Finite Group Databasebeta

← C2×#13067854 #14729552

Subgroups — C2×#13067854 #14729552

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×#10622295C211yesmaximal, characteristic, complemented
3C2×#10622620C211yesmaximal, characteristic, complemented
4C2×#10622454C211yesmaximal, characteristic, complemented
5#13067854C218yesmaximal, direct product factor
6C2×#10622120C211yesmaximal, characteristic, complemented
7C2×#10622097C211yesmaximal, characteristic, complemented
8C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
9C22×#4339—21no—
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66991—21no—
12C2×#66977—21no—
13C22×#4314—21no—
14#10623082—22no—
15#10623082—22no—
16#10623082—22no—
17#10623082C2214yes—
18C2×C4⋊C4×D11—21no—
19C2×#66936—22no—
20C2×C4×D44C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C2×#66896—21no—
26C2×#66882—22no—
27C2×#66880—21no—
28#10622620—22no—
29#10622620C2214yescomplemented
30C2×#66871—21no—
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32#10622454—22no—
33#10622454C2214yescomplemented
34#10622295—22no—
35#10622295C2214yescomplemented
36C11×D4⋊C8C2214yescomplemented
37#10622120C2214yescomplemented
38#10622097C2214yescomplemented
39C22×D4×C11D411yescharacteristic
40C23×C4×C11—21no—
41C22×C22⋊D11—22no—
42C2×#4339—24no—
43C2×#4339—24no—
44C2×#4339—44no—
45C2×#4339—44no—
46C22×D44D411yescharacteristic
47C22×C4×D11—22no—
48C22×C4×D11—21no—
49C22×Dic22—21no—
50C22×Dic22—21no—
51C22×C8×C11—21no—
52C22×C8×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C4×D4×C11D412yes—
56C4×D4×C11C2312yes—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C22⋊C4—21no—
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11—22no—
61#66991—24no—
62#66991—24no—
63C2×(C2×D11)⋊C4—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11D412yes—
68C2×C4⋊Dic11D411yescharacteristic
69#66977—24no—
70#66977—24no—
71C2×Dic11⋊C4—22no—
72C22×C11⋊C8—21no—
73C2×#4314—24no—
74C2×#4314—44no—
75C4⋊C4×D11—24no—
76C4⋊C4×D11—24no—
77#66936—28no—
78#66936—28no—
79C4×D44—21no—
80C4×D44—21no—
81C4×D44D412yes—
82C4×D44C2312yes—
83#66922—21no—
84#66922—21no—
85#66922—21no—
86#66922—21no—
87#66922—21no—
88#66922D412yes—
89#66922C2312yes—
90#66922C2312yes—
91C11×C4⋊C8—21no—
92C11×C4⋊C8C2312yes—
93C4×C8×C11—21no—
94C4×C8×C11C2312yes—
95#66896—24no—
96#66882—28no—
97#66880—24no—
98#66871—24no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)C2312yes—
101C2×#1647—111nomaximal, Sylow
102C24×C11—21no—
103C23×D11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11C2×D412yes—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C2×C22⋊D11—28no—
117C2×C22⋊D11—48no—
118C22×Dic11—21no—
119C22×Dic11—22no—
120C22×Dic11—41no—
121#4339—48no—
122#4339—416no—
123#4339—48no—
124C2×D44—21no—
125C2×D44—22no—
126C2×D44D814yes—
127C2×D44C2×D412yes—
128C2×C4×D11—28no—
129C2×C4×D11—22no—
130C2×C4×D11—22no—
131C2×C4×D11—48no—
132C2×C4×D11—42no—
133C2×C4×D11—42no—
134C2×Dic22—22no—
135C2×Dic22—22no—
136C2×Dic22—22no—
137C2×Dic22—41no—
138C2×Dic22—42no—
139C2×Dic22—42no—
140C2×Dic22—42no—
141C2×Dic22—42no—
142C2×C8×C11—24no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—42no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4C2×D412yes—
148C11×C22⋊C4—22no—
149C11×C22⋊C4—22no—
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11C2411yescharacteristic
154C22⋊Dic11—28no—
155(C2×D11)⋊C4—22no—
156(C2×D11)⋊C4—22no—
157C4⋊Dic11—22no—
158C4⋊Dic11—22no—
159C4⋊Dic11—21no—
160C4⋊Dic11—22no—
161C4⋊Dic11—22no—
162C4⋊Dic11—22no—
163C4⋊Dic11—41no—
164C4⋊Dic11—41no—
165C4⋊Dic11C2×D412yes—
166C4⋊Dic11C2×D414yes—
167Dic11⋊C4—28no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—42no—
170#4314—48no—
171C2×#547—111no—
172C2×#500—111no—
173C2×#474—111no—
174C2×#461—111no—
175#1647—118no—
176C2×#332—111no—
177C2×D4⋊C8—111no—
178C2×D4⋊C8D1111yescharacteristic, complemented
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—
188D4×C11—22no—
189D4×C11—22no—
190D4×C11—42no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—44no—
197C2×C4×C11#12011yescharacteristic
198C2×C4×C11#12011yescharacteristic
199C2×C4×C11#12011yescharacteristic
200C2×C4×C11C2×D812yes—
201C2×C4×C11#13512yes—
202C2×C4×C11AGL(1,ℤ/8)12yes—
203C2×C4×C11#13712yes—
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C22⋊D11—416no—
208C2×Dic11—22no—
209C2×Dic11—24no—
210C2×Dic11—44no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—82no—
214D44—22no—
215D44—24no—
216D44C2×D814yes—
217C4×D11—416no—
218C4×D11—42no—
219C4×D11—42no—
220C4×D11—44no—
221Dic22—42no—
222Dic22—42no—
223Dic22—44no—
224Dic22—42no—
225Dic22—42no—
226Dic22—82no—
227C8×C11—24no—
228C8×C11—42no—
229C11⋊C8—42no—
230C22×#41—221no—
231C22×SD16—221no—
232#547—114no—
233#547—222no—
234#547—222no—
235#547—222no—
236C2×C4⋊Q8—111no—
237C2×C4⋊Q8—111no—
238C2×#123—222no—
239C2×C22⋊Q8—221no—
240C2×#121—221no—
241C2×C4×D4—111no—
242C2×C4×D4C2×D1111yescharacteristic
243C22×C4⋊C4—221no—
244#500—114no—
245#500—222no—
246#474—114no—
247#474—222no—
248#461—114no—
249#461—222no—
250C2×#107—222no—
251C2×#107—221no—
252C2×C4⋊C8—111no—
253C2×C4⋊C8C2×D1111yescharacteristic
254C2×#103—221no—
255C2×#102—221no—
256C2×C4×C8C2×D1111yescharacteristic
257#332—114no—
258D4⋊C8—114no—
259D4⋊C8C2×D1114yescomplemented
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—84no—
264C22×C11#44712yes—
265C22×C11#45212yes—
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#44712yes—
276C4×C11#45212yes—
277C4×C11C22×D811yescharacteristic
278C4×C11C2×#13511yescharacteristic
279C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
280C4×C11C2×#13711yescharacteristic
281Dic11—44no—
282Dic11—42no—
283Dic11—82no—
284C2×#41—224no—
285C2×#41—224no—
286C2×#41—444no—
287C2×#41—444no—
288C22×Q8—221no—
289C22×Q8—221no—
290C22×D4—111no—
291C22×D4—222no—
292C22×D4D4411yescharacteristic
293C23×C4—21no—
294C23×C4—222no—
295C23×C4—221no—
296C2×SD16—224no—
297C2×SD16—444no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—221no—
301C4⋊Q8—112no—
302C4⋊Q8—112no—
303C4⋊Q8—112no—
304C4⋊Q8—221no—
305C4⋊Q8—221no—
306C4⋊Q8—221no—
307C4⋊Q8—221no—
308C4⋊Q8—221no—
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×D4D4412yes—
322C4×D4C22×D1112yes—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—112no—
325C2×C4⋊C4—224no—
326C2×C4⋊C4—222no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—224no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4D4411yescharacteristic
332C2×C22⋊C4—21no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4—221no—
335C2×C42C22×D1111yescharacteristic
336#107—228no—
337#107—224no—
338C4⋊C8—21no—
339C4⋊C8—112no—
340C4⋊C8—221no—
341C4⋊C8C22×D1112yes—
342#103—224no—
343#102—224no—
344C4×C8—21no—
345C4×C8C22×D1112yes—
346C2×C11—82no—
347C2×C11#164714yescomplemented
348C2×C11C2×#44711yescharacteristic
349C2×C11C2×#45211yescharacteristic
350C2×C11C2×#45611yescharacteristic
351D11—44no—
352C24—21no—
353C24—221no—
354#41—448no—
355#41—448no—
356#41—4416no—
357C2×Q8—222no—
358C2×Q8—222no—
359C2×Q8—222no—
360C2×Q8—441no—
361C2×Q8—442no—
362C2×Q8—442no—
363C2×Q8—442no—
364C2×Q8—442no—
365C2×D4—21no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—114no—
369C2×D4—112no—
370C2×D4—228no—
371C2×D4—221no—
372C2×D4—222no—
373C2×D4—448no—
374C2×D4C2×D4412yes—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—228no—
381C22×C4—221no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—448no—
386C22×C4—442no—
387C22×C4—442no—
388C22×C4—441no—
389C22×C4C2×D4411yescharacteristic
390C22×C4D4×D1111yescharacteristic
391C22×C4D4×D1111yescharacteristic
392SD16—448no—
393C2×C8—24no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—42no—
397C2×C8—222no—
398C2×C8—442no—
399C4⋊C4—21no—
400C4⋊C4—112no—
401C4⋊C4—114no—
402C4⋊C4—228no—
403C4⋊C4—221no—
404C4⋊C4—222no—
405C4⋊C4—222no—
406C4⋊C4—222no—
407C4⋊C4—222no—
408C4⋊C4—222no—
409C4⋊C4—441no—
410C4⋊C4—441no—
411C4⋊C4C2×D4412yes—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—228no—
415C22⋊C4—222no—
416C22⋊C4—222no—
417C42C2×D4411yescharacteristic
418C42D4×D1111yescharacteristic
419C42D4×D1111yescharacteristic
420C42C23×D1111yescharacteristic
421C11C2×#164711yescharacteristic, complemented, Sylow
422C23—22no—
423C23—42no—
424C23—42no—
425C23—42no—
426C23—222no—
427C23—224no—
428C23—442no—
429C23—442no—
430C23#6693511yescharacteristic
431Q8—442no—
432Q8—442no—
433Q8—444no—
434Q8—442no—
435Q8—442no—
436Q8—882no—
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—222no—
451C2×C4—224no—
452C2×C4—4416no—
453C2×C4—442no—
454C2×C4—444no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—444no—
458C2×C4—442no—
459C2×C4—882no—
460C2×C4#6693511yescharacteristic
461C2×C4#6693511yescharacteristic
462C2×C4#6693511yescharacteristic
463C2×C4#6695712yes—
464C2×C4#6696212yes—
465C2×C4D8×D1112yes—
466C2×C4#6696712yes—
467C2×C4C22×D4411yescharacteristic
468C2×C4C2×D4×D1111yescharacteristic
469C2×C4C2×D4×D1111yescharacteristic
470C8—24no—
471C8—42no—
472C8—442no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—84no—
477C22—224no—
478C22—442no—
479C22—448no—
480C22—442no—
481C22#1062234612yes—
482C22#1062238612yes—
483C22#1062243912yes—
484C22C2×#6693511yescharacteristic
485C4—21no—
486C4—21no—
487C4—42no—
488C4—444no—
489C4—442no—
490C4—882no—
491C4#1062234612yes—
492C4#1062238612yes—
493C4C2×#6695711yescharacteristic
494C4C2×#6696211yescharacteristic
495C4C2×D8×D1111yescharacteristic
496C4C2×#6696711yescharacteristic
497C2—82no—
498C2—444no—
499C2#1306785414yesdirect product factor
500C2C2×#1062238611yescharacteristic
501C2C2×#1062234611yescharacteristic
502C2C2×#1062243911yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×D4⋊C8C2
socleC23×C11#120
prime radicalC2×#10623082C2
hypercenterC2×D4⋊C8D11
hypocenterC11C2×#1647
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#10622295C2semidirect
3. C2×#10622620C2semidirect
4. C2×#10622454C2semidirect
5. #13067854C2direct (N × H)
6. C2×#10622120C2semidirect
7. C2×#10622097C2semidirect
8. C2×C11×D4⋊C8C2semidirect
29. #10622620C22semidirect
33. #10622454C22semidirect
35. #10622295C22semidirect
36. C11×D4⋊C8C22semidirect
37. #10622120C22semidirect
38. #10622097C22semidirect
178. C2×D4⋊C8D11semidirect
259. D4⋊C8C2×D11semidirect
347. C2×C11#1647semidirect
421. C11C2×#1647semidirect
499. C2#13067854direct (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×#106222952
C2×#106226202
C2×#106224542
#130678542
C2×#106221202
C2×#106220972
C2×C11×D4⋊C82
C2×#164711