Finite Group Databasebeta

← C4×#10622509 #14760666

Subgroups — C4×#10622509 #14760666

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×#10622509C211yesmaximal, characteristic
2C4×#66962C212yesmaximal
3C2×C4×Dic44C211yesmaximal, characteristic, complemented
4C4×#66954C211yesmaximal, characteristic
5#13069529C211yesmaximal, characteristic, complemented
6#13069402C211yesmaximal, characteristic, complemented
7#13069272C212yesmaximal, complemented
8#13069130C212yesmaximal
9#13068677C211yesmaximal, characteristic
10C4×#66888C212yesmaximal, complemented
11C4×C11×#108C211yesmaximal, characteristic, complemented
12C2×#66962C2212yes—
13C22×Dic44C2211yescharacteristic
14C2×#66954C2211yescharacteristic
15C2×#66954C2211yescharacteristic
16C4×#4339C2211yescharacteristic
17C2×C4×Dic22C2212yes—
18C2×C11×#108C2211yescharacteristic
19C2×C11×#108C2211yescharacteristic
20C4×C11×M16C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22C2×#66888C2212yes—
23C2×#66888C2212yes—
24#10622746C2212yes—
25#10622734C2212yes—
26#10622733C2212yes—
27C2×#66882C2211yescharacteristic
28C2×#66880C2212yes—
29#10622714C2211yescharacteristic
30#10622714C2211yescharacteristic
31C4×#4318C2211yescharacteristic
32#10622509C418yesdirect product factor
33#10622329—22no—
34#10622323—22no—
35C4×Dic44—22no—
36C4×Dic44—21no—
37C4×Dic44—21no—
38C4×Dic44—21no—
39C4×Dic44—21no—
40C4×#4314—22no—
41#10622302—21no—
42#10622302—21no—
43C4×#4313—21no—
44C4×C8×D11—21no—
45C11×#341C2212yes—
46#10622192C2212yes—
47#10622192C2212yes—
48C2×#4339C2311yescharacteristic
49C22×Dic22C2312yes—
50C2×C11×M16C2312yes—
51C2×C11×M16C2312yes—
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C4×C22⋊D11—21no—
56C4×C22⋊D11—21no—
57#66979C2311yescharacteristic
58C2×C4⋊Dic11C2312yes—
59C2×Dic11⋊C4—22no—
60C2×C4×Dic11—22no—
61C2×#4318C2311yescharacteristic
62C2×#4318C2311yescharacteristic
63#66962—24no—
64#66962C2×C418yes—
65C2×Dic44—22no—
66C2×Dic44—21no—
67C2×Dic44—21no—
68C2×Dic44—22no—
69C2×Dic44C2×C414yescomplemented
70C2×#4314—22no—
71#66954—22no—
72#66954—22no—
73#66954—22no—
74#66954C2×C414yes—
75C2×#4313—21no—
76C2×#4313—21no—
77C2×C8×D11—21no—
78C2×C8×D11—21no—
79C4×D44D411yescharacteristic
80C4×D44D411yescharacteristic
81#66925—21no—
82C42×D11—21no—
83C4×Dic22—22no—
84C4×Dic22—22no—
85C4×Dic22—22no—
86C4×Dic22—22no—
87C4×Dic22D411yescharacteristic
88C4×Dic22D411yescharacteristic
89C11×#108—22no—
90C11×#108C2×C414yescomplemented
91C11×#97—22no—
92C4×C8×C11—22no—
93C4×C8×C11D411yescharacteristic
94C4×C8×C11D411yescharacteristic
95C4×C8×C11D411yescharacteristic
96C4×C8×C11D411yescharacteristic
97#66888—24no—
98#66888C2×C418yescomplemented
99#66885—22no—
100#66882—21no—
101#66882—21no—
102#66882—22no—
103#66881—22no—
104#66880—22no—
105#66880—22no—
106#66880—22no—
107#66880—22no—
108#66880—22no—
109#66879—21no—
110#66879—21no—
111C8×Dic11—21no—
112C8×Dic11—21no—
113#66867—21no—
114C4×C11⋊C8—21no—
115C4×#473—111nomaximal, Sylow
116C22×C4×C11#4111yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C22×C4×C11C2411yescharacteristic
119C2×C22⋊D11—21no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122#4339—21no—
123#4339—21no—
124#4339C22×C412yes—
125#4339#4112yes—
126C2×D44C2×D411yescharacteristic
127C2×C4×D11—21no—
128C2×C4×D11—21no—
129C2×C4×D11—21no—
130C2×Dic22—22no—
131C2×Dic22—22no—
132C2×Dic22—22no—
133C2×Dic22—22no—
134C2×Dic22—22no—
135C2×Dic22C22×C414yes—
136C2×Dic22C2×D411yescharacteristic
137C11×M16—22no—
138C11×M16—22no—
139C11×M16—22no—
140C11×M16C22×C414yes—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11C22×C412yes—
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2×D411yescharacteristic
148C2×C8×C11C2×D411yescharacteristic
149C2×C8×C11C2×D411yescharacteristic
150C2×C8×C11#4112yes—
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C22⋊Dic11—21no—
156(C2×D11)⋊C4—21no—
157(C2×D11)⋊C4—21no—
158C4⋊Dic11—22no—
159C4⋊Dic11—22no—
160C4⋊Dic11C2×D411yescharacteristic
161C4⋊Dic11C2×D411yescharacteristic
162Dic11⋊C4—21no—
163Dic11⋊C4—21no—
164Dic11⋊C4—42no—
165Dic11⋊C4—42no—
166C4×Dic11—21no—
167C4×Dic11—21no—
168C4×Dic11—21no—
169C4×Dic11—42no—
170C4×Dic11—42no—
171#4318—21no—
172#4318—21no—
173#4318C22×C412yes—
174#4318#4112yes—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—21no—
177Dic44—28no—
178Dic44—24no—
179Dic44—24no—
180#4314—28no—
181#4313—24no—
182#4313—24no—
183C8×D11—24no—
184C8×D11—24no—
185C2×#473—111no—
186C4×#137—112no—
187C2×C4×Q16—111no—
188C4×#131—111no—
189#1979—111no—
190#1952—111no—
191#1930—112no—
192#1908—112no—
193#1816—111no—
194C4×#108D1111yescharacteristic, complemented
195C4×#101—112no—
196C23×C11C2×#4111yescharacteristic
197C22×D11—21no—
198C2×C4×C11—22no—
199C2×C4×C11—41no—
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#12111yescharacteristic
202C2×C4×C11#12111yescharacteristic
203C2×C4×C11#12111yescharacteristic
204C2×C4×C11C23×C411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C22⋊D11—22no—
211C22⋊D11—22no—
212C2×Dic11—21no—
213C2×Dic11—24no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—82no—
220D44—21no—
221D44C4×D412yes—
222C4×D11—22no—
223C4×D11—22no—
224C4×D11—42no—
225C4×D11—42no—
226Dic22—21no—
227Dic22—24no—
228Dic22—24no—
229Dic22—42no—
230Dic22—42no—
231Dic22C4×D412yes—
232C8×C11—24no—
233C8×C11—21no—
234C8×C11—21no—
235C8×C11—42no—
236C8×C11C4×D412yes—
237C8×C11C4×D412yes—
238C11⋊C8—22no—
239C11⋊C8—22no—
240C2×#137—112no—
241C22×Q16—111no—
242C2×#131—111no—
243C2×#131—111no—
244C4×#41—111no—
245C2×C4×Q8—112no—
246#473—118no—
247#441—222no—
248#440—222no—
249C4×Q16—222no—
250C4×Q16—221no—
251C4×Q16—221no—
252C4×Q16—221no—
253C4×Q16—221no—
254C4×SD16—222no—
255C2×#108C2×D1111yescharacteristic
256C2×#108C2×D1111yescharacteristic
257#428—112no—
258C2×#107—111no—
259#419—112no—
260#417—112no—
261C2×#103—112no—
262C2×#101—112no—
263C2×#101—112no—
264#405—111no—
265#405—111no—
266#405—221no—
267#405—221no—
268C4×M16—111no—
269C4×M16—221no—
270C4×M16C2×D1112yes—
271C2×C4×C8—221no—
272C2×C4×C8C2×D1111yescharacteristic
273#343—112no—
274#343—112no—
275#341C2×D1112yes—
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#47312yescomplemented
288C4×C11C2×C4×D411yescharacteristic
289C4×C11C2×C4×D411yescharacteristic
290C4×C11#52511yescharacteristic
291C4×C11#53211yescharacteristic
292Dic11—22no—
293Dic11—41no—
294Dic11—41no—
295Dic11—44no—
296Dic11—82no—
297C2×#41—111no—
298C22×Q8—112no—
299#137—118no—
300#137—224no—
301C2×Q16—114no—
302C2×Q16—222no—
303C2×Q16—221no—
304C2×Q16—221no—
305C2×Q16—222no—
306C2×SD16—222no—
307#131—114no—
308#131—222no—
309#131—222no—
310#131—222no—
311C2×M16—111no—
312C2×M16—111no—
313C2×M16—221no—
314C2×M16—221no—
315C2×M16C22×D1112yes—
316C2×M16C22×D1112yes—
317C22×C8—221no—
318C22×C8—221no—
319C22×C8C22×D1111yescharacteristic
320C22×C8C22×D1111yescharacteristic
321C4×Q8—111no—
322C4×Q8—111no—
323C4×Q8—222no—
324C4×Q8—222no—
325C4×Q8—222no—
326C4×Q8—222no—
327C4×D4—111no—
328C4×D4—111no—
329C4×D4—221no—
330C4×D4—221no—
331#117—111no—
332#117—221no—
333C2×C4⋊C4—112no—
334C2×C4⋊C4—222no—
335C2×C42—221no—
336C2×C42—222no—
337C2×C42C22×D1111yescharacteristic
338#108—22no—
339#108C4×D1114yescomplemented
340#107—222no—
341#107—221no—
342#107—221no—
343#106—222no—
344#103—222no—
345#103—222no—
346#103—222no—
347#103—222no—
348#103—222no—
349#102—222no—
350#101—118no—
351#101—224no—
352#97—22no—
353#97—221no—
354#97—221no—
355#97—221no—
356C4×C8—22no—
357C4×C8—221no—
358C4×C8—221no—
359C4×C8—221no—
360C4×C8D4411yescharacteristic
361C4×C8D4411yescharacteristic
362C4×C8D4411yescharacteristic
363C4×C8D4411yescharacteristic
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—114no—
375C2×Q8—111no—
376C2×Q8—222no—
377C2×Q8—222no—
378C2×Q8—222no—
379C2×Q8—222no—
380C2×Q8—222no—
381C2×D4—111no—
382C2×D4—221no—
383C22×C4—221no—
384C22×C4—222no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—222no—
388C22×C4#434311yescharacteristic
389C22×C4#434311yescharacteristic
390C22×C4C23×D1111yescharacteristic
391Q16—228no—
392Q16—224no—
393Q16—224no—
394SD16—228no—
395M16—22no—
396M16—22no—
397M16—22no—
398M16—112no—
399M16—112no—
400M16—224no—
401M16—221no—
402M16—221no—
403M16—224no—
404M16C2×C4×D1114yes—
405C2×C8—22no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8—22no—
409C2×C8—224no—
410C2×C8—221no—
411C2×C8—221no—
412C2×C8—224no—
413C2×C8C2×C4×D1112yes—
414C2×C8C2×D4411yescharacteristic
415C2×C8C2×D4411yescharacteristic
416C2×C8C2×D4411yescharacteristic
417C2×C8C2×D4411yescharacteristic
418C2×C8#433912yes—
419C4⋊C4—111no—
420C4⋊C4—111no—
421C4⋊C4—221no—
422C4⋊C4—221no—
423C4⋊C4—222no—
424C4⋊C4—222no—
425C4⋊C4—442no—
426C4⋊C4—442no—
427C22⋊C4—221no—
428C22⋊C4—221no—
429C22⋊C4—221no—
430C42—221no—
431C42—221no—
432C42—221no—
433C42—442no—
434C42—442no—
435C42C2×D4411yescharacteristic
436C42C2×D4411yescharacteristic
437C42D4×D1111yescharacteristic
438C42D4×D1111yescharacteristic
439C11C4×#47311yescharacteristic, complemented, Sylow
440C23—221no—
441C23C2×#434311yescharacteristic
442Q8—112no—
443Q8—221no—
444Q8—224no—
445Q8—224no—
446Q8—442no—
447Q8—442no—
448D4—112no—
449D4—222no—
450D4—222no—
451D4—221no—
452C2×C4—22no—
453C2×C4—41no—
454C2×C4—221no—
455C2×C4—222no—
456C2×C4—222no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—224no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—882no—
466C2×C4#6694811yescharacteristic
467C2×C4#6694811yescharacteristic
468C2×C4#6694811yescharacteristic
469C2×C4#6694811yescharacteristic
470C2×C4C22×C4×D1111yescharacteristic
471C2×C4C22×D4411yescharacteristic
472C2×C4C2×#433911yescharacteristic
473C2×C4C2×D4×D1111yescharacteristic
474C2×C4#41×D1111yescharacteristic
475C2×C4#41×D1111yescharacteristic
476C8—21no—
477C8—21no—
478C8—24no—
479C8—42no—
480C8—222no—
481C8—222no—
482C8C4×D4412yes—
483C8C4×D4412yes—
484C22—21no—
485C22—21no—
486C22—222no—
487C22—441no—
488C22—441no—
489C22C2×#6694811yescharacteristic
490C22C4×#434311yescharacteristic
491C22#1062311111yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—222no—
496C4—444no—
497C4—441no—
498C4—441no—
499C4—882no—
500C4#1062250912yesdirect product factor
501C4C2×C4×D4411yescharacteristic
502C4#1062305511yescharacteristic
503C4C4×D4×D1111yescharacteristic
504C4#1062307911yescharacteristic
505C2—21no—
506C2—21no—
507C2—442no—
508C2C4×#6694811yescharacteristic
509C2C2×#1062250911yescharacteristic
510C2#1307833711yescharacteristic
subgroupG/H
centerC2×C4#66948
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#108C2
socleC22×C11C2×#121
prime radicalC2×#4339C23
cosocleC22×C4×C11C24
hypercenterC4×#108D11
hypocenterC11C4×#473
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#108

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic44C2semidirect
5. #13069529C2semidirect
6. #13069402C2semidirect
7. #13069272C2semidirect
10. C4×#66888C2semidirect
11. C4×C11×#108C2semidirect
32. #10622509C4direct (N × H)
69. C2×Dic44C2×C4semidirect
90. C11×#108C2×C4semidirect
98. #66888C2×C4semidirect
194. C4×#108D11semidirect
287. C4×C11#473semidirect
339. #108C4×D11semidirect
439. C11C4×#473semidirect
500. C4#10622509direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106225092
C4×#669622
C2×C4×Dic442
C4×#669542
#130695292
#130694022
#130692722
#130691302
#130686772
C4×#668882
C4×C11×#1082
C4×#47311