Finite Group Databasebeta

← C2×#20282788 #27590625

Subgroups — C2×#20282788 #27590625

Order 13568.

2502 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133212C211yesmaximal, characteristic, complemented
2C22×#13133210C211yesmaximal, characteristic, complemented
3#20282788C2116yesmaximal, direct product factor
4C2×#16810556C211yesmaximal, characteristic, complemented
5C2×#16810555C211yesmaximal, characteristic, complemented
6C2×#16810554C211yesmaximal, characteristic, complemented
7C2×#16810547C211yesmaximal, characteristic, complemented
8C2×#16810546C211yesmaximal, characteristic, complemented
9C2×#16810546C211yesmaximal, characteristic, complemented
10C2×#16810545C211yesmaximal, characteristic, complemented
11C2×#16810545C211yesmaximal, characteristic, complemented
12C2×#16810539C211yesmaximal, characteristic
13C2×#16810538C211yesmaximal, characteristic
14C2×#16810538C211yesmaximal, characteristic
15C2×#16810492C211yesmaximal, characteristic, complemented
16C2×C53×#396C211yesmaximal, characteristic, complemented
17C23×C22⋊D53C2211yescharacteristic
18C2×#13133212—28no—
19C2×#13133212C2218yescomplemented
20C2×#13133210—28no—
21C2×#13133210C2218yescomplemented
22C22×C4⋊Dic53C2211yescharacteristic
23C22×C4⋊Dic53C2211yescharacteristic
24C22×C4⋊Dic53C2211yescharacteristic
25C22×C4⋊Dic53C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×#11719919C2211yescharacteristic
29C22×#11719919C2211yescharacteristic
30C22×#11719919C2211yescharacteristic
31C22×#11719919C2211yescharacteristic
32C22×#11719919C2211yescharacteristic
33C22×#11719919C2211yescharacteristic
34C22×C22⋊Dic53C2211yescharacteristic
35C22×C22⋊Dic53C2211yescharacteristic
36C22×C22⋊Dic53C2211yescharacteristic
37C22×#11719921C2211yescharacteristic
38C22×#11719921C2211yescharacteristic
39C22×#11719921C2211yescharacteristic
40C22×#11719921C2211yescharacteristic
41C22×#11719921C2211yescharacteristic
42C22×#11719921C2211yescharacteristic
43C22×C4×Dic53C2211yescharacteristic
44#16810556C2218yescomplemented
45#16810555C2218yescomplemented
46#16810554C2218yescomplemented
47#16810547C2218yescomplemented
48#16810546C2218yescomplemented
49#16810546C2218yescomplemented
50#16810545C2218yescomplemented
51#16810545C2218yescomplemented
52#16810539C2218yes—
53#16810538C2218yes—
54#16810538C2218yes—
55#16810492C2218yescomplemented
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—42no—
71C22×C22⋊D53—42no—
72C22×C22⋊D53—42no—
73C22×C22⋊D53C2314yes—
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2311yescharacteristic
81#13133212—232no—
82#13133210—232no—
83C2×C4⋊Dic53—24no—
84C2×C4⋊Dic53—24no—
85C2×C4⋊Dic53—42no—
86C2×C4⋊Dic53—42no—
87C2×C4⋊Dic53C2314yes—
88C2×C4⋊Dic53C2314yes—
89C2×C4⋊Dic53C2314yes—
90C2×C4⋊Dic53C2314yes—
91C2×#11719919—24no—
92C2×#11719919—24no—
93C2×#11719919—24no—
94C2×#11719919—42no—
95C2×#11719919—42no—
96C2×#11719919—42no—
97C2×#11719919—42no—
98C2×#11719919—42no—
99C2×#11719919C2314yes—
100C2×#11719919C2314yes—
101C2×#11719919C2314yes—
102C2×#11719919C2314yes—
103C2×#11719919C2314yes—
104C2×#11719919C2314yes—
105C2×#11719919C2314yes—
106C2×#11719919C2314yes—
107C2×C22⋊Dic53—24no—
108C2×C22⋊Dic53—24no—
109C2×C22⋊Dic53—42no—
110C2×C22⋊Dic53C2314yes—
111C2×C22⋊Dic53C2314yes—
112C2×C22⋊Dic53C2314yes—
113C2×#11719921—24no—
114C2×#11719921—24no—
115C2×#11719921—24no—
116C2×#11719921—42no—
117C2×#11719921—42no—
118C2×#11719921—42no—
119C2×#11719921C2314yes—
120C2×#11719921C2314yes—
121C2×#11719921C2314yes—
122C2×#11719921C2314yes—
123C2×#11719921C2314yes—
124C2×#11719921C2314yes—
125C2×C4×Dic53D418yescomplemented
126C2×C4×Dic53C2314yes—
127#13133124C2314yes—
128#13133124C2314yes—
129#13133124C2314yes—
130#13133124C2314yes—
131#13133124C2314yes—
132C25×C53C2311yescharacteristic
133C23×C4×C53C2311yescharacteristic
134C23×C4×C53C2311yescharacteristic
135C23×C4×C53C2311yescharacteristic
136C23×C4×C53C2311yescharacteristic
137C23×C4×C53C2311yescharacteristic
138C23×C4×C53C2311yescharacteristic
139C2×C4⋊C4×C53—24no—
140C2×C4⋊C4×C53—42no—
141C2×C4⋊C4×C53—42no—
142C2×C4⋊C4×C53C2314yes—
143C2×C4⋊C4×C53C2314yes—
144C2×C4⋊C4×C53C2314yes—
145C2×C22⋊C4×C53—24no—
146C2×C22⋊C4×C53—42no—
147C2×C22⋊C4×C53—42no—
148C2×C22⋊C4×C53C2314yes—
149C2×C22⋊C4×C53C2314yes—
150C2×C22⋊C4×C53C2314yes—
151#95×C53C2314yes—
152C24×C53—22no—
153C24×C53—22no—
154C24×C53—22no—
155C24×C53—22no—
156C24×C53—22no—
157C24×C53—22no—
158C24×C53—22no—
159C24×C53C2412yes—
160C24×C53C2411yescharacteristic
161C23×D53—22no—
162C23×D53—22no—
163C23×D53—22no—
164C23×D53—22no—
165C23×D53—22no—
166C23×D53—22no—
167C23×D53—22no—
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×C53C2×D414yes—
187C22×C4×C53C2412yes—
188C22×C4×C53C2412yes—
189C22×C4×C53C2412yes—
190C22×C4×C53C2412yes—
191C22×C4×C53C2412yes—
192C22×C4×C53C2412yes—
193C2×C22⋊D53—44no—
194C2×C22⋊D53—44no—
195C2×C22⋊D53—44no—
196C2×C22⋊D53—416no—
197C22×Dic53—22no—
198C22×Dic53—22no—
199C22×Dic53—22no—
200C22×Dic53—22no—
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×Dic53C2×D414yes—
217C22×Dic53C2×D414yes—
218C22×Dic53C2412yes—
219C22×Dic53C2412yes—
220C22×Dic53C2412yes—
221C22×Dic53C2412yes—
222C22×Dic53C2412yes—
223C22×Dic53C2412yes—
224C22×Dic53C2412yes—
225C4⋊C4×C53—28no—
226C4⋊C4×C53—44no—
227C4⋊C4×C53—44no—
228C22⋊C4×C53—28no—
229C22⋊C4×C53—44no—
230C22⋊C4×C53—44no—
231C22⋊Dic53—28no—
232C22⋊Dic53—28no—
233C22⋊Dic53—44no—
234#11719921—28no—
235#11719921—28no—
236#11719921—28no—
237#11719921—44no—
238#11719921—44no—
239#11719921—44no—
240C4⋊Dic53—28no—
241C4⋊Dic53—28no—
242C4⋊Dic53—44no—
243C4⋊Dic53—44no—
244#11719919—28no—
245#11719919—28no—
246#11719919—28no—
247#11719919—44no—
248#11719919—44no—
249#11719919—44no—
250#11719919—44no—
251#11719919—44no—
252C4×Dic53C2×D4116yescomplemented
253C23×C53—22no—
254C23×C53—22no—
255C23×C53—22no—
256C23×C53—22no—
257C23×C53—22no—
258C23×C53—22no—
259C23×C53—22no—
260C23×C53—44no—
261C23×C53—44no—
262C23×C53—44no—
263C23×C53—44no—
264C23×C53—44no—
265C23×C53—44no—
266C23×C53—44no—
267C23×C53C22×D412yes—
268C23×C53H(5,𝔽2)12yes—
269C23×C53H(5,𝔽2)12yes—
270C23×C53H(5,𝔽2)12yes—
271C23×C532−1+412yes—
272C23×C532−1+412yes—
273C23×C532−1+412yes—
274C23×C53C2511yescharacteristic
275C22×D53—22no—
276C22×D53—22no—
277C22×D53—22no—
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—22no—
281C22×D53—22no—
282C22×D53—44no—
283C22×D53—44no—
284C22×D53—44no—
285C22×D53—44no—
286C22×D53—44no—
287C22×D53—44no—
288C22×D53—44no—
289C2×C4×C53—28no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
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—44no—
308C2×C4×C53—44no—
309C2×C4×C53—44no—
310C2×C4×C53—44no—
311C2×C4×C53—44no—
312C2×C4×C53C22×D414yes—
313C22⋊D53—416no—
314C2×Dic53—28no—
315C2×Dic53—28no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
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—44no—
336C2×Dic53—44no—
337C2×Dic53—44no—
338C2×Dic53—44no—
339C2×Dic53—44no—
340C2×Dic53C22×D414yes—
341C2×Dic53C22×D414yes—
342C2×#2823—531nomaximal, Sylow
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—42no—
346C22×C53—42no—
347C22×C53—42no—
348C22×C53—42no—
349C22×C53—42no—
350C22×C53—88no—
351C22×C53#53714yes—
352C22×C53#53714yes—
353C22×C53#53714yes—
354C22×C53#56014yes—
355C22×C53#56314yes—
356C22×C53#56314yes—
357C22×C53#56314yes—
358C22×C53C23×D411yescharacteristic
359C22×C53C2×H(5,𝔽2)11yescharacteristic
360C22×C53C2×H(5,𝔽2)11yescharacteristic
361C22×C53C2×H(5,𝔽2)11yescharacteristic
362C22×C53C2×2−1+411yescharacteristic
363C22×C53C2×2−1+411yescharacteristic
364C22×C53C2×2−1+411yescharacteristic
365C2×D53—42no—
366C2×D53—42no—
367C2×D53—42no—
368C2×D53—42no—
369C2×D53—42no—
370C2×D53—42no—
371C2×D53—42no—
372C2×D53—88no—
373C4×C53—24no—
374C4×C53—42no—
375C4×C53—42no—
376C4×C53—42no—
377C4×C53—42no—
378C4×C53—42no—
379Dic53—24no—
380Dic53—24no—
381Dic53—42no—
382Dic53—42no—
383Dic53—42no—
384Dic53—42no—
385Dic53—42no—
386C22×#126—531no—
387C22×#126—531no—
388#2823—5316no—
389C2×#398—531no—
390C2×#398—531no—
391C2×#398—531no—
392C2×#396—531no—
393C2×#396—531no—
394C2×#396—531no—
395C2×#396—531no—
396C2×#396—531no—
397C2×#396D5311yescharacteristic, complemented
398C2×#394—531no—
399C2×#394—531no—
400C2×#394—531no—
401C2×#384—531no—
402C2×C53—82no—
403C2×C53#282318yescomplemented
404C2×C53C2×#53711yescharacteristic
405C2×C53C2×#53711yescharacteristic
406C2×C53C2×#53711yescharacteristic
407C2×C53C2×#56011yescharacteristic
408C2×C53C2×#56311yescharacteristic
409C2×C53C2×#56311yescharacteristic
410C2×C53C2×#56311yescharacteristic
411D53—82no—
412C23×D4—531no—
413C2×#126—538no—
414C2×#126—538no—
415C2×#126—1068no—
416C2×#126—1068no—
417C22×C4⋊C4—531no—
418C22×C4⋊C4—531no—
419C22×C4⋊C4—531no—
420C22×C4⋊C4—531no—
421C22×C4⋊C4—531no—
422C22×C4⋊C4—531no—
423C22×C4⋊C4—531no—
424C22×C4⋊C4—531no—
425C22×C4⋊C4—531no—
426C22×C4⋊C4—531no—
427C22×C4⋊C4—531no—
428C22×C4⋊C4—531no—
429C22×C4⋊C4C2×D5311yescharacteristic
430C22×C4⋊C4C2×D5311yescharacteristic
431C22×C4⋊C4C2×D5311yescharacteristic
432C22×C22⋊C4—531no—
433C22×C22⋊C4—531no—
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⋊C4C2×D5311yescharacteristic
442C22×C22⋊C4C2×D5311yescharacteristic
443C22×C22⋊C4C2×D5311yescharacteristic
444C22×C42—531no—
445#398—538no—
446#398—538no—
447#398—538no—
448#396—538no—
449#396—538no—
450#396—538no—
451#396—538no—
452#396—538no—
453#396C2×D5318yescomplemented
454#394—538no—
455#394—538no—
456#394—538no—
457#384—538no—
458C2×#95—531no—
459C2×#95—531no—
460C2×#95—531no—
461C2×#95—531no—
462C2×#95—531no—
463C2×#95C2×D5311yescharacteristic
464C53C2×#282311yescharacteristic, complemented, Sylow
465C25—531no—
466C25C22×D5311yescharacteristic
467C22×D4—534no—
468C22×D4—2122no—
469C22×D4—2122no—
470C22×D4—2122no—
471C23×C4—531no—
472C23×C4—531no—
473C23×C4—531no—
474C23×C4—531no—
475C23×C4—531no—
476C23×C4—531no—
477C23×C4—531no—
478C23×C4C22×D5311yescharacteristic
479C23×C4C22×D5311yescharacteristic
480C23×C4C22×D5311yescharacteristic
481C23×C4C22×D5311yescharacteristic
482C23×C4C22×D5311yescharacteristic
483C23×C4C22×D5311yescharacteristic
484#126—10632no—
485#126—10632no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—534no—
490C2×C4⋊C4—534no—
491C2×C4⋊C4—534no—
492C2×C4⋊C4—534no—
493C2×C4⋊C4—534no—
494C2×C4⋊C4—534no—
495C2×C4⋊C4—534no—
496C2×C4⋊C4—534no—
497C2×C4⋊C4—534no—
498C2×C4⋊C4—534no—
499C2×C4⋊C4—534no—
500C2×C4⋊C4—534no—
501C2×C4⋊C4—1064no—
502C2×C4⋊C4—1064no—
503C2×C4⋊C4—1064no—
504C2×C4⋊C4—1064no—
505C2×C4⋊C4—1064no—
506C2×C4⋊C4—2122no—
507C2×C4⋊C4—2122no—
508C2×C4⋊C4—2122no—
509C2×C4⋊C4—2122no—
510C2×C4⋊C4—2122no—
511C2×C4⋊C4—2122no—
512C2×C4⋊C4—2122no—
513C2×C4⋊C4C22×D5314yes—
514C2×C4⋊C4C22×D5314yes—
515C2×C4⋊C4C22×D5314yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—534no—
520C2×C22⋊C4—534no—
521C2×C22⋊C4—534no—
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—1064no—
529C2×C22⋊C4—1064no—
530C2×C22⋊C4—1064no—
531C2×C22⋊C4—1064no—
532C2×C22⋊C4—1064no—
533C2×C22⋊C4—2122no—
534C2×C22⋊C4—2122no—
535C2×C22⋊C4—2122no—
536C2×C22⋊C4—2122no—
537C2×C22⋊C4C22×D5314yes—
538C2×C22⋊C4C22×D5314yes—
539C2×C22⋊C4C22×D5314yes—
540C2×C42—538no—
541C2×C42—534no—
542#95—534no—
543#95—534no—
544#95—534no—
545#95—534no—
546#95—534no—
547#95C22×D5314yes—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—532no—
556C24—1062no—
557C24—1062no—
558C24—1062no—
559C24—1062no—
560C24—1062no—
561C24—1062no—
562C24—1062no—
563C24C23×D5312yes—
564C24C23×D5311yescharacteristic
565C2×D4—2124no—
566C2×D4—2124no—
567C2×D4—2124no—
568C2×D4—21216no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—534no—
587C22×C4—534no—
588C22×C4—532no—
589C22×C4—532no—
590C22×C4—532no—
591C22×C4—532no—
592C22×C4—532no—
593C22×C4—532no—
594C22×C4—532no—
595C22×C4—1062no—
596C22×C4—1062no—
597C22×C4—1062no—
598C22×C4—1062no—
599C22×C4—1062no—
600C22×C4—1062no—
601C22×C4—1062no—
602C22×C4—1062no—
603C22×C4—1062no—
604C22×C4—1062no—
605C22×C4—1062no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1062no—
609C22×C4—1062no—
610C22×C4—1062no—
611C22×C4—1062no—
612C22×C4—1062no—
613C22×C4—1062no—
614C22×C4D4×D5314yes—
615C22×C4C23×D5312yes—
616C22×C4C23×D5312yes—
617C22×C4C23×D5312yes—
618C22×C4C23×D5312yes—
619C22×C4C23×D5312yes—
620C22×C4C23×D5312yes—
621C4⋊C4—28no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—1068no—
625C4⋊C4—1068no—
626C4⋊C4—1068no—
627C4⋊C4—1068no—
628C4⋊C4—1068no—
629C4⋊C4—2124no—
630C4⋊C4—2124no—
631C4⋊C4—2124no—
632C4⋊C4—2124no—
633C4⋊C4—2124no—
634C4⋊C4—2124no—
635C4⋊C4—2124no—
636C22⋊C4—28no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—1068no—
640C22⋊C4—1068no—
641C22⋊C4—1068no—
642C22⋊C4—1068no—
643C22⋊C4—1068no—
644C22⋊C4—2124no—
645C22⋊C4—2124no—
646C22⋊C4—2124no—
647C22⋊C4—2124no—
648C42—5316no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—1062no—
664C23—1062no—
665C23—1062no—
666C23—1062no—
667C23—1062no—
668C23—1062no—
669C23—1062no—
670C23—2124no—
671C23—2124no—
672C23—2124no—
673C23—2124no—
674C23—2124no—
675C23—2124no—
676C23—2124no—
677C23C2×D4×D5312yes—
678C23#1313326212yes—
679C23#1313326212yes—
680C23#1313326312yes—
681C23#1313326412yes—
682C23#1313326412yes—
683C23#1313326512yes—
684C23C24×D5311yescharacteristic
685D4—21216no—
686C2×C4—22no—
687C2×C4—28no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—534no—
710C2×C4—534no—
711C2×C4—1062no—
712C2×C4—1062no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1068no—
716C2×C4—1068no—
717C2×C4—1062no—
718C2×C4—1062no—
719C2×C4—1062no—
720C2×C4—1062no—
721C2×C4—1062no—
722C2×C4—1062no—
723C2×C4—1062no—
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—2124no—
733C2×C4—2124no—
734C2×C4—2124no—
735C2×C4—2124no—
736C2×C4—2124no—
737C2×C4C2×D4×D5314yes—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—88no—
746C22—4248no—
747C22—2122no—
748C22—2122no—
749C22—2122no—
750C22—2122no—
751C22—2122no—
752C22—2122no—
753C22—2122no—
754C22#1681120014yes—
755C22#1681120214yes—
756C22#1681120314yes—
757C22#1681136114yes—
758C22#1681137414yes—
759C22#1681137414yes—
760C22#1681137514yes—
761C22C22×D4×D5311yescharacteristic
762C22C2×#1313326211yescharacteristic
763C22C2×#1313326211yescharacteristic
764C22C2×#1313326311yescharacteristic
765C22C2×#1313326411yescharacteristic
766C22C2×#1313326411yescharacteristic
767C22C2×#1313326511yescharacteristic
768C4—24no—
769C4—42no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—1064no—
775C4—1064no—
776C4—2122no—
777C4—2122no—
778C4—2122no—
779C4—2122no—
780C4—2122no—
781C2—82no—
782C2—4242no—
783C2#2028278818yesdirect product factor
784C2C2×#1681120011yescharacteristic
785C2C2×#1681120211yescharacteristic
786C2C2×#1681120311yescharacteristic
787C2C2×#1681136111yescharacteristic
788C2C2×#1681137411yescharacteristic
789C2C2×#1681137411yescharacteristic
790C2C2×#1681137511yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#396C2
socleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC2×#396D53
hypocenterC53C2×#2823
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#13133212C2semidirect
2. C22×#13133210C2semidirect
3. #20282788C2direct (N × H)
4. C2×#16810556C2semidirect
5. C2×#16810555C2semidirect
6. C2×#16810554C2semidirect
7. C2×#16810547C2semidirect
8. C2×#16810546C2semidirect
9. C2×#16810546C2semidirect
10. C2×#16810545C2semidirect
11. C2×#16810545C2semidirect
15. C2×#16810492C2semidirect
16. C2×C53×#396C2semidirect
19. C2×#13133212C22semidirect
21. C2×#13133210C22semidirect
44. #16810556C22semidirect
45. #16810555C22semidirect
46. #16810554C22semidirect
47. #16810547C22semidirect
48. #16810546C22semidirect
49. #16810546C22semidirect
50. #16810545C22semidirect
51. #16810545C22semidirect
55. #16810492C22semidirect
67. C53×#396C22semidirect
125. C2×C4×Dic53D4semidirect
252. C4×Dic53C2×D4semidirect
397. C2×#396D53semidirect
403. C2×C53#2823semidirect
453. #396C2×D53semidirect
464. C53C2×#2823semidirect
783. C2#20282788direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332122
C22×#131332102
#202827882
C2×#168105562
C2×#168105552
C2×#168105542
C2×#168105472
C2×#168105462
C2×#168105452
C2×#168105392
C2×#168105382
C2×#168104922
C2×C53×#3962
C2×#282353