Finite Group Databasebeta

← C2×#13072490 #14921941

Subgroups — C2×#13072490 #14921941

Order 2816.

3094 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66923C211yesmaximal, characteristic, complemented
2C22×D4×Dic11C211yesmaximal, characteristic
3#13072490C2116yesmaximal, direct product factor
4C2×#10622562C212yesmaximal, complemented
5C2×#10622561C212yesmaximal, complemented
6C2×#10622834C211yesmaximal, characteristic
7C2×#10622598C211yesmaximal, characteristic, complemented
8C2×#10622586C211yesmaximal, characteristic, complemented
9C2×#10622559C212yesmaximal, complemented
10C2×#10622555C212yesmaximal, complemented
11C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
12C2×C11×#390C211yesmaximal, characteristic
13C23×D4×C11C2211yescharacteristic
14C24×Dic11C2212yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C11×C22⋊C4C2212yes—
18C22×C42×C11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C2×D4×Dic11—28no—
23C2×D4×Dic11C2218yes—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2212yes—
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2212yes—
28C22×Dic11⋊C4C2212yes—
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C2×#66923—28no—
35C2×#66923C2218yescomplemented
36C11×#390C2218yes—
37#10622834C2218yes—
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622598C2218yescomplemented
43#10622586C2218yescomplemented
44#10622562C22116yescomplemented
45#10622561C22116yescomplemented
46#10622559C22116yescomplemented
47#10622555C22116yescomplemented
48C4×Dic11⋊C4C2218yescomplemented
49C25×C11C2312yes—
50C22×D4×C11—24no—
51C22×D4×C11—24no—
52C22×D4×C11Q818yes—
53C22×D4×C11C2314yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×Dic11—28no—
59C23×Dic11—28no—
60C23×Dic11—44no—
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2312yes—
64C23×Dic11C2318yes—
65C23×Dic11C2312yes—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C22⋊C4—44no—
71C2×C11×C22⋊C4—44no—
72C2×C11×C22⋊C4C2318yes—
73C2×C11×C22⋊C4C2318yes—
74C2×C42×C11—24no—
75C2×C42×C11C2314yes—
76C2×C22⋊Dic11—28no—
77C2×C22⋊Dic11—28no—
78C2×C22⋊Dic11—44no—
79C2×C22⋊Dic11C2318yes—
80C2×C22⋊Dic11C2318yes—
81C2×C22⋊Dic11C2318yes—
82D4×Dic11—232no—
83C2×C4⋊Dic11—24no—
84C2×C4⋊Dic11—44no—
85C2×C4⋊Dic11D418yes—
86C2×C4⋊Dic11C2314yes—
87C2×C4⋊Dic11C2318yes—
88C2×C4⋊Dic11C2314yes—
89C2×Dic11⋊C4—28no—
90C2×Dic11⋊C4—28no—
91C2×Dic11⋊C4—24no—
92C2×Dic11⋊C4—24no—
93C2×Dic11⋊C4—44no—
94C2×Dic11⋊C4C2318yes—
95C2×Dic11⋊C4C2318yes—
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2314yes—
98C2×Dic11⋊C4C2318yes—
99C2×C4×Dic11—24no—
100C2×C4×Dic11—24no—
101C2×C4×Dic11C2314yes—
102C2×C4×Dic11C2314yes—
103#66923—232no—
104C11⋊#95C2314yes—
105C11⋊#95C2314yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C2×#2454—111nomaximal, Sylow
109C24×C11—24no—
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11C2×Q818yes—
116C24×C11C2414yes—
117C24×C11C2411yescharacteristic
118C2×D4×C11—232no—
119C2×D4×C11—28no—
120C2×D4×C11—28no—
121C2×D4×C11C2×Q8116yes—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11C2×D414yes—
132C22×C4×C11C2×Q814yes—
133C22×C4×C11#4114yes—
134C22×C4×C11C2414yes—
135C22×C4×C11C2412yes—
136C22×C4×C11C2412yes—
137C22×C4×C11C2412yes—
138C22×Dic11—216no—
139C22×Dic11—216no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—24no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—24no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—24no—
154C22×Dic11—22no—
155C22×Dic11—48no—
156C22×Dic11—432no—
157C22×Dic11C2×D418yes—
158C22×Dic11#4114yes—
159C22×Dic11#4114yes—
160C22×Dic11C2412yes—
161C22×Dic11C2412yes—
162C22×Dic11C2414yes—
163C22×Dic11C2414yes—
164C22×Dic11C2412yes—
165C22×Dic11C2412yes—
166C11×C4⋊C4—28no—
167C11×C22⋊C4—48no—
168C11×C22⋊C4—48no—
169C42×C11—28no—
170C22⋊Dic11—216no—
171C22⋊Dic11—216no—
172C22⋊Dic11—48no—
173C4⋊Dic11—28no—
174C4⋊Dic11—48no—
175C4⋊Dic11C2×D4116yes—
176Dic11⋊C4—216no—
177Dic11⋊C4—216no—
178Dic11⋊C4—28no—
179Dic11⋊C4—28no—
180Dic11⋊C4—48no—
181C4×Dic11—28no—
182C4×Dic11—28no—
183C22×#125—111no—
184C22×C4×D4—111no—
185#2454—1116no—
186C2×#399—112no—
187C2×#396—112no—
188C2×#390—111no—
189C2×#390D1111yescharacteristic
190C2×#389—111no—
191C2×#389—111no—
192C2×#385—112no—
193C2×#380—112no—
194C2×C4×C4⋊C4—111no—
195C23×C11—216no—
196C23×C11—216no—
197C23×C11—216no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—48no—
205C23×C11—48no—
206C23×C11—48no—
207C23×C11—48no—
208C23×C11C22×D412yes—
209C23×C11C22×Q818yes—
210C23×C11C22×Q812yes—
211C23×C11C2×#4112yes—
212C23×C11C2×#4112yes—
213C23×C11C2×#4112yes—
214C23×C11H(5,𝔽2)12yes—
215C23×C11H(5,𝔽2)12yes—
216C23×C11C2511yescharacteristic
217D4×C11—232no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—48no—
228C2×C4×C11—44no—
229C2×C4×C11—44no—
230C2×C4×C11C22⋊Q8116yes—
231C2×C4×C11C22×D414yes—
232C2×C4×C11C22×Q814yes—
233C2×C4×C11C2×#4114yes—
234C2×Dic11—28no—
235C2×Dic11—28no—
236C2×Dic11—216no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—432no—
253C2×Dic11—44no—
254C2×Dic11—44no—
255C2×Dic11—48no—
256C2×Dic11C22×D418yes—
257C2×Dic11C2×#4114yes—
258C2×Dic11C2×#4114yes—
259C23×D4C2×D1111yescharacteristic
260C24×C4—112no—
261C2×#125—118no—
262C2×#125—228no—
263C2×C4×D4—118no—
264C2×C4×D4—228no—
265C22×C4⋊C4—111no—
266C22×C4⋊C4—112no—
267C22×C4⋊C4—111no—
268C22×C4⋊C4—112no—
269C22×C4⋊C4—111no—
270C22×C4⋊C4—111no—
271C22×C4⋊C4—112no—
272C22×C4⋊C4—112no—
273C22×C4⋊C4C2×D1111yescharacteristic
274C22×C22⋊C4—112no—
275C22×C22⋊C4—112no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4C2×D1112yes—
278C22×C22⋊C4C2×D1112yes—
279C22×C42—111no—
280C22×C42—111no—
281C22×C42C2×D1111yescharacteristic
282#399—1116no—
283#396—1116no—
284#390—118no—
285#390C2×D1118yes—
286#389—118no—
287#389—118no—
288#385—1116no—
289#380—1116no—
290C4×C4⋊C4—118no—
291C2×#95—111no—
292C2×#95—112no—
293C2×#95—111no—
294C2×#95—112no—
295C22×C11—28no—
296C22×C11—28no—
297C22×C11—28no—
298C22×C11—44no—
299C22×C11—44no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—432no—
303C22×C11C2×C22⋊Q814yes—
304C22×C11#52914yes—
305C22×C11#54014yes—
306C22×C11#54614yes—
307C22×C11#55014yes—
308C22×C11#55414yes—
309C22×C11#55414yes—
310C22×C11C23×D411yescharacteristic
311C22×C11C23×Q811yescharacteristic
312C22×C11C22×#4111yescharacteristic
313C22×C11C22×#4111yescharacteristic
314C22×C11C22×#4111yescharacteristic
315C22×C11C2×H(5,𝔽2)11yescharacteristic
316C22×C11C2×H(5,𝔽2)11yescharacteristic
317C4×C11—44no—
318C4×C11—42no—
319C4×C11—42no—
320C4×C11C2×C22⋊Q818yes—
321Dic11—24no—
322Dic11—24no—
323Dic11—28no—
324Dic11—42no—
325Dic11—42no—
326Dic11—44no—
327C25C22×D1112yes—
328C22×D4—24no—
329C22×D4—24no—
330C22×D4Dic2218yes—
331C22×D4C22×D1114yes—
332C23×C4—111no—
333C23×C4—112no—
334C23×C4—111no—
335C23×C4—112no—
336C23×C4—111no—
337C23×C4—111no—
338C23×C4—118no—
339C23×C4—228no—
340C23×C4—228no—
341C23×C4—444no—
342C23×C4C22×D1111yescharacteristic
343C23×C4C22×D1111yescharacteristic
344C23×C4C22×D1112yes—
345C23×C4C22×D1111yescharacteristic
346#125—2232no—
347C4×D4—2232no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—118no—
350C2×C4⋊C4—114no—
351C2×C4⋊C4—118no—
352C2×C4⋊C4—118no—
353C2×C4⋊C4—114no—
354C2×C4⋊C4—114no—
355C2×C4⋊C4—114no—
356C2×C4⋊C4—118no—
357C2×C4⋊C4—118no—
358C2×C4⋊C4—228no—
359C2×C4⋊C4—228no—
360C2×C4⋊C4—224no—
361C2×C4⋊C4—224no—
362C2×C4⋊C4—224no—
363C2×C4⋊C4—444no—
364C2×C4⋊C4—444no—
365C2×C4⋊C4C22×D1114yes—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—118no—
369C2×C22⋊C4—118no—
370C2×C22⋊C4—118no—
371C2×C22⋊C4—228no—
372C2×C22⋊C4—228no—
373C2×C22⋊C4—444no—
374C2×C22⋊C4C22×D1118yes—
375C2×C22⋊C4C22×D1118yes—
376C2×C42—24no—
377C2×C42—114no—
378C2×C42—114no—
379C2×C42—224no—
380C2×C42—224no—
381C2×C42C22×D1114yes—
382#95—114no—
383#95—114no—
384#95—118no—
385#95—118no—
386C2×C11—48no—
387C2×C11#245418yescomplemented
388C2×C11C22×C22⋊Q811yescharacteristic
389C2×C11C2×#52911yescharacteristic
390C2×C11C2×#54011yescharacteristic
391C2×C11C2×#54611yescharacteristic
392C2×C11C2×#55011yescharacteristic
393C2×C11C2×#55411yescharacteristic
394C2×C11C2×#55411yescharacteristic
395C24—24no—
396C24—24no—
397C24—24no—
398C24—24no—
399C24—24no—
400C24—24no—
401C24C2×Dic2218yes—
402C24C23×D1114yes—
403C24C23×D1111yescharacteristic
404C2×D4—232no—
405C2×D4—28no—
406C2×D4—28no—
407C2×D4C2×Dic22116yes—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—118no—
418C22×C4—114no—
419C22×C4—114no—
420C22×C4—112no—
421C22×C4—112no—
422C22×C4—114no—
423C22×C4—112no—
424C22×C4—112no—
425C22×C4—114no—
426C22×C4—2216no—
427C22×C4—2216no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—224no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—224no—
434C22×C4—222no—
435C22×C4—224no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—224no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—224no—
442C22×C4—222no—
443C22×C4—448no—
444C22×C4—4432no—
445C22×C4C2×Dic2214yes—
446C22×C4D4×D1114yes—
447C22×C4#434114yes—
448C22×C4C23×D1114yes—
449C22×C4C23×D1112yes—
450C22×C4C23×D1112yes—
451C22×C4C23×D1112yes—
452C4⋊C4—28no—
453C4⋊C4—1116no—
454C4⋊C4—2216no—
455C4⋊C4—2216no—
456C4⋊C4—228no—
457C4⋊C4—228no—
458C4⋊C4—228no—
459C4⋊C4—448no—
460C4⋊C4—448no—
461C22⋊C4—48no—
462C22⋊C4—48no—
463C22⋊C4—2216no—
464C22⋊C4—2216no—
465C22⋊C4—448no—
466C42—28no—
467C42—228no—
468C42—228no—
469C11C2×#245411yescharacteristic, complemented, Sylow
470C23—216no—
471C23—216no—
472C23—216no—
473C23—24no—
474C23—24no—
475C23—24no—
476C23—24no—
477C23—24no—
478C23—24no—
479C23—48no—
480C23—48no—
481C23—48no—
482C23—48no—
483C23C22×Dic2218yes—
484C23C22×Dic2212yes—
485C23C2×D4×D1112yes—
486C23C2×#434112yes—
487C23#6703712yes—
488C23#6703712yes—
489C23#41×D1112yes—
490C23#41×D1112yes—
491C23C24×D1111yescharacteristic
492D4—232no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—48no—
503C2×C4—44no—
504C2×C4—44no—
505C2×C4—118no—
506C2×C4—114no—
507C2×C4—114no—
508C2×C4—228no—
509C2×C4—2216no—
510C2×C4—222no—
511C2×C4—222no—
512C2×C4—224no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—224no—
516C2×C4—228no—
517C2×C4—222no—
518C2×C4—224no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—224no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—224no—
525C2×C4—222no—
526C2×C4—4432no—
527C2×C4—444no—
528C2×C4—444no—
529C2×C4—448no—
530C2×C4#66931116yes—
531C2×C4C22×Dic2214yes—
532C2×C4C2×D4×D1114yes—
533C2×C4C2×#434114yes—
534C22—28no—
535C22—28no—
536C22—28no—
537C22—44no—
538C22—432no—
539C22—44no—
540C22—44no—
541C22—44no—
542C22C2×#6693114yes—
543C22#1062307014yes—
544C22#1062307014yes—
545C22#1062313014yes—
546C22#1062314314yes—
547C22#1062321114yes—
548C22#1062325014yes—
549C22C23×Dic2211yescharacteristic
550C22C22×D4×D1111yescharacteristic
551C22C22×#434111yescharacteristic
552C22C2×#6703711yescharacteristic
553C22C2×#6703711yescharacteristic
554C22C2×#41×D1111yescharacteristic
555C22C2×#41×D1111yescharacteristic
556C4—44no—
557C4—42no—
558C4—42no—
559C4—224no—
560C4—224no—
561C4—228no—
562C4—442no—
563C4—442no—
564C4—444no—
565C4C2×#6693118yes—
566C2—48no—
567C2#1307249018yesdirect product factor
568C2C22×#6693111yescharacteristic
569C2C2×#1062321111yescharacteristic
570C2C2×#1062325011yescharacteristic
571C2C2×#1062314311yescharacteristic
572C2C2×#1062313011yescharacteristic
573C2C2×#1062307011yescharacteristic
574C2C2×#1062307011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#390C2
socleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11C2×#2454
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#66923C2semidirect
3. #13072490C2direct (N × H)
4. C2×#10622562C2semidirect
5. C2×#10622561C2semidirect
7. C2×#10622598C2semidirect
8. C2×#10622586C2semidirect
9. C2×#10622559C2semidirect
10. C2×#10622555C2semidirect
11. C2×C4×Dic11⋊C4C2semidirect
35. C2×#66923C22semidirect
42. #10622598C22semidirect
43. #10622586C22semidirect
44. #10622562C22semidirect
45. #10622561C22semidirect
46. #10622559C22semidirect
47. #10622555C22semidirect
48. C4×Dic11⋊C4C22semidirect
387. C2×C11#2454semidirect
469. C11C2×#2454semidirect
567. C2#13072490direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669232
C22×D4×Dic112
#130724902
C2×#106225622
C2×#106225612
C2×#106228342
C2×#106225982
C2×#106225862
C2×#106225592
C2×#106225552
C2×C4×Dic11⋊C42
C2×C11×#3902
C2×#245411