Finite Group Databasebeta

← C4×#10622580 #14760880

Subgroups — C4×#10622580 #14760880

Order 2816.

1060 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622580C211yesmaximal, characteristic
2C4×#66983C211yesmaximal, characteristic
3#13069236C212yesmaximal, complemented
4#13069187C212yesmaximal, complemented
5#13068933C211yesmaximal, characteristic
6#13068804C211yesmaximal, characteristic, complemented
7#13068702C211yesmaximal, characteristic, complemented
8C4×#66871C212yesmaximal, complemented
9C4×#66873C212yesmaximal, complemented
10C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11—21no—
15C22×C42×C11C2211yescharacteristic
16C2×#66983C2211yescharacteristic
17C2×C4×C22⋊D11—21no—
18C2×C4×D44C2211yescharacteristic
19C4×C11×C4⋊C4—21no—
20C4×C11×C4⋊C4—21no—
21C4×C11×C4⋊C4C2212yes—
22C4×C11×C4⋊C4C2212yes—
23C2×C11×#95—21no—
24#10622826—21no—
25#10622825C2211yescharacteristic
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28#10622580C418yesdirect product factor
29C2×#66873C2212yes—
30C2×#66873C2212yes—
31C2×#66871C2212yes—
32C2×#66871C2212yes—
33#10622553—21no—
34#10622552C2211yescharacteristic
35C4×(C2×D11)⋊C4—21no—
36C4×C4⋊Dic11C2211yescharacteristic
37#10622541C2211yescharacteristic
38C2×C4×C11⋊C8C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622162C2212yes—
44C23×C4×C11—21no—
45C23×C4×C11—21no—
46C23×C4×C11D411yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11—21no—
50C22×D44C2311yescharacteristic
51C22×C4×D11—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—24no—
56C2×C11×C4⋊C4C2×C414yescomplemented
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2312yes—
59C2×C42×C11—24no—
60C2×C42×C11—22no—
61C2×C42×C11—22no—
62C2×C42×C11—44no—
63C2×C42×C11D411yescharacteristic
64C2×C42×C11D411yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C22⋊Dic11—21no—
68#66983—22no—
69#66983C2×C414yes—
70C4×C22⋊D11—44no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×Dic11⋊C4—21no—
79C2×C4×Dic11—21no—
80C22×C11⋊C8C2312yes—
81C22×C11⋊C8C2312yes—
82C4×D44—24no—
83C11×#95—22no—
84C11×#95—22no—
85C11⋊#95—21no—
86C11⋊#95—21no—
87C11⋊#95—21no—
88C22⋊(C11⋊C8)—22no—
89C22⋊(C11⋊C8)C2×C414yescomplemented
90#66873—24no—
91#66873C2×C418yescomplemented
92#66871—24no—
93#66871C2×C418yescomplemented
94C4×C11⋊C8—24no—
95C4×#480—111nomaximal, Sylow
96C24×C11C2×D411yescharacteristic
97C23×D11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—24no—
103C22×C4×C11—24no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—41no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11D814yes—
114C22×C4×C11C22×C412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11#4112yes—
121C22×C4×C11C2411yescharacteristic
122C2×C22⋊D11—24no—
123C2×C22⋊D11—42no—
124C2×C22⋊D11—42no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C2×D44—21no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44C22×C412yes—
132C2×C4×D11—42no—
133C2×C4×D11—42no—
134C2×C4×D11—42no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4C22×C414yes—
140C11×C4⋊C4#4114yes—
141C42×C11—22no—
142C42×C11—22no—
143C42×C11—22no—
144C42×C11—44no—
145C42×C11—44no—
146C42×C11#4114yes—
147C22⋊Dic11—42no—
148(C2×D11)⋊C4—24no—
149(C2×D11)⋊C4—42no—
150(C2×D11)⋊C4—42no—
151(C2×D11)⋊C4—42no—
152C4⋊Dic11—21no—
153C4⋊Dic11—22no—
154C4⋊Dic11—22no—
155C4⋊Dic11C22×C412yes—
156Dic11⋊C4—42no—
157C4×Dic11—42no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8C22×C414yes—
164C2×#480—111no—
165C4×#121—111no—
166C2×C4×C4⋊C4D1111yescharacteristic, complemented
167#1925—112no—
168#1918—112no—
169#1874—111no—
170#1852—111no—
171#1823—111no—
172C4×#107—112no—
173C4×#102—112no—
174C4×C22⋊C8—111no—
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11C4×D412yes—
180C23×C11C2×D812yes—
181C23×C11#13512yes—
182C23×C11C22×D411yescharacteristic
183C22×D11—22no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—41no—
189C22×D11—41no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—28no—
199C2×C4×C11—24no—
200C2×C4×C11—21no—
201C2×C4×C11—24no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—44no—
205C2×C4×C11—48no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—48no—
211C2×C4×C11C4×D412yes—
212C2×C4×C11#12312yes—
213C2×C4×C11#12312yes—
214C2×C4×C11C2×D812yes—
215C2×C4×C11C2×D812yes—
216C2×C4×C11#13712yes—
217C2×C4×C11C23×C411yescharacteristic
218C2×C4×C11C2×#4112yes—
219C2×C4×C11C2×#4112yes—
220C2×C4×C11C2×#4111yescharacteristic
221C22⋊D11—48no—
222C2×Dic11—22no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231D44—24no—
232D44—42no—
233C4×D11—84no—
234C11⋊C8—24no—
235C11⋊C8—42no—
236C2×#121—111no—
237C2×C4×D4—111no—
238C2×C4×D4—221no—
239C22×C4⋊C4C2×D1111yescharacteristic
240C22×C4⋊C4C2×D1111yescharacteristic
241C22×C42—21no—
242C22×C42C2×D1111yescharacteristic
243#480—118no—
244C2×#107—112no—
245C2×#107—112no—
246C2×#102—112no—
247C2×#102—112no—
248C2×C22⋊C8—111no—
249C2×C22⋊C8—111no—
250C2×C4×C8—112no—
251#390—111no—
252#389—111no—
253#388—221no—
254#386—221no—
255#380—111no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—111no—
259C4×C4⋊C4C2×D1112yes—
260C4×C4⋊C4C2×D1112yes—
261C4×C22⋊C4—221no—
262C2×#95—21no—
263#340—112no—
264#340—112no—
265#340—112no—
266#340—112no—
267#336—112no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11C4×D814yes—
275C22×C11C2×C4×D411yescharacteristic
276C22×C11C2×#12311yescharacteristic
277C22×C11#52511yescharacteristic
278C22×C11C22×D811yescharacteristic
279C22×C11C2×#13511yescharacteristic
280C22×C11C2×#13711yescharacteristic
281C22×C11#57511yescharacteristic
282C2×D11—42no—
283C2×D11—42no—
284C2×D11—42no—
285C2×D11—81no—
286C2×D11—81no—
287C2×D11—81no—
288C2×D11—81no—
289C4×C11—22no—
290C4×C11—22no—
291C4×C11—22no—
292C4×C11—41no—
293C4×C11—44no—
294C4×C11—44no—
295C4×C11#48014yescomplemented
296C4×C11C4×#4112yes—
297C4×C11#52912yes—
298Dic11—42no—
299Dic11—81no—
300Dic11—81no—
301C22×D4—111no—
302C22×D4—221no—
303C23×C4—21no—
304C23×C4—21no—
305C23×C4—221no—
306C23×C4C22⋊D1111yescharacteristic
307C23×C4C22⋊D1111yescharacteristic
308C23×C4C22×D1111yescharacteristic
309C22×C8—112no—
310C22×C8—112no—
311#121—114no—
312#121—222no—
313C4×D4—224no—
314C4×D4—444no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—111no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4C4×D1114yescomplemented
324C2×C4⋊C4C22×D1112yes—
325C2×C4⋊C4C22×D1112yes—
326C2×C22⋊C4—221no—
327C2×C22⋊C4—221no—
328C2×C22⋊C4—221no—
329C2×C22⋊C4—221no—
330C2×C22⋊C4—221no—
331C2×C42—24no—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—44no—
335C2×C42—221no—
336C2×C42C22⋊D1111yescharacteristic
337C2×C42C22⋊D1111yescharacteristic
338C2×C42C22×D1111yescharacteristic
339C2×C42C22×D1111yescharacteristic
340#107—118no—
341#107—224no—
342#102—118no—
343#102—224no—
344C22⋊C8—114no—
345C22⋊C8—222no—
346C4×C8—224no—
347#95—22no—
348#95—22no—
349#95—221no—
350#95—221no—
351#95—221no—
352C2×C11—24no—
353C2×C11C4×#12311yescharacteristic
354C2×C11C2×C4×D811yescharacteristic
355C2×C11C4×#13711yescharacteristic
356C2×C11C2×#48011yescharacteristic
357C2×C11#309111yescharacteristic
358C2×C11#310011yescharacteristic
359C2×C11#310811yescharacteristic
360D11—82no—
361C24—221no—
362C24C2×C22⋊D1111yescharacteristic
363C2×D4—112no—
364C2×D4—224no—
365C2×D4—222no—
366C2×D4—222no—
367C2×D4—221no—
368C2×D4—442no—
369C2×D4—442no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—41no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4—442no—
389C22×C4—442no—
390C22×C4—442no—
391C22×C4#432314yes—
392C22×C4C2×C4×D1112yes—
393C22×C4#433912yes—
394C22×C4C2×C22⋊D1111yescharacteristic
395C22×C4C2×C22⋊D1111yescharacteristic
396C22×C4C2×C22⋊D1111yescharacteristic
397C22×C4C2×C22⋊D1111yescharacteristic
398C22×C4C2×C22⋊D1111yescharacteristic
399C22×C4C23×D1111yescharacteristic
400C2×C8—114no—
401C2×C8—222no—
402C2×C8—222no—
403C2×C8—222no—
404C2×C8—222no—
405C2×C8—222no—
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—112no—
411C4⋊C4—221no—
412C4⋊C4—222no—
413C4⋊C4—222no—
414C4⋊C4—442no—
415C4⋊C4C2×C4×D1114yes—
416C4⋊C4#433914yes—
417C22⋊C4—224no—
418C22⋊C4—442no—
419C22⋊C4—442no—
420C22⋊C4—442no—
421C22⋊C4—442no—
422C42—22no—
423C42—22no—
424C42—22no—
425C42—44no—
426C42—44no—
427C42—442no—
428C42#433914yes—
429C11C4×#48011yescharacteristic, complemented, Sylow
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—222no—
435C23—441no—
436C23—441no—
437C23—441no—
438C23—441no—
439C23—441no—
440C23—441no—
441C23C4×C22⋊D1112yes—
442C23C2×#432312yes—
443C23#6700312yes—
444C23C22×C22⋊D1111yescharacteristic
445D4—224no—
446D4—448no—
447D4—442no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—28no—
457C2×C4—24no—
458C2×C4—21no—
459C2×C4—24no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—44no—
463C2×C4—48no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—48no—
469C2×C4—222no—
470C2×C4—441no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—884no—
479C2×C4C4×C22⋊D1112yes—
480C2×C4#6698212yes—
481C2×C4#6698212yes—
482C2×C4C2×#432312yes—
483C2×C4C2×#432312yes—
484C2×C4#6699512yes—
485C2×C4C22×C4×D1111yescharacteristic
486C2×C4C2×#433912yes—
487C2×C4C2×#433912yes—
488C2×C4C2×#433911yescharacteristic
489C8—224no—
490C8—442no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—442no—
498C22—442no—
499C22—442no—
500C22—881no—
501C22—881no—
502C22—881no—
503C22—881no—
504C22C4×#432314yes—
505C22C2×C4×C22⋊D1111yescharacteristic
506C22C2×#6698211yescharacteristic
507C22#1062332211yescharacteristic
508C22C22×#432311yescharacteristic
509C22C2×#6699511yescharacteristic
510C22C2×#6700311yescharacteristic
511C22#1062335311yescharacteristic
512C4—22no—
513C4—22no—
514C4—22no—
515C4—41no—
516C4—44no—
517C4—44no—
518C4—442no—
519C4—881no—
520C4—881no—
521C4#1062258014yesdirect product factor
522C4C4×#433912yes—
523C4#1062301012yes—
524C2—24no—
525C2—882no—
526C2C4×#6698211yescharacteristic
527C2C2×C4×#432311yescharacteristic
528C2C4×#6699511yescharacteristic
529C2C2×#1062258011yescharacteristic
530C2#1307852911yescharacteristic
531C2#1307861611yescharacteristic
532C2#1307869611yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C4×#480
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13069236C2semidirect
4. #13069187C2semidirect
6. #13068804C2semidirect
7. #13068702C2semidirect
8. C4×#66871C2semidirect
9. C4×#66873C2semidirect
10. C4×C22⋊(C11⋊C8)C2semidirect
11. C2×C4×C11×C4⋊C4C2semidirect
28. #10622580C4direct (N × H)
56. C2×C11×C4⋊C4C2×C4semidirect
89. C22⋊(C11⋊C8)C2×C4semidirect
91. #66873C2×C4semidirect
93. #66871C2×C4semidirect
166. C2×C4×C4⋊C4D11semidirect
295. C4×C11#480semidirect
323. C2×C4⋊C4C4×D11semidirect
429. C11C4×#480semidirect
521. C4#10622580direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106225802
C4×#669832
#130692362
#130691872
#130689332
#130688042
#130687022
C4×#668712
C4×#668732
C4×C22⋊(C11⋊C8)2
C2×C4×C11×C4⋊C42
C4×#48011