Finite Group Databasebeta

← C2×#13067898 #14729556

Subgroups — C2×#13067898 #14729556

Order 2816.

1238 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623082C211yesmaximal, characteristic
2C2×#10622692C211yesmaximal, characteristic, complemented
3C2×#10622700C211yesmaximal, characteristic, complemented
4#13067898C218yesmaximal, direct product factor
5C2×#10622124C211yesmaximal, characteristic, complemented
6C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×#10622121C211yesmaximal, characteristic, complemented
8C2×C11×#461C211yesmaximal, characteristic, complemented
9C22×#4339—21no—
10C22×C11×SD16—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66991—21no—
14C2×#66977—21no—
15#10623082—22no—
16#10623082—22no—
17#10623082—22no—
18#10623082C2214yes—
19C2×C4⋊C4×D11—21no—
20C2×#66936—22no—
21C2×C4×D44C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C11×#461—22no—
24C11×#461C2214yescomplemented
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103—21no—
27#10622700—22no—
28#10622700C2214yescomplemented
29#10622692—22no—
30#10622692C2214yescomplemented
31C2×#66873—21no—
32C2×#66872—22no—
33C2×#66871—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36D4⋊(C11⋊C8)C2214yescomplemented
37#10622124C2214yescomplemented
38#10622121C2214yescomplemented
39C22×Q8×C11—21no—
40C22×D4×C11D411yescharacteristic
41C23×C4×C11—21no—
42C22×C22⋊D11—22no—
43C2×#4339—24no—
44C2×#4339—24no—
45C2×#4339—44no—
46C2×#4339—44no—
47C22×D44D411yescharacteristic
48C22×C4×D11—22no—
49C22×C4×D11—21no—
50C22×Dic22—21no—
51C2×C11×SD16—24no—
52C2×C11×SD16—44no—
53C22×C8×C11—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8C2312yes—
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11D412yes—
61C4×D4×C11C2312yes—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C42×C11C2311yescharacteristic
67C2×C22⋊Dic11—22no—
68#66991—24no—
69#66991—24no—
70C2×(C2×D11)⋊C4—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11D412yes—
73C2×C4⋊Dic11D411yescharacteristic
74#66977—24no—
75#66977—24no—
76C2×Dic11⋊C4—22no—
77C22×C11⋊C8—21no—
78C22×C11⋊C8—21no—
79C4⋊C4×D11—24no—
80C4⋊C4×D11—24no—
81#66936—28no—
82#66936—28no—
83C4×D44—21no—
84C4×D44—21no—
85C4×D44D412yes—
86C4×D44C2312yes—
87#66922—21no—
88#66922—21no—
89#66922D412yes—
90#66922C2312yes—
91C11×C4⋊C8—21no—
92C11×C4⋊C8C2312yes—
93C11×#103—24no—
94#66873—24no—
95#66872—28no—
96#66871—24no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)C2312yes—
99C4×C11⋊C8—21no—
100C4×C11⋊C8C2312yes—
101C2×#1654—111nomaximal, Sylow
102C24×C11—21no—
103C23×D11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—41no—
106C2×Q8×C11—42no—
107C2×Q8×C11—42no—
108C2×D4×C11—21no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11C2×D412yes—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—41no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C2×C22⋊D11—28no—
122C2×C22⋊D11—48no—
123C22×Dic11—21no—
124C22×Dic11—22no—
125#4339—48no—
126#4339—416no—
127#4339—48no—
128C2×D44—21no—
129C2×D44—22no—
130C2×D44SD1614yescomplemented
131C2×D44C2×D412yes—
132C2×C4×D11—28no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—48no—
136C2×C4×D11—42no—
137C2×C4×D11—42no—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C2×Dic22—42no—
141C2×Dic22—42no—
142C11×SD16—48no—
143C2×C8×C11—22no—
144C2×C8×C11—42no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—41no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4C2×D412yes—
151C11×C22⋊C4—22no—
152C11×C22⋊C4—22no—
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11C2411yescharacteristic
157C22⋊Dic11—28no—
158(C2×D11)⋊C4—22no—
159(C2×D11)⋊C4—22no—
160C4⋊Dic11—22no—
161C4⋊Dic11—22no—
162C4⋊Dic11—21no—
163C4⋊Dic11—22no—
164C4⋊Dic11C2×D412yes—
165C4⋊Dic11C2×D414yes—
166Dic11⋊C4—28no—
167C2×C11⋊C8—24no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—42no—
171C2×#547—111no—
172C2×#498—111no—
173C2×#474—111no—
174C2×#461D1111yescharacteristic, complemented
175#1654—118no—
176C2×#332—111no—
177C2×D4⋊C8—111no—
178C2×D4⋊C8—111no—
179C23×C11—22no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11#12011yescharacteristic
184C22×D11—22no—
185C22×D11—24no—
186C22×D11—42no—
187C22×D11—42no—
188Q8×C11—42no—
189Q8×C11—42no—
190Q8×C11—82no—
191D4×C11—22no—
192D4×C11—22no—
193D4×C11—42no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—44no—
200C2×C4×C11—42no—
201C2×C4×C11—82no—
202C2×C4×C11#12011yescharacteristic
203C2×C4×C11#12011yescharacteristic
204C2×C4×C11#12011yescharacteristic
205C2×C4×C11C2×SD1612yes—
206C2×C4×C11#13512yes—
207C2×C4×C11AGL(1,ℤ/8)12yes—
208C2×C4×C11AGL(1,ℤ/8)12yes—
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C22⋊D11—416no—
213C2×Dic11—22no—
214C2×Dic11—24no—
215C2×Dic11—42no—
216C2×Dic11—44no—
217D44—22no—
218D44—24no—
219D44C2×SD1614yescomplemented
220C4×D11—416no—
221C4×D11—42no—
222C4×D11—42no—
223C4×D11—44no—
224Dic22—42no—
225Dic22—42no—
226Dic22—44no—
227C8×C11—42no—
228C11⋊C8—24no—
229C11⋊C8—42no—
230C22×#41—221no—
231C22×SD16—21no—
232#547—114no—
233#547—222no—
234#547—222no—
235#547—222no—
236C2×C4⋊Q8—111no—
237C2×C4⋊Q8C2×D1111yescharacteristic
238C2×#123—222no—
239C2×C22⋊Q8—221no—
240C2×#121—221no—
241C2×C4×D4—111no—
242C2×C4×D4C2×D1111yescharacteristic
243C22×C4⋊C4—221no—
244#498—114no—
245#498—222no—
246#474—114no—
247#474—222no—
248#461—22no—
249#461C2×D1114yescomplemented
250C2×#107—221no—
251C2×#106—222no—
252C2×C4⋊C8—111no—
253C2×C4⋊C8C2×D1111yescharacteristic
254C2×#103—21no—
255C2×#102—221no—
256C2×C4×C8—111no—
257#332—114no—
258D4⋊C8—114no—
259D4⋊C8—114no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—84no—
264C22×C11#44912yes—
265C22×C11#45012yes—
266C22×C11#45612yes—
267C22×C11C2×#12011yescharacteristic
268C2×D11—24no—
269C2×D11—48no—
270C2×D11—42no—
271C2×D11—42no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—42no—
275C4×C11—82no—
276C4×C11#44912yes—
277C4×C11#45012yes—
278C4×C11C22×SD1611yescharacteristic
279C4×C11C2×#13511yescharacteristic
280C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
281C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
282Dic11—44no—
283Dic11—42no—
284C2×#41—224no—
285C2×#41—224no—
286C2×#41—444no—
287C2×#41—444no—
288C22×Q8—21no—
289C22×Q8—221no—
290C22×D4—111no—
291C22×D4—222no—
292C22×D4C22⋊D1111yescharacteristic
293C23×C4—21no—
294C23×C4—222no—
295C23×C4—221no—
296C2×SD16—24no—
297C2×SD16—44no—
298C22×C8—21no—
299C22×C8—221no—
300C22×C8—221no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—112no—
305C4⋊Q8—112no—
306C4⋊Q8—221no—
307C4⋊Q8—221no—
308C4⋊Q8C22×D1112yes—
309#123—228no—
310#123—228no—
311C22⋊Q8—224no—
312C22⋊Q8—224no—
313#121—224no—
314#121—224no—
315C4×D4—21no—
316C4×D4—21no—
317C4×D4—112no—
318C4×D4—112no—
319C4×D4—221no—
320C4×D4—221no—
321C4×D4C22⋊D1112yes—
322C4×D4C22×D1112yes—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—111no—
326C2×C4⋊C4—112no—
327C2×C4⋊C4—224no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4—224no—
331C2×C4⋊C4C22⋊D1111yescharacteristic
332C2×C22⋊C4—21no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4—221no—
335C2×C42C22×D1111yescharacteristic
336#107—224no—
337#106—228no—
338C4⋊C8—21no—
339C4⋊C8—112no—
340C4⋊C8—221no—
341C4⋊C8C22×D1112yes—
342#103—24no—
343#102—224no—
344C4×C8—112no—
345C4×C8—221no—
346C2×C11—82no—
347C2×C11#165414yescomplemented
348C2×C11C2×#45011yescharacteristic
349C2×C11C2×#44911yescharacteristic
350C2×C11C2×#45611yescharacteristic
351D11—44no—
352C24—21no—
353C24—221no—
354#41—448no—
355#41—448no—
356#41—4416no—
357C2×Q8—22no—
358C2×Q8—41no—
359C2×Q8—42no—
360C2×Q8—42no—
361C2×Q8—222no—
362C2×Q8—222no—
363C2×Q8—442no—
364C2×Q8—442no—
365C2×D4—22no—
366C2×D4—21no—
367C2×D4—22no—
368C2×D4—114no—
369C2×D4—112no—
370C2×D4—228no—
371C2×D4—222no—
372C2×D4—221no—
373C2×D4—448no—
374C2×D4C2×C22⋊D1112yes—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—41no—
381C22×C4—228no—
382C22×C4—221no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—448no—
387C22×C4—442no—
388C22×C4—442no—
389C22×C4D4×D1111yescharacteristic
390C22×C4D4×D1111yescharacteristic
391C22×C4C2×C22⋊D1111yescharacteristic
392SD16—48no—
393C2×C8—22no—
394C2×C8—42no—
395C2×C8—224no—
396C2×C8—222no—
397C2×C8—222no—
398C2×C8—442no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—114no—
405C4⋊C4—112no—
406C4⋊C4—228no—
407C4⋊C4—221no—
408C4⋊C4—222no—
409C4⋊C4—222no—
410C4⋊C4—222no—
411C4⋊C4C2×C22⋊D1112yes—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—228no—
415C22⋊C4—222no—
416C22⋊C4—222no—
417C42D4×D1111yescharacteristic
418C42D4×D1111yescharacteristic
419C42C2×C22⋊D1111yescharacteristic
420C42C23×D1111yescharacteristic
421C11C2×#165411yescharacteristic, complemented, Sylow
422C23—22no—
423C23—42no—
424C23—42no—
425C23—42no—
426C23—224no—
427C23—222no—
428C23—442no—
429C23—442no—
430C23#6699011yescharacteristic
431Q8—42no—
432Q8—42no—
433Q8—82no—
434Q8—442no—
435Q8—442no—
436Q8—444no—
437D4—22no—
438D4—22no—
439D4—42no—
440D4—114no—
441D4—222no—
442D4—224no—
443D4—4416no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—44no—
450C2×C4—42no—
451C2×C4—82no—
452C2×C4—222no—
453C2×C4—224no—
454C2×C4—4416no—
455C2×C4—444no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—444no—
460C2×C4SD16×D1112yes—
461C2×C4#6696712yes—
462C2×C4#6698512yes—
463C2×C4#6699011yescharacteristic
464C2×C4#6699011yescharacteristic
465C2×C4#6699011yescharacteristic
466C2×C4#6700312yes—
467C2×C4C2×D4×D1111yescharacteristic
468C2×C4C2×D4×D1111yescharacteristic
469C2×C4C22×C22⋊D1111yescharacteristic
470C8—42no—
471C8—224no—
472C8—442no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—84no—
477C22—224no—
478C22—442no—
479C22—448no—
480C22—442no—
481C22#1062265012yes—
482C22#1062278212yes—
483C22#1062281812yes—
484C22C2×#6699011yescharacteristic
485C4—21no—
486C4—21no—
487C4—42no—
488C4—82no—
489C4—444no—
490C4—442no—
491C4#1062265012yes—
492C4#1062278212yes—
493C4C2×SD16×D1111yescharacteristic
494C4C2×#6696711yescharacteristic
495C4C2×#6698511yescharacteristic
496C4C2×#6700311yescharacteristic
497C2—82no—
498C2—444no—
499C2#1306789814yesdirect product factor
500C2C2×#1062278211yescharacteristic
501C2C2×#1062265011yescharacteristic
502C2C2×#1062281811yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#461C2
socleC23×C11#120
prime radicalC2×#10623082C2
hypercenterC2×#461D11
hypocenterC11C2×#1654
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
2. C2×#10622692C2semidirect
3. C2×#10622700C2semidirect
4. #13067898C2direct (N × H)
5. C2×#10622124C2semidirect
6. C2×D4⋊(C11⋊C8)C2semidirect
7. C2×#10622121C2semidirect
8. C2×C11×#461C2semidirect
24. C11×#461C22semidirect
28. #10622700C22semidirect
30. #10622692C22semidirect
36. D4⋊(C11⋊C8)C22semidirect
37. #10622124C22semidirect
38. #10622121C22semidirect
130. C2×D44SD16semidirect
174. C2×#461D11semidirect
219. D44C2×SD16semidirect
249. #461C2×D11semidirect
347. C2×C11#1654semidirect
421. C11C2×#1654semidirect
499. C2#13067898direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230822
C2×#106226922
C2×#106227002
#130678982
C2×#106221242
C2×D4⋊(C11⋊C8)2
C2×#106221212
C2×C11×#4612
C2×#165411