Finite Group Databasebeta

← C2×#13072926 #14922940

Subgroups — C2×#13072926 #14922940

Order 2816.

3374 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
3#13072926C2116yesmaximal, direct product factor
4C2×#10622272C211yesmaximal, characteristic, complemented
5C2×#10622595C211yesmaximal, characteristic, complemented
6C2×#10622562C211yesmaximal, characteristic, complemented
7C2×#10622585C212yesmaximal, complemented
8C2×#10622569C212yesmaximal
9C2×#10622602C212yesmaximal, complemented
10C2×#10622280C211yesmaximal, characteristic, complemented
11C2×#10622555C212yesmaximal, complemented
12C2×C11×#399C211yesmaximal, characteristic, complemented
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C23×C4×D11C2212yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2212yes—
29C22×C4×Dic11C2211yescharacteristic
30C2×C4⋊C4×D11—28no—
31C2×C4⋊C4×D11C2218yescomplemented
32C2×(C22⋊D11)⋊C4—28no—
33C2×(C22⋊D11)⋊C4C2218yes—
34C11×#399C2218yescomplemented
35C2×C11×#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622602C22116yescomplemented
42#10622595C2218yescomplemented
43#10622585C22116yescomplemented
44#10622569C22116yes—
45#10622562C2218yescomplemented
46#10622555C22116yescomplemented
47#10622280C2218yescomplemented
48#10622272C2218yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C22×C22⋊D11—24no—
56C22×C22⋊D11—24no—
57C22×C22⋊D11Q818yes—
58C22×C22⋊D11C2314yes—
59C23×Dic11—24no—
60C23×Dic11—28no—
61C23×Dic11C2314yes—
62C23×Dic11C2312yes—
63C23×Dic11C2312yes—
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C22×C4×D11—28no—
68C22×C4×D11—28no—
69C22×C4×D11—44no—
70C22×C4×D11—44no—
71C22×C4×D11D418yes—
72C22×C4×D11C2314yes—
73C22×C4×D11C2318yes—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4—44no—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C4⋊C4C2318yes—
78C2×C11×C22⋊C4—24no—
79C2×C11×C22⋊C4—44no—
80C2×C11×C22⋊C4C2314yes—
81C2×C11×C22⋊C4C2318yes—
82C2×C22⋊Dic11—44no—
83C2×C22⋊Dic11C2318yes—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—28no—
86C2×(C2×D11)⋊C4C2314yes—
87C2×(C2×D11)⋊C4C2318yes—
88C2×C4⋊Dic11—24no—
89C2×C4⋊Dic11C2314yes—
90C2×Dic11⋊C4—24no—
91C2×Dic11⋊C4—28no—
92C2×Dic11⋊C4—28no—
93C2×Dic11⋊C4—44no—
94C2×Dic11⋊C4C2314yes—
95C2×Dic11⋊C4C2318yes—
96C2×Dic11⋊C4C2318yes—
97C2×Dic11⋊C4C2318yes—
98C2×C4×Dic11—24no—
99C2×C4×Dic11C2314yes—
100C4⋊C4×D11—232no—
101(C22⋊D11)⋊C4—232no—
102C11×#95C2314yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2314yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C2×#2487—111nomaximal, Sylow
109C24×C11—22no—
110C24×C11—24no—
111C24×C11—22no—
112C24×C11—24no—
113C24×C11C2×Q814yes—
114C24×C11C2412yes—
115C24×C11C2411yescharacteristic
116C23×D11—24no—
117C23×D11—24no—
118C23×D11C2×D414yes—
119C23×D11C2×Q814yes—
120C23×D11#4114yes—
121C23×D11C2412yes—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11C2×D414yes—
132C22×C4×C11C2414yes—
133C22×C4×C11C2414yes—
134C22×C4×C11C2412yes—
135C22×C4×C11C2412yes—
136C2×C22⋊D11—232no—
137C2×C22⋊D11—28no—
138C2×C22⋊D11—28no—
139C2×C22⋊D11C2×Q8116yes—
140C22×Dic11—28no—
141C22×Dic11—216no—
142C22×Dic11—22no—
143C22×Dic11—24no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—416no—
153C22×Dic11C2×D414yes—
154C22×Dic11C2×Q814yes—
155C22×Dic11#4118yes—
156C22×Dic11C2412yes—
157C22×Dic11C2414yes—
158C22×Dic11C2414yes—
159C22×Dic11C2412yes—
160C22×Dic11C2412yes—
161C2×C4×D11—232no—
162C2×C4×D11—216no—
163C2×C4×D11—216no—
164C2×C4×D11—48no—
165C2×C4×D11—48no—
166C2×C4×D11—432no—
167C2×C4×D11C2×D4116yes—
168C11×C4⋊C4—28no—
169C11×C4⋊C4—48no—
170C11×C22⋊C4—28no—
171C11×C22⋊C4—48no—
172C22⋊Dic11—48no—
173(C2×D11)⋊C4—28no—
174(C2×D11)⋊C4—216no—
175C4⋊Dic11—28no—
176Dic11⋊C4—216no—
177Dic11⋊C4—216no—
178Dic11⋊C4—28no—
179Dic11⋊C4—48no—
180C4×Dic11—28no—
181C22×C4×D4—111no—
182C23×C4⋊C4—111no—
183#2487—1116no—
184C2×#400—111no—
185C2×#400—111no—
186C2×#399—111no—
187C2×#399D1111yescharacteristic, complemented
188C2×#389—112no—
189C2×#386—112no—
190C2×#385—112no—
191C2×#380—111no—
192C2×#380—112no—
193C23×C11—28no—
194C23×C11—216no—
195C23×C11—22no—
196C23×C11—24no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—44no—
200C23×C11—44no—
201C23×C11—48no—
202C23×C11C22×D412yes—
203C23×C11C22×Q814yes—
204C23×C11C22×Q812yes—
205C23×C11C2×#4112yes—
206C23×C11C2×#4114yes—
207C23×C11H(5,𝔽2)14yes—
208C23×C11C2511yescharacteristic
209C22×D11—28no—
210C22×D11—28no—
211C22×D11—216no—
212C22×D11—216no—
213C22×D11—24no—
214C22×D11—24no—
215C22×D11C22⋊Q8116yes—
216C22×D11C22×D414yes—
217C22×D11C22×Q814yes—
218C22×D11C2×#4114yes—
219C2×C4×C11—28no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—48no—
230C2×C4×C11—44no—
231C2×C4×C11—48no—
232C2×C4×C11C22×D414yes—
233C22⋊D11—232no—
234C2×Dic11—28no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—22no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—44no—
246C2×Dic11—48no—
247C2×Dic11—48no—
248C2×Dic11—416no—
249C2×Dic11#123116yes—
250C2×Dic11C22×D414yes—
251C2×Dic11C22×Q814yes—
252C2×Dic11C2×#4118yes—
253C4×D11—232no—
254C4×D11—432no—
255C23×D4—111no—
256C24×C4—111no—
257C24×C4—111no—
258C24×C4—112no—
259C2×C4×D4—118no—
260C2×C4×D4—228no—
261C22×C4⋊C4—111no—
262C22×C4⋊C4—112no—
263C22×C4⋊C4—112no—
264C22×C4⋊C4—111no—
265C22×C4⋊C4—112no—
266C22×C4⋊C4—118no—
267C22×C4⋊C4—228no—
268C22×C4⋊C4C2×D1111yescharacteristic
269C22×C4⋊C4C2×D1112yes—
270C22×C22⋊C4—111no—
271C22×C22⋊C4—112no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4C2×D1111yescharacteristic
274C22×C22⋊C4C2×D1112yes—
275C22×C42—111no—
276#400—118no—
277#400—118no—
278#399—118no—
279#399C2×D1118yescomplemented
280#389—1116no—
281#386—1116no—
282#385—1116no—
283#380—1116no—
284#380—118no—
285C2×#95—111no—
286C2×#95—112no—
287C2×#95—112no—
288C2×#95—112no—
289C2×#95—112no—
290C2×#95C2×D1111yescharacteristic
291C22×C11—24no—
292C22×C11—28no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—44no—
296C22×C11—416no—
297C22×C11C2×C22⋊Q814yes—
298C22×C11C2×#12314yes—
299C22×C11#53514yes—
300C22×C11#55318yes—
301C22×C11#55418yes—
302C22×C11C23×D411yescharacteristic
303C22×C11C23×Q811yescharacteristic
304C22×C11C22×#4111yescharacteristic
305C22×C11C22×#4112yes—
306C22×C11C2×H(5,𝔽2)12yes—
307C2×D11—24no—
308C2×D11—24no—
309C2×D11—28no—
310C2×D11—28no—
311C2×D11—232no—
312C2×D11C2×C22⋊Q818yes—
313C4×C11—24no—
314C4×C11—42no—
315C4×C11—44no—
316C4×C11—44no—
317Dic11—24no—
318Dic11—42no—
319Dic11—44no—
320Dic11—44no—
321Dic11C2×#12318yes—
322C25—111no—
323C25C22×D1111yescharacteristic
324C22×D4—118no—
325C22×D4—114no—
326C22×D4—224no—
327C22×D4—224no—
328C23×C4—111no—
329C23×C4—111no—
330C23×C4—118no—
331C23×C4—114no—
332C23×C4—114no—
333C23×C4—112no—
334C23×C4—112no—
335C23×C4—111no—
336C23×C4—118no—
337C23×C4—228no—
338C23×C4—228no—
339C23×C4—224no—
340C23×C4—228no—
341C23×C4—444no—
342C23×C4—444no—
343C23×C4C22×D1111yescharacteristic
344C23×C4C22×D1112yes—
345C23×C4C22×D1112yes—
346C23×C4C22×D1111yescharacteristic
347C4×D4—2232no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—118no—
351C2×C4⋊C4—114no—
352C2×C4⋊C4—114no—
353C2×C4⋊C4—118no—
354C2×C4⋊C4—118no—
355C2×C4⋊C4—2232no—
356C2×C4⋊C4—228no—
357C2×C4⋊C4—228no—
358C2×C4⋊C4—224no—
359C2×C4⋊C4—224no—
360C2×C4⋊C4—444no—
361C2×C4⋊C4C22×D1114yes—
362C2×C4⋊C4C22×D1118yes—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—114no—
366C2×C22⋊C4—118no—
367C2×C22⋊C4—118no—
368C2×C22⋊C4—224no—
369C2×C22⋊C4—228no—
370C2×C22⋊C4—444no—
371C2×C22⋊C4C22×D1114yes—
372C2×C22⋊C4C22×D1118yes—
373C2×C42—114no—
374C2×C42—224no—
375#95—118no—
376#95—118no—
377#95—114no—
378#95—118no—
379#95—118no—
380#95C22×D1114yes—
381C2×C11—44no—
382C2×C11#248718yescomplemented
383C2×C11C22×C22⋊Q811yescharacteristic
384C2×C11C22×#12311yescharacteristic
385C2×C11C2×#53511yescharacteristic
386C2×C11C2×#55312yes—
387C2×C11C2×#55412yes—
388D11—28no—
389C24—22no—
390C24—24no—
391C24—24no—
392C24—22no—
393C24—114no—
394C24—114no—
395C24—114no—
396C24—112no—
397C24—224no—
398C24—224no—
399C24Q8×D1114yes—
400C24C23×D1112yes—
401C24C23×D1111yescharacteristic
402C2×D4—1116no—
403C2×D4—228no—
404C2×D4—2232no—
405C2×D4—228no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—114no—
416C22×C4—118no—
417C22×C4—112no—
418C22×C4—114no—
419C22×C4—112no—
420C22×C4—1116no—
421C22×C4—112no—
422C22×C4—114no—
423C22×C4—114no—
424C22×C4—2232no—
425C22×C4—2216no—
426C22×C4—2216no—
427C22×C4—228no—
428C22×C4—2216no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—224no—
433C22×C4—224no—
434C22×C4—224no—
435C22×C4—224no—
436C22×C4—224no—
437C22×C4—224no—
438C22×C4—224no—
439C22×C4—448no—
440C22×C4—448no—
441C22×C4—4432no—
442C22×C4—4416no—
443C22×C4D4×D1114yes—
444C22×C4C23×D1114yes—
445C22×C4C23×D1114yes—
446C22×C4C23×D1112yes—
447C22×C4C23×D1112yes—
448C4⋊C4—28no—
449C4⋊C4—48no—
450C4⋊C4—2216no—
451C4⋊C4—2216no—
452C4⋊C4—228no—
453C4⋊C4—228no—
454C4⋊C4—448no—
455C22⋊C4—28no—
456C22⋊C4—48no—
457C22⋊C4—228no—
458C22⋊C4—2216no—
459C22⋊C4—448no—
460C42—228no—
461C11C2×#248711yescharacteristic, complemented, Sylow
462C23—28no—
463C23—216no—
464C23—22no—
465C23—24no—
466C23—24no—
467C23—22no—
468C23—44no—
469C23—44no—
470C23—48no—
471C23—1116no—
472C23—114no—
473C23—114no—
474C23—114no—
475C23—228no—
476C23—2216no—
477C23—228no—
478C23—224no—
479C23—2216no—
480C23—224no—
481C23C2×D4×D1112yes—
482C23#6703714yes—
483C23C2×Q8×D1114yes—
484C23C2×Q8×D1112yes—
485C23#41×D1112yes—
486C23#41×D1114yes—
487C23C24×D1111yescharacteristic
488D4—2232no—
489C2×C4—28no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—44no—
500C2×C4—48no—
501C2×C4—48no—
502C2×C4—1116no—
503C2×C4—114no—
504C2×C4—118no—
505C2×C4—114no—
506C2×C4—2232no—
507C2×C4—228no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—224no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—4432no—
519C2×C4—4416no—
520C2×C4—448no—
521C2×C4—444no—
522C2×C4—448no—
523C2×C4C2×D4×D1114yes—
524C22—28no—
525C22—24no—
526C22—44no—
527C22—416no—
528C22—42no—
529C22—42no—
530C22—118no—
531C22—228no—
532C22—2232no—
533C22—228no—
534C22—224no—
535C22—224no—
536C22D11×C22⋊Q814yes—
537C22#1062316718yes—
538C22D11×#12314yes—
539C22#1062319218yes—
540C22#1062324614yes—
541C22C22×D4×D1111yescharacteristic
542C22C2×#6703712yes—
543C22C22×Q8×D1111yescharacteristic
544C22C2×#41×D1111yescharacteristic
545C22C2×#41×D1112yes—
546C4—24no—
547C4—44no—
548C4—44no—
549C4—42no—
550C4—118no—
551C4—224no—
552C4—444no—
553C4—444no—
554C4—442no—
555C2—44no—
556C2—228no—
557C2#1307292618yesdirect product factor
558C2C2×D11×C22⋊Q811yescharacteristic
559C2C2×D11×#12311yescharacteristic
560C2C2×#1062324611yescharacteristic
561C2C2×#1062319212yes—
562C2C2×#1062316712yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#399C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#399D11
hypocenterC11C2×#2487
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D11C2semidirect
3. #13072926C2direct (N × H)
4. C2×#10622272C2semidirect
5. C2×#10622595C2semidirect
6. C2×#10622562C2semidirect
7. C2×#10622585C2semidirect
9. C2×#10622602C2semidirect
10. C2×#10622280C2semidirect
11. C2×#10622555C2semidirect
12. C2×C11×#399C2semidirect
31. C2×C4⋊C4×D11C22semidirect
34. C11×#399C22semidirect
41. #10622602C22semidirect
42. #10622595C22semidirect
43. #10622585C22semidirect
45. #10622562C22semidirect
46. #10622555C22semidirect
47. #10622280C22semidirect
48. #10622272C22semidirect
187. C2×#399D11semidirect
279. #399C2×D11semidirect
382. C2×C11#2487semidirect
461. C11C2×#2487semidirect
557. C2#13072926direct (N × H)

Maximal subgroups

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

subgroupindex
C22×(C22⋊D11)⋊C42
C22×C4⋊C4×D112
#130729262
C2×#106222722
C2×#106225952
C2×#106225622
C2×#106225852
C2×#106225692
C2×#106226022
C2×#106222802
C2×#106225552
C2×C11×#3992
C2×#248711