Finite Group Databasebeta

← C2×#13072141 #14921781

Subgroups — C2×#13072141 #14921781

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×#66977C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic, complemented
3#13072141C2116yesmaximal, direct product factor
4C2×#10622562C212yesmaximal
5C2×#10622270C212yesmaximal, complemented
6C2×#10622542C211yesmaximal, characteristic, complemented
7C2×#10622541C211yesmaximal, characteristic, complemented
8C2×#10622564C212yesmaximal
9C2×#10622267C212yesmaximal, complemented
10C2×#10622548C211yesmaximal, characteristic, complemented
11C2×#10622825C211yesmaximal, characteristic
12C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
13C24×C4×C11C2211yescharacteristic
14C23×Dic22C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2212yes—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2212yes—
26C2×#66977—28no—
27C2×#66977C2218yes—
28C22×Dic11⋊C4C2212yes—
29C22×Dic11⋊C4C2212yes—
30C22×Dic11⋊C4C2212yes—
31C22×C4×Dic11C2212yes—
32C2×C4×Dic22—28no—
33C2×C4×Dic22C2218yescomplemented
34C4×C11×C22⋊C4C2218yes—
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37#10622825C2218yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622564C22116yes—
43#10622562C22116yes—
44#10622548C2218yescomplemented
45#10622542C2218yescomplemented
46#10622541C2218yescomplemented
47#10622270C22116yescomplemented
48#10622267C22116yescomplemented
49C25×C11C2311yescharacteristic
50C23×C4×C11—24no—
51C23×C4×C11—24no—
52C23×C4×C11—24no—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2314yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×Dic11C2312yes—
61C23×Dic11C2312yes—
62C23×Dic11C2312yes—
63C23×Dic11C2312yes—
64C22×Dic22—24no—
65C22×Dic22—24no—
66C22×Dic22D418yes—
67C22×Dic22C2314yes—
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4Q818yescomplemented
70C2×C11×C22⋊C4C2314yes—
71C2×C11×C22⋊C4C2314yes—
72C2×C42×C11—24no—
73C2×C42×C11—24no—
74C2×C42×C11C2314yes—
75C2×C42×C11C2314yes—
76C2×C22⋊Dic11—28no—
77C2×C22⋊Dic11—44no—
78C2×C22⋊Dic11C2318yes—
79C2×C22⋊Dic11C2318yes—
80C2×C4⋊Dic11—24no—
81C2×C4⋊Dic11—24no—
82C2×C4⋊Dic11—28no—
83C2×C4⋊Dic11—24no—
84C2×C4⋊Dic11—44no—
85C2×C4⋊Dic11C2314yes—
86C2×C4⋊Dic11C2318yes—
87C2×C4⋊Dic11C2314yes—
88C2×C4⋊Dic11C2314yes—
89C2×C4⋊Dic11C2318yes—
90#66977—232no—
91C2×Dic11⋊C4—28no—
92C2×Dic11⋊C4—28no—
93C2×Dic11⋊C4—44no—
94C2×Dic11⋊C4C2318yes—
95C2×Dic11⋊C4C2318yes—
96C2×Dic11⋊C4C2318yes—
97C2×C4×Dic11—28no—
98C2×C4×Dic11C2318yes—
99C4×Dic22—232no—
100C11×#95C2314yes—
101C11×#95C2314yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C2×#2423—111nomaximal, Sylow
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11C2×Q814yes—
114C24×C11C2412yes—
115C24×C11C2411yescharacteristic
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—28no—
129C22×C4×C11—28no—
130C22×C4×C11—28no—
131C22×C4×C11—416no—
132C22×C4×C11C2×D414yes—
133C22×C4×C11C2×Q814yes—
134C22×C4×C11C2×Q814yes—
135C22×C4×C11#4114yes—
136C22×C4×C11#4114yes—
137C22×C4×C11#4114yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2412yes—
142C22×C4×C11C2412yes—
143C22×C4×C11C2412yes—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11C2×D418yes—
156C22×Dic11C2414yes—
157C22×Dic11C2414yes—
158C22×Dic11C2414yes—
159C22×Dic11C2414yes—
160C2×Dic22—232no—
161C2×Dic22—28no—
162C2×Dic22—28no—
163C2×Dic22C2×D4116yes—
164C11×C22⋊C4—28no—
165C11×C22⋊C4C2×Q8116yescomplemented
166C42×C11—28no—
167C42×C11—28no—
168C22⋊Dic11—216no—
169C22⋊Dic11—48no—
170C4⋊Dic11—28no—
171C4⋊Dic11—28no—
172C4⋊Dic11—216no—
173C4⋊Dic11—28no—
174C4⋊Dic11—48no—
175Dic11⋊C4—216no—
176Dic11⋊C4—216no—
177Dic11⋊C4—48no—
178C4×Dic11—216no—
179C22×C22⋊Q8—111no—
180C22×C4×Q8—111no—
181#2423—1116no—
182C2×#399—112no—
183C2×#398—112no—
184C2×#391—111no—
185C2×#389—111no—
186C2×#388—112no—
187C2×#387—112no—
188C2×#384—111no—
189C2×#380—111no—
190C2×C4×C22⋊C4D1111yescharacteristic
191C23×C11—28no—
192C23×C11—28no—
193C23×C11—28no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—44no—
201C23×C11—44no—
202C23×C11—44no—
203C23×C11—44no—
204C23×C11C22×D412yes—
205C23×C11C22×Q814yes—
206C23×C11C22×Q812yes—
207C23×C11C2×#4112yes—
208C23×C11C2×#4112yes—
209C23×C11C2×#4112yes—
210C23×C11H(5,𝔽2)12yes—
211C23×C112−1+412yes—
212C23×C11C2511yescharacteristic
213C2×C4×C11—28no—
214C2×C4×C11—28no—
215C2×C4×C11—28no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—44no—
229C2×C4×C11—44no—
230C2×C4×C11—416no—
231C2×C4×C11#123116yes—
232C2×C4×C11C22×D414yes—
233C2×C4×C11C22×Q814yes—
234C2×C4×C11C22×Q814yes—
235C2×C4×C11C2×#4114yes—
236C2×C4×C11C2×#4114yes—
237C2×C4×C11C2×#4114yes—
238C2×Dic11—216no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—48no—
251C2×Dic11—48no—
252C2×Dic11—48no—
253C2×Dic11C22×D418yes—
254Dic22—232no—
255C23×Q8—111no—
256C24×C4C2×D1111yescharacteristic
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—111no—
266C22×C4⋊C4—111no—
267C22×C4⋊C4—112no—
268C22×C4⋊C4—112no—
269C22×C22⋊C4—112no—
270C22×C22⋊C4—112no—
271C22×C22⋊C4C2×D1111yescharacteristic
272C22×C22⋊C4C2×D1111yescharacteristic
273C22×C42—112no—
274C22×C42C2×D1111yescharacteristic
275C22×C42C2×D1111yescharacteristic
276#399—1116no—
277#398—1116no—
278#391—118no—
279#389—118no—
280#388—1116no—
281#387—1116no—
282#384—118no—
283#380—118no—
284C4×C22⋊C4C2×D1118yes—
285C2×#95—112no—
286C2×#95—112no—
287C2×#95—112no—
288C2×#95—112no—
289C2×#95C2×D1111yescharacteristic
290C2×#95C2×D1111yescharacteristic
291C22×C11—24no—
292C22×C11—24no—
293C22×C11—24no—
294C22×C11—42no—
295C22×C11—416no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11C2×#12314yes—
300C22×C11#53314yes—
301C22×C11#54214yes—
302C22×C11D4×Q814yes—
303C22×C11#55014yes—
304C22×C11#55214yes—
305C22×C11#55414yes—
306C22×C11C23×D411yescharacteristic
307C22×C11C23×Q811yescharacteristic
308C22×C11C22×#4111yescharacteristic
309C22×C11C22×#4111yescharacteristic
310C22×C11C22×#4111yescharacteristic
311C22×C11C2×H(5,𝔽2)11yescharacteristic
312C22×C11C2×2−1+411yescharacteristic
313C4×C11—24no—
314C4×C11—24no—
315C4×C11—24no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11C2×#12318yes—
319Dic11—28no—
320Dic11—44no—
321Dic11—44no—
322Dic11—44no—
323C25C22×D1111yescharacteristic
324C22×Q8—118no—
325C22×Q8—114no—
326C22×Q8—224no—
327C22×Q8—224no—
328C23×C4—24no—
329C23×C4—24no—
330C23×C4—24no—
331C23×C4—112no—
332C23×C4—112no—
333C23×C4—112no—
334C23×C4—112no—
335C23×C4C22×D1114yes—
336C23×C4C22×D1111yescharacteristic
337C23×C4C22×D1111yescharacteristic
338C23×C4C22×D1111yescharacteristic
339C23×C4C22×D1111yescharacteristic
340C23×C4C22×D1111yescharacteristic
341C23×C4C22×D1111yescharacteristic
342C22⋊Q8—2232no—
343C4×Q8—2232no—
344C2×C4⋊C4—114no—
345C2×C4⋊C4—118no—
346C2×C4⋊C4—114no—
347C2×C4⋊C4—118no—
348C2×C4⋊C4—114no—
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—224no—
357C2×C4⋊C4—224no—
358C2×C4⋊C4—444no—
359C2×C4⋊C4—444no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—118no—
362C2×C22⋊C4—118no—
363C2×C22⋊C4—228no—
364C2×C22⋊C4—444no—
365C2×C22⋊C4Dic2218yescomplemented
366C2×C22⋊C4C22×D1114yes—
367C2×C22⋊C4C22×D1114yes—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—118no—
371C2×C42—228no—
372C2×C42C22×D1114yes—
373C2×C42C22×D1114yes—
374#95—118no—
375#95—118no—
376#95—118no—
377#95—118no—
378#95C22×D1114yes—
379#95C22×D1114yes—
380C2×C11—44no—
381C2×C11#242318yescomplemented
382C2×C11C22×#12311yescharacteristic
383C2×C11C2×#53311yescharacteristic
384C2×C11C2×#54211yescharacteristic
385C2×C11C2×D4×Q811yescharacteristic
386C2×C11C2×#55011yescharacteristic
387C2×C11C2×#55211yescharacteristic
388C2×C11C2×#55411yescharacteristic
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24C2×Dic2214yes—
396C24C23×D1112yes—
397C24C23×D1111yescharacteristic
398C2×Q8—1116no—
399C2×Q8—2232no—
400C2×Q8—228no—
401C2×Q8—228no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—28no—
415C22×C4—28no—
416C22×C4—28no—
417C22×C4—416no—
418C22×C4—118no—
419C22×C4—114no—
420C22×C4—114no—
421C22×C4—114no—
422C22×C4—114no—
423C22×C4—224no—
424C22×C4—224no—
425C22×C4—224no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—224no—
429C22×C4—224no—
430C22×C4—224no—
431C22×C4—224no—
432C22×C4—224no—
433C22×C4—224no—
434C22×C4C2×Dic2214yes—
435C22×C4C2×Dic2214yes—
436C22×C4#433914yes—
437C22×C4#433914yes—
438C22×C4D4×D1114yes—
439C22×C4#434114yes—
440C22×C4C23×D1112yes—
441C22×C4C23×D1112yes—
442C22×C4C23×D1112yes—
443C22×C4C23×D1112yes—
444C22×C4C23×D1112yes—
445C22×C4C23×D1112yes—
446C4⋊C4—2216no—
447C4⋊C4—2216no—
448C4⋊C4—2216no—
449C4⋊C4—228no—
450C4⋊C4—228no—
451C4⋊C4—228no—
452C4⋊C4—448no—
453C4⋊C4—448no—
454C22⋊C4—28no—
455C22⋊C4—2216no—
456C22⋊C4—448no—
457C22⋊C4C2×Dic22116yescomplemented
458C42—28no—
459C42—28no—
460C42—2216no—
461C11C2×#242311yescharacteristic, complemented, Sylow
462C23—28no—
463C23—28no—
464C23—28no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—22no—
470C23—22no—
471C23—44no—
472C23—44no—
473C23—44no—
474C23—44no—
475C23C22×Dic2214yes—
476C23C22×Dic2212yes—
477C23C2×#433912yes—
478C23C2×#433912yes—
479C23C2×D4×D1112yes—
480C23C2×#434112yes—
481C23#6704212yes—
482C23#6704312yes—
483C23C24×D1111yescharacteristic
484Q8—2232no—
485C2×C4—28no—
486C2×C4—28no—
487C2×C4—28no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—416no—
503C2×C4—118no—
504C2×C4—2216no—
505C2×C4—224no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—224no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—448no—
517C2×C4—448no—
518C2×C4—448no—
519C2×C4#66936116yes—
520C2×C4C22×Dic2214yes—
521C2×C4C22×Dic2214yes—
522C2×C4C2×#433914yes—
523C2×C4C2×#433914yes—
524C2×C4C2×D4×D1114yes—
525C2×C4C2×#434114yes—
526C22—24no—
527C22—24no—
528C22—24no—
529C22—416no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22#1062300114yes—
535C22C2×#6693614yes—
536C22#1062306514yes—
537C22D4×Dic2214yes—
538C22#1062307214yes—
539C22#1062307414yes—
540C22#1062308414yes—
541C22C23×Dic2211yescharacteristic
542C22C22×#433911yescharacteristic
543C22C22×#433911yescharacteristic
544C22C22×D4×D1111yescharacteristic
545C22C22×#434111yescharacteristic
546C22C2×#6704211yescharacteristic
547C22C2×#6704311yescharacteristic
548C4—24no—
549C4—24no—
550C4—24no—
551C4—42no—
552C4—42no—
553C4—228no—
554C4—444no—
555C4—444no—
556C4—444no—
557C4C2×#6693618yes—
558C2—44no—
559C2#1307214118yesdirect product factor
560C2C22×#6693611yescharacteristic
561C2C2×#1062300111yescharacteristic
562C2C2×#1062306511yescharacteristic
563C2C2×D4×Dic2211yescharacteristic
564C2C2×#1062308411yescharacteristic
565C2C2×#1062307211yescharacteristic
566C2C2×#1062307411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#2423
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic22C2semidirect
3. #13072141C2direct (N × H)
5. C2×#10622270C2semidirect
6. C2×#10622542C2semidirect
7. C2×#10622541C2semidirect
9. C2×#10622267C2semidirect
10. C2×#10622548C2semidirect
33. C2×C4×Dic22C22semidirect
44. #10622548C22semidirect
45. #10622542C22semidirect
46. #10622541C22semidirect
47. #10622270C22semidirect
48. #10622267C22semidirect
69. C2×C11×C22⋊C4Q8semidirect
165. C11×C22⋊C4C2×Q8semidirect
365. C2×C22⋊C4Dic22semidirect
381. C2×C11#2423semidirect
457. C22⋊C4C2×Dic22semidirect
461. C11C2×#2423semidirect
559. C2#13072141direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669772
C22×C4×Dic222
#130721412
C2×#106225622
C2×#106222702
C2×#106225422
C2×#106225412
C2×#106225642
C2×#106222672
C2×#106225482
C2×#106228252
C2×C4×C11×C22⋊C42
C2×#242311