Finite Group Databasebeta

← C4⋊C4×C4⋊Dic11 #14675212

Subgroups — C4⋊C4×C4⋊Dic11 #14675212

Order 2816.

1838 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622548C211yesmaximal, characteristic
2C2×C4⋊C4×Dic11C212yesmaximal
3C2×C4×C4⋊Dic11C212yesmaximal
4C2×C4×C4⋊Dic11C211yesmaximal, characteristic
5#13066850C214yesmaximal
6#13066846C212yesmaximal
7#13066845C212yesmaximal
8C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C42×C11C2212yes—
12C22×C42×C11C2211yescharacteristic
13C22×C4⋊Dic11C2212yes—
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4⋊Dic11C2212yes—
16C22×C4⋊Dic11C2212yes—
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4×Dic11C2214yes—
19C22×C4×Dic11C2212yes—
20C4×C11×C4⋊C4C418yescomplemented
21C2×C11×#95C2212yes—
22C2×C11⋊#95C2214yes—
23C2×C11⋊#95C2214yes—
24C2×C11⋊#95C2214yes—
25C2×C11⋊#95C2212yes—
26C4⋊C4×Dic11—28no—
27#10622548C418yescomplemented
28C4×C4⋊Dic11—28no—
29C4×C4⋊Dic11C418yescomplemented
30C23×C4×C11C2312yes—
31C23×C4×C11C2311yescharacteristic
32C23×C4×C11C2312yes—
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×Dic11C2314yes—
36C23×Dic11C2312yes—
37C23×Dic11C2312yes—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4C2×C414yes—
41C2×C11×C4⋊C4C2×C414yes—
42C2×C11×C4⋊C4D414yes—
43C2×C11×C4⋊C4Q814yes—
44C2×C42×C11—24no—
45C2×C42×C11—24no—
46C2×C42×C11C2×C414yes—
47C2×C42×C11C2×C414yes—
48C2×C42×C11C2×C418yes—
49C2×C42×C11C2×C414yes—
50C2×C4⋊Dic11—24no—
51C2×C4⋊Dic11—24no—
52C2×C4⋊Dic11—24no—
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11—22no—
55C2×C4⋊Dic11—24no—
56C2×C4⋊Dic11—42no—
57C2×C4⋊Dic11—42no—
58C2×C4⋊Dic11C2×C414yes—
59C2×C4⋊Dic11C2×C418yes—
60C2×C4⋊Dic11C2×C418yes—
61C2×C4⋊Dic11C2×C418yes—
62C2×C4⋊Dic11C2×C414yes—
63C2×C4⋊Dic11D414yes—
64C2×C4⋊Dic11Q814yes—
65C2×C4×Dic11—24no—
66C2×C4×Dic11—24no—
67C2×C4×Dic11—28no—
68C2×C4×Dic11—28no—
69C2×C4×Dic11—44no—
70C2×C4×Dic11C2×C418yes—
71C11×#95C2×C418yes—
72C11⋊#95—28no—
73C11⋊#95—28no—
74C11⋊#95—44no—
75C11⋊#95C2×C418yes—
76C4⋊C42—111nomaximal, Sylow
77C24×C11C2411yescharacteristic
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11C22×C414yes—
93C22×C4×C11C22×C412yes—
94C22×C4×C11C22×C412yes—
95C22×C4×C11C22×C412yes—
96C22×C4×C11C22×C414yes—
97C22×C4×C11C22×C412yes—
98C22×C4×C11C22×C412yes—
99C22×C4×C11C22×C412yes—
100C22×C4×C11C22×C412yes—
101C22×C4×C11C22×C412yes—
102C22×C4×C11C22×C412yes—
103C22×C4×C11C2×D414yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×Q814yes—
107C22×C4×C11C2×Q812yes—
108C22×C4×C11C2×Q812yes—
109C22×C4×C11#4112yes—
110C22×C4×C11#4112yes—
111C22×C4×C11#4112yes—
112C22×C4×C11#4112yes—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—24no—
116C22×Dic11—24no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—24no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—24no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—24no—
126C22×Dic11—24no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11C22×C414yes—
130C22×Dic11C22×C418yes—
131C22×Dic11C22×C414yes—
132C22×Dic11C2×D414yes—
133C22×Dic11C2×Q814yes—
134C11×C4⋊C4—28no—
135C11×C4⋊C4C4⋊C4116yescomplemented
136C42×C11—216no—
137C42×C11C42116yescomplemented
138C4⋊Dic11—28no—
139C4⋊Dic11—216no—
140C4⋊Dic11—216no—
141C4⋊Dic11—48no—
142C4⋊Dic11C4⋊C4116yesdirect product factor
143C4×Dic11—216no—
144C4×Dic11—416no—
145C2×#384—111no—
146C2×C4×C4⋊C4—111no—
147C2×C4×C4⋊C4—112no—
148C2×C4×C4⋊C4—112no—
149C2×C4×C4⋊C4D1111yescharacteristic
150#1436—114no—
151C4⋊#95—112no—
152C4⋊#95—112no—
153C23×C11C23×C411yescharacteristic
154C23×C11C23×C411yescharacteristic
155C23×C11C23×C411yescharacteristic
156C23×C11C22×D411yescharacteristic
157C23×C11C22×D411yescharacteristic
158C23×C11C22×Q811yescharacteristic
159C23×C11C22×Q811yescharacteristic
160C23×C11C2×#4111yescharacteristic
161C23×C11C2×#4111yescharacteristic
162C23×C11C2×#4111yescharacteristic
163C23×C11C2×#4111yescharacteristic
164C23×C11H(5,𝔽2)11yescharacteristic
165C23×C11H(5,𝔽2)11yescharacteristic
166C23×C112−1+411yescharacteristic
167C23×C112−1+411yescharacteristic
168C2×C4×C11—24no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—24no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11C2×C4214yes—
188C2×C4×C11C2×C4214yes—
189C2×C4×C11C2×C4214yes—
190C2×C4×C11C2×C4⋊C414yes—
191C2×C4×C11C2×C4⋊C418yes—
192C2×C4×C11C2×C4⋊C414yes—
193C2×C4×C11#11714yes—
194C2×C4×C11#11714yes—
195C2×C4×C11C4×D414yes—
196C2×C4×C11C4×D414yes—
197C2×C4×C11C4×D414yes—
198C2×C4×C11C4×D414yes—
199C2×C4×C11C4×Q814yes—
200C2×C4×C11C4×Q814yes—
201C2×C4×C11C4×Q814yes—
202C2×C4×C11C4×Q814yes—
203C2×Dic11—24no—
204C2×Dic11—24no—
205C2×Dic11—24no—
206C2×Dic11—24no—
207C2×Dic11—24no—
208C2×Dic11—24no—
209C2×Dic11—24no—
210C2×Dic11—24no—
211C2×Dic11—28no—
212C2×Dic11—28no—
213C2×Dic11—28no—
214C2×Dic11—24no—
215C2×Dic11—44no—
216C2×Dic11—42no—
217C2×Dic11—44no—
218C2×Dic11—42no—
219C2×Dic11—44no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—44no—
223C2×Dic11C2×C4⋊C418yes—
224C22×C4⋊C4—111no—
225C22×C4⋊C4—111no—
226C22×C4⋊C4—112no—
227C22×C4⋊C4—112no—
228C22×C4⋊C4—112no—
229C22×C4⋊C4C2×D1111yescharacteristic
230C22×C4⋊C4C2×D1111yescharacteristic
231C22×C42—112no—
232C22×C42—114no—
233C22×C42C2×D1112yes—
234C22×C42C2×D1111yescharacteristic
235#384—118no—
236C4×C4⋊C4—118no—
237C4×C4⋊C4—228no—
238C4×C4⋊C4—228no—
239C4×C4⋊C4Dic1118yescomplemented
240C2×#95—112no—
241C2×#95—114no—
242C2×#95—114no—
243C2×#95—114no—
244C2×#95C2×D1112yes—
245C22×C11C22×C4211yescharacteristic
246C22×C11C22×C4⋊C411yescharacteristic
247C22×C11C22×C4⋊C411yescharacteristic
248C22×C11C2×#11711yescharacteristic
249C22×C11C2×#11711yescharacteristic
250C22×C11C2×C4×D411yescharacteristic
251C22×C11C2×C4×D411yescharacteristic
252C22×C11C2×C4×D411yescharacteristic
253C22×C11C2×C4×D411yescharacteristic
254C22×C11C2×C4×Q811yescharacteristic
255C22×C11C2×C4×Q811yescharacteristic
256C22×C11C2×C4×Q811yescharacteristic
257C22×C11C2×C4×Q811yescharacteristic
258C22×C11#51811yescharacteristic
259C22×C11#51911yescharacteristic
260C22×C11#52011yescharacteristic
261C22×C11#52011yescharacteristic
262C22×C11#52011yescharacteristic
263C22×C11#52011yescharacteristic
264C22×C11D4211yescharacteristic
265C22×C11#54711yescharacteristic
266C22×C11#54711yescharacteristic
267C22×C11D4×Q811yescharacteristic
268C22×C11D4×Q811yescharacteristic
269C22×C11#55011yescharacteristic
270C22×C11#55011yescharacteristic
271C22×C11#55411yescharacteristic
272C22×C11#55411yescharacteristic
273C22×C11#55511yescharacteristic
274C22×C11#55611yescharacteristic
275C22×C11#55611yescharacteristic
276C22×C11#55711yescharacteristic
277C22×C11#55711yescharacteristic
278C22×C11Q8211yescharacteristic
279C22×C11#55911yescharacteristic
280C4×C11—28no—
281C4×C11—24no—
282C4×C11—44no—
283C4×C11C4×C4⋊C418yescomplemented
284C4×C11C4×C4⋊C418yescomplemented
285Dic11—28no—
286Dic11—44no—
287Dic11—48no—
288C23×C4—112no—
289C23×C4—114no—
290C23×C4—112no—
291C23×C4C22×D1112yes—
292C23×C4C22×D1112yes—
293C23×C4C22×D1111yescharacteristic
294C23×C4C22×D1111yescharacteristic
295C23×C4C22×D1111yescharacteristic
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—114no—
299C2×C4⋊C4—114no—
300C2×C4⋊C4—114no—
301C2×C4⋊C4—114no—
302C2×C4⋊C4—118no—
303C2×C4⋊C4—118no—
304C2×C4⋊C4—118no—
305C2×C4⋊C4—224no—
306C2×C4⋊C4—224no—
307C2×C4⋊C4—224no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—224no—
311C2×C4⋊C4—442no—
312C2×C4⋊C4—442no—
313C2×C4⋊C4Dic2214yes—
314C2×C4⋊C4D4414yes—
315C2×C4⋊C4C2×Dic1114yes—
316C2×C4⋊C4C2×Dic1114yes—
317C2×C42—24no—
318C2×C42—24no—
319C2×C42—118no—
320C2×C42—224no—
321C2×C42—224no—
322C2×C42—228no—
323C2×C42—228no—
324C2×C42—444no—
325C2×C42C4×D1114yes—
326C2×C42C4×D1114yes—
327C2×C42C2×Dic1118yes—
328C2×C42C2×Dic1114yes—
329#95—118no—
330#95—228no—
331#95—228no—
332#95—444no—
333#95C2×Dic1118yes—
334C2×C11C2×C4×C4⋊C411yescharacteristic
335C2×C11C2×C4×C4⋊C411yescharacteristic
336C2×C11#227411yescharacteristic
337C2×C11D4×C4⋊C411yescharacteristic
338C2×C11D4×C4⋊C411yescharacteristic
339C2×C11Q8×C4⋊C411yescharacteristic
340C2×C11Q8×C4⋊C411yescharacteristic
341C2×C11#235411yescharacteristic
342C2×C11#235411yescharacteristic
343C2×C11#235511yescharacteristic
344C2×C11#235511yescharacteristic
345C2×C11#236511yescharacteristic
346C2×C11#236511yescharacteristic
347C2×C11#236611yescharacteristic
348C2×C11#236911yescharacteristic
349C24C23×D1111yescharacteristic
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—114no—
365C22×C4—114no—
366C22×C4—114no—
367C22×C4—114no—
368C22×C4—118no—
369C22×C4—222no—
370C22×C4—222no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—224no—
375C22×C4—222no—
376C22×C4—224no—
377C22×C4—224no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—224no—
381C22×C4—222no—
382C22×C4—224no—
383C22×C4—224no—
384C22×C4—222no—
385C22×C4C2×Dic2214yes—
386C22×C4C2×Dic2212yes—
387C22×C4C2×C4×D1112yes—
388C22×C4C2×C4×D1112yes—
389C22×C4C2×C4×D1112yes—
390C22×C4C2×C4×D1112yes—
391C22×C4C2×C4×D1112yes—
392C22×C4C2×C4×D1112yes—
393C22×C4C2×D4414yes—
394C22×C4C2×D4412yes—
395C22×C4#433912yes—
396C22×C4#433912yes—
397C22×C4D4×D1112yes—
398C22×C4#434112yes—
399C22×C4Q8×D1112yes—
400C22×C4#434312yes—
401C22×C4C22×Dic1114yes—
402C22×C4C22×Dic1112yes—
403C22×C4C22×Dic1114yes—
404C22×C4C22×Dic1112yes—
405C22×C4C22×Dic1112yes—
406C4⋊C4—28no—
407C4⋊C4—1116no—
408C4⋊C4—2216no—
409C4⋊C4—228no—
410C4⋊C4—2216no—
411C4⋊C4—448no—
412C4⋊C4C4⋊Dic11116yesdirect product factor
413C42—216no—
414C42—2216no—
415C42—4416no—
416C42C4×Dic11116yescomplemented
417C11C4⋊C4211yescharacteristic, complemented, Sylow
418C23C22×Dic2211yescharacteristic
419C23C22×C4×D1111yescharacteristic
420C23C22×C4×D1111yescharacteristic
421C23C22×D4411yescharacteristic
422C23C2×#433911yescharacteristic
423C23C2×#433911yescharacteristic
424C23C2×D4×D1111yescharacteristic
425C23C2×#434111yescharacteristic
426C23C2×Q8×D1111yescharacteristic
427C23C2×#434311yescharacteristic
428C23#6704211yescharacteristic
429C23#6704211yescharacteristic
430C23#6704311yescharacteristic
431C23#6704311yescharacteristic
432C23C23×Dic1111yescharacteristic
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—118no—
453C2×C4—224no—
454C2×C4—224no—
455C2×C4—224no—
456C2×C4—224no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—224no—
460C2×C4—228no—
461C2×C4—224no—
462C2×C4—228no—
463C2×C4—228no—
464C2×C4—224no—
465C2×C4—444no—
466C2×C4—444no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—444no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—444no—
473C2×C4C4×Dic2214yes—
474C2×C4C4×Dic2214yes—
475C2×C4C4×D4414yes—
476C2×C4C4×D4414yes—
477C2×C4#6694014yes—
478C2×C4C4⋊C4×D1114yes—
479C2×C4#6694514yes—
480C2×C4#6694614yes—
481C2×C4C2×C4×Dic1114yes—
482C2×C4C2×C4×Dic1114yes—
483C2×C4C2×C4×Dic1114yes—
484C2×C4C2×C4⋊Dic1118yes—
485C2×C4C2×C4⋊Dic1114yes—
486C2×C4#6697914yes—
487C2×C4D4×Dic1114yes—
488C2×C4Q8×Dic1114yes—
489C22C2×C4×Dic2211yescharacteristic
490C22C2×C4×Dic2211yescharacteristic
491C22C2×C4×D4411yescharacteristic
492C22C2×C4×D4411yescharacteristic
493C22C2×#6694011yescharacteristic
494C22C2×C4⋊C4×D1111yescharacteristic
495C22C2×#6694511yescharacteristic
496C22C2×#6694611yescharacteristic
497C22#1062304711yescharacteristic
498C22#1062305211yescharacteristic
499C22#1062305411yescharacteristic
500C22#1062305411yescharacteristic
501C22D4×Dic2211yescharacteristic
502C22#1062307311yescharacteristic
503C22#1062307411yescharacteristic
504C22D4×D4411yescharacteristic
505C22#1062308211yescharacteristic
506C22#1062308411yescharacteristic
507C22#1062308611yescharacteristic
508C22#1062309411yescharacteristic
509C22Q8×Dic2211yescharacteristic
510C22#1062309811yescharacteristic
511C22#1062310111yescharacteristic
512C22Q8×D4411yescharacteristic
513C22#1062310811yescharacteristic
514C22#1062311011yescharacteristic
515C22#1062311511yescharacteristic
516C22#1062311611yescharacteristic
517C22C22×C4×Dic1111yescharacteristic
518C22C22×C4⋊Dic1111yescharacteristic
519C22C2×#6697911yescharacteristic
520C22C2×D4×Dic1111yescharacteristic
521C22C2×Q8×Dic1111yescharacteristic
522C22#1062335811yescharacteristic
523C22#1062335811yescharacteristic
524C4—24no—
525C4—28no—
526C4—44no—
527C4—228no—
528C4—448no—
529C4—444no—
530C4C4×C4⋊Dic1118yescomplemented
531C4C4⋊C4×Dic1118yescomplemented
532C2C2×C4×C4⋊Dic1111yescharacteristic
533C2C2×C4⋊C4×Dic1111yescharacteristic
534C2#1307097211yescharacteristic
535C2D4×C4⋊Dic1111yescharacteristic
536C2C4⋊C4×D4411yescharacteristic
537C2C4⋊C4×Dic2211yescharacteristic
538C2Q8×C4⋊Dic1111yescharacteristic
539C2#1307156311yescharacteristic
540C2#1307156511yescharacteristic
541C2#1307157111yescharacteristic
542C2#1307157311yescharacteristic
543C2#1307167211yescharacteristic
544C2#1307167411yescharacteristic
545C2#1307168011yescharacteristic
546C2#1307170511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C4×C11×C4⋊C4C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C4⋊C42
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
20. C4×C11×C4⋊C4C4semidirect
27. #10622548C4semidirect
29. C4×C4⋊Dic11C4semidirect
135. C11×C4⋊C4C4⋊C4semidirect
137. C42×C11C42semidirect
142. C4⋊Dic11C4⋊C4direct (N × H)
239. C4×C4⋊C4Dic11semidirect
283. C4×C11C4×C4⋊C4semidirect
284. C4×C11C4×C4⋊C4semidirect
412. C4⋊C4C4⋊Dic11direct (N × H)
416. C42C4×Dic11semidirect
417. C11C4⋊C42semidirect
530. C4C4×C4⋊Dic11semidirect
531. C4C4⋊C4×Dic11semidirect

Maximal subgroups

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

subgroupindex
C2×#106225482
C2×C4⋊C4×Dic112
C2×C4×C4⋊Dic112
#130668502
#130668462
#130668452
C2×C4×C11×C4⋊C42
C4⋊C4211