Finite Group Databasebeta

← C2×#13067645 #14725919

Subgroups — C2×#13067645 #14725919

Order 2816.

1016 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623046C211yesmaximal, characteristic
2C2×#10622583C211yesmaximal, characteristic, complemented
3C2×#10622581C211yesmaximal, characteristic
4#13067645C218yesmaximal, direct product factor
5C2×#10622090C211yesmaximal, characteristic, complemented
6C2×#10622089C211yesmaximal, characteristic
7C2×#10622166C211yesmaximal, characteristic, complemented
8C2×C11×#400C211yesmaximal, characteristic, complemented
9C22×C11×C4⋊C4C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C2×#66983C2211yescharacteristic
12C2×#66982—21no—
13C2×C4×C22⋊D11—21no—
14C2×#66977C2211yescharacteristic
15#10623046—22no—
16#10623046—22no—
17#10623046—22no—
18#10623046C2214yes—
19C2×#66951—21no—
20C2×#66949—21no—
21C2×#66947—21no—
22C2×#66942—21no—
23C11×#400—22no—
24C11×#400C2214yescomplemented
25C2×C11×#95—21no—
26C2×C11×#95—21no—
27C2×C11×#95C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30#10622583—22no—
31#10622583C2214yescomplemented
32C2×#66874—21no—
33#10622581—22no—
34#10622581C2214yes—
35C2×#66873—21no—
36C2×#66872—21no—
37C2×#66871—21no—
38#10622166C2214yescomplemented
39#10622090C2214yescomplemented
40#10622089C2214yes—
41C23×C4×C11—21no—
42C23×C4×C11—21no—
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11—21no—
47C22×D44D411yescharacteristic
48C22×C4×D11—21no—
49C22×Dic22D411yescharacteristic
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4D412yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C22⋊Dic11—21no—
63#66983—21no—
64#66983—21no—
65#66983D412yes—
66#66983C2312yes—
67#66982—24no—
68#66982—24no—
69C4×C22⋊D11—24no—
70C4×C22⋊D11—24no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11D411yescharacteristic
76C2×C4⋊Dic11D411yescharacteristic
77#66977—21no—
78#66977—21no—
79#66977D412yes—
80#66977C2312yes—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×C4×Dic11—21no—
86C22×C11⋊C8—21no—
87C22×C11⋊C8—21no—
88#66951—24no—
89#66951—24no—
90#66949—24no—
91#66949—24no—
92#66947—24no—
93#66947—24no—
94#66942—24no—
95#66942—24no—
96C11×#95—24no—
97C11×#95—24no—
98C11×#95—21no—
99C11×#95C2312yes—
100C22⋊(C11⋊C8)—21no—
101C22⋊(C11⋊C8)—21no—
102C22⋊(C11⋊C8)C2312yes—
103C22⋊(C11⋊C8)C2312yes—
104#66874—24no—
105#66873—24no—
106#66872—24no—
107#66871—24no—
108C2×#1615—111nomaximal, Sylow
109C24×C11C2×D411yescharacteristic
110C23×D11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11—44no—
124C22×C4×C11—41no—
125C22×C4×C11—41no—
126C22×C4×C11—42no—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C2×C22⋊D11—22no—
136C2×C22⋊D11—22no—
137C2×C22⋊D11—42no—
138C2×C22⋊D11—42no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C2×D44—21no—
143C2×D44—42no—
144C2×D44C2×D412yes—
145C2×C4×D11—24no—
146C2×C4×D11—82no—
147C2×Dic22—21no—
148C2×Dic22—42no—
149C2×Dic22C2×D412yes—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4—41no—
158C22⋊Dic11—22no—
159C22⋊Dic11—22no—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—24no—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4—22no—
164(C2×D11)⋊C4—22no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11C2×D412yes—
168C4⋊Dic11C2×D412yes—
169Dic11⋊C4—24no—
170Dic11⋊C4—24no—
171Dic11⋊C4—24no—
172Dic11⋊C4—22no—
173Dic11⋊C4—22no—
174C4×Dic11—24no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—42no—
178C2×C11⋊C8—42no—
179C2×#539—111no—
180C2×#484—111no—
181C2×#481—111no—
182C2×#400D1111yescharacteristic, complemented
183#1615—118no—
184C2×#328—111no—
185C2×#327—111no—
186C2×#324—111no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11#12011yescharacteristic
190C23×C11#12011yescharacteristic
191C23×C11#13512yes—
192C23×C11#13712yes—
193C23×C11C22×D411yescharacteristic
194C22×D11—22no—
195C22×D11—42no—
196C22×D11—42no—
197C22×D11—42no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—44no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—81no—
218C2×C4×C11—84no—
219C2×C4×C11—82no—
220C2×C4×C11—82no—
221C2×C4×C11#12011yescharacteristic
222C2×C4×C11#12011yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C22⋊D11—42no—
226C22⋊D11—42no—
227C22⋊D11—44no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234D44—42no—
235D44—81no—
236C4×D11—84no—
237Dic22—42no—
238Dic22—81no—
239C11⋊C8—42no—
240C11⋊C8—42no—
241#539—114no—
242#539—222no—
243#539—222no—
244#539—222no—
245C2×#126—221no—
246C2×#125—221no—
247C2×#123—221no—
248C2×#123—221no—
249C2×C22⋊Q8—111no—
250C2×C22⋊Q8—221no—
251C2×#121—111no—
252C2×C4×D4—221no—
253C22×C4⋊C4C2×D1111yescharacteristic
254C22×C4⋊C4C2×D1111yescharacteristic
255#484—114no—
256#484—222no—
257#481—114no—
258#481—222no—
259C2×#107—221no—
260C2×#106—221no—
261C2×#103—221no—
262C2×#102—221no—
263C2×C22⋊C8—111no—
264C2×C22⋊C8—111no—
265#400—22no—
266#400C2×D1114yescomplemented
267C2×#95—21no—
268C2×#95—21no—
269C2×#95C2×D1111yescharacteristic
270#328—114no—
271#327—114no—
272#324—114no—
273C22×C11—24no—
274C22×C11—24no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11—21no—
279C22×C11#45212yes—
280C22×C11#45212yes—
281C22×C11#45412yes—
282C22×C11#45812yes—
283C22×C11C2×#12011yescharacteristic
284C22×C11C2×#13511yescharacteristic
285C22×C11C2×#13711yescharacteristic
286C2×D11—42no—
287C2×D11—42no—
288C2×D11—42no—
289C2×D11—84no—
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—42no—
295C4×C11—42no—
296C4×C11—82no—
297C4×C11—82no—
298Dic11—42no—
299Dic11—42no—
300Dic11—42no—
301C22×Q8—111no—
302C22×D4—111no—
303C22×D4—221no—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4—221no—
307C23×C4C22⋊D1111yescharacteristic
308C23×C4C22⋊D1111yescharacteristic
309C23×C4C22×D1111yescharacteristic
310C22×C8—221no—
311C22×C8—221no—
312#126—224no—
313#126—224no—
314#125—224no—
315#125—224no—
316#123—224no—
317#123—224no—
318#123—224no—
319#123—224no—
320C22⋊Q8—112no—
321C22⋊Q8—112no—
322C22⋊Q8—224no—
323C22⋊Q8—224no—
324C22⋊Q8—221no—
325C22⋊Q8—221no—
326#121—112no—
327#121—112no—
328#121—221no—
329#121—221no—
330C4×D4—224no—
331C4×D4—224no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—111no—
342C2×C4⋊C4—111no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4C22⋊D1112yes—
348C2×C4⋊C4C22×D1112yes—
349C2×C4⋊C4C22×D1112yes—
350C2×C22⋊C4—221no—
351C2×C22⋊C4—221no—
352C2×C22⋊C4—221no—
353C2×C22⋊C4—221no—
354C2×C22⋊C4—221no—
355C2×C42—221no—
356#107—224no—
357#106—224no—
358#103—224no—
359#102—224no—
360C22⋊C8—112no—
361C22⋊C8—112no—
362C22⋊C8—221no—
363C22⋊C8—221no—
364#95—24no—
365#95—24no—
366#95—21no—
367#95C22×D1112yes—
368C2×C11—21no—
369C2×C11—21no—
370C2×C11—22no—
371C2×C11#161514yescomplemented
372C2×C11C2×#45211yescharacteristic
373C2×C11C2×#45411yescharacteristic
374C2×C11C2×#45811yescharacteristic
375D11—82no—
376C24—221no—
377C24C2×C22⋊D1111yescharacteristic
378C2×Q8—112no—
379C2×Q8—221no—
380C2×Q8—442no—
381C2×D4—112no—
382C2×D4—222no—
383C2×D4—222no—
384C2×D4—221no—
385C2×D4—442no—
386C2×D4—442no—
387C2×D4—442no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—44no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—42no—
404C22×C4—224no—
405C22×C4—221no—
406C22×C4—221no—
407C22×C4—221no—
408C22×C4—882no—
409C22×C4D4×D1111yescharacteristic
410C22×C4D4×D1111yescharacteristic
411C22×C4D4×D1111yescharacteristic
412C22×C4D4×D1111yescharacteristic
413C22×C4C2×C22⋊D1112yes—
414C22×C4C2×C22⋊D1112yes—
415C22×C4C2×C22⋊D1111yescharacteristic
416C22×C4C23×D1111yescharacteristic
417C2×C8—222no—
418C2×C8—222no—
419C2×C8—442no—
420C2×C8—442no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4—112no—
430C4⋊C4—112no—
431C4⋊C4—224no—
432C4⋊C4—224no—
433C4⋊C4—224no—
434C4⋊C4—221no—
435C4⋊C4—221no—
436C4⋊C4—222no—
437C4⋊C4—222no—
438C22⋊C4—224no—
439C22⋊C4—224no—
440C22⋊C4—224no—
441C22⋊C4—222no—
442C22⋊C4—222no—
443C22⋊C4—222no—
444C22⋊C4—222no—
445C42—224no—
446C11C2×#161511yescharacteristic, complemented, Sylow
447C23—22no—
448C23—22no—
449C23—222no—
450C23—442no—
451C23—442no—
452C23—442no—
453C23#6699011yescharacteristic
454C23#6699011yescharacteristic
455C23#6699512yes—
456C23#6700312yes—
457C23C22×C22⋊D1111yescharacteristic
458Q8—442no—
459Q8—881no—
460D4—442no—
461D4—442no—
462D4—442no—
463D4—444no—
464D4—881no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—44no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—81no—
485C2×C4—84no—
486C2×C4—82no—
487C2×C4—82no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4—442no—
494C2×C4—884no—
495C2×C4#6699011yescharacteristic
496C2×C4#6699011yescharacteristic
497C2×C4C2×D4×D1111yescharacteristic
498C2×C4C2×D4×D1111yescharacteristic
499C8—442no—
500C8—442no—
501C22—24no—
502C22—24no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—442no—
508C22—442no—
509C22—442no—
510C22—884no—
511C22#1062266012yes—
512C22#1062266012yes—
513C22#1062266612yes—
514C22#1062267512yes—
515C22C2×#6699011yescharacteristic
516C22C2×#6699511yescharacteristic
517C22C2×#6700311yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—42no—
524C4—82no—
525C4—82no—
526C4—442no—
527C4—442no—
528C4—442no—
529C2—21no—
530C2—21no—
531C2—22no—
532C2—882no—
533C2#1306764514yesdirect product factor
534C2C2×#1062266011yescharacteristic
535C2C2×#1062267511yescharacteristic
536C2C2×#1062266611yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#400C2
socleC23×C11#120
prime radicalC2×#66983C22
hypercenterC2×#400D11
hypocenterC11C2×#1615
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
2. C2×#10622583C2semidirect
4. #13067645C2direct (N × H)
5. C2×#10622090C2semidirect
7. C2×#10622166C2semidirect
8. C2×C11×#400C2semidirect
24. C11×#400C22semidirect
31. #10622583C22semidirect
38. #10622166C22semidirect
39. #10622090C22semidirect
182. C2×#400D11semidirect
266. #400C2×D11semidirect
371. C2×C11#1615semidirect
446. C11C2×#1615semidirect
533. C2#13067645direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230462
C2×#106225832
C2×#106225812
#130676452
C2×#106220902
C2×#106220892
C2×#106221662
C2×C11×#4002
C2×#161511