Finite Group Databasebeta

← C2×#20287536 #28263851

Subgroups — C2×#20287536 #28263851

Order 13568.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811333C211yesmaximal, characteristic, complemented
2#20287536C2116yesmaximal, direct product factor
3C2×#16810991C211yesmaximal, characteristic, complemented
4C2×#16810982C211yesmaximal, characteristic, complemented
5C2×#16810977C211yesmaximal, characteristic, complemented
6C2×#16810930C211yesmaximal, characteristic, complemented
7C2×#16810908C211yesmaximal, characteristic, complemented
8C2×#16810923C211yesmaximal, characteristic, complemented
9C2×#16810835C211yesmaximal, characteristic
10C2×#16810835C211yesmaximal, characteristic
11C2×#16810825C211yesmaximal, characteristic, complemented
12C2×#16810754C211yesmaximal, characteristic, complemented
13C2×#16810733C211yesmaximal, characteristic
14C2×#16810721C211yesmaximal, characteristic, complemented
15C2×C4×#11719924C211yesmaximal, characteristic, complemented
16C2×C53×#556C211yesmaximal, characteristic, complemented
17C22×#11719924C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19C22×#11719922C2211yescharacteristic
20#16811333—24no—
21#16811333C2218yescomplemented
22C2×#13133217C2211yescharacteristic
23C2×#13133209C2211yescharacteristic
24C2×#13133209C2211yescharacteristic
25C2×#13133195—21no—
26C2×#13133195—21no—
27C2×#13133193—21no—
28C2×C4×D212C2211yescharacteristic
29C2×C4×D212C2211yescharacteristic
30C2×C4×D212C2211yescharacteristic
31C2×C4⋊C4×D53—21no—
32#16810991C2218yescomplemented
33#16810982C2218yescomplemented
34#16810977C2218yescomplemented
35#16810930C2218yescomplemented
36#16810923C2218yescomplemented
37#16810908C2218yescomplemented
38#16810835C2218yes—
39#16810835C2218yes—
40#16810825C2218yescomplemented
41#16810754C2218yescomplemented
42#16810733C2218yes—
43#16810721C2218yescomplemented
44C4×#11719924C2218yescomplemented
45C2×#13133150C2211yescharacteristic
46C2×#13133148C2211yescharacteristic
47C2×#13133148C2211yescharacteristic
48C2×C4⋊#88322C2211yescharacteristic
49C2×C4⋊#88322C2211yescharacteristic
50C2×C4⋊#88322C2211yescharacteristic
51C2×#13133141C2211yescharacteristic
52C2×#13133141C2211yescharacteristic
53C2×#13133141C2211yescharacteristic
54C2×#13133141C2211yescharacteristic
55C2×#13133141C2211yescharacteristic
56C2×#13133141C2211yescharacteristic
57C2×#13133138C2211yescharacteristic
58C2×#13133138C2211yescharacteristic
59C2×#13133138C2211yescharacteristic
60C2×#13133137C2211yescharacteristic
61C2×#13133128C2211yescharacteristic
62C2×#13133128C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C53×#556—24no—
65C53×#556C2218yescomplemented
66C2×C4⋊Q8×C53C2211yescharacteristic
67C2×#126×C53—21no—
68C2×#126×C53—21no—
69C2×#124×C53C2211yescharacteristic
70C2×#124×C53C2211yescharacteristic
71C2×C22⋊Q8×C53—21no—
72C2×C4×Q8×C53C2211yescharacteristic
73C2×C4×Q8×C53C2211yescharacteristic
74C2×C4×Q8×C53C2211yescharacteristic
75C2×C4×D4×C53C2211yescharacteristic
76C2×#117×C53—21no—
77C22×Dic106—21no—
78C22×D212C2311yescharacteristic
79C22×C4×D53—21no—
80C22×C4×D53—21no—
81C22×C4×D53—21no—
82C2×#11719924—24no—
83C2×#11719924—24no—
84C2×#11719924C2314yes—
85C2×#11719924C2314yes—
86C2×#11719922—24no—
87C2×#11719922C2314yes—
88C22×#88322C2311yescharacteristic
89C22×#88322C2311yescharacteristic
90C22×#88322C2311yescharacteristic
91C22×#88322C2311yescharacteristic
92#13133217—22no—
93#13133217C2314yes—
94#13133209—22no—
95#13133209—22no—
96#13133209C2314yes—
97#13133209C2314yes—
98#13133195—28no—
99#13133195—28no—
100#13133193—28no—
101C4×D212—22no—
102C4×D212—22no—
103C4×D212—22no—
104C4×D212C2314yes—
105C4×D212C2314yes—
106C4×D212C2314yes—
107C2×C4⋊Dic53—21no—
108C2×C4⋊Dic53C2311yescharacteristic
109C2×C4⋊Dic53C2311yescharacteristic
110C2×C4⋊Dic53C2311yescharacteristic
111C2×#11719919—21no—
112C2×#11719919—21no—
113C2×#11719919—21no—
114C2×#11719919—21no—
115C4⋊C4×D53—28no—
116C2×#11719921—21no—
117C2×#11719921—21no—
118C2×#11719921—21no—
119#13133150C2314yes—
120#13133148C2314yes—
121#13133148C2314yes—
122C4⋊#88322C2314yes—
123C4⋊#88322C2314yes—
124C4⋊#88322C2314yes—
125#13133141C2314yes—
126#13133141C2314yes—
127#13133141C2314yes—
128#13133141C2314yes—
129#13133141C2314yes—
130#13133141C2314yes—
131#13133138C2314yes—
132#13133138C2314yes—
133#13133138C2314yes—
134#13133137C2314yes—
135#13133128C2314yes—
136#13133128C2314yes—
137C4×#88322C2314yes—
138C22×Q8×C53D411yescharacteristic
139C22×Q8×C53C2311yescharacteristic
140C22×Q8×C53C2311yescharacteristic
141C22×D4×C53C2311yescharacteristic
142C23×C4×C53—21no—
143C4⋊Q8×C53—22no—
144C4⋊Q8×C53C2314yes—
145#126×C53—28no—
146#126×C53—28no—
147#124×C53—22no—
148#124×C53—22no—
149#124×C53C2314yes—
150#124×C53C2314yes—
151C22⋊Q8×C53—28no—
152C4×Q8×C53—22no—
153C4×Q8×C53—22no—
154C4×Q8×C53D414yes—
155C4×Q8×C53C2314yes—
156C4×Q8×C53C2314yes—
157C4×Q8×C53C2314yes—
158C4×D4×C53—22no—
159C4×D4×C53C2314yes—
160#117×C53—28no—
161C2×C4⋊C4×C53—21no—
162C2×C4⋊C4×C53—21no—
163C2×C4⋊C4×C53—21no—
164C2×C4⋊C4×C53—21no—
165C2×C4⋊C4×C53D411yescharacteristic
166C2×C4⋊C4×C53D411yescharacteristic
167C2×C4⋊C4×C53D411yescharacteristic
168C2×C4⋊C4×C53C2311yescharacteristic
169C2×C22⋊C4×C53—21no—
170C2×C22⋊C4×C53—21no—
171C2×C22⋊C4×C53—21no—
172C2×C22⋊C4×C53—21no—
173C2×C22⋊C4×C53—21no—
174C2×C42×C53—21no—
175C2×C42×C53—21no—
176C2×C42×C53C2311yescharacteristic
177C2×C42×C53C2311yescharacteristic
178C2×C42×C53C2311yescharacteristic
179C24×C53—21no—
180C23×D53—21no—
181C2×Q8×C53—21no—
182C2×Q8×C53—21no—
183C2×Q8×C53—22no—
184C2×Q8×C53—22no—
185C2×Q8×C53—22no—
186C2×Q8×C53—22no—
187C2×Q8×C53—42no—
188C2×Q8×C53C2×D414yes—
189C2×Q8×C53C2412yes—
190C2×Q8×C53C2412yes—
191C2×D4×C53—21no—
192C2×D4×C53—22no—
193C2×D4×C53—22no—
194C2×D4×C53C2412yes—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—24no—
199C22×C4×C53—44no—
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2411yescharacteristic
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C2×D212—21no—
211C2×D212—22no—
212C2×D212#4114yes—
213C2×D212C2412yes—
214C2×C4×D53—24no—
215C2×C4×D53—24no—
216C2×C4×D53—24no—
217C2×C4×D53—44no—
218C2×C4×D53—82no—
219C2×C4×D53—82no—
220C2×Dic106—24no—
221C2×Dic106—82no—
222C4⋊C4×C53—24no—
223C4⋊C4×C53—24no—
224C4⋊C4×C53—24no—
225C4⋊C4×C53—24no—
226C4⋊C4×C53—21no—
227C4⋊C4×C53C2×D414yes—
228C4⋊C4×C53C2×D414yes—
229C4⋊C4×C53C2×D414yes—
230C4⋊C4×C53C2412yes—
231C22⋊C4×C53—24no—
232C22⋊C4×C53—24no—
233C22⋊C4×C53—24no—
234C22⋊C4×C53—24no—
235C22⋊C4×C53—24no—
236C42×C53—24no—
237C42×C53—24no—
238C42×C53C2×D412yes—
239C42×C53C2×D412yes—
240C42×C53C2×D412yes—
241C42×C53C2412yes—
242C42×C53C2412yes—
243C42×C53C2412yes—
244#11719924—28no—
245#11719924—28no—
246#11719922—28no—
247#11719921—24no—
248#11719921—24no—
249#11719921—24no—
250C4⋊Dic53—24no—
251C4⋊Dic53—21no—
252C4⋊Dic53—21no—
253C4⋊Dic53—21no—
254C4⋊Dic53C2412yes—
255C4⋊Dic53C2412yes—
256C4⋊Dic53C2412yes—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261C2×#88322—22no—
262C2×#88322—22no—
263C2×#88322—22no—
264C2×#88322—22no—
265C2×#88322C2412yes—
266C2×#88322C2412yes—
267C2×#88322C2412yes—
268C2×#88322C2412yes—
269C23×C53—22no—
270C23×C53—42no—
271C23×C53—42no—
272C23×C53—42no—
273C23×C53C22×D411yescharacteristic
274C22×D53—24no—
275C22×D53—22no—
276C22×D53—42no—
277C22×D53—42no—
278Q8×C53—22no—
279Q8×C53—22no—
280Q8×C53—22no—
281Q8×C53—22no—
282Q8×C53—44no—
283Q8×C53—42no—
284Q8×C53—42no—
285D4×C53—22no—
286D4×C53—22no—
287D4×C53—42no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
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—48no—
298C2×C4×C53—42no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53C22×D412yes—
302C2×C4×C53C22×D412yes—
303C2×C4×C53C22×D412yes—
304C2×C4×C53C22×D412yes—
305C2×C4×C53C22×D412yes—
306C2×C4×C53C22×D412yes—
307C2×C4×C53C22×D411yescharacteristic
308C2×C4×C53C2×#4112yes—
309C2×C4×C532−1+412yes—
310C2×C4×C53C2511yescharacteristic
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317D212—24no—
318D212—22no—
319D212C2×#4114yes—
320C4×D53—48no—
321C4×D53—84no—
322C4×D53—84no—
323Dic106—84no—
324#88322—22no—
325#88322—22no—
326#88322—22no—
327#88322—22no—
328C2×#3376—531nomaximal, Sylow
329C22×C53—42no—
330C22×C53—42no—
331C22×C53—42no—
332C22×C53—84no—
333C22×C53#54812yes—
334C22×C53#57512yes—
335C22×C53#57712yes—
336C22×C53C23×D411yescharacteristic
337C2×D53—24no—
338C2×D53—48no—
339C2×D53—42no—
340C2×D53—42no—
341C4×C53—22no—
342C4×C53—22no—
343C4×C53—22no—
344C4×C53—22no—
345C4×C53—22no—
346C4×C53—22no—
347C4×C53—42no—
348C4×C53—42no—
349C4×C53—42no—
350C4×C53#54812yes—
351C4×C53C22×#4111yescharacteristic
352C4×C53C2×2−1+411yescharacteristic
353Dic53—42no—
354Dic53—42no—
355Dic53—42no—
356C2×#556D5311yescharacteristic, complemented
357C2×#554—531no—
358#3376—5316no—
359C2×#491—531no—
360C2×#489—531no—
361C2×#488—531no—
362C2×#479—531no—
363C2×#475—531no—
364C2×#478—531no—
365C2×#463—531no—
366C2×#463—531no—
367C2×#461—531no—
368C2×#446—531no—
369C2×#442—531no—
370C2×#440—531no—
371C2×C4×SD16—531no—
372C2×C53—82no—
373C2×C53#337614yescomplemented
374C2×C53C2×#54811yescharacteristic
375C2×C53C2×#57511yescharacteristic
376C2×C53C2×#57711yescharacteristic
377D53—44no—
378C22×SD16—531no—
379C22×SD16—531no—
380C22×D8—531no—
381#556—24no—
382#556C2×D5318yescomplemented
383#554—538no—
384#554—1064no—
385C2×C4⋊Q8—531no—
386C2×C4⋊Q8C2×D5311yescharacteristic
387C2×#126—21no—
388C2×#126—21no—
389C2×#125—531no—
390C2×#125—531no—
391C2×#124C2×D5311yescharacteristic
392C2×#124C2×D5311yescharacteristic
393C2×C22⋊Q8—21no—
394C2×C22⋊Q8—1061no—
395C2×C22⋊Q8—1061no—
396C2×C22⋊Q8—1061no—
397C2×C4×Q8C2×D5311yescharacteristic
398C2×C4×Q8C2×D5311yescharacteristic
399C2×C4×Q8C2×D5311yescharacteristic
400C2×C4×D4—531no—
401C2×C4×D4—531no—
402C2×C4×D4—531no—
403C2×C4×D4C2×D5311yescharacteristic
404C2×#117—21no—
405C22×C4⋊C4—1061no—
406#491—538no—
407#489—538no—
408#488—538no—
409#479—538no—
410#478—538no—
411#475—538no—
412#463—538no—
413#463—538no—
414#461—538no—
415#446—538no—
416#442—538no—
417#440—538no—
418C4×SD16—538no—
419C2×#107—531no—
420C2×#106—531no—
421C2×#106—531no—
422C2×C4⋊C8—531no—
423C2×C4⋊C8—531no—
424C2×C4⋊C8—531no—
425C2×#103—531no—
426C2×#103—531no—
427C2×#103—531no—
428C2×#103—531no—
429C2×#103—531no—
430C2×#103—531no—
431C2×#102—531no—
432C2×#102—531no—
433C2×#102—531no—
434C2×#102—531no—
435C2×#97—531no—
436C2×#97—531no—
437C2×C4×C8—531no—
438C53C2×#337611yescharacteristic, complemented, Sylow
439C22×Q8—1061no—
440C22×Q8C22⋊D5311yescharacteristic
441C22×Q8C22×D5311yescharacteristic
442C22×Q8C22×D5311yescharacteristic
443C22×D4—531no—
444C22×D4C22×D5311yescharacteristic
445C23×C4—21no—
446C23×C4—1061no—
447C23×C4—1061no—
448C23×C4—1061no—
449C2×SD16—534no—
450C2×SD16—534no—
451C2×SD16—1064no—
452C2×SD16—1064no—
453C2×D8—534no—
454C2×D8—1064no—
455C22×C8—531no—
456C22×C8—531no—
457C22×C8—531no—
458C22×C8—531no—
459C4⋊Q8—22no—
460C4⋊Q8—534no—
461C4⋊Q8—1062no—
462C4⋊Q8C22×D5314yes—
463#126—28no—
464#126—28no—
465#125—534no—
466#125—534no—
467#125—1062no—
468#125—1062no—
469#124—22no—
470#124—22no—
471#124C22×D5314yes—
472#124C22×D5314yes—
473C22⋊Q8—28no—
474C22⋊Q8—1068no—
475C22⋊Q8—1068no—
476C22⋊Q8—1068no—
477C4×Q8—22no—
478C4×Q8—22no—
479C4×Q8C22⋊D5314yes—
480C4×Q8C22×D5314yes—
481C4×Q8C22×D5314yes—
482C4×Q8C22×D5314yes—
483C4×D4—22no—
484C4×D4—534no—
485C4×D4—534no—
486C4×D4—534no—
487C4×D4—1062no—
488C4×D4—1062no—
489C4×D4—1062no—
490C4×D4C22×D5314yes—
491#117—28no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—531no—
497C2×C4⋊C4—531no—
498C2×C4⋊C4—531no—
499C2×C4⋊C4—1061no—
500C2×C4⋊C4—1061no—
501C2×C4⋊C4—1061no—
502C2×C4⋊C4—1061no—
503C2×C4⋊C4—1061no—
504C2×C4⋊C4—1068no—
505C2×C4⋊C4C22⋊D5311yescharacteristic
506C2×C4⋊C4C22⋊D5311yescharacteristic
507C2×C4⋊C4C22⋊D5311yescharacteristic
508C2×C4⋊C4C22×D5311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—1061no—
515C2×C22⋊C4—1061no—
516C2×C22⋊C4—1061no—
517C2×C42—21no—
518C2×C42—21no—
519C2×C42C22×D5311yescharacteristic
520C2×C42C22×D5311yescharacteristic
521C2×C42C22×D5311yescharacteristic
522#107—534no—
523#106—534no—
524#106—534no—
525C4⋊C8—534no—
526C4⋊C8—534no—
527C4⋊C8—534no—
528#103—534no—
529#103—534no—
530#103—534no—
531#103—534no—
532#103—534no—
533#103—534no—
534#102—534no—
535#102—534no—
536#102—534no—
537#102—534no—
538#97—534no—
539#97—534no—
540C4×C8—534no—
541C24—21no—
542C24—1061no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—42no—
550C2×Q8—1064no—
551C2×Q8—4242no—
552C2×Q8C2×C22⋊D5314yes—
553C2×Q8C23×D5312yes—
554C2×Q8C23×D5312yes—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—534no—
559C2×D4—532no—
560C2×D4—1061no—
561C2×D4—1062no—
562C2×D4C23×D5312yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—44no—
568C22×C4—1061no—
569C22×C4—1061no—
570C22×C4—1061no—
571C22×C4—1064no—
572C22×C4—1064no—
573C22×C4—1064no—
574C22×C4—4242no—
575C22×C4—4242no—
576C22×C4—2124no—
577C22×C4C2×C22⋊D5311yescharacteristic
578C22×C4C2×C22⋊D5311yescharacteristic
579C22×C4C2×C22⋊D5311yescharacteristic
580C22×C4C2×C22⋊D5311yescharacteristic
581C22×C4C2×C22⋊D5311yescharacteristic
582C22×C4C2×C22⋊D5311yescharacteristic
583C22×C4C23×D5311yescharacteristic
584SD16—1068no—
585SD16—1068no—
586D8—1068no—
587C2×C8—532no—
588C2×C8—532no—
589C2×C8—532no—
590C2×C8—532no—
591C2×C8—1062no—
592C2×C8—1062no—
593C2×C8—1062no—
594C2×C8—1062no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—21no—
600C4⋊C4—532no—
601C4⋊C4—532no—
602C4⋊C4—532no—
603C4⋊C4—1061no—
604C4⋊C4—1061no—
605C4⋊C4—1061no—
606C4⋊C4—1064no—
607C4⋊C4—1064no—
608C4⋊C4—1064no—
609C4⋊C4—1064no—
610C4⋊C4—1064no—
611C4⋊C4C2×C22⋊D5314yes—
612C4⋊C4C2×C22⋊D5314yes—
613C4⋊C4C2×C22⋊D5314yes—
614C4⋊C4C23×D5312yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—24no—
620C22⋊C4—1064no—
621C22⋊C4—1064no—
622C22⋊C4—1064no—
623C42—24no—
624C42—24no—
625C42C2×C22⋊D5312yes—
626C42C2×C22⋊D5312yes—
627C42C2×C22⋊D5312yes—
628C42C23×D5312yes—
629C42C23×D5312yes—
630C42C23×D5312yes—
631C23—22no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—1064no—
636C23—1062no—
637C23—2122no—
638C23—2122no—
639C23C22×C22⋊D5311yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—44no—
645Q8—42no—
646Q8—42no—
647Q8—4244no—
648D4—22no—
649D4—22no—
650D4—42no—
651D4—534no—
652D4—1064no—
653D4—1062no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—48no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—1062no—
668C2×C4—1062no—
669C2×C4—1062no—
670C2×C4—4244no—
671C2×C4—4244no—
672C2×C4—2128no—
673C2×C4—2122no—
674C2×C4—2122no—
675C2×C4—2122no—
676C2×C4C22×C22⋊D5312yes—
677C2×C4C22×C22⋊D5312yes—
678C2×C4C22×C22⋊D5312yes—
679C2×C4C22×C22⋊D5312yes—
680C2×C4C22×C22⋊D5312yes—
681C2×C4C22×C22⋊D5312yes—
682C2×C4C22×C22⋊D5311yescharacteristic
683C2×C4#41×D5312yes—
684C2×C4#1313326412yes—
685C2×C4C24×D5311yescharacteristic
686C8—1062no—
687C8—1062no—
688C8—1062no—
689C8—1062no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—84no—
694C22—1064no—
695C22—2128no—
696C22—2122no—
697C22—2122no—
698C22#1681128012yes—
699C22#1681142112yes—
700C22#1681143112yes—
701C22C23×C22⋊D5311yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—2122no—
712C4—2122no—
713C4—2122no—
714C4#1681128012yes—
715C4C2×#41×D5311yescharacteristic
716C4C2×#1313326411yescharacteristic
717C2—82no—
718C2—2124no—
719C2#2028753614yesdirect product factor
720C2C2×#1681128011yescharacteristic
721C2C2×#1681142111yescharacteristic
722C2C2×#1681143111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#556C2
socleC23×C53C22×D4
prime radicalC22×#11719922C22
hypercenterC2×#556D53
hypocenterC53C2×#3376
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#16811333C2semidirect
2. #20287536C2direct (N × H)
3. C2×#16810991C2semidirect
4. C2×#16810982C2semidirect
5. C2×#16810977C2semidirect
6. C2×#16810930C2semidirect
7. C2×#16810908C2semidirect
8. C2×#16810923C2semidirect
11. C2×#16810825C2semidirect
12. C2×#16810754C2semidirect
14. C2×#16810721C2semidirect
15. C2×C4×#11719924C2semidirect
16. C2×C53×#556C2semidirect
21. #16811333C22semidirect
32. #16810991C22semidirect
33. #16810982C22semidirect
34. #16810977C22semidirect
35. #16810930C22semidirect
36. #16810923C22semidirect
37. #16810908C22semidirect
40. #16810825C22semidirect
41. #16810754C22semidirect
43. #16810721C22semidirect
44. C4×#11719924C22semidirect
65. C53×#556C22semidirect
356. C2×#556D53semidirect
373. C2×C53#3376semidirect
382. #556C2×D53semidirect
438. C53C2×#3376semidirect
719. C2#20287536direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113332
#202875362
C2×#168109912
C2×#168109822
C2×#168109772
C2×#168109302
C2×#168109082
C2×#168109232
C2×#168108352
C2×#168108252
C2×#168107542
C2×#168107332
C2×#168107212
C2×C4×#117199242
C2×C53×#5562
C2×#337653