Finite Group Databasebeta

← C4×#11719127 #16796887

Subgroups — C4×#11719127 #16796887

Order 3328.

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×#11719127C212yesmaximal
2C2×C4×#6118C212yesmaximal, complemented
3#13130563C212yesmaximal, complemented
4#13130562C212yesmaximal, complemented
5C4×#88111C212yesmaximal, complemented
6C4×C22⋊#1057C212yesmaximal, complemented
7#13130500C212yesmaximal, complemented
8C22×C42×D13C211yesmaximal, characteristic
9C23×C4×D13C411yescharacteristic
10C23×C4×D13C411yescharacteristic
11C23×C4×D13C2211yescharacteristic
12C22×#6118C2214yes—
13C22×C42×C13C411yescharacteristic
14C22×C4×Dic13C411yescharacteristic
15C22×C4×Dic13C2211yescharacteristic
16C22×C4×Dic13C2211yescharacteristic
17C2×C42×D13—28no—
18C2×C42×D13C411yescharacteristic
19C2×C42×D13C411yescharacteristic
20C2×C42×D13C411yescharacteristic
21C2×C42×D13C411yescharacteristic
22C2×C42×D13C2211yescharacteristic
23C2×C42×D13C2211yescharacteristic
24C2×C42×D13C2211yescharacteristic
25C2×C42×D13C2211yescharacteristic
26C2×C22⋊#1057C2214yes—
27#11719127C4116yesdirect product factor
28C2×#88111C2214yes—
29C2×#88110C2214yescomplemented
30C2×C4×#1057C2214yescomplemented
31C4×#6118—28no—
32#11718290C2214yescomplemented
33#11718290C2214yescomplemented
34C24×D13C2×C411yescharacteristic
35C23×C4×C13C2×C411yescharacteristic
36C23×C4×C13C2×C411yescharacteristic
37C23×C4×C13C2×C411yescharacteristic
38C23×Dic13C2×C411yescharacteristic
39C23×Dic13C2×C411yescharacteristic
40C23×Dic13C2311yescharacteristic
41C22×C4×D13—24no—
42C22×C4×D13—24no—
43C22×C4×D13—24no—
44C22×C4×D13—24no—
45C22×C4×D13—24no—
46C22×C4×D13—24no—
47C22×C4×D13—24no—
48C22×C4×D13—24no—
49C22×C4×D13C2×C411yescharacteristic
50C22×C4×D13C2×C411yescharacteristic
51C22×C4×D13C2×C411yescharacteristic
52C22×C4×D13C2×C411yescharacteristic
53C22×C4×D13C2×C411yescharacteristic
54C22×C4×D13C2×C411yescharacteristic
55C22×C4×D13C2×C418yes—
56C22×C4×D13C2×C411yescharacteristic
57C22×C4×D13C2×C411yescharacteristic
58C22×C4×D13C2×C411yescharacteristic
59C22×C4×D13C2×C411yescharacteristic
60C22×C4×D13C2311yescharacteristic
61C22×C4×D13C2311yescharacteristic
62C22×#1057C2318yes—
63C2×#6118—28no—
64C2×#6118—28no—
65C2×#6118C2×C4116yescomplemented
66C2×C42×C13—24no—
67C2×C42×C13C2×C411yescharacteristic
68C2×C42×C13C2×C411yescharacteristic
69C2×C42×C13C2×C411yescharacteristic
70C2×C42×C13C2×C411yescharacteristic
71C2×C4×Dic13—24no—
72C2×C4×Dic13—24no—
73C2×C4×Dic13—24no—
74C2×C4×Dic13C2×C411yescharacteristic
75C2×C4×Dic13C2×C411yescharacteristic
76C2×C4×Dic13C2×C411yescharacteristic
77C2×C4×Dic13C2×C411yescharacteristic
78C2×C4×Dic13C2×C411yescharacteristic
79C2×C4×Dic13C2×C411yescharacteristic
80C2×C4×Dic13C2×C411yescharacteristic
81C2×C4×Dic13C2×C411yescharacteristic
82C2×C4×Dic13C2311yescharacteristic
83C2×C4×Dic13C2311yescharacteristic
84C2×C4×Dic13C2311yescharacteristic
85C2×C4×Dic13C2311yescharacteristic
86C42×D13—24no—
87C42×D13—24no—
88C42×D13—24no—
89C42×D13—24no—
90C42×D13—24no—
91C42×D13—24no—
92C42×D13—24no—
93C42×D13D418yes—
94C22⋊#1057C2×C4116yescomplemented
95#88111C2×C4116yescomplemented
96#88110—28no—
97C4×#1057—28no—
98C4×#407—131nomaximal, Sylow
99C24×C13C22×C411yescharacteristic
100C23×D13—22no—
101C23×D13—22no—
102C23×D13—22no—
103C23×D13—22no—
104C23×D13—22no—
105C23×D13—22no—
106C23×D13C4214yes—
107C23×D13C22×C411yescharacteristic
108C23×D13C22×C411yescharacteristic
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13C4214yes—
117C22×C4×C13M1614yescomplemented
118C22×C4×C13C22×C411yescharacteristic
119C22×C4×C13C22×C411yescharacteristic
120C22×C4×C13C22×C411yescharacteristic
121C22×C4×C13C22×C411yescharacteristic
122C22×C4×C13C22×C411yescharacteristic
123C22×C4×C13C22×C411yescharacteristic
124C22×Dic13—22no—
125C22×Dic13—22no—
126C22×Dic13—22no—
127C22×Dic13—22no—
128C22×Dic13—22no—
129C22×Dic13—22no—
130C22×Dic13—22no—
131C22×Dic13M1614yescomplemented
132C22×Dic13C22×C411yescharacteristic
133C22×Dic13C22×C414yes—
134C22×Dic13C22×C411yescharacteristic
135C22×Dic13C22×C411yescharacteristic
136C22×Dic13C22×C411yescharacteristic
137C22×Dic13C22×C411yescharacteristic
138C22×Dic13C2411yescharacteristic
139C2×C4×D13—232no—
140C2×C4×D13—232no—
141C2×C4×D13—22no—
142C2×C4×D13—22no—
143C2×C4×D13—22no—
144C2×C4×D13—22no—
145C2×C4×D13—22no—
146C2×C4×D13—22no—
147C2×C4×D13—22no—
148C2×C4×D13—22no—
149C2×C4×D13—22no—
150C2×C4×D13—22no—
151C2×C4×D13—22no—
152C2×C4×D13—22no—
153C2×C4×D13—22no—
154C2×C4×D13—22no—
155C2×C4×D13—22no—
156C2×C4×D13—22no—
157C2×C4×D13—22no—
158C2×C4×D13—22no—
159C2×C4×D13—22no—
160C2×C4×D13—22no—
161C2×C4×D13—22no—
162C2×C4×D13—22no—
163C2×C4×D13—22no—
164C2×C4×D13—22no—
165C2×C4×D13—22no—
166C2×C4×D13—22no—
167C2×C4×D13—232no—
168C2×C4×D13C4214yes—
169C2×C4×D13C4214yes—
170C2×C4×D13C22⋊C414yes—
171C2×C4×D13C22⋊C414yes—
172C2×C4×D13M1614yescomplemented
173C2×C4×D13M1614yescomplemented
174C2×C4×D13C22×C414yes—
175C2×C4×D13C22×C414yes—
176C2×C4×D13C2×D414yes—
177C2×C4×D13#4114yes—
178C2×#1057—28no—
179C2×#1057—28no—
180C2×#1057C22×C4116yescomplemented
181#6118—232no—
182C42×C13—22no—
183C42×C13—22no—
184C42×C13—22no—
185C42×C13C22⋊C414yes—
186C4×Dic13—22no—
187C4×Dic13—22no—
188C4×Dic13—22no—
189C4×Dic13—22no—
190C4×Dic13—22no—
191C4×Dic13—22no—
192C4×Dic13—22no—
193C4×Dic13—22no—
194C4×Dic13—22no—
195C4×Dic13C22⋊C414yes—
196C4×Dic13C2×D414yes—
197C4×Dic13C2×D414yes—
198C23×C42—131no—
199C2×#407—132no—
200C2×C4×M16—132no—
201#1749—132no—
202#1749—132no—
203C4×C22⋊C8—132no—
204C4×C22⋊C8—132no—
205#1728—132no—
206C23×C13—21no—
207C23×C13—21no—
208C23×C13—21no—
209C23×C13—21no—
210C23×C13C2×C4212yes—
211C23×C13C2×M1612yes—
212C23×C13C2×M1612yes—
213C23×C13C23×C411yescharacteristic
214C22×D13—28no—
215C22×D13—28no—
216C22×D13—28no—
217C22×D13—28no—
218C22×D13—21no—
219C22×D13—21no—
220C22×D13—21no—
221C22×D13—21no—
222C22×D13—21no—
223C22×D13—21no—
224C22×D13—21no—
225C22×D13—21no—
226C22×D13—28no—
227C22×D13—28no—
228C22×D13—28no—
229C22×D13C2×C4212yes—
230C22×D13C2×C4212yes—
231C22×D13C2×C22⋊C412yes—
232C22×D13#11712yes—
233C22×D13C2×M1612yes—
234C22×D13C2×M1612yes—
235C2×C4×C13—28no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—28no—
245C2×C4×C13—28no—
246C2×C4×C13C2×C4212yes—
247C2×C4×C13C2×C4212yes—
248C2×C4×C13C2×C22⋊C412yes—
249C2×C4×C13C2×C22⋊C412yes—
250C2×C4×C13C2×C22⋊C412yes—
251C2×C4×C13#11712yes—
252C2×C4×C13C2×M1612yes—
253C2×C4×C13C2×M1612yes—
254C2×C4×C13C2×M1612yes—
255C2×C4×C13C2×M1612yes—
256C2×Dic13—28no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—28no—
266C2×Dic13—28no—
267C2×Dic13C2×C4212yes—
268C2×Dic13C2×C22⋊C412yes—
269C2×Dic13C2×C22⋊C412yes—
270C2×Dic13C2×M1612yes—
271C2×Dic13C2×M1612yes—
272C2×Dic13C2×M1612yes—
273C2×Dic13C2×M1612yes—
274C2×Dic13C23×C412yes—
275C2×Dic13C22×D412yes—
276C2×Dic13C2×#4112yes—
277C4×D13—28no—
278C4×D13—28no—
279C4×D13—28no—
280C4×D13—28no—
281C4×D13—28no—
282C4×D13—28no—
283C4×D13—28no—
284C4×D13—28no—
285C4×D13—28no—
286C4×D13—28no—
287C4×D13—28no—
288C4×D13C4×D4116yes—
289#1057—216no—
290C24×C4—131no—
291C24×C4—131no—
292C24×C4—131no—
293C22×M16—134no—
294C22×C42—131no—
295C22×C42—131no—
296C22×C42—131no—
297C22×C42—131no—
298C22×C42—131no—
299C22×C42—131no—
300C22×C42—131no—
301C22×C42—131no—
302C22×C42—131no—
303C22×C42—131no—
304C22×C42—131no—
305C22×C42—268no—
306C22×C42#26111yescharacteristic
307#407—1316no—
308C2×C22⋊C8—134no—
309C2×C22⋊C8—134no—
310C4×M16—268no—
311C2×#97—134no—
312C2×C4×C8—134no—
313#336—134no—
314#336—134no—
315C22×C13—22no—
316C22×C13—22no—
317C22×C13—22no—
318C22×C13—22no—
319C22×C13—22no—
320C22×C13—22no—
321C22×C13C4×M1614yescomplemented
322C22×C13C22×C4211yescharacteristic
323C22×C13C22×C22⋊C411yescharacteristic
324C22×C13C2×#11711yescharacteristic
325C22×C13C22×M1611yescharacteristic
326C22×C13C22×M1611yescharacteristic
327C22×C13C22×M1611yescharacteristic
328C22×C13C22×M1611yescharacteristic
329C2×D13—232no—
330C2×D13—22no—
331C2×D13—22no—
332C2×D13—22no—
333C2×D13—22no—
334C2×D13—22no—
335C2×D13—22no—
336C2×D13—22no—
337C2×D13—22no—
338C2×D13—22no—
339C2×D13—22no—
340C2×D13—22no—
341C2×D13—22no—
342C2×D13C4×C22⋊C414yes—
343C2×D13C4×M1614yescomplemented
344C4×C13—22no—
345C4×C13—22no—
346C4×C13—22no—
347C4×C13—22no—
348C4×C13C4×C22⋊C414yes—
349C4×C13#40714yescomplemented
350Dic13—22no—
351Dic13—22no—
352Dic13—22no—
353Dic13—22no—
354Dic13#40714yescomplemented
355Dic13C2×C4×D414yes—
356C25—131no—
357C23×C4—131no—
358C23×C4—131no—
359C23×C4—131no—
360C23×C4—138no—
361C23×C4—131no—
362C23×C4—131no—
363C23×C4—131no—
364C23×C4—131no—
365C23×C4—131no—
366C23×C4—131no—
367C23×C4—131no—
368C23×C4—131no—
369C23×C4—131no—
370C23×C4—131no—
371C23×C4—131no—
372C23×C4—131no—
373C23×C4—264no—
374C23×C4—264no—
375C23×C4—264no—
376C23×C4—264no—
377C23×C4—264no—
378C23×C4—264no—
379C23×C4—264no—
380C23×C4—264no—
381C23×C4C2×#26111yescharacteristic
382C23×C4C2×#26111yescharacteristic
383C23×C4C2×#26111yescharacteristic
384C2×M16—1316no—
385C2×M16—268no—
386C2×M16—268no—
387C22×C8—138no—
388C2×C42—24no—
389C2×C42—131no—
390C2×C42—131no—
391C2×C42—131no—
392C2×C42—138no—
393C2×C42—131no—
394C2×C42—131no—
395C2×C42—131no—
396C2×C42—131no—
397C2×C42—131no—
398C2×C42—131no—
399C2×C42—131no—
400C2×C42—131no—
401C2×C42—131no—
402C2×C42—264no—
403C2×C42—264no—
404C2×C42—264no—
405C2×C42—264no—
406C2×C42—264no—
407C2×C42—264no—
408C2×C42—264no—
409C2×C42—264no—
410C2×C42—264no—
411C2×C42—264no—
412C2×C42C2×#26111yescharacteristic
413C2×C42C2×#26111yescharacteristic
414C2×C42C2×#26111yescharacteristic
415C2×C42C2×#26111yescharacteristic
416C22⋊C8—1316no—
417C22⋊C8—1316no—
418#97—268no—
419C4×C8—268no—
420C2×C13—24no—
421C2×C13C2×C4×C22⋊C411yescharacteristic
422C2×C13C2×C4×M1611yescharacteristic
423C2×C13C2×C4×M1611yescharacteristic
424C2×C13C2×#40711yescharacteristic
425C2×C13C2×#40711yescharacteristic
426C2×C13#292011yescharacteristic
427C2×C13#292011yescharacteristic
428D13—24no—
429D13—24no—
430C24—131no—
431C24—131no—
432C24—134no—
433C24—262no—
434C24—262no—
435C24—262no—
436C24—262no—
437C24—262no—
438C24—262no—
439C24C22×#26111yescharacteristic
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—131no—
448C22×C4—131no—
449C22×C4—134no—
450C22×C4—134no—
451C22×C4—134no—
452C22×C4—134no—
453C22×C4—134no—
454C22×C4—131no—
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—131no—
458C22×C4—134no—
459C22×C4—134no—
460C22×C4—134no—
461C22×C4—134no—
462C22×C4—134no—
463C22×C4—134no—
464C22×C4—134no—
465C22×C4—262no—
466C22×C4—262no—
467C22×C4—262no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—2632no—
476C22×C4—262no—
477C22×C4—262no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—2632no—
483C22×C4—2632no—
484C22×C4—262no—
485C22×C4—262no—
486C22×C4—262no—
487C22×C4—262no—
488C22×C4—262no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4—262no—
492C22×C4—262no—
493C22×C4—262no—
494C22×C4—262no—
495C22×C4—262no—
496C22×C4—262no—
497C22×C4—262no—
498C22×C4—262no—
499C22×C4—262no—
500C22×C4—262no—
501C22×C4#611814yescomplemented
502C22×C4C4×#26114yes—
503C22×C4C22×#26111yescharacteristic
504C22×C4C22×#26111yescharacteristic
505C22×C4C22×#26111yescharacteristic
506C22×C4C22×#26111yescharacteristic
507C22×C4C22×#26111yescharacteristic
508C22×C4C22×#26111yescharacteristic
509M16—2632no—
510C2×C8—1316no—
511C2×C8—268no—
512C2×C8—268no—
513C42—22no—
514C42—22no—
515C42—22no—
516C42—134no—
517C42—134no—
518C42—134no—
519C42—262no—
520C42—262no—
521C42—262no—
522C42—262no—
523C42—262no—
524C42—262no—
525C42—262no—
526C42—262no—
527C42—262no—
528C42C22⋊#26114yes—
529C13C4×#40711yescharacteristic, complemented, Sylow
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—132no—
535C23—132no—
536C23—132no—
537C23—132no—
538C23—132no—
539C23—132no—
540C23—268no—
541C23—268no—
542C23—268no—
543C23—268no—
544C23—268no—
545C23—268no—
546C23—268no—
547C23—261no—
548C23—261no—
549C23—261no—
550C23—261no—
551C23—261no—
552C23—261no—
553C23—261no—
554C23—261no—
555C23C2×#611812yes—
556C23D13⋊M1612yes—
557C23C2×C4×#26112yes—
558C23C23×#26111yescharacteristic
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—132no—
571C2×C4—132no—
572C2×C4—132no—
573C2×C4—132no—
574C2×C4—132no—
575C2×C4—132no—
576C2×C4—1316no—
577C2×C4—132no—
578C2×C4—132no—
579C2×C4—132no—
580C2×C4—132no—
581C2×C4—268no—
582C2×C4—268no—
583C2×C4—268no—
584C2×C4—268no—
585C2×C4—268no—
586C2×C4—268no—
587C2×C4—268no—
588C2×C4—268no—
589C2×C4—268no—
590C2×C4—268no—
591C2×C4—268no—
592C2×C4—261no—
593C2×C4—261no—
594C2×C4—261no—
595C2×C4—261no—
596C2×C4—261no—
597C2×C4—261no—
598C2×C4—261no—
599C2×C4—261no—
600C2×C4—268no—
601C2×C4—268no—
602C2×C4—268no—
603C2×C4C2×#611812yes—
604C2×C4C2×#611812yes—
605C2×C4D13⋊M1612yes—
606C2×C4D13⋊M1612yes—
607C2×C4C2×C4×#26112yes—
608C2×C4C2×C4×#26112yes—
609C2×C4#8823712yes—
610C2×C4C2×C22⋊#26112yes—
611C2×C4C2×C22⋊#26112yes—
612C2×C4C2×C22⋊#26112yes—
613C8—2616no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—134no—
621C22—134no—
622C22—2632no—
623C22—262no—
624C22—262no—
625C22—262no—
626C22—262no—
627C22—262no—
628C22—262no—
629C22—262no—
630C22—262no—
631C22—262no—
632C22—262no—
633C22—262no—
634C22—262no—
635C22C4×#611814yescomplemented
636C22C22×#611811yescharacteristic
637C22C2×D13⋊M1611yescharacteristic
638C22C2×D13⋊M1611yescharacteristic
639C22C2×D13⋊M1611yescharacteristic
640C22C22×C4×#26111yescharacteristic
641C22C2×#8823711yescharacteristic
642C22C22×C22⋊#26111yescharacteristic
643C4—22no—
644C4—22no—
645C4—22no—
646C4—22no—
647C4—134no—
648C4—134no—
649C4—262no—
650C4—262no—
651C4—262no—
652C4—262no—
653C4#1171912714yesdirect product factor
654C4C4×C22⋊#26114yes—
655C2—24no—
656C2—264no—
657C2—264no—
658C2C2×C4×C22⋊#26111yescharacteristic
659C2C4×D13⋊M1611yescharacteristic
660C2C2×C4×#611811yescharacteristic
661C2D13⋊#40711yescharacteristic
662C2C2×#1171912711yescharacteristic
663C2#1313151311yescharacteristic
664C2#1313151511yescharacteristic
subgroupG/H
centerC22×C4C22×#261
commutatorC22×C13C22×C42
FrattiniC23C23×#261
FittingC22×C42×C13C4
socleC23×C13C23×C4
prime radicalC24×D13C2×C4
cosocleC22×Dic13C24
hypercenterC22×C42#261
hypocenterC13C4×#407
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6118C2semidirect
3. #13130563C2semidirect
4. #13130562C2semidirect
5. C4×#88111C2semidirect
6. C4×C22⋊#1057C2semidirect
7. #13130500C2semidirect
27. #11719127C4direct (N × H)
29. C2×#88110C22semidirect
30. C2×C4×#1057C22semidirect
32. #11718290C22semidirect
33. #11718290C22semidirect
65. C2×#6118C2×C4semidirect
94. C22⋊#1057C2×C4semidirect
95. #88111C2×C4semidirect
117. C22×C4×C13M16semidirect
131. C22×Dic13M16semidirect
172. C2×C4×D13M16semidirect
173. C2×C4×D13M16semidirect
180. C2×#1057C22×C4semidirect
321. C22×C13C4×M16semidirect
343. C2×D13C4×M16semidirect
349. C4×C13#407semidirect
354. Dic13#407semidirect
501. C22×C4#6118semidirect
529. C13C4×#407semidirect
635. C22C4×#6118semidirect
653. C4#11719127direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191272
C2×C4×#61182
#131305632
#131305622
C4×#881112
C4×C22⋊#10572
#131305002
C22×C42×D132
C4×#40713