Finite Group Databasebeta

← C2×D53⋊#328 #28314976

Subgroups — C2×D53⋊#328 #28314976

Order 13568.

1846 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D53⋊(C22⋊C8)C211yesmaximal, characteristic
2C22×(C2×#6157)⋊C4C211yesmaximal, characteristic
3C2×#16811477C212yesmaximal, complemented
4D53⋊#328C218yesmaximal, direct product factor
5C2×#16811476C212yesmaximal, complemented
6C2×C22⋊Q8×D53C211yesmaximal, characteristic
7C24×#6157—21no—
8C22×D53⋊C8—21no—
9C2×#13133274C2212yes—
10D53⋊(C22⋊C8)—22no—
11D53⋊(C22⋊C8)C2214yes—
12C2×C22⋊#88324—21no—
13C2×(C2×#6157)⋊C4—22no—
14C2×(C2×#6157)⋊C4—21no—
15C2×(C2×#6157)⋊C4C2212yes—
16C2×(C2×#6157)⋊C4C2214yes—
17#16811477C2218yescomplemented
18#16811476C2218yescomplemented
19C22×Q8×D53C411yescharacteristic, complemented
20C23×C4×D53C2211yescharacteristic
21C2×#13133197C2211yescharacteristic
22C2×#13133196C411yescharacteristic, complemented
23C2×#13133195—21no—
24C2×#13133194—21no—
25C2×#13133193C2211yescharacteristic
26C22⋊Q8×D53—22no—
27C22⋊Q8×D53—22no—
28C22⋊Q8×D53C414yescomplemented
29C22⋊Q8×D53C2214yes—
30C2×C4⋊C4×D53—21no—
31C2×C4⋊C4×D53C411yescharacteristic, complemented
32C2×C22⋊C4×D53—21no—
33C2×C22⋊Q8×C53C411yescharacteristic, complemented
34C23×#6157—28no—
35C23×#6157—24no—
36C23×#6157—22no—
37C23×#6157—44no—
38C23×#6157—44no—
39C2×D53⋊C8—24no—
40C2×D53⋊C8—44no—
41C22×#88324—22no—
42#13133274—22no—
43#13133274C2314yes—
44C22⋊#88324—24no—
45(C2×#6157)⋊C4—22no—
46(C2×#6157)⋊C4—24no—
47(C2×#6157)⋊C4C2314yes—
48C24×D53D411yescharacteristic
49C22×Dic106—21no—
50C22×Dic106C2×C411yescharacteristic, complemented
51C2×Q8×D53—22no—
52C2×Q8×D53—44no—
53C2×Q8×D53C2×C414yescomplemented
54C23×Dic53D411yescharacteristic
55C22×C4×D53—21no—
56C22×C4×D53—21no—
57C22×C4×D53—44no—
58C22×C4×D53C2×C411yescharacteristic
59C22×C4×D53C2×C412yes—
60C22×C4×D53D411yescharacteristic
61C22×C4×D53D412yes—
62C22×C4×D53D411yescharacteristic
63C22×C4×D53D412yes—
64C22×C4×D53C2312yes—
65C22×C4×D53C2311yescharacteristic
66#13133197—21no—
67#13133197—21no—
68#13133197C2×C412yescomplemented
69#13133197C2312yes—
70#13133196—22no—
71#13133196C2×C414yescomplemented
72#13133195—24no—
73#13133195—24no—
74#13133194—24no—
75#13133194—24no—
76#13133193—21no—
77#13133193—21no—
78#13133193C2×C412yescomplemented
79#13133193C2312yes—
80C2×C4⋊Dic53—21no—
81C2×C4⋊Dic53C2×C411yescharacteristic, complemented
82C2×#11719919—21no—
83C2×#11719919—21no—
84C2×#11719919—21no—
85C4⋊C4×D53—24no—
86C4⋊C4×D53—22no—
87C4⋊C4×D53—24no—
88C4⋊C4×D53C2×C414yescomplemented
89C2×C22⋊Dic53—21no—
90C2×#11719921—21no—
91C2×#11719921—21no—
92C22⋊C4×D53—24no—
93C22⋊C4×D53—24no—
94C22×Q8×C53C2×C411yescharacteristic, complemented
95C23×C4×C53C2×C411yescharacteristic
96C22⋊Q8×C53—22no—
97C22⋊Q8×C53C2×C414yescomplemented
98C2×C4⋊C4×C53—21no—
99C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
100C2×C22⋊C4×C53—21no—
101C24×C53C22⋊C411yescharacteristic
102C23×D53—24no—
103C23×D53—24no—
104C23×D53C22⋊C412yes—
105C23×D53C22⋊C411yescharacteristic
106C23×D53SD1614yes—
107C23×D53Q1614yes—
108C23×D53C2×D412yes—
109C23×D53C2×D411yescharacteristic
110C22×#6157—28no—
111C22×#6157—216no—
112C22×#6157—24no—
113C22×#6157—44no—
114C22×#6157—432no—
115C22×#6157—48no—
116C22×#6157—44no—
117C22×#6157—48no—
118C2×Q8×C53—21no—
119C2×Q8×C53—42no—
120C2×Q8×C53C22×C412yescomplemented
121C22×C4×C53—21no—
122C22×C4×C53—21no—
123C22×C4×C53—42no—
124C22×C4×C53C22⋊C411yescharacteristic
125C22×C4×C53C22⋊C412yes—
126C22×C4×C53C22×C411yescharacteristic
127C22×C4×C53C22×C412yes—
128C22×Dic53—21no—
129C22×Dic53—21no—
130C22×Dic53—42no—
131C22×Dic53C22⋊C411yescharacteristic
132C22×Dic53C22⋊C412yes—
133C22×Dic53C2×D411yescharacteristic
134C22×Dic53C2×D412yes—
135Q8×D53—48no—
136Q8×D53—48no—
137C2×C4×D53—24no—
138C2×C4×D53—24no—
139C2×C4×D53—24no—
140C2×C4×D53—24no—
141C2×C4×D53—44no—
142C2×C4×D53—44no—
143C2×C4×D53—44no—
144C2×C4×D53—44no—
145C2×C4×D53—42no—
146C2×C4×D53—42no—
147C2×C4×D53—44no—
148C2×C4×D53—44no—
149C2×C4×D53C22⋊C412yes—
150C2×C4×D53C22⋊C412yes—
151C2×C4×D53C22⋊C412yes—
152C2×C4×D53C22×C412yes—
153C2×C4×D53C22×C411yescharacteristic
154C2×C4×D53C2×D412yes—
155C2×C4×D53C2×D411yescharacteristic
156C2×C4×D53C2×D412yes—
157C2×C4×D53C2×D411yescharacteristic
158C2×C4×D53C2411yescharacteristic
159C2×Dic106—21no—
160C2×Dic106—24no—
161C2×Dic106—44no—
162C2×Dic106—42no—
163C2×Dic106C22×C412yescomplemented
164C2×#88324—24no—
165C2×#88324—44no—
166D53⋊C8—48no—
167C4⋊C4×C53—24no—
168C4⋊C4×C53—21no—
169C4⋊C4×C53C22×C412yescomplemented
170C22⋊C4×C53—24no—
171C22⋊Dic53—24no—
172#11719921—22no—
173#11719921—22no—
174#11719921—22no—
175#11719921—22no—
176C4⋊Dic53—21no—
177C4⋊Dic53—22no—
178C4⋊Dic53—22no—
179C4⋊Dic53C22×C412yescomplemented
180#11719919—24no—
181#11719919—22no—
182#11719919—24no—
183#11719919—22no—
184C23×C53—22no—
185C23×C53—22no—
186C23×C53#10314yes—
187C23×C53C2×C22⋊C412yes—
188C23×C53C2×C22⋊C411yescharacteristic
189C22×D53—22no—
190C22×D53—22no—
191C22×D53—216no—
192C22×D53—216no—
193C22×D53—24no—
194C22×D53—24no—
195C22×D53—24no—
196C22×D53—24no—
197C22×D53#9914yes—
198C22×D53#10318yes—
199C22×D53#10314yes—
200C22×D53#10414yes—
201C22×D53C2×C22⋊C411yescharacteristic
202C22×D53C2×C22⋊C412yes—
203C22×D53C2×SD1612yes—
204C22×D53C2×SD1614yes—
205C22×D53C2×Q1612yes—
206C22×D53C2×Q1614yes—
207C22×D53C22×D411yescharacteristic
208C2×#6157—28no—
209C2×#6157—44no—
210C2×#6157—416no—
211C2×#6157—432no—
212C2×#6157—44no—
213Q8×C53—42no—
214Q8×C53—42no—
215C2×C4×C53—22no—
216C2×C4×C53—22no—
217C2×C4×C53—22no—
218C2×C4×C53—22no—
219C2×C4×C53—42no—
220C2×C4×C53—42no—
221C2×C4×C53—42no—
222C2×C4×C53—42no—
223C2×C4×C53C2×C22⋊C411yescharacteristic
224C2×C4×C53C2×C22⋊C412yes—
225C2×C4×C53C23×C411yescharacteristic
226C2×Dic53—22no—
227C2×Dic53—22no—
228C2×Dic53—22no—
229C2×Dic53—22no—
230C2×Dic53—42no—
231C2×Dic53—42no—
232C2×Dic53—42no—
233C2×Dic53—42no—
234C2×Dic53C2×C22⋊C412yes—
235C2×Dic53C2×C22⋊C411yescharacteristic
236C2×Dic53C22×D411yescharacteristic
237C4×D53—24no—
238C4×D53—24no—
239C4×D53—24no—
240C4×D53—24no—
241C4×D53—42no—
242C4×D53—41no—
243C4×D53—41no—
244C4×D53—42no—
245C4×D53—41no—
246C4×D53—41no—
247C4×D53—48no—
248C4×D53—48no—
249Dic106—48no—
250Dic106—42no—
251Dic106—42no—
252#88324—44no—
253C22×#328—531nomaximal, Sylow
254C22×C53—22no—
255C22×C53—22no—
256C22×C53—28no—
257C22×C53C2×#9912yes—
258C22×C53C2×#10314yes—
259C22×C53C2×#10312yes—
260C22×C53C2×#10412yes—
261C22×C53C22×C22⋊C411yescharacteristic
262C2×D53—21no—
263C2×D53—21no—
264C2×D53—21no—
265C2×D53—21no—
266C2×D53—24no—
267C2×D53—24no—
268C2×D53—28no—
269C2×D53—216no—
270C2×D53—28no—
271C2×D53#328116yescomplemented
272C2×D53C2×#9914yes—
273C2×D53C2×#10312yes—
274C2×D53C2×#10314yes—
275C2×D53C2×#10414yes—
276C2×D53C22×SD1611yescharacteristic
277C2×D53C22×Q1611yescharacteristic
278#6157—48no—
279C4×C53—21no—
280C4×C53—21no—
281C4×C53—22no—
282C4×C53—42no—
283C4×C53—42no—
284Dic53—21no—
285Dic53—22no—
286Dic53—21no—
287Dic53—42no—
288Dic53—42no—
289C22×C22⋊Q8—531no—
290C22×C22⋊C8—531no—
291C22×#95—531no—
292C2×#328—532no—
293C2×#328—538no—
294C2×#328—532no—
295C2×C53—24no—
296C2×C53C2×#32814yescomplemented
297C2×C53C22×#9911yescharacteristic
298C2×C53C22×#10311yescharacteristic
299C2×C53C22×#10411yescharacteristic
300D53—21no—
301D53—21no—
302D53—22no—
303D53C2×#32818yescomplemented
304C23×Q8—531no—
305C24×C4—531no—
306C24×C4—1061no—
307C23×C8—1061no—
308C2×C22⋊Q8—531no—
309C2×C22⋊Q8—531no—
310C2×C22⋊Q8—534no—
311C2×C22⋊Q8—534no—
312C2×C22⋊Q8—531no—
313C2×C22⋊Q8—1061no—
314C2×C22⋊Q8—1061no—
315C2×C22⋊Q8—1062no—
316C2×C22⋊Q8—1062no—
317C2×C22⋊Q8#615711yescharacteristic, complemented
318C22×C4⋊C4—531no—
319C22×C4⋊C4—1061no—
320C22×C22⋊C4—1061no—
321C2×C22⋊C8—534no—
322C2×C22⋊C8—532no—
323C2×C22⋊C8—1061no—
324C2×C22⋊C8—1062no—
325C2×#95—532no—
326C2×#95—534no—
327C2×#95—1061no—
328C2×#95—1062no—
329#328—538no—
330#328—538no—
331C53C22×#32811yescharacteristic, complemented, Sylow
332C25—531no—
333C22×Q8—534no—
334C22×Q8—531no—
335C22×Q8—1061no—
336C22×Q8—1062no—
337C22×Q8—2124no—
338C22×Q8C2×#615711yescharacteristic, complemented
339C23×C4—531no—
340C23×C4—531no—
341C23×C4—531no—
342C23×C4—531no—
343C23×C4—532no—
344C23×C4—532no—
345C23×C4—531no—
346C23×C4—532no—
347C23×C4—532no—
348C23×C4—1061no—
349C23×C4—1061no—
350C23×C4—1064no—
351C23×C4—1062no—
352C23×C4—1068no—
353C23×C4—2124no—
354C23×C4—2124no—
355C23×C4—2124no—
356C23×C4C2×#615711yescharacteristic
357C22×C8—1062no—
358C22×C8—1064no—
359C22×C8—2124no—
360C22⋊Q8—22no—
361C22⋊Q8—532no—
362C22⋊Q8—532no—
363C22⋊Q8—534no—
364C22⋊Q8—532no—
365C22⋊Q8—532no—
366C22⋊Q8—1064no—
367C22⋊Q8—1064no—
368C22⋊Q8—1064no—
369C22⋊Q8—1064no—
370C22⋊Q8—1061no—
371C22⋊Q8—1061no—
372C22⋊Q8—1061no—
373C22⋊Q8—1061no—
374C22⋊Q8—1062no—
375C22⋊Q8C2×#615714yescomplemented
376C2×C4⋊C4—21no—
377C2×C4⋊C4—531no—
378C2×C4⋊C4—534no—
379C2×C4⋊C4—1062no—
380C2×C4⋊C4—1064no—
381C2×C4⋊C4—1064no—
382C2×C4⋊C4—1061no—
383C2×C4⋊C4—1061no—
384C2×C4⋊C4—1061no—
385C2×C4⋊C4—1061no—
386C2×C4⋊C4C2×#615711yescharacteristic, complemented
387C2×C22⋊C4—21no—
388C2×C22⋊C4—1064no—
389C2×C22⋊C4—1064no—
390C2×C22⋊C4—1061no—
391C2×C22⋊C4—1061no—
392C2×C22⋊C4—1061no—
393C22⋊C8—534no—
394C22⋊C8—1064no—
395C22⋊C8—1062no—
396#95—534no—
397#95—1062no—
398#95—1064no—
399C24—531no—
400C24—534no—
401C24—534no—
402C24—532no—
403C24—532no—
404C24—531no—
405C24—1064no—
406C24—1064no—
407C24C22⋊#615711yescharacteristic
408C2×Q8—21no—
409C2×Q8—42no—
410C2×Q8—532no—
411C2×Q8—1064no—
412C2×Q8—1061no—
413C2×Q8—2122no—
414C2×Q8—2124no—
415C2×Q8—2128no—
416C2×Q8—2128no—
417C2×Q8C22×#615712yescomplemented
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—42no—
421C22×C4—531no—
422C22×C4—531no—
423C22×C4—532no—
424C22×C4—532no—
425C22×C4—532no—
426C22×C4—532no—
427C22×C4—532no—
428C22×C4—532no—
429C22×C4—532no—
430C22×C4—531no—
431C22×C4—532no—
432C22×C4—531no—
433C22×C4—531no—
434C22×C4—531no—
435C22×C4—1064no—
436C22×C4—1064no—
437C22×C4—1064no—
438C22×C4—1064no—
439C22×C4—1064no—
440C22×C4—10616no—
441C22×C4—1068no—
442C22×C4—1061no—
443C22×C4—1061no—
444C22×C4—2122no—
445C22×C4—2122no—
446C22×C4—2124no—
447C22×C4—2124no—
448C22×C4—2124no—
449C22×C4—2124no—
450C22×C4—2124no—
451C22×C4—2124no—
452C22×C4—2122no—
453C22×C4—2128no—
454C22×C4—2124no—
455C22×C4—2128no—
456C22×C4—21232no—
457C22×C4—2124no—
458C22×C4C22⋊#615711yescharacteristic
459C22×C4C22⋊#615712yes—
460C22×C4C22×#615711yescharacteristic
461C22×C4C22×#615712yes—
462C2×C8—1064no—
463C2×C8—2124no—
464C2×C8—2128no—
465C4⋊C4—24no—
466C4⋊C4—21no—
467C4⋊C4—532no—
468C4⋊C4—1064no—
469C4⋊C4—1062no—
470C4⋊C4—1062no—
471C4⋊C4—1062no—
472C4⋊C4—1062no—
473C4⋊C4—1061no—
474C4⋊C4—1064no—
475C4⋊C4C22×#615712yescomplemented
476C22⋊C4—24no—
477C22⋊C4—1062no—
478C22⋊C4—1062no—
479C22⋊C4—1062no—
480C22⋊C4—1062no—
481C22⋊C4—1064no—
482C23—22no—
483C23—22no—
484C23—534no—
485C23—534no—
486C23—534no—
487C23—532no—
488C23—538no—
489C23—534no—
490C23—532no—
491C23—534no—
492C23—532no—
493C23—531no—
494C23—531no—
495C23—1064no—
496C23—1064no—
497C23—10616no—
498C23—1064no—
499C23—1064no—
500C23—10616no—
501C23—1062no—
502C23—1062no—
503C23#1313328014yes—
504C23C2×C22⋊#615712yes—
505C23C2×C22⋊#615711yescharacteristic
506Q8—42no—
507Q8—42no—
508Q8—2122no—
509Q8—2122no—
510Q8—2128no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—531no—
520C2×C4—532no—
521C2×C4—531no—
522C2×C4—1064no—
523C2×C4—1064no—
524C2×C4—1064no—
525C2×C4—1064no—
526C2×C4—1062no—
527C2×C4—1062no—
528C2×C4—1068no—
529C2×C4—1062no—
530C2×C4—1062no—
531C2×C4—2122no—
532C2×C4—2122no—
533C2×C4—2121no—
534C2×C4—2121no—
535C2×C4—2121no—
536C2×C4—2121no—
537C2×C4—2128no—
538C2×C4—2128no—
539C2×C4—2122no—
540C2×C4—2122no—
541C2×C4—2124no—
542C2×C4—21232no—
543C2×C4—21216no—
544C2×C4—2124no—
545C2×C4—2122no—
546C2×C4—2122no—
547C2×C4C2×C22⋊#615712yes—
548C2×C4C2×C22⋊#615711yescharacteristic
549C2×C4C23×#615711yescharacteristic
550C8—2124no—
551C22—22no—
552C22—28no—
553C22—22no—
554C22—534no—
555C22—534no—
556C22—5316no—
557C22—534no—
558C22—531no—
559C22—531no—
560C22—532no—
561C22—1068no—
562C22—10616no—
563C22—1068no—
564C22—1061no—
565C22—1061no—
566C22—1064no—
567C22—1064no—
568C22—1061no—
569C22—1061no—
570C22D53⋊#9912yes—
571C22C2×#1313328014yes—
572C22C2×#1313328012yes—
573C22D53⋊#10412yes—
574C22C22×C22⋊#615711yescharacteristic
575C4—22no—
576C4—21no—
577C4—21no—
578C4—42no—
579C4—42no—
580C4—1061no—
581C4—1061no—
582C4—1062no—
583C4—2128no—
584C4—2122no—
585C4—2122no—
586C2—24no—
587C2—538no—
588C2—1061no—
589C2—1061no—
590C2—1062no—
591C2D53⋊#32814yesdirect product factor
592C2C2×D53⋊#9911yescharacteristic
593C2C22×#1313328011yescharacteristic
594C2C2×D53⋊#10411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6157
commutatorC2×C4×C53C23×C4
FrattiniC2×C4C23×#6157
FittingC2×C22⋊Q8×C53C4
socleC23×C53C2×C22⋊C4
prime radicalC24×D53D4
cosocleC2×C4×D53C24
hypercenterC2×C22⋊Q8#6157
hypocenterC53C22×#328
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×#16811477C2semidirect
4. D53⋊#328C2direct (N × H)
5. C2×#16811476C2semidirect
17. #16811477C22semidirect
18. #16811476C22semidirect
19. C22×Q8×D53C4semidirect
22. C2×#13133196C4semidirect
28. C22⋊Q8×D53C4semidirect
31. C2×C4⋊C4×D53C4semidirect
33. C2×C22⋊Q8×C53C4semidirect
50. C22×Dic106C2×C4semidirect
53. C2×Q8×D53C2×C4semidirect
68. #13133197C2×C4semidirect
71. #13133196C2×C4semidirect
78. #13133193C2×C4semidirect
81. C2×C4⋊Dic53C2×C4semidirect
88. C4⋊C4×D53C2×C4semidirect
94. C22×Q8×C53C2×C4semidirect
97. C22⋊Q8×C53C2×C4semidirect
99. C2×C4⋊C4×C53C2×C4semidirect
120. C2×Q8×C53C22×C4semidirect
163. C2×Dic106C22×C4semidirect
169. C4⋊C4×C53C22×C4semidirect
179. C4⋊Dic53C22×C4semidirect
271. C2×D53#328semidirect
296. C2×C53C2×#328semidirect
303. D53C2×#328semidirect
317. C2×C22⋊Q8#6157semidirect
331. C53C22×#328semidirect
338. C22×Q8C2×#6157semidirect
375. C22⋊Q8C2×#6157semidirect
386. C2×C4⋊C4C2×#6157semidirect
417. C2×Q8C22×#6157semidirect
475. C4⋊C4C22×#6157semidirect
591. C2D53⋊#328direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D53⋊(C22⋊C8)2
C22×(C2×#6157)⋊C42
C2×#168114772
D53⋊#3282
C2×#168114762
C2×C22⋊Q8×D532
C22×#32853