Finite Group Databasebeta

← C2×#20287176 #28262645

Subgroups — C2×#20287176 #28262645

Order 13568.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811331C211yesmaximal, characteristic
2C2×#16811315C211yesmaximal, characteristic
3#20287176C2116yesmaximal, direct product factor
4C2×#16811031C211yesmaximal, characteristic, complemented
5C2×#16810956C211yesmaximal, characteristic, complemented
6C2×#16810962C211yesmaximal, characteristic, complemented
7C2×#16810952C211yesmaximal, characteristic, complemented
8C2×#16810951C211yesmaximal, characteristic, complemented
9C2×#16810928C211yesmaximal, characteristic, complemented
10C2×#16810906C211yesmaximal, characteristic, complemented
11C2×#16810878C211yesmaximal, characteristic, complemented
12C2×#16810730C211yesmaximal, characteristic, complemented
13C2×#16810694C211yesmaximal, characteristic
14C2×#16810664C211yesmaximal, characteristic, complemented
15C22×#13133149C211yesmaximal, characteristic, complemented
16C2×C53×#467C211yesmaximal, characteristic, complemented
17C22×#11719912C2211yescharacteristic
18#16811331—24no—
19#16811331C2218yes—
20#16811315—24no—
21#16811315C2218yes—
22C2×#13133216C2211yescharacteristic
23C2×#13133212—21no—
24C2×#13133208—21no—
25C2×#13133208C2211yescharacteristic
26C2×#13133207—21no—
27C2×#13133201—21no—
28C2×#13133197—21no—
29C2×#13133194—21no—
30C2×#13133193C2211yescharacteristic
31C2×#13133193C2211yescharacteristic
32C2×Q8×Dic53C2211yescharacteristic
33C2×Q8×Dic53C2211yescharacteristic
34C2×C4×C22⋊D53C2211yescharacteristic
35C2×#13133177—21no—
36C2×#13133175C2211yescharacteristic
37C2×#13133173—21no—
38C22×C4⋊Dic53C2211yescharacteristic
39C22×C4⋊Dic53C2211yescharacteristic
40C2×C4⋊C4×D53C2211yescharacteristic
41#16811031C2218yescomplemented
42#16810962C2218yescomplemented
43#16810956C2218yescomplemented
44#16810952C2218yescomplemented
45#16810951C2218yescomplemented
46#16810928C2218yescomplemented
47#16810906C2218yescomplemented
48#16810878C2218yescomplemented
49#16810730C2218yescomplemented
50#16810694C2218yes—
51#16810664C2218yescomplemented
52C2×#13133150C2211yescharacteristic
53C2×#13133150C2211yescharacteristic
54C2×#13133149C2211yescharacteristic
55C2×#13133149C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133149C2211yescharacteristic
58C2×#13133149C2218yescomplemented
59C2×#13133148C2211yescharacteristic
60C2×#13133148C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133141C2211yescharacteristic
65C2×#13133141C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C22×Q16×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C2×C22⋊Q8×C53C2211yescharacteristic
72C2×C22⋊Q8×C53C2211yescharacteristic
73C53×#467C2218yescomplemented
74C2×#107×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×C22⋊D53D411yescharacteristic
79C23×Dic53—21no—
80C23×Dic53—21no—
81C22×C4×D53—21no—
82C22×C4×D53C2311yescharacteristic
83C2×#11719912—24no—
84C2×#11719912C2314yes—
85C22×#88322C2311yescharacteristic
86C22×#88322C2311yescharacteristic
87#13133216—22no—
88#13133216C2314yes—
89#13133212—28no—
90#13133208—28no—
91#13133208—22no—
92#13133208C2314yes—
93#13133207—28no—
94#13133201—28no—
95#13133197—28no—
96#13133194—28no—
97#13133193—22no—
98#13133193—22no—
99#13133193C2314yes—
100#13133193C2314yes—
101Q8×Dic53—22no—
102Q8×Dic53—22no—
103Q8×Dic53C2314yes—
104Q8×Dic53C2314yes—
105C4×C22⋊D53D414yes—
106C4×C22⋊D53C2314yes—
107#13133177—28no—
108#13133175—22no—
109#13133175C2314yes—
110#13133173—28no—
111C2×C4⋊Dic53—22no—
112C2×C4⋊Dic53—22no—
113C2×C4⋊Dic53—21no—
114C2×C4⋊Dic53—21no—
115C2×C4⋊Dic53—21no—
116C2×C4⋊Dic53—21no—
117C2×C4⋊Dic53—21no—
118C2×C4⋊Dic53C2314yes—
119C2×C4⋊Dic53C2311yescharacteristic
120C2×C4⋊Dic53C2314yes—
121C2×C4⋊Dic53C2311yescharacteristic
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×#11719919—21no—
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919D411yescharacteristic
130C4⋊C4×D53—22no—
131C4⋊C4×D53C2314yes—
132C2×C22⋊Dic53D411yescharacteristic
133C2×#11719921—21no—
134C2×#11719921—21no—
135C2×#11719921—21no—
136C2×#11719921D411yescharacteristic
137C2×C4×Dic53—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53C2311yescharacteristic
141#13133150C2314yes—
142#13133150C2314yes—
143#13133149C2314yes—
144#13133149C2314yes—
145#13133149C2314yes—
146#13133149C2314yes—
147#13133148C2314yes—
148#13133148C2314yes—
149#13133146C2314yes—
150#13133141C2314yes—
151#13133141C2314yes—
152#13133141C2314yes—
153#13133141C2314yes—
154C22⋊#88322C2314yes—
155#13133129C2314yes—
156#13133127C2314yes—
157C22×Q8×C53C2311yescharacteristic
158C22×Q8×C53C2311yescharacteristic
159C23×C4×C53C2311yescharacteristic
160C2×Q16×C53—24no—
161C2×Q16×C53C2314yes—
162C22×C8×C53—24no—
163C22×C8×C53C2311yescharacteristic
164C22×C8×C53C2314yes—
165C22×C8×C53C2311yescharacteristic
166C22⋊Q8×C53—22no—
167C22⋊Q8×C53—22no—
168C22⋊Q8×C53C2314yes—
169C22⋊Q8×C53C2314yes—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176#107×C53C2314yes—
177#103×C53C2314yes—
178#103×C53C2314yes—
179C24×C53C2×D411yescharacteristic
180C23×D53C2×D411yescharacteristic
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×C53C2412yes—
188C2×Q8×C53C2412yes—
189C22×C4×C53—22no—
190C22×C4×C53—22no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D412yes—
197C22×C4×C53C2412yes—
198C22×C4×C53C2411yescharacteristic
199C2×C22⋊D53—24no—
200C2×C22⋊D53C2×D414yes—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—24no—
206C22×Dic53—24no—
207C22×Dic53—44no—
208C22×Dic53—82no—
209C22×Dic53C2×D411yescharacteristic
210C22×Dic53C2×D411yescharacteristic
211C22×Dic53C2×D411yescharacteristic
212C2×C4×D53—22no—
213C2×C4×D53—22no—
214C2×C4×D53—24no—
215C2×C4×D53—82no—
216C2×C4×D53C2×D412yes—
217C2×C4×D53C2412yes—
218C2×Dic106—24no—
219C2×Dic106—82no—
220Q16×C53—28no—
221C2×C8×C53—22no—
222C2×C8×C53—28no—
223C2×C8×C53#4114yes—
224C2×C8×C53C2412yes—
225C2×C8×C53C2412yes—
226C4⋊C4×C53—24no—
227C4⋊C4×C53—24no—
228C4⋊C4×C53—21no—
229C4⋊C4×C53—21no—
230C4⋊C4×C53C2412yes—
231C4⋊C4×C53C2412yes—
232C22⋊C4×C53—24no—
233C22⋊C4×C53—24no—
234C22⋊Dic53C2×D414yes—
235#11719921—24no—
236#11719921—24no—
237#11719921—24no—
238#11719921C2×D414yes—
239C4⋊Dic53—21no—
240C4⋊Dic53—21no—
241C4⋊Dic53—21no—
242C4⋊Dic53—21no—
243C4⋊Dic53—24no—
244C4⋊Dic53—24no—
245C4⋊Dic53—24no—
246C4⋊Dic53—24no—
247C4⋊Dic53—24no—
248C4⋊Dic53C2412yes—
249C4⋊Dic53C2412yes—
250C4⋊Dic53C2412yes—
251C4⋊Dic53C2412yes—
252#11719919—24no—
253#11719919—24no—
254#11719919—24no—
255#11719919—24no—
256#11719919—24no—
257#11719919C2×D414yes—
258C4×Dic53—24no—
259C4×Dic53—24no—
260C4×Dic53—24no—
261C4×Dic53C2×D412yes—
262C4×Dic53C2412yes—
263C2×#88322—22no—
264C2×#88322—22no—
265C2×#88322C2412yes—
266C2×#88322C2412yes—
267#11719912—28no—
268C23×C53—22no—
269C23×C53—22no—
270C23×C53#13714yes—
271C23×C53C22×D412yes—
272C23×C53C22×D411yescharacteristic
273C22×D53—22no—
274C22×D53—22no—
275C22×D53—22no—
276C22×D53C22×D412yes—
277Q8×C53—22no—
278Q8×C53—22no—
279Q8×C53—22no—
280Q8×C53—22no—
281Q8×C53—42no—
282Q8×C53—42no—
283C2×C4×C53—22no—
284C2×C4×C53—24no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—42no—
292C2×C4×C53—42no—
293C2×C4×C53—42no—
294C2×C4×C53—42no—
295C2×C4×C53C22×D412yes—
296C2×C4×C53C22×D411yescharacteristic
297C2×C4×C53C2×#4112yes—
298C2×C4×C532−1+412yes—
299C2×C4×C53C2511yescharacteristic
300C22⋊D53—28no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—48no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53—42no—
312C2×Dic53—42no—
313C2×Dic53—84no—
314C2×Dic53C22×D412yes—
315C2×Dic53C22×D412yes—
316C2×Dic53C22×D412yes—
317C4×D53—24no—
318C4×D53—22no—
319C4×D53—22no—
320C4×D53—84no—
321Dic106—84no—
322C8×C53—22no—
323C8×C53C2×#4114yes—
324#88322—22no—
325#88322—22no—
326C2×#3344—531nomaximal, Sylow
327C22×C53—28no—
328C22×C53—22no—
329C22×C53—22no—
330C22×C53#54712yes—
331C22×C53C2×#13714yes—
332C22×C53C2×#13712yes—
333C22×C53#57712yes—
334C22×C53C23×D411yescharacteristic
335C2×D53—22no—
336C2×D53—22no—
337C2×D53—22no—
338C2×D53—44no—
339C4×C53—22no—
340C4×C53—42no—
341C4×C53—42no—
342C4×C53—42no—
343C4×C53—42no—
344C4×C53#54712yes—
345C4×C53C22×#4111yescharacteristic
346C4×C53C2×2−1+411yescharacteristic
347Dic53—22no—
348Dic53—22no—
349Dic53—22no—
350Dic53—42no—
351Dic53—42no—
352Dic53—42no—
353Dic53—42no—
354C2×#554—531no—
355C2×#552—531no—
356#3344—5316no—
357C2×#501—531no—
358C2×#484—531no—
359C2×#485—531no—
360C2×#483—531no—
361C2×#483—531no—
362C2×#479—531no—
363C2×#475—531no—
364C2×#470—531no—
365C2×#467D5311yescharacteristic, complemented
366C2×#441—531no—
367C2×#435—531no—
368C2×#428—531no—
369C22×#106—531no—
370C2×C53—24no—
371C2×C53#334414yescomplemented
372C2×C53C2×#54711yescharacteristic
373C2×C53C22×#13711yescharacteristic
374C2×C53C2×#57711yescharacteristic
375D53—42no—
376C22×Q16C2×D5311yescharacteristic
377C22×M16—531no—
378C23×C8C2×D5311yescharacteristic
379#554—538no—
380#554—1064no—
381#552—538no—
382#552—1064no—
383C2×C4⋊Q8—531no—
384C2×#126—1061no—
385C2×#125—531no—
386C2×#125—1061no—
387C2×#125—1061no—
388C2×#123—1061no—
389C2×C22⋊Q8—531no—
390C2×C22⋊Q8—531no—
391C2×C22⋊Q8—1061no—
392C2×C22⋊Q8—1061no—
393C2×C22⋊Q8C2×D5311yescharacteristic
394C2×C22⋊Q8C2×D5311yescharacteristic
395C2×C4×Q8—531no—
396C2×C4×Q8—531no—
397C2×C4×D4—531no—
398C2×C4×D4—1061no—
399C2×#117—531no—
400C2×#117—1061no—
401C22×C4⋊C4—531no—
402C22×C4⋊C4—531no—
403C22×C4⋊C4—531no—
404#501—538no—
405#485—538no—
406#484—538no—
407#483—538no—
408#483—538no—
409#479—538no—
410#475—538no—
411#470—538no—
412#467C2×D5318yescomplemented
413#441—538no—
414#435—538no—
415#428—538no—
416C2×#107—531no—
417C2×#107—531no—
418C2×#107C2×D5311yescharacteristic
419C2×#106—531no—
420C2×#106—531no—
421C2×#106—538no—
422C2×#106—531no—
423C2×#106—531no—
424C2×#106—531no—
425C2×#106—531no—
426C2×C4⋊C8—531no—
427C2×#103—531no—
428C2×#103—531no—
429C2×#103—531no—
430C2×#103—531no—
431C2×#103C2×D5311yescharacteristic
432C2×#103C2×D5311yescharacteristic
433C2×C22⋊C8—531no—
434C2×C22⋊C8—531no—
435C2×#97—531no—
436C53C2×#334411yescharacteristic, complemented, Sylow
437C22×Q8—1061no—
438C22×Q8C22×D5311yescharacteristic
439C22×Q8C22×D5311yescharacteristic
440C22×D4—531no—
441C23×C4—531no—
442C23×C4—1061no—
443C23×C4—1061no—
444C23×C4—1061no—
445C23×C4C22×D5311yescharacteristic
446C2×Q16—24no—
447C2×Q16C22×D5314yes—
448C2×M16—534no—
449C2×M16—1064no—
450C22×C8—24no—
451C22×C8—531no—
452C22×C8—531no—
453C22×C8C22×D5311yescharacteristic
454C22×C8C22×D5314yes—
455C22×C8C22×D5311yescharacteristic
456C4⋊Q8—534no—
457C4⋊Q8—1062no—
458#126—1068no—
459#125—534no—
460#125—1062no—
461#125—1068no—
462#125—1068no—
463#123—1068no—
464C22⋊Q8—22no—
465C22⋊Q8—22no—
466C22⋊Q8—534no—
467C22⋊Q8—534no—
468C22⋊Q8—1068no—
469C22⋊Q8—1068no—
470C22⋊Q8—1062no—
471C22⋊Q8—1062no—
472C22⋊Q8C22×D5314yes—
473C22⋊Q8C22×D5314yes—
474C4×Q8—534no—
475C4×Q8—534no—
476C4×Q8—1062no—
477C4×Q8—1062no—
478C4×D4—534no—
479C4×D4—534no—
480C4×D4—1068no—
481#117—534no—
482#117—1068no—
483#117—1062no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—531no—
487C2×C4⋊C4—531no—
488C2×C4⋊C4—531no—
489C2×C4⋊C4—531no—
490C2×C4⋊C4—531no—
491C2×C4⋊C4—534no—
492C2×C4⋊C4—534no—
493C2×C4⋊C4—534no—
494C2×C4⋊C4—1062no—
495C2×C4⋊C4—1061no—
496C2×C4⋊C4—1061no—
497C2×C4⋊C4—1061no—
498C2×C4⋊C4—1061no—
499C2×C4⋊C4—1061no—
500C2×C4⋊C4—1061no—
501C2×C4⋊C4—1061no—
502C2×C4⋊C4—1061no—
503C2×C4⋊C4—1061no—
504C2×C4⋊C4—1061no—
505C2×C4⋊C4—1062no—
506C2×C4⋊C4—1062no—
507C2×C4⋊C4C22×D5311yescharacteristic
508C2×C4⋊C4C22×D5311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—531no—
512C2×C22⋊C4—531no—
513C2×C22⋊C4—1061no—
514C2×C22⋊C4—1061no—
515C2×C22⋊C4—1061no—
516C2×C42—531no—
517C2×C42—1061no—
518C2×C42—1061no—
519C2×C42—1061no—
520#107—534no—
521#107—534no—
522#107C22×D5314yes—
523#106—534no—
524#106—534no—
525#106—534no—
526#106—534no—
527#106—534no—
528#106—534no—
529C4⋊C8—534no—
530#103—534no—
531#103—534no—
532#103—534no—
533#103—534no—
534#103C22×D5314yes—
535#103C22×D5314yes—
536C22⋊C8—534no—
537C22⋊C8—534no—
538#97—534no—
539C24—531no—
540C24D4×D5311yescharacteristic
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—1064no—
548C2×Q8—4242no—
549C2×Q8C23×D5312yes—
550C2×Q8C23×D5312yes—
551C2×D4—534no—
552C2×D4—1064no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—531no—
560C22×C4—531no—
561C22×C4—531no—
562C22×C4—532no—
563C22×C4—532no—
564C22×C4—1064no—
565C22×C4—1062no—
566C22×C4—1062no—
567C22×C4—1064no—
568C22×C4—1064no—
569C22×C4—1061no—
570C22×C4—1061no—
571C22×C4—1061no—
572C22×C4—1061no—
573C22×C4—4242no—
574C22×C4—4242no—
575C22×C4—2124no—
576C22×C4D4×D5312yes—
577C22×C4D4×D5311yescharacteristic
578C22×C4C23×D5312yes—
579C22×C4C23×D5311yescharacteristic
580Q16—28no—
581M16—1068no—
582C2×C8—22no—
583C2×C8—28no—
584C2×C8—532no—
585C2×C8—532no—
586C2×C8—1062no—
587C2×C8—1062no—
588C2×C8#1171994714yes—
589C2×C8C23×D5312yes—
590C2×C8C23×D5312yes—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—534no—
596C4⋊C4—532no—
597C4⋊C4—532no—
598C4⋊C4—532no—
599C4⋊C4—532no—
600C4⋊C4—1064no—
601C4⋊C4—1064no—
602C4⋊C4—1064no—
603C4⋊C4—1064no—
604C4⋊C4—1064no—
605C4⋊C4—1064no—
606C4⋊C4—1064no—
607C4⋊C4—1064no—
608C4⋊C4—1061no—
609C4⋊C4—1061no—
610C4⋊C4—1064no—
611C4⋊C4—1061no—
612C4⋊C4—1061no—
613C4⋊C4—1064no—
614C4⋊C4C23×D5312yes—
615C4⋊C4C23×D5312yes—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—534no—
619C22⋊C4—534no—
620C22⋊C4—1064no—
621C22⋊C4—1064no—
622C22⋊C4—1064no—
623C42—532no—
624C42—532no—
625C42—1064no—
626C42—1064no—
627C42—1064no—
628C23—22no—
629C23—22no—
630C23—532no—
631C23—1062no—
632C23—1062no—
633C23—1062no—
634C23#1313324914yes—
635C23C2×D4×D5312yes—
636C23C2×D4×D5311yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—22no—
640Q8—22no—
641Q8—42no—
642Q8—42no—
643Q8—4244no—
644D4—1068no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—532no—
658C2×C4—532no—
659C2×C4—532no—
660C2×C4—1062no—
661C2×C4—1062no—
662C2×C4—1062no—
663C2×C4—1064no—
664C2×C4—1062no—
665C2×C4—1062no—
666C2×C4—1062no—
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×C4—2122no—
677C2×C4C2×D4×D5312yes—
678C2×C4C2×D4×D5311yescharacteristic
679C2×C4C2×#1171994712yes—
680C2×C4#1313326412yes—
681C2×C4C24×D5311yescharacteristic
682C8—22no—
683C8—1062no—
684C8—1062no—
685C8C2×#1171994714yes—
686C22—22no—
687C22—22no—
688C22—28no—
689C22—1062no—
690C22—1062no—
691C22—1062no—
692C22—2124no—
693C22#1681127312yes—
694C22C2×#1313324914yes—
695C22C2×#1313324912yes—
696C22#1681143012yes—
697C22C22×D4×D5311yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—1062no—
704C4—1062no—
705C4—1062no—
706C4—2122no—
707C4—2122no—
708C4—2122no—
709C4—2122no—
710C4#1681127312yes—
711C4C22×#1171994711yescharacteristic
712C4C2×#1313326411yescharacteristic
713C2—24no—
714C2—2122no—
715C2#2028717614yesdirect product factor
716C2C2×#1681127311yescharacteristic
717C2C22×#1313324911yescharacteristic
718C2C2×#1681143011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#467C2
socleC23×C53C22×D4
prime radicalC22×C22⋊D53D4
hypercenterC2×#467D53
hypocenterC53C2×#3344
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
3. #20287176C2direct (N × H)
4. C2×#16811031C2semidirect
5. C2×#16810956C2semidirect
6. C2×#16810962C2semidirect
7. C2×#16810952C2semidirect
8. C2×#16810951C2semidirect
9. C2×#16810928C2semidirect
10. C2×#16810906C2semidirect
11. C2×#16810878C2semidirect
12. C2×#16810730C2semidirect
14. C2×#16810664C2semidirect
15. C22×#13133149C2semidirect
16. C2×C53×#467C2semidirect
41. #16811031C22semidirect
42. #16810962C22semidirect
43. #16810956C22semidirect
44. #16810952C22semidirect
45. #16810951C22semidirect
46. #16810928C22semidirect
47. #16810906C22semidirect
48. #16810878C22semidirect
49. #16810730C22semidirect
51. #16810664C22semidirect
58. C2×#13133149C22semidirect
73. C53×#467C22semidirect
365. C2×#467D53semidirect
371. C2×C53#3344semidirect
412. #467C2×D53semidirect
436. C53C2×#3344semidirect
715. C2#20287176direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113312
C2×#168113152
#202871762
C2×#168110312
C2×#168109562
C2×#168109622
C2×#168109522
C2×#168109512
C2×#168109282
C2×#168109062
C2×#168108782
C2×#168107302
C2×#168106942
C2×#168106642
C22×#131331492
C2×C53×#4672
C2×#334453