Finite Group Databasebeta

← C2×#13067644 #14725918

Subgroups — C2×#13067644 #14725918

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×#10623133C211yesmaximal, characteristic
2C2×#10622583C211yesmaximal, characteristic, complemented
3C2×#10622595C211yesmaximal, characteristic, complemented
4#13067644C218yesmaximal, direct product factor
5C2×#10622105C211yesmaximal, characteristic, complemented
6C2×#10622175C211yesmaximal, characteristic
7C2×#10622107C211yesmaximal, characteristic, complemented
8C2×C11×#481C211yesmaximal, characteristic
9C2×C11×#121C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C2×#66988—21no—
12C2×#66988—21no—
13C2×D4×Dic11—21no—
14C2×#66977C2211yescharacteristic
15C22×Dic11⋊C4C2211yescharacteristic
16#10623133—22no—
17#10623133—22no—
18#10623133—22no—
19#10623133C2214yes—
20C2×#66942—21no—
21C2×#66932—21no—
22C2×#66931—21no—
23C11×#481—22no—
24C11×#481C2214yes—
25C2×C11×#106—21no—
26C2×C11×#102—21no—
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11⋊#95—21no—
29C2×C11⋊#95—21no—
30C2×C11⋊#95C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32#10622595—22no—
33#10622595C2214yescomplemented
34#10622583—22no—
35#10622583C2214yescomplemented
36C2×#66874—21no—
37C2×#66871—21no—
38#10622175C2214yes—
39#10622107C2214yescomplemented
40#10622105C2214yescomplemented
41C22×D4×C11—21no—
42C22×D4×C11D411yescharacteristic
43C23×C4×C11—21no—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11—21no—
46C23×Dic11—21no—
47C23×Dic11D411yescharacteristic
48C23×Dic11D411yescharacteristic
49C22×Dic22D411yescharacteristic
50C22×C8×C11—21no—
51C11×#121—21no—
52C11×#121—21no—
53C11×#121D412yes—
54C11×#121C2312yes—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C22⋊C4—21no—
63C2×C22⋊Dic11—21no—
64C2×C22⋊Dic11—21no—
65C2×C22⋊Dic11—21no—
66C2×C22⋊Dic11—21no—
67#66988—24no—
68#66988—24no—
69#66988—24no—
70#66988—24no—
71D4×Dic11—24no—
72D4×Dic11—24no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11D411yescharacteristic
75#66977—21no—
76#66977—21no—
77#66977D412yes—
78#66977C2312yes—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4D412yes—
87C2×Dic11⋊C4C2312yes—
88C2×C4×Dic11—21no—
89C22×C11⋊C8—21no—
90#66942—24no—
91#66942—24no—
92#66932—24no—
93#66932—24no—
94#66931—24no—
95#66931—24no—
96C11×#106—24no—
97C11×#102—24no—
98C11×C22⋊C8—21no—
99C11×C22⋊C8C2312yes—
100C11⋊#95—21no—
101C11⋊#95—24no—
102C11⋊#95—24no—
103C11⋊#95C2312yes—
104C22⋊(C11⋊C8)—21no—
105C22⋊(C11⋊C8)C2312yes—
106#66874—24no—
107#66871—24no—
108C2×#1615—111nomaximal, Sylow
109C24×C11—21no—
110C24×C11C2×D411yescharacteristic
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—21no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11C2×D412yes—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—42no—
121C22×C4×C11—44no—
122C22×C4×C11—41no—
123C22×C4×C11—41no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C22×Dic11—24no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—42no—
141C22×Dic11—42no—
142C22×Dic11—42no—
143C22×Dic11—42no—
144C22×Dic11—82no—
145C22×Dic11C2×D412yes—
146C22×Dic11C2×D412yes—
147C2×Dic22—21no—
148C2×Dic22—42no—
149C2×Dic22C2×D412yes—
150C2×C8×C11—22no—
151C2×C8×C11—42no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4C2×D412yes—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—22no—
160C22⋊Dic11—24no—
161C22⋊Dic11—24no—
162C22⋊Dic11—24no—
163C22⋊Dic11—22no—
164C22⋊Dic11—22no—
165C4⋊Dic11—24no—
166C4⋊Dic11—21no—
167C4⋊Dic11C2×D412yes—
168Dic11⋊C4—24no—
169Dic11⋊C4—24no—
170Dic11⋊C4—22no—
171Dic11⋊C4—22no—
172Dic11⋊C4—22no—
173Dic11⋊C4—22no—
174Dic11⋊C4—22no—
175Dic11⋊C4—22no—
176C4×Dic11—24no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—42no—
179C2×#539—111no—
180C2×#484—111no—
181C2×#481D1111yescharacteristic
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
198D4×C11—42no—
199D4×C11—42no—
200D4×C11—42no—
201D4×C11—44no—
202D4×C11—81no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—44no—
212C2×C4×C11—42no—
213C2×C4×C11—82no—
214C2×C4×C11—82no—
215C2×C4×C11#12011yescharacteristic
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—81no—
235C2×Dic11—84no—
236C2×Dic11—84no—
237Dic22—42no—
238Dic22—81no—
239C8×C11—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×#121C2×D1111yescharacteristic
252C2×C4×D4—221no—
253C22×C4⋊C4—111no—
254C22×C4⋊C4C2×D1111yescharacteristic
255#484—114no—
256#484—222no—
257#481—22no—
258#481C2×D1114yes—
259C2×#107—221no—
260C2×#106—21no—
261C2×#103—221no—
262C2×#102—21no—
263C2×C22⋊C8—111no—
264C2×C22⋊C8C2×D1111yescharacteristic
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—82no—
296Dic11—42no—
297Dic11—42no—
298Dic11—42no—
299Dic11—42no—
300Dic11—82no—
301C22×Q8—111no—
302C22×D4—21no—
303C22×D4C22⋊D1111yescharacteristic
304C23×C4—21no—
305C23×C4—111no—
306C23×C4—111no—
307C23×C4—221no—
308C23×C4—221no—
309C23×C4C22×D1111yescharacteristic
310C22×C8—21no—
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—21no—
327#121—21no—
328#121C22⋊D1112yes—
329#121C22×D1112yes—
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—111no—
338C2×C4⋊C4—112no—
339C2×C4⋊C4—112no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4C22⋊D1111yescharacteristic
349C2×C4⋊C4C22×D1112yes—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—221no—
352C2×C22⋊C4—221no—
353C2×C22⋊C4—221no—
354C2×C22⋊C4—221no—
355C2×C42—221no—
356#107—224no—
357#106—24no—
358#103—224no—
359#102—24no—
360C22⋊C8—21no—
361C22⋊C8—112no—
362C22⋊C8—221no—
363C22⋊C8C22×D1112yes—
364#95—112no—
365#95—224no—
366#95—224no—
367#95—221no—
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—
377C24D4×D1111yescharacteristic
378C2×Q8—112no—
379C2×Q8—221no—
380C2×Q8—442no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—21no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4C2×C22⋊D1112yes—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—42no—
391C22×C4—44no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—112no—
395C22×C4—112no—
396C22×C4—222no—
397C22×C4—222no—
398C22×C4—221no—
399C22×C4—221no—
400C22×C4—221no—
401C22×C4—221no—
402C22×C4—221no—
403C22×C4—224no—
404C22×C4—221no—
405C22×C4—222no—
406C22×C4—442no—
407C22×C4—442no—
408C22×C4—442no—
409C22×C4—442no—
410C22×C4—882no—
411C22×C4D4×D1111yescharacteristic
412C22×C4D4×D1111yescharacteristic
413C22×C4D4×D1111yescharacteristic
414C22×C4C2×C22⋊D1111yescharacteristic
415C22×C4C2×C22⋊D1111yescharacteristic
416C22×C4C23×D1111yescharacteristic
417C2×C8—22no—
418C2×C8—42no—
419C2×C8—222no—
420C2×C8—442no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C4⋊C4—112no—
427C4⋊C4—224no—
428C4⋊C4—224no—
429C4⋊C4—224no—
430C4⋊C4—222no—
431C4⋊C4—222no—
432C4⋊C4—221no—
433C4⋊C4—222no—
434C4⋊C4—222no—
435C4⋊C4—222no—
436C4⋊C4—222no—
437C4⋊C4C2×C22⋊D1112yes—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—224no—
441C22⋊C4—224no—
442C22⋊C4—224no—
443C22⋊C4—222no—
444C22⋊C4—222no—
445C42—224no—
446C11C2×#161511yescharacteristic, complemented, Sylow
447C23—22no—
448C23—22no—
449C23—22no—
450C23—42no—
451C23—42no—
452C23—42no—
453C23#6696812yes—
454C23#6696912yes—
455C23#6699011yescharacteristic
456C23#6699011yescharacteristic
457C23C2×D4×D1111yescharacteristic
458Q8—442no—
459Q8—881no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—44no—
464D4—81no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—44no—
474C2×C4—42no—
475C2×C4—82no—
476C2×C4—82no—
477C2×C4—222no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—222no—
481C2×C4—222no—
482C2×C4—222no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4—442no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—881no—
493C2×C4—884no—
494C2×C4—884no—
495C2×C4#6699011yescharacteristic
496C2×C4#6699011yescharacteristic
497C2×C4C2×D4×D1111yescharacteristic
498C2×C4C22×C22⋊D1111yescharacteristic
499C8—42no—
500C8—442no—
501C22—24no—
502C22—24no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—84no—
511C22#1062266612yes—
512C22#1062278612yes—
513C22#1062278612yes—
514C22#1062281412yes—
515C22C2×#6696811yescharacteristic
516C22C2×#6696911yescharacteristic
517C22C2×#6699011yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—82no—
524C4—442no—
525C4—442no—
526C4—442no—
527C4—442no—
528C4—882no—
529C2—21no—
530C2—21no—
531C2—22no—
532C2—82no—
533C2#1306764414yesdirect product factor
534C2C2×#1062278611yescharacteristic
535C2C2×#1062281411yescharacteristic
536C2C2×#1062266611yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#481C2
socleC23×C11#120
prime radicalC2×C11×#121C22
hypercenterC2×#481D11
hypocenterC11C2×#1615
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. C2×#10622583C2semidirect
3. C2×#10622595C2semidirect
4. #13067644C2direct (N × H)
5. C2×#10622105C2semidirect
7. C2×#10622107C2semidirect
33. #10622595C22semidirect
35. #10622583C22semidirect
39. #10622107C22semidirect
40. #10622105C22semidirect
372. C2×C11#1615semidirect
446. C11C2×#1615semidirect
533. C2#13067644direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231332
C2×#106225832
C2×#106225952
#130676442
C2×#106221052
C2×#106221752
C2×#106221072
C2×C11×#4812
C2×#161511