Finite Group Databasebeta

← C2×#13074548 #14920212

Subgroups — C2×#13074548 #14920212

Order 2816.

3326 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic, complemented
2C22×#66948C211yesmaximal, characteristic
3#13074548C2116yesmaximal, direct product factor
4C2×#10622595C211yesmaximal, characteristic, complemented
5C2×#10622288C212yesmaximal, complemented
6C2×#10622285C211yesmaximal, characteristic, complemented
7C2×#10622604C211yesmaximal, characteristic, complemented
8C2×#10622286C212yesmaximal, complemented
9C2×#10622278C212yesmaximal, complemented
10C2×#10622278C212yesmaximal, complemented
11C2×D11×#95C211yesmaximal, characteristic, complemented
12C2×C11×#400C211yesmaximal, characteristic, complemented
13C23×D44C2212yes—
14C23×D44C2211yescharacteristic
15C23×C4×D11C2212yes—
16C23×C4×D11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C2×#66949—28no—
30C2×#66949C2218yescomplemented
31C2×#66948—28no—
32C2×#66948C2218yes—
33C11×#400C2218yescomplemented
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2212yes—
36C2×C11×#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622604C2218yescomplemented
42#10622595C2218yescomplemented
43#10622288C22116yescomplemented
44#10622286C22116yescomplemented
45#10622285C2218yescomplemented
46#10622278C22116yescomplemented
47#10622278C22116yescomplemented
48D11×#95C2218yescomplemented
49C24×D11C2312yes—
50C24×D11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C22×D44—28no—
61C22×D44—28no—
62C22×D44—28no—
63C22×D44—24no—
64C22×D44—44no—
65C22×D44C2318yes—
66C22×D44C2314yes—
67C22×C4×D11—28no—
68C22×C4×D11—44no—
69C22×C4×D11—44no—
70C22×C4×D11—44no—
71C22×C4×D11D418yes—
72C22×C4×D11C2318yes—
73C22×C4×D11C2314yes—
74C22×Dic22—24no—
75C22×Dic22—44no—
76C22×Dic22C2314yes—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2314yes—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—24no—
83C2×(C2×D11)⋊C4—28no—
84C2×(C2×D11)⋊C4—44no—
85C2×(C2×D11)⋊C4—44no—
86C2×(C2×D11)⋊C4—44no—
87C2×(C2×D11)⋊C4—44no—
88C2×(C2×D11)⋊C4C2318yes—
89C2×(C2×D11)⋊C4C2314yes—
90C2×(C2×D11)⋊C4C2314yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×(C2×D11)⋊C4C2318yes—
94C2×(C2×D11)⋊C4C2318yes—
95C2×Dic11⋊C4—24no—
96C2×Dic11⋊C4—24no—
97C2×Dic11⋊C4C2314yes—
98C2×Dic11⋊C4C2314yes—
99#66949—232no—
100#66948—232no—
101C11×#95C2314yes—
102C11×#95C2318yes—
103C11×#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2314yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C2×#2639—111nomaximal, Sylow
109C24×C11C2411yescharacteristic
110C23×D11—24no—
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—24no—
114C23×D11—24no—
115C23×D11—24no—
116C23×D11—24no—
117C23×D11—24no—
118C23×D11—24no—
119C23×D11—24no—
120C23×D11C2×D414yes—
121C23×D11#4118yes—
122C23×D11C2414yes—
123C23×D11C2412yes—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11C2×D414yes—
137C22×C4×C11C2414yes—
138C22×C4×C11C2414yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2412yes—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—22no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—22no—
151C22×Dic11C2×D414yes—
152C22×Dic11C2414yes—
153C22×Dic11C2412yes—
154C22×Dic11C2412yes—
155C22×Dic11C2412yes—
156C2×D44—216no—
157C2×D44—216no—
158C2×D44—216no—
159C2×D44—28no—
160C2×D44—48no—
161C2×D44—416no—
162C2×D44—432no—
163C2×C4×D11—216no—
164C2×C4×D11—416no—
165C2×C4×D11—48no—
166C2×C4×D11—48no—
167C2×C4×D11—48no—
168C2×C4×D11—432no—
169C2×C4×D11C2×D4116yes—
170C2×Dic22—28no—
171C2×Dic22—48no—
172C2×Dic22—416no—
173C11×C4⋊C4—28no—
174C11×C4⋊C4—28no—
175(C2×D11)⋊C4—216no—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4—28no—
178(C2×D11)⋊C4—48no—
179(C2×D11)⋊C4—48no—
180(C2×D11)⋊C4—48no—
181(C2×D11)⋊C4—48no—
182Dic11⋊C4—28no—
183Dic11⋊C4—28no—
184C22×C22⋊Q8—111no—
185C22×#121—111no—
186#2639—1116no—
187C2×#400—111no—
188C2×#400D1111yescharacteristic, complemented
189C2×#397—112no—
190C2×#394—111no—
191C2×#394—111no—
192C2×#393—112no—
193C2×#386—112no—
194C2×#386—112no—
195C22×#95—111no—
196C23×C11C22×D412yes—
197C23×C11C2×#4114yes—
198C23×C11H(5,𝔽2)14yes—
199C23×C11H(5,𝔽2)12yes—
200C23×C112−1+412yes—
201C23×C11C2511yescharacteristic
202C22×D11—28no—
203C22×D11—28no—
204C22×D11—216no—
205C22×D11—216no—
206C22×D11—24no—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—24no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—48no—
217C22×D11—48no—
218C22×D11—48no—
219C22×D11—48no—
220C22×D11—48no—
221C22×D11—48no—
222C22×D11—48no—
223C22×D11#124116yes—
224C22×D11C22×D414yes—
225C22×D11C2×#4118yes—
226C2×C4×C11—28no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—48no—
240C2×C4×C11—44no—
241C2×C4×C11—44no—
242C2×C4×C11—48no—
243C2×C4×C11C22×D414yes—
244C2×Dic11—28no—
245C2×Dic11—24no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—22no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—22no—
254C2×Dic11—44no—
255C2×Dic11—44no—
256C2×Dic11—48no—
257C2×Dic11C22×D414yes—
258D44—416no—
259D44—432no—
260C4×D11—416no—
261C4×D11—432no—
262Dic22—416no—
263C23×Q8—111no—
264C23×D4—112no—
265C23×D4—111no—
266C24×C4—111no—
267C24×C4—112no—
268C2×C22⋊Q8—118no—
269C2×C22⋊Q8—228no—
270C2×#121—118no—
271C2×#121—228no—
272C22×C4⋊C4—111no—
273C22×C4⋊C4—111no—
274C22×C4⋊C4C2×D1111yescharacteristic
275C22×C4⋊C4C2×D1111yescharacteristic
276C22×C22⋊C4—112no—
277C22×C22⋊C4—111no—
278C22×C22⋊C4—111no—
279C22×C22⋊C4—112no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4—112no—
282C22×C22⋊C4—112no—
283#400—118no—
284#400C2×D1118yescomplemented
285#397—1116no—
286#394—118no—
287#394—118no—
288#393—1116no—
289#386—1116no—
290#386—1116no—
291C2×#95—112no—
292C2×#95—112no—
293C2×#95—111no—
294C2×#95—112no—
295C2×#95—118no—
296C2×#95C2×D1112yes—
297C2×#95C2×D1111yescharacteristic
298C2×#95C2×D1112yes—
299C22×C11C2×#12414yes—
300C22×C11#53414yes—
301C22×C11#53714yes—
302C22×C11#53818yes—
303C22×C11#53918yes—
304C22×C11C23×D411yescharacteristic
305C22×C11C22×#4112yes—
306C22×C11C2×H(5,𝔽2)12yes—
307C22×C11C2×H(5,𝔽2)11yescharacteristic
308C22×C11C2×2−1+411yescharacteristic
309C2×D11—232no—
310C2×D11—24no—
311C2×D11—24no—
312C2×D11—28no—
313C2×D11—28no—
314C2×D11—44no—
315C2×D11—44no—
316C2×D11—44no—
317C2×D11—44no—
318C2×D11—44no—
319C2×D11—44no—
320C2×D11—44no—
321C2×D11—816no—
322C2×D11C2×#12418yes—
323C4×C11—24no—
324C4×C11—44no—
325C4×C11—42no—
326C4×C11—42no—
327C4×C11—44no—
328Dic11—24no—
329Dic11—42no—
330Dic11—42no—
331Dic11—44no—
332C25—111no—
333C25—112no—
334C22×Q8—114no—
335C22×Q8—224no—
336C22×Q8—444no—
337C22×D4—118no—
338C22×D4—114no—
339C22×D4—228no—
340C22×D4—228no—
341C22×D4—228no—
342C22×D4—224no—
343C22×D4—444no—
344C23×C4—111no—
345C23×C4—118no—
346C23×C4—114no—
347C23×C4—111no—
348C23×C4—111no—
349C23×C4—112no—
350C23×C4—118no—
351C23×C4—228no—
352C23×C4—444no—
353C23×C4—444no—
354C23×C4—444no—
355C23×C4C22×D1111yescharacteristic
356C23×C4C22×D1111yescharacteristic
357C23×C4C22×D1112yes—
358C23×C4C22×D1112yes—
359C23×C4C22×D1111yescharacteristic
360C22⋊Q8—2232no—
361#121—2232no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—224no—
367C2×C4⋊C4—224no—
368C2×C4⋊C4C22×D1114yes—
369C2×C4⋊C4C22×D1114yes—
370C2×C22⋊C4—118no—
371C2×C22⋊C4—114no—
372C2×C22⋊C4—114no—
373C2×C22⋊C4—118no—
374C2×C22⋊C4—118no—
375C2×C22⋊C4—118no—
376C2×C22⋊C4—118no—
377C2×C22⋊C4—228no—
378C2×C22⋊C4—224no—
379C2×C22⋊C4—224no—
380C2×C22⋊C4—444no—
381C2×C22⋊C4—444no—
382C2×C22⋊C4—444no—
383C2×C22⋊C4—444no—
384#95—118no—
385#95—114no—
386#95—118no—
387#95—118no—
388#95C22×D1114yes—
389#95C22×D1118yes—
390#95C22×D1118yes—
391C2×C11#263918yescomplemented
392C2×C11C22×#12411yescharacteristic
393C2×C11C2×#53411yescharacteristic
394C2×C11C2×#53711yescharacteristic
395C2×C11C2×#53812yes—
396C2×C11C2×#53912yes—
397D11—28no—
398D11—84no—
399C24—114no—
400C24—118no—
401C24—112no—
402C24—114no—
403C24—222no—
404C24—222no—
405C24—224no—
406C24—224no—
407C24—224no—
408C24—224no—
409C24—224no—
410C24—224no—
411C24—224no—
412C24—224no—
413C24C23×D1111yescharacteristic
414C2×Q8—228no—
415C2×Q8—448no—
416C2×Q8—4416no—
417C2×D4—2216no—
418C2×D4—2216no—
419C2×D4—2216no—
420C2×D4—228no—
421C2×D4—448no—
422C2×D4—4416no—
423C2×D4—4432no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—114no—
437C22×C4—112no—
438C22×C4—1116no—
439C22×C4—114no—
440C22×C4—112no—
441C22×C4—112no—
442C22×C4—2216no—
443C22×C4—224no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—224no—
448C22×C4—222no—
449C22×C4—224no—
450C22×C4—224no—
451C22×C4—224no—
452C22×C4—4416no—
453C22×C4—448no—
454C22×C4—448no—
455C22×C4—448no—
456C22×C4—4432no—
457C22×C4D4×D1114yes—
458C22×C4C23×D1114yes—
459C22×C4C23×D1114yes—
460C22×C4C23×D1112yes—
461C22×C4C23×D1112yes—
462C22×C4C23×D1112yes—
463C4⋊C4—28no—
464C4⋊C4—28no—
465C4⋊C4—228no—
466C4⋊C4—228no—
467C22⋊C4—2216no—
468C22⋊C4—228no—
469C22⋊C4—228no—
470C22⋊C4—448no—
471C22⋊C4—448no—
472C22⋊C4—448no—
473C22⋊C4—448no—
474C11C2×#263911yescharacteristic, complemented, Sylow
475C23—114no—
476C23—118no—
477C23—1116no—
478C23—2216no—
479C23—228no—
480C23—228no—
481C23—222no—
482C23—224no—
483C23—222no—
484C23—2216no—
485C23—224no—
486C23—224no—
487C23—224no—
488C23—224no—
489C23—224no—
490C23—224no—
491C23—224no—
492C23—448no—
493C23—448no—
494C23—448no—
495C23—448no—
496C23—448no—
497C23—448no—
498C23—448no—
499C23C2×D4×D1112yes—
500C23#6704012yes—
501C23#41×D1114yes—
502C23#6704212yes—
503C23#6704214yes—
504C23C24×D1111yescharacteristic
505Q8—4416no—
506D4—4416no—
507D4—4432no—
508C2×C4—28no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—48no—
522C2×C4—44no—
523C2×C4—44no—
524C2×C4—48no—
525C2×C4—114no—
526C2×C4—228no—
527C2×C4—224no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—224no—
532C2×C4—222no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—4416no—
537C2×C4—4432no—
538C2×C4—448no—
539C2×C4—444no—
540C2×C4—444no—
541C2×C4C2×D4×D1114yes—
542C22—118no—
543C22—224no—
544C22—224no—
545C22—228no—
546C22—228no—
547C22—2232no—
548C22—444no—
549C22—444no—
550C22—444no—
551C22—444no—
552C22—444no—
553C22—444no—
554C22—444no—
555C22—8816no—
556C22#1062316014yes—
557C22#1062318414yes—
558C22D11×#12414yes—
559C22#1062322318yes—
560C22#1062323518yes—
561C22C22×D4×D1111yescharacteristic
562C22C2×#6704011yescharacteristic
563C22C2×#41×D1112yes—
564C22C2×#6704212yes—
565C22C2×#6704211yescharacteristic
566C4—24no—
567C4—44no—
568C4—42no—
569C4—42no—
570C4—44no—
571C4—224no—
572C4—442no—
573C4—442no—
574C4—444no—
575C2—228no—
576C2—884no—
577C2#1307454818yesdirect product factor
578C2C2×D11×#12411yescharacteristic
579C2C2×#1062318411yescharacteristic
580C2C2×#1062316011yescharacteristic
581C2C2×#1062323512yes—
582C2C2×#1062322312yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#400C2
socleC24×C11C24
prime radicalC22×#66948C2
hypercenterC2×#400D11
hypocenterC11C2×#2639
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. C22×#66949C2semidirect
3. #13074548C2direct (N × H)
4. C2×#10622595C2semidirect
5. C2×#10622288C2semidirect
6. C2×#10622285C2semidirect
7. C2×#10622604C2semidirect
8. C2×#10622286C2semidirect
9. C2×#10622278C2semidirect
10. C2×#10622278C2semidirect
11. C2×D11×#95C2semidirect
12. C2×C11×#400C2semidirect
30. C2×#66949C22semidirect
33. C11×#400C22semidirect
41. #10622604C22semidirect
42. #10622595C22semidirect
43. #10622288C22semidirect
44. #10622286C22semidirect
45. #10622285C22semidirect
46. #10622278C22semidirect
47. #10622278C22semidirect
48. D11×#95C22semidirect
188. C2×#400D11semidirect
284. #400C2×D11semidirect
391. C2×C11#2639semidirect
474. C11C2×#2639semidirect
577. C2#13074548direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669492
C22×#669482
#130745482
C2×#106225952
C2×#106222882
C2×#106222852
C2×#106226042
C2×#106222862
C2×#106222782
C2×D11×#952
C2×C11×#4002
C2×#263911