Finite Group Databasebeta

← C22×#10622645 #15620485

Subgroups — C22×#10622645 #15620485

Order 2816.

7014 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67037C211yesmaximal, characteristic, complemented
2C22×#67006C212yesmaximal, complemented
3C2×#10622645C2124yesmaximal, direct product factor
4C22×#66898C211yesmaximal, characteristic, complemented
5C22×#66870C212yesmaximal, complemented
6C22×C11×#120C211yesmaximal, characteristic, complemented
7C26×C11C2211yescharacteristic, complemented
8C23×D4×C11—21no—
9C23×D4×C11C2211yescharacteristic
10C23×C22⋊D11—21no—
11C23×C22⋊D11—22no—
12C23×C22⋊D11C2212yes—
13C2×#67037—26no—
14C2×#67037—212no—
15C2×#67037C22112yescomplemented
16C22×#4341—22no—
17C22×D4×D11—22no—
18C22×#4339—21no—
19C2×C11×#120—26no—
20C2×C11×#120C22112yescomplemented
21C22×C11×C22⋊C4—21no—
22C22×C11×C22⋊C4C2211yescharacteristic, complemented
23C2×#67006—212no—
24C2×#67006C22124yescomplemented
25C22×C22⋊Dic11—22no—
26C22×C22⋊Dic11C2212yescomplemented
27C2×#66898C22112yescomplemented
28#10622645C22164yesdirect product factor
29C2×#66870C22124yescomplemented
30C25×C11—22no—
31C25×C11—21no—
32C25×C11—26no—
33C25×C11—23no—
34C25×C11—48no—
35C25×C11D411yescharacteristic, complemented
36C25×C11C2311yescharacteristic
37C25×C11C2316yescomplemented
38C24×D11—21no—
39C24×D11D412yescomplemented
40C22×D4×C11—22no—
41C22×D4×C11—26no—
42C22×D4×C11—212no—
43C22×D4×C11—48no—
44C22×D4×C11D416yescomplemented
45C22×D4×C11C2316yes—
46C23×C4×C11—21no—
47C23×C4×C11D411yescharacteristic, complemented
48C22×C22⋊D11—22no—
49C22×C22⋊D11—212no—
50C22×C22⋊D11—22no—
51C22×C22⋊D11—22no—
52C22×C22⋊D11—26no—
53C22×C22⋊D11—26no—
54C22×C22⋊D11—212no—
55C22×C22⋊D11—224no—
56C22×C22⋊D11—416no—
57C22×C22⋊D11D4112yescomplemented
58C22×C22⋊D11C23112yes—
59C23×Dic11—21no—
60C23×Dic11—22no—
61C23×Dic11D412yescomplemented
62#67037—248no—
63#67037—224no—
64#67037—248no—
65#67037C23116yescomplemented
66C2×#4341—224no—
67C2×#4341—224no—
68C2×D4×D11—224no—
69C2×D4×D11—224no—
70C2×#4339—212no—
71C2×#4339—212no—
72C22×D44—21no—
73C22×C4×D11—22no—
74C22×Dic22—21no—
75C11×#120—224no—
76C11×#120C23116yescomplemented
77C2×C11×C22⋊C4—23no—
78C2×C11×C22⋊C4—212no—
79C2×C11×C22⋊C4C2316yescomplemented
80#67006—248no—
81#67006C23132yescomplemented
82C2×C22⋊Dic11—26no—
83C2×C22⋊Dic11—224no—
84C2×C22⋊Dic11C23112yescomplemented
85#66898C23116yescomplemented
86#66870C23132yescomplemented
87C22×B(4,𝔽2)—111nomaximal, Sylow
88C24×C11—216no—
89C24×C11—28no—
90C24×C11—21no—
91C24×C11—212no—
92C24×C11—26no—
93C24×C11—23no—
94C24×C11—212no—
95C24×C11—26no—
96C24×C11—44no—
97C24×C11—424no—
98C24×C11—48no—
99C24×C11—44no—
100C24×C11—448no—
101C24×C11—424no—
102C24×C11—44no—
103C24×C11—46no—
104C24×C11—43no—
105C24×C11—46no—
106C24×C11—41no—
107C24×C11C2×D412yes—
108C24×C11C2×D411yescharacteristic
109C24×C11C2×D416yes—
110C24×C11C2×D413yes—
111C24×C11C2×D416yescomplemented
112C24×C11C2413yes—
113C24×C11C2414yescomplemented
114C23×D11—22no—
115C23×D11—212no—
116C23×D11—26no—
117C23×D11—48no—
118C23×D11—84no—
119C23×D11C2×D4112yescomplemented
120C2×D4×C11—212no—
121C2×D4×C11—212no—
122C2×D4×C11—212no—
123C2×D4×C11—212no—
124C2×D4×C11—216no—
125C2×D4×C11—448no—
126C2×D4×C11C2×D4112yescomplemented
127C2×D4×C11C2414yes—
128C22×C4×C11—21no—
129C22×C4×C11—23no—
130C22×C4×C11—26no—
131C22×C4×C11—44no—
132C22×C4×C11C2×D416yescomplemented
133C2×C22⋊D11—224no—
134C2×C22⋊D11—248no—
135C2×C22⋊D11—212no—
136C2×C22⋊D11—212no—
137C2×C22⋊D11—224no—
138C2×C22⋊D11—212no—
139C2×C22⋊D11—212no—
140C2×C22⋊D11—212no—
141C2×C22⋊D11—212no—
142C2×C22⋊D11—216no—
143C2×C22⋊D11—232no—
144C2×C22⋊D11—496no—
145C2×C22⋊D11C2×D4124yescomplemented
146C2×C22⋊D11C2418yes—
147C22×Dic11—212no—
148C22×Dic11—22no—
149C22×Dic11—26no—
150C22×Dic11—212no—
151C22×Dic11—48no—
152C22×Dic11C2×D4112yescomplemented
153#4341—296no—
154#4341—232no—
155D4×D11—296no—
156D4×D11—232no—
157#4339—248no—
158#4339—216no—
159C2×D44—212no—
160C2×C4×D11—224no—
161C2×Dic22—212no—
162C11×C22⋊C4—26no—
163C11×C22⋊C4—216no—
164C11×C22⋊C4C2414yescomplemented
165C22⋊Dic11—232no—
166C22⋊Dic11—212no—
167C22⋊Dic11C2418yescomplemented
168C22×H(5,𝔽2)—111no—
169C22×#120—112no—
170C22×#120D1111yescharacteristic, complemented
171C2×B(4,𝔽2)—1124no—
172C22×#99—111no—
173C22×#99—112no—
174C23×C11—28no—
175C23×C11—24no—
176C23×C11—248no—
177C23×C11—224no—
178C23×C11—26no—
179C23×C11—28no—
180C23×C11—24no—
181C23×C11—26no—
182C23×C11—412no—
183C23×C11—46no—
184C23×C11—46no—
185C23×C11—48no—
186C23×C11—412no—
187C23×C11—424no—
188C23×C11—448no—
189C23×C11—424no—
190C23×C11—424no—
191C23×C11—448no—
192C23×C11—412no—
193C23×C11—448no—
194C23×C11—46no—
195C23×C11—412no—
196C23×C11—46no—
197C23×C11—44no—
198C23×C11—48no—
199C23×C11—86no—
200C23×C11#12016yes—
201C23×C11#12013yes—
202C23×C11#12016yes—
203C23×C11#12011yescharacteristic
204C23×C11C22×D416yes—
205C23×C11C22×D416yes—
206C23×C11C22×D413yes—
207C23×C11C22×D413yes—
208C23×C11C22×D414yescomplemented
209C23×C11C2511yescharacteristic
210C22×D11—212no—
211C22×D11—216no—
212C22×D11—212no—
213C22×D11—48no—
214C22×D11—424no—
215C22×D11—812no—
216C22×D11—824no—
217C22×D11C22×D418yescomplemented
218D4×C11—224no—
219D4×C11—28no—
220D4×C11—432no—
221C2×C4×C11—26no—
222C2×C4×C11—26no—
223C2×C4×C11—24no—
224C2×C4×C11—412no—
225C2×C4×C11C22×D414yescomplemented
226C22⋊D11—232no—
227C22⋊D11—224no—
228C22⋊D11—224no—
229C22⋊D11—28no—
230C22⋊D11—28no—
231C22⋊D11—464no—
232C2×Dic11—216no—
233C2×Dic11—212no—
234C2×Dic11—212no—
235C2×Dic11—28no—
236C2×Dic11—424no—
237C2×Dic11C22×D418yescomplemented
238D44—216no—
239C4×D11—232no—
240Dic22—216no—
241C26C2×D1111yescharacteristic, complemented
242C2×H(5,𝔽2)—1112no—
243C2×H(5,𝔽2)—2212no—
244C2×H(5,𝔽2)—226no—
245C22×#41—222no—
246C22×#41—221no—
247C23×D4—21no—
248C23×D4—112no—
249C23×D4—222no—
250C23×D4—221no—
251C23×D4—222no—
252C23×D4C2×D1111yescharacteristic
253C2×#120—26no—
254C2×#120—1124no—
255C2×#120—2212no—
256C2×#120C2×D11112yescomplemented
257C22×C22⋊C4—21no—
258C22×C22⋊C4—112no—
259C22×C22⋊C4—222no—
260C22×C22⋊C4C2×D1111yescharacteristic, complemented
261B(4,𝔽2)—1164no—
262C2×#99—1112no—
263C2×#99—1124no—
264C22×C11—26no—
265C22×C11—212no—
266C22×C11—212no—
267C22×C11—26no—
268C22×C11—28no—
269C22×C11—216no—
270C22×C11—24no—
271C22×C11—46no—
272C22×C11—46no—
273C22×C11—43no—
274C22×C11—41no—
275C22×C11—44no—
276C22×C11—48no—
277C22×C11—44no—
278C22×C11—448no—
279C22×C11—424no—
280C22×C11—44no—
281C22×C11—412no—
282C22×C11—424no—
283C22×C11—86no—
284C22×C11B(4,𝔽2)14yescomplemented
285C22×C11C2×#12013yes—
286C22×C11C2×#12016yes—
287C22×C11C2×#12013yes—
288C22×C11C23×D412yes—
289C22×C11C23×D411yescharacteristic
290C2×D11—28no—
291C2×D11—424no—
292C2×D11—48no—
293C2×D11—812no—
294C2×D11—816no—
295C4×C11—24no—
296C4×C11—44no—
297Dic11—28no—
298Dic11—48no—
299C25—22no—
300C25—21no—
301C25—26no—
302C25—23no—
303C25—48no—
304C25—112no—
305C25—221no—
306C25C22⋊D1111yescharacteristic, complemented
307C25C22×D1111yescharacteristic
308C25C22×D1116yescomplemented
309H(5,𝔽2)—1116no—
310H(5,𝔽2)—2248no—
311H(5,𝔽2)—2248no—
312H(5,𝔽2)—2224no—
313C2×#41—2212no—
314C2×#41—2224no—
315C2×#41—2224no—
316C2×#41—2212no—
317C22×Q8—221no—
318C22×D4—22no—
319C22×D4—26no—
320C22×D4—212no—
321C22×D4—48no—
322C22×D4—1112no—
323C22×D4—1112no—
324C22×D4—221no—
325C22×D4—2224no—
326C22×D4—2224no—
327C22×D4—222no—
328C22×D4—2212no—
329C22×D4—222no—
330C22×D4—226no—
331C22×D4—222no—
332C22×D4—226no—
333C22×D4—2212no—
334C22×D4—2224no—
335C22×D4—4416no—
336C22×D4C22⋊D1116yescomplemented
337C22×D4C22×D1116yes—
338C23×C4—21no—
339C23×C4—112no—
340C23×C4—222no—
341C23×C4—221no—
342C23×C4—222no—
343C23×C4C22⋊D1111yescharacteristic, complemented
344#120—224no—
345#120—1132no—
346#120—2248no—
347#120C22×D11116yescomplemented
348C2×C22⋊C4—23no—
349C2×C22⋊C4—212no—
350C2×C22⋊C4—1112no—
351C2×C22⋊C4—2224no—
352C2×C22⋊C4—226no—
353C2×C22⋊C4C22×D1116yescomplemented
354#99—1116no—
355#99—1132no—
356C2×C11—22no—
357C2×C11—21no—
358C2×C11—26no—
359C2×C11—23no—
360C2×C11—44no—
361C2×C11—48no—
362C2×C11C2×B(4,𝔽2)16yescomplemented
363C2×C11C22×#12011yescharacteristic
364D11—48no—
365C24—28no—
366C24—216no—
367C24—21no—
368C24—212no—
369C24—26no—
370C24—23no—
371C24—212no—
372C24—26no—
373C24—44no—
374C24—424no—
375C24—44no—
376C24—48no—
377C24—424no—
378C24—448no—
379C24—44no—
380C24—43no—
381C24—46no—
382C24—46no—
383C24—41no—
384C24—1112no—
385C24—2212no—
386C24—222no—
387C24—226no—
388C24—448no—
389C24—884no—
390C24D4×D1112yes—
391C24D4×D1116yes—
392C24C2×C22⋊D1111yescharacteristic
393C24C2×C22⋊D1113yes—
394C24C2×C22⋊D1116yescomplemented
395C24C23×D1113yes—
396C24C23×D1114yescomplemented
397#41—2248no—
398#41—2232no—
399#41—2296no—
400#41—2216no—
401C2×Q8—2212no—
402C2×D4—212no—
403C2×D4—212no—
404C2×D4—212no—
405C2×D4—212no—
406C2×D4—216no—
407C2×D4—448no—
408C2×D4—1124no—
409C2×D4—118no—
410C2×D4—2212no—
411C2×D4—2232no—
412C2×D4—2296no—
413C2×D4—2224no—
414C2×D4—2248no—
415C2×D4—2212no—
416C2×D4—2212no—
417C2×D4—2224no—
418C2×D4—2212no—
419C2×D4—2212no—
420C2×D4—2212no—
421C2×D4—2212no—
422C2×D4—2216no—
423C2×D4—2232no—
424C2×D4—4496no—
425C2×D4C2×C22⋊D11112yescomplemented
426C2×D4C23×D1114yes—
427C22×C4—23no—
428C22×C4—21no—
429C22×C4—26no—
430C22×C4—44no—
431C22×C4—1112no—
432C22×C4—2224no—
433C22×C4—2212no—
434C22×C4—226no—
435C22×C4—222no—
436C22×C4—2212no—
437C22×C4—448no—
438C22×C4C2×C22⋊D1116yescomplemented
439C22⋊C4—26no—
440C22⋊C4—216no—
441C22⋊C4—118no—
442C22⋊C4—2232no—
443C22⋊C4—2212no—
444C22⋊C4C23×D1114yescomplemented
445C11C22×B(4,𝔽2)11yescharacteristic, complemented, Sylow
446C23—24no—
447C23—28no—
448C23—224no—
449C23—248no—
450C23—26no—
451C23—28no—
452C23—24no—
453C23—26no—
454C23—412no—
455C23—46no—
456C23—46no—
457C23—48no—
458C23—412no—
459C23—424no—
460C23—424no—
461C23—448no—
462C23—424no—
463C23—448no—
464C23—412no—
465C23—448no—
466C23—46no—
467C23—412no—
468C23—46no—
469C23—48no—
470C23—44no—
471C23—86no—
472C23—118no—
473C23—2216no—
474C23—2212no—
475C23—2212no—
476C23—4424no—
477C23—448no—
478C23—8812no—
479C23—8824no—
480C23#6699013yes—
481C23#6699016yes—
482C23#6699016yes—
483C23#6699011yescharacteristic
484C23C2×D4×D1116yes—
485C23C2×D4×D1116yes—
486C23C22×C22⋊D1113yes—
487C23C22×C22⋊D1113yes—
488C23C22×C22⋊D1114yescomplemented
489C23C24×D1111yescharacteristic
490Q8—2216no—
491D4—224no—
492D4—28no—
493D4—432no—
494D4—2216no—
495D4—2232no—
496D4—2224no—
497D4—2224no—
498D4—228no—
499D4—228no—
500D4—4464no—
501C2×C4—26no—
502C2×C4—26no—
503C2×C4—24no—
504C2×C4—412no—
505C2×C4—118no—
506C2×C4—2232no—
507C2×C4—2216no—
508C2×C4—2212no—
509C2×C4—2212no—
510C2×C4—228no—
511C2×C4—4424no—
512C2×C4C22×C22⋊D1114yescomplemented
513C22—26no—
514C22—212no—
515C22—26no—
516C22—212no—
517C22—28no—
518C22—216no—
519C22—24no—
520C22—46no—
521C22—46no—
522C22—43no—
523C22—41no—
524C22—44no—
525C22—44no—
526C22—48no—
527C22—424no—
528C22—448no—
529C22—44no—
530C22—424no—
531C22—412no—
532C22—86no—
533C22—228no—
534C22—448no—
535C22—4424no—
536C22—8812no—
537C22—8816no—
538C22#1062264514yesdirect product factor
539C22C2×#6699013yes—
540C22C2×#6699016yes—
541C22C2×#6699013yes—
542C22C22×D4×D1112yes—
543C22C23×C22⋊D1111yescharacteristic
544C4—24no—
545C4—44no—
546C4—228no—
547C4—448no—
548C2—21no—
549C2—22no—
550C2—23no—
551C2—26no—
552C2—48no—
553C2—44no—
554C2—448no—
555C2C2×#1062264516yesdirect product factor
556C2C22×#6699011yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#120C2
socleC23×C11#120
hypercenterC22×#120D11
hypocenterC11C22×B(4,𝔽2)
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C25 ◁ C22×#120

Complements

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

NH ≅ G/Ntype
1. C22×#67037C2semidirect
2. C22×#67006C2semidirect
3. C2×#10622645C2direct (N × H)
4. C22×#66898C2semidirect
5. C22×#66870C2semidirect
6. C22×C11×#120C2semidirect
7. C26×C11C22semidirect
15. C2×#67037C22semidirect
20. C2×C11×#120C22semidirect
22. C22×C11×C22⋊C4C22semidirect
24. C2×#67006C22semidirect
26. C22×C22⋊Dic11C22semidirect
27. C2×#66898C22semidirect
28. #10622645C22direct (N × H)
29. C2×#66870C22semidirect
35. C25×C11D4semidirect
37. C25×C11C23semidirect
39. C24×D11D4semidirect
44. C22×D4×C11D4semidirect
47. C23×C4×C11D4semidirect
57. C22×C22⋊D11D4semidirect
61. C23×Dic11D4semidirect
65. #67037C23semidirect
76. C11×#120C23semidirect
79. C2×C11×C22⋊C4C23semidirect
81. #67006C23semidirect
84. C2×C22⋊Dic11C23semidirect
85. #66898C23semidirect
86. #66870C23semidirect
111. C24×C11C2×D4semidirect
113. C24×C11C24semidirect
119. C23×D11C2×D4semidirect
126. C2×D4×C11C2×D4semidirect
132. C22×C4×C11C2×D4semidirect
145. C2×C22⋊D11C2×D4semidirect
152. C22×Dic11C2×D4semidirect
164. C11×C22⋊C4C24semidirect
167. C22⋊Dic11C24semidirect
170. C22×#120D11semidirect
208. C23×C11C22×D4semidirect
217. C22×D11C22×D4semidirect
225. C2×C4×C11C22×D4semidirect
237. C2×Dic11C22×D4semidirect
241. C26C2×D11semidirect
256. C2×#120C2×D11semidirect
260. C22×C22⋊C4C2×D11semidirect
284. C22×C11B(4,𝔽2)semidirect
306. C25C22⋊D11semidirect
308. C25C22×D11semidirect
336. C22×D4C22⋊D11semidirect
343. C23×C4C22⋊D11semidirect
347. #120C22×D11semidirect
353. C2×C22⋊C4C22×D11semidirect
362. C2×C11C2×B(4,𝔽2)semidirect
394. C24C2×C22⋊D11semidirect
396. C24C23×D11semidirect
425. C2×D4C2×C22⋊D11semidirect
438. C22×C4C2×C22⋊D11semidirect
444. C22⋊C4C23×D11semidirect
445. C11C22×B(4,𝔽2)semidirect
488. C23C22×C22⋊D11semidirect
512. C2×C4C22×C22⋊D11semidirect
538. C22#10622645direct (N × H)
555. C2C2×#10622645direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670372
C22×#670062
C2×#106226452
C22×#668982
C22×#668702
C22×C11×#1202
C22×B(4,𝔽2)11