Finite Group Databasebeta

← C4⋊C4×#4325 #14772177

Subgroups — C4⋊C4×#4325 #14772177

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×#4325C212yesmaximal
2C2×C4×#4325C211yesmaximal, characteristic
3C4⋊C4×D44C211yesmaximal, characteristic
4#13069341C212yesmaximal, complemented
5#13068884C212yesmaximal, complemented
6#13068876C212yesmaximal
7#13068772C211yesmaximal, characteristic, complemented
8#13068621C211yesmaximal, characteristic, complemented
9#13068613C211yesmaximal, characteristic
10C4⋊C4×C11⋊C8C211yesmaximal, characteristic, complemented
11Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2212yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C22×#4325C2211yescharacteristic
15C2×C4⋊C4×D11—21no—
16C2×C4×D44C2212yes—
17C2×C4×D44C2211yescharacteristic
18C11×#389—22no—
19C11×#389C2212yes—
20C11×#384—21no—
21C11×#384C2211yescharacteristic
22C4×C11×C4⋊C4—21no—
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66899C2212yes—
25C2×#66899C2211yescharacteristic
26C4×#4325—28no—
27C4×#4325C418yescomplemented
28#10622600—21no—
29C2×#66873C2212yes—
30C2×#66873C2211yescharacteristic
31C2×#66872C2212yes—
32C2×#66872C2212yes—
33C2×#66872C2211yescharacteristic
34#10622548C2211yescharacteristic
35#10622541C2212yes—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4×C11⋊C8C2212yes—
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622281—22no—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×C4×D11—22no—
47C4×Q8×C11—22no—
48C4×Q8×C11—24no—
49C4×Q8×C11—42no—
50C4×Q8×C11C2×C414yescomplemented
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11—22no—
62C2×C42×C11C2312yes—
63C2×C42×C11C2311yescharacteristic
64C2×#4325C2×C414yes—
65C2×#4325D414yes—
66C2×#4325Q814yes—
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—22no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11C2312yes—
72C2×C4⋊Dic11C2311yescharacteristic
73C2×Dic11⋊C4—22no—
74C22×C11⋊C8C2312yes—
75C22×C11⋊C8C2311yescharacteristic
76C22×C11⋊C8C2311yescharacteristic
77C4⋊C4×D11—44no—
78C4×D44—22no—
79C4×D44—24no—
80C4×D44—42no—
81C4×D44C2×C414yes—
82C11×#95—22no—
83C11×#95D412yes—
84#66899—24no—
85#66899C2×C414yescomplemented
86C11⋊#95—22no—
87#66873—24no—
88#66873C2×C414yes—
89#66872—24no—
90#66872—42no—
91#66872C2×C414yescomplemented
92C4⋊(C11⋊C8)—22no—
93C4×C11⋊C8—24no—
94C4×C11⋊C8C2×C414yescomplemented
95C4⋊C4×SD16—111nomaximal, Sylow
96C23×D11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11C22×C412yes—
101C2×Q8×C11C2×D412yes—
102C2×Q8×C11C2×Q812yes—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—22no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44C22×C412yes—
117C2×D44C2×D412yes—
118C2×D44C2×Q812yes—
119C2×C4×D11—24no—
120C2×C4×D11—44no—
121C2×C4×D11—42no—
122C2×C4×D11—44no—
123C2×C4×D11—42no—
124C2×C4×D11—82no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—44no—
131C11×C4⋊C4—42no—
132C11×C4⋊C4—81no—
133C11×C4⋊C4—82no—
134C11×C4⋊C4SD1614yescomplemented
135C11×C4⋊C4C22×C412yes—
136C42×C11—24no—
137C42×C11—22no—
138C42×C11—22no—
139C42×C11—44no—
140C42×C11C22×C412yes—
141C42×C11#4112yes—
142#4325C4⋊C4116yesdirect product factor
143(C2×D11)⋊C4—24no—
144(C2×D11)⋊C4—44no—
145C4⋊Dic11—22no—
146C4⋊Dic11—21no—
147C4⋊Dic11—22no—
148C4⋊Dic11—42no—
149C4⋊Dic11—81no—
150C4⋊Dic11C22×C412yes—
151Dic11⋊C4—44no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8C22×C412yes—
158C2×C11⋊C8C22×C412yes—
159C2×C11⋊C8C2×D412yes—
160C2×C11⋊C8C2×Q812yes—
161C2×C4×SD16—111no—
162C2×C4×SD16—112no—
163Q8×C4⋊C4D1111yescharacteristic, complemented
164D4×C4⋊C4—111no—
165#1941—112no—
166#1865—112no—
167#1864—112no—
168#1844—111no—
169#1803—111no—
170#1802—111no—
171C8×C4⋊C4—111no—
172C23×C11C22×D411yescharacteristic
173C22×D11—22no—
174C22×D11—22no—
175C22×D11—22no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—41no—
180Q8×C11—22no—
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11C2×C4⋊C414yescomplemented
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11C4×D412yes—
201C2×C4×C11C4×D412yes—
202C2×C4×C11C2×SD1614yes—
203C2×C4×C11C2×SD1612yes—
204C2×C4×C11#13512yes—
205C2×C4×C11C23×C411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×Q811yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11H(5,𝔽2)11yescharacteristic
210C2×C4×C112−1+411yescharacteristic
211C2×Dic11—22no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217D44—22no—
218D44—22no—
219D44—22no—
220D44C2×C4⋊C414yes—
221C4×D11—48no—
222C4×D11—88no—
223C11⋊C8—22no—
224C11⋊C8—42no—
225C11⋊C8C2×C4⋊C414yescomplemented
226C22×SD16—111no—
227C2×C4×Q8C2×D1112yes—
228C2×C4×Q8C2×D1111yescharacteristic
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⋊C8—111no—
238C2×#103—111no—
239C2×#103—112no—
240C2×#102—111no—
241C2×#102—112no—
242C2×C4×C8—111no—
243C2×C4×C8—112no—
244#389—22no—
245#389—112no—
246#389C2×D1112yes—
247#385—222no—
248#384—21no—
249#384—111no—
250#384C2×D1111yescharacteristic
251#380—221no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4C2×D1111yescharacteristic
254#340—112no—
255#340—112no—
256#336—112no—
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—24no—
272C4×C11—22no—
273C4×C11—24no—
274C4×C11—42no—
275C4×C11—42no—
276C4×C11—82no—
277C4×C11C4×SD1614yescomplemented
278C4×C11C22×C4⋊C411yescharacteristic
279C4×C11#52011yescharacteristic
280C4×C11#54711yescharacteristic
281C4×C11#55411yescharacteristic
282Dic11—42no—
283Dic11—82no—
284C22×Q8C22×D1111yescharacteristic
285C22×D4—111no—
286C23×C4—221no—
287C23×C4—222no—
288C2×SD16—114no—
289C2×SD16—114no—
290C2×SD16—114no—
291C22×C8—111no—
292C22×C8—111no—
293C22×C8—112no—
294C4×Q8—22no—
295C4×Q8—24no—
296C4×Q8—42no—
297C4×Q8C4×D1114yescomplemented
298C4×D4—114no—
299C4×D4—224no—
300C4×D4—222no—
301C4×D4—442no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—112no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4—222no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—444no—
313C2×C4⋊C4C22⋊D1111yescharacteristic
314C2×C4⋊C4C22⋊D1111yescharacteristic
315C2×C4⋊C4C22×D1112yes—
316C2×C4⋊C4C22×D1111yescharacteristic
317C2×C22⋊C4—221no—
318C2×C22⋊C4—222no—
319C2×C42—21no—
320C2×C42—22no—
321C2×C42C22×D1112yes—
322C2×C42C22×D1111yescharacteristic
323#106—114no—
324#106—224no—
325#106—442no—
326C4⋊C8—222no—
327#103—114no—
328#103—224no—
329#102—114no—
330#102—224no—
331C4×C8—114no—
332C4×C8—224no—
333#95—22no—
334#95—222no—
335#95C22⋊D1112yes—
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—21no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8C2×C4×D1112yes—
349C2×Q8D4×D1112yes—
350C2×Q8Q8×D1112yes—
351C2×D4—112no—
352C2×D4—112no—
353C2×D4—112no—
354C2×D4—221no—
355C2×D4—221no—
356C2×D4—221no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—221no—
361C22×C4—224no—
362C22×C4—222no—
363C22×C4—444no—
364C22×C4—442no—
365C22×C4—442no—
366C22×C4—444no—
367C22×C4—882no—
368C22×C4C2×C22⋊D1112yes—
369C22×C4C2×C22⋊D1111yescharacteristic
370C22×C4C2×C22⋊D1112yes—
371C22×C4C2×C22⋊D1111yescharacteristic
372C22×C4C23×D1111yescharacteristic
373SD16—1116no—
374C2×C8—112no—
375C2×C8—112no—
376C2×C8—112no—
377C2×C8—112no—
378C2×C8—221no—
379C2×C8—221no—
380C2×C8—222no—
381C2×C8—222no—
382C2×C8—222no—
383C4⋊C4—24no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—44no—
389C4⋊C4—42no—
390C4⋊C4—81no—
391C4⋊C4—82no—
392C4⋊C4—112no—
393C4⋊C4—221no—
394C4⋊C4—222no—
395C4⋊C4—222no—
396C4⋊C4—444no—
397C4⋊C4—442no—
398C4⋊C4—881no—
399C4⋊C4#432514yesdirect product factor
400C4⋊C4C2×C4×D1112yes—
401C22⋊C4—224no—
402C22⋊C4—444no—
403C42—24no—
404C42—22no—
405C42—22no—
406C42—44no—
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×C22⋊D1111yescharacteristic
418Q8—22no—
419Q8—22no—
420Q8—22no—
421Q8C4⋊C4×D1114yescomplemented
422D4—114no—
423D4—222no—
424D4—222no—
425D4—222no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—222no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—448no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—888no—
450C2×C4C4×C22⋊D1112yes—
451C2×C4C4×C22⋊D1112yes—
452C2×C4C2×#432514yes—
453C2×C4C2×#432512yes—
454C2×C4#6700312yes—
455C2×C4C22×C4×D1111yescharacteristic
456C2×C4C2×#433911yescharacteristic
457C2×C4C2×D4×D1111yescharacteristic
458C2×C4#6703711yescharacteristic
459C2×C4C2×Q8×D1111yescharacteristic
460C2×C4#6704011yescharacteristic
461C8—114no—
462C8—222no—
463C8—442no—
464C22—224no—
465C22—442no—
466C22—442no—
467C22—442no—
468C22—442no—
469C22—442no—
470C22—442no—
471C22C2×C4×C22⋊D1111yescharacteristic
472C22D4×C22⋊D1111yescharacteristic
473C22C22×#432511yescharacteristic
474C22Q8×C22⋊D1111yescharacteristic
475C22C2×#6700311yescharacteristic
476C22#1062336711yescharacteristic
477C22#1062336811yescharacteristic
478C4—24no—
479C4—24no—
480C4—22no—
481C4—42no—
482C4—42no—
483C4—82no—
484C4—442no—
485C4—882no—
486C4C4×#432514yescomplemented
487C4C2×C4⋊C4×D1111yescharacteristic
488C4#1062303511yescharacteristic
489C4#1062303811yescharacteristic
490C4#1062304211yescharacteristic
491C2—444no—
492C2C4⋊C4×C22⋊D1111yescharacteristic
493C2C2×C4×#432511yescharacteristic
494C2#1307749711yescharacteristic
495C2D4×#432511yescharacteristic
496C2#1308034611yescharacteristic
497C2Q8×#432511yescharacteristic
498C2#1308148711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingQ8×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenterQ8×C4⋊C4D11
hypocenterC11C4⋊C4×SD16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #13069341C2semidirect
5. #13068884C2semidirect
7. #13068772C2semidirect
8. #13068621C2semidirect
10. C4⋊C4×C11⋊C8C2semidirect
11. Q8×C11×C4⋊C4C2semidirect
27. C4×#4325C4semidirect
50. C4×Q8×C11C2×C4semidirect
85. #66899C2×C4semidirect
91. #66872C2×C4semidirect
94. C4×C11⋊C8C2×C4semidirect
134. C11×C4⋊C4SD16semidirect
142. #4325C4⋊C4direct (N × H)
163. Q8×C4⋊C4D11semidirect
183. Q8×C11C2×C4⋊C4semidirect
225. C11⋊C8C2×C4⋊C4semidirect
277. C4×C11C4×SD16semidirect
297. C4×Q8C4×D11semidirect
399. C4⋊C4#4325direct (N × H)
409. C11C4⋊C4×SD16semidirect
421. Q8C4⋊C4×D11semidirect
486. C4C4×#4325semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43252
C4⋊C4×D442
#130693412
#130688842
#130688762
#130687722
#130686212
#130686132
C4⋊C4×C11⋊C82
Q8×C11×C4⋊C42
C4⋊C4×SD1611