Finite Group Databasebeta

← C4×#16811594 #28318060

Subgroups — C4×#16811594 #28318060

Order 13568.

2246 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811594C212yesmaximal
2C2×C4×#11719936C212yesmaximal, complemented
3#20290442C212yesmaximal, complemented
4#20290441C212yesmaximal, complemented
5C4×#13133274C212yesmaximal, complemented
6C4×C22⋊#88324C212yesmaximal, complemented
7#20290379C212yesmaximal, complemented
8C22×C42×D53C211yesmaximal, characteristic
9C22×#11719936C2214yes—
10#16811594C4116yesdirect product factor
11C2×#13133274C2214yes—
12C2×C22⋊#88324C2214yes—
13C4×#11719936—28no—
14C2×#13133272C2214yescomplemented
15C2×C4×#88324C2214yescomplemented
16#16811489C2214yescomplemented
17#16811489C2214yescomplemented
18C23×C4×D53C411yescharacteristic
19C23×C4×D53C411yescharacteristic
20C23×C4×D53C2211yescharacteristic
21C22×C4×Dic53C411yescharacteristic
22C22×C4×Dic53C2211yescharacteristic
23C22×C4×Dic53C2211yescharacteristic
24C2×C42×D53—28no—
25C2×C42×D53C411yescharacteristic
26C2×C42×D53C411yescharacteristic
27C2×C42×D53C411yescharacteristic
28C2×C42×D53C411yescharacteristic
29C2×C42×D53C2211yescharacteristic
30C2×C42×D53C2211yescharacteristic
31C2×C42×D53C2211yescharacteristic
32C2×C42×D53C2211yescharacteristic
33C22×C42×C53C411yescharacteristic
34C2×#11719936—28no—
35C2×#11719936—28no—
36C2×#11719936C2×C4116yescomplemented
37C22×#88324C2318yes—
38#13133274C2×C4116yescomplemented
39C22⋊#88324C2×C4116yescomplemented
40#13133272—28no—
41C4×#88324—28no—
42C24×D53C2×C411yescharacteristic
43C23×Dic53C2×C411yescharacteristic
44C23×Dic53C2×C411yescharacteristic
45C23×Dic53C2311yescharacteristic
46C22×C4×D53—24no—
47C22×C4×D53—24no—
48C22×C4×D53—24no—
49C22×C4×D53—24no—
50C22×C4×D53—24no—
51C22×C4×D53—24no—
52C22×C4×D53—24no—
53C22×C4×D53—24no—
54C22×C4×D53C2×C411yescharacteristic
55C22×C4×D53C2×C411yescharacteristic
56C22×C4×D53C2×C411yescharacteristic
57C22×C4×D53C2×C411yescharacteristic
58C22×C4×D53C2×C411yescharacteristic
59C22×C4×D53C2×C411yescharacteristic
60C22×C4×D53C2×C418yes—
61C22×C4×D53C2×C411yescharacteristic
62C22×C4×D53C2×C411yescharacteristic
63C22×C4×D53C2×C411yescharacteristic
64C22×C4×D53C2×C411yescharacteristic
65C22×C4×D53C2311yescharacteristic
66C22×C4×D53C2311yescharacteristic
67C2×C4×Dic53—24no—
68C2×C4×Dic53—24no—
69C2×C4×Dic53—24no—
70C2×C4×Dic53C2×C411yescharacteristic
71C2×C4×Dic53C2×C411yescharacteristic
72C2×C4×Dic53C2×C411yescharacteristic
73C2×C4×Dic53C2×C411yescharacteristic
74C2×C4×Dic53C2×C411yescharacteristic
75C2×C4×Dic53C2×C411yescharacteristic
76C2×C4×Dic53C2×C411yescharacteristic
77C2×C4×Dic53C2×C411yescharacteristic
78C2×C4×Dic53C2311yescharacteristic
79C2×C4×Dic53C2311yescharacteristic
80C2×C4×Dic53C2311yescharacteristic
81C2×C4×Dic53C2311yescharacteristic
82C42×D53—24no—
83C42×D53—24no—
84C42×D53—24no—
85C42×D53—24no—
86C42×D53—24no—
87C42×D53—24no—
88C42×D53—24no—
89C42×D53D418yes—
90C23×C4×C53C2×C411yescharacteristic
91C23×C4×C53C2×C411yescharacteristic
92C23×C4×C53C2×C411yescharacteristic
93C2×C42×C53—24no—
94C2×C42×C53C2×C411yescharacteristic
95C2×C42×C53C2×C411yescharacteristic
96C2×C42×C53C2×C411yescharacteristic
97C2×C42×C53C2×C411yescharacteristic
98C24×C53C22×C411yescharacteristic
99C23×D53—22no—
100C23×D53—22no—
101C23×D53—22no—
102C23×D53—22no—
103C23×D53—22no—
104C23×D53—22no—
105C23×D53C4214yes—
106C23×D53C22×C411yescharacteristic
107C23×D53C22×C411yescharacteristic
108C22×C4×C53—22no—
109C22×C4×C53—22no—
110C22×C4×C53—22no—
111C22×C4×C53—22no—
112C22×C4×C53—22no—
113C22×C4×C53—22no—
114C22×C4×C53—22no—
115C22×C4×C53C4214yes—
116C22×C4×C53M1614yescomplemented
117C22×C4×C53C22×C411yescharacteristic
118C22×C4×C53C22×C411yescharacteristic
119C22×C4×C53C22×C411yescharacteristic
120C22×C4×C53C22×C411yescharacteristic
121C22×C4×C53C22×C411yescharacteristic
122C22×C4×C53C22×C411yescharacteristic
123C22×Dic53—22no—
124C22×Dic53—22no—
125C22×Dic53—22no—
126C22×Dic53—22no—
127C22×Dic53—22no—
128C22×Dic53—22no—
129C22×Dic53—22no—
130C22×Dic53M1614yescomplemented
131C22×Dic53C22×C411yescharacteristic
132C22×Dic53C22×C414yes—
133C22×Dic53C22×C411yescharacteristic
134C22×Dic53C22×C411yescharacteristic
135C22×Dic53C22×C411yescharacteristic
136C22×Dic53C22×C411yescharacteristic
137C22×Dic53C2411yescharacteristic
138C2×C4×D53—232no—
139C2×C4×D53—232no—
140C2×C4×D53—22no—
141C2×C4×D53—22no—
142C2×C4×D53—22no—
143C2×C4×D53—22no—
144C2×C4×D53—22no—
145C2×C4×D53—22no—
146C2×C4×D53—22no—
147C2×C4×D53—22no—
148C2×C4×D53—22no—
149C2×C4×D53—22no—
150C2×C4×D53—22no—
151C2×C4×D53—22no—
152C2×C4×D53—22no—
153C2×C4×D53—22no—
154C2×C4×D53—22no—
155C2×C4×D53—22no—
156C2×C4×D53—22no—
157C2×C4×D53—22no—
158C2×C4×D53—22no—
159C2×C4×D53—22no—
160C2×C4×D53—22no—
161C2×C4×D53—22no—
162C2×C4×D53—22no—
163C2×C4×D53—22no—
164C2×C4×D53—22no—
165C2×C4×D53—22no—
166C2×C4×D53—232no—
167C2×C4×D53C4214yes—
168C2×C4×D53C4214yes—
169C2×C4×D53C22⋊C414yes—
170C2×C4×D53C22⋊C414yes—
171C2×C4×D53M1614yescomplemented
172C2×C4×D53M1614yescomplemented
173C2×C4×D53C22×C414yes—
174C2×C4×D53C22×C414yes—
175C2×C4×D53C2×D414yes—
176C2×C4×D53#4114yes—
177C2×#88324—28no—
178C2×#88324—28no—
179C2×#88324C22×C4116yescomplemented
180#11719936—232no—
181C42×C53—22no—
182C42×C53—22no—
183C42×C53—22no—
184C42×C53C22⋊C414yes—
185C4×Dic53—22no—
186C4×Dic53—22no—
187C4×Dic53—22no—
188C4×Dic53—22no—
189C4×Dic53—22no—
190C4×Dic53—22no—
191C4×Dic53—22no—
192C4×Dic53—22no—
193C4×Dic53—22no—
194C4×Dic53C22⋊C414yes—
195C4×Dic53C2×D414yes—
196C4×Dic53C2×D414yes—
197C23×C53—21no—
198C23×C53—21no—
199C23×C53—21no—
200C23×C53—21no—
201C23×C53C2×C4212yes—
202C23×C53C2×M1612yes—
203C23×C53C2×M1612yes—
204C23×C53C23×C411yescharacteristic
205C22×D53—28no—
206C22×D53—28no—
207C22×D53—28no—
208C22×D53—28no—
209C22×D53—21no—
210C22×D53—21no—
211C22×D53—21no—
212C22×D53—21no—
213C22×D53—21no—
214C22×D53—21no—
215C22×D53—21no—
216C22×D53—21no—
217C22×D53—28no—
218C22×D53—28no—
219C22×D53—28no—
220C22×D53C2×C4212yes—
221C22×D53C2×C4212yes—
222C22×D53C2×C22⋊C412yes—
223C22×D53#11712yes—
224C22×D53C2×M1612yes—
225C22×D53C2×M1612yes—
226C2×C4×C53—28no—
227C2×C4×C53—21no—
228C2×C4×C53—21no—
229C2×C4×C53—21no—
230C2×C4×C53—21no—
231C2×C4×C53—21no—
232C2×C4×C53—21no—
233C2×C4×C53—21no—
234C2×C4×C53—21no—
235C2×C4×C53—28no—
236C2×C4×C53—28no—
237C2×C4×C53C2×C4212yes—
238C2×C4×C53C2×C4212yes—
239C2×C4×C53C2×C22⋊C412yes—
240C2×C4×C53C2×C22⋊C412yes—
241C2×C4×C53C2×C22⋊C412yes—
242C2×C4×C53#11712yes—
243C2×C4×C53C2×M1612yes—
244C2×C4×C53C2×M1612yes—
245C2×C4×C53C2×M1612yes—
246C2×C4×C53C2×M1612yes—
247C2×Dic53—28no—
248C2×Dic53—21no—
249C2×Dic53—21no—
250C2×Dic53—21no—
251C2×Dic53—21no—
252C2×Dic53—21no—
253C2×Dic53—21no—
254C2×Dic53—21no—
255C2×Dic53—21no—
256C2×Dic53—28no—
257C2×Dic53—28no—
258C2×Dic53C2×C4212yes—
259C2×Dic53C2×C22⋊C412yes—
260C2×Dic53C2×C22⋊C412yes—
261C2×Dic53C2×M1612yes—
262C2×Dic53C2×M1612yes—
263C2×Dic53C2×M1612yes—
264C2×Dic53C2×M1612yes—
265C2×Dic53C23×C412yes—
266C2×Dic53C22×D412yes—
267C2×Dic53C2×#4112yes—
268C4×D53—28no—
269C4×D53—28no—
270C4×D53—28no—
271C4×D53—28no—
272C4×D53—28no—
273C4×D53—28no—
274C4×D53—28no—
275C4×D53—28no—
276C4×D53—28no—
277C4×D53—28no—
278C4×D53—28no—
279C4×D53C4×D4116yes—
280#88324—216no—
281C4×#407—531nomaximal, Sylow
282C22×C53—22no—
283C22×C53—22no—
284C22×C53—22no—
285C22×C53—22no—
286C22×C53—22no—
287C22×C53—22no—
288C22×C53C4×M1614yescomplemented
289C22×C53C22×C4211yescharacteristic
290C22×C53C22×C22⋊C411yescharacteristic
291C22×C53C2×#11711yescharacteristic
292C22×C53C22×M1611yescharacteristic
293C22×C53C22×M1611yescharacteristic
294C22×C53C22×M1611yescharacteristic
295C22×C53C22×M1611yescharacteristic
296C2×D53—232no—
297C2×D53—22no—
298C2×D53—22no—
299C2×D53—22no—
300C2×D53—22no—
301C2×D53—22no—
302C2×D53—22no—
303C2×D53—22no—
304C2×D53—22no—
305C2×D53—22no—
306C2×D53—22no—
307C2×D53—22no—
308C2×D53—22no—
309C2×D53C4×C22⋊C414yes—
310C2×D53C4×M1614yescomplemented
311C4×C53—22no—
312C4×C53—22no—
313C4×C53—22no—
314C4×C53—22no—
315C4×C53C4×C22⋊C414yes—
316C4×C53#40714yescomplemented
317Dic53—22no—
318Dic53—22no—
319Dic53—22no—
320Dic53—22no—
321Dic53#40714yescomplemented
322Dic53C2×C4×D414yes—
323C23×C42—531no—
324C2×#407—532no—
325C2×C4×M16—532no—
326#1749—532no—
327#1749—532no—
328C4×C22⋊C8—532no—
329C4×C22⋊C8—532no—
330#1728—532no—
331C2×C53—24no—
332C2×C53C2×C4×C22⋊C411yescharacteristic
333C2×C53C2×C4×M1611yescharacteristic
334C2×C53C2×C4×M1611yescharacteristic
335C2×C53C2×#40711yescharacteristic
336C2×C53C2×#40711yescharacteristic
337C2×C53#292011yescharacteristic
338C2×C53#292011yescharacteristic
339D53—24no—
340D53—24no—
341C24×C4—531no—
342C24×C4—531no—
343C24×C4—531no—
344C22×M16—534no—
345C22×C42—531no—
346C22×C42—531no—
347C22×C42—531no—
348C22×C42—531no—
349C22×C42—531no—
350C22×C42—531no—
351C22×C42—531no—
352C22×C42—531no—
353C22×C42—531no—
354C22×C42—531no—
355C22×C42—531no—
356C22×C42—1068no—
357C22×C42#615711yescharacteristic
358#407—5316no—
359C2×C22⋊C8—534no—
360C2×C22⋊C8—534no—
361C4×M16—1068no—
362C2×#97—534no—
363C2×C4×C8—534no—
364#336—534no—
365#336—534no—
366C53C4×#40711yescharacteristic, complemented, Sylow
367C25—531no—
368C23×C4—531no—
369C23×C4—531no—
370C23×C4—531no—
371C23×C4—538no—
372C23×C4—531no—
373C23×C4—531no—
374C23×C4—531no—
375C23×C4—531no—
376C23×C4—531no—
377C23×C4—531no—
378C23×C4—531no—
379C23×C4—531no—
380C23×C4—531no—
381C23×C4—531no—
382C23×C4—531no—
383C23×C4—531no—
384C23×C4—1064no—
385C23×C4—1064no—
386C23×C4—1064no—
387C23×C4—1064no—
388C23×C4—1064no—
389C23×C4—1064no—
390C23×C4—1064no—
391C23×C4—1064no—
392C23×C4C2×#615711yescharacteristic
393C23×C4C2×#615711yescharacteristic
394C23×C4C2×#615711yescharacteristic
395C2×M16—5316no—
396C2×M16—1068no—
397C2×M16—1068no—
398C22×C8—538no—
399C2×C42—24no—
400C2×C42—531no—
401C2×C42—531no—
402C2×C42—531no—
403C2×C42—538no—
404C2×C42—531no—
405C2×C42—531no—
406C2×C42—531no—
407C2×C42—531no—
408C2×C42—531no—
409C2×C42—531no—
410C2×C42—531no—
411C2×C42—531no—
412C2×C42—531no—
413C2×C42—1064no—
414C2×C42—1064no—
415C2×C42—1064no—
416C2×C42—1064no—
417C2×C42—1064no—
418C2×C42—1064no—
419C2×C42—1064no—
420C2×C42—1064no—
421C2×C42—1064no—
422C2×C42—1064no—
423C2×C42C2×#615711yescharacteristic
424C2×C42C2×#615711yescharacteristic
425C2×C42C2×#615711yescharacteristic
426C2×C42C2×#615711yescharacteristic
427C22⋊C8—5316no—
428C22⋊C8—5316no—
429#97—1068no—
430C4×C8—1068no—
431C24—531no—
432C24—531no—
433C24—534no—
434C24—1062no—
435C24—1062no—
436C24—1062no—
437C24—1062no—
438C24—1062no—
439C24—1062no—
440C24C22×#615711yescharacteristic
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—531no—
449C22×C4—531no—
450C22×C4—534no—
451C22×C4—534no—
452C22×C4—534no—
453C22×C4—534no—
454C22×C4—534no—
455C22×C4—531no—
456C22×C4—531no—
457C22×C4—531no—
458C22×C4—531no—
459C22×C4—534no—
460C22×C4—534no—
461C22×C4—534no—
462C22×C4—534no—
463C22×C4—534no—
464C22×C4—534no—
465C22×C4—534no—
466C22×C4—1062no—
467C22×C4—1062no—
468C22×C4—1062no—
469C22×C4—1062no—
470C22×C4—1062no—
471C22×C4—1062no—
472C22×C4—1062no—
473C22×C4—1062no—
474C22×C4—1062no—
475C22×C4—1062no—
476C22×C4—10632no—
477C22×C4—1062no—
478C22×C4—1062no—
479C22×C4—1062no—
480C22×C4—1062no—
481C22×C4—1062no—
482C22×C4—1062no—
483C22×C4—10632no—
484C22×C4—10632no—
485C22×C4—1062no—
486C22×C4—1062no—
487C22×C4—1062no—
488C22×C4—1062no—
489C22×C4—1062no—
490C22×C4—1062no—
491C22×C4—1062no—
492C22×C4—1062no—
493C22×C4—1062no—
494C22×C4—1062no—
495C22×C4—1062no—
496C22×C4—1062no—
497C22×C4—1062no—
498C22×C4—1062no—
499C22×C4—1062no—
500C22×C4—1062no—
501C22×C4—1062no—
502C22×C4#1171993614yescomplemented
503C22×C4C4×#615714yes—
504C22×C4C22×#615711yescharacteristic
505C22×C4C22×#615711yescharacteristic
506C22×C4C22×#615711yescharacteristic
507C22×C4C22×#615711yescharacteristic
508C22×C4C22×#615711yescharacteristic
509C22×C4C22×#615711yescharacteristic
510M16—10632no—
511C2×C8—5316no—
512C2×C8—1068no—
513C2×C8—1068no—
514C42—22no—
515C42—22no—
516C42—22no—
517C42—534no—
518C42—534no—
519C42—534no—
520C42—1062no—
521C42—1062no—
522C42—1062no—
523C42—1062no—
524C42—1062no—
525C42—1062no—
526C42—1062no—
527C42—1062no—
528C42—1062no—
529C42C22⋊#615714yes—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—532no—
535C23—532no—
536C23—532no—
537C23—532no—
538C23—532no—
539C23—532no—
540C23—1068no—
541C23—1068no—
542C23—1068no—
543C23—1068no—
544C23—1068no—
545C23—1068no—
546C23—1068no—
547C23—1061no—
548C23—1061no—
549C23—1061no—
550C23—1061no—
551C23—1061no—
552C23—1061no—
553C23—1061no—
554C23—1061no—
555C23C2×C4×#615712yes—
556C23D53⋊M1612yes—
557C23C2×#1171993612yes—
558C23C23×#615711yescharacteristic
559C2×C4—28no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—28no—
569C2×C4—28no—
570C2×C4—532no—
571C2×C4—532no—
572C2×C4—532no—
573C2×C4—532no—
574C2×C4—532no—
575C2×C4—532no—
576C2×C4—5316no—
577C2×C4—532no—
578C2×C4—532no—
579C2×C4—532no—
580C2×C4—532no—
581C2×C4—1068no—
582C2×C4—1068no—
583C2×C4—1068no—
584C2×C4—1068no—
585C2×C4—1068no—
586C2×C4—1068no—
587C2×C4—1068no—
588C2×C4—1068no—
589C2×C4—1068no—
590C2×C4—1068no—
591C2×C4—1068no—
592C2×C4—1061no—
593C2×C4—1061no—
594C2×C4—1061no—
595C2×C4—1061no—
596C2×C4—1061no—
597C2×C4—1061no—
598C2×C4—1061no—
599C2×C4—1061no—
600C2×C4—1068no—
601C2×C4—1068no—
602C2×C4—1068no—
603C2×C4C2×C4×#615712yes—
604C2×C4C2×C4×#615712yes—
605C2×C4C2×C22⋊#615712yes—
606C2×C4C2×C22⋊#615712yes—
607C2×C4C2×C22⋊#615712yes—
608C2×C4#1313329612yes—
609C2×C4D53⋊M1612yes—
610C2×C4D53⋊M1612yes—
611C2×C4C2×#1171993612yes—
612C2×C4C2×#1171993612yes—
613C8—10616no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—534no—
621C22—534no—
622C22—10632no—
623C22—1062no—
624C22—1062no—
625C22—1062no—
626C22—1062no—
627C22—1062no—
628C22—1062no—
629C22—1062no—
630C22—1062no—
631C22—1062no—
632C22—1062no—
633C22—1062no—
634C22—1062no—
635C22C4×#1171993614yescomplemented
636C22C22×C4×#615711yescharacteristic
637C22C22×C22⋊#615711yescharacteristic
638C22C2×#1313329611yescharacteristic
639C22C2×D53⋊M1611yescharacteristic
640C22C2×D53⋊M1611yescharacteristic
641C22C2×D53⋊M1611yescharacteristic
642C22C22×#1171993611yescharacteristic
643C4—22no—
644C4—22no—
645C4—22no—
646C4—22no—
647C4—534no—
648C4—534no—
649C4—1062no—
650C4—1062no—
651C4—1062no—
652C4—1062no—
653C4C4×C22⋊#615714yes—
654C4#1681159414yesdirect product factor
655C2—24no—
656C2—1064no—
657C2—1064no—
658C2C2×C4×C22⋊#615711yescharacteristic
659C2C4×D53⋊M1611yescharacteristic
660C2C2×C4×#1171993611yescharacteristic
661C2D53⋊#40711yescharacteristic
662C2C2×#1681159411yescharacteristic
663C2#2029139211yescharacteristic
664C2#2029139411yescharacteristic
subgroupG/H
centerC22×C4C22×#6157
commutatorC22×C53C22×C42
FrattiniC23C23×#6157
FittingC22×C42×C53C4
socleC23×C53C23×C4
prime radicalC24×D53C2×C4
cosocleC22×Dic53C24
hypercenterC22×C42#6157
hypocenterC53C4×#407
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11719936C2semidirect
3. #20290442C2semidirect
4. #20290441C2semidirect
5. C4×#13133274C2semidirect
6. C4×C22⋊#88324C2semidirect
7. #20290379C2semidirect
10. #16811594C4direct (N × H)
14. C2×#13133272C22semidirect
15. C2×C4×#88324C22semidirect
16. #16811489C22semidirect
17. #16811489C22semidirect
36. C2×#11719936C2×C4semidirect
38. #13133274C2×C4semidirect
39. C22⋊#88324C2×C4semidirect
116. C22×C4×C53M16semidirect
130. C22×Dic53M16semidirect
171. C2×C4×D53M16semidirect
172. C2×C4×D53M16semidirect
179. C2×#88324C22×C4semidirect
288. C22×C53C4×M16semidirect
310. C2×D53C4×M16semidirect
316. C4×C53#407semidirect
321. Dic53#407semidirect
366. C53C4×#407semidirect
502. C22×C4#11719936semidirect
635. C22C4×#11719936semidirect
654. C4#16811594direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168115942
C2×C4×#117199362
#202904422
#202904412
C4×#131332742
C4×C22⋊#883242
#202903792
C22×C42×D532
C4×#40753