Finite Group Databasebeta

← C4×#10622528 #14907097

Subgroups — C4×#10622528 #14907097

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622528C211yesmaximal, characteristic
2C4×#66965C211yesmaximal, characteristic
3C4×Q16×D11C211yesmaximal, characteristic, complemented
4#13070486C211yesmaximal, characteristic, complemented
5#13070484C211yesmaximal, characteristic, complemented
6#13070481C211yesmaximal, characteristic, complemented
7#13070477C211yesmaximal, characteristic, complemented
8C4×Dic88C211yesmaximal, characteristic, complemented
9C4×#66893C211yesmaximal, characteristic, complemented
10C4×#66891C211yesmaximal, characteristic, complemented
11#13070403C211yesmaximal, characteristic, complemented
12#13070334C211yesmaximal, characteristic, complemented
13#13070325C211yesmaximal, characteristic
14C4×#66862C211yesmaximal, characteristic, complemented
15C4×C11×SD32C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17C2×#66965C2211yescharacteristic
18C4×Q8×D11—21no—
19C4×#4341—21no—
20C2×C11×SD32C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic
22C4×C11×D8C2211yescharacteristic
23Q16×Dic11C2211yescharacteristic
24C2×#66893C2211yescharacteristic
25D8×Dic11C2211yescharacteristic
26C2×#66891C2211yescharacteristic
27C4×#4326—21no—
28C4×#4324—21no—
29#10622528C418yesdirect product factor
30C2×Dic88C2211yescharacteristic
31C2×#66862C2211yescharacteristic
32C2×#66862C2211yescharacteristic
33#10622493C2211yescharacteristic
34D11×#107C2211yescharacteristic
35#10622486C2211yescharacteristic
36#10622486C2211yescharacteristic
37D11×#103—21no—
38#10622403—21no—
39#10622385—21no—
40#10622371—21no—
41C4×Dic44C2211yescharacteristic
42C4×Dic44C2211yescharacteristic
43C4×C8×D11C2211yescharacteristic
44C11×#367C2211yescharacteristic
45C11×#358C2211yescharacteristic
46C11×#357C2211yescharacteristic
47C4×C11×C16C2211yescharacteristic
48#10622202C2211yescharacteristic
49#10622200C2211yescharacteristic
50#10622142C2211yescharacteristic
51#10622141C2211yescharacteristic
52#10622141C2211yescharacteristic
53#10622140C2211yescharacteristic
54#10622140C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622130C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622127C2211yescharacteristic
59C4×C11⋊C16C2211yescharacteristic
60C2×Q8×D11—21no—
61C2×#4341—21no—
62C2×C11×Q16C2311yescharacteristic
63C2×C11×D8C2311yescharacteristic
64C4×Q8×C11—21no—
65C4×D4×C11—21no—
66Q8×Dic11—21no—
67C2×#4326—21no—
68D4×Dic11—21no—
69C2×#4324—21no—
70C4×C22⋊D11—41no—
71C2×C4×Dic11—41no—
72Q16×D11—22no—
73Q16×D11C2×C414yescomplemented
74#66965—22no—
75#66965C2×C414yes—
76C2×Dic44C2311yescharacteristic
77C2×Dic44C2311yescharacteristic
78C2×C8×D11D411yescharacteristic
79C2×C8×D11C2311yescharacteristic
80#66945—21no—
81C4⋊C4×D11—21no—
82C4⋊C4×D11—41no—
83#66940—21no—
84#66940—21no—
85#66940—41no—
86(C22⋊D11)⋊C4—41no—
87#66930—41no—
88C42×D11—41no—
89C42×D11D411yescharacteristic
90C4×Dic22—21no—
91C4×Dic22—21no—
92C4×Dic22—41no—
93C11×SD32C2×C414yescomplemented
94C2×C11×C16C2311yescharacteristic
95C2×C11×C16C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#103—21no—
99C11×#102—21no—
100C4×C8×C11C2311yescharacteristic
101#66899—21no—
102#66896—21no—
103#66893C2×C414yescomplemented
104#66891C2×C414yescomplemented
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66880—21no—
108#66880—21no—
109C8×Dic11D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#66874—21no—
114#66874—21no—
115#66872—21no—
116#66871—21no—
117C4×C11⋊C8D411yescharacteristic
118Dic88C2×C414yescomplemented
119#66862—22no—
120#66862C2×C414yescomplemented
121C4×#510—111nomaximal, Sylow
122C2×Q8×C11—21no—
123C2×D4×C11—21no—
124C22×C4×C11—41no—
125C2×C22⋊D11—41no—
126C22×Dic11—41no—
127C22×Dic11—41no—
128Q8×D11—24no—
129Q8×D11—42no—
130#4341—24no—
131#4341—42no—
132C2×C4×D11—41no—
133C2×C4×D11—41no—
134C2×C4×D11D811yescharacteristic
135C2×C4×D11D811yescharacteristic
136C2×C4×D11C2×D411yescharacteristic
137C2×Dic22—21no—
138C2×Dic22—21no—
139C2×Dic22—41no—
140C11×Q16—21no—
141C11×Q16C22×C412yes—
142C11×D8—21no—
143C11×D8C22×C412yes—
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2411yescharacteristic
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—41no—
149C11×C22⋊C4—41no—
150C42×C11—41no—
151C42×C11C2×D411yescharacteristic
152C22⋊Dic11—41no—
153#4326—24no—
154#4324—24no—
155(C2×D11)⋊C4—41no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163Dic11⋊C4—41no—
164C4×Dic11—41no—
165C4×Dic11—41no—
166C4×Dic11—41no—
167C4×Dic11—41no—
168C4×Dic11—41no—
169C4×Dic11—41no—
170C4×Dic11D811yescharacteristic
171C4×Dic11D811yescharacteristic
172C4×Dic11C2×D411yescharacteristic
173C2×C11⋊C8C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175Dic44—21no—
176Dic44—21no—
177Dic44C22×C412yes—
178Dic44C22×C412yes—
179C8×D11—22no—
180C8×D11C22×C412yes—
181C8×D11#4112yes—
182C11×C16—21no—
183C11×C16C22×C412yes—
184C11⋊C16—21no—
185C11⋊C16C22×C412yes—
186C2×#510—111no—
187C4×#135—111no—
188C2×C4×Q16—111no—
189#2176—111no—
190#2176—111no—
191#2175—111no—
192#2175—111no—
193C4×Q32—111no—
194C4×Q32—111no—
195C4×SD32—111no—
196C4×SD32D1111yescharacteristic, complemented
197#2159—111no—
198#2141—111no—
199#2139—111no—
200C4×M32—111no—
201C23×C11—41no—
202C22×D11C2×D811yescharacteristic
203Q8×C11—22no—
204Q8×C11—41no—
205D4×C11—22no—
206D4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—82no—
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C22⋊D11—44no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—44no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—82no—
221C2×Dic11C2×D811yescharacteristic
222C2×Dic11C2×D811yescharacteristic
223C2×Dic11C2×D811yescharacteristic
224C4×D11—22no—
225C4×D11—41no—
226C4×D11—44no—
227C4×D11—82no—
228C4×D11C4×D412yes—
229C4×D11#13512yes—
230Dic22—22no—
231Dic22—22no—
232Dic22—41no—
233Dic22—41no—
234Dic22—44no—
235C8×C11—21no—
236C8×C11C23×C411yescharacteristic
237C8×C11C2×#4111yescharacteristic
238C11⋊C8—21no—
239C11⋊C8C4×D412yes—
240C2×#135—111no—
241C22×Q16—111no—
242C4×#41—221no—
243C2×C4×Q8—221no—
244#510—118no—
245C2×Q32—111no—
246C2×Q32—111no—
247C2×SD32—111no—
248C2×SD32C2×D1111yescharacteristic
249C2×M32—111no—
250C2×M32—111no—
251C4×Q16—111no—
252C4×Q16—111no—
253C4×Q16—111no—
254C4×Q16—111no—
255C4×Q16—111no—
256C4×Q16—221no—
257C4×Q16—221no—
258C4×Q16C2×D1111yescharacteristic
259C4×SD16—221no—
260C4×SD16—221no—
261C4×D8—111no—
262C4×D8C2×D1111yescharacteristic
263#427—111no—
264C2×#107—111no—
265#416—221no—
266C2×#103—221no—
267C2×C4×C8—111no—
268#367—111no—
269#367C2×D1111yescharacteristic
270#366—111no—
271#366—111no—
272#358—111no—
273#358—111no—
274#358—111no—
275#358—111no—
276#358—111no—
277#358C2×D1111yescharacteristic
278#357—111no—
279#357C2×D1111yescharacteristic
280#346—111no—
281#346—111no—
282C4×C16—111no—
283C4×C16C2×D1111yescharacteristic
284C22×C11—42no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11C22×D811yescharacteristic
288C2×D11—21no—
289C2×D11—21no—
290C2×D11C4×D812yes—
291C4×C11—21no—
292C4×C11—42no—
293C4×C11—81no—
294C4×C11—81no—
295C4×C11#51012yescomplemented
296C4×C11C2×C4×D411yescharacteristic
297C4×C11C2×#13511yescharacteristic
298Dic11—21no—
299Dic11—21no—
300Dic11—42no—
301Dic11—42no—
302Dic11—81no—
303Dic11—81no—
304Dic11C4×D812yes—
305C2×#41—221no—
306C22×Q8—221no—
307#135—114no—
308#135—222no—
309C2×Q16—114no—
310C2×Q16—111no—
311C2×Q16—111no—
312C2×Q16—222no—
313C2×Q16—221no—
314C2×Q16C22×D1111yescharacteristic
315C2×SD16—221no—
316C2×D8C22×D1111yescharacteristic
317C22×C8—111no—
318C22×C8—111no—
319C4×Q8—21no—
320C4×Q8—221no—
321C4×Q8—221no—
322C4×Q8—221no—
323C4×Q8—221no—
324C4×Q8—221no—
325C4×Q8—441no—
326C4×Q8—441no—
327C4×D4—21no—
328C4×D4—221no—
329C4×D4—441no—
330C4×D4—441no—
331#117—221no—
332#117—441no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4—441no—
335C2×C42—111no—
336C2×C42—441no—
337C2×C42—441no—
338Q32—114no—
339Q32—114no—
340SD32—114no—
341SD32C4×D1114yescomplemented
342M32—114no—
343M32—222no—
344C2×C16—111no—
345C2×C16—111no—
346C2×C16C22×D1111yescharacteristic
347C2×C16C22×D1111yescharacteristic
348#107—111no—
349#107—111no—
350#107—221no—
351#107C22×D1111yescharacteristic
352#107C22×D1111yescharacteristic
353#106—221no—
354#103—21no—
355#103—221no—
356#103—221no—
357#103—221no—
358#103—221no—
359#103—221no—
360#102—21no—
361#102—221no—
362C4×C8—111no—
363C4×C8—111no—
364C4×C8—111no—
365C4×C8C22×D1111yescharacteristic
366C2×C11—82no—
367C2×C11C2×C4×D811yescharacteristic
368C2×C11C2×#51011yescharacteristic
369C2×C11#341411yescharacteristic
370D11—22no—
371#41—224no—
372#41—442no—
373C2×Q8—21no—
374C2×Q8—224no—
375C2×Q8—221no—
376C2×Q8—221no—
377C2×Q8—441no—
378C2×Q8—442no—
379C2×D4—21no—
380C2×D4—441no—
381C22×C4—41no—
382C22×C4—111no—
383C22×C4—111no—
384C22×C4—111no—
385C22×C4—441no—
386C22×C4—441no—
387C22×C4—441no—
388C22×C4—441no—
389Q16—21no—
390Q16—112no—
391Q16—112no—
392Q16—224no—
393Q16—221no—
394Q16—221no—
395Q16C2×C4×D1112yes—
396SD16—224no—
397D8—21no—
398D8C2×C4×D1112yes—
399C2×C8—111no—
400C2×C8—112no—
401C2×C8—112no—
402C2×C8—111no—
403C2×C8—222no—
404C2×C8D4×D1111yescharacteristic
405C2×C8C23×D1111yescharacteristic
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—41no—
409C4⋊C4—221no—
410C4⋊C4—221no—
411C4⋊C4—441no—
412C4⋊C4—441no—
413C4⋊C4—441no—
414C4⋊C4—441no—
415C4⋊C4—441no—
416C4⋊C4—441no—
417C22⋊C4—41no—
418C22⋊C4—441no—
419C22⋊C4—441no—
420C42—41no—
421C42—111no—
422C42—111no—
423C42—111no—
424C42—441no—
425C42—441no—
426C42—441no—
427C42—441no—
428C42—441no—
429C42—441no—
430C42D4×D1111yescharacteristic
431C16—21no—
432C16—112no—
433C16—221no—
434C16C2×C4×D1112yes—
435C11C4×#51011yescharacteristic, complemented, Sylow
436C23—41no—
437C23—111no—
438Q8—22no—
439Q8—41no—
440Q8—222no—
441Q8—222no—
442Q8—444no—
443Q8—441no—
444Q8—441no—
445D4—22no—
446D4—41no—
447D4—444no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—82no—
452C2×C4—111no—
453C2×C4—112no—
454C2×C4—112no—
455C2×C4—111no—
456C2×C4—111no—
457C2×C4—222no—
458C2×C4—441no—
459C2×C4—444no—
460C2×C4—444no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—882no—
466C2×C4—882no—
467C2×C4D8×D1111yescharacteristic
468C2×C4D8×D1111yescharacteristic
469C2×C4C2×D4×D1111yescharacteristic
470C8—21no—
471C8—112no—
472C8—221no—
473C8C22×C4×D1111yescharacteristic
474C8#41×D1111yescharacteristic
475C22—42no—
476C22—81no—
477C22—81no—
478C22—112no—
479C22—221no—
480C22—221no—
481C22C2×D8×D1111yescharacteristic
482C4—21no—
483C4—42no—
484C4—81no—
485C4—81no—
486C4—112no—
487C4—221no—
488C4—221no—
489C4—442no—
490C4—442no—
491C4—881no—
492C4—881no—
493C4#1062252812yesdirect product factor
494C4C4×D4×D1111yescharacteristic
495C4D11×#13511yescharacteristic
496C2—82no—
497C2—222no—
498C2C4×D8×D1111yescharacteristic
499C2C2×#1062252811yescharacteristic
500C2#1308174911yescharacteristic
subgroupG/H
centerC2×C4D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC4×C11×SD32C2
socleC22×C11C22×D8
prime radicalC2×#66965C22
cosocleC2×C8×C11C24
hypercenterC4×SD32D11
hypocenterC11C4×#510
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
3. C4×Q16×D11C2semidirect
4. #13070486C2semidirect
5. #13070484C2semidirect
6. #13070481C2semidirect
7. #13070477C2semidirect
8. C4×Dic88C2semidirect
9. C4×#66893C2semidirect
10. C4×#66891C2semidirect
11. #13070403C2semidirect
12. #13070334C2semidirect
14. C4×#66862C2semidirect
15. C4×C11×SD32C2semidirect
29. #10622528C4direct (N × H)
73. Q16×D11C2×C4semidirect
93. C11×SD32C2×C4semidirect
103. #66893C2×C4semidirect
104. #66891C2×C4semidirect
118. Dic88C2×C4semidirect
120. #66862C2×C4semidirect
196. C4×SD32D11semidirect
295. C4×C11#510semidirect
341. SD32C4×D11semidirect
435. C11C4×#510semidirect
493. C4#10622528direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106225282
C4×#669652
C4×Q16×D112
#130704862
#130704842
#130704812
#130704772
C4×Dic882
C4×#668932
C4×#668912
#130704032
#130703342
#130703252
C4×#668622
C4×C11×SD322
C4×#51011