Finite Group Databasebeta

← C2×#20280130 #27554375

Subgroups — C2×#20280130 #27554375

Order 13568.

2270 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20280130C2116yesmaximal, direct product factor
2C2×#16810565C211yesmaximal, characteristic, complemented
3C2×#16810557C211yesmaximal, characteristic, complemented
4C2×#16810546C211yesmaximal, characteristic
5C2×#16810546C211yesmaximal, characteristic
6C2×#16810521C211yesmaximal, characteristic, complemented
7C2×#16810521C211yesmaximal, characteristic, complemented
8C2×#16810520C211yesmaximal, characteristic, complemented
9C2×#16810516C211yesmaximal, characteristic
10C2×#16810516C211yesmaximal, characteristic
11C2×#16810510C211yesmaximal, characteristic, complemented
12C2×#16810507C211yesmaximal, characteristic, complemented
13C2×#16810496C211yesmaximal, characteristic
14C2×#16810496C211yesmaximal, characteristic
15C2×C4×#11719919C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C53C211yesmaximal, characteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×#11719919C2211yescharacteristic
29C22×C22⋊Dic53C2211yescharacteristic
30C22×C22⋊Dic53C2211yescharacteristic
31C22×C22⋊Dic53C2211yescharacteristic
32C22×C22⋊Dic53C2211yescharacteristic
33C22×C4×Dic53C2211yescharacteristic
34C22×C4×Dic53C2211yescharacteristic
35#16810565C2218yescomplemented
36#16810557C2218yescomplemented
37#16810546C2218yes—
38#16810546C2218yes—
39#16810521C2218yescomplemented
40#16810521C2218yescomplemented
41#16810520C2218yescomplemented
42#16810516C2218yes—
43#16810516C2218yes—
44#16810510C2218yescomplemented
45#16810507C2218yescomplemented
46#16810496C2218yes—
47#16810496C2218yes—
48C4×#11719919C2218yescomplemented
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C24×C4×C53C2211yescharacteristic
60C22×C22⋊C4×C53C2211yescharacteristic
61C22×C22⋊C4×C53C2211yescharacteristic
62C22×C42×C53C2211yescharacteristic
63C22×C42×C53C2211yescharacteristic
64C4×C22⋊C4×C53C2218yes—
65C2×#95×C53C2211yescharacteristic
66C2×#95×C53C2211yescharacteristic
67C23×Dic53C2311yescharacteristic
68C23×Dic53C2311yescharacteristic
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C2×C4⋊Dic53—24no—
76C2×C4⋊Dic53—24no—
77C2×C4⋊Dic53—42no—
78C2×C4⋊Dic53—42no—
79C2×C4⋊Dic53C2314yes—
80C2×C4⋊Dic53C2314yes—
81C2×C4⋊Dic53C2314yes—
82C2×C4⋊Dic53C2314yes—
83C2×#11719919—24no—
84C2×#11719919—24no—
85C2×#11719919—24no—
86C2×#11719919—24no—
87C2×#11719919—24no—
88C2×#11719919—42no—
89C2×#11719919—42no—
90C2×#11719919—42no—
91C2×#11719919C2314yes—
92C2×#11719919C2314yes—
93C2×#11719919C2314yes—
94C2×#11719919C2314yes—
95C2×#11719919C2314yes—
96C2×#11719919C2314yes—
97C2×#11719919C2314yes—
98C2×#11719919C2314yes—
99C2×C22⋊Dic53—24no—
100C2×C22⋊Dic53—24no—
101C2×C22⋊Dic53—42no—
102C2×C22⋊Dic53—42no—
103C2×C22⋊Dic53C2314yes—
104C2×C22⋊Dic53C2314yes—
105C2×C22⋊Dic53C2314yes—
106C2×C22⋊Dic53C2314yes—
107C2×C4×Dic53—24no—
108C2×C4×Dic53—42no—
109C2×C4×Dic53C2314yes—
110C2×C4×Dic53C2314yes—
111#13133124C2314yes—
112#13133124C2314yes—
113#13133124C2314yes—
114#13133124C2314yes—
115#13133124C2314yes—
116#13133124C2314yes—
117#13133124C2314yes—
118#13133124C2314yes—
119#13133124C2314yes—
120#13133124C2314yes—
121C25×C53C2311yescharacteristic
122C23×C4×C53—24no—
123C23×C4×C53—42no—
124C23×C4×C53—42no—
125C23×C4×C53C2311yescharacteristic
126C23×C4×C53C2311yescharacteristic
127C23×C4×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C23×C4×C53C2311yescharacteristic
131C23×C4×C53C2314yes—
132C2×C22⋊C4×C53—24no—
133C2×C22⋊C4×C53Q818yes—
134C2×C22⋊C4×C53C2314yes—
135C2×C22⋊C4×C53C2314yes—
136C2×C42×C53—42no—
137C2×C42×C53—42no—
138C2×C42×C53C2314yes—
139C2×C42×C53C2314yes—
140#95×C53C2314yes—
141#95×C53C2314yes—
142C24×C53—22no—
143C24×C53—22no—
144C24×C53—22no—
145C24×C53—22no—
146C24×C53—22no—
147C24×C53—22no—
148C24×C53C2×Q814yes—
149C24×C53C2412yes—
150C24×C53C2411yescharacteristic
151C22×C4×C53—22no—
152C22×C4×C53—22no—
153C22×C4×C53—22no—
154C22×C4×C53—22no—
155C22×C4×C53—22no—
156C22×C4×C53—22no—
157C22×C4×C53—22no—
158C22×C4×C53—22no—
159C22×C4×C53—22no—
160C22×C4×C53—22no—
161C22×C4×C53—22no—
162C22×C4×C53—22no—
163C22×C4×C53—22no—
164C22×C4×C53—22no—
165C22×C4×C53—28no—
166C22×C4×C53—44no—
167C22×C4×C53—44no—
168C22×C4×C53—416no—
169C22×C4×C53C2×Q814yes—
170C22×C4×C53C2×Q814yes—
171C22×C4×C53#4114yes—
172C22×C4×C53#4114yes—
173C22×C4×C53C2412yes—
174C22×C4×C53C2412yes—
175C22×C4×C53C2412yes—
176C22×C4×C53C2412yes—
177C22×C4×C53C2412yes—
178C22×C4×C53C2412yes—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—22no—
196C22×Dic53—22no—
197C22×Dic53—22no—
198C22×Dic53—22no—
199C22×Dic53—22no—
200C22×Dic53—22no—
201C22×Dic53#4114yes—
202C22×Dic53#4114yes—
203C22×Dic53C2412yes—
204C22×Dic53C2412yes—
205C22×Dic53C2412yes—
206C22×Dic53C2412yes—
207C22×Dic53C2412yes—
208C22×Dic53C2412yes—
209C22×Dic53C2412yes—
210C22×Dic53C2412yes—
211C22⋊C4×C53—28no—
212C22⋊C4×C53C2×Q8116yes—
213C42×C53—44no—
214C42×C53—44no—
215C22⋊Dic53—28no—
216C22⋊Dic53—28no—
217C22⋊Dic53—44no—
218C22⋊Dic53—44no—
219C4⋊Dic53—28no—
220C4⋊Dic53—28no—
221C4⋊Dic53—44no—
222C4⋊Dic53—44no—
223#11719919—28no—
224#11719919—28no—
225#11719919—28no—
226#11719919—28no—
227#11719919—28no—
228#11719919—44no—
229#11719919—44no—
230#11719919—44no—
231C4×Dic53—28no—
232C4×Dic53—44no—
233C23×C53—28no—
234C23×C53—28no—
235C23×C53—28no—
236C23×C53—22no—
237C23×C53—22no—
238C23×C53—22no—
239C23×C53—22no—
240C23×C53—22no—
241C23×C53—22no—
242C23×C53—44no—
243C23×C53—44no—
244C23×C53—44no—
245C23×C53—44no—
246C23×C53C22×Q814yes—
247C23×C53C22×Q812yes—
248C23×C53C2×#4112yes—
249C23×C53C2×#4112yes—
250C23×C53C2×#4112yes—
251C23×C53C2×#4112yes—
252C23×C53H(5,𝔽2)12yes—
253C23×C53H(5,𝔽2)12yes—
254C23×C53C2511yescharacteristic
255C2×C4×C53—28no—
256C2×C4×C53—28no—
257C2×C4×C53—28no—
258C2×C4×C53—28no—
259C2×C4×C53—22no—
260C2×C4×C53—22no—
261C2×C4×C53—22no—
262C2×C4×C53—22no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—416no—
274C2×C4×C53—44no—
275C2×C4×C53—44no—
276C2×C4×C53C22×Q814yes—
277C2×C4×C53C22×Q814yes—
278C2×C4×C53C2×#4114yes—
279C2×C4×C53C2×#4114yes—
280C2×Dic53—28no—
281C2×Dic53—28no—
282C2×Dic53—22no—
283C2×Dic53—22no—
284C2×Dic53—22no—
285C2×Dic53—22no—
286C2×Dic53—22no—
287C2×Dic53—22no—
288C2×Dic53—22no—
289C2×Dic53—22no—
290C2×Dic53—22no—
291C2×Dic53—22no—
292C2×Dic53—22no—
293C2×Dic53—22no—
294C2×Dic53—22no—
295C2×Dic53—22no—
296C2×Dic53—22no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—44no—
305C2×Dic53—44no—
306C2×Dic53—44no—
307C2×Dic53—44no—
308C2×Dic53—44no—
309C2×Dic53—44no—
310C2×Dic53C2×#4114yes—
311C2×Dic53C2×#4114yes—
312C2×#2587—531nomaximal, Sylow
313C22×C53—24no—
314C22×C53—24no—
315C22×C53—24no—
316C22×C53—416no—
317C22×C53—42no—
318C22×C53—42no—
319C22×C53—42no—
320C22×C53—42no—
321C22×C53#52914yes—
322C22×C53#53314yes—
323C22×C53#53814yes—
324C22×C53#55314yes—
325C22×C53#55314yes—
326C22×C53#55414yes—
327C22×C53#55414yes—
328C22×C53C23×Q811yescharacteristic
329C22×C53C22×#4111yescharacteristic
330C22×C53C22×#4111yescharacteristic
331C22×C53C22×#4111yescharacteristic
332C22×C53C22×#4111yescharacteristic
333C22×C53C2×H(5,𝔽2)11yescharacteristic
334C22×C53C2×H(5,𝔽2)11yescharacteristic
335C4×C53—24no—
336C4×C53—24no—
337C4×C53—24no—
338C4×C53—24no—
339C4×C53—42no—
340C4×C53—42no—
341Dic53—24no—
342Dic53—24no—
343Dic53—42no—
344Dic53—42no—
345Dic53—42no—
346Dic53—42no—
347Dic53—42no—
348Dic53—42no—
349#2587—5316no—
350C2×#400—531no—
351C2×#398—531no—
352C2×#396—531no—
353C2×#396—531no—
354C2×#389—531no—
355C2×#389—531no—
356C2×#389—531no—
357C2×#388—531no—
358C2×#388—531no—
359C2×#387—531no—
360C2×#387—531no—
361C2×#385—531no—
362C2×#385—531no—
363C2×C4×C4⋊C4—531no—
364C2×C4×C22⋊C4D5311yescharacteristic
365C2×C53—44no—
366C2×C53#258718yescomplemented
367C2×C53C2×#52911yescharacteristic
368C2×C53C2×#53311yescharacteristic
369C2×C53C2×#53811yescharacteristic
370C2×C53C2×#55311yescharacteristic
371C2×C53C2×#55311yescharacteristic
372C2×C53C2×#55411yescharacteristic
373C2×C53C2×#55411yescharacteristic
374C24×C4C2×D5311yescharacteristic
375C22×C4⋊C4—531no—
376C22×C4⋊C4—531no—
377C22×C4⋊C4—531no—
378C22×C4⋊C4—531no—
379C22×C4⋊C4—531no—
380C22×C4⋊C4—531no—
381C22×C4⋊C4—531no—
382C22×C4⋊C4—531no—
383C22×C4⋊C4—531no—
384C22×C4⋊C4—531no—
385C22×C4⋊C4—531no—
386C22×C4⋊C4—531no—
387C22×C22⋊C4—531no—
388C22×C22⋊C4—531no—
389C22×C22⋊C4—531no—
390C22×C22⋊C4—531no—
391C22×C22⋊C4C2×D5311yescharacteristic
392C22×C22⋊C4C2×D5311yescharacteristic
393C22×C42—531no—
394C22×C42—531no—
395C22×C42C2×D5311yescharacteristic
396C22×C42C2×D5311yescharacteristic
397#400—538no—
398#398—538no—
399#396—538no—
400#396—538no—
401#389—538no—
402#389—538no—
403#389—538no—
404#388—538no—
405#388—538no—
406#387—538no—
407#387—538no—
408#385—538no—
409#385—538no—
410C4×C4⋊C4—538no—
411C4×C22⋊C4C2×D5318yes—
412C2×#95—531no—
413C2×#95—531no—
414C2×#95—531no—
415C2×#95—531no—
416C2×#95—531no—
417C2×#95—531no—
418C2×#95—531no—
419C2×#95—531no—
420C2×#95—531no—
421C2×#95—531no—
422C2×#95C2×D5311yescharacteristic
423C2×#95C2×D5311yescharacteristic
424C53C2×#258711yescharacteristic, complemented, Sylow
425C25C22×D5311yescharacteristic
426C23×C4—24no—
427C23×C4—42no—
428C23×C4—42no—
429C23×C4—531no—
430C23×C4—531no—
431C23×C4—531no—
432C23×C4—531no—
433C23×C4—531no—
434C23×C4—531no—
435C23×C4—531no—
436C23×C4—531no—
437C23×C4C22×D5311yescharacteristic
438C23×C4C22×D5311yescharacteristic
439C23×C4C22×D5311yescharacteristic
440C23×C4C22×D5311yescharacteristic
441C23×C4C22×D5311yescharacteristic
442C23×C4C22×D5311yescharacteristic
443C23×C4C22×D5314yes—
444C2×C4⋊C4—534no—
445C2×C4⋊C4—534no—
446C2×C4⋊C4—534no—
447C2×C4⋊C4—534no—
448C2×C4⋊C4—534no—
449C2×C4⋊C4—534no—
450C2×C4⋊C4—534no—
451C2×C4⋊C4—534no—
452C2×C4⋊C4—534no—
453C2×C4⋊C4—534no—
454C2×C4⋊C4—534no—
455C2×C4⋊C4—534no—
456C2×C4⋊C4—1064no—
457C2×C4⋊C4—1064no—
458C2×C4⋊C4—1064no—
459C2×C4⋊C4—1064no—
460C2×C4⋊C4—1064no—
461C2×C4⋊C4—1064no—
462C2×C4⋊C4—1064no—
463C2×C4⋊C4—2122no—
464C2×C4⋊C4—2122no—
465C2×C4⋊C4—2122no—
466C2×C4⋊C4—2122no—
467C2×C4⋊C4—2122no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—534no—
470C2×C22⋊C4—534no—
471C2×C22⋊C4—534no—
472C2×C22⋊C4—534no—
473C2×C22⋊C4—1064no—
474C2×C22⋊C4—1064no—
475C2×C22⋊C4—2122no—
476C2×C22⋊C4—2122no—
477C2×C22⋊C4Dic10618yes—
478C2×C22⋊C4C22×D5314yes—
479C2×C22⋊C4C22×D5314yes—
480C2×C42—42no—
481C2×C42—42no—
482C2×C42—534no—
483C2×C42—534no—
484C2×C42—1064no—
485C2×C42—2122no—
486C2×C42C22×D5314yes—
487C2×C42C22×D5314yes—
488#95—534no—
489#95—534no—
490#95—534no—
491#95—534no—
492#95—534no—
493#95—534no—
494#95—534no—
495#95—534no—
496#95—534no—
497#95—534no—
498#95C22×D5314yes—
499#95C22×D5314yes—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24C2×Dic10614yes—
507C24C23×D5312yes—
508C24C23×D5311yescharacteristic
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—28no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—416no—
527C22×C4—534no—
528C22×C4—534no—
529C22×C4—532no—
530C22×C4—532no—
531C22×C4—532no—
532C22×C4—532no—
533C22×C4—532no—
534C22×C4—532no—
535C22×C4—532no—
536C22×C4—532no—
537C22×C4—1062no—
538C22×C4—1062no—
539C22×C4—1062no—
540C22×C4—1062no—
541C22×C4—1062no—
542C22×C4—1062no—
543C22×C4—1062no—
544C22×C4—1062no—
545C22×C4—1062no—
546C22×C4—1062no—
547C22×C4—1062no—
548C22×C4—1062no—
549C22×C4—1062no—
550C22×C4—1062no—
551C22×C4—1062no—
552C22×C4—1062no—
553C22×C4—1062no—
554C22×C4—1062no—
555C22×C4—1062no—
556C22×C4—1062no—
557C22×C4—1062no—
558C22×C4—1062no—
559C22×C4C2×Dic10614yes—
560C22×C4C2×Dic10614yes—
561C22×C4#1171994514yes—
562C22×C4#1171994514yes—
563C22×C4C23×D5312yes—
564C22×C4C23×D5312yes—
565C22×C4C23×D5312yes—
566C22×C4C23×D5312yes—
567C22×C4C23×D5312yes—
568C22×C4C23×D5312yes—
569C4⋊C4—1068no—
570C4⋊C4—1068no—
571C4⋊C4—1068no—
572C4⋊C4—1068no—
573C4⋊C4—1068no—
574C4⋊C4—1068no—
575C4⋊C4—1068no—
576C4⋊C4—2124no—
577C4⋊C4—2124no—
578C4⋊C4—2124no—
579C4⋊C4—2124no—
580C4⋊C4—2124no—
581C22⋊C4—28no—
582C22⋊C4—1068no—
583C22⋊C4—1068no—
584C22⋊C4—2124no—
585C22⋊C4—2124no—
586C22⋊C4C2×Dic106116yes—
587C42—44no—
588C42—44no—
589C42—1068no—
590C42—2124no—
591C23—28no—
592C23—28no—
593C23—28no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—44no—
601C23—44no—
602C23—44no—
603C23—44no—
604C23C22×Dic10614yes—
605C23C22×Dic10612yes—
606C23#41×D5312yes—
607C23#41×D5312yes—
608C23C2×#1171994512yes—
609C23C2×#1171994512yes—
610C23#1313326212yes—
611C23#1313326212yes—
612C23C24×D5311yescharacteristic
613C2×C4—28no—
614C2×C4—28no—
615C2×C4—28no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—28no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—416no—
632C2×C4—44no—
633C2×C4—44no—
634C2×C4—534no—
635C2×C4—534no—
636C2×C4—1068no—
637C2×C4—1068no—
638C2×C4—1062no—
639C2×C4—1062no—
640C2×C4—1062no—
641C2×C4—1062no—
642C2×C4—1062no—
643C2×C4—1062no—
644C2×C4—1062no—
645C2×C4—1062no—
646C2×C4—1062no—
647C2×C4—1062no—
648C2×C4—1062no—
649C2×C4—1062no—
650C2×C4—1062no—
651C2×C4—1062no—
652C2×C4—1062no—
653C2×C4—1062no—
654C2×C4—1062no—
655C2×C4—1062no—
656C2×C4—1062no—
657C2×C4—1062no—
658C2×C4—1062no—
659C2×C4—1062no—
660C2×C4—2124no—
661C2×C4—2124no—
662C2×C4—2124no—
663C2×C4—2124no—
664C2×C4—2124no—
665C2×C4—2124no—
666C2×C4C22×Dic10614yes—
667C2×C4C22×Dic10614yes—
668C2×C4C2×#1171994514yes—
669C2×C4C2×#1171994514yes—
670C22—24no—
671C22—24no—
672C22—24no—
673C22—42no—
674C22—416no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22#1681115114yes—
679C22#1681118014yes—
680C22#1681121114yes—
681C22#1681132214yes—
682C22#1681132314yes—
683C22#1681133214yes—
684C22#1681133214yes—
685C22C23×Dic10611yescharacteristic
686C22C2×#41×D5311yescharacteristic
687C22C2×#41×D5311yescharacteristic
688C22C22×#1171994511yescharacteristic
689C22C22×#1171994511yescharacteristic
690C22C2×#1313326211yescharacteristic
691C22C2×#1313326211yescharacteristic
692C4—24no—
693C4—24no—
694C4—24no—
695C4—24no—
696C4—42no—
697C4—42no—
698C4—1064no—
699C4—1064no—
700C4—2122no—
701C4—2122no—
702C4—2122no—
703C4—2122no—
704C4—2122no—
705C4—2122no—
706C2—44no—
707C2#2028013018yesdirect product factor
708C2C2×#1681115111yescharacteristic
709C2C2×#1681118011yescharacteristic
710C2C2×#1681121111yescharacteristic
711C2C2×#1681132211yescharacteristic
712C2C2×#1681132311yescharacteristic
713C2C2×#1681133211yescharacteristic
714C2C2×#1681133211yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C4×C22⋊C4×C53C2
socleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×C4×C22⋊C4D53
hypocenterC53C2×#2587
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #20280130C2direct (N × H)
2. C2×#16810565C2semidirect
3. C2×#16810557C2semidirect
6. C2×#16810521C2semidirect
7. C2×#16810521C2semidirect
8. C2×#16810520C2semidirect
11. C2×#16810510C2semidirect
12. C2×#16810507C2semidirect
15. C2×C4×#11719919C2semidirect
35. #16810565C22semidirect
36. #16810557C22semidirect
39. #16810521C22semidirect
40. #16810521C22semidirect
41. #16810520C22semidirect
44. #16810510C22semidirect
45. #16810507C22semidirect
48. C4×#11719919C22semidirect
366. C2×C53#2587semidirect
424. C53C2×#2587semidirect
707. C2#20280130direct (N × H)

Maximal subgroups

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

subgroupindex
#202801302
C2×#168105652
C2×#168105572
C2×#168105462
C2×#168105212
C2×#168105202
C2×#168105162
C2×#168105102
C2×#168105072
C2×#168104962
C2×C4×#117199192
C2×C4×C22⋊C4×C532
C2×#258753