Finite Group Databasebeta

← C4×#10622805 #14760658

Subgroups — C4×#10622805 #14760658

Order 2816.

882 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622805C211yesmaximal, characteristic
2C4×#66995C212yesmaximal
3C4×#66954C211yesmaximal, characteristic
4#13069532C211yesmaximal, characteristic, complemented
5#13069399C211yesmaximal, characteristic, complemented
6#13069268C212yesmaximal, complemented
7#13069134C212yesmaximal
8#13068681C211yesmaximal, characteristic
9C4×#66883C211yesmaximal, characteristic, complemented
10C4×#66900C212yesmaximal, complemented
11C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C2×#66995C2212yes—
15C2×#66954C2211yescharacteristic
16C2×#66954C2211yescharacteristic
17C4×#4339C2211yescharacteristic
18C4×C11×Q16—21no—
19C4×C11×Q16—21no—
20C4×C11×Q16—21no—
21C4×C11×Q16—21no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#103C2212yes—
24C2×C4×C8×C11C2211yescharacteristic
25C2×#66900C2212yes—
26C2×#66900C2212yes—
27#10622838C2212yes—
28#10622805C418yesdirect product factor
29C2×#66883C2211yescharacteristic
30C2×#66883C2211yescharacteristic
31#10622714C2211yescharacteristic
32#10622714C2211yescharacteristic
33#10622643—22no—
34C4×#4326—22no—
35#10622639—22no—
36C4×#4325—22no—
37#10622579C2212yes—
38#10622577C2212yes—
39C4×#4318C2211yescharacteristic
40C4×#4318C2212yes—
41#10622302—21no—
42#10622302—21no—
43C4×#4313—21no—
44C4×C8×D11—21no—
45#10622190C2212yes—
46#10622168C2212yes—
47#10622168C2212yes—
48C22×Q8×C11C2312yes—
49C2×#4339C2311yescharacteristic
50C2×C11×Q16—21no—
51C2×C11×Q16—21no—
52C2×C11×Q16—22no—
53C2×C11×Q16C2×C414yescomplemented
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4C2312yes—
62C2×C42×C11—22no—
63C2×C42×C11C2311yescharacteristic
64C2×#4326—22no—
65#66995—24no—
66#66995C2×C418yes—
67C2×#4325—22no—
68C4×C22⋊D11—21no—
69C4×C22⋊D11—21no—
70#66979C2311yescharacteristic
71C2×#4318C2312yes—
72C2×#4318C2312yes—
73C2×#4318C2311yescharacteristic
74C2×#4318C2311yescharacteristic
75#66954—22no—
76#66954—22no—
77#66954—22no—
78#66954C2×C414yes—
79C2×#4313—21no—
80C2×#4313—21no—
81C2×C8×D11—21no—
82C2×C8×D11—21no—
83C4×D44D411yescharacteristic
84C4×D44D411yescharacteristic
85#66925—21no—
86C42×D11—21no—
87C4×Dic22D411yescharacteristic
88C4×Dic22D411yescharacteristic
89C11×#107—21no—
90C11×#107—21no—
91C11×#103—22no—
92C11×#103—22no—
93C4×C8×C11D411yescharacteristic
94C4×C8×C11D411yescharacteristic
95C4×C8×C11D411yescharacteristic
96C4×C8×C11D411yescharacteristic
97#66900—24no—
98#66900C2×C418yescomplemented
99#66899—22no—
100#66899—22no—
101#66883—22no—
102#66883C2×C414yescomplemented
103#66879—21no—
104#66879—21no—
105C8×Dic11—21no—
106C8×Dic11—21no—
107#66874—22no—
108#66873—22no—
109#66872—22no—
110#66871—22no—
111#66867—21no—
112#66867—22no—
113C4×C11⋊C8—21no—
114C4×C11⋊C8—22no—
115C4×#473—111nomaximal, Sylow
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11C22×C414yes—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11#4111yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C2×C22⋊D11—21no—
128#4339—21no—
129#4339—21no—
130#4339C22×C412yes—
131#4339#4112yes—
132C2×D44C2×D411yescharacteristic
133C2×C4×D11—21no—
134C2×C4×D11—21no—
135C2×C4×D11—21no—
136C2×Dic22C2×D411yescharacteristic
137C11×Q16—24no—
138C11×Q16—24no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11C22×C412yes—
142C2×C8×C11C2×D411yescharacteristic
143C2×C8×C11C2×D411yescharacteristic
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11#4112yes—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—42no—
150C11×C4⋊C4—42no—
151C42×C11—42no—
152C42×C11—42no—
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C22⋊Dic11—21no—
158#4326—28no—
159#4325—28no—
160(C2×D11)⋊C4—21no—
161(C2×D11)⋊C4—21no—
162C4⋊Dic11C2×D411yescharacteristic
163C4⋊Dic11C2×D411yescharacteristic
164Dic11⋊C4—21no—
165Dic11⋊C4—21no—
166C4×Dic11—21no—
167C4×Dic11—21no—
168C4×Dic11—21no—
169#4318—21no—
170#4318—21no—
171#4318—22no—
172#4318—22no—
173#4318—22no—
174#4318C22×C414yes—
175#4318C22×C412yes—
176#4318#4112yes—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—22no—
181#4313—24no—
182#4313—24no—
183C8×D11—24no—
184C8×D11—24no—
185C2×#473—111no—
186C4×#137—112no—
187C2×C4×Q16D1111yescharacteristic, complemented
188C4×#131—111no—
189#1979—111no—
190#1952—111no—
191#1930—112no—
192#1908—112no—
193#1816—111no—
194C4×#108—111no—
195C4×#101—112no—
196C23×C11C2×#4111yescharacteristic
197C22×D11—21no—
198Q8×C11—24no—
199Q8×C11—24no—
200Q8×C11—42no—
201Q8×C11—42no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—82no—
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#12111yescharacteristic
211C2×C4×C11#12111yescharacteristic
212C2×C4×C11#12111yescharacteristic
213C2×C4×C11C23×C411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C22⋊D11—22no—
220C22⋊D11—22no—
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—21no—
224D44—21no—
225D44C4×D412yes—
226C4×D11—22no—
227C4×D11—22no—
228C4×D11—42no—
229C4×D11—42no—
230Dic22—21no—
231Dic22C4×D412yes—
232C8×C11—21no—
233C8×C11—21no—
234C8×C11C4×D412yes—
235C8×C11C4×D412yes—
236C11⋊C8—22no—
237C11⋊C8—24no—
238C11⋊C8—22no—
239C11⋊C8—42no—
240C2×#137—112no—
241C22×Q16C2×D1111yescharacteristic
242C2×#131—111no—
243C2×#131—111no—
244C4×#41—111no—
245C2×C4×Q8C2×D1112yes—
246#473—118no—
247#441—222no—
248#440—222no—
249C4×Q16—21no—
250C4×Q16—21no—
251C4×Q16—21no—
252C4×Q16—21no—
253C4×Q16—222no—
254C4×SD16—222no—
255C2×#108—111no—
256C2×#108—111no—
257#428—112no—
258C2×#107C2×D1111yescharacteristic
259#419—112no—
260#417—112no—
261C2×#103C2×D1112yes—
262C2×#101—112no—
263C2×#101—112no—
264#405—111no—
265#405—111no—
266#405—221no—
267#405—221no—
268C4×M16—111no—
269C4×M16—112no—
270C4×M16—221no—
271C2×C4×C8—221no—
272C2×C4×C8C2×D1111yescharacteristic
273#343—112no—
274#343—112no—
275#341—112no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11C4×#4111yescharacteristic
279C22×C11C2×#12111yescharacteristic
280C22×C11#52911yescharacteristic
281C2×D11—22no—
282C2×D11—41no—
283C2×D11—41no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—44no—
288C4×C11—82no—
289C4×C11#47312yescomplemented
290C4×C11C2×C4×D411yescharacteristic
291C4×C11C2×C4×D411yescharacteristic
292C4×C11#52511yescharacteristic
293C4×C11#53211yescharacteristic
294Dic11—22no—
295Dic11—41no—
296Dic11—41no—
297C2×#41—111no—
298C22×Q8C22×D1112yes—
299#137—118no—
300#137—224no—
301C2×Q16—22no—
302C2×Q16—21no—
303C2×Q16—21no—
304C2×Q16—222no—
305C2×Q16C4×D1114yescomplemented
306C2×SD16—222no—
307#131—114no—
308#131—222no—
309#131—222no—
310#131—222no—
311C2×M16—111no—
312C2×M16—111no—
313C2×M16—112no—
314C2×M16—112no—
315C2×M16—221no—
316C2×M16—221no—
317C22×C8—221no—
318C22×C8—221no—
319C22×C8C22×D1111yescharacteristic
320C22×C8C22×D1111yescharacteristic
321C4×Q8—22no—
322C4×Q8—22no—
323C4×Q8—22no—
324C4×Q8—22no—
325C4×Q8—111no—
326C4×Q8—111no—
327C4×D4—111no—
328C4×D4—111no—
329C4×D4—221no—
330C4×D4—221no—
331#117—111no—
332#117—221no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4C22×D1112yes—
335C2×C42—22no—
336C2×C42—221no—
337C2×C42C22×D1111yescharacteristic
338#108—114no—
339#108—222no—
340#107—21no—
341#107—21no—
342#107—222no—
343#106—222no—
344#103—22no—
345#103—22no—
346#103—222no—
347#103—222no—
348#103—222no—
349#102—222no—
350#101—118no—
351#101—224no—
352#97—221no—
353#97—221no—
354#97—222no—
355#97—221no—
356C4×C8—221no—
357C4×C8—221no—
358C4×C8—222no—
359C4×C8—221no—
360C4×C8C22⋊D1111yescharacteristic
361C4×C8C22⋊D1111yescharacteristic
362C4×C8C22⋊D1111yescharacteristic
363C4×C8C22⋊D1111yescharacteristic
364C2×C11—21no—
365C2×C11—21no—
366C2×C11C4×#12111yescharacteristic
367C2×C11C2×#47311yescharacteristic
368C2×C11#306711yescharacteristic
369D11—42no—
370#41—112no—
371#41—112no—
372#41—221no—
373#41—221no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—111no—
380C2×Q8C2×C4×D1114yes—
381C2×D4—111no—
382C2×D4—221no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4#434111yescharacteristic
389C22×C4#434111yescharacteristic
390C22×C4C23×D1111yescharacteristic
391Q16—24no—
392Q16—24no—
393Q16—228no—
394SD16—228no—
395M16—112no—
396M16—114no—
397M16—112no—
398M16—224no—
399M16—221no—
400M16—221no—
401M16—222no—
402M16—224no—
403M16—222no—
404M16—222no—
405C2×C8—21no—
406C2×C8—21no—
407C2×C8—224no—
408C2×C8—222no—
409C2×C8—221no—
410C2×C8—221no—
411C2×C8—224no—
412C2×C8—222no—
413C2×C8C2×C4×D1112yes—
414C2×C8#433912yes—
415C2×C8C2×C22⋊D1111yescharacteristic
416C2×C8C2×C22⋊D1111yescharacteristic
417C2×C8C2×C22⋊D1111yescharacteristic
418C2×C8C2×C22⋊D1111yescharacteristic
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—42no—
422C4⋊C4—42no—
423C4⋊C4—111no—
424C4⋊C4—111no—
425C4⋊C4—221no—
426C4⋊C4—221no—
427C22⋊C4—221no—
428C22⋊C4—221no—
429C22⋊C4—221no—
430C42—42no—
431C42—42no—
432C42—221no—
433C42—221no—
434C42—221no—
435C42D4×D1111yescharacteristic
436C42D4×D1111yescharacteristic
437C42C2×C22⋊D1111yescharacteristic
438C42C2×C22⋊D1111yescharacteristic
439C11C4×#47311yescharacteristic, complemented, Sylow
440C23—221no—
441C23C2×#434111yescharacteristic
442Q8—24no—
443Q8—24no—
444Q8—42no—
445Q8—42no—
446Q8—112no—
447Q8—221no—
448D4—112no—
449D4—222no—
450D4—222no—
451D4—221no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—82no—
459C2×C4—221no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—221no—
463C2×C4—221no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4#6699111yescharacteristic
467C2×C4#6699111yescharacteristic
468C2×C4#6699111yescharacteristic
469C2×C4#6699111yescharacteristic
470C2×C4C22×C4×D1111yescharacteristic
471C2×C4C2×#433911yescharacteristic
472C2×C4C2×D4×D1111yescharacteristic
473C2×C4#41×D1111yescharacteristic
474C2×C4#41×D1111yescharacteristic
475C2×C4C22×C22⋊D1111yescharacteristic
476C8—21no—
477C8—21no—
478C8—222no—
479C8—224no—
480C8—222no—
481C8—442no—
482C8C4×C22⋊D1112yes—
483C8C4×C22⋊D1112yes—
484C22—21no—
485C22—21no—
486C22—222no—
487C22—441no—
488C22—441no—
489C22C4×#434111yescharacteristic
490C22#1062308811yescharacteristic
491C22C2×#6699111yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—44no—
496C4—82no—
497C4—222no—
498C4—441no—
499C4—441no—
500C4#1062280512yesdirect product factor
501C4C4×D4×D1111yescharacteristic
502C4#1062307911yescharacteristic
503C4C2×C4×C22⋊D1111yescharacteristic
504C4#1062335911yescharacteristic
505C2—21no—
506C2—21no—
507C2—442no—
508C2C4×#6699111yescharacteristic
509C2C2×#1062280511yescharacteristic
510C2#1307833211yescharacteristic
subgroupG/H
centerC2×C4#66991
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×Q16C2
socleC22×C11C2×#121
prime radicalC2×#4339C23
cosocleC22×C4×C11C24
hypercenterC2×C4×Q16D11
hypocenterC11C4×#473
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
4. #13069532C2semidirect
5. #13069399C2semidirect
6. #13069268C2semidirect
9. C4×#66883C2semidirect
10. C4×#66900C2semidirect
11. C2×C4×C11×Q16C2semidirect
28. #10622805C4direct (N × H)
53. C2×C11×Q16C2×C4semidirect
98. #66900C2×C4semidirect
102. #66883C2×C4semidirect
187. C2×C4×Q16D11semidirect
289. C4×C11#473semidirect
305. C2×Q16C4×D11semidirect
439. C11C4×#473semidirect
500. C4#10622805direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106228052
C4×#669952
C4×#669542
#130695322
#130693992
#130692682
#130691342
#130686812
C4×#668832
C4×#669002
C2×C4×C11×Q162
C4×#47311