Finite Group Databasebeta

← C4⋊C4×#4314 #14772179

Subgroups — C4⋊C4×#4314 #14772179

Order 2816.

1030 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4314C212yesmaximal
2C2×C4×#4314C211yesmaximal, characteristic
3C4⋊C4×Dic22C211yesmaximal, characteristic, complemented
4C4⋊C4×D44C211yesmaximal, characteristic
5#13069344C212yesmaximal, complemented
6#13068887C212yesmaximal, complemented
7#13068880C212yesmaximal
8#13068773C211yesmaximal, characteristic, complemented
9#13068622C211yesmaximal, characteristic, complemented
10#13068617C211yesmaximal, characteristic
11C8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C22×#4314C2211yescharacteristic
13C2×C4⋊C4×D11—21no—
14C2×C4×D44C2212yes—
15C2×C4×D44C2211yescharacteristic
16C2×C4×Dic22C2212yes—
17C2×C4×Dic22C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C4×C8×C11C2212yes—
20C2×C4×C8×C11C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×#66885C2212yes—
23C2×#66885C2211yescharacteristic
24C2×#66881C2212yes—
25C2×#66881C2212yes—
26C2×#66881C2211yescharacteristic
27C2×#66880C2212yes—
28C2×#66880C2211yescharacteristic
29#10622600—21no—
30#10622589—21no—
31C4⋊C4×Dic11—21no—
32#10622548C2211yescharacteristic
33#10622548C2211yescharacteristic
34#10622541C2212yes—
35#10622541C2212yes—
36C4×#4314—28no—
37C4×#4314C418yescomplemented
38#10622281—22no—
39#10622260—22no—
40C11×#336C2212yes—
41#10622189C2212yes—
42#10622189C2212yes—
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C22×C4×D11—22no—
46C22×Dic22C2311yescharacteristic
47C22×C8×C11C2312yes—
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C42×C11C2312yes—
53C2×C42×C11C2311yescharacteristic
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—22no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2312yes—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×C4×Dic11—21no—
69C2×C4×Dic11—22no—
70C2×#4314C2×C414yes—
71C2×#4314D414yes—
72C2×#4314Q814yes—
73C4⋊C4×D11—44no—
74C4×D44—22no—
75C4×D44—24no—
76C4×D44—42no—
77C4×D44C2×C414yes—
78C4×Dic22—22no—
79C4×Dic22—24no—
80C4×Dic22—42no—
81C4×Dic22C2×C414yescomplemented
82C11×C4⋊C8—22no—
83C4×C8×C11—24no—
84C4×C8×C11C2×C414yescomplemented
85C11×#95D412yes—
86C11⋊#95—22no—
87C11⋊#95—22no—
88#66885—24no—
89#66885C2×C414yes—
90#66881—24no—
91#66881—42no—
92#66881C2×C414yescomplemented
93#66880—24no—
94#66880C2×C414yescomplemented
95C4⋊C4×SD16—111nomaximal, Sylow
96C23×D11—21no—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—22no—
106C22×Dic11—22no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44C22×C412yes—
111C2×D44C2×D412yes—
112C2×D44C2×Q812yes—
113C2×C4×D11—24no—
114C2×C4×D11—44no—
115C2×C4×D11—42no—
116C2×C4×D11—44no—
117C2×C4×D11—42no—
118C2×C4×D11—82no—
119C2×Dic22—21no—
120C2×Dic22—21no—
121C2×Dic22—21no—
122C2×Dic22C22×C412yes—
123C2×Dic22C2×D412yes—
124C2×Dic22C2×Q812yes—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—22no—
130C2×C8×C11C22×C412yes—
131C2×C8×C11C22×C412yes—
132C2×C8×C11C2×D412yes—
133C2×C8×C11C2×Q812yes—
134C11×C4⋊C4—22no—
135C11×C4⋊C4SD1614yescomplemented
136C42×C11—22no—
137C42×C11—22no—
138C42×C11C22×C412yes—
139C42×C11#4112yes—
140(C2×D11)⋊C4—24no—
141(C2×D11)⋊C4—44no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—42no—
149C4⋊Dic11—42no—
150C4⋊Dic11—81no—
151C4⋊Dic11—81no—
152C4⋊Dic11C22×C412yes—
153C4⋊Dic11C22×C412yes—
154Dic11⋊C4—24no—
155Dic11⋊C4—44no—
156Dic11⋊C4—44no—
157Dic11⋊C4—82no—
158C4×Dic11—24no—
159C4×Dic11—44no—
160#4314C4⋊C4116yesdirect product factor
161C2×C4×SD16—111no—
162C2×C4×SD16—112no—
163Q8×C4⋊C4—111no—
164D4×C4⋊C4—111no—
165#1941—112no—
166#1865—112no—
167#1864—112no—
168#1844—111no—
169#1803—111no—
170#1802—111no—
171C8×C4⋊C4D1111yescharacteristic, complemented
172C23×C11C22×D411yescharacteristic
173C22×D11—22no—
174C22×D11—22no—
175C22×D11—22no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—41no—
180C2×C4×C11—22no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11C4×D412yes—
188C2×C4×C11C4×D412yes—
189C2×C4×C11C2×SD1614yes—
190C2×C4×C11C2×SD1612yes—
191C2×C4×C11#13512yes—
192C2×C4×C11C23×C411yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×Q811yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11H(5,𝔽2)11yescharacteristic
197C2×C4×C112−1+411yescharacteristic
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213D44—22no—
214D44—22no—
215D44—22no—
216D44C2×C4⋊C414yes—
217C4×D11—48no—
218C4×D11—88no—
219Dic22—22no—
220Dic22—22no—
221Dic22—22no—
222Dic22C2×C4⋊C414yescomplemented
223C8×C11—22no—
224C8×C11—42no—
225C8×C11C2×C4⋊C414yescomplemented
226C22×SD16—111no—
227C2×C4×Q8—111no—
228C2×C4×Q8—112no—
229C2×C4×D4—111no—
230C2×C4×D4—112no—
231C22×C4⋊C4—221no—
232C4×SD16—118no—
233C4×SD16—228no—
234C2×#106—111no—
235C2×#106—112no—
236C2×#106—112no—
237C2×C4⋊C8C2×D1111yescharacteristic
238C2×#103—111no—
239C2×#103—112no—
240C2×#102—111no—
241C2×#102—112no—
242C2×C4×C8C2×D1112yes—
243C2×C4×C8C2×D1111yescharacteristic
244#389—112no—
245#389—112no—
246#389—222no—
247#385—222no—
248#384—111no—
249#384—111no—
250#384—221no—
251#380—221no—
252C4×C4⋊C4—221no—
253C4×C4⋊C4C2×D1111yescharacteristic
254#340—112no—
255#340—112no—
256#336C2×D1112yes—
257C22×C11C2×C4×D411yescharacteristic
258C22×C11D4211yescharacteristic
259C22×C11D4×Q811yescharacteristic
260C22×C11C22×SD1611yescharacteristic
261C22×C11C2×#13511yescharacteristic
262C22×C11#57711yescharacteristic
263C22×C11#57711yescharacteristic
264C2×D11—24no—
265C2×D11—42no—
266C2×D11—42no—
267C2×D11—42no—
268C2×D11—42no—
269C2×D11—42no—
270C2×D11—42no—
271C4×C11—22no—
272C4×C11—24no—
273C4×C11—42no—
274C4×C11C4×SD1614yescomplemented
275C4×C11C22×C4⋊C411yescharacteristic
276C4×C11#52011yescharacteristic
277C4×C11#54711yescharacteristic
278C4×C11#55411yescharacteristic
279Dic11—24no—
280Dic11—42no—
281Dic11—42no—
282Dic11—82no—
283Dic11—82no—
284C22×Q8—111no—
285C22×D4—111no—
286C23×C4—221no—
287C23×C4—222no—
288C2×SD16—114no—
289C2×SD16—114no—
290C2×SD16—114no—
291C22×C8C22×D1112yes—
292C22×C8C22×D1111yescharacteristic
293C22×C8C22×D1111yescharacteristic
294C4×Q8—114no—
295C4×Q8—224no—
296C4×Q8—222no—
297C4×Q8—442no—
298C4×D4—114no—
299C4×D4—224no—
300C4×D4—222no—
301C4×D4—442no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—112no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—444no—
315C2×C4⋊C4D4411yescharacteristic
316C2×C4⋊C4D4411yescharacteristic
317C2×C22⋊C4—221no—
318C2×C22⋊C4—222no—
319C2×C42—221no—
320C2×C42—222no—
321C2×C42C22×D1112yes—
322C2×C42C22×D1111yescharacteristic
323#106—114no—
324#106—224no—
325#106—442no—
326C4⋊C8—22no—
327#103—114no—
328#103—224no—
329#102—114no—
330#102—224no—
331C4×C8—24no—
332C4×C8C4×D1114yescomplemented
333#95—222no—
334#95—222no—
335#95D4412yes—
336C2×C11D4×C4⋊C411yescharacteristic
337C2×C11C2×C4×SD1611yescharacteristic
338C2×C11#295211yescharacteristic
339C2×C11D4×SD1611yescharacteristic
340C2×C11#328411yescharacteristic
341C2×C11Q8×SD1611yescharacteristic
342C2×C11#338111yescharacteristic
343D11—44no—
344C24—221no—
345C2×Q8—112no—
346C2×Q8—112no—
347C2×Q8—112no—
348C2×Q8—221no—
349C2×Q8—221no—
350C2×Q8—221no—
351C2×D4—112no—
352C2×D4—112no—
353C2×D4—112no—
354C2×D4—221no—
355C2×D4—221no—
356C2×D4—221no—
357C22×C4—221no—
358C22×C4—221no—
359C22×C4—221no—
360C22×C4—224no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—444no—
364C22×C4—442no—
365C22×C4—442no—
366C22×C4—444no—
367C22×C4—882no—
368C22×C4C2×D4412yes—
369C22×C4C2×D4411yescharacteristic
370C22×C4C2×D4412yes—
371C22×C4C2×D4411yescharacteristic
372C22×C4C23×D1111yescharacteristic
373SD16—1116no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8C2×C4×D1112yes—
380C2×C8C2×C4×D1112yes—
381C2×C8D4×D1112yes—
382C2×C8Q8×D1112yes—
383C4⋊C4—22no—
384C4⋊C4—112no—
385C4⋊C4—112no—
386C4⋊C4—224no—
387C4⋊C4—221no—
388C4⋊C4—221no—
389C4⋊C4—222no—
390C4⋊C4—222no—
391C4⋊C4—222no—
392C4⋊C4—222no—
393C4⋊C4—444no—
394C4⋊C4—444no—
395C4⋊C4—442no—
396C4⋊C4—442no—
397C4⋊C4—882no—
398C4⋊C4—881no—
399C4⋊C4—881no—
400C4⋊C4#431414yesdirect product factor
401C22⋊C4—224no—
402C22⋊C4—444no—
403C42—22no—
404C42—22no—
405C42—224no—
406C42—444no—
407C42C2×C4×D1112yes—
408C42#433912yes—
409C11C4⋊C4×SD1611yescharacteristic, complemented, Sylow
410C23—222no—
411C23—222no—
412C23—222no—
413C23—441no—
414C23—441no—
415C23—441no—
416C23—441no—
417C23C22×D4411yescharacteristic
418Q8—114no—
419Q8—222no—
420Q8—222no—
421Q8—222no—
422D4—114no—
423D4—222no—
424D4—222no—
425D4—222no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—222no—
434C2×C4—222no—
435C2×C4—222no—
436C2×C4—222no—
437C2×C4—222no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—448no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—888no—
450C2×C4C4×D4412yes—
451C2×C4C4×D4412yes—
452C2×C4C2×#431414yes—
453C2×C4C2×#431412yes—
454C2×C4#6695712yes—
455C2×C4C22×C4×D1111yescharacteristic
456C2×C4C2×#433911yescharacteristic
457C2×C4C2×D4×D1111yescharacteristic
458C2×C4C2×Q8×D1111yescharacteristic
459C2×C4#6704211yescharacteristic
460C2×C4#6704311yescharacteristic
461C8—22no—
462C8—42no—
463C8C4⋊C4×D1114yescomplemented
464C22—224no—
465C22—442no—
466C22—442no—
467C22—442no—
468C22—442no—
469C22—442no—
470C22—442no—
471C22C2×C4×D4411yescharacteristic
472C22D4×D4411yescharacteristic
473C22Q8×D4411yescharacteristic
474C22C22×#431411yescharacteristic
475C22C2×#6695711yescharacteristic
476C22#1062328211yescharacteristic
477C22#1062328211yescharacteristic
478C4—24no—
479C4—22no—
480C4—42no—
481C4—224no—
482C4—442no—
483C4—442no—
484C4—882no—
485C4—882no—
486C4C4×#431414yescomplemented
487C4C2×C4⋊C4×D1111yescharacteristic
488C4#1062305411yescharacteristic
489C4#1062308211yescharacteristic
490C4#1062311011yescharacteristic
491C2—444no—
492C2C4⋊C4×D4411yescharacteristic
493C2C2×C4×#431411yescharacteristic
494C2#1307750111yescharacteristic
495C2D4×#431411yescharacteristic
496C2#1308034811yescharacteristic
497C2Q8×#431411yescharacteristic
498C2#1308149311yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC8×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenterC8×C4⋊C4D11
hypocenterC11C4⋊C4×SD16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C4⋊C4×Dic22C2semidirect
5. #13069344C2semidirect
6. #13068887C2semidirect
8. #13068773C2semidirect
9. #13068622C2semidirect
11. C8×C11×C4⋊C4C2semidirect
37. C4×#4314C4semidirect
81. C4×Dic22C2×C4semidirect
84. C4×C8×C11C2×C4semidirect
92. #66881C2×C4semidirect
94. #66880C2×C4semidirect
135. C11×C4⋊C4SD16semidirect
160. #4314C4⋊C4direct (N × H)
171. C8×C4⋊C4D11semidirect
222. Dic22C2×C4⋊C4semidirect
225. C8×C11C2×C4⋊C4semidirect
274. C4×C11C4×SD16semidirect
332. C4×C8C4×D11semidirect
400. C4⋊C4#4314direct (N × H)
409. C11C4⋊C4×SD16semidirect
463. C8C4⋊C4×D11semidirect
486. C4C4×#4314semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43142
C4⋊C4×Dic222
C4⋊C4×D442
#130693442
#130688872
#130688802
#130687732
#130686222
#130686172
C8×C11×C4⋊C42
C4⋊C4×SD1611