Finite Group Databasebeta

← C2×#13067876 #14729562

Subgroups — C2×#13067876 #14729562

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×#10623258C211yesmaximal, characteristic
2C2×#10622707C211yesmaximal, characteristic, complemented
3C2×#10622696C211yesmaximal, characteristic
4#13067876C218yesmaximal, direct product factor
5C2×#10622185C211yesmaximal, characteristic, complemented
6C2×#10622094C211yesmaximal, characteristic, complemented
7C2×#10622097C211yesmaximal, characteristic
8C2×C11×#498C211yesmaximal, characteristic, complemented
9C22×Q8×D11—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#66999—21no—
13C22×#4325—21no—
14#10623258—22no—
15#10623258—22no—
16#10623258—22no—
17#10623258C2214yes—
18C2×#66949—22no—
19C2×#66946—21no—
20C2×#66941—21no—
21C2×C4×D44C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#498—22no—
24C11×#498C2214yescomplemented
25C2×C11×#106—22no—
26C2×C4×C8×C11C2211yescharacteristic
27C2×#66899—21no—
28#10622707—22no—
29#10622707C2214yescomplemented
30#10622696—22no—
31#10622696C2214yes—
32C2×#66874—21no—
33C2×#66872—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622185C2214yescomplemented
37#10622097C2214yes—
38#10622094C2214yescomplemented
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
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×Dic22D411yescharacteristic
50C22×C8×C11—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8D412yes—
57C11×C4⋊Q8C2312yes—
58C11×C4⋊Q8C2312yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D412yes—
63C2×C42×C11C2311yescharacteristic
64#66999—24no—
65#66999—24no—
66C2×#4325—24no—
67C2×#4325—44no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—21no—
70C2×C4⋊Dic11D411yescharacteristic
71C2×C4⋊Dic11D411yescharacteristic
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—21no—
74C2×C4×Dic11—21no—
75C22×C11⋊C8—21no—
76C22×C11⋊C8—21no—
77#66949—28no—
78#66949—28no—
79#66946—24no—
80#66946—24no—
81#66941—24no—
82#66941—24no—
83C4×D44—21no—
84C4×D44—21no—
85C4×D44D412yes—
86C4×D44C2312yes—
87C4×Dic22—21no—
88C4×Dic22—21no—
89C4×Dic22D412yes—
90C4×Dic22C2312yes—
91C11×#106—28no—
92C4×C8×C11—21no—
93C4×C8×C11C2312yes—
94#66899—24no—
95#66874—24no—
96#66872—24no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2312yes—
101C2×#1651—111nomaximal, Sylow
102C23×D11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—41no—
107C2×Q8×C11—42no—
108C2×Q8×C11—42no—
109C2×Q8×C11—42no—
110C2×Q8×C11—42no—
111C22×C4×C11—22no—
112C22×C4×C11—41no—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×Dic11—21no—
117C22×Dic11—21no—
118C22×Dic11—21no—
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—21no—
134C2×Dic22—22no—
135C2×Dic22—48no—
136C2×Dic22SD1614yescomplemented
137C2×Dic22C2×D412yes—
138C2×C8×C11—24no—
139C2×C8×C11—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4C2×D414yes—
148C42×C11C2×D411yescharacteristic
149C42×C11C2×D411yescharacteristic
150C42×C11C2×D411yescharacteristic
151C42×C11C2411yescharacteristic
152#4325—48no—
153(C2×D11)⋊C4—28no—
154(C2×D11)⋊C4—22no—
155(C2×D11)⋊C4—22no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11C2×D412yes—
159C4⋊Dic11C2×D412yes—
160Dic11⋊C4—28no—
161Dic11⋊C4—22no—
162Dic11⋊C4—22no—
163C4×Dic11—22no—
164C4×Dic11—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—42no—
168C2×C11⋊C8—42no—
169C2×D4×Q8—111no—
170C2×#498D1111yescharacteristic, complemented
171C2×#475—111no—
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—42no—
183Q8×C11—42no—
184Q8×C11—44no—
185Q8×C11—42no—
186Q8×C11—42no—
187Q8×C11—82no—
188C2×C4×C11—22no—
189C2×C4×C11—24no—
190C2×C4×C11—44no—
191C2×C4×C11—42no—
192C2×C4×C11—82no—
193C2×C4×C11#12011yescharacteristic
194C2×C4×C11#12011yescharacteristic
195C2×C4×C11#12011yescharacteristic
196C2×C4×C11C2×SD1612yes—
197C2×C4×C11C2×SD1612yes—
198C2×C4×C11AGL(1,ℤ/8)12yes—
199C2×C4×C11#13712yes—
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×Dic11—22no—
204C2×Dic11—24no—
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209D44—22no—
210D44—24no—
211D44C2×SD1614yes—
212C4×D11—416no—
213C4×D11—42no—
214C4×D11—42no—
215C4×D11—44no—
216Dic22—22no—
217Dic22—24no—
218Dic22—416no—
219Dic22C2×SD1614yescomplemented
220C8×C11—24no—
221C11⋊C8—42no—
222C11⋊C8—42no—
223C23×Q8—221no—
224C22×SD16—221no—
225D4×Q8—114no—
226D4×Q8—222no—
227D4×Q8—222no—
228D4×Q8—222no—
229C2×C4⋊Q8—221no—
230C2×C4⋊Q8C2×D1111yescharacteristic
231C2×C4⋊Q8C2×D1111yescharacteristic
232C2×C22⋊Q8—221no—
233C2×C22⋊Q8—222no—
234C2×C4×Q8—111no—
235C2×C4×D4—111no—
236C2×C4×D4—221no—
237#498—22no—
238#498C2×D1114yescomplemented
239#475—114no—
240#475—222no—
241#461—114no—
242#461—222no—
243C2×#106—22no—
244C2×#106—221no—
245C2×C4⋊C8—111no—
246C2×C4⋊C8—111no—
247C2×#103—221no—
248C2×#103—221no—
249C2×C4×C8C2×D1111yescharacteristic
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—21no—
262C4×C11—21no—
263C4×C11—44no—
264C4×C11—82no—
265C4×C11#44812yes—
266C4×C11#45012yes—
267C4×C11C22×SD1611yescharacteristic
268C4×C11C22×SD1611yescharacteristic
269C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
270C4×C11C2×#13711yescharacteristic
271Dic11—24no—
272Dic11—42no—
273Dic11—42no—
274C22×Q8—21no—
275C22×Q8—21no—
276C22×Q8—111no—
277C22×Q8—222no—
278C22×Q8—224no—
279C22×Q8—224no—
280C22×Q8—444no—
281C22×Q8—444no—
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—21no—
294C4⋊Q8—21no—
295C4⋊Q8—224no—
296C4⋊Q8—224no—
297C4⋊Q8C22⋊D1112yes—
298C4⋊Q8C22×D1112yes—
299C4⋊Q8C22×D1112yes—
300C22⋊Q8—228no—
301C22⋊Q8—224no—
302C22⋊Q8—224no—
303C22⋊Q8—228no—
304C4×Q8—112no—
305C4×Q8—112no—
306C4×Q8—221no—
307C4×Q8—221no—
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—111no—
319C2×C4⋊C4—222no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4C22⋊D1112yes—
322C2×C22⋊C4—222no—
323C2×C22⋊C4—221no—
324C2×C42—221no—
325C2×C42C22×D1111yescharacteristic
326#106—28no—
327#106—224no—
328C4⋊C8—112no—
329C4⋊C8—112no—
330C4⋊C8—221no—
331C4⋊C8—221no—
332#103—224no—
333#103—224no—
334C4×C8—21no—
335C4×C8C22×D1112yes—
336C2×C11#165114yescomplemented
337C2×C11C2×#45011yescharacteristic
338C2×C11C2×#44811yescharacteristic
339C2×C11C2×#45611yescharacteristic
340D11—44no—
341C24—221no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—42no—
346C2×Q8—42no—
347C2×Q8—41no—
348C2×Q8—42no—
349C2×Q8—42no—
350C2×Q8—114no—
351C2×Q8—112no—
352C2×Q8—228no—
353C2×Q8—222no—
354C2×Q8—221no—
355C2×Q8—448no—
356C2×Q8—448no—
357C2×Q8—448no—
358C2×Q8—4416no—
359C2×D4—114no—
360C2×D4—112no—
361C2×D4—222no—
362C2×D4—221no—
363C22×C4—22no—
364C22×C4—41no—
365C22×C4—228no—
366C22×C4—221no—
367C22×C4—221no—
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—24no—
379C2×C8—22no—
380C2×C8—222no—
381C2×C8—222no—
382C2×C8—442no—
383C2×C8—442no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—112no—
392C4⋊C4—112no—
393C4⋊C4—228no—
394C4⋊C4—221no—
395C4⋊C4—221no—
396C4⋊C4—222no—
397C4⋊C4—222no—
398C4⋊C4C2×C22⋊D1114yes—
399C22⋊C4—228no—
400C22⋊C4—222no—
401C22⋊C4—222no—
402C42—222no—
403C42—222no—
404C42D4×D1111yescharacteristic
405C42D4×D1111yescharacteristic
406C42C2×C22⋊D1111yescharacteristic
407C42C23×D1111yescharacteristic
408C11C2×#165111yescharacteristic, complemented, Sylow
409C23—224no—
410C23—222no—
411C23—442no—
412C23—442no—
413C23#6699011yescharacteristic
414Q8—42no—
415Q8—42no—
416Q8—44no—
417Q8—42no—
418Q8—42no—
419Q8—82no—
420Q8—114no—
421Q8—222no—
422Q8—224no—
423Q8—4416no—
424D4—114no—
425D4—222no—
426D4—224no—
427C2×C4—22no—
428C2×C4—24no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—82no—
432C2×C4—224no—
433C2×C4—222no—
434C2×C4—222no—
435C2×C4—222no—
436C2×C4—4416no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—442no—
441C2×C4—444no—
442C2×C4SD16×D1112yes—
443C2×C4SD16×D1112yes—
444C2×C4#6696712yes—
445C2×C4#6696812yes—
446C2×C4#6699011yescharacteristic
447C2×C4#6699011yescharacteristic
448C2×C4#6699011yescharacteristic
449C2×C4C2×D4×D1111yescharacteristic
450C2×C4C2×D4×D1111yescharacteristic
451C2×C4C22×C22⋊D1111yescharacteristic
452C8—24no—
453C8—442no—
454C8—442no—
455C22—224no—
456C22—442no—
457C22—448no—
458C22—442no—
459C22#1062270812yes—
460C22#1062278212yes—
461C22#1062278312yes—
462C22C2×#6699011yescharacteristic
463C4—21no—
464C4—21no—
465C4—44no—
466C4—82no—
467C4—224no—
468C4—442no—
469C4—442no—
470C4#1062278212yes—
471C4#1062278312yes—
472C4C2×SD16×D1111yescharacteristic
473C4C2×SD16×D1111yescharacteristic
474C4C2×#6696711yescharacteristic
475C4C2×#6696811yescharacteristic
476C2—444no—
477C2#1306787614yesdirect product factor
478C2C2×#1062278211yescharacteristic
479C2C2×#1062278311yescharacteristic
480C2C2×#1062270811yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#498C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenterC2×#498D11
hypocenterC11C2×#1651
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
2. C2×#10622707C2semidirect
4. #13067876C2direct (N × H)
5. C2×#10622185C2semidirect
6. C2×#10622094C2semidirect
8. C2×C11×#498C2semidirect
24. C11×#498C22semidirect
29. #10622707C22semidirect
36. #10622185C22semidirect
38. #10622094C22semidirect
136. C2×Dic22SD16semidirect
170. C2×#498D11semidirect
219. Dic22C2×SD16semidirect
238. #498C2×D11semidirect
336. C2×C11#1651semidirect
408. C11C2×#1651semidirect
477. C2#13067876direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232582
C2×#106227072
C2×#106226962
#130678762
C2×#106221852
C2×#106220942
C2×#106220972
C2×C11×#4982
C2×#165111