Finite Group Databasebeta

← C2×#13072893 #14922694

Subgroups — C2×#13072893 #14922694

Order 2816.

4382 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D11C212yesmaximal
2#13072893C2116yesmaximal, direct product factor
3C2×#10622565C212yesmaximal, complemented
4C2×#10622566C211yesmaximal, characteristic, complemented
5C2×#10622281C212yesmaximal, complemented
6C2×#10622602C212yesmaximal, complemented
7C2×#10622277C212yesmaximal, complemented
8C2×#10622277C212yesmaximal, complemented
9C2×#10622568C211yesmaximal, characteristic
10C2×C11×#397C211yesmaximal, characteristic, complemented
11C25×D11C2211yescharacteristic
12C23×C4×D11C2212yes—
13C23×C4×D11C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic, complemented
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic, complemented
24C22×Dic11⋊C4C2212yescomplemented
25C2×C22⋊C4×D11—216no—
26C2×C22⋊C4×D11C22116yes—
27C11×#397C2218yescomplemented
28C2×C11×#95C2211yescharacteristic, complemented
29C2×C11×#95C2212yescomplemented
30C2×C11⋊#95C2211yescharacteristic, complemented
31C2×C11⋊#95C2212yescomplemented
32C2×C11⋊#95C2212yescomplemented
33C2×C11⋊#95C2212yescomplemented
34C2×C11⋊#95C2212yescomplemented
35#10622602C22116yescomplemented
36#10622568C2218yes—
37#10622566C2218yescomplemented
38#10622565C22116yescomplemented
39#10622281C22116yescomplemented
40#10622277C22116yescomplemented
41#10622277C22116yescomplemented
42C25×C11C2311yescharacteristic
43C24×D11—28no—
44C24×D11—28no—
45C24×D11—42no—
46C24×D11—42no—
47C24×D11D418yes—
48C24×D11C2314yes—
49C24×D11C2312yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×Dic11C2312yes—
55C23×Dic11C2312yes—
56C23×Dic11C2312yes—
57C22×C4×D11—28no—
58C22×C4×D11—28no—
59C22×C4×D11—28no—
60C22×C4×D11—28no—
61C22×C4×D11—44no—
62C22×C4×D11—44no—
63C22×C4×D11C2318yes—
64C22×C4×D11C2318yes—
65C2×C11×C4⋊C4—42no—
66C2×C11×C4⋊C4C2314yescomplemented
67C2×C11×C22⋊C4—28no—
68C2×C11×C22⋊C4—42no—
69C2×C11×C22⋊C4C2318yes—
70C2×C11×C22⋊C4C2314yes—
71C2×C22⋊Dic11—28no—
72C2×C22⋊Dic11—42no—
73C2×C22⋊Dic11C2318yes—
74C2×C22⋊Dic11C2314yes—
75C2×(C2×D11)⋊C4—28no—
76C2×(C2×D11)⋊C4—28no—
77C2×(C2×D11)⋊C4—28no—
78C2×(C2×D11)⋊C4—28no—
79C2×(C2×D11)⋊C4C2318yes—
80C2×(C2×D11)⋊C4C2318yes—
81C2×(C2×D11)⋊C4C2318yes—
82C2×(C2×D11)⋊C4C2318yes—
83C2×C4⋊Dic11—42no—
84C2×C4⋊Dic11C2314yescomplemented
85C2×Dic11⋊C4—44no—
86C2×Dic11⋊C4C2318yescomplemented
87C22⋊C4×D11—264no—
88C11×#95C2314yescomplemented
89C11×#95C2318yescomplemented
90C11⋊#95C2318yescomplemented
91C11⋊#95C2314yescomplemented
92C11⋊#95C2318yescomplemented
93C11⋊#95C2318yescomplemented
94C11⋊#95C2318yescomplemented
95C2×#2483—111nomaximal, Sylow
96C24×C11—24no—
97C24×C11—24no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11C2×D414yes—
101C24×C11C2412yes—
102C24×C11C2411yescharacteristic
103C23×D11—24no—
104C23×D11—24no—
105C23×D11—24no—
106C23×D11—24no—
107C23×D11—264no—
108C23×D11—216no—
109C23×D11—216no—
110C23×D11—416no—
111C23×D11—44no—
112C23×D11—44no—
113C23×D11—432no—
114C23×D11—416no—
115C23×D11—416no—
116C23×D11C2×D4116yes—
117C23×D11C2×D418yes—
118C23×D11#4118yes—
119C23×D11#4118yes—
120C23×D11C2414yes—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11C2414yes—
132C22×C4×C11C2412yes—
133C22×C4×C11C2412yes—
134C22×C4×C11C2414yes—
135C22×Dic11—24no—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11C2414yes—
145C22×Dic11C2414yes—
146C22×Dic11C2414yes—
147C2×C4×D11—216no—
148C2×C4×D11—216no—
149C2×C4×D11—216no—
150C2×C4×D11—216no—
151C2×C4×D11—48no—
152C2×C4×D11—48no—
153C2×C4×D11—432no—
154C2×C4×D11—432no—
155C11×C4⋊C4—44no—
156C11×C22⋊C4—216no—
157C11×C22⋊C4—44no—
158C22⋊Dic11—216no—
159C22⋊Dic11—44no—
160(C2×D11)⋊C4—216no—
161(C2×D11)⋊C4—216no—
162(C2×D11)⋊C4—216no—
163(C2×D11)⋊C4—216no—
164C4⋊Dic11—44no—
165Dic11⋊C4—48no—
166C23×C22⋊C4—112no—
167#2483—1116no—
168C2×#397—111no—
169C2×#397—112no—
170C2×#397D1111yescharacteristic, complemented
171C2×#385—112no—
172C2×#385—112no—
173C2×#381—112no—
174C2×#381—112no—
175C2×#379—111no—
176C23×C11—216no—
177C23×C11—28no—
178C23×C11—24no—
179C23×C11—24no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—48no—
183C23×C11—44no—
184C23×C11—44no—
185C23×C11C22×D414yes—
186C23×C11C22×D412yes—
187C23×C11C2×#4114yes—
188C23×C11C2×#4114yes—
189C23×C11H(5,𝔽2)12yes—
190C23×C11H(5,𝔽2)12yes—
191C23×C11C2511yescharacteristic
192C22×D11—216no—
193C22×D11—216no—
194C22×D11—216no—
195C22×D11—216no—
196C22×D11—216no—
197C22×D11—216no—
198C22×D11—24no—
199C22×D11—24no—
200C22×D11—24no—
201C22×D11—24no—
202C22×D11—264no—
203C22×D11—416no—
204C22×D11—432no—
205C22×D11—416no—
206C22×D11—416no—
207C22×D11—4128no—
208C22×D11#123132yes—
209C22×D11C22×D418yes—
210C22×D11C2×#4118yes—
211C22×D11C2×#4118yes—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—48no—
223C2×C4×C11—48no—
224C2×C4×C11—44no—
225C2×C4×C11—44no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—48no—
236C2×Dic11—48no—
237C2×Dic11—48no—
238C4×D11—432no—
239C4×D11—432no—
240C26—111no—
241C24×C4—112no—
242C24×C4—112no—
243C22×C4⋊C4—112no—
244C22×C4⋊C4—111no—
245C22×C4⋊C4C2×D1111yescharacteristic, complemented
246C22×C22⋊C4—112no—
247C22×C22⋊C4—112no—
248C22×C22⋊C4—112no—
249C22×C22⋊C4—112no—
250C22×C22⋊C4—112no—
251C22×C22⋊C4—111no—
252C22×C22⋊C4—1116no—
253C22×C22⋊C4—2216no—
254C22×C22⋊C4C2×D1112yes—
255C22×C22⋊C4C2×D1111yescharacteristic
256#397—1116no—
257#397—118no—
258#397C2×D1118yescomplemented
259#385—1116no—
260#385—1116no—
261#381—1116no—
262#381—1116no—
263#379—118no—
264C2×#95—112no—
265C2×#95—111no—
266C2×#95—112no—
267C2×#95—112no—
268C2×#95—112no—
269C2×#95C2×D1111yescharacteristic, complemented
270C2×#95C2×D1112yescomplemented
271C22×C11—28no—
272C22×C11—24no—
273C22×C11—44no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—416no—
277C22×C11C2×#12318yes—
278C22×C11#53414yes—
279C22×C11#55118yes—
280C22×C11#55114yes—
281C22×C11#55114yes—
282C22×C11C23×D411yescharacteristic
283C22×C11C22×#4112yes—
284C22×C11C22×#4112yes—
285C22×C11C2×H(5,𝔽2)11yescharacteristic
286C22×C11C2×H(5,𝔽2)11yescharacteristic
287C2×D11—28no—
288C2×D11—28no—
289C2×D11—28no—
290C2×D11—28no—
291C2×D11—28no—
292C2×D11—28no—
293C2×D11—264no—
294C2×D11—464no—
295C2×D11C2×#123116yes—
296C4×C11—44no—
297C4×C11—44no—
298C4×C11—42no—
299C4×C11—42no—
300Dic11—44no—
301Dic11—44no—
302Dic11—44no—
303C25—112no—
304C25—118no—
305C25—114no—
306C25—228no—
307C25—228no—
308C25—442no—
309C25—442no—
310C25C22×D1111yescharacteristic
311C23×C4—112no—
312C23×C4—112no—
313C23×C4—112no—
314C23×C4—118no—
315C23×C4—118no—
316C23×C4—228no—
317C23×C4—228no—
318C23×C4—228no—
319C23×C4—228no—
320C23×C4—444no—
321C23×C4—444no—
322C23×C4C22×D1111yescharacteristic
323C23×C4C22×D1111yescharacteristic
324C23×C4C22×D1112yes—
325C23×C4C22×D1112yes—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—118no—
328C2×C4⋊C4—114no—
329C2×C4⋊C4—444no—
330C2×C4⋊C4—442no—
331C2×C4⋊C4C22×D1114yescomplemented
332C2×C22⋊C4—28no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—118no—
335C2×C22⋊C4—118no—
336C2×C22⋊C4—118no—
337C2×C22⋊C4—118no—
338C2×C22⋊C4—118no—
339C2×C22⋊C4—114no—
340C2×C22⋊C4—2264no—
341C2×C22⋊C4—228no—
342C2×C22⋊C4—228no—
343C2×C22⋊C4—228no—
344C2×C22⋊C4—228no—
345C2×C22⋊C4—228no—
346C2×C22⋊C4—442no—
347C2×C22⋊C4C22×D1118yes—
348C2×C22⋊C4C22×D1114yes—
349#95—114no—
350#95—118no—
351#95—118no—
352#95—118no—
353#95—118no—
354#95C22×D1114yescomplemented
355#95C22×D1118yescomplemented
356C2×C11—44no—
357C2×C11#248318yescomplemented
358C2×C11C22×#12312yes—
359C2×C11C2×#53411yescharacteristic
360C2×C11C2×#55112yes—
361C2×C11C2×#55111yescharacteristic
362C2×C11C2×#55111yescharacteristic
363D11—216no—
364C24—22no—
365C24—24no—
366C24—24no—
367C24—22no—
368C24—118no—
369C24—118no—
370C24—118no—
371C24—114no—
372C24—1116no—
373C24—2264no—
374C24—2216no—
375C24—2216no—
376C24—224no—
377C24—224no—
378C24—224no—
379C24—224no—
380C24—4416no—
381C24—444no—
382C24—444no—
383C24—4432no—
384C24—4416no—
385C24—4416no—
386C24D4×D1114yes—
387C24C23×D1112yes—
388C24C23×D1111yescharacteristic
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—114no—
400C22×C4—114no—
401C22×C4—114no—
402C22×C4—2216no—
403C22×C4—2216no—
404C22×C4—2216no—
405C22×C4—2216no—
406C22×C4—224no—
407C22×C4—224no—
408C22×C4—224no—
409C22×C4—224no—
410C22×C4—224no—
411C22×C4—224no—
412C22×C4—224no—
413C22×C4—224no—
414C22×C4—224no—
415C22×C4—448no—
416C22×C4—448no—
417C22×C4—4432no—
418C22×C4—4432no—
419C22×C4C23×D1114yes—
420C22×C4C23×D1112yes—
421C22×C4C23×D1112yes—
422C22×C4C23×D1114yes—
423C4⋊C4—44no—
424C4⋊C4—448no—
425C4⋊C4—444no—
426C22⋊C4—216no—
427C22⋊C4—44no—
428C22⋊C4—2216no—
429C22⋊C4—2216no—
430C22⋊C4—2216no—
431C22⋊C4—2216no—
432C22⋊C4—2216no—
433C22⋊C4—444no—
434C11C2×#248311yescharacteristic, complemented, Sylow
435C23—28no—
436C23—216no—
437C23—22no—
438C23—24no—
439C23—24no—
440C23—22no—
441C23—48no—
442C23—44no—
443C23—44no—
444C23—1132no—
445C23—118no—
446C23—118no—
447C23—118no—
448C23—2264no—
449C23—2216no—
450C23—2216no—
451C23—2216no—
452C23—2216no—
453C23—2216no—
454C23—224no—
455C23—224no—
456C23—224no—
457C23—224no—
458C23—2216no—
459C23—4416no—
460C23—4432no—
461C23—4416no—
462C23—4416no—
463C23—44128no—
464C23C2×D4×D1114yes—
465C23C2×D4×D1112yes—
466C23#6703712yes—
467C23#41×D1114yes—
468C23#41×D1114yes—
469C23#6704212yes—
470C23C24×D1111yescharacteristic
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—48no—
482C2×C4—48no—
483C2×C4—44no—
484C2×C4—44no—
485C2×C4—224no—
486C2×C4—224no—
487C2×C4—224no—
488C2×C4—224no—
489C2×C4—224no—
490C2×C4—224no—
491C2×C4—224no—
492C2×C4—224no—
493C2×C4—224no—
494C2×C4—4432no—
495C2×C4—4432no—
496C2×C4—448no—
497C2×C4—448no—
498C2×C4—448no—
499C22—24no—
500C22—28no—
501C22—44no—
502C22—42no—
503C22—42no—
504C22—416no—
505C22—1116no—
506C22—228no—
507C22—228no—
508C22—228no—
509C22—228no—
510C22—228no—
511C22—228no—
512C22—2264no—
513C22—4464no—
514C22#1062313614yes—
515C22D11×#12318yes—
516C22#1062319014yes—
517C22#1062321014yes—
518C22#1062323618yes—
519C22C22×D4×D1111yescharacteristic
520C22C2×#6703711yescharacteristic
521C22C2×#41×D1112yes—
522C22C2×#41×D1112yes—
523C22C2×#6704211yescharacteristic
524C4—42no—
525C4—42no—
526C4—44no—
527C4—44no—
528C4—444no—
529C4—444no—
530C4—444no—
531C2—44no—
532C2—2216no—
533C2#1307289318yesdirect product factor
534C2C2×D11×#12312yes—
535C2C2×#1062313611yescharacteristic
536C2C2×#1062323612yes—
537C2C2×#1062319011yescharacteristic
538C2C2×#1062321011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#397C2
socleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×#397D11
hypocenterC11C2×#2483
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
2. #13072893C2direct (N × H)
3. C2×#10622565C2semidirect
4. C2×#10622566C2semidirect
5. C2×#10622281C2semidirect
6. C2×#10622602C2semidirect
7. C2×#10622277C2semidirect
8. C2×#10622277C2semidirect
10. C2×C11×#397C2semidirect
14. C22×C11×C4⋊C4C22semidirect
23. C22×C4⋊Dic11C22semidirect
24. C22×Dic11⋊C4C22semidirect
27. C11×#397C22semidirect
28. C2×C11×#95C22semidirect
29. C2×C11×#95C22semidirect
30. C2×C11⋊#95C22semidirect
31. C2×C11⋊#95C22semidirect
32. C2×C11⋊#95C22semidirect
33. C2×C11⋊#95C22semidirect
34. C2×C11⋊#95C22semidirect
35. #10622602C22semidirect
37. #10622566C22semidirect
38. #10622565C22semidirect
39. #10622281C22semidirect
40. #10622277C22semidirect
41. #10622277C22semidirect
66. C2×C11×C4⋊C4C23semidirect
84. C2×C4⋊Dic11C23semidirect
86. C2×Dic11⋊C4C23semidirect
88. C11×#95C23semidirect
89. C11×#95C23semidirect
90. C11⋊#95C23semidirect
91. C11⋊#95C23semidirect
92. C11⋊#95C23semidirect
93. C11⋊#95C23semidirect
94. C11⋊#95C23semidirect
170. C2×#397D11semidirect
245. C22×C4⋊C4C2×D11semidirect
258. #397C2×D11semidirect
269. C2×#95C2×D11semidirect
270. C2×#95C2×D11semidirect
331. C2×C4⋊C4C22×D11semidirect
354. #95C22×D11semidirect
355. #95C22×D11semidirect
357. C2×C11#2483semidirect
434. C11C2×#2483semidirect
533. C2#13072893direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×D112
#130728932
C2×#106225652
C2×#106225662
C2×#106222812
C2×#106226022
C2×#106222772
C2×#106225682
C2×C11×#3972
C2×#248311