Finite Group Databasebeta

← C2×#13073021 #14923116

Subgroups — C2×#13073021 #14923116

Order 2816.

2182 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
1#13073021C2116yesmaximal, direct product factor
2C2×#10622271C212yesmaximal, complemented
3C2×#10622288C212yesmaximal
4C2×#10622541C211yesmaximal, characteristic, complemented
5C2×#10622586C211yesmaximal, characteristic, complemented
6C2×#10622553C212yesmaximal
7C2×#10622550C212yesmaximal, complemented
8C2×#10622590C211yesmaximal, characteristic, complemented
9C2×#10622600C211yesmaximal, characteristic
10C2×#10622600C211yesmaximal, characteristic
11C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
12C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
13C23×C4×D11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×C42×C11C2212yes—
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×C4×Dic11C2211yescharacteristic
27C4×C11×C4⋊C4C2218yescomplemented
28C2×C11×#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37#10622600C2218yes—
38#10622600C2218yes—
39#10622590C2218yescomplemented
40#10622586C2218yescomplemented
41#10622553C22116yes—
42C4×(C2×D11)⋊C4C2218yes—
43#10622550C22116yescomplemented
44#10622541C2218yescomplemented
45#10622288C22116yes—
46#10622271C22116yescomplemented
47C24×D11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2312yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×Dic11C2311yescharacteristic
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2312yes—
56C23×Dic11C2312yes—
57C23×Dic11C2311yescharacteristic
58C22×C4×D11—24no—
59C22×C4×D11—24no—
60C22×C4×D11—24no—
61C22×C4×D11C2314yes—
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4C2314yes—
65C2×C11×C4⋊C4C2314yes—
66C2×C42×C11—24no—
67C2×C42×C11—28no—
68C2×C42×C11C2314yes—
69C2×C42×C11C2318yes—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4—28no—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—44no—
74C2×(C2×D11)⋊C4C2314yes—
75C2×(C2×D11)⋊C4C2318yes—
76C2×(C2×D11)⋊C4C2314yes—
77C2×(C2×D11)⋊C4C2318yes—
78C2×C4⋊Dic11—24no—
79C2×C4⋊Dic11—24no—
80C2×C4⋊Dic11C2314yes—
81C2×C4⋊Dic11C2314yes—
82C2×Dic11⋊C4—44no—
83C2×Dic11⋊C4—44no—
84C2×Dic11⋊C4C2318yes—
85C2×Dic11⋊C4C2318yes—
86C2×C4×Dic11—24no—
87C2×C4×Dic11C2314yes—
88C11×#95C2318yes—
89C11⋊#95C2314yes—
90C11⋊#95C2318yes—
91C11⋊#95C2318yes—
92C11⋊#95C2318yes—
93C11⋊#95C2318yes—
94C11⋊#95C2318yes—
95C11⋊#95C2318yes—
96C11⋊#95C2314yes—
97C2×#2495—111nomaximal, Sylow
98C24×C11C2411yescharacteristic
99C23×D11—22no—
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—22no—
103C23×D11—22no—
104C23×D11—22no—
105C23×D11#4114yes—
106C23×D11C2412yes—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—24no—
110C22×C4×C11—22no—
111C22×C4×C11—24no—
112C22×C4×C11—22no—
113C22×C4×C11—24no—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—24no—
118C22×C4×C11#4114yes—
119C22×C4×C11#4114yes—
120C22×C4×C11#4114yes—
121C22×C4×C11#4114yes—
122C22×C4×C11C2414yes—
123C22×C4×C11C2414yes—
124C22×C4×C11C2412yes—
125C22×C4×C11C2412yes—
126C22×C4×C11C2412yes—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—24no—
130C22×Dic11—24no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—24no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—24no—
138C22×Dic11—22no—
139C22×Dic11—24no—
140C22×Dic11—24no—
141C22×Dic11—22no—
142C22×Dic11C2412yes—
143C22×Dic11C2412yes—
144C22×Dic11C2414yes—
145C22×Dic11C2412yes—
146C22×Dic11C2414yes—
147C2×C4×D11—28no—
148C2×C4×D11—28no—
149C2×C4×D11—28no—
150C2×C4×D11—416no—
151C11×C4⋊C4—28no—
152C11×C4⋊C4—28no—
153C42×C11—28no—
154C42×C11—216no—
155(C2×D11)⋊C4—28no—
156(C2×D11)⋊C4—216no—
157(C2×D11)⋊C4—28no—
158(C2×D11)⋊C4—48no—
159C4⋊Dic11—28no—
160C4⋊Dic11—28no—
161Dic11⋊C4—48no—
162Dic11⋊C4—48no—
163C4×Dic11—28no—
164#2495—1116no—
165C2×#400—112no—
166C2×#397—112no—
167C2×#389—111no—
168C2×#389—111no—
169C2×#388—112no—
170C2×#383—112no—
171C2×#382—111no—
172C2×#380—111no—
173C2×#380—111no—
174C2×C4×C4⋊C4D1111yescharacteristic, complemented
175C2×C4×C22⋊C4—111no—
176C23×C11C2×#4112yes—
177C23×C11C2×#4112yes—
178C23×C11C2×#4112yes—
179C23×C11C2×#4112yes—
180C23×C11C2×#4112yes—
181C23×C11H(5,𝔽2)12yes—
182C23×C112−1+412yes—
183C23×C11C2511yescharacteristic
184C22×D11—28no—
185C22×D11—28no—
186C22×D11—28no—
187C22×D11—22no—
188C22×D11—22no—
189C22×D11—22no—
190C22×D11—22no—
191C22×D11—22no—
192C22×D11—22no—
193C22×D11—44no—
194C22×D11—44no—
195C22×D11—44no—
196C22×D11—44no—
197C22×D11C2×#4114yes—
198C2×C4×C11—28no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—22no—
209C2×C4×C11—24no—
210C2×C4×C11—48no—
211C2×C4×C11—44no—
212C2×C4×C11—48no—
213C2×C4×C11#126116yes—
214C2×C4×C11C2×#4114yes—
215C2×C4×C11C2×#4114yes—
216C2×C4×C11C2×#4114yes—
217C2×C4×C11C2×#4114yes—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—24no—
221C2×Dic11—24no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—24no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—24no—
229C2×Dic11—22no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—22no—
233C2×Dic11—44no—
234C2×Dic11—48no—
235C2×Dic11—44no—
236C2×Dic11—48no—
237C2×Dic11—44no—
238C4×D11—416no—
239C24×C4—111no—
240C22×C4⋊C4—111no—
241C22×C4⋊C4—111no—
242C22×C4⋊C4—112no—
243C22×C4⋊C4—112no—
244C22×C4⋊C4C2×D1111yescharacteristic
245C22×C4⋊C4C2×D1111yescharacteristic
246C22×C22⋊C4—111no—
247C22×C22⋊C4—112no—
248C22×C22⋊C4—111no—
249C22×C22⋊C4—112no—
250C22×C42—111no—
251C22×C42C2×D1111yescharacteristic
252C22×C42C2×D1112yes—
253#400—1116no—
254#397—1116no—
255#389—118no—
256#389—118no—
257#388—1116no—
258#383—1116no—
259#382—118no—
260#380—118no—
261#380—118no—
262C4×C4⋊C4C2×D1118yescomplemented
263C4×C22⋊C4—118no—
264C2×#95—112no—
265C2×#95—112no—
266C2×#95—111no—
267C2×#95—112no—
268C2×#95—112no—
269C2×#95—112no—
270C2×#95—111no—
271C2×#95—112no—
272C2×#95C2×D1112yes—
273C22×C11C2×#12614yes—
274C22×C11#52914yes—
275C22×C11#54214yes—
276C22×C11#55214yes—
277C22×C11#55214yes—
278C22×C11#55314yes—
279C22×C11#55514yes—
280C22×C11C22×#4111yescharacteristic
281C22×C11C22×#4111yescharacteristic
282C22×C11C22×#4111yescharacteristic
283C22×C11C22×#4111yescharacteristic
284C22×C11C22×#4111yescharacteristic
285C22×C11C2×H(5,𝔽2)11yescharacteristic
286C22×C11C2×2−1+411yescharacteristic
287C2×D11—24no—
288C2×D11—24no—
289C2×D11—24no—
290C2×D11—42no—
291C2×D11—42no—
292C2×D11—42no—
293C2×D11—42no—
294C2×D11—416no—
295C4×C11—24no—
296C4×C11—44no—
297C4×C11—42no—
298C4×C11—44no—
299C4×C11C2×#12618yes—
300Dic11—42no—
301Dic11—44no—
302Dic11—42no—
303Dic11—44no—
304Dic11—42no—
305C25—111no—
306C23×C4—112no—
307C23×C4—112no—
308C23×C4—111no—
309C23×C4—111no—
310C23×C4—111no—
311C23×C4—114no—
312C23×C4—224no—
313C23×C4—224no—
314C23×C4—224no—
315C23×C4C22×D1111yescharacteristic
316C23×C4C22×D1112yes—
317C23×C4C22×D1112yes—
318C23×C4C22×D1111yescharacteristic
319C23×C4C22×D1111yescharacteristic
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—114no—
323C2×C4⋊C4—114no—
324C2×C4⋊C4—118no—
325C2×C4⋊C4—118no—
326C2×C4⋊C4—224no—
327C2×C4⋊C4—224no—
328C2×C4⋊C4—444no—
329C2×C4⋊C4—444no—
330C2×C4⋊C4C22×D1114yes—
331C2×C4⋊C4C22×D1114yes—
332C2×C22⋊C4—114no—
333C2×C22⋊C4—114no—
334C2×C22⋊C4—118no—
335C2×C22⋊C4—118no—
336C2×C22⋊C4—224no—
337C2×C22⋊C4—228no—
338C2×C22⋊C4—224no—
339C2×C22⋊C4—444no—
340C2×C42—24no—
341C2×C42—28no—
342C2×C42—114no—
343C2×C42—224no—
344C2×C42C22×D1114yes—
345C2×C42C22×D1118yes—
346#95—114no—
347#95—114no—
348#95—118no—
349#95—118no—
350#95—118no—
351#95—118no—
352#95—118no—
353#95—118no—
354#95C22×D1118yes—
355C2×C11#249518yescomplemented
356C2×C11C22×#12611yescharacteristic
357C2×C11C2×#52911yescharacteristic
358C2×C11C2×#54211yescharacteristic
359C2×C11C2×#55211yescharacteristic
360C2×C11C2×#55211yescharacteristic
361C2×C11C2×#55311yescharacteristic
362C2×C11C2×#55511yescharacteristic
363D11—44no—
364C24—114no—
365C24—112no—
366C24—222no—
367C24—222no—
368C24—222no—
369C24—222no—
370C24—222no—
371C24—222no—
372C24C23×D1111yescharacteristic
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—22no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—112no—
385C22×C4—112no—
386C22×C4—114no—
387C22×C4—112no—
388C22×C4—114no—
389C22×C4—222no—
390C22×C4—222no—
391C22×C4—224no—
392C22×C4—224no—
393C22×C4—222no—
394C22×C4—222no—
395C22×C4—222no—
396C22×C4—222no—
397C22×C4—222no—
398C22×C4—224no—
399C22×C4—224no—
400C22×C4—222no—
401C22×C4—224no—
402C22×C4—224no—
403C22×C4—222no—
404C22×C4—228no—
405C22×C4—228no—
406C22×C4—228no—
407C22×C4—4416no—
408C22×C4#433914yes—
409C22×C4#433914yes—
410C22×C4#433914yes—
411C22×C4#434114yes—
412C22×C4C23×D1114yes—
413C22×C4C23×D1114yes—
414C22×C4C23×D1112yes—
415C22×C4C23×D1112yes—
416C22×C4C23×D1112yes—
417C4⋊C4—28no—
418C4⋊C4—28no—
419C4⋊C4—228no—
420C4⋊C4—228no—
421C4⋊C4—448no—
422C4⋊C4—448no—
423C22⋊C4—228no—
424C22⋊C4—2216no—
425C22⋊C4—228no—
426C22⋊C4—448no—
427C42—28no—
428C42—216no—
429C42—228no—
430C11C2×#249511yescharacteristic, complemented, Sylow
431C23—114no—
432C23—228no—
433C23—228no—
434C23—228no—
435C23—222no—
436C23—222no—
437C23—222no—
438C23—222no—
439C23—222no—
440C23—222no—
441C23—444no—
442C23—444no—
443C23—444no—
444C23—444no—
445C23C2×#433912yes—
446C23C2×#433912yes—
447C23C2×#433912yes—
448C23C2×#434112yes—
449C23#6704012yes—
450C23#41×D1112yes—
451C23#6704212yes—
452C23C24×D1111yescharacteristic
453C2×C4—28no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—44no—
466C2×C4—48no—
467C2×C4—48no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—224no—
471C2×C4—224no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—222no—
476C2×C4—222no—
477C2×C4—224no—
478C2×C4—222no—
479C2×C4—224no—
480C2×C4—224no—
481C2×C4—224no—
482C2×C4—222no—
483C2×C4—444no—
484C2×C4—448no—
485C2×C4—444no—
486C2×C4—444no—
487C2×C4—448no—
488C2×C4—4416no—
489C2×C4#66929116yes—
490C2×C4C2×#433914yes—
491C2×C4C2×#433914yes—
492C2×C4C2×#433914yes—
493C2×C4C2×#434114yes—
494C22—224no—
495C22—224no—
496C22—224no—
497C22—442no—
498C22—442no—
499C22—442no—
500C22—4416no—
501C22—442no—
502C22C2×#6692914yes—
503C22#1062304414yes—
504C22#1062306114yes—
505C22#1062308814yes—
506C22#1062309414yes—
507C22#1062311214yes—
508C22#1062311314yes—
509C22C22×#433911yescharacteristic
510C22C22×#433911yescharacteristic
511C22C22×#433911yescharacteristic
512C22C22×#434111yescharacteristic
513C22C2×#6704011yescharacteristic
514C22C2×#41×D1111yescharacteristic
515C22C2×#6704211yescharacteristic
516C4—24no—
517C4—42no—
518C4—44no—
519C4—44no—
520C4—442no—
521C4—442no—
522C4—444no—
523C4—442no—
524C4—444no—
525C4C2×#6692918yes—
526C2—444no—
527C2#1307302118yesdirect product factor
528C2C22×#6692911yescharacteristic
529C2C2×#1062308811yescharacteristic
530C2C2×#1062311311yescharacteristic
531C2C2×#1062304411yescharacteristic
532C2C2×#1062311211yescharacteristic
533C2C2×#1062306111yescharacteristic
534C2C2×#1062309411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C4⋊C4C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C2×#2495
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #13073021C2direct (N × H)
2. C2×#10622271C2semidirect
4. C2×#10622541C2semidirect
5. C2×#10622586C2semidirect
7. C2×#10622550C2semidirect
8. C2×#10622590C2semidirect
12. C2×C4×C11×C4⋊C4C2semidirect
27. C4×C11×C4⋊C4C22semidirect
39. #10622590C22semidirect
40. #10622586C22semidirect
43. #10622550C22semidirect
44. #10622541C22semidirect
46. #10622271C22semidirect
174. C2×C4×C4⋊C4D11semidirect
262. C4×C4⋊C4C2×D11semidirect
355. C2×C11#2495semidirect
430. C11C2×#2495semidirect
527. C2#13073021direct (N × H)

Maximal subgroups

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

subgroupindex
#130730212
C2×#106222712
C2×#106222882
C2×#106225412
C2×#106225862
C2×#106225532
C2×#106225502
C2×#106225902
C2×#106226002
C2×C4×(C2×D11)⋊C42
C2×C4×C11×C4⋊C42
C2×#249511