Finite Group Databasebeta

← C4⋊C4×#4323 #14772164

Subgroups — C4⋊C4×#4323 #14772164

Order 2816.

1134 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4323C212yesmaximal
2C2×C4×#4323C211yesmaximal, characteristic
3C4⋊C4×D44C211yesmaximal, characteristic, complemented
4#13069346C212yesmaximal, complemented
5#13068863C212yesmaximal, complemented
6#13068862C212yesmaximal, complemented
7#13068775C211yesmaximal, characteristic, complemented
8#13068616C211yesmaximal, characteristic, complemented
9#13068613C211yesmaximal, characteristic, complemented
10C4⋊C4×C11⋊C8C211yesmaximal, characteristic, complemented
11D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C22×C11×C4⋊C4—21no—
15C22×#4323C2211yescharacteristic
16C2×C4⋊C4×D11—21no—
17C2×C4×D44C2212yes—
18C2×C4×D44C2211yescharacteristic
19C11×#389C2212yes—
20C11×#385—22no—
21C11×#384C2211yescharacteristic
22C11×#380—21no—
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66896C2212yes—
25C2×#66896C2211yescharacteristic
26C4×#4323—28no—
27C4×#4323C418yescomplemented
28#10622600—21no—
29C2×#66873C2212yes—
30C2×#66873C2211yescharacteristic
31C2×#66871C2212yes—
32C2×#66871C2212yes—
33C2×#66871C2211yescharacteristic
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×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C23×C4×C11—22no—
46C22×D44C2311yescharacteristic
47C22×C4×D11—21no—
48C22×C4×D11—22no—
49C4×D4×C11—24no—
50C4×D4×C11—22no—
51C4×D4×C11—42no—
52C4×D4×C11C2×C414yescomplemented
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—44no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4—22no—
63C2×C42×C11C2312yes—
64C2×C42×C11C2311yescharacteristic
65C2×#4323C2×C414yes—
66C2×#4323D414yes—
67C2×#4323Q814yes—
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×Dic11⋊C4—22no—
75C22×C11⋊C8C2312yes—
76C22×C11⋊C8C2311yescharacteristic
77C22×C11⋊C8C2311yescharacteristic
78C4⋊C4×D11—44no—
79C4×D44—22no—
80C4×D44—24no—
81C4×D44—42no—
82C4×D44C2×C414yescomplemented
83C11×#95—22no—
84C11×#95D412yes—
85#66896—24no—
86#66896C2×C414yescomplemented
87C11⋊#95—22no—
88#66873—24no—
89#66873C2×C414yescomplemented
90#66871—24no—
91#66871—42no—
92#66871C2×C414yescomplemented
93C4⋊(C11⋊C8)—22no—
94C4×C11⋊C8—24no—
95C4×C11⋊C8C2×C414yescomplemented
96C4⋊C4×D8—111nomaximal, Sylow
97C24×C11—21no—
98C23×D11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11C22×C412yes—
103C2×D4×C11C2×D412yes—
104C2×D4×C11C2×Q812yes—
105C22×C4×C11—21no—
106C22×C4×C11—24no—
107C22×C4×C11—22no—
108C22×C4×C11—44no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11—44no—
112C22×C4×C11—82no—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—21no—
119C22×Dic11—22no—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44C22×C412yes—
124C2×D44C2×D412yes—
125C2×D44C2×Q812yes—
126C2×C4×D11—24no—
127C2×C4×D11—44no—
128C2×C4×D11—42no—
129C2×C4×D11—44no—
130C2×C4×D11—42no—
131C2×C4×D11—82no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—44no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4—81no—
139C11×C4⋊C4D814yescomplemented
140C11×C4⋊C4C22×C412yes—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—44no—
143C42×C11—22no—
144C42×C11—22no—
145C42×C11C22×C412yes—
146C42×C11#4112yes—
147#4323C4⋊C4116yesdirect product factor
148(C2×D11)⋊C4—24no—
149(C2×D11)⋊C4—44no—
150C4⋊Dic11—22no—
151C4⋊Dic11—21no—
152C4⋊Dic11—22no—
153C4⋊Dic11—42no—
154C4⋊Dic11—81no—
155C4⋊Dic11C22×C412yes—
156Dic11⋊C4—44no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8C22×C412yes—
163C2×C11⋊C8C22×C412yes—
164C2×C11⋊C8C2×D412yes—
165C2×C11⋊C8C2×Q812yes—
166C2×C4×D8—111no—
167C2×C4×D8—112no—
168D4×C4⋊C4—111no—
169D4×C4⋊C4D1111yescharacteristic, complemented
170#1942—112no—
171#1862—112no—
172#1862—112no—
173#1845—111no—
174#1802—111no—
175#1802—111no—
176C8×C4⋊C4—111no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11C22×D411yescharacteristic
185C22×D11—22no—
186C22×D11—22no—
187C22×D11—22no—
188C22×D11—41no—
189C22×D11—41no—
190C22×D11—41no—
191C22×D11—41no—
192D4×C11—22no—
193D4×C11—22no—
194D4×C11—22no—
195D4×C11C2×C4⋊C414yescomplemented
196C2×C4×C11—22no—
197C2×C4×C11—21no—
198C2×C4×C11—22no—
199C2×C4×C11—21no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—48no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—88no—
211C2×C4×C11C4×D412yes—
212C2×C4×C11C4×D412yes—
213C2×C4×C11C2×D814yes—
214C2×C4×C11C2×D812yes—
215C2×C4×C11#13512yes—
216C2×C4×C11C23×C411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×Q811yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11H(5,𝔽2)11yescharacteristic
221C2×C4×C112−1+411yescharacteristic
222C2×Dic11—22no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228D44—22no—
229D44—22no—
230D44—22no—
231D44C2×C4⋊C414yescomplemented
232C4×D11—48no—
233C4×D11—88no—
234C11⋊C8—22no—
235C11⋊C8—42no—
236C11⋊C8C2×C4⋊C414yescomplemented
237C22×D8—111no—
238C2×C4×D4—111no—
239C2×C4×D4—112no—
240C2×C4×D4C2×D1112yes—
241C2×C4×D4C2×D1111yescharacteristic
242C22×C4⋊C4—21no—
243C22×C4⋊C4—221no—
244C4×D8—118no—
245C4×D8—228no—
246C2×#107—111no—
247C2×#107—112no—
248C2×#107—112no—
249C2×C4⋊C8—111no—
250C2×#102—111no—
251C2×#102—111no—
252C2×#102—112no—
253C2×#102—112no—
254C2×C4×C8—111no—
255C2×C4×C8—112no—
256#389—112no—
257#389C2×D1112yes—
258#385—22no—
259#385—222no—
260#384—111no—
261#384C2×D1111yescharacteristic
262#380—21no—
263#380—221no—
264C4×C4⋊C4C2×D1111yescharacteristic
265#340—112no—
266#340—112no—
267#336—112no—
268C22×C11—24no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—42no—
275C22×C11C2×C4×D411yescharacteristic
276C22×C11D4211yescharacteristic
277C22×C11D4×Q811yescharacteristic
278C22×C11C22×D811yescharacteristic
279C22×C11C2×#13511yescharacteristic
280C22×C11#57611yescharacteristic
281C22×C11#57811yescharacteristic
282C2×D11—24no—
283C2×D11—42no—
284C2×D11—42no—
285C2×D11—42no—
286C2×D11—42no—
287C2×D11—42no—
288C2×D11—42no—
289C4×C11—22no—
290C4×C11—24no—
291C4×C11—42no—
292C4×C11—42no—
293C4×C11—82no—
294C4×C11C4×D814yescomplemented
295C4×C11C22×C4⋊C411yescharacteristic
296C4×C11#52011yescharacteristic
297C4×C11#54711yescharacteristic
298C4×C11#55411yescharacteristic
299Dic11—42no—
300Dic11—82no—
301C22×D4—111no—
302C22×D4C22×D1111yescharacteristic
303C23×C4—21no—
304C23×C4—22no—
305C23×C4—221no—
306C23×C4—222no—
307C2×D8—114no—
308C2×D8—114no—
309C2×D8—114no—
310C22×C8—111no—
311C22×C8—111no—
312C22×C8—112no—
313C4×D4—24no—
314C4×D4—22no—
315C4×D4—42no—
316C4×D4—114no—
317C4×D4—224no—
318C4×D4—222no—
319C4×D4—442no—
320C4×D4C4×D1114yescomplemented
321C2×C4⋊C4—21no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—111no—
326C2×C4⋊C4—112no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4—444no—
331C2×C4⋊C4C22⋊D1111yescharacteristic
332C2×C4⋊C4C22⋊D1111yescharacteristic
333C2×C4⋊C4C22×D1112yes—
334C2×C4⋊C4C22×D1111yescharacteristic
335C2×C22⋊C4—21no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—221no—
338C2×C22⋊C4—222no—
339C2×C42C22×D1112yes—
340C2×C42C22×D1111yescharacteristic
341#107—114no—
342#107—224no—
343#107—442no—
344C4⋊C8—222no—
345#102—114no—
346#102—114no—
347#102—224no—
348#102—224no—
349C4×C8—114no—
350C4×C8—224no—
351#95—22no—
352#95—222no—
353#95C22⋊D1112yes—
354C2×C11—44no—
355C2×C11D4×C4⋊C411yescharacteristic
356C2×C11C2×C4×D811yescharacteristic
357C2×C11#295111yescharacteristic
358C2×C11D4×D811yescharacteristic
359C2×C11#328311yescharacteristic
360C2×C11Q8×D811yescharacteristic
361C2×C11#338011yescharacteristic
362D11—44no—
363C24—21no—
364C24—221no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—112no—
369C2×D4—112no—
370C2×D4—112no—
371C2×D4—221no—
372C2×D4—221no—
373C2×D4—221no—
374C2×D4C2×C4×D1112yes—
375C2×D4D4×D1112yes—
376C2×D4Q8×D1112yes—
377C22×C4—21no—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—44no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—44no—
384C22×C4—82no—
385C22×C4—221no—
386C22×C4—224no—
387C22×C4—222no—
388C22×C4—444no—
389C22×C4—442no—
390C22×C4—442no—
391C22×C4—444no—
392C22×C4—882no—
393C22×C4C2×C22⋊D1112yes—
394C22×C4C2×C22⋊D1111yescharacteristic
395C22×C4C2×C22⋊D1112yes—
396C22×C4C2×C22⋊D1111yescharacteristic
397C22×C4C23×D1111yescharacteristic
398D8—1116no—
399C2×C8—112no—
400C2×C8—112no—
401C2×C8—112no—
402C2×C8—112no—
403C2×C8—221no—
404C2×C8—221no—
405C2×C8—222no—
406C2×C8—222no—
407C2×C8—222no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—44no—
413C4⋊C4—42no—
414C4⋊C4—81no—
415C4⋊C4—112no—
416C4⋊C4—221no—
417C4⋊C4—222no—
418C4⋊C4—222no—
419C4⋊C4—444no—
420C4⋊C4—442no—
421C4⋊C4—881no—
422C4⋊C4#432314yesdirect product factor
423C4⋊C4C2×C4×D1112yes—
424C22⋊C4—24no—
425C22⋊C4—44no—
426C22⋊C4—224no—
427C22⋊C4—444no—
428C42—22no—
429C42—22no—
430C42C2×C4×D1112yes—
431C42#433912yes—
432C11C4⋊C4×D811yescharacteristic, complemented, Sylow
433C23—22no—
434C23—22no—
435C23—22no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—222no—
441C23—222no—
442C23—222no—
443C23—441no—
444C23—441no—
445C23—441no—
446C23—441no—
447C23C22×C22⋊D1111yescharacteristic
448D4—22no—
449D4—22no—
450D4—22no—
451D4—114no—
452D4—222no—
453D4—222no—
454D4—222no—
455D4C4⋊C4×D1114yescomplemented
456C2×C4—22no—
457C2×C4—21no—
458C2×C4—22no—
459C2×C4—21no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—48no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—88no—
471C2×C4—222no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—448no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—888no—
479C2×C4C4×C22⋊D1112yes—
480C2×C4C4×C22⋊D1112yes—
481C2×C4C2×#432314yes—
482C2×C4C2×#432312yes—
483C2×C4#6700312yes—
484C2×C4C22×C4×D1111yescharacteristic
485C2×C4C2×#433911yescharacteristic
486C2×C4C2×D4×D1111yescharacteristic
487C2×C4#6703711yescharacteristic
488C2×C4C2×Q8×D1111yescharacteristic
489C2×C4#6704011yescharacteristic
490C8—114no—
491C8—222no—
492C8—442no—
493C22—24no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—224no—
501C22—442no—
502C22—442no—
503C22—442no—
504C22—442no—
505C22—442no—
506C22—442no—
507C22C2×C4×C22⋊D1111yescharacteristic
508C22C22×#432311yescharacteristic
509C22D4×C22⋊D1111yescharacteristic
510C22Q8×C22⋊D1111yescharacteristic
511C22C2×#6700311yescharacteristic
512C22#1062336611yescharacteristic
513C22#1062336911yescharacteristic
514C4—24no—
515C4—22no—
516C4—42no—
517C4—42no—
518C4—82no—
519C4—442no—
520C4—882no—
521C4C4×#432314yescomplemented
522C4C2×C4⋊C4×D1111yescharacteristic
523C4#1062303511yescharacteristic
524C4#1062303811yescharacteristic
525C4#1062304211yescharacteristic
526C2—44no—
527C2—444no—
528C2C4⋊C4×C22⋊D1111yescharacteristic
529C2C2×C4×#432311yescharacteristic
530C2#1307748911yescharacteristic
531C2D4×#432311yescharacteristic
532C2#1308033411yescharacteristic
533C2Q8×#432311yescharacteristic
534C2#1308147911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
cosocleC22×C4×C11C24
hypercenterD4×C4⋊C4D11
hypocenterC11C4⋊C4×D8
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C4⋊C4×D44C2semidirect
4. #13069346C2semidirect
5. #13068863C2semidirect
6. #13068862C2semidirect
7. #13068775C2semidirect
8. #13068616C2semidirect
9. #13068613C2semidirect
10. C4⋊C4×C11⋊C8C2semidirect
11. D4×C11×C4⋊C4C2semidirect
27. C4×#4323C4semidirect
52. C4×D4×C11C2×C4semidirect
82. C4×D44C2×C4semidirect
86. #66896C2×C4semidirect
89. #66873C2×C4semidirect
92. #66871C2×C4semidirect
95. C4×C11⋊C8C2×C4semidirect
139. C11×C4⋊C4D8semidirect
147. #4323C4⋊C4direct (N × H)
169. D4×C4⋊C4D11semidirect
195. D4×C11C2×C4⋊C4semidirect
231. D44C2×C4⋊C4semidirect
236. C11⋊C8C2×C4⋊C4semidirect
294. C4×C11C4×D8semidirect
320. C4×D4C4×D11semidirect
422. C4⋊C4#4323direct (N × H)
432. C11C4⋊C4×D8semidirect
455. D4C4⋊C4×D11semidirect
521. C4C4×#4323semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43232
C4⋊C4×D442
#130693462
#130688632
#130688622
#130687752
#130686162
#130686132
C4⋊C4×C11⋊C82
D4×C11×C4⋊C42
C4⋊C4×D811