Finite Group Databasebeta

← C2×#13067647 #14725921

Subgroups — C2×#13067647 #14725921

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×#10622657C211yesmaximal, characteristic, complemented
2C2×#10622647C211yesmaximal, characteristic
3C2×#10622599C211yesmaximal, characteristic, complemented
4#13067647C218yesmaximal, direct product factor
5C2×#10622176C211yesmaximal, characteristic, complemented
6C2×#10622175C211yesmaximal, characteristic
7C2×#10622166C211yesmaximal, characteristic, complemented
8C2×C11×#539C211yesmaximal, characteristic
9C11×#539—22no—
10C11×#539—22no—
11C11×#539—22no—
12C11×#539C2214yes—
13C2×C11×#126—21no—
14C2×C11×#125—21no—
15C2×C11×#123—21no—
16C2×C11×#123—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C2×#66899—21no—
24C2×#66896—21no—
25C2×C11⋊#95—21no—
26C2×C11⋊#95—21no—
27C2×C11⋊#95C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30#10622657—22no—
31#10622657C2214yescomplemented
32#10622647—22no—
33#10622647C2214yes—
34#10622599—22no—
35#10622599C2214yescomplemented
36C2×#66872—21no—
37C2×#66871—21no—
38#10622176C2214yescomplemented
39#10622175C2214yes—
40#10622166C2214yescomplemented
41C22×Q8×C11D411yescharacteristic
42C22×D4×C11—21no—
43C22×D4×C11D411yescharacteristic
44C23×C4×C11—21no—
45C23×C4×C11D411yescharacteristic
46C23×C4×C11D411yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11—21no—
49C23×Dic11—21no—
50C11×#126—24no—
51C11×#126—24no—
52C11×#125—24no—
53C11×#125—24no—
54C11×#123—24no—
55C11×#123—24no—
56C11×#123—24no—
57C11×#123—24no—
58C11×C22⋊Q8—24no—
59C11×C22⋊Q8—24no—
60C11×C22⋊Q8—21no—
61C11×C22⋊Q8—21no—
62C11×C22⋊Q8D412yes—
63C11×C22⋊Q8C2312yes—
64C11×#121—21no—
65C11×#121—21no—
66C11×#121D412yes—
67C11×#121C2312yes—
68C4×D4×C11—24no—
69C4×D4×C11—24no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4D412yes—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C42×C11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2312yes—
94C22×C11⋊C8—21no—
95C22×C11⋊C8—21no—
96#66899—24no—
97#66896—24no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95—21no—
101C11⋊#95C2312yes—
102C22⋊(C11⋊C8)—21no—
103C22⋊(C11⋊C8)—21no—
104C22⋊(C11⋊C8)C2312yes—
105C22⋊(C11⋊C8)C2312yes—
106#66872—24no—
107#66871—24no—
108C2×#1615—111nomaximal, Sylow
109C24×C11—21no—
110C24×C11C2×D411yescharacteristic
111C2×Q8×C11—21no—
112C2×Q8×C11—42no—
113C2×Q8×C11C2×D412yes—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—21no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11C2×D412yes—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—24no—
130C22×C4×C11—21no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—82no—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—42no—
145C22×Dic11—44no—
146C22×Dic11—42no—
147C22×Dic11—41no—
148C22×Dic11—41no—
149C22×Dic11—42no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4C2×D412yes—
162C11×C4⋊C4C2×D412yes—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C42×C11—24no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4⋊Dic11—41no—
174C4⋊Dic11—41no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—42no—
178C2×C11⋊C8—42no—
179C2×#539D1111yescharacteristic
180C2×#484—111no—
181C2×#481—111no—
182C2×#400—111no—
183#1615—118no—
184C2×#328—111no—
185C2×#327—111no—
186C2×#324—111no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11#12011yescharacteristic
194C23×C11#12011yescharacteristic
195C23×C11#13512yes—
196C23×C11#13712yes—
197C23×C11C22×D411yescharacteristic
198Q8×C11—42no—
199Q8×C11—81no—
200D4×C11—42no—
201D4×C11—42no—
202D4×C11—42no—
203D4×C11—44no—
204D4×C11—81no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—81no—
226C2×C4×C11—84no—
227C2×C4×C11#12011yescharacteristic
228C2×C4×C11#12011yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—44no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—84no—
237C2×Dic11—82no—
238C2×Dic11—82no—
239C11⋊C8—42no—
240C11⋊C8—42no—
241#539—22no—
242#539—22no—
243#539—22no—
244#539C2×D1114yes—
245C2×#126—21no—
246C2×#125—21no—
247C2×#123—21no—
248C2×#123—21no—
249C2×C22⋊Q8—21no—
250C2×C22⋊Q8C2×D1111yescharacteristic
251C2×#121C2×D1111yescharacteristic
252C2×C4×D4—21no—
253C22×C4⋊C4—111no—
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—114no—
266#400—222no—
267C2×#95—111no—
268C2×#95—221no—
269C2×#95—221no—
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—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—84no—
283C22×C11#45212yes—
284C22×C11#45212yes—
285C22×C11#45412yes—
286C22×C11#45812yes—
287C22×C11C2×#12011yescharacteristic
288C22×C11C2×#13511yescharacteristic
289C22×C11C2×#13711yescharacteristic
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—42no—
295C4×C11—42no—
296C4×C11—42no—
297C4×C11—42no—
298C4×C11—42no—
299Dic11—82no—
300Dic11—82no—
301C22×Q8C22⋊D1111yescharacteristic
302C22×D4—21no—
303C22×D4C22⋊D1111yescharacteristic
304C23×C4—21no—
305C23×C4—221no—
306C23×C4—221no—
307C23×C4C22⋊D1111yescharacteristic
308C23×C4C22⋊D1111yescharacteristic
309C23×C4C22×D1111yescharacteristic
310C22×C8—221no—
311C22×C8—221no—
312#126—24no—
313#126—24no—
314#125—24no—
315#125—24no—
316#123—24no—
317#123—24no—
318#123—24no—
319#123—24no—
320C22⋊Q8—24no—
321C22⋊Q8—24no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8C22⋊D1112yes—
325C22⋊Q8C22×D1112yes—
326#121—21no—
327#121—21no—
328#121C22⋊D1112yes—
329#121C22×D1112yes—
330C4×D4—24no—
331C4×D4—24no—
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—112no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4C22⋊D1112yes—
347C2×C4⋊C4C22⋊D1111yescharacteristic
348C2×C4⋊C4C22⋊D1111yescharacteristic
349C2×C4⋊C4C22×D1112yes—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C42—21no—
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—112no—
365#95—221no—
366#95—224no—
367#95—224no—
368C2×C11—21no—
369C2×C11—21no—
370C2×C11—22no—
371C2×C11—82no—
372C2×C11#161514yescomplemented
373C2×C11C2×#45211yescharacteristic
374C2×C11C2×#45411yescharacteristic
375C2×C11C2×#45811yescharacteristic
376C24—21no—
377C24C2×C22⋊D1111yescharacteristic
378C2×Q8—21no—
379C2×Q8—42no—
380C2×Q8C2×C22⋊D1112yes—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—21no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4C2×C22⋊D1112yes—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—24no—
397C22×C4—21no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—82no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4—442no—
404C22×C4—442no—
405C22×C4—444no—
406C22×C4—442no—
407C22×C4—441no—
408C22×C4—441no—
409C22×C4C2×C22⋊D1112yes—
410C22×C4C2×C22⋊D1111yescharacteristic
411C22×C4C2×C22⋊D1111yescharacteristic
412C22×C4C2×C22⋊D1112yes—
413C22×C4C2×C22⋊D1111yescharacteristic
414C22×C4C2×C22⋊D1111yescharacteristic
415C22×C4C2×C22⋊D1111yescharacteristic
416C22×C4C23×D1111yescharacteristic
417C2×C8—222no—
418C2×C8—222no—
419C2×C8—442no—
420C2×C8—442no—
421C4⋊C4—24no—
422C4⋊C4—24no—
423C4⋊C4—24no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—222no—
433C4⋊C4—222no—
434C4⋊C4—441no—
435C4⋊C4—441no—
436C4⋊C4C2×C22⋊D1112yes—
437C4⋊C4C2×C22⋊D1112yes—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C42—24no—
446C11C2×#161511yescharacteristic, complemented, Sylow
447C23—22no—
448C23—22no—
449C23—22no—
450C23—42no—
451C23—42no—
452C23—42no—
453C23#6700312yes—
454C23#6700412yes—
455C23#6700611yescharacteristic
456C23#6700611yescharacteristic
457C23C22×C22⋊D1111yescharacteristic
458Q8—42no—
459Q8—81no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—44no—
464D4—81no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—81no—
486C2×C4—84no—
487C2×C4—442no—
488C2×C4—442no—
489C2×C4—444no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—884no—
493C2×C4—882no—
494C2×C4—882no—
495C2×C4#6700611yescharacteristic
496C2×C4#6700611yescharacteristic
497C2×C4C22×C22⋊D1111yescharacteristic
498C2×C4C22×C22⋊D1111yescharacteristic
499C8—442no—
500C8—442no—
501C22—24no—
502C22—24no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—84no—
511C22#1062285212yes—
512C22#1062285212yes—
513C22#1062285612yes—
514C22#1062285812yes—
515C22C2×#6700311yescharacteristic
516C22C2×#6700411yescharacteristic
517C22C2×#6700611yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—882no—
528C4—882no—
529C2—21no—
530C2—21no—
531C2—22no—
532C2—82no—
533C2#1306764714yesdirect product factor
534C2C2×#1062285211yescharacteristic
535C2C2×#1062285811yescharacteristic
536C2C2×#1062285611yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#539C2
socleC23×C11#120
prime radicalC2×C11×#121C22
hypercenterC2×#539D11
hypocenterC11C2×#1615
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#539

Complements

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

NH ≅ G/Ntype
1. C2×#10622657C2semidirect
3. C2×#10622599C2semidirect
4. #13067647C2direct (N × H)
5. C2×#10622176C2semidirect
7. C2×#10622166C2semidirect
31. #10622657C22semidirect
35. #10622599C22semidirect
38. #10622176C22semidirect
40. #10622166C22semidirect
372. C2×C11#1615semidirect
446. C11C2×#1615semidirect
533. C2#13067647direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226572
C2×#106226472
C2×#106225992
#130676472
C2×#106221762
C2×#106221752
C2×#106221662
C2×C11×#5392
C2×#161511