Finite Group Databasebeta

← C2×#13071135 #14912206

Subgroups — C2×#13071135 #14912206

Order 2816.

4070 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66939C211yesmaximal, characteristic
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
3C23×C4×Dic11C211yesmaximal, characteristic, complemented
4#13071135C2116yesmaximal, direct product factor
5C2×#10622603C212yesmaximal, complemented
6C2×#10622267C212yesmaximal, complemented
7C2×#10622826C211yesmaximal, characteristic
8C2×#10622556C211yesmaximal, characteristic, complemented
9C2×C4⋊C4×Dic11C212yesmaximal, complemented
10C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
11C2×#10622279C212yesmaximal, complemented
12C2×C11×#385C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C24×Dic11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×C4⋊Dic11C2212yes—
26C22×Dic11⋊C4C2211yescharacteristic
27C22×C4×Dic11—28no—
28C22×C4×Dic11C2212yes—
29C22×C4×Dic11C2212yes—
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2212yes—
32C22×C4×Dic11C2218yescomplemented
33C2×#66939C4116yescomplemented
34C2×#66939C2218yes—
35C2×(C22⋊D11)⋊C4—28no—
36C2×(C22⋊D11)⋊C4C2218yes—
37C11×#385C2218yescomplemented
38C2×C11×#95C2212yes—
39#10622826C2218yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44#10622603C22116yescomplemented
45C4⋊C4×Dic11C22116yescomplemented
46#10622556C2218yescomplemented
47C22⋊C4×Dic11C2218yescomplemented
48#10622279C22116yescomplemented
49#10622267C22116yescomplemented
50C25×C11C2311yescharacteristic
51C24×D11C2311yescharacteristic
52C23×C4×C11—24no—
53C23×C4×C11—28no—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2314yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2312yes—
58C23×C4×C11C2312yes—
59C22×C22⋊D11—24no—
60C22×C22⋊D11—24no—
61C22×C22⋊D11C2×C418yes—
62C22×C22⋊D11C2314yes—
63C23×Dic11—24no—
64C23×Dic11—24no—
65C23×Dic11—28no—
66C23×Dic11C2×C418yescomplemented
67C23×Dic11D418yes—
68C23×Dic11C2312yes—
69C23×Dic11C2312yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2314yes—
72C23×Dic11C2314yes—
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C22×C4×D11—24no—
76C22×C4×D11—28no—
77C22×C4×D11C2314yes—
78C2×C11×C4⋊C4—28no—
79C2×C11×C4⋊C4C2318yes—
80C2×C11×C22⋊C4—24no—
81C2×C11×C22⋊C4C2×C418yescomplemented
82C2×C11×C22⋊C4C2314yes—
83C2×C11×C22⋊C4C2314yes—
84C2×C22⋊Dic11—24no—
85C2×C22⋊Dic11C2314yes—
86C2×(C2×D11)⋊C4—28no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4C2×C4116yescomplemented
89C2×(C2×D11)⋊C4C2314yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×C4⋊Dic11C2×C4116yescomplemented
93C2×C4⋊Dic11C2318yes—
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4C2314yes—
96C2×C4×Dic11—24no—
97C2×C4×Dic11—28no—
98C2×C4×Dic11—28no—
99C2×C4×Dic11—232no—
100C2×C4×Dic11—28no—
101C2×C4×Dic11C2314yes—
102C2×C4×Dic11C2318yes—
103C2×C4×Dic11C2318yes—
104C2×C4×Dic11C2318yes—
105#66939C2×C4164yescomplemented
106(C22⋊D11)⋊C4—232no—
107C11×#95C2318yes—
108C11⋊#95C2318yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C11⋊#95C2318yes—
112C2×C4×#123—111nomaximal, Sylow
113C24×C11—24no—
114C24×C11—24no—
115C24×C11C22×C414yes—
116C24×C11C2×D414yes—
117C24×C11#4114yes—
118C24×C11C2412yes—
119C24×C11C2411yescharacteristic
120C23×D11—22no—
121C23×D11—24no—
122C23×D11—24no—
123C23×D11—22no—
124C23×D11C22×C414yes—
125C23×D11C2412yes—
126C22×C4×C11—232no—
127C22×C4×C11—28no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—216no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11C22×C418yes—
138C22×C4×C11#4118yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2414yes—
142C22×C4×C11C2414yes—
143C2×C22⋊D11—232no—
144C2×C22⋊D11—28no—
145C2×C22⋊D11—28no—
146C2×C22⋊D11C22×C4116yes—
147C22×Dic11—232no—
148C22×Dic11—216no—
149C22×Dic11—232no—
150C22×Dic11—28no—
151C22×Dic11—24no—
152C22×Dic11—22no—
153C22×Dic11—28no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—22no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11C22×C414yes—
161C22×Dic11C22×C418yes—
162C22×Dic11C22×C4116yescomplemented
163C22×Dic11C2×D4116yes—
164C22×Dic11C2×D414yes—
165C22×Dic11C2×D414yes—
166C22×Dic11#4118yes—
167C22×Dic11C2414yes—
168C22×Dic11C2414yes—
169C22×Dic11C2412yes—
170C22×Dic11C2412yes—
171C22×Dic11C2412yes—
172C2×C4×D11—28no—
173C2×C4×D11—216no—
174C2×C4×D11—416no—
175C11×C4⋊C4—216no—
176C11×C22⋊C4—28no—
177C11×C22⋊C4C22×C4116yescomplemented
178C22⋊Dic11—28no—
179(C2×D11)⋊C4—28no—
180(C2×D11)⋊C4—216no—
181(C2×D11)⋊C4C22×C4132yescomplemented
182C4⋊Dic11C22×C4132yescomplemented
183Dic11⋊C4—28no—
184C4×Dic11—28no—
185C4×Dic11—216no—
186C4×Dic11—216no—
187C4×Dic11—216no—
188C22×#123—111no—
189C22×C4×D4—111no—
190C23×C42—111no—
191C4×#123—1116no—
192C2×#388—112no—
193C2×#387—112no—
194C2×#386—111no—
195C2×#385D1111yescharacteristic, complemented
196C2×#381—111no—
197C2×C4×C4⋊C4—112no—
198C2×C4×C22⋊C4—112no—
199C2×C4×C22⋊C4—111no—
200C23×C11—216no—
201C23×C11—28no—
202C23×C11—28no—
203C23×C11—216no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11C4×D4116yes—
207C23×C11C23×C414yes—
208C23×C11C23×C412yes—
209C23×C11C22×D414yes—
210C23×C11C22×D412yes—
211C23×C11C2×#4114yes—
212C23×C11C2×#4114yes—
213C23×C11C2×#4112yes—
214C23×C11C2×#4114yes—
215C23×C11C2511yescharacteristic
216C22×D11—28no—
217C22×D11—216no—
218C22×D11—22no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—22no—
222C22×D11—44no—
223C22×D11—44no—
224C22×D11—48no—
225C22×D11C23×C414yes—
226C2×C4×C11—232no—
227C2×C4×C11—216no—
228C2×C4×C11—216no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—44no—
238C2×C4×C11—44no—
239C2×C4×C11C23×C418yes—
240C2×C4×C11C2×#4118yes—
241C22⋊D11—232no—
242C2×Dic11—216no—
243C2×Dic11—232no—
244C2×Dic11—28no—
245C2×Dic11—28no—
246C2×Dic11—24no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—22no—
251C2×Dic11—232no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—48no—
256C2×Dic11#123116yescomplemented
257C2×Dic11C23×C414yes—
258C2×Dic11C23×C418yes—
259C2×Dic11C22×D414yes—
260C2×Dic11C22×D414yes—
261C2×Dic11C2×#4118yes—
262C4×D11—416no—
263C23×D4—111no—
264C24×C4—111no—
265C24×C4—111no—
266C24×C4—111no—
267C24×C4C2×D1111yescharacteristic
268C2×#123—118no—
269C2×#123—1116no—
270C2×C4×D4—118no—
271C2×C4×D4—228no—
272C22×C4⋊C4—112no—
273C22×C4⋊C4—111no—
274C22×C4⋊C4C2×D1112yes—
275C22×C22⋊C4—112no—
276C22×C22⋊C4—111no—
277C22×C22⋊C4—111no—
278C22×C22⋊C4—112no—
279C22×C22⋊C4C2×D1111yescharacteristic
280C22×C22⋊C4C2×D1111yescharacteristic
281C22×C42—112no—
282C22×C42—112no—
283C22×C42—111no—
284C22×C42—112no—
285C22×C42—118no—
286C22×C42—228no—
287#388—1116no—
288#387—1116no—
289#386—118no—
290#385C2×D1118yescomplemented
291#381—118no—
292C4×C4⋊C4—1116no—
293C4×C22⋊C4—118no—
294C4×C22⋊C4—1116no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95C2×D1112yes—
300C22×C11—28no—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11—28no—
304C22×C11—232no—
305C22×C11C2×C4×D418yes—
306C22×C11C2×C4×D414yes—
307C22×C11C4×#4118yes—
308C22×C11C2×#12314yes—
309C22×C11#52514yes—
310C22×C11#52918yes—
311C22×C11C24×C411yescharacteristic
312C22×C11C23×D411yescharacteristic
313C22×C11C22×#4112yes—
314C22×C11C22×#4111yescharacteristic
315C22×C11C22×#4112yes—
316C2×D11—24no—
317C2×D11—28no—
318C2×D11—42no—
319C2×D11—42no—
320C2×D11—44no—
321C2×D11—416no—
322C4×C11—28no—
323C4×C11—28no—
324C4×C11—42no—
325C4×C11—42no—
326Dic11—28no—
327Dic11—24no—
328Dic11—24no—
329Dic11—44no—
330Dic11C2×#12318yescomplemented
331C25—111no—
332C25C22×D1111yescharacteristic
333C22×D4—118no—
334C22×D4—114no—
335C22×D4—224no—
336C22×D4—224no—
337C23×C4—24no—
338C23×C4—28no—
339C23×C4—111no—
340C23×C4—118no—
341C23×C4—118no—
342C23×C4—114no—
343C23×C4—114no—
344C23×C4—112no—
345C23×C4—111no—
346C23×C4—111no—
347C23×C4—112no—
348C23×C4—114no—
349C23×C4—224no—
350C23×C4—228no—
351C23×C4—228no—
352C23×C4—224no—
353C23×C4—224no—
354C23×C4C22×D1114yes—
355C23×C4C22×D1111yescharacteristic
356C23×C4C22×D1111yescharacteristic
357C23×C4C22×D1112yes—
358C23×C4C22×D1112yes—
359#123—1164no—
360C4×D4—2232no—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—1116no—
363C2×C4⋊C4—118no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—224no—
366C2×C4⋊C4C22×D1118yes—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—1116no—
369C2×C22⋊C4—118no—
370C2×C22⋊C4—114no—
371C2×C22⋊C4—114no—
372C2×C22⋊C4—118no—
373C2×C22⋊C4—224no—
374C2×C22⋊C4—224no—
375C2×C22⋊C4—228no—
376C2×C22⋊C4C4×D1118yescomplemented
377C2×C22⋊C4C22×D1114yes—
378C2×C22⋊C4C22×D1114yes—
379C2×C42—114no—
380C2×C42—118no—
381C2×C42—118no—
382C2×C42—118no—
383C2×C42—224no—
384C2×C42—228no—
385C2×C42—228no—
386C2×C42—228no—
387C2×C42—2232no—
388#95—118no—
389#95—118no—
390#95—118no—
391#95—118no—
392#95C22×D1118yes—
393C2×C11—28no—
394C2×C11C4×#12318yescomplemented
395C2×C11C22×C4×D411yescharacteristic
396C2×C11C2×C4×#4112yes—
397C2×C11C22×#12311yescharacteristic
398C2×C11C2×#52511yescharacteristic
399C2×C11C2×#52912yes—
400D11—44no—
401C24—24no—
402C24—24no—
403C24—114no—
404C24—112no—
405C24—222no—
406C24—224no—
407C24—222no—
408C24—224no—
409C24C2×C4×D1114yes—
410C24D4×D1114yes—
411C24#434314yes—
412C24C23×D1112yes—
413C24C23×D1111yescharacteristic
414C2×D4—1116no—
415C2×D4—2232no—
416C2×D4—228no—
417C2×D4—228no—
418C22×C4—232no—
419C22×C4—28no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—216no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—114no—
430C22×C4—118no—
431C22×C4—112no—
432C22×C4—118no—
433C22×C4—114no—
434C22×C4—1116no—
435C22×C4—114no—
436C22×C4—1116no—
437C22×C4—114no—
438C22×C4—112no—
439C22×C4—112no—
440C22×C4—114no—
441C22×C4—228no—
442C22×C4—2216no—
443C22×C4—2232no—
444C22×C4—2216no—
445C22×C4—2232no—
446C22×C4—228no—
447C22×C4—224no—
448C22×C4—222no—
449C22×C4—228no—
450C22×C4—224no—
451C22×C4—222no—
452C22×C4—224no—
453C22×C4—224no—
454C22×C4—224no—
455C22×C4—224no—
456C22×C4—4416no—
457C22×C4C2×C4×D1118yes—
458C22×C4#434118yes—
459C22×C4C23×D1112yes—
460C22×C4C23×D1112yes—
461C22×C4C23×D1114yes—
462C22×C4C23×D1114yes—
463C4⋊C4—216no—
464C4⋊C4—1132no—
465C4⋊C4—228no—
466C22⋊C4—28no—
467C22⋊C4—1132no—
468C22⋊C4—228no—
469C22⋊C4—228no—
470C22⋊C4—2216no—
471C22⋊C4C2×C4×D11116yescomplemented
472C42—2216no—
473C42—2216no—
474C42—228no—
475C42—2216no—
476C11C2×C4×#12311yescharacteristic, complemented, Sylow
477C23—216no—
478C23—28no—
479C23—216no—
480C23—28no—
481C23—24no—
482C23—24no—
483C23—114no—
484C23—228no—
485C23—2216no—
486C23—222no—
487C23—224no—
488C23—222no—
489C23—224no—
490C23—444no—
491C23—448no—
492C23—444no—
493C23#66946116yes—
494C23C22×C4×D1114yes—
495C23C22×C4×D1112yes—
496C23C2×D4×D1114yes—
497C23C2×D4×D1112yes—
498C23C2×#434114yes—
499C23C2×#434314yes—
500C23C2×#434312yes—
501C23#41×D1114yes—
502C23C24×D1111yescharacteristic
503D4—2232no—
504C2×C4—232no—
505C2×C4—216no—
506C2×C4—216no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—44no—
516C2×C4—44no—
517C2×C4—1116no—
518C2×C4—114no—
519C2×C4—118no—
520C2×C4—118no—
521C2×C4—114no—
522C2×C4—114no—
523C2×C4—2232no—
524C2×C4—2232no—
525C2×C4—2216no—
526C2×C4—228no—
527C2×C4—228no—
528C2×C4—224no—
529C2×C4—222no—
530C2×C4—224no—
531C2×C4—222no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—4416no—
537C2×C4—448no—
538C2×C4C22×C4×D1118yes—
539C2×C4C2×#434118yes—
540C22—28no—
541C22—232no—
542C22—28no—
543C22—24no—
544C22—24no—
545C22—224no—
546C22—228no—
547C22—444no—
548C22—4416no—
549C22—442no—
550C22—442no—
551C22C2×#6694618yes—
552C22C2×#6694614yes—
553C22C4×#434118yes—
554C22#1062311714yes—
555C22#1062315518yes—
556C22D11×#12314yes—
557C22C23×C4×D1111yescharacteristic
558C22C22×D4×D1111yescharacteristic
559C22C22×#434112yes—
560C22C22×#434311yescharacteristic
561C22C2×#41×D1112yes—
562C4—28no—
563C4—28no—
564C4—42no—
565C4—42no—
566C4—118no—
567C4—228no—
568C4—224no—
569C4—224no—
570C4—444no—
571C2—28no—
572C2—444no—
573C2#1307113518yesdirect product factor
574C2C22×#6694611yescharacteristic
575C2C2×C4×#434112yes—
576C2C2×D11×#12311yescharacteristic
577C2C2×#1062311711yescharacteristic
578C2C2×#1062315512yes—
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#385C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
cosocleC23×C11C25
hypercenterC2×#385D11
hypocenterC11C2×C4×#123
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C23×C4×Dic11C2semidirect
4. #13071135C2direct (N × H)
5. C2×#10622603C2semidirect
6. C2×#10622267C2semidirect
8. C2×#10622556C2semidirect
9. C2×C4⋊C4×Dic11C2semidirect
10. C2×C22⋊C4×Dic11C2semidirect
11. C2×#10622279C2semidirect
12. C2×C11×#385C2semidirect
32. C22×C4×Dic11C22semidirect
33. C2×#66939C4semidirect
37. C11×#385C22semidirect
44. #10622603C22semidirect
45. C4⋊C4×Dic11C22semidirect
46. #10622556C22semidirect
47. C22⋊C4×Dic11C22semidirect
48. #10622279C22semidirect
49. #10622267C22semidirect
66. C23×Dic11C2×C4semidirect
81. C2×C11×C22⋊C4C2×C4semidirect
88. C2×(C2×D11)⋊C4C2×C4semidirect
92. C2×C4⋊Dic11C2×C4semidirect
105. #66939C2×C4semidirect
162. C22×Dic11C22×C4semidirect
177. C11×C22⋊C4C22×C4semidirect
181. (C2×D11)⋊C4C22×C4semidirect
182. C4⋊Dic11C22×C4semidirect
195. C2×#385D11semidirect
256. C2×Dic11#123semidirect
290. #385C2×D11semidirect
330. Dic11C2×#123semidirect
376. C2×C22⋊C4C4×D11semidirect
394. C2×C11C4×#123semidirect
471. C22⋊C4C2×C4×D11semidirect
476. C11C2×C4×#123semidirect
573. C2#13071135direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669392
C22×(C22⋊D11)⋊C42
C23×C4×Dic112
#130711352
C2×#106226032
C2×#106222672
C2×#106228262
C2×#106225562
C2×C4⋊C4×Dic112
C2×C22⋊C4×Dic112
C2×#106222792
C2×C11×#3852
C2×C4×#12311