Finite Group Databasebeta

← C2×#20280289 #27554841

Subgroups — C2×#20280289 #27554841

Order 13568.

2766 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic106C211yesmaximal, characteristic, complemented
2C22×#13133173C211yesmaximal, characteristic
3#20280289C2116yesmaximal, direct product factor
4C2×#16810557C211yesmaximal, characteristic, complemented
5C2×#16810551C211yesmaximal, characteristic
6C2×#16810543C211yesmaximal, characteristic, complemented
7C2×#16810535C211yesmaximal, characteristic
8C2×#16810511C211yesmaximal, characteristic
9C2×#16810509C211yesmaximal, characteristic, complemented
10C2×#16810508C211yesmaximal, characteristic, complemented
11C2×#16810507C211yesmaximal, characteristic, complemented
12C2×#16810505C211yesmaximal, characteristic, complemented
13C2×#16810498C211yesmaximal, characteristic
14C2×#16810495C211yesmaximal, characteristic
15C2×#16810490C211yesmaximal, characteristic, complemented
16C2×C53×#388C211yesmaximal, characteristic
17C23×Dic106C2211yescharacteristic
18C24×Dic53C2211yescharacteristic
19C2×C4×Dic106—28no—
20C2×C4×Dic106C2218yescomplemented
21C2×#13133173—28no—
22C2×#13133173C2218yes—
23C22×C4⋊Dic53C2211yescharacteristic
24C22×C4⋊Dic53C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×#11719919C2211yescharacteristic
29C22×#11719919C2211yescharacteristic
30C22×#11719919C2211yescharacteristic
31C22×C22⋊Dic53C2211yescharacteristic
32C22×C22⋊Dic53C2211yescharacteristic
33C22×C22⋊Dic53C2211yescharacteristic
34C22×C4×Dic53C2211yescharacteristic
35C22×C4×Dic53C2211yescharacteristic
36C22×C4×Dic53C2211yescharacteristic
37#16810557C2218yescomplemented
38#16810551C2218yes—
39#16810543C2218yescomplemented
40#16810535C2218yes—
41#16810511C2218yes—
42#16810509C2218yescomplemented
43#16810508C2218yescomplemented
44#16810507C2218yescomplemented
45#16810505C2218yescomplemented
46#16810498C2218yes—
47#16810495C2218yes—
48#16810490C2218yescomplemented
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60C2×#13133124C2211yescharacteristic
61C22×C4⋊C4×C53C2211yescharacteristic
62C22×C22⋊C4×C53C2211yescharacteristic
63C22×C22⋊C4×C53C2211yescharacteristic
64C22×C22⋊C4×C53C2211yescharacteristic
65C22×C42×C53C2211yescharacteristic
66C53×#388C2218yes—
67C2×#95×C53C2211yescharacteristic
68C2×#95×C53C2211yescharacteristic
69C22×Dic106—24no—
70C22×Dic106—24no—
71C22×Dic106—24no—
72C22×Dic106C2314yes—
73C23×Dic53—24no—
74C23×Dic53—24no—
75C23×Dic53—24no—
76C23×Dic53C2314yes—
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2311yescharacteristic
81C23×Dic53C2311yescharacteristic
82C23×Dic53C2311yescharacteristic
83C23×Dic53C2311yescharacteristic
84C23×Dic53C2311yescharacteristic
85C4×Dic106—232no—
86#13133173—232no—
87C2×C4⋊Dic53—24no—
88C2×C4⋊Dic53—24no—
89C2×C4⋊Dic53C2314yes—
90C2×C4⋊Dic53C2314yes—
91C2×#11719919—24no—
92C2×#11719919—24no—
93C2×#11719919—24no—
94C2×#11719919—24no—
95C2×#11719919—24no—
96C2×#11719919—24no—
97C2×#11719919C2314yes—
98C2×#11719919C2314yes—
99C2×#11719919C2314yes—
100C2×#11719919C2314yes—
101C2×#11719919C2314yes—
102C2×#11719919C2314yes—
103C2×C22⋊Dic53—24no—
104C2×C22⋊Dic53—24no—
105C2×C22⋊Dic53—24no—
106C2×C22⋊Dic53C2314yes—
107C2×C22⋊Dic53C2314yes—
108C2×C22⋊Dic53C2314yes—
109C2×C4×Dic53—24no—
110C2×C4×Dic53—24no—
111C2×C4×Dic53D418yes—
112C2×C4×Dic53C2314yes—
113C2×C4×Dic53C2314yes—
114C2×C4×Dic53C2314yes—
115#13133124C2314yes—
116#13133124C2314yes—
117#13133124C2314yes—
118#13133124C2314yes—
119#13133124C2314yes—
120#13133124C2314yes—
121#13133124C2314yes—
122#13133124C2314yes—
123#13133124C2314yes—
124#13133124C2314yes—
125#13133124C2314yes—
126#13133124C2314yes—
127C25×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C23×C4×C53C2311yescharacteristic
131C23×C4×C53C2311yescharacteristic
132C23×C4×C53C2311yescharacteristic
133C23×C4×C53C2311yescharacteristic
134C2×C4⋊C4×C53—24no—
135C2×C4⋊C4×C53C2314yes—
136C2×C22⋊C4×C53—24no—
137C2×C22⋊C4×C53—24no—
138C2×C22⋊C4×C53—24no—
139C2×C22⋊C4×C53C2314yes—
140C2×C22⋊C4×C53C2314yes—
141C2×C22⋊C4×C53C2314yes—
142C2×C42×C53—24no—
143C2×C42×C53C2314yes—
144#95×C53C2314yes—
145#95×C53C2314yes—
146C24×C53—22no—
147C24×C53—22no—
148C24×C53—22no—
149C24×C53—22no—
150C24×C53—22no—
151C24×C53—22no—
152C24×C53#4114yes—
153C24×C53C2412yes—
154C24×C53C2411yescharacteristic
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—22no—
166C22×C4×C53—22no—
167C22×C4×C53—22no—
168C22×C4×C53—22no—
169C22×C4×C53—22no—
170C22×C4×C53—22no—
171C22×C4×C53C2×D414yes—
172C22×C4×C53#4114yes—
173C22×C4×C53C2412yes—
174C22×C4×C53C2412yes—
175C22×C4×C53C2412yes—
176C22×C4×C53C2412yes—
177C22×C4×C53C2412yes—
178C22×C4×C53C2412yes—
179C22×Dic53—232no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53—28no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—28no—
190C22×Dic53—28no—
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—22no—
202C22×Dic53—22no—
203C22×Dic53C2×D414yes—
204C22×Dic53C2×D414yes—
205C22×Dic53#4114yes—
206C22×Dic53#4114yes—
207C22×Dic53C2412yes—
208C22×Dic53C2412yes—
209C22×Dic53C2412yes—
210C22×Dic53C2412yes—
211C22×Dic53C2412yes—
212C22×Dic53C2412yes—
213C22×Dic53C2412yes—
214C22×Dic53C2412yes—
215C2×Dic106—232no—
216C2×Dic106—28no—
217C2×Dic106—28no—
218C2×Dic106—28no—
219C4⋊C4×C53—28no—
220C22⋊C4×C53—28no—
221C22⋊C4×C53—28no—
222C22⋊C4×C53—28no—
223C42×C53—28no—
224C22⋊Dic53—28no—
225C22⋊Dic53—28no—
226C22⋊Dic53—28no—
227C4⋊Dic53—28no—
228C4⋊Dic53—28no—
229#11719919—28no—
230#11719919—28no—
231#11719919—28no—
232#11719919—28no—
233#11719919—28no—
234#11719919—28no—
235C4×Dic53—28no—
236C4×Dic53—28no—
237C4×Dic53C2×D4116yes—
238C23×C53—28no—
239C23×C53—28no—
240C23×C53—28no—
241C23×C53—22no—
242C23×C53—22no—
243C23×C53—22no—
244C23×C53—22no—
245C23×C53—22no—
246C23×C53—22no—
247C23×C53—44no—
248C23×C53—44no—
249C23×C53—44no—
250C23×C53—44no—
251C23×C53C22×D412yes—
252C23×C53C2×#4112yes—
253C23×C53C2×#4112yes—
254C23×C53C2×#4112yes—
255C23×C53C2×#4114yes—
256C23×C53C2×#4112yes—
257C23×C532−1+412yes—
258C23×C532−1+412yes—
259C23×C53C2511yescharacteristic
260C2×C4×C53—28no—
261C2×C4×C53—28no—
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—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—44no—
279C2×C4×C53—44no—
280C2×C4×C53—44no—
281C2×C4×C53—44no—
282C2×C4×C53C22×D414yes—
283C2×C4×C53C2×#4114yes—
284C2×Dic53—232no—
285C2×Dic53—28no—
286C2×Dic53—28no—
287C2×Dic53—28no—
288C2×Dic53—28no—
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—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—44no—
310C2×Dic53—44no—
311C2×Dic53—44no—
312C2×Dic53—44no—
313C2×Dic53C22×D414yes—
314C2×Dic53C22×D414yes—
315C2×Dic53C2×#4114yes—
316C2×Dic53C2×#4114yes—
317Dic106—232no—
318C2×#2599—531nomaximal, Sylow
319C22×C53—24no—
320C22×C53—24no—
321C22×C53—24no—
322C22×C53—416no—
323C22×C53—42no—
324C22×C53—42no—
325C22×C53—42no—
326C22×C53—42no—
327C22×C53#52514yes—
328C22×C53#52514yes—
329C22×C53#53614yes—
330C22×C53#55214yes—
331C22×C53#55214yes—
332C22×C53#55614yes—
333C22×C53#55614yes—
334C22×C53C23×D411yescharacteristic
335C22×C53C22×#4111yescharacteristic
336C22×C53C22×#4111yescharacteristic
337C22×C53C22×#4111yescharacteristic
338C22×C53C22×#4111yescharacteristic
339C22×C53C2×2−1+411yescharacteristic
340C22×C53C2×2−1+411yescharacteristic
341C4×C53—24no—
342C4×C53—24no—
343C4×C53—42no—
344C4×C53—42no—
345C4×C53—42no—
346C4×C53—42no—
347Dic53—24no—
348Dic53—24no—
349Dic53—24no—
350Dic53—24no—
351Dic53—42no—
352Dic53—42no—
353Dic53—42no—
354Dic53—42no—
355C22×C4×Q8—531no—
356C22×#117—531no—
357#2599—5316no—
358C2×#398—531no—
359C2×#397—531no—
360C2×#395—531no—
361C2×#393—531no—
362C2×#388—531no—
363C2×#388D5311yescharacteristic
364C2×#387—531no—
365C2×#387—531no—
366C2×#387—531no—
367C2×#387—531no—
368C2×#385—531no—
369C2×#385—531no—
370C2×#383—531no—
371C2×C53—44no—
372C2×C53#259918yescomplemented
373C2×C53C2×#52511yescharacteristic
374C2×C53C2×#52511yescharacteristic
375C2×C53C2×#53611yescharacteristic
376C2×C53C2×#55211yescharacteristic
377C2×C53C2×#55211yescharacteristic
378C2×C53C2×#55611yescharacteristic
379C2×C53C2×#55611yescharacteristic
380C23×Q8—531no—
381C24×C4—531no—
382C2×C4×Q8—538no—
383C2×C4×Q8—1068no—
384C2×#117—538no—
385C2×#117—1068no—
386C22×C4⋊C4—531no—
387C22×C4⋊C4—531no—
388C22×C4⋊C4—531no—
389C22×C4⋊C4—531no—
390C22×C4⋊C4—531no—
391C22×C4⋊C4—531no—
392C22×C4⋊C4—531no—
393C22×C4⋊C4—531no—
394C22×C4⋊C4C2×D5311yescharacteristic
395C22×C22⋊C4—531no—
396C22×C22⋊C4—531no—
397C22×C22⋊C4—531no—
398C22×C22⋊C4C2×D5311yescharacteristic
399C22×C22⋊C4C2×D5311yescharacteristic
400C22×C22⋊C4C2×D5311yescharacteristic
401C22×C42—531no—
402C22×C42—531no—
403C22×C42—531no—
404C22×C42C2×D5311yescharacteristic
405#398—538no—
406#397—538no—
407#395—538no—
408#393—538no—
409#388—538no—
410#388C2×D5318yes—
411#387—538no—
412#387—538no—
413#387—538no—
414#387—538no—
415#385—538no—
416#385—538no—
417#383—538no—
418C2×#95—531no—
419C2×#95—531no—
420C2×#95—531no—
421C2×#95—531no—
422C2×#95—531no—
423C2×#95—531no—
424C2×#95—531no—
425C2×#95—531no—
426C2×#95—531no—
427C2×#95—531no—
428C2×#95—531no—
429C2×#95—531no—
430C2×#95C2×D5311yescharacteristic
431C2×#95C2×D5311yescharacteristic
432C53C2×#259911yescharacteristic, complemented, Sylow
433C25C22×D5311yescharacteristic
434C22×Q8—534no—
435C22×Q8—1064no—
436C22×Q8—1064no—
437C22×Q8—1064no—
438C23×C4—531no—
439C23×C4—531no—
440C23×C4—531no—
441C23×C4—531no—
442C23×C4—534no—
443C23×C4—531no—
444C23×C4—531no—
445C23×C4—531no—
446C23×C4—531no—
447C23×C4—1064no—
448C23×C4—1064no—
449C23×C4—1064no—
450C23×C4C22×D5311yescharacteristic
451C23×C4C22×D5311yescharacteristic
452C23×C4C22×D5311yescharacteristic
453C23×C4C22×D5311yescharacteristic
454C23×C4C22×D5311yescharacteristic
455C23×C4C22×D5311yescharacteristic
456C4×Q8—10632no—
457#117—10632no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—534no—
460C2×C4⋊C4—534no—
461C2×C4⋊C4—534no—
462C2×C4⋊C4—534no—
463C2×C4⋊C4—534no—
464C2×C4⋊C4—534no—
465C2×C4⋊C4—534no—
466C2×C4⋊C4—534no—
467C2×C4⋊C4—1064no—
468C2×C4⋊C4—1064no—
469C2×C4⋊C4—1064no—
470C2×C4⋊C4—1064no—
471C2×C4⋊C4—1064no—
472C2×C4⋊C4—1064no—
473C2×C4⋊C4—1064no—
474C2×C4⋊C4—1064no—
475C2×C4⋊C4C22×D5314yes—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—534no—
480C2×C22⋊C4—534no—
481C2×C22⋊C4—534no—
482C2×C22⋊C4—1064no—
483C2×C22⋊C4—1064no—
484C2×C22⋊C4—1064no—
485C2×C22⋊C4C22×D5314yes—
486C2×C22⋊C4C22×D5314yes—
487C2×C22⋊C4C22×D5314yes—
488C2×C42—24no—
489C2×C42—538no—
490C2×C42—534no—
491C2×C42—534no—
492C2×C42—534no—
493C2×C42—1064no—
494C2×C42—1064no—
495C2×C42C22×D5314yes—
496#95—534no—
497#95—534no—
498#95—534no—
499#95—534no—
500#95—534no—
501#95—534no—
502#95—534no—
503#95—534no—
504#95—534no—
505#95—534no—
506#95—534no—
507#95—534no—
508#95C22×D5314yes—
509#95C22×D5314yes—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24#1171994514yes—
517C24C23×D5312yes—
518C24C23×D5311yescharacteristic
519C2×Q8—1068no—
520C2×Q8—1068no—
521C2×Q8—10632no—
522C2×Q8—1068no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—534no—
540C22×C4—534no—
541C22×C4—534no—
542C22×C4—534no—
543C22×C4—532no—
544C22×C4—532no—
545C22×C4—532no—
546C22×C4—532no—
547C22×C4—532no—
548C22×C4—532no—
549C22×C4—532no—
550C22×C4—532no—
551C22×C4—1068no—
552C22×C4—1068no—
553C22×C4—10632no—
554C22×C4—1062no—
555C22×C4—1062no—
556C22×C4—1062no—
557C22×C4—1062no—
558C22×C4—1062no—
559C22×C4—1062no—
560C22×C4—1068no—
561C22×C4—1062no—
562C22×C4—1062no—
563C22×C4—1062no—
564C22×C4—1062no—
565C22×C4—1062no—
566C22×C4—1062no—
567C22×C4—1062no—
568C22×C4—1062no—
569C22×C4—1062no—
570C22×C4—1062no—
571C22×C4—1062no—
572C22×C4—1062no—
573C22×C4—1062no—
574C22×C4—1062no—
575C22×C4D4×D5314yes—
576C22×C4#1171994714yes—
577C22×C4C23×D5312yes—
578C22×C4C23×D5312yes—
579C22×C4C23×D5312yes—
580C22×C4C23×D5312yes—
581C22×C4C23×D5312yes—
582C22×C4C23×D5312yes—
583C4⋊C4—28no—
584C4⋊C4—1068no—
585C4⋊C4—1068no—
586C4⋊C4—1068no—
587C4⋊C4—1068no—
588C4⋊C4—1068no—
589C4⋊C4—1068no—
590C4⋊C4—1068no—
591C4⋊C4—1068no—
592C22⋊C4—28no—
593C22⋊C4—28no—
594C22⋊C4—28no—
595C22⋊C4—1068no—
596C22⋊C4—1068no—
597C22⋊C4—1068no—
598C42—28no—
599C42—5316no—
600C42—1068no—
601C42—1068no—
602C23—28no—
603C23—28no—
604C23—28no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23C2×D4×D5312yes—
616C23#41×D5312yes—
617C23#41×D5312yes—
618C23C2×#1171994712yes—
619C23C2×#1171994514yes—
620C23C2×#1171994512yes—
621C23#1313326412yes—
622C23#1313326412yes—
623C23C24×D5311yescharacteristic
624Q8—10632no—
625C2×C4—28no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—28no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—534no—
648C2×C4—534no—
649C2×C4—534no—
650C2×C4—534no—
651C2×C4—10632no—
652C2×C4—1068no—
653C2×C4—1068no—
654C2×C4—1068no—
655C2×C4—1068no—
656C2×C4—1062no—
657C2×C4—1062no—
658C2×C4—1062no—
659C2×C4—1062no—
660C2×C4—1062no—
661C2×C4—1062no—
662C2×C4—1062no—
663C2×C4—1062no—
664C2×C4—1062no—
665C2×C4—1062no—
666C2×C4—1062no—
667C2×C4—1062no—
668C2×C4—1062no—
669C2×C4—1062no—
670C2×C4—1062no—
671C2×C4—1062no—
672C2×C4—1062no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1062no—
676C2×C4—2124no—
677C2×C4—2124no—
678C2×C4—2124no—
679C2×C4—2124no—
680C2×C4C2×D4×D5314yes—
681C2×C4C2×#1171994714yes—
682C22—24no—
683C22—24no—
684C22—24no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—416no—
690C22#1681113214yes—
691C22#1681113314yes—
692C22#1681119514yes—
693C22#1681130614yes—
694C22#1681131314yes—
695C22#1681134014yes—
696C22#1681134214yes—
697C22C22×D4×D5311yescharacteristic
698C22C2×#41×D5311yescharacteristic
699C22C2×#41×D5311yescharacteristic
700C22C22×#1171994711yescharacteristic
701C22C22×#1171994511yescharacteristic
702C22C2×#1313326411yescharacteristic
703C22C2×#1313326411yescharacteristic
704C4—24no—
705C4—24no—
706C4—42no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—1064no—
711C4—1064no—
712C4—1064no—
713C4—1064no—
714C4—2122no—
715C4—2122no—
716C4—2122no—
717C4—2122no—
718C2—44no—
719C2#2028028918yesdirect product factor
720C2C2×#1681113211yescharacteristic
721C2C2×#1681113311yescharacteristic
722C2C2×#1681119511yescharacteristic
723C2C2×#1681130611yescharacteristic
724C2C2×#1681131311yescharacteristic
725C2C2×#1681134011yescharacteristic
726C2C2×#1681134211yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#388C2
socleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×#388D53
hypocenterC53C2×#2599
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic106C2semidirect
3. #20280289C2direct (N × H)
4. C2×#16810557C2semidirect
6. C2×#16810543C2semidirect
9. C2×#16810509C2semidirect
10. C2×#16810508C2semidirect
11. C2×#16810507C2semidirect
12. C2×#16810505C2semidirect
15. C2×#16810490C2semidirect
20. C2×C4×Dic106C22semidirect
37. #16810557C22semidirect
39. #16810543C22semidirect
42. #16810509C22semidirect
43. #16810508C22semidirect
44. #16810507C22semidirect
45. #16810505C22semidirect
48. #16810490C22semidirect
372. C2×C53#2599semidirect
432. C53C2×#2599semidirect
719. C2#20280289direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Dic1062
C22×#131331732
#202802892
C2×#168105572
C2×#168105512
C2×#168105432
C2×#168105352
C2×#168105112
C2×#168105092
C2×#168105082
C2×#168105072
C2×#168105052
C2×#168104982
C2×#168104952
C2×#168104902
C2×C53×#3882
C2×#259953