Finite Group Databasebeta

← C2×#13067878 #14729564

Subgroups — C2×#13067878 #14729564

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×D44C211yesmaximal, characteristic
2C2×#10622692C211yesmaximal, characteristic, complemented
3C2×#10622696C211yesmaximal, characteristic
4#13067878C218yesmaximal, direct product factor
5C2×#10622120C211yesmaximal, characteristic, complemented
6C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×#10622121C211yesmaximal, characteristic
8C2×C11×#475C211yesmaximal, characteristic, complemented
9C22×Q8×D11—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C22×#4325—21no—
13Q8×D44—22no—
14Q8×D44—22no—
15Q8×D44—22no—
16Q8×D44C2214yes—
17C2×#66950—21no—
18C2×#66950—22no—
19C2×C4×D44—21no—
20C2×C4×D44C2211yescharacteristic
21C2×#66922—21no—
22C2×#66922C2211yescharacteristic
23C11×#475—22no—
24C11×#475C2214yescomplemented
25C2×C11×#106—21no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103—21no—
28C2×#66899—21no—
29#10622696—22no—
30#10622696C2214yes—
31#10622692—22no—
32#10622692C2214yescomplemented
33C2×#66872—22no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36Q8⋊(C11⋊C8)C2214yescomplemented
37#10622121C2214yes—
38#10622120C2214yescomplemented
39C22×Q8×C11—21no—
40C22×Q8×C11D411yescharacteristic
41C2×Q8×D11—24no—
42C2×Q8×D11—24no—
43C2×Q8×D11—44no—
44C2×Q8×D11—44no—
45C22×D44D411yescharacteristic
46C22×C4×D11—22no—
47C22×C4×D11—21no—
48C22×Dic22—22no—
49C22×Dic22—21no—
50C22×C8×C11—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8C2312yes—
55C4×Q8×C11—21no—
56C4×Q8×C11—21no—
57C4×Q8×C11D412yes—
58C4×Q8×C11C2312yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C42×C11—21no—
64C2×C42×C11C2311yescharacteristic
65C2×#4325—24no—
66C2×#4325—44no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—21no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11D411yescharacteristic
72C2×C4⋊Dic11D412yes—
73C22×C11⋊C8—21no—
74C22×C11⋊C8—21no—
75#66950—24no—
76#66950—28no—
77#66950—24no—
78#66950—28no—
79C4×D44—24no—
80C4×D44—24no—
81C4×D44—21no—
82C4×D44—21no—
83C4×D44D412yes—
84C4×D44C2312yes—
85#66922—24no—
86#66922—21no—
87#66922—21no—
88#66922—24no—
89#66922D412yes—
90#66922C2312yes—
91C11×#106—24no—
92C11×C4⋊C8—21no—
93C11×C4⋊C8C2312yes—
94C11×#103—24no—
95#66899—24no—
96#66872—28no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)C2312yes—
99C4×C11⋊C8—21no—
100C4×C11⋊C8C2312yes—
101C2×#1651—111nomaximal, Sylow
102C23×D11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—41no—
107C2×Q8×C11—42no—
108C2×Q8×C11—42no—
109C2×Q8×C11SD1614yescomplemented
110C2×Q8×C11C2×D412yes—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—41no—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×Dic11—21no—
118C22×Dic11—22no—
119Q8×D11—48no—
120Q8×D11—416no—
121Q8×D11—48no—
122C2×D44—21no—
123C2×D44—22no—
124C2×D44SD1614yes—
125C2×D44C2×D412yes—
126C2×C4×D11—28no—
127C2×C4×D11—22no—
128C2×C4×D11—22no—
129C2×C4×D11—48no—
130C2×C4×D11—42no—
131C2×C4×D11—42no—
132C2×Dic22—28no—
133C2×Dic22—22no—
134C2×Dic22—22no—
135C2×Dic22—48no—
136C2×Dic22—42no—
137C2×Dic22—42no—
138C2×C8×C11—22no—
139C2×C8×C11—42no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4C2×D412yes—
148C42×C11—22no—
149C42×C11—22no—
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11C2411yescharacteristic
154#4325—48no—
155(C2×D11)⋊C4—28no—
156(C2×D11)⋊C4—22no—
157(C2×D11)⋊C4—22no—
158C4⋊Dic11—28no—
159C4⋊Dic11—21no—
160C4⋊Dic11—22no—
161C4⋊Dic11—22no—
162C4⋊Dic11—22no—
163C4⋊Dic11C2×D414yes—
164C4⋊Dic11C2×D412yes—
165C2×C11⋊C8—24no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—42no—
169C2×D4×Q8—111no—
170C2×#498—111no—
171C2×#475D1111yescharacteristic, complemented
172C2×#461—111no—
173#1651—118no—
174C2×#332—111no—
175C2×Q8⋊C8—111no—
176C2×D4⋊C8—111no—
177C23×C11#12011yescharacteristic
178C22×D11—22no—
179C22×D11—24no—
180C22×D11—42no—
181C22×D11—42no—
182Q8×C11—22no—
183Q8×C11—24no—
184Q8×C11—42no—
185Q8×C11—42no—
186Q8×C11—82no—
187Q8×C11C2×SD1614yescomplemented
188C2×C4×C11—22no—
189C2×C4×C11—24no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—82no—
195C2×C4×C11#12011yescharacteristic
196C2×C4×C11#12011yescharacteristic
197C2×C4×C11#12011yescharacteristic
198C2×C4×C11C2×SD1612yes—
199C2×C4×C11C2×SD1612yes—
200C2×C4×C11AGL(1,ℤ/8)12yes—
201C2×C4×C11#13712yes—
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C2×Dic11—22no—
206C2×Dic11—24no—
207C2×Dic11—42no—
208C2×Dic11—44no—
209D44—22no—
210D44—24no—
211D44C2×SD1614yes—
212C4×D11—416no—
213C4×D11—42no—
214C4×D11—42no—
215C4×D11—44no—
216Dic22—416no—
217Dic22—42no—
218Dic22—42no—
219Dic22—44no—
220C8×C11—42no—
221C11⋊C8—24no—
222C11⋊C8—42no—
223C23×Q8—221no—
224C22×SD16—221no—
225D4×Q8—114no—
226D4×Q8—222no—
227D4×Q8—222no—
228D4×Q8—222no—
229C2×C4⋊Q8—111no—
230C2×C4⋊Q8—221no—
231C2×C4⋊Q8C2×D1111yescharacteristic
232C2×C22⋊Q8—222no—
233C2×C22⋊Q8—221no—
234C2×C4×Q8C2×D1111yescharacteristic
235C2×C4×D4—111no—
236C2×C4×D4—221no—
237#498—114no—
238#498—222no—
239#475—22no—
240#475C2×D1114yescomplemented
241#461—114no—
242#461—222no—
243C2×#106—21no—
244C2×#106—222no—
245C2×C4⋊C8—111no—
246C2×C4⋊C8C2×D1111yescharacteristic
247C2×#103—21no—
248C2×#103—221no—
249C2×C4×C8—111no—
250#332—114no—
251Q8⋊C8—114no—
252D4⋊C8—114no—
253C22×C11#44812yes—
254C22×C11#45012yes—
255C22×C11#45612yes—
256C22×C11C2×#12011yescharacteristic
257C2×D11—24no—
258C2×D11—48no—
259C2×D11—42no—
260C2×D11—42no—
261C4×C11—24no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—42no—
265C4×C11—82no—
266C4×C11#44812yes—
267C4×C11#45012yes—
268C4×C11C22×SD1611yescharacteristic
269C4×C11C22×SD1611yescharacteristic
270C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
271C4×C11C2×#13711yescharacteristic
272Dic11—42no—
273Dic11—44no—
274C22×Q8—21no—
275C22×Q8—222no—
276C22×Q8—224no—
277C22×Q8—224no—
278C22×Q8—221no—
279C22×Q8—444no—
280C22×Q8—444no—
281C22×Q8C22⋊D1111yescharacteristic
282C22×D4—111no—
283C23×C4—222no—
284C23×C4—221no—
285C2×SD16—224no—
286C2×SD16—444no—
287C22×C8—21no—
288C22×C8—221no—
289C22×C8—221no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8—112no—
294C4⋊Q8—112no—
295C4⋊Q8—224no—
296C4⋊Q8—224no—
297C4⋊Q8—221no—
298C4⋊Q8—221no—
299C4⋊Q8C22×D1112yes—
300C22⋊Q8—228no—
301C22⋊Q8—224no—
302C22⋊Q8—228no—
303C22⋊Q8—224no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8C22⋊D1112yes—
307C4×Q8C22×D1112yes—
308C4×D4—112no—
309C4×D4—112no—
310C4×D4—224no—
311C4×D4—224no—
312C4×D4—221no—
313C4×D4—221no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—111no—
318C2×C4⋊C4—112no—
319C2×C4⋊C4—222no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4C22⋊D1111yescharacteristic
322C2×C22⋊C4—222no—
323C2×C22⋊C4—221no—
324C2×C42—21no—
325C2×C42C22×D1111yescharacteristic
326#106—24no—
327#106—228no—
328C4⋊C8—21no—
329C4⋊C8—112no—
330C4⋊C8—221no—
331C4⋊C8C22×D1112yes—
332#103—24no—
333#103—224no—
334C4×C8—112no—
335C4×C8—221no—
336C2×C11#165114yescomplemented
337C2×C11C2×#45011yescharacteristic
338C2×C11C2×#44811yescharacteristic
339C2×C11C2×#45611yescharacteristic
340D11—44no—
341C24—221no—
342C2×Q8—21no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—41no—
346C2×Q8—42no—
347C2×Q8—42no—
348C2×Q8—228no—
349C2×Q8—222no—
350C2×Q8—222no—
351C2×Q8—448no—
352C2×Q8—448no—
353C2×Q8—4416no—
354C2×Q8—448no—
355C2×Q8—442no—
356C2×Q8—442no—
357C2×Q8#432514yescomplemented
358C2×Q8C2×C22⋊D1112yes—
359C2×D4—114no—
360C2×D4—112no—
361C2×D4—222no—
362C2×D4—221no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—41no—
366C22×C4—228no—
367C22×C4—222no—
368C22×C4—221no—
369C22×C4—222no—
370C22×C4—222no—
371C22×C4—448no—
372C22×C4—442no—
373C22×C4—442no—
374C22×C4D4×D1111yescharacteristic
375C22×C4D4×D1111yescharacteristic
376C22×C4C2×C22⋊D1111yescharacteristic
377SD16—448no—
378C2×C8—22no—
379C2×C8—42no—
380C2×C8—224no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—442no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—112no—
392C4⋊C4—114no—
393C4⋊C4—228no—
394C4⋊C4—221no—
395C4⋊C4—222no—
396C4⋊C4—222no—
397C4⋊C4—222no—
398C4⋊C4C2×C22⋊D1112yes—
399C22⋊C4—228no—
400C22⋊C4—222no—
401C22⋊C4—222no—
402C42—22no—
403C42—22no—
404C42D4×D1111yescharacteristic
405C42D4×D1111yescharacteristic
406C42C2×C22⋊D1111yescharacteristic
407C42C23×D1111yescharacteristic
408C11C2×#165111yescharacteristic, complemented, Sylow
409C23—224no—
410C23—222no—
411C23—442no—
412C23—442no—
413C23#6699011yescharacteristic
414Q8—22no—
415Q8—24no—
416Q8—42no—
417Q8—42no—
418Q8—82no—
419Q8—4416no—
420Q8—442no—
421Q8—442no—
422Q8—444no—
423Q8C2×#432514yescomplemented
424D4—114no—
425D4—222no—
426D4—224no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—24no—
430C2×C4—22no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—82no—
434C2×C4—224no—
435C2×C4—222no—
436C2×C4—4416no—
437C2×C4—444no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—442no—
441C2×C4—444no—
442C2×C4SD16×D1112yes—
443C2×C4#6696812yes—
444C2×C4#6699011yescharacteristic
445C2×C4#6699011yescharacteristic
446C2×C4#6699011yescharacteristic
447C2×C4C2×#432512yes—
448C2×C4#6700212yes—
449C2×C4C2×D4×D1111yescharacteristic
450C2×C4C2×D4×D1111yescharacteristic
451C2×C4C22×C22⋊D1111yescharacteristic
452C8—42no—
453C8—224no—
454C8—442no—
455C22—224no—
456C22—442no—
457C22—448no—
458C22—442no—
459C22#1062265912yes—
460C22#1062278312yes—
461C22#1062281812yes—
462C22C2×#6699011yescharacteristic
463C4—24no—
464C4—21no—
465C4—21no—
466C4—42no—
467C4—82no—
468C4—444no—
469C4—442no—
470C4#1062265912yes—
471C4#1062278312yes—
472C4C2×SD16×D1111yescharacteristic
473C4C2×#6696811yescharacteristic
474C4C22×#432511yescharacteristic
475C4C2×#6700211yescharacteristic
476C2—444no—
477C2#1306787814yesdirect product factor
478C2C2×#1062265911yescharacteristic
479C2C2×#1062278311yescharacteristic
480C2C2×#1062281811yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#475C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenterC2×#475D11
hypocenterC11C2×#1651
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
2. C2×#10622692C2semidirect
4. #13067878C2direct (N × H)
5. C2×#10622120C2semidirect
6. C2×Q8⋊(C11⋊C8)C2semidirect
8. C2×C11×#475C2semidirect
24. C11×#475C22semidirect
32. #10622692C22semidirect
36. Q8⋊(C11⋊C8)C22semidirect
38. #10622120C22semidirect
109. C2×Q8×C11SD16semidirect
171. C2×#475D11semidirect
187. Q8×C11C2×SD16semidirect
240. #475C2×D11semidirect
336. C2×C11#1651semidirect
357. C2×Q8#4325semidirect
408. C11C2×#1651semidirect
423. Q8C2×#4325semidirect
477. C2#13067878direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×D442
C2×#106226922
C2×#106226962
#130678782
C2×#106221202
C2×Q8⋊(C11⋊C8)2
C2×#106221212
C2×C11×#4752
C2×#165111