—
702C23#41×D5312yes—
703C23#41×D5312yes—
704C23#1313326212yes—
705C23#1313326212yes—
706C23C24×D5311yescharacteristic
707D4—10632no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—28no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—5316no—
732C2×C4—534no—
733C2×C4—534no—
734C2×C4—534no—
735C2×C4—534no—
736C2×C4—534no—
737C2×C4—534no—
738C2×C4—1068no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—1062no—
742C2×C4—1062no—
743C2×C4—1062no—
744C2×C4—1062no—
745C2×C4—1068no—
746C2×C4—1068no—
747C2×C4—1062no—
748C2×C4—1062no—
749C2×C4—1062no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—1062no—
756C2×C4—21216no—
757C2×C4—21216no—
758C2×C4—2124no—
759C2×C4—2124no—
760C2×C4—2124no—
761C2×C4C2×D4×D5314yes—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—416no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—1064no—
771C22—1064no—
772C22—1064no—
773C22—21216no—
774C22—2122no—
775C22—2122no—
776C22—2122no—
777C22—2122no—
778C22C22⋊Q8×D5314yes—
779C22#1681115614yes—
780C22#1681122314yes—
781C22#1681126214yes—
782C22#1681129114yes—
783C22#1681132714yes—
784C22#1681132714yes—
785C22C22×D4×D5311yescharacteristic
786C22C22×Q8×D5311yescharacteristic
787C22C2×#41×D5311yescharacteristic
788C22C2×#41×D5311yescharacteristic
789C22C2×#41×D5311yescharacteristic
790C22C2×#1313326211yescharacteristic
791C22C2×#1313326211yescharacteristic
792C4—24no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—538no—
799C4—1064no—
800C4—1064no—
801C4—1064no—
802C4—2122no—
803C4—2122no—
804C4—2122no—
805C2—44no—
806C2—2124no—
807C2#2027858018yesdirect product factor
808C2C2×C22⋊Q8×D5311yescharacteristic
809C2C2×#1681115611yescharacteristic
810C2C2×#1681122311yescharacteristic
811C2C2×#1681126211yescharacteristic
812C2C2×#1681129111yescharacteristic
813C2C2×#1681132711yescharacteristic
814C2C2×#1681132711yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#396C2
socleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC2×#396D53
hypocenterC53C2×#2454
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#13133207C2semidirect
3. #20278580C2direct (N × H)
4. C2×#16810559C2semidirect
5. C2×#16810558C2semidirect
6. C2×#16810547C2semidirect
9. C2×#16810518C2semidirect
10. C2×#16810518C2semidirect
11. C2×#16810495C2semidirect
12. C2×#16810494C2semidirect
13. C2×#16810481C2semidirect
14. C2×#16810480C2semidirect
15. C2×#16810474C2semidirect
16. C2×C53×#396C2semidirect
21. C2×#13133207C22semidirect
44. #16810559C22semidirect
45. #16810558C22semidirect
46. #16810547C22semidirect
49. #16810518C22semidirect
50. #16810518C22semidirect
51. #16810495C22semidirect
52. #16810494C22semidirect
53. #16810481C22semidirect
54. #16810480C22semidirect
55. #16810474C22semidirect
67. C53×#396C22semidirect
404. C2×#396D53semidirect
415. C2×C53#2454semidirect
460. #396C2×D53semidirect
476. C53C2×#2454semidirect
807. C2#20278580direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332072
C22×#131331772
#202785802
C2×#168105592
C2×#168105582
C2×#168105472
C2×#168105232
C2×#168105182
C2×#168104952
C2×#168104942
C2×#168104812
C2×#168104802
C2×#168104742
C2×C53×#3962
C2×#245453