Finite Group Databasebeta

← C2×#13072142 #14921783

Subgroups — C2×#13072142 #14921783

Order 2816.

2790 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66950C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic, complemented
3#13072142C2116yesmaximal, direct product factor
4C2×#10622605C212yesmaximal
5C2×#10622597C212yesmaximal, complemented
6C2×#10622587C211yesmaximal, characteristic, complemented
7C2×#10622282C212yesmaximal
8C2×#10622268C212yesmaximal, complemented
9C2×#10622589C211yesmaximal, characteristic, complemented
10C2×#10622600C211yesmaximal, characteristic
11C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
12C2×C11×#389C211yesmaximal, characteristic, complemented
13C23×C4×D11C2211yescharacteristic
14C23×Dic22C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2212yes—
18C22×C42×C11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2212yes—
28C22×C4×Dic11C2211yescharacteristic
29C22×C4×Dic11C2212yes—
30C2×#66950—28no—
31C2×#66950C2218yes—
32C2×C4×Dic22—28no—
33C2×C4×Dic22C2218yescomplemented
34C11×#389C2218yescomplemented
35C2×C11×#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622605C22116yes—
42#10622600C2218yes—
43#10622597C22116yescomplemented
44#10622589C2218yescomplemented
45#10622587C2218yescomplemented
46C4×(C2×D11)⋊C4C2218yes—
47#10622282C22116yes—
48#10622268C22116yescomplemented
49C24×D11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×Dic11C2312yes—
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C22×C4×D11—24no—
61C22×C4×D11—24no—
62C22×C4×D11—24no—
63C22×C4×D11C2314yes—
64C22×Dic22—24no—
65C22×Dic22—24no—
66C22×Dic22D418yes—
67C22×Dic22C2314yes—
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4—44no—
71C2×C11×C4⋊C4C2314yes—
72C2×C11×C4⋊C4C2314yes—
73C2×C11×C4⋊C4C2318yes—
74C2×C42×C11—24no—
75C2×C42×C11C2314yes—
76C2×(C2×D11)⋊C4—28no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—44no—
79C2×(C2×D11)⋊C4Q818yescomplemented
80C2×(C2×D11)⋊C4C2318yes—
81C2×(C2×D11)⋊C4C2314yes—
82C2×(C2×D11)⋊C4C2318yes—
83C2×(C2×D11)⋊C4C2314yes—
84C2×C4⋊Dic11—24no—
85C2×C4⋊Dic11—28no—
86C2×C4⋊Dic11C2314yes—
87C2×C4⋊Dic11C2318yes—
88C2×Dic11⋊C4—28no—
89C2×Dic11⋊C4—28no—
90C2×Dic11⋊C4—44no—
91C2×Dic11⋊C4C2318yes—
92C2×Dic11⋊C4C2318yes—
93C2×Dic11⋊C4C2318yes—
94C2×C4×Dic11—24no—
95C2×C4×Dic11—28no—
96C2×C4×Dic11C2318yes—
97C2×C4×Dic11C2314yes—
98#66950—232no—
99C4×Dic22—232no—
100C11×#95C2318yes—
101C11⋊#95C2314yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2314yes—
106C2×#2423—111nomaximal, Sylow
107C24×C11C2411yescharacteristic
108C23×D11—22no—
109C23×D11—22no—
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—22no—
114C23×D11C2×Q814yes—
115C23×D11C2412yes—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—22no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11C2×D414yes—
128C22×C4×C11C2×Q814yes—
129C22×C4×C11#4114yes—
130C22×C4×C11#4114yes—
131C22×C4×C11C2414yes—
132C22×C4×C11C2412yes—
133C22×C4×C11C2414yes—
134C22×C4×C11C2412yes—
135C22×C4×C11C2412yes—
136C22×Dic11—24no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—24no—
147C22×Dic11—22no—
148C22×Dic11C2×D418yes—
149C22×Dic11C2×Q814yes—
150C22×Dic11#4114yes—
151C22×Dic11C2412yes—
152C22×Dic11C2414yes—
153C22×Dic11C2414yes—
154C22×Dic11C2412yes—
155C22×Dic11C2412yes—
156C2×C4×D11—28no—
157C2×C4×D11—28no—
158C2×C4×D11—28no—
159C2×C4×D11—416no—
160C2×Dic22—232no—
161C2×Dic22—28no—
162C2×Dic22—28no—
163C2×Dic22C2×D4116yes—
164C11×C4⋊C4—28no—
165C11×C4⋊C4—28no—
166C11×C4⋊C4—48no—
167C42×C11—28no—
168(C2×D11)⋊C4—216no—
169(C2×D11)⋊C4—28no—
170(C2×D11)⋊C4—48no—
171(C2×D11)⋊C4C2×Q8116yescomplemented
172C4⋊Dic11—216no—
173C4⋊Dic11—28no—
174Dic11⋊C4—216no—
175Dic11⋊C4—216no—
176Dic11⋊C4—48no—
177C4×Dic11—216no—
178C4×Dic11—28no—
179C22×C22⋊Q8—111no—
180C22×C4×Q8—111no—
181#2423—1116no—
182C2×#399—112no—
183C2×#398—112no—
184C2×#391—111no—
185C2×#389D1111yescharacteristic, complemented
186C2×#388—112no—
187C2×#387—112no—
188C2×#384—111no—
189C2×#380—111no—
190C2×C4×C22⋊C4—111no—
191C23×C11C22×D412yes—
192C23×C11C22×Q812yes—
193C23×C11C2×#4112yes—
194C23×C11C2×#4112yes—
195C23×C11C2×#4112yes—
196C23×C11H(5,𝔽2)12yes—
197C23×C112−1+412yes—
198C23×C11C2511yescharacteristic
199C22×D11—28no—
200C22×D11—28no—
201C22×D11—28no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—44no—
209C22×D11—44no—
210C22×D11—44no—
211C22×D11—44no—
212C22×D11C22×Q814yes—
213C2×C4×C11—28no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—48no—
226C2×C4×C11—44no—
227C2×C4×C11—48no—
228C2×C4×C11#123116yes—
229C2×C4×C11C22×D414yes—
230C2×C4×C11C22×Q814yes—
231C2×C4×C11C2×#4114yes—
232C2×C4×C11C2×#4114yes—
233C2×Dic11—216no—
234C2×Dic11—28no—
235C2×Dic11—28no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—44no—
249C2×Dic11—48no—
250C2×Dic11C22×D418yes—
251C2×Dic11C22×Q814yes—
252C2×Dic11C2×#4114yes—
253C4×D11—416no—
254Dic22—232no—
255C23×Q8—111no—
256C24×C4—111no—
257C2×C22⋊Q8—118no—
258C2×C22⋊Q8—228no—
259C2×C4×Q8—118no—
260C2×C4×Q8—228no—
261C22×C4⋊C4—112no—
262C22×C4⋊C4—112no—
263C22×C4⋊C4—112no—
264C22×C4⋊C4—111no—
265C22×C4⋊C4—112no—
266C22×C4⋊C4C2×D1111yescharacteristic
267C22×C4⋊C4C2×D1111yescharacteristic
268C22×C4⋊C4C2×D1112yes—
269C22×C22⋊C4—111no—
270C22×C22⋊C4—111no—
271C22×C22⋊C4—112no—
272C22×C22⋊C4—112no—
273C22×C42—112no—
274C22×C42—111no—
275C22×C42C2×D1111yescharacteristic
276#399—1116no—
277#398—1116no—
278#391—118no—
279#389C2×D1118yescomplemented
280#388—1116no—
281#387—1116no—
282#384—118no—
283#380—118no—
284C4×C22⋊C4—118no—
285C2×#95—111no—
286C2×#95—112no—
287C2×#95—112no—
288C2×#95—112no—
289C2×#95—111no—
290C2×#95C2×D1112yes—
291C22×C11C2×#12314yes—
292C22×C11#53314yes—
293C22×C11#54214yes—
294C22×C11D4×Q814yes—
295C22×C11#55014yes—
296C22×C11#55214yes—
297C22×C11#55414yes—
298C22×C11C23×D411yescharacteristic
299C22×C11C23×Q811yescharacteristic
300C22×C11C22×#4111yescharacteristic
301C22×C11C22×#4111yescharacteristic
302C22×C11C22×#4111yescharacteristic
303C22×C11C2×H(5,𝔽2)11yescharacteristic
304C22×C11C2×2−1+411yescharacteristic
305C2×D11—24no—
306C2×D11—24no—
307C2×D11—24no—
308C2×D11—42no—
309C2×D11—416no—
310C2×D11—42no—
311C2×D11—42no—
312C2×D11—42no—
313C4×C11—24no—
314C4×C11—44no—
315C4×C11—42no—
316C4×C11—44no—
317C4×C11C2×#12318yes—
318Dic11—28no—
319Dic11—24no—
320Dic11—24no—
321Dic11—42no—
322Dic11—44no—
323C25—111no—
324C22×Q8—118no—
325C22×Q8—114no—
326C22×Q8—224no—
327C22×Q8—224no—
328C23×C4—112no—
329C23×C4—111no—
330C23×C4—111no—
331C23×C4—112no—
332C23×C4—111no—
333C23×C4—114no—
334C23×C4—224no—
335C23×C4—224no—
336C23×C4—224no—
337C23×C4C22×D1112yes—
338C23×C4C22×D1111yescharacteristic
339C23×C4C22×D1112yes—
340C23×C4C22×D1111yescharacteristic
341C23×C4C22×D1111yescharacteristic
342C22⋊Q8—2232no—
343C4×Q8—2232no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—114no—
348C2×C4⋊C4—118no—
349C2×C4⋊C4—118no—
350C2×C4⋊C4—118no—
351C2×C4⋊C4—118no—
352C2×C4⋊C4—228no—
353C2×C4⋊C4—228no—
354C2×C4⋊C4—228no—
355C2×C4⋊C4—224no—
356C2×C4⋊C4—444no—
357C2×C4⋊C4C22×D1114yes—
358C2×C4⋊C4C22×D1114yes—
359C2×C4⋊C4C22×D1118yes—
360C2×C22⋊C4—118no—
361C2×C22⋊C4—114no—
362C2×C22⋊C4—118no—
363C2×C22⋊C4—114no—
364C2×C22⋊C4—118no—
365C2×C22⋊C4—228no—
366C2×C22⋊C4—224no—
367C2×C22⋊C4—444no—
368C2×C42—24no—
369C2×C42—118no—
370C2×C42—114no—
371C2×C42—228no—
372C2×C42—224no—
373C2×C42C22×D1114yes—
374#95—114no—
375#95—114no—
376#95—118no—
377#95—118no—
378#95—118no—
379#95C22×D1118yes—
380C2×C11#242318yescomplemented
381C2×C11C22×#12311yescharacteristic
382C2×C11C2×#53311yescharacteristic
383C2×C11C2×#54211yescharacteristic
384C2×C11C2×D4×Q811yescharacteristic
385C2×C11C2×#55011yescharacteristic
386C2×C11C2×#55211yescharacteristic
387C2×C11C2×#55411yescharacteristic
388D11—44no—
389C24—114no—
390C24—112no—
391C24—222no—
392C24—222no—
393C24—222no—
394C24—222no—
395C24—222no—
396C24—222no—
397C24C23×D1111yescharacteristic
398C2×Q8—1116no—
399C2×Q8—2232no—
400C2×Q8—228no—
401C2×Q8—228no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—22no—
409C22×C4—24no—
410C22×C4—22no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—118no—
414C22×C4—114no—
415C22×C4—114no—
416C22×C4—112no—
417C22×C4—112no—
418C22×C4—114no—
419C22×C4—112no—
420C22×C4—114no—
421C22×C4—224no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—224no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—224no—
429C22×C4—222no—
430C22×C4—224no—
431C22×C4—222no—
432C22×C4—224no—
433C22×C4—228no—
434C22×C4—228no—
435C22×C4—228no—
436C22×C4—4416no—
437C22×C4#433914yes—
438C22×C4D4×D1114yes—
439C22×C4Q8×D1114yes—
440C22×C4#434314yes—
441C22×C4C23×D1114yes—
442C22×C4C23×D1112yes—
443C22×C4C23×D1114yes—
444C22×C4C23×D1112yes—
445C22×C4C23×D1112yes—
446C4⋊C4—28no—
447C4⋊C4—28no—
448C4⋊C4—48no—
449C4⋊C4—2216no—
450C4⋊C4—2216no—
451C4⋊C4—2216no—
452C4⋊C4—228no—
453C4⋊C4—448no—
454C22⋊C4—1116no—
455C22⋊C4—2216no—
456C22⋊C4—228no—
457C22⋊C4—448no—
458C42—28no—
459C42—2216no—
460C42—228no—
461C11C2×#242311yescharacteristic, complemented, Sylow
462C23—114no—
463C23—228no—
464C23—228no—
465C23—228no—
466C23—222no—
467C23—222no—
468C23—222no—
469C23—222no—
470C23—222no—
471C23—222no—
472C23—444no—
473C23—444no—
474C23—444no—
475C23—444no—
476C23C2×#433912yes—
477C23C2×D4×D1112yes—
478C23#6703712yes—
479C23C2×Q8×D1112yes—
480C23C2×#434312yes—
481C23#41×D1112yes—
482C23#6704312yes—
483C23C24×D1111yescharacteristic
484Q8—2232no—
485C2×C4—28no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—48no—
498C2×C4—44no—
499C2×C4—48no—
500C2×C4—118no—
501C2×C4—114no—
502C2×C4—114no—
503C2×C4—228no—
504C2×C4—2216no—
505C2×C4—224no—
506C2×C4—222no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—224no—
510C2×C4—222no—
511C2×C4—228no—
512C2×C4—222no—
513C2×C4—224no—
514C2×C4—222no—
515C2×C4—224no—
516C2×C4—222no—
517C2×C4—224no—
518C2×C4—444no—
519C2×C4—448no—
520C2×C4—4416no—
521C2×C4#66947116yes—
522C2×C4C2×#433914yes—
523C2×C4C2×D4×D1114yes—
524C2×C4C2×Q8×D1114yes—
525C2×C4C2×#434314yes—
526C22—224no—
527C22—224no—
528C22—224no—
529C22—4416no—
530C22—442no—
531C22—442no—
532C22—442no—
533C22—442no—
534C22C2×#6694714yes—
535C22#1062309214yes—
536C22#1062310914yes—
537C22#1062313014yes—
538C22#1062316314yes—
539C22#1062322514yes—
540C22#1062326114yes—
541C22C22×#433911yescharacteristic
542C22C22×D4×D1111yescharacteristic
543C22C2×#6703711yescharacteristic
544C22C22×Q8×D1111yescharacteristic
545C22C22×#434311yescharacteristic
546C22C2×#41×D1111yescharacteristic
547C22C2×#6704311yescharacteristic
548C4—24no—
549C4—44no—
550C4—42no—
551C4—44no—
552C4—224no—
553C4—224no—
554C4—228no—
555C4—444no—
556C4—442no—
557C4C2×#6694718yes—
558C2—444no—
559C2#1307214218yesdirect product factor
560C2C22×#6694711yescharacteristic
561C2C2×#1062310911yescharacteristic
562C2C2×#1062309211yescharacteristic
563C2C2×#1062316311yescharacteristic
564C2C2×#1062313011yescharacteristic
565C2C2×#1062322511yescharacteristic
566C2C2×#1062326111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#389C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#389D11
hypocenterC11C2×#2423
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic22C2semidirect
3. #13072142C2direct (N × H)
5. C2×#10622597C2semidirect
6. C2×#10622587C2semidirect
8. C2×#10622268C2semidirect
9. C2×#10622589C2semidirect
12. C2×C11×#389C2semidirect
33. C2×C4×Dic22C22semidirect
34. C11×#389C22semidirect
43. #10622597C22semidirect
44. #10622589C22semidirect
45. #10622587C22semidirect
48. #10622268C22semidirect
79. C2×(C2×D11)⋊C4Q8semidirect
171. (C2×D11)⋊C4C2×Q8semidirect
185. C2×#389D11semidirect
279. #389C2×D11semidirect
380. C2×C11#2423semidirect
461. C11C2×#2423semidirect
559. C2#13072142direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669502
C22×C4×Dic222
#130721422
C2×#106226052
C2×#106225972
C2×#106225872
C2×#106222822
C2×#106222682
C2×#106225892
C2×#106226002
C2×C4×(C2×D11)⋊C42
C2×C11×#3892
C2×#242311