Finite Group Databasebeta

← C2×#20280636 #27550499

Subgroups — C2×#20280636 #27550499

Order 13568.

2958 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133195C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D53C211yesmaximal, characteristic
3#20280636C2116yesmaximal, direct product factor
4C2×#16810557C211yesmaximal, characteristic, complemented
5C2×#16810552C211yesmaximal, characteristic, complemented
6C2×#16810551C211yesmaximal, characteristic, complemented
7C2×#16810549C211yesmaximal, characteristic, complemented
8C2×#16810543C211yesmaximal, characteristic, complemented
9C2×#16810539C211yesmaximal, characteristic
10C2×#16810538C211yesmaximal, characteristic
11C2×#16810535C211yesmaximal, characteristic, complemented
12C2×#16810508C211yesmaximal, characteristic, complemented
13C2×#16810504C211yesmaximal, characteristic, complemented
14C2×#16810496C211yesmaximal, characteristic, complemented
15C2×#16810485C211yesmaximal, characteristic, complemented
16C2×C53×#385C211yesmaximal, characteristic, complemented
17C23×Dic106C2211yescharacteristic
18C23×C22⋊D53C2211yescharacteristic
19C23×C4×D53C2211yescharacteristic
20C2×#13133195—28no—
21C2×#13133195C2218yescomplemented
22C2×C4×C22⋊D53—28no—
23C2×C4×C22⋊D53C2218yes—
24C22×C4⋊Dic53C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×#11719919C2211yescharacteristic
29C22×#11719919C2211yescharacteristic
30C22×C22⋊Dic53C2211yescharacteristic
31C22×C22⋊Dic53C2211yescharacteristic
32C22×C22⋊Dic53C2211yescharacteristic
33C22×#11719921C2211yescharacteristic
34C22×#11719921C2211yescharacteristic
35C22×#11719921C2211yescharacteristic
36C22×#11719921C2211yescharacteristic
37C22×#11719921C2211yescharacteristic
38C22×C4×Dic53C2211yescharacteristic
39#16810557C2218yescomplemented
40#16810552C2218yescomplemented
41#16810551C2218yescomplemented
42#16810549C2218yescomplemented
43#16810543C2218yescomplemented
44#16810539C2218yes—
45#16810538C2218yes—
46#16810535C2218yescomplemented
47#16810508C2218yescomplemented
48#16810504C2218yescomplemented
49#16810496C2218yescomplemented
50#16810485C2218yescomplemented
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60C2×#13133124C2211yescharacteristic
61C24×C4×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×C4⋊C4×C53C2211yescharacteristic
64C22×C22⋊C4×C53C2211yescharacteristic
65C22×C22⋊C4×C53C2211yescharacteristic
66C53×#385C2218yescomplemented
67C2×#95×C53C2211yescharacteristic
68C2×#95×C53C2211yescharacteristic
69C24×D53C2311yescharacteristic
70C22×Dic106—24no—
71C22×Dic106—42no—
72C22×Dic106—42no—
73C22×Dic106C2314yes—
74C22×C22⋊D53—24no—
75C22×C22⋊D53—24no—
76C22×C22⋊D53—24no—
77C22×C22⋊D53C2314yes—
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2311yescharacteristic
81C23×Dic53C2311yescharacteristic
82C23×Dic53C2311yescharacteristic
83C23×Dic53C2311yescharacteristic
84C23×Dic53C2311yescharacteristic
85C22×C4×D53—42no—
86C22×C4×D53—42no—
87C22×C4×D53D418yes—
88C22×C4×D53C2314yes—
89#13133195—232no—
90C4×C22⋊D53—232no—
91C2×C4⋊Dic53—24no—
92C2×C4⋊Dic53C2314yes—
93C2×#11719919—24no—
94C2×#11719919—24no—
95C2×#11719919—24no—
96C2×#11719919—24no—
97C2×#11719919—42no—
98C2×#11719919C2314yes—
99C2×#11719919C2314yes—
100C2×#11719919C2314yes—
101C2×#11719919C2314yes—
102C2×#11719919C2314yes—
103C2×C22⋊Dic53—24no—
104C2×C22⋊Dic53—24no—
105C2×C22⋊Dic53—42no—
106C2×C22⋊Dic53C2314yes—
107C2×C22⋊Dic53C2314yes—
108C2×C22⋊Dic53C2314yes—
109C2×#11719921—24no—
110C2×#11719921—24no—
111C2×#11719921—24no—
112C2×#11719921—42no—
113C2×#11719921—42no—
114C2×#11719921C2314yes—
115C2×#11719921C2314yes—
116C2×#11719921C2314yes—
117C2×#11719921C2314yes—
118C2×#11719921C2314yes—
119C2×C4×Dic53—24no—
120C2×C4×Dic53C2314yes—
121#13133124C2314yes—
122#13133124C2314yes—
123#13133124C2314yes—
124#13133124C2314yes—
125#13133124C2314yes—
126#13133124C2314yes—
127#13133124C2314yes—
128#13133124C2314yes—
129#13133124C2314yes—
130#13133124C2314yes—
131C25×C53C2311yescharacteristic
132C23×C4×C53—24no—
133C23×C4×C53—42no—
134C23×C4×C53—42no—
135C23×C4×C53C2311yescharacteristic
136C23×C4×C53C2311yescharacteristic
137C23×C4×C53C2311yescharacteristic
138C23×C4×C53C2311yescharacteristic
139C23×C4×C53C2311yescharacteristic
140C23×C4×C53C2311yescharacteristic
141C23×C4×C53C2314yes—
142C2×C4⋊C4×C53—24no—
143C2×C4⋊C4×C53—42no—
144C2×C4⋊C4×C53C2314yes—
145C2×C4⋊C4×C53C2314yes—
146C2×C22⋊C4×C53—24no—
147C2×C22⋊C4×C53—42no—
148C2×C22⋊C4×C53C2314yes—
149C2×C22⋊C4×C53C2314yes—
150#95×C53C2314yes—
151#95×C53C2314yes—
152C24×C53—22no—
153C24×C53—22no—
154C24×C53—22no—
155C24×C53—22no—
156C24×C53—22no—
157C24×C53—22no—
158C24×C53#4114yes—
159C24×C53C2412yes—
160C24×C53C2411yescharacteristic
161C23×D53—22no—
162C23×D53—22no—
163C23×D53—22no—
164C23×D53—22no—
165C23×D53—22no—
166C23×D53—22no—
167C23×D53C2×D414yes—
168C23×D53C2412yes—
169C22×C4×C53—22no—
170C22×C4×C53—22no—
171C22×C4×C53—22no—
172C22×C4×C53—22no—
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—28no—
187C22×C4×C53—44no—
188C22×C4×C53—44no—
189C22×C4×C53—416no—
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⋊D53—28no—
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×Dic53—22no—
218C22×Dic53—22no—
219C22×Dic53—22no—
220C22×Dic53C2×D414yes—
221C22×Dic53#4114yes—
222C22×Dic53C2412yes—
223C22×Dic53C2412yes—
224C22×Dic53C2412yes—
225C22×Dic53C2412yes—
226C22×Dic53C2412yes—
227C22×Dic53C2412yes—
228C22×Dic53C2412yes—
229C2×C4×D53—416no—
230C2×C4×D53—44no—
231C2×C4×D53—44no—
232C2×C4×D53C2×D4116yes—
233C2×Dic106—28no—
234C2×Dic106—44no—
235C2×Dic106—44no—
236C2×Dic106—416no—
237C4⋊C4×C53—28no—
238C4⋊C4×C53—44no—
239C22⋊C4×C53—28no—
240C22⋊C4×C53—44no—
241C22⋊Dic53—28no—
242C22⋊Dic53—28no—
243C22⋊Dic53—44no—
244#11719921—28no—
245#11719921—28no—
246#11719921—28no—
247#11719921—44no—
248#11719921—44no—
249C4⋊Dic53—28no—
250#11719919—28no—
251#11719919—28no—
252#11719919—28no—
253#11719919—28no—
254#11719919—44no—
255C4×Dic53—28no—
256C23×C53—28no—
257C23×C53—28no—
258C23×C53—28no—
259C23×C53—22no—
260C23×C53—22no—
261C23×C53—22no—
262C23×C53—22no—
263C23×C53—22no—
264C23×C53—22no—
265C23×C53—44no—
266C23×C53—44no—
267C23×C53—44no—
268C23×C53—44no—
269C23×C53C22×D412yes—
270C23×C53C2×#4112yes—
271C23×C53C2×#4114yes—
272C23×C53C2×#4112yes—
273C23×C53H(5,𝔽2)12yes—
274C23×C53H(5,𝔽2)12yes—
275C23×C532−1+412yes—
276C23×C532−1+412yes—
277C23×C53C2511yescharacteristic
278C22×D53—28no—
279C22×D53—28no—
280C22×D53—28no—
281C22×D53—22no—
282C22×D53—22no—
283C22×D53—22no—
284C22×D53—22no—
285C22×D53—22no—
286C22×D53—22no—
287C22×D53—44no—
288C22×D53—44no—
289C22×D53—44no—
290C22×D53—44no—
291C22×D53C22×D414yes—
292C2×C4×C53—28no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
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—416no—
311C2×C4×C53—44no—
312C2×C4×C53—44no—
313C2×C4×C53—44no—
314C2×C4×C53—44no—
315C2×C4×C53—44no—
316C2×C4×C53C22×D414yes—
317C22⋊D53—232no—
318C2×Dic53—28no—
319C2×Dic53—28no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
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—44no—
340C2×Dic53—44no—
341C2×Dic53—44no—
342C2×Dic53—44no—
343C2×Dic53—44no—
344C2×Dic53C22×D414yes—
345C2×Dic53C2×#4114yes—
346C4×D53—416no—
347Dic106—416no—
348C2×#2638—531nomaximal, Sylow
349C22×C53—24no—
350C22×C53—24no—
351C22×C53—24no—
352C22×C53—416no—
353C22×C53—42no—
354C22×C53—42no—
355C22×C53—42no—
356C22×C53—42no—
357C22×C53#52514yes—
358C22×C53#53414yes—
359C22×C53#53614yes—
360C22×C53#53914yes—
361C22×C53#53914yes—
362C22×C53#54214yes—
363C22×C53#54214yes—
364C22×C53C23×D411yescharacteristic
365C22×C53C22×#4111yescharacteristic
366C22×C53C22×#4111yescharacteristic
367C22×C53C2×H(5,𝔽2)11yescharacteristic
368C22×C53C2×H(5,𝔽2)11yescharacteristic
369C22×C53C2×2−1+411yescharacteristic
370C22×C53C2×2−1+411yescharacteristic
371C2×D53—24no—
372C2×D53—24no—
373C2×D53—24no—
374C2×D53—416no—
375C2×D53—42no—
376C2×D53—42no—
377C2×D53—42no—
378C2×D53—42no—
379C4×C53—24no—
380C4×C53—42no—
381C4×C53—42no—
382C4×C53—42no—
383C4×C53—42no—
384C4×C53—42no—
385Dic53—24no—
386Dic53—24no—
387Dic53—42no—
388Dic53—42no—
389Dic53—42no—
390Dic53—42no—
391Dic53—42no—
392C22×C22⋊Q8—531no—
393C22×C4×D4—531no—
394#2638—5316no—
395C2×#398—531no—
396C2×#397—531no—
397C2×#397—531no—
398C2×#397—531no—
399C2×#395—531no—
400C2×#394—531no—
401C2×#394—531no—
402C2×#393—531no—
403C2×#387—531no—
404C2×#387—531no—
405C2×#385—531no—
406C2×#385D5311yescharacteristic, complemented
407C2×#381—531no—
408C2×C53—44no—
409C2×C53#263818yescomplemented
410C2×C53C2×#52511yescharacteristic
411C2×C53C2×#53411yescharacteristic
412C2×C53C2×#53611yescharacteristic
413C2×C53C2×#53911yescharacteristic
414C2×C53C2×#53911yescharacteristic
415C2×C53C2×#54211yescharacteristic
416C2×C53C2×#54211yescharacteristic
417D53—44no—
418C23×Q8—531no—
419C23×D4—531no—
420C24×C4—531no—
421C24×C4C2×D5311yescharacteristic
422C2×C22⋊Q8—538no—
423C2×C22⋊Q8—1068no—
424C2×C4×D4—538no—
425C2×C4×D4—1068no—
426C22×C4⋊C4—531no—
427C22×C4⋊C4—531no—
428C22×C4⋊C4—531no—
429C22×C4⋊C4—531no—
430C22×C4⋊C4—531no—
431C22×C4⋊C4—531no—
432C22×C4⋊C4C2×D5311yescharacteristic
433C22×C4⋊C4C2×D5311yescharacteristic
434C22×C22⋊C4—531no—
435C22×C22⋊C4—531no—
436C22×C22⋊C4—531no—
437C22×C22⋊C4—531no—
438C22×C22⋊C4—531no—
439C22×C22⋊C4—531no—
440C22×C22⋊C4—531no—
441C22×C22⋊C4—531no—
442C22×C22⋊C4C2×D5311yescharacteristic
443C22×C22⋊C4C2×D5311yescharacteristic
444C22×C42—531no—
445#398—538no—
446#397—538no—
447#397—538no—
448#397—538no—
449#395—538no—
450#394—538no—
451#394—538no—
452#393—538no—
453#387—538no—
454#387—538no—
455#385—538no—
456#385C2×D5318yescomplemented
457#381—538no—
458C2×#95—531no—
459C2×#95—531no—
460C2×#95—531no—
461C2×#95—531no—
462C2×#95—531no—
463C2×#95—531no—
464C2×#95—531no—
465C2×#95—531no—
466C2×#95—531no—
467C2×#95—531no—
468C2×#95C2×D5311yescharacteristic
469C2×#95C2×D5311yescharacteristic
470C53C2×#263811yescharacteristic, complemented, Sylow
471C25—531no—
472C25C22×D5311yescharacteristic
473C22×Q8—534no—
474C22×Q8—1064no—
475C22×Q8—2122no—
476C22×Q8—2122no—
477C22×D4—534no—
478C22×D4—1064no—
479C22×D4—1064no—
480C22×D4—1064no—
481C23×C4—24no—
482C23×C4—42no—
483C23×C4—42no—
484C23×C4—531no—
485C23×C4—531no—
486C23×C4—538no—
487C23×C4—534no—
488C23×C4—531no—
489C23×C4—531no—
490C23×C4—531no—
491C23×C4—531no—
492C23×C4—531no—
493C23×C4—2122no—
494C23×C4—2122no—
495C23×C4C22×D5311yescharacteristic
496C23×C4C22×D5311yescharacteristic
497C23×C4C22×D5311yescharacteristic
498C23×C4C22×D5311yescharacteristic
499C23×C4C22×D5311yescharacteristic
500C23×C4C22×D5311yescharacteristic
501C23×C4C22×D5314yes—
502C22⋊Q8—10632no—
503C4×D4—10632no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—42no—
506C2×C4⋊C4—534no—
507C2×C4⋊C4—534no—
508C2×C4⋊C4—534no—
509C2×C4⋊C4—534no—
510C2×C4⋊C4—534no—
511C2×C4⋊C4—534no—
512C2×C4⋊C4—1064no—
513C2×C4⋊C4—1064no—
514C2×C4⋊C4—1064no—
515C2×C4⋊C4—1064no—
516C2×C4⋊C4—1064no—
517C2×C4⋊C4—2122no—
518C2×C4⋊C4C22×D5314yes—
519C2×C4⋊C4C22×D5314yes—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—534no—
523C2×C22⋊C4—534no—
524C2×C22⋊C4—534no—
525C2×C22⋊C4—534no—
526C2×C22⋊C4—534no—
527C2×C22⋊C4—534no—
528C2×C22⋊C4—534no—
529C2×C22⋊C4—534no—
530C2×C22⋊C4—1064no—
531C2×C22⋊C4—1064no—
532C2×C22⋊C4—1064no—
533C2×C22⋊C4—1064no—
534C2×C22⋊C4—1064no—
535C2×C22⋊C4—2122no—
536C2×C22⋊C4—2122no—
537C2×C22⋊C4—2122no—
538C2×C22⋊C4C22×D5314yes—
539C2×C22⋊C4C22×D5314yes—
540C2×C42—534no—
541C2×C42—1064no—
542#95—534no—
543#95—534no—
544#95—534no—
545#95—534no—
546#95—534no—
547#95—534no—
548#95—534no—
549#95—534no—
550#95—534no—
551#95—534no—
552#95C22×D5314yes—
553#95C22×D5314yes—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—534no—
561C24—532no—
562C24—1062no—
563C24—1062no—
564C24—1062no—
565C24—1062no—
566C24—1062no—
567C24—1062no—
568C24#1171994514yes—
569C24C23×D5312yes—
570C24C23×D5311yescharacteristic
571C2×Q8—1068no—
572C2×Q8—2124no—
573C2×Q8—2124no—
574C2×Q8—21216no—
575C2×D4—1068no—
576C2×D4—1068no—
577C2×D4—10632no—
578C2×D4—1068no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
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—28no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—416no—
600C22×C4—534no—
601C22×C4—534no—
602C22×C4—532no—
603C22×C4—532no—
604C22×C4—5316no—
605C22×C4—532no—
606C22×C4—532no—
607C22×C4—532no—
608C22×C4—532no—
609C22×C4—532no—
610C22×C4—1062no—
611C22×C4—1062no—
612C22×C4—1062no—
613C22×C4—1062no—
614C22×C4—1062no—
615C22×C4—1062no—
616C22×C4—1062no—
617C22×C4—1062no—
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—21216no—
630C22×C4—2124no—
631C22×C4—2124no—
632C22×C4D4×D5314yes—
633C22×C4C23×D5312yes—
634C22×C4C23×D5312yes—
635C22×C4C23×D5312yes—
636C22×C4C23×D5312yes—
637C22×C4C23×D5312yes—
638C22×C4C23×D5312yes—
639C4⋊C4—28no—
640C4⋊C4—44no—
641C4⋊C4—1068no—
642C4⋊C4—1068no—
643C4⋊C4—1068no—
644C4⋊C4—1068no—
645C4⋊C4—1068no—
646C4⋊C4—2124no—
647C22⋊C4—28no—
648C22⋊C4—44no—
649C22⋊C4—1068no—
650C22⋊C4—1068no—
651C22⋊C4—1068no—
652C22⋊C4—1068no—
653C22⋊C4—1068no—
654C22⋊C4—2124no—
655C22⋊C4—2124no—
656C22⋊C4—2124no—
657C42—1068no—
658C23—28no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—28no—
666C23—28no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—534no—
672C23—1068no—
673C23—1068no—
674C23—1062no—
675C23—1062no—
676C23—1068no—
677C23—1062no—
678C23—1062no—
679C23—1062no—
680C23—1062no—
681C23—2124no—
682C23—2124no—
683C23—2124no—
684C23—2124no—
685C23C2×D4×D5312yes—
686C23#41×D5312yes—
687C23C2×#1171994514yes—
688C23C2×#1171994512yes—
689C23#1313326212yes—
690C23#1313326212yes—
691C23#1313326412yes—
692C23#1313326512yes—
693C23C24×D5311yescharacteristic
694Q8—21216no—
695D4—10632no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—416no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—534no—
721C2×C4—534no—
722C2×C4—1068no—
723C2×C4—1068no—
724C2×C4—1062no—
725C2×C4—1062no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—1062no—
738C2×C4—1062no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—1062no—
742C2×C4—1062no—
743C2×C4—21216no—
744C2×C4—2124no—
745C2×C4—2124no—
746C2×C4—2124no—
747C2×C4—2124no—
748C2×C4—2124no—
749C2×C4C2×D4×D5314yes—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—42no—
754C22—42no—
755C22—416no—
756C22—42no—
757C22—42no—
758C22—1064no—
759C22—1064no—
760C22—1064no—
761C22—21216no—
762C22—2122no—
763C22—2122no—
764C22—2122no—
765C22—2122no—
766C22#1681113214yes—
767C22#1681118314yes—
768C22#1681119614yes—
769C22#1681121514yes—
770C22#1681122014yes—
771C22#1681124114yes—
772C22#1681124314yes—
773C22C22×D4×D5311yescharacteristic
774C22C2×#41×D5311yescharacteristic
775C22C22×#1171994511yescharacteristic
776C22C2×#1313326211yescharacteristic
777C22C2×#1313326211yescharacteristic
778C22C2×#1313326411yescharacteristic
779C22C2×#1313326511yescharacteristic
780C4—24no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—1064no—
787C4—1064no—
788C4—2122no—
789C4—2122no—
790C4—2122no—
791C4—2122no—
792C4—2122no—
793C2—44no—
794C2—2124no—
795C2#2028063618yesdirect product factor
796C2C2×#1681113211yescharacteristic
797C2C2×#1681118311yescharacteristic
798C2C2×#1681119611yescharacteristic
799C2C2×#1681121511yescharacteristic
800C2C2×#1681122011yescharacteristic
801C2C2×#1681124111yescharacteristic
802C2C2×#1681124311yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#385C2
socleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC2×#385D53
hypocenterC53C2×#2638
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#13133195C2semidirect
3. #20280636C2direct (N × H)
4. C2×#16810557C2semidirect
5. C2×#16810552C2semidirect
6. C2×#16810551C2semidirect
7. C2×#16810549C2semidirect
8. C2×#16810543C2semidirect
11. C2×#16810535C2semidirect
12. C2×#16810508C2semidirect
13. C2×#16810504C2semidirect
14. C2×#16810496C2semidirect
15. C2×#16810485C2semidirect
16. C2×C53×#385C2semidirect
21. C2×#13133195C22semidirect
39. #16810557C22semidirect
40. #16810552C22semidirect
41. #16810551C22semidirect
42. #16810549C22semidirect
43. #16810543C22semidirect
46. #16810535C22semidirect
47. #16810508C22semidirect
48. #16810504C22semidirect
49. #16810496C22semidirect
50. #16810485C22semidirect
66. C53×#385C22semidirect
406. C2×#385D53semidirect
409. C2×C53#2638semidirect
456. #385C2×D53semidirect
470. C53C2×#2638semidirect
795. C2#20280636direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131331952
C22×C4×C22⋊D532
#202806362
C2×#168105572
C2×#168105522
C2×#168105512
C2×#168105492
C2×#168105432
C2×#168105392
C2×#168105382
C2×#168105352
C2×#168105082
C2×#168105042
C2×#168104962
C2×#168104852
C2×C53×#3852
C2×#263853