Finite Group Databasebeta

← C2×#20279693 #27555428

Subgroups — C2×#20279693 #27555428

Order 13568.

3310 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133216C211yesmaximal, characteristic, complemented
2C22×#13133203C211yesmaximal, characteristic
3C22×#13133203C211yesmaximal, characteristic
4C22×C4×Dic106C211yesmaximal, characteristic, complemented
5#20279693C2116yesmaximal, direct product factor
6C2×#16810547C211yesmaximal, characteristic, complemented
7C2×#16810546C211yesmaximal, characteristic, complemented
8C2×#16810546C211yesmaximal, characteristic, complemented
9C2×#16810545C211yesmaximal, characteristic, complemented
10C2×#16810527C211yesmaximal, characteristic, complemented
11C2×#16810523C211yesmaximal, characteristic
12C2×#16810515C211yesmaximal, characteristic, complemented
13C2×#16810514C211yesmaximal, characteristic, complemented
14C2×#16810511C211yesmaximal, characteristic, complemented
15C2×#16810474C211yesmaximal, characteristic, complemented
16C2×C53×#388C211yesmaximal, characteristic, complemented
17C23×Dic106C2211yescharacteristic
18C23×Dic106C2211yescharacteristic
19C23×C22⋊D53C2211yescharacteristic
20C2×#13133216—28no—
21C2×#13133216C2218yescomplemented
22C2×#13133203—28no—
23C2×#13133203—28no—
24C2×#13133203C2218yes—
25C2×#13133203C2218yes—
26C2×C4×Dic106—28no—
27C2×C4×Dic106C2218yescomplemented
28C22×C4⋊Dic53C2211yescharacteristic
29C22×C4⋊Dic53C2211yescharacteristic
30C22×#11719919C2211yescharacteristic
31C22×#11719919C2211yescharacteristic
32C22×#11719919C2211yescharacteristic
33C22×#11719919C2211yescharacteristic
34C22×#11719919C2211yescharacteristic
35C22×#11719919C2211yescharacteristic
36C22×C22⋊Dic53C2211yescharacteristic
37C22×C22⋊Dic53C2211yescharacteristic
38C22×C22⋊Dic53C2211yescharacteristic
39C22×#11719921C2211yescharacteristic
40C22×#11719921C2211yescharacteristic
41C22×#11719921C2211yescharacteristic
42C22×#11719921C2211yescharacteristic
43C22×#11719921C2211yescharacteristic
44C22×#11719921C2211yescharacteristic
45C22×C4×Dic53C2211yescharacteristic
46C22×C4×Dic53C2211yescharacteristic
47C22×C4×Dic53C2211yescharacteristic
48C22×C4×Dic53C2211yescharacteristic
49#16810547C2218yescomplemented
50#16810546C2218yescomplemented
51#16810546C2218yescomplemented
52#16810545C2218yescomplemented
53#16810527C2218yescomplemented
54#16810523C2218yes—
55#16810515C2218yescomplemented
56#16810514C2218yescomplemented
57#16810511C2218yescomplemented
58#16810474C2218yescomplemented
59C2×#13133124C2211yescharacteristic
60C2×#13133124C2211yescharacteristic
61C2×#13133124C2211yescharacteristic
62C2×#13133124C2211yescharacteristic
63C22×C4⋊C4×C53C2211yescharacteristic
64C22×C22⋊C4×C53C2211yescharacteristic
65C22×C22⋊C4×C53C2211yescharacteristic
66C22×C22⋊C4×C53C2211yescharacteristic
67C22×C42×C53C2211yescharacteristic
68C53×#388C2218yescomplemented
69C2×#95×C53C2211yescharacteristic
70C2×#95×C53C2211yescharacteristic
71C24×D53C2311yescharacteristic
72C22×Dic106—24no—
73C22×Dic106—24no—
74C22×Dic106—24no—
75C22×Dic106—24no—
76C22×Dic106—24no—
77C22×Dic106D418yes—
78C22×Dic106C2314yes—
79C22×Dic106C2314yes—
80C22×C22⋊D53—24no—
81C22×C22⋊D53—24no—
82C22×C22⋊D53—24no—
83C22×C22⋊D53C2314yes—
84C23×Dic53C2311yescharacteristic
85C23×Dic53C2311yescharacteristic
86C23×Dic53C2311yescharacteristic
87C23×Dic53C2311yescharacteristic
88C23×Dic53C2311yescharacteristic
89C23×Dic53C2311yescharacteristic
90C23×Dic53C2311yescharacteristic
91#13133216—232no—
92#13133203—232no—
93#13133203—232no—
94C4×Dic106—232no—
95C2×C4⋊Dic53—24no—
96C2×C4⋊Dic53—24no—
97C2×C4⋊Dic53C2314yes—
98C2×C4⋊Dic53C2314yes—
99C2×#11719919—24no—
100C2×#11719919—24no—
101C2×#11719919—24no—
102C2×#11719919—24no—
103C2×#11719919—24no—
104C2×#11719919—24no—
105C2×#11719919C2314yes—
106C2×#11719919C2314yes—
107C2×#11719919C2314yes—
108C2×#11719919C2314yes—
109C2×#11719919C2314yes—
110C2×#11719919C2314yes—
111C2×C22⋊Dic53—24no—
112C2×C22⋊Dic53—24no—
113C2×C22⋊Dic53—24no—
114C2×C22⋊Dic53C2314yes—
115C2×C22⋊Dic53C2314yes—
116C2×C22⋊Dic53C2314yes—
117C2×#11719921—24no—
118C2×#11719921—24no—
119C2×#11719921—24no—
120C2×#11719921—24no—
121C2×#11719921—24no—
122C2×#11719921—24no—
123C2×#11719921C2314yes—
124C2×#11719921C2314yes—
125C2×#11719921C2314yes—
126C2×#11719921C2314yes—
127C2×#11719921C2314yes—
128C2×#11719921C2314yes—
129C2×C4×Dic53—24no—
130C2×C4×Dic53—24no—
131C2×C4×Dic53—24no—
132C2×C4×Dic53D418yes—
133C2×C4×Dic53C2314yes—
134C2×C4×Dic53C2314yes—
135C2×C4×Dic53C2314yes—
136C2×C4×Dic53C2314yes—
137#13133124C2314yes—
138#13133124C2314yes—
139#13133124C2314yes—
140#13133124C2314yes—
141C25×C53C2311yescharacteristic
142C23×C4×C53C2311yescharacteristic
143C23×C4×C53C2311yescharacteristic
144C23×C4×C53C2311yescharacteristic
145C23×C4×C53C2311yescharacteristic
146C23×C4×C53C2311yescharacteristic
147C23×C4×C53C2311yescharacteristic
148C2×C4⋊C4×C53—24no—
149C2×C4⋊C4×C53C2314yes—
150C2×C22⋊C4×C53—24no—
151C2×C22⋊C4×C53—24no—
152C2×C22⋊C4×C53—24no—
153C2×C22⋊C4×C53C2314yes—
154C2×C22⋊C4×C53C2314yes—
155C2×C22⋊C4×C53C2314yes—
156C2×C42×C53—24no—
157C2×C42×C53C2314yes—
158#95×C53C2314yes—
159#95×C53C2314yes—
160C24×C53—22no—
161C24×C53—22no—
162C24×C53—22no—
163C24×C53—22no—
164C24×C53—22no—
165C24×C53—22no—
166C24×C53—22no—
167C24×C53C2412yes—
168C24×C53C2411yescharacteristic
169C23×D53—22no—
170C23×D53—22no—
171C23×D53—22no—
172C23×D53—22no—
173C23×D53—22no—
174C23×D53—22no—
175C23×D53—22no—
176C23×D53C2412yes—
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×C53—22no—
191C22×C4×C53—22no—
192C22×C4×C53C2×D414yes—
193C22×C4×C53C2×D414yes—
194C22×C4×C53#4114yes—
195C22×C4×C53C2412yes—
196C22×C4×C53C2412yes—
197C22×C4×C53C2412yes—
198C22×C4×C53C2412yes—
199C22×C4×C53C2412yes—
200C22×C4×C53C2412yes—
201C2×C22⋊D53—28no—
202C2×C22⋊D53—28no—
203C2×C22⋊D53—28no—
204C2×C22⋊D53—416no—
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—22no—
217C22×Dic53—22no—
218C22×Dic53—22no—
219C22×Dic53—22no—
220C22×Dic53C2×D414yes—
221C22×Dic53C2×D414yes—
222C22×Dic53C2×D414yes—
223C22×Dic53C2×D414yes—
224C22×Dic53#4114yes—
225C22×Dic53#4114yes—
226C22×Dic53C2412yes—
227C22×Dic53C2412yes—
228C22×Dic53C2412yes—
229C22×Dic53C2412yes—
230C22×Dic53C2412yes—
231C22×Dic53C2412yes—
232C22×Dic53C2412yes—
233C2×Dic106—232no—
234C2×Dic106—28no—
235C2×Dic106—28no—
236C2×Dic106—28no—
237C2×Dic106—28no—
238C2×Dic106—28no—
239C2×Dic106—416no—
240C2×Dic106C2×D4116yes—
241C4⋊C4×C53—28no—
242C22⋊C4×C53—28no—
243C22⋊C4×C53—28no—
244C22⋊C4×C53—28no—
245C42×C53—28no—
246C22⋊Dic53—28no—
247C22⋊Dic53—28no—
248C22⋊Dic53—28no—
249#11719921—28no—
250#11719921—28no—
251#11719921—28no—
252#11719921—28no—
253#11719921—28no—
254#11719921—28no—
255C4⋊Dic53—28no—
256C4⋊Dic53—28no—
257#11719919—28no—
258#11719919—28no—
259#11719919—28no—
260#11719919—28no—
261#11719919—28no—
262#11719919—28no—
263C4×Dic53—28no—
264C4×Dic53—28no—
265C4×Dic53—28no—
266C4×Dic53C2×D4116yes—
267C23×C53—22no—
268C23×C53—22no—
269C23×C53—22no—
270C23×C53—22no—
271C23×C53—22no—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53—44no—
275C23×C53—44no—
276C23×C53—44no—
277C23×C53—44no—
278C23×C53—44no—
279C23×C53—44no—
280C23×C53—44no—
281C23×C53C22×D412yes—
282C23×C53C22×D412yes—
283C23×C53C2×#4112yes—
284C23×C53C2×#4112yes—
285C23×C53C2×#4112yes—
286C23×C532−1+412yes—
287C23×C532−1+412yes—
288C23×C53C2511yescharacteristic
289C22×D53—22no—
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—22no—
293C22×D53—22no—
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—44no—
297C22×D53—44no—
298C22×D53—44no—
299C22×D53—44no—
300C22×D53—44no—
301C22×D53—44no—
302C22×D53—44no—
303C2×C4×C53—28no—
304C2×C4×C53—28no—
305C2×C4×C53—28no—
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—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—44no—
322C2×C4×C53—44no—
323C2×C4×C53—44no—
324C2×C4×C53C22×D414yes—
325C2×C4×C53C22×D414yes—
326C2×C4×C53C2×#4114yes—
327C22⋊D53—416no—
328C2×Dic53—28no—
329C2×Dic53—28no—
330C2×Dic53—28no—
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—22no—
343C2×Dic53—22no—
344C2×Dic53—22no—
345C2×Dic53—22no—
346C2×Dic53—44no—
347C2×Dic53—44no—
348C2×Dic53—44no—
349C2×Dic53#121116yes—
350C2×Dic53C22×D414yes—
351C2×Dic53C22×D414yes—
352C2×Dic53C22×D414yes—
353C2×Dic53C22×D414yes—
354C2×Dic53C2×#4114yes—
355C2×Dic53C2×#4114yes—
356Dic106—232no—
357Dic106—416no—
358C2×#2545—531nomaximal, Sylow
359C22×C53—42no—
360C22×C53—42no—
361C22×C53—42no—
362C22×C53—42no—
363C22×C53—42no—
364C22×C53—42no—
365C22×C53—42no—
366C22×C53—88no—
367C22×C53C2×#12114yes—
368C22×C53#53214yes—
369C22×C53#53614yes—
370C22×C53#54814yes—
371C22×C53#54814yes—
372C22×C53#55614yes—
373C22×C53#55614yes—
374C22×C53C23×D411yescharacteristic
375C22×C53C23×D411yescharacteristic
376C22×C53C22×#4111yescharacteristic
377C22×C53C22×#4111yescharacteristic
378C22×C53C22×#4111yescharacteristic
379C22×C53C2×2−1+411yescharacteristic
380C22×C53C2×2−1+411yescharacteristic
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—42no—
384C2×D53—42no—
385C2×D53—42no—
386C2×D53—42no—
387C2×D53—42no—
388C2×D53—88no—
389C4×C53—24no—
390C4×C53—24no—
391C4×C53—24no—
392C4×C53—42no—
393C4×C53—42no—
394C4×C53—42no—
395Dic53—24no—
396Dic53—24no—
397Dic53—24no—
398Dic53—42no—
399Dic53—42no—
400Dic53—42no—
401Dic53C2×#12118yes—
402C22×C4⋊Q8—531no—
403C22×#124—531no—
404C22×#124—531no—
405C22×C4×Q8—531no—
406#2545—5316no—
407C2×#396—531no—
408C2×#396—531no—
409C2×#396—531no—
410C2×#396—531no—
411C2×#391—531no—
412C2×#390—531no—
413C2×#388—531no—
414C2×#388—531no—
415C2×#388—531no—
416C2×#388D5311yescharacteristic, complemented
417C2×C4×C4⋊C4—531no—
418C2×C53—82no—
419C2×C53#254518yescomplemented
420C2×C53C22×#12111yescharacteristic
421C2×C53C2×#53211yescharacteristic
422C2×C53C2×#53611yescharacteristic
423C2×C53C2×#54811yescharacteristic
424C2×C53C2×#54811yescharacteristic
425C2×C53C2×#55611yescharacteristic
426C2×C53C2×#55611yescharacteristic
427D53—82no—
428C23×Q8—531no—
429C23×Q8—531no—
430C23×D4—531no—
431C2×C4⋊Q8—538no—
432C2×C4⋊Q8—1068no—
433C2×#124—538no—
434C2×#124—538no—
435C2×#124—1068no—
436C2×#124—1068no—
437C2×C4×Q8—538no—
438C2×C4×Q8—1068no—
439C22×C4⋊C4—531no—
440C22×C4⋊C4—531no—
441C22×C4⋊C4—531no—
442C22×C4⋊C4—531no—
443C22×C4⋊C4—531no—
444C22×C4⋊C4—531no—
445C22×C4⋊C4—531no—
446C22×C4⋊C4—531no—
447C22×C4⋊C4C2×D5311yescharacteristic
448C22×C22⋊C4—531no—
449C22×C22⋊C4—531no—
450C22×C22⋊C4—531no—
451C22×C22⋊C4—531no—
452C22×C22⋊C4—531no—
453C22×C22⋊C4—531no—
454C22×C22⋊C4—531no—
455C22×C22⋊C4—531no—
456C22×C22⋊C4—531no—
457C22×C22⋊C4C2×D5311yescharacteristic
458C22×C22⋊C4C2×D5311yescharacteristic
459C22×C22⋊C4C2×D5311yescharacteristic
460C22×C42—531no—
461C22×C42—531no—
462C22×C42—531no—
463C22×C42—531no—
464C22×C42C2×D5311yescharacteristic
465#396—538no—
466#396—538no—
467#396—538no—
468#396—538no—
469#391—538no—
470#390—538no—
471#388—538no—
472#388—538no—
473#388—538no—
474#388C2×D5318yescomplemented
475C4×C4⋊C4—538no—
476C2×#95—531no—
477C2×#95—531no—
478C2×#95—531no—
479C2×#95—531no—
480C2×#95C2×D5311yescharacteristic
481C2×#95C2×D5311yescharacteristic
482C53C2×#254511yescharacteristic, complemented, Sylow
483C25—531no—
484C25C22×D5311yescharacteristic
485C22×Q8—538no—
486C22×Q8—534no—
487C22×Q8—534no—
488C22×Q8—1064no—
489C22×Q8—1064no—
490C22×Q8—1064no—
491C22×Q8—1064no—
492C22×Q8—1064no—
493C22×D4—534no—
494C22×D4—1064no—
495C22×D4—1064no—
496C22×D4—1064no—
497C23×C4—531no—
498C23×C4—531no—
499C23×C4—531no—
500C23×C4—531no—
501C23×C4—531no—
502C23×C4—531no—
503C23×C4—531no—
504C23×C4C22×D5311yescharacteristic
505C23×C4C22×D5311yescharacteristic
506C23×C4C22×D5311yescharacteristic
507C23×C4C22×D5311yescharacteristic
508C23×C4C22×D5311yescharacteristic
509C23×C4C22×D5311yescharacteristic
510C4⋊Q8—10632no—
511#124—10632no—
512#124—10632no—
513C4×Q8—10632no—
514C2×C4⋊C4—24no—
515C2×C4⋊C4—534no—
516C2×C4⋊C4—534no—
517C2×C4⋊C4—534no—
518C2×C4⋊C4—534no—
519C2×C4⋊C4—534no—
520C2×C4⋊C4—534no—
521C2×C4⋊C4—534no—
522C2×C4⋊C4—534no—
523C2×C4⋊C4—1064no—
524C2×C4⋊C4—1064no—
525C2×C4⋊C4—1064no—
526C2×C4⋊C4—1064no—
527C2×C4⋊C4—1064no—
528C2×C4⋊C4—1064no—
529C2×C4⋊C4—1064no—
530C2×C4⋊C4—1064no—
531C2×C4⋊C4C22×D5314yes—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
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—534no—
543C2×C22⋊C4—534no—
544C2×C22⋊C4—1064no—
545C2×C22⋊C4—1064no—
546C2×C22⋊C4—1064no—
547C2×C22⋊C4—1064no—
548C2×C22⋊C4—1064no—
549C2×C22⋊C4—1064no—
550C2×C22⋊C4—1064no—
551C2×C22⋊C4—1064no—
552C2×C22⋊C4—1064no—
553C2×C22⋊C4C22×D5314yes—
554C2×C22⋊C4C22×D5314yes—
555C2×C22⋊C4C22×D5314yes—
556C2×C42—24no—
557C2×C42—538no—
558C2×C42—534no—
559C2×C42—534no—
560C2×C42—534no—
561C2×C42—534no—
562C2×C42—1064no—
563C2×C42—1064no—
564C2×C42—1064no—
565C2×C42C22×D5314yes—
566#95—534no—
567#95—534no—
568#95—534no—
569#95—534no—
570#95C22×D5314yes—
571#95C22×D5314yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—532no—
580C24—1062no—
581C24—1062no—
582C24—1062no—
583C24—1062no—
584C24—1062no—
585C24—1062no—
586C24—1062no—
587C24C23×D5312yes—
588C24C23×D5311yescharacteristic
589C2×Q8—5316no—
590C2×Q8—1068no—
591C2×Q8—10632no—
592C2×Q8—1068no—
593C2×Q8—1068no—
594C2×Q8—1068no—
595C2×Q8—1068no—
596C2×Q8—21216no—
597C2×D4—1068no—
598C2×D4—1068no—
599C2×D4—1068no—
600C2×D4—21216no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—534no—
617C22×C4—534no—
618C22×C4—534no—
619C22×C4—532no—
620C22×C4—534no—
621C22×C4—534no—
622C22×C4—534no—
623C22×C4—532no—
624C22×C4—532no—
625C22×C4—532no—
626C22×C4—532no—
627C22×C4—532no—
628C22×C4—532no—
629C22×C4—1062no—
630C22×C4—1062no—
631C22×C4—1062no—
632C22×C4—1062no—
633C22×C4—1062no—
634C22×C4—1062no—
635C22×C4—1062no—
636C22×C4—1062no—
637C22×C4—1062no—
638C22×C4—1062no—
639C22×C4—1062no—
640C22×C4—1062no—
641C22×C4—1062no—
642C22×C4—1062no—
643C22×C4—1062no—
644C22×C4#1171994514yes—
645C22×C4D4×D5314yes—
646C22×C4D4×D5314yes—
647C22×C4C23×D5312yes—
648C22×C4C23×D5312yes—
649C22×C4C23×D5312yes—
650C22×C4C23×D5312yes—
651C22×C4C23×D5312yes—
652C22×C4C23×D5312yes—
653C4⋊C4—28no—
654C4⋊C4—1068no—
655C4⋊C4—1068no—
656C4⋊C4—1068no—
657C4⋊C4—1068no—
658C4⋊C4—1068no—
659C4⋊C4—1068no—
660C4⋊C4—1068no—
661C4⋊C4—1068no—
662C22⋊C4—28no—
663C22⋊C4—28no—
664C22⋊C4—28no—
665C22⋊C4—1068no—
666C22⋊C4—1068no—
667C22⋊C4—1068no—
668C22⋊C4—1068no—
669C22⋊C4—1068no—
670C22⋊C4—1068no—
671C22⋊C4—1068no—
672C22⋊C4—1068no—
673C22⋊C4—1068no—
674C42—28no—
675C42—5316no—
676C42—1068no—
677C42—1068no—
678C42—1068no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—1062no—
694C23—1062no—
695C23—1062no—
696C23—1062no—
697C23—1062no—
698C23—1062no—
699C23—1062no—
700C23—2124no—
701C23—2124no—
702C23—2124no—
703C23—2124no—
704C23—2124no—
705C23—2124no—
706C23—2124no—
707C23C2×D4×D5312yes—
708C23C2×D4×D5312yes—
709C23#41×D5312yes—
710C23#41×D5312yes—
711C23C2×#1171994512yes—
712C23#1313326412yes—
713C23#1313326412yes—
714C23C24×D5311yescharacteristic
715Q8—10632no—
716Q8—21216no—
717D4—21216no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—28no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—5316no—
740C2×C4—534no—
741C2×C4—534no—
742C2×C4—534no—
743C2×C4—534no—
744C2×C4—534no—
745C2×C4—534no—
746C2×C4—1068no—
747C2×C4—1068no—
748C2×C4—1068no—
749C2×C4—1062no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—1062no—
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—1062no—
764C2×C4—2124no—
765C2×C4—2124no—
766C2×C4—2124no—
767C2×C4C2×D4×D5314yes—
768C2×C4C2×D4×D5314yes—
769C2×C4C2×#1171994514yes—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—88no—
778C22—4248no—
779C22—2122no—
780C22—2122no—
781C22—2122no—
782C22—2122no—
783C22—2122no—
784C22—2122no—
785C22—2122no—
786C22#121×D5314yes—
787C22#1681117014yes—
788C22#1681119514yes—
789C22#1681128114yes—
790C22#1681128214yes—
791C22#1681134014yes—
792C22#1681134114yes—
793C22C22×D4×D5311yescharacteristic
794C22C22×D4×D5311yescharacteristic
795C22C2×#41×D5311yescharacteristic
796C22C2×#41×D5311yescharacteristic
797C22C22×#1171994511yescharacteristic
798C22C2×#1313326411yescharacteristic
799C22C2×#1313326411yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—538no—
807C4—1064no—
808C4—1064no—
809C4—1064no—
810C4—2122no—
811C4—2122no—
812C4—2122no—
813C2—82no—
814C2—4242no—
815C2#2027969318yesdirect product factor
816C2C2×#121×D5311yescharacteristic
817C2C2×#1681117011yescharacteristic
818C2C2×#1681119511yescharacteristic
819C2C2×#1681128111yescharacteristic
820C2C2×#1681128211yescharacteristic
821C2C2×#1681134011yescharacteristic
822C2C2×#1681134111yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#388C2
socleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC2×#388D53
hypocenterC53C2×#2545
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#13133216C2semidirect
4. C22×C4×Dic106C2semidirect
5. #20279693C2direct (N × H)
6. C2×#16810547C2semidirect
7. C2×#16810546C2semidirect
8. C2×#16810546C2semidirect
9. C2×#16810545C2semidirect
10. C2×#16810527C2semidirect
12. C2×#16810515C2semidirect
13. C2×#16810514C2semidirect
14. C2×#16810511C2semidirect
15. C2×#16810474C2semidirect
16. C2×C53×#388C2semidirect
21. C2×#13133216C22semidirect
27. C2×C4×Dic106C22semidirect
49. #16810547C22semidirect
50. #16810546C22semidirect
51. #16810546C22semidirect
52. #16810545C22semidirect
53. #16810527C22semidirect
55. #16810515C22semidirect
56. #16810514C22semidirect
57. #16810511C22semidirect
58. #16810474C22semidirect
68. C53×#388C22semidirect
416. C2×#388D53semidirect
419. C2×C53#2545semidirect
474. #388C2×D53semidirect
482. C53C2×#2545semidirect
815. C2#20279693direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332162
C22×#131332032
C22×C4×Dic1062
#202796932
C2×#168105472
C2×#168105462
C2×#168105452
C2×#168105272
C2×#168105232
C2×#168105152
C2×#168105142
C2×#168105112
C2×#168104742
C2×C53×#3882
C2×#254553