Finite Group Databasebeta

← C2×#20280066 #27554299

Subgroups — C2×#20280066 #27554299

Order 13568.

3374 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×C4×D212C211yesmaximal, characteristic
2C22×C4⋊C4×D53C211yesmaximal, characteristic, complemented
3#20280066C2116yesmaximal, direct product factor
4C2×#16810557C211yesmaximal, characteristic, complemented
5C2×#16810555C211yesmaximal, characteristic, complemented
6C2×#16810547C211yesmaximal, characteristic, complemented
7C2×#16810545C211yesmaximal, characteristic, complemented
8C2×#16810507C211yesmaximal, characteristic, complemented
9C2×#16810501C211yesmaximal, characteristic
10C2×#16810501C211yesmaximal, characteristic
11C2×#16810497C211yesmaximal, characteristic, complemented
12C2×#16810497C211yesmaximal, characteristic, complemented
13C2×#16810494C211yesmaximal, characteristic, complemented
14C2×#16810494C211yesmaximal, characteristic, complemented
15C2×#16810482C211yesmaximal, characteristic, complemented
16C2×C53×#387C211yesmaximal, characteristic, complemented
17C23×D212C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C23×C4×D53C2211yescharacteristic
20C23×C4×D53C2211yescharacteristic
21C23×C4×D53C2211yescharacteristic
22C2×C4×D212—28no—
23C2×C4×D212C2218yes—
24C22×C4⋊Dic53C2211yescharacteristic
25C22×C4⋊Dic53C2211yescharacteristic
26C22×C4⋊Dic53C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×#11719919C2211yescharacteristic
29C22×#11719919C2211yescharacteristic
30C22×#11719919C2211yescharacteristic
31C22×#11719919C2211yescharacteristic
32C22×#11719919C2211yescharacteristic
33C2×C4⋊C4×D53—28no—
34C2×C4⋊C4×D53C2218yescomplemented
35C22×#11719921C2211yescharacteristic
36C22×#11719921C2211yescharacteristic
37C22×#11719921C2211yescharacteristic
38C22×#11719921C2211yescharacteristic
39C22×#11719921C2211yescharacteristic
40C22×#11719921C2211yescharacteristic
41C22×#11719921C2211yescharacteristic
42C22×#11719921C2211yescharacteristic
43#16810557C2218yescomplemented
44#16810555C2218yescomplemented
45#16810547C2218yescomplemented
46#16810545C2218yescomplemented
47#16810507C2218yescomplemented
48#16810501C2218yes—
49#16810501C2218yes—
50#16810497C2218yescomplemented
51#16810497C2218yescomplemented
52#16810494C2218yescomplemented
53#16810494C2218yescomplemented
54#16810482C2218yescomplemented
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60C2×#13133124C2211yescharacteristic
61C22×C4⋊C4×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×C42×C53C2211yescharacteristic
64C53×#387C2218yescomplemented
65C2×#95×C53C2211yescharacteristic
66C2×#95×C53C2211yescharacteristic
67C2×#95×C53C2211yescharacteristic
68C2×#95×C53C2211yescharacteristic
69C24×D53C2311yescharacteristic
70C24×D53C2311yescharacteristic
71C22×D212—24no—
72C22×D212—24no—
73C22×D212Q818yes—
74C22×D212C2314yes—
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2311yescharacteristic
81C22×C4×D53—24no—
82C22×C4×D53—24no—
83C22×C4×D53—24no—
84C22×C4×D53—24no—
85C22×C4×D53—24no—
86C22×C4×D53—42no—
87C22×C4×D53—42no—
88C22×C4×D53—42no—
89C22×C4×D53—42no—
90C22×C4×D53—42no—
91C22×C4×D53—42no—
92C22×C4×D53D418yes—
93C22×C4×D53C2314yes—
94C22×C4×D53C2314yes—
95C22×C4×D53C2314yes—
96C22×C4×D53C2314yes—
97C4×D212—232no—
98C2×C4⋊Dic53—24no—
99C2×C4⋊Dic53—24no—
100C2×C4⋊Dic53—42no—
101C2×C4⋊Dic53C2314yes—
102C2×C4⋊Dic53C2314yes—
103C2×C4⋊Dic53C2314yes—
104C2×#11719919—24no—
105C2×#11719919—24no—
106C2×#11719919—24no—
107C2×#11719919—42no—
108C2×#11719919—42no—
109C2×#11719919—42no—
110C2×#11719919C2314yes—
111C2×#11719919C2314yes—
112C2×#11719919C2314yes—
113C2×#11719919C2314yes—
114C2×#11719919C2314yes—
115C2×#11719919C2314yes—
116C4⋊C4×D53—232no—
117C2×#11719921—24no—
118C2×#11719921—24no—
119C2×#11719921—24no—
120C2×#11719921—24no—
121C2×#11719921—24no—
122C2×#11719921—24no—
123C2×#11719921—42no—
124C2×#11719921—42no—
125C2×#11719921C2314yes—
126C2×#11719921C2314yes—
127C2×#11719921C2314yes—
128C2×#11719921C2314yes—
129C2×#11719921C2314yes—
130C2×#11719921C2314yes—
131C2×#11719921C2314yes—
132C2×#11719921C2314yes—
133#13133124C2314yes—
134#13133124C2314yes—
135#13133124C2314yes—
136#13133124C2314yes—
137#13133124C2314yes—
138#13133124C2314yes—
139C23×C4×C53C2311yescharacteristic
140C23×C4×C53C2311yescharacteristic
141C23×C4×C53C2311yescharacteristic
142C23×C4×C53C2311yescharacteristic
143C23×C4×C53C2311yescharacteristic
144C23×C4×C53C2311yescharacteristic
145C23×C4×C53C2311yescharacteristic
146C2×C4⋊C4×C53—24no—
147C2×C4⋊C4×C53—24no—
148C2×C4⋊C4×C53C2314yes—
149C2×C4⋊C4×C53C2314yes—
150C2×C42×C53—24no—
151C2×C42×C53C2314yes—
152#95×C53C2314yes—
153#95×C53C2314yes—
154#95×C53C2314yes—
155#95×C53C2314yes—
156C24×C53C2411yescharacteristic
157C23×D53—22no—
158C23×D53—22no—
159C23×D53—22no—
160C23×D53—22no—
161C23×D53—22no—
162C23×D53—22no—
163C23×D53—22no—
164C23×D53—22no—
165C23×D53—22no—
166C23×D53—22no—
167C23×D53C2×D414yes—
168C23×D53C2×Q814yes—
169C23×D53C2×Q814yes—
170C23×D53#4114yes—
171C23×D53C2412yes—
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×C53—22no—
191C22×C4×C53C2×D414yes—
192C22×C4×C53C2×Q814yes—
193C22×C4×C53#4114yes—
194C22×C4×C53C2412yes—
195C22×C4×C53C2412yes—
196C22×C4×C53C2412yes—
197C22×C4×C53C2412yes—
198C22×C4×C53C2412yes—
199C22×C4×C53C2412yes—
200C22×C4×C53C2412yes—
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—22no—
217C22×Dic53C2×D414yes—
218C22×Dic53#4114yes—
219C22×Dic53C2412yes—
220C22×Dic53C2412yes—
221C22×Dic53C2412yes—
222C22×Dic53C2412yes—
223C22×Dic53C2412yes—
224C22×Dic53C2412yes—
225C2×D212—232no—
226C2×D212—28no—
227C2×D212—28no—
228C2×D212C2×Q8116yes—
229C2×C4×D53—232no—
230C2×C4×D53—28no—
231C2×C4×D53—28no—
232C2×C4×D53—28no—
233C2×C4×D53—28no—
234C2×C4×D53—28no—
235C2×C4×D53—416no—
236C2×C4×D53—44no—
237C2×C4×D53—44no—
238C2×C4×D53—44no—
239C2×C4×D53—44no—
240C2×C4×D53—44no—
241C2×C4×D53—44no—
242C2×C4×D53—416no—
243C2×C4×D53—416no—
244C2×C4×D53C2×D4116yes—
245C4⋊C4×C53—28no—
246C4⋊C4×C53—28no—
247C42×C53—28no—
248#11719921—28no—
249#11719921—28no—
250#11719921—28no—
251#11719921—28no—
252#11719921—28no—
253#11719921—28no—
254#11719921—44no—
255#11719921—44no—
256C4⋊Dic53—28no—
257C4⋊Dic53—28no—
258C4⋊Dic53—44no—
259#11719919—28no—
260#11719919—28no—
261#11719919—28no—
262#11719919—44no—
263#11719919—44no—
264#11719919—44no—
265C23×C53C22×D412yes—
266C23×C53C22×Q812yes—
267C23×C53C2×#4112yes—
268C23×C53C2×#4112yes—
269C23×C53C2×#4112yes—
270C23×C53H(5,𝔽2)12yes—
271C23×C53H(5,𝔽2)12yes—
272C23×C53C2511yescharacteristic
273C22×D53—28no—
274C22×D53—28no—
275C22×D53—28no—
276C22×D53—28no—
277C22×D53—28no—
278C22×D53—28no—
279C22×D53—22no—
280C22×D53—22no—
281C22×D53—22no—
282C22×D53—22no—
283C22×D53—28no—
284C22×D53—28no—
285C22×D53—28no—
286C22×D53—22no—
287C22×D53—22no—
288C22×D53—22no—
289C22×D53—22no—
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—44no—
293C22×D53—44no—
294C22×D53—44no—
295C22×D53—44no—
296C22×D53C22⋊Q8116yes—
297C22×D53C22×D414yes—
298C22×D53C22×Q814yes—
299C22×D53C22×Q814yes—
300C22×D53C2×#4114yes—
301C2×C4×C53—28no—
302C2×C4×C53—28no—
303C2×C4×C53—28no—
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—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—44no—
323C2×C4×C53—44no—
324C2×C4×C53—44no—
325C2×C4×C53—44no—
326C2×C4×C53C22×D414yes—
327C2×C4×C53C22×Q814yes—
328C2×C4×C53C2×#4114yes—
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—22no—
347C2×Dic53—44no—
348C2×Dic53—44no—
349C2×Dic53—44no—
350C2×Dic53—44no—
351C2×Dic53C22×D414yes—
352C2×Dic53C2×#4114yes—
353D212—232no—
354C4×D53—232no—
355C4×D53—416no—
356C4×D53—416no—
357C4×D53—416no—
358C2×#2579—531nomaximal, Sylow
359C22×C53C2×C22⋊Q814yes—
360C22×C53#52514yes—
361C22×C53#53414yes—
362C22×C53#55314yes—
363C22×C53#55314yes—
364C22×C53#55414yes—
365C22×C53#55414yes—
366C22×C53C23×D411yescharacteristic
367C22×C53C23×Q811yescharacteristic
368C22×C53C22×#4111yescharacteristic
369C22×C53C22×#4111yescharacteristic
370C22×C53C22×#4111yescharacteristic
371C22×C53C2×H(5,𝔽2)11yescharacteristic
372C22×C53C2×H(5,𝔽2)11yescharacteristic
373C2×D53—232no—
374C2×D53—24no—
375C2×D53—24no—
376C2×D53—24no—
377C2×D53—24no—
378C2×D53—24no—
379C2×D53—24no—
380C2×D53—24no—
381C2×D53—24no—
382C2×D53—24no—
383C2×D53—416no—
384C2×D53—42no—
385C2×D53—42no—
386C2×D53—42no—
387C2×D53—42no—
388C2×D53C2×C22⋊Q818yes—
389C4×C53—24no—
390C4×C53—24no—
391C4×C53—24no—
392C4×C53—42no—
393C4×C53—42no—
394C4×C53—42no—
395C4×C53—42no—
396Dic53—24no—
397Dic53—24no—
398Dic53—42no—
399Dic53—42no—
400Dic53—42no—
401Dic53—42no—
402C22×C4×D4—531no—
403C23×C4⋊C4—531no—
404#2579—5316no—
405C2×#398—531no—
406C2×#398—531no—
407C2×#396—531no—
408C2×#396—531no—
409C2×#387—531no—
410C2×#387D5311yescharacteristic, complemented
411C2×#386—531no—
412C2×#386—531no—
413C2×#385—531no—
414C2×#385—531no—
415C2×#385—531no—
416C2×#385—531no—
417C2×#380—531no—
418C2×C53#257918yescomplemented
419C2×C53C22×C22⋊Q811yescharacteristic
420C2×C53C2×#52511yescharacteristic
421C2×C53C2×#53411yescharacteristic
422C2×C53C2×#55311yescharacteristic
423C2×C53C2×#55311yescharacteristic
424C2×C53C2×#55411yescharacteristic
425C2×C53C2×#55411yescharacteristic
426D53—28no—
427D53—44no—
428C23×D4—531no—
429C24×C4—531no—
430C24×C4—531no—
431C24×C4—531no—
432C24×C4—531no—
433C2×C4×D4—538no—
434C2×C4×D4—1068no—
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⋊C4—531no—
442C22×C4⋊C4—531no—
443C22×C4⋊C4—531no—
444C22×C4⋊C4—538no—
445C22×C4⋊C4—1068no—
446C22×C4⋊C4C2×D5311yescharacteristic
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×C42C2×D5311yescharacteristic
457#398—538no—
458#398—538no—
459#396—538no—
460#396—538no—
461#387—538no—
462#387C2×D5318yescomplemented
463#386—538no—
464#386—538no—
465#385—538no—
466#385—538no—
467#385—538no—
468#385—538no—
469#380—538no—
470C2×#95—531no—
471C2×#95—531no—
472C2×#95—531no—
473C2×#95—531no—
474C2×#95—531no—
475C2×#95—531no—
476C2×#95C2×D5311yescharacteristic
477C2×#95C2×D5311yescharacteristic
478C2×#95C2×D5311yescharacteristic
479C2×#95C2×D5311yescharacteristic
480C53C2×#257911yescharacteristic, complemented, Sylow
481C25—531no—
482C25—531no—
483C22×D4—538no—
484C22×D4—534no—
485C22×D4—1064no—
486C22×D4—1064no—
487C23×C4—531no—
488C23×C4—531no—
489C23×C4—538no—
490C23×C4—534no—
491C23×C4—531no—
492C23×C4—531no—
493C23×C4—531no—
494C23×C4—531no—
495C23×C4—534no—
496C23×C4—534no—
497C23×C4—534no—
498C23×C4—1064no—
499C23×C4—1064no—
500C23×C4—1064no—
501C23×C4—1064no—
502C23×C4—1064no—
503C23×C4—2122no—
504C23×C4—2122no—
505C23×C4—2122no—
506C23×C4—2122no—
507C23×C4—2122no—
508C23×C4—2122no—
509C23×C4C22×D5311yescharacteristic
510C23×C4C22×D5311yescharacteristic
511C23×C4C22×D5311yescharacteristic
512C23×C4C22×D5311yescharacteristic
513C23×C4C22×D5311yescharacteristic
514C23×C4C22×D5311yescharacteristic
515C23×C4C22×D5311yescharacteristic
516C4×D4—10632no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—24no—
519C2×C4⋊C4—534no—
520C2×C4⋊C4—534no—
521C2×C4⋊C4—534no—
522C2×C4⋊C4—534no—
523C2×C4⋊C4—534no—
524C2×C4⋊C4—534no—
525C2×C4⋊C4—534no—
526C2×C4⋊C4—534no—
527C2×C4⋊C4—534no—
528C2×C4⋊C4—10632no—
529C2×C4⋊C4—1064no—
530C2×C4⋊C4—1064no—
531C2×C4⋊C4—1064no—
532C2×C4⋊C4—1064no—
533C2×C4⋊C4—1064no—
534C2×C4⋊C4—2122no—
535C2×C4⋊C4—2122no—
536C2×C4⋊C4—2122no—
537C2×C4⋊C4—2122no—
538C2×C4⋊C4C22×D5314yes—
539C2×C4⋊C4C22×D5314yes—
540C2×C22⋊C4—534no—
541C2×C22⋊C4—534no—
542C2×C22⋊C4—534no—
543C2×C22⋊C4—534no—
544C2×C22⋊C4—534no—
545C2×C22⋊C4—534no—
546C2×C22⋊C4—534no—
547C2×C22⋊C4—534no—
548C2×C22⋊C4—1064no—
549C2×C22⋊C4—1064no—
550C2×C22⋊C4—1064no—
551C2×C22⋊C4—1064no—
552C2×C22⋊C4—1064no—
553C2×C22⋊C4—1064no—
554C2×C22⋊C4—2122no—
555C2×C22⋊C4—2122no—
556C2×C42—24no—
557C2×C42C22×D5314yes—
558#95—534no—
559#95—534no—
560#95—534no—
561#95—534no—
562#95—534no—
563#95—534no—
564#95C22×D5314yes—
565#95C22×D5314yes—
566#95C22×D5314yes—
567#95C22×D5314yes—
568C24—534no—
569C24—534no—
570C24—534no—
571C24—532no—
572C24—534no—
573C24—532no—
574C24—1062no—
575C24—1062no—
576C24—1062no—
577C24—1062no—
578C24—1062no—
579C24—1062no—
580C24—1062no—
581C24—1062no—
582C24—1062no—
583C24—1062no—
584C24C23×D5311yescharacteristic
585C2×D4—5316no—
586C2×D4—1068no—
587C2×D4—10632no—
588C2×D4—1068no—
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—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—534no—
608C22×C4—534no—
609C22×C4—532no—
610C22×C4—532no—
611C22×C4—5316no—
612C22×C4—532no—
613C22×C4—532no—
614C22×C4—532no—
615C22×C4—532no—
616C22×C4—1068no—
617C22×C4—1068no—
618C22×C4—10632no—
619C22×C4—1068no—
620C22×C4—1062no—
621C22×C4—1062no—
622C22×C4—1062no—
623C22×C4—1062no—
624C22×C4—1068no—
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—1062no—
634C22×C4—1062no—
635C22×C4—1062no—
636C22×C4—1062no—
637C22×C4—1068no—
638C22×C4—21216no—
639C22×C4—2124no—
640C22×C4—2124no—
641C22×C4—2124no—
642C22×C4—2124no—
643C22×C4—2124no—
644C22×C4—2124no—
645C22×C4—21216no—
646C22×C4—21216no—
647C22×C4#1171994514yes—
648C22×C4D4×D5314yes—
649C22×C4Q8×D5314yes—
650C22×C4C23×D5312yes—
651C22×C4C23×D5312yes—
652C22×C4C23×D5312yes—
653C22×C4C23×D5312yes—
654C22×C4C23×D5312yes—
655C22×C4C23×D5312yes—
656C22×C4C23×D5312yes—
657C4⋊C4—28no—
658C4⋊C4—28no—
659C4⋊C4—1068no—
660C4⋊C4—1068no—
661C4⋊C4—1068no—
662C4⋊C4—1068no—
663C4⋊C4—1068no—
664C4⋊C4—2124no—
665C4⋊C4—2124no—
666C4⋊C4—2124no—
667C4⋊C4—2124no—
668C22⋊C4—1068no—
669C22⋊C4—1068no—
670C22⋊C4—1068no—
671C22⋊C4—1068no—
672C22⋊C4—1068no—
673C22⋊C4—1068no—
674C22⋊C4—2124no—
675C22⋊C4—2124no—
676C42—28no—
677C23—5316no—
678C23—534no—
679C23—534no—
680C23—534no—
681C23—534no—
682C23—1068no—
683C23—1068no—
684C23—1068no—
685C23—1068no—
686C23—1068no—
687C23—1068no—
688C23—1062no—
689C23—1062no—
690C23—1062no—
691C23—1062no—
692C23—1068no—
693C23—1068no—
694C23—1068no—
695C23—1062no—
696C23—1062no—
697C23—1062no—
698C23—1062no—
699C23—1062no—
700C23—1062no—
701C23—2124no—
702C23—2124no—
703C23—2124no—
704C23—2124no—
705C23C2×D4×D5312yes—
706C23C2×Q8×D5312yes—
707C23#41×D5312yes—
708C23#41×D5312yes—
709C23C2×#1171994512yes—
710C23#1313326312yes—
711C23#1313326312yes—
712C23C24×D5311yescharacteristic
713D4—10632no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—28no—
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—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—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—534no—
740C2×C4—534no—
741C2×C4—10632no—
742C2×C4—1068no—
743C2×C4—1068no—
744C2×C4—1062no—
745C2×C4—1062no—
746C2×C4—1062no—
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—1062no—
757C2×C4—1062no—
758C2×C4—1062no—
759C2×C4—1062no—
760C2×C4—21216no—
761C2×C4—21216no—
762C2×C4—21216no—
763C2×C4—2124no—
764C2×C4—2124no—
765C2×C4—2124no—
766C2×C4—2124no—
767C2×C4C2×D4×D5314yes—
768C2×C4C2×Q8×D5314yes—
769C2×C4C2×#1171994514yes—
770C22—538no—
771C22—10632no—
772C22—1064no—
773C22—1064no—
774C22—1064no—
775C22—1064no—
776C22—1064no—
777C22—1064no—
778C22—1064no—
779C22—1064no—
780C22—1064no—
781C22—21216no—
782C22—2122no—
783C22—2122no—
784C22—2122no—
785C22—2122no—
786C22C22⋊Q8×D5314yes—
787C22#1681113214yes—
788C22#1681118414yes—
789C22#1681131714yes—
790C22#1681132414yes—
791C22#1681132914yes—
792C22#1681133314yes—
793C22C22×D4×D5311yescharacteristic
794C22C22×Q8×D5311yescharacteristic
795C22C2×#41×D5311yescharacteristic
796C22C2×#41×D5311yescharacteristic
797C22C22×#1171994511yescharacteristic
798C22C2×#1313326311yescharacteristic
799C22C2×#1313326311yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—1064no—
808C4—1064no—
809C4—2122no—
810C4—2122no—
811C4—2122no—
812C4—2122no—
813C2—1068no—
814C2—2124no—
815C2#2028006618yesdirect product factor
816C2C2×C22⋊Q8×D5311yescharacteristic
817C2C2×#1681113211yescharacteristic
818C2C2×#1681118411yescharacteristic
819C2C2×#1681131711yescharacteristic
820C2C2×#1681132411yescharacteristic
821C2C2×#1681132911yescharacteristic
822C2C2×#1681133311yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#387C2
socleC24×C53C24
prime radicalC23×D212C22
hypercenterC2×#387D53
hypocenterC53C2×#2579
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D53C2semidirect
3. #20280066C2direct (N × H)
4. C2×#16810557C2semidirect
5. C2×#16810555C2semidirect
6. C2×#16810547C2semidirect
7. C2×#16810545C2semidirect
8. C2×#16810507C2semidirect
11. C2×#16810497C2semidirect
12. C2×#16810497C2semidirect
13. C2×#16810494C2semidirect
14. C2×#16810494C2semidirect
15. C2×#16810482C2semidirect
16. C2×C53×#387C2semidirect
34. C2×C4⋊C4×D53C22semidirect
43. #16810557C22semidirect
44. #16810555C22semidirect
45. #16810547C22semidirect
46. #16810545C22semidirect
47. #16810507C22semidirect
50. #16810497C22semidirect
51. #16810497C22semidirect
52. #16810494C22semidirect
53. #16810494C22semidirect
54. #16810482C22semidirect
64. C53×#387C22semidirect
410. C2×#387D53semidirect
418. C2×C53#2579semidirect
462. #387C2×D53semidirect
480. C53C2×#2579semidirect
815. C2#20280066direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D2122
C22×C4⋊C4×D532
#202800662
C2×#168105572
C2×#168105552
C2×#168105472
C2×#168105452
C2×#168105072
C2×#168105012
C2×#168104972
C2×#168104942
C2×#168104822
C2×C53×#3872
C2×#257953