Finite Group Databasebeta

← C2×#13072486 #14921939

Subgroups — C2×#13072486 #14921939

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×#66943C211yesmaximal, characteristic, complemented
2C22×#66946C211yesmaximal, characteristic
3#13072486C2116yesmaximal, direct product factor
4C2×#10622290C212yesmaximal, complemented
5C2×#10622607C212yesmaximal, complemented
6C2×#10622552C211yesmaximal, characteristic
7C2×#10622601C211yesmaximal, characteristic
8C2×#10622598C211yesmaximal, characteristic, complemented
9C2×#10622281C212yesmaximal, complemented
10C2×#10622600C212yesmaximal, complemented
11C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
12C2×C11×#389C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C23×C4×D11C2212yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×C4⋊Dic11C2212yes—
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2212yes—
29C22×Dic11⋊C4C2212yes—
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C2×#66946—28no—
33C2×#66946C2218yes—
34C2×#66943—28no—
35C2×#66943C2218yescomplemented
36C11×#389C2218yescomplemented
37C2×C11×#95C2212yes—
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41#10622607C22116yescomplemented
42#10622601C2218yes—
43#10622600C22116yescomplemented
44#10622598C2218yescomplemented
45#10622552C2218yes—
46C4×C4⋊Dic11C2218yescomplemented
47#10622290C22116yescomplemented
48#10622281C22116yescomplemented
49C24×D11C2312yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C22×D44—24no—
61C22×D44—24no—
62C22×D44Q818yes—
63C22×D44C2314yes—
64C22×C4×D11—28no—
65C22×C4×D11—28no—
66C22×C4×D11—44no—
67C22×C4×D11C2318yes—
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4—44no—
70C2×C11×C4⋊C4D418yes—
71C2×C11×C4⋊C4C2314yes—
72C2×C11×C4⋊C4C2318yes—
73C2×C11×C4⋊C4C2314yes—
74C2×C42×C11—24no—
75C2×C42×C11C2314yes—
76C2×(C2×D11)⋊C4—28no—
77C2×(C2×D11)⋊C4—28no—
78C2×(C2×D11)⋊C4—44no—
79C2×(C2×D11)⋊C4—44no—
80C2×(C2×D11)⋊C4—44no—
81C2×(C2×D11)⋊C4C2318yes—
82C2×(C2×D11)⋊C4C2318yes—
83C2×(C2×D11)⋊C4C2318yes—
84C2×(C2×D11)⋊C4C2318yes—
85C2×(C2×D11)⋊C4C2318yes—
86C2×C4⋊Dic11—28no—
87C2×C4⋊Dic11—24no—
88C2×C4⋊Dic11—24no—
89C2×C4⋊Dic11—24no—
90C2×C4⋊Dic11—44no—
91C2×C4⋊Dic11C2318yes—
92C2×C4⋊Dic11C2314yes—
93C2×C4⋊Dic11C2314yes—
94C2×C4⋊Dic11C2314yes—
95C2×C4⋊Dic11C2318yes—
96C2×Dic11⋊C4—28no—
97C2×Dic11⋊C4C2318yes—
98C2×C4×Dic11—24no—
99C2×C4×Dic11—24no—
100C2×C4×Dic11C2314yes—
101C2×C4×Dic11C2314yes—
102#66946—232no—
103#66943—232no—
104C11×#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2314yes—
107C11⋊#95C2314yes—
108C2×#2454—111nomaximal, Sylow
109C24×C11C2411yescharacteristic
110C23×D11—24no—
111C23×D11—24no—
112C23×D11—24no—
113C23×D11—24no—
114C23×D11—24no—
115C23×D11—24no—
116C23×D11C2×Q818yes—
117C23×D11C2414yes—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11C2×D418yes—
129C22×C4×C11C2×D414yes—
130C22×C4×C11C2×Q814yes—
131C22×C4×C11#4114yes—
132C22×C4×C11#4114yes—
133C22×C4×C11C2412yes—
134C22×C4×C11C2414yes—
135C22×C4×C11C2414yes—
136C22×C4×C11C2412yes—
137C22×C4×C11C2412yes—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—24no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—24no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—24no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11#4114yes—
153C22×Dic11C2412yes—
154C22×Dic11C2412yes—
155C22×Dic11C2412yes—
156C22×Dic11C2414yes—
157C22×Dic11C2412yes—
158C2×D44—232no—
159C2×D44—28no—
160C2×D44—28no—
161C2×D44C2×Q8116yes—
162C2×C4×D11—216no—
163C2×C4×D11—216no—
164C2×C4×D11—48no—
165C2×C4×D11—432no—
166C11×C4⋊C4—28no—
167C11×C4⋊C4—48no—
168C11×C4⋊C4C2×D4116yes—
169C42×C11—28no—
170(C2×D11)⋊C4—216no—
171(C2×D11)⋊C4—216no—
172(C2×D11)⋊C4—48no—
173(C2×D11)⋊C4—48no—
174(C2×D11)⋊C4—48no—
175C4⋊Dic11—28no—
176C4⋊Dic11—216no—
177C4⋊Dic11—28no—
178C4⋊Dic11—28no—
179C4⋊Dic11—48no—
180Dic11⋊C4—216no—
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×#390—111no—
190C2×#389—111no—
191C2×#389D1111yescharacteristic, complemented
192C2×#385—112no—
193C2×#380—112no—
194C2×C4×C4⋊C4—111no—
195C23×C11C22×D412yes—
196C23×C11C22×Q812yes—
197C23×C11C2×#4112yes—
198C23×C11C2×#4112yes—
199C23×C11C2×#4112yes—
200C23×C11H(5,𝔽2)12yes—
201C23×C11H(5,𝔽2)12yes—
202C23×C11C2511yescharacteristic
203C22×D11—216no—
204C22×D11—216no—
205C22×D11—216no—
206C22×D11—24no—
207C22×D11—24no—
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—48no—
213C22×D11—48no—
214C22×D11—48no—
215C22×D11—48no—
216C22×D11C22×Q818yes—
217C2×C4×C11—28no—
218C2×C4×C11—216no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—44no—
230C2×C4×C11—48no—
231C2×C4×C11C22⋊Q8116yes—
232C2×C4×C11C22×D418yes—
233C2×C4×C11C22×D414yes—
234C2×C4×C11C22×Q814yes—
235C2×C4×C11C2×#4114yes—
236C2×C4×C11C2×#4114yes—
237C2×Dic11—28no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—24no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—44no—
253C2×Dic11—44no—
254C2×Dic11—44no—
255C2×Dic11—48no—
256C2×Dic11C2×#4114yes—
257D44—232no—
258C4×D11—432no—
259C23×D4—111no—
260C24×C4—112no—
261C2×#125—118no—
262C2×#125—228no—
263C2×C4×D4—118no—
264C2×C4×D4—228no—
265C22×C4⋊C4—112no—
266C22×C4⋊C4—111no—
267C22×C4⋊C4—112no—
268C22×C4⋊C4—111no—
269C22×C4⋊C4—111no—
270C22×C4⋊C4—112no—
271C22×C4⋊C4C2×D1111yescharacteristic
272C22×C4⋊C4C2×D1112yes—
273C22×C4⋊C4C2×D1111yescharacteristic
274C22×C22⋊C4—112no—
275C22×C22⋊C4—112no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4—112no—
279C22×C42—111no—
280C22×C42—111no—
281C22×C42C2×D1111yescharacteristic
282#399—1116no—
283#396—1116no—
284#390—118no—
285#390—118no—
286#389—118no—
287#389C2×D1118yescomplemented
288#385—1116no—
289#380—1116no—
290C4×C4⋊C4—118no—
291C2×#95—111no—
292C2×#95—111no—
293C2×#95—112no—
294C2×#95C2×D1112yes—
295C22×C11C2×C22⋊Q814yes—
296C22×C11#52914yes—
297C22×C11#54014yes—
298C22×C11#54614yes—
299C22×C11#55014yes—
300C22×C11#55414yes—
301C22×C11#55414yes—
302C22×C11C23×D411yescharacteristic
303C22×C11C23×Q811yescharacteristic
304C22×C11C22×#4111yescharacteristic
305C22×C11C22×#4111yescharacteristic
306C22×C11C22×#4111yescharacteristic
307C22×C11C2×H(5,𝔽2)11yescharacteristic
308C22×C11C2×H(5,𝔽2)11yescharacteristic
309C2×D11—28no—
310C2×D11—28no—
311C2×D11—28no—
312C2×D11—44no—
313C2×D11—44no—
314C2×D11—44no—
315C2×D11—44no—
316C2×D11—432no—
317C4×C11—24no—
318C4×C11—28no—
319C4×C11—42no—
320C4×C11—44no—
321C4×C11C2×C22⋊Q818yes—
322Dic11—24no—
323Dic11—42no—
324Dic11—42no—
325Dic11—42no—
326Dic11—44no—
327C25—112no—
328C22×D4—118no—
329C22×D4—114no—
330C22×D4—224no—
331C22×D4—224no—
332C23×C4—111no—
333C23×C4—112no—
334C23×C4—111no—
335C23×C4—111no—
336C23×C4—111no—
337C23×C4—118no—
338C23×C4—228no—
339C23×C4—228no—
340C23×C4—444no—
341C23×C4C22×D1112yes—
342C23×C4C22×D1111yescharacteristic
343C23×C4C22×D1112yes—
344C23×C4C22×D1111yescharacteristic
345C23×C4C22×D1111yescharacteristic
346#125—2232no—
347C4×D4—2232no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—118no—
351C2×C4⋊C4—118no—
352C2×C4⋊C4—114no—
353C2×C4⋊C4—114no—
354C2×C4⋊C4—114no—
355C2×C4⋊C4—118no—
356C2×C4⋊C4—224no—
357C2×C4⋊C4—228no—
358C2×C4⋊C4—228no—
359C2×C4⋊C4—224no—
360C2×C4⋊C4—224no—
361C2×C4⋊C4—444no—
362C2×C4⋊C4D4418yes—
363C2×C4⋊C4C22×D1114yes—
364C2×C4⋊C4C22×D1118yes—
365C2×C4⋊C4C22×D1114yes—
366C2×C22⋊C4—118no—
367C2×C22⋊C4—118no—
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⋊C4—444no—
375C2×C22⋊C4—444no—
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#95C22×D1118yes—
386C2×C11#245418yescomplemented
387C2×C11C22×C22⋊Q811yescharacteristic
388C2×C11C2×#52911yescharacteristic
389C2×C11C2×#54011yescharacteristic
390C2×C11C2×#54611yescharacteristic
391C2×C11C2×#55011yescharacteristic
392C2×C11C2×#55411yescharacteristic
393C2×C11C2×#55411yescharacteristic
394D11—48no—
395C24—118no—
396C24—114no—
397C24—224no—
398C24—224no—
399C24—224no—
400C24—224no—
401C24—224no—
402C24—224no—
403C24C23×D1111yescharacteristic
404C2×D4—1116no—
405C2×D4—2232no—
406C2×D4—228no—
407C2×D4—228no—
408C22×C4—22no—
409C22×C4—24no—
410C22×C4—22no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—114no—
419C22×C4—112no—
420C22×C4—112no—
421C22×C4—112no—
422C22×C4—112no—
423C22×C4—114no—
424C22×C4—2216no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—224no—
431C22×C4—222no—
432C22×C4—224no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—224no—
438C22×C4—222no—
439C22×C4—2216no—
440C22×C4—448no—
441C22×C4—4432no—
442C22×C4C2×D4418yes—
443C22×C4C2×D4414yes—
444C22×C4#434114yes—
445C22×C4Q8×D1114yes—
446C22×C4#434314yes—
447C22×C4C23×D1112yes—
448C22×C4C23×D1114yes—
449C22×C4C23×D1114yes—
450C22×C4C23×D1112yes—
451C22×C4C23×D1112yes—
452C4⋊C4—28no—
453C4⋊C4—48no—
454C4⋊C4—228no—
455C4⋊C4—2216no—
456C4⋊C4—2216no—
457C4⋊C4—228no—
458C4⋊C4—228no—
459C4⋊C4—448no—
460C4⋊C4C2×D44116yes—
461C22⋊C4—2216no—
462C22⋊C4—2216no—
463C22⋊C4—448no—
464C22⋊C4—448no—
465C22⋊C4—448no—
466C42—28no—
467C42—228no—
468C42—228no—
469C11C2×#245411yescharacteristic, complemented, Sylow
470C23—118no—
471C23—2216no—
472C23—2216no—
473C23—224no—
474C23—224no—
475C23—224no—
476C23—224no—
477C23—224no—
478C23—224no—
479C23—2216no—
480C23—448no—
481C23—448no—
482C23—448no—
483C23—448no—
484C23C22×D4412yes—
485C23C2×#434112yes—
486C23#6703712yes—
487C23C2×Q8×D1112yes—
488C23C2×#434312yes—
489C23#41×D1112yes—
490C23#6704212yes—
491C23C24×D1111yescharacteristic
492D4—2232no—
493C2×C4—216no—
494C2×C4—28no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—44no—
506C2×C4—48no—
507C2×C4—114no—
508C2×C4—228no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—222no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—222no—
516C2×C4—224no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—224no—
522C2×C4—222no—
523C2×C4—4432no—
524C2×C4—444no—
525C2×C4—444no—
526C2×C4—444no—
527C2×C4—448no—
528C2×C4#66950116yes—
529C2×C4C22×D4418yes—
530C2×C4C22×D4414yes—
531C2×C4C2×#434114yes—
532C2×C4C2×Q8×D1114yes—
533C2×C4C2×#434314yes—
534C22—228no—
535C22—228no—
536C22—228no—
537C22—444no—
538C22—4432no—
539C22—444no—
540C22—444no—
541C22—444no—
542C22C2×#6695014yes—
543C22#1062308514yes—
544C22#1062310814yes—
545C22#1062315014yes—
546C22#1062315514yes—
547C22#1062322114yes—
548C22#1062326114yes—
549C22C23×D4411yescharacteristic
550C22C22×#434111yescharacteristic
551C22C2×#6703711yescharacteristic
552C22C22×Q8×D1111yescharacteristic
553C22C22×#434311yescharacteristic
554C22C2×#41×D1111yescharacteristic
555C22C2×#6704211yescharacteristic
556C4—24no—
557C4—28no—
558C4—42no—
559C4—44no—
560C4—224no—
561C4—442no—
562C4—442no—
563C4—442no—
564C4—444no—
565C4C2×#6695018yes—
566C2—448no—
567C2#1307248618yesdirect product factor
568C2C22×#6695011yescharacteristic
569C2C2×#1062315511yescharacteristic
570C2C2×#1062315011yescharacteristic
571C2C2×#1062308511yescharacteristic
572C2C2×#1062310811yescharacteristic
573C2C2×#1062322111yescharacteristic
574C2C2×#1062326111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#389C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#389D11
hypocenterC11C2×#2454
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#66943C2semidirect
3. #13072486C2direct (N × H)
4. C2×#10622290C2semidirect
5. C2×#10622607C2semidirect
8. C2×#10622598C2semidirect
9. C2×#10622281C2semidirect
10. C2×#10622600C2semidirect
11. C2×C4×C4⋊Dic11C2semidirect
12. C2×C11×#389C2semidirect
35. C2×#66943C22semidirect
36. C11×#389C22semidirect
41. #10622607C22semidirect
43. #10622600C22semidirect
44. #10622598C22semidirect
46. C4×C4⋊Dic11C22semidirect
47. #10622290C22semidirect
48. #10622281C22semidirect
191. C2×#389D11semidirect
287. #389C2×D11semidirect
386. C2×C11#2454semidirect
469. C11C2×#2454semidirect
567. C2#13072486direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669432
C22×#669462
#130724862
C2×#106222902
C2×#106226072
C2×#106225522
C2×#106226012
C2×#106225982
C2×#106222812
C2×#106226002
C2×C4×C4⋊Dic112
C2×C11×#3892
C2×#245411