Finite Group Databasebeta

← C4×#10622802 #14760422

Subgroups — C4×#10622802 #14760422

Order 2816.

1002 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622802C211yesmaximal, characteristic
2C2×C4×#4313C211yesmaximal, characteristic
3C4×#66999C212yesmaximal
4#13069488C211yesmaximal, characteristic, complemented
5#13069357C211yesmaximal, characteristic, complemented
6#13069303C212yesmaximal, complemented
7#13069046C212yesmaximal
8#13068650C211yesmaximal, characteristic
9C4×#66881C211yesmaximal, characteristic, complemented
10C4×#66899C212yesmaximal, complemented
11C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C2×#66999C2212yes—
15C22×#4313C2211yescharacteristic
16C22×#4313C2211yescharacteristic
17C2×C42×D11C2211yescharacteristic
18C4×C11×Q16—24no—
19C2×C11×#107C2211yescharacteristic
20C2×C11×#103C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22#10622843C2212yes—
23C2×#66899C2212yes—
24C2×#66899C2212yes—
25#10622802C418yesdirect product factor
26C2×#66881C2211yescharacteristic
27C2×#66881C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×#66879C2211yescharacteristic
30#10622602—22no—
31#10622600C2212yes—
32#10622591—22no—
33#10622586C2212yes—
34C4×(C2×D11)⋊C4—22no—
35C4×C4⋊Dic11C2212yes—
36C4×Dic11⋊C4—22no—
37C2×C4×C11⋊C8C2211yescharacteristic
38C4×#4313—24no—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×Q8×C11C2312yes—
43C22×C4×D11D411yescharacteristic
44C22×C4×D11D411yescharacteristic
45C22×C4×D11C2311yescharacteristic
46C2×C11×Q16—22no—
47C2×C11×Q16—22no—
48C2×C11×Q16C2×C414yescomplemented
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C4×Q8×C11—24no—
52C4×Q8×C11—24no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4C2312yes—
55C2×C42×C11—22no—
56C2×C42×C11C2311yescharacteristic
57#66999—24no—
58#66999C2×C418yes—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×C4⋊Dic11C2312yes—
62C2×C4⋊Dic11C2312yes—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11D411yescharacteristic
67C2×C4×Dic11D411yescharacteristic
68C2×C4×Dic11C2311yescharacteristic
69C22×C11⋊C8C2311yescharacteristic
70C22×C11⋊C8C2311yescharacteristic
71C2×#4313—22no—
72C2×#4313—22no—
73C2×#4313—22no—
74C2×#4313—22no—
75C2×#4313—22no—
76C2×#4313C2×C414yes—
77C42×D11—22no—
78C42×D11—22no—
79C11×#107—22no—
80C11×#103—24no—
81C4×C8×C11D414yes—
82#66899—24no—
83#66899C2×C418yescomplemented
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89#66881—22no—
90#66881C2×C414yescomplemented
91#66879—22no—
92#66879—22no—
93C4×C11⋊C8—22no—
94C4×#470—111nomaximal, Sylow
95C23×D11C2×D411yescharacteristic
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11C22×C414yes—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11C2×D411yescharacteristic
110C22×Dic11C2×D411yescharacteristic
111C22×Dic11C2×D411yescharacteristic
112C2×C4×D11—22no—
113C2×C4×D11—22no—
114C2×C4×D11—24no—
115C2×C4×D11—21no—
116C2×C4×D11—21no—
117C2×C4×D11—21no—
118C2×C4×D11—21no—
119C2×C4×D11—42no—
120C2×C4×D11C22×C412yes—
121C2×C4×D11#4112yes—
122C11×Q16—28no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11C22×C412yes—
126C2×C8×C11C2×D412yes—
127C2×C8×C11C2×D412yes—
128C2×C8×C11#4112yes—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—44no—
132C42×C11—44no—
133C42×C11C2×D412yes—
134C42×C11#4112yes—
135(C2×D11)⋊C4—28no—
136(C2×D11)⋊C4—44no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139C4⋊Dic11—22no—
140C4⋊Dic11C22×C414yes—
141Dic11⋊C4—28no—
142Dic11⋊C4—44no—
143C4×Dic11—22no—
144C4×Dic11—22no—
145C4×Dic11—21no—
146C4×Dic11—21no—
147C4×Dic11—44no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8C22×C412yes—
153C2×C11⋊C8#4112yes—
154#4313—28no—
155#4313—28no—
156C2×#470—111no—
157C2×C4×Q16D1111yescharacteristic, complemented
158C2×C4×M16—111no—
159C4×C22⋊Q8—112no—
160#1971—111no—
161#1944—111no—
162#1935—112no—
163#1894—112no—
164#1809—111no—
165C4×#106—111no—
166C4×#103—112no—
167C23×C11C22×D411yescharacteristic
168C22×D11—21no—
169C22×D11—21no—
170C22×D11—22no—
171C22×D11—22no—
172C22×D11C4×D412yes—
173Q8×C11—24no—
174Q8×C11—24no—
175Q8×C11—42no—
176Q8×C11—42no—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11#12112yes—
185C2×C4×C11#12112yes—
186C2×C4×C11#13714yes—
187C2×C4×C11C23×C411yescharacteristic
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C2×#4111yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—24no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11C4×D412yes—
206C4×D11—22no—
207C4×D11—22no—
208C4×D11—22no—
209C4×D11—22no—
210C4×D11—44no—
211C4×D11—44no—
212C8×C11—22no—
213C8×C11C4×D414yes—
214C11⋊C8—22no—
215C11⋊C8—22no—
216C22×Q16C2×D1111yescharacteristic
217C22×M16—111no—
218C22×M16—111no—
219C2×C22⋊Q8—112no—
220C2×C4×Q8C2×D1112yes—
221C22×C42—111no—
222#470—118no—
223C4×Q16—24no—
224C2×#107C2×D1111yescharacteristic
225C2×#106—111no—
226C2×#106—111no—
227C2×#103—112no—
228C2×#103—112no—
229C2×#103C2×D1112yes—
230C4×M16—224no—
231C2×#97—111no—
232C2×#97—111no—
233C2×C4×C8—111no—
234C2×C4×C8C2×D1111yescharacteristic
235#391—112no—
236#389—112no—
237#387—222no—
238#385—222no—
239#380—112no—
240C4×C4⋊C4—112no—
241C4×C4⋊C4—222no—
242C4×C22⋊C4—222no—
243#340—112no—
244#340—112no—
245#340—112no—
246C22×C11C2×C4×D411yescharacteristic
247C22×C11C2×#12111yescharacteristic
248C22×C11#53211yescharacteristic
249C22×C11C2×#13712yes—
250C22×C11#57512yes—
251C2×D11—24no—
252C2×D11—22no—
253C2×D11—42no—
254C2×D11—41no—
255C2×D11—41no—
256C4×C11—22no—
257C4×C11—44no—
258C4×C11—82no—
259C4×C11#47014yescomplemented
260C4×C11C2×C4×D411yescharacteristic
261C4×C11C4×#4111yescharacteristic
262C4×C11#52511yescharacteristic
263C4×C11#52911yescharacteristic
264Dic11—22no—
265Dic11—44no—
266Dic11—41no—
267Dic11—41no—
268Dic11—82no—
269C22×Q8C22×D1112yes—
270C23×C4—111no—
271C23×C4—111no—
272C23×C4—111no—
273C2×Q16—22no—
274C2×Q16—22no—
275C2×Q16C4×D1114yescomplemented
276C2×M16—114no—
277C2×M16—222no—
278C2×M16—222no—
279C2×M16—222no—
280C2×M16—222no—
281C2×M16—222no—
282C22×C8—111no—
283C22×C8—111no—
284C22×C8C22×D1111yescharacteristic
285C22×C8C22×D1111yescharacteristic
286C22⋊Q8—118no—
287C22⋊Q8—224no—
288C4×Q8—24no—
289C4×Q8—24no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—112no—
292C2×C4⋊C4—112no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4C22×D1112yes—
296C2×C22⋊C4—222no—
297C2×C22⋊C4—222no—
298C2×C42—22no—
299C2×C42—111no—
300C2×C42—111no—
301C2×C42—111no—
302C2×C42—222no—
303C2×C42—222no—
304C2×C42—222no—
305C2×C42C22×D1111yescharacteristic
306#107—22no—
307#106—114no—
308#106—222no—
309#103—24no—
310#103—118no—
311#103—224no—
312#97—222no—
313#97—222no—
314C4×C8—222no—
315C4×C8C22⋊D1114yes—
316#95—222no—
317#95—222no—
318#95—222no—
319#95—222no—
320#95—222no—
321C2×C11C4×#12111yescharacteristic
322C2×C11C4×#13712yes—
323C2×C11C2×#47011yescharacteristic
324C2×C11#305411yescharacteristic
325C2×C11#317212yes—
326D11—42no—
327C24—111no—
328C2×Q8—22no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8C2×C4×D1114yes—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—111no—
337C22×C4—112no—
338C22×C4—112no—
339C22×C4—111no—
340C22×C4—111no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4—222no—
346C22×C4—224no—
347C22×C4—222no—
348C22×C4—222no—
349C22×C4—222no—
350C22×C4—442no—
351C22×C4D4×D1111yescharacteristic
352C22×C4D4×D1111yescharacteristic
353C22×C4C23×D1111yescharacteristic
354Q16—28no—
355M16—228no—
356M16—228no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—112no—
360C2×C8—112no—
361C2×C8—221no—
362C2×C8—221no—
363C2×C8—221no—
364C2×C8—221no—
365C2×C8C2×C4×D1112yes—
366C2×C8#433912yes—
367C2×C8C2×C22⋊D1112yes—
368C2×C8C2×C22⋊D1112yes—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—44no—
372C4⋊C4—114no—
373C4⋊C4—228no—
374C4⋊C4—222no—
375C4⋊C4—222no—
376C4⋊C4—222no—
377C4⋊C4—444no—
378C22⋊C4—228no—
379C22⋊C4—444no—
380C42—44no—
381C42—222no—
382C42—222no—
383C42—221no—
384C42—221no—
385C42—444no—
386C42#434112yes—
387C42C2×C22⋊D1112yes—
388C11C4×#47011yescharacteristic, complemented, Sylow
389C23—112no—
390C23—222no—
391C23—222no—
392C23—221no—
393C23—221no—
394C23C2×D4×D1111yescharacteristic
395Q8—24no—
396Q8—24no—
397Q8—42no—
398Q8—42no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—112no—
407C2×C4—221no—
408C2×C4—221no—
409C2×C4—222no—
410C2×C4—222no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—224no—
416C2×C4—221no—
417C2×C4—221no—
418C2×C4—444no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—444no—
422C2×C4—442no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4#6697114yes—
426C2×C4#6699112yes—
427C2×C4#6699112yes—
428C2×C4C22×C4×D1111yescharacteristic
429C2×C4C2×#433911yescharacteristic
430C2×C4C2×#434111yescharacteristic
431C2×C4#41×D1111yescharacteristic
432C2×C4#41×D1111yescharacteristic
433C2×C4C22×C22⋊D1111yescharacteristic
434C8—22no—
435C8—222no—
436C8—222no—
437C8C4×C22⋊D1114yes—
438C22—222no—
439C22—224no—
440C22—442no—
441C22—441no—
442C22—441no—
443C22C4×D4×D1111yescharacteristic
444C22#1062307911yescharacteristic
445C22C2×#6697112yes—
446C22#1062329912yes—
447C22C2×#6699111yescharacteristic
448C4—22no—
449C4—44no—
450C4—82no—
451C4—222no—
452C4—444no—
453C4—441no—
454C4—441no—
455C4—882no—
456C4#1062280214yesdirect product factor
457C4C4×#434111yescharacteristic
458C4#1062308811yescharacteristic
459C4C2×C4×C22⋊D1111yescharacteristic
460C4#1062335911yescharacteristic
461C2—442no—
462C2C4×#6699111yescharacteristic
463C2C4×#6697112yes—
464C2C2×#1062280211yescharacteristic
465C2#1307822111yescharacteristic
466C2#1307922012yes—
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×Q16C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×C4×Q16D11
hypocenterC11C4×#470
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
4. #13069488C2semidirect
5. #13069357C2semidirect
6. #13069303C2semidirect
9. C4×#66881C2semidirect
10. C4×#66899C2semidirect
11. C2×C4×C11×Q16C2semidirect
25. #10622802C4direct (N × H)
48. C2×C11×Q16C2×C4semidirect
83. #66899C2×C4semidirect
90. #66881C2×C4semidirect
157. C2×C4×Q16D11semidirect
259. C4×C11#470semidirect
275. C2×Q16C4×D11semidirect
388. C11C4×#470semidirect
456. C4#10622802direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106228022
C2×C4×#43132
C4×#669992
#130694882
#130693572
#130693032
#130690462
#130686502
C4×#668812
C4×#668992
C2×C4×C11×Q162
C4×#47011