Finite Group Databasebeta

← #14769414

Subgroups — #14769414

Order 2816.

1426 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622625C211yesmaximal, characteristic
2C2×#10622838C212yesmaximal, complemented
3#13071565C211yesmaximal, characteristic
4#13069540C211yesmaximal, characteristic, complemented
5#13069419C211yesmaximal, characteristic, complemented
6#13069050C212yesmaximal, complemented
7#13068929C212yesmaximal, complemented
8#13068621C211yesmaximal, characteristic, complemented
9#13068551C212yesmaximal, complemented
10C4×#66899C211yesmaximal, characteristic, complemented
11C2×D4×Q8×C11C211yesmaximal, characteristic
12C23×Q8×C11C2212yes—
13D4×Q8×C11—24no—
14D4×Q8×C11C418yescomplemented
15C2×C11×C4⋊Q8—21no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8—22no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66979C2212yes—
23C22×#4318C2212yes—
24#10622838—28no—
25C2×#66899C2211yescharacteristic
26C2×#66899C2212yes—
27C2×#66899C2212yes—
28C2×#66899C2212yes—
29C2×#66899C2212yes—
30C2×#66899C2212yes—
31C2×#66899C2211yescharacteristic
32#10622834—21no—
33#10622825C2212yes—
34C2×C22⋊(C11⋊C8)C2212yes—
35#10622625—24no—
36C4⋊C4×Dic11—21no—
37#10622564—22no—
38#10622548C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2211yescharacteristic
44#10622167C2211yescharacteristic
45C22×Q8×C11—22no—
46C22×Q8×C11—24no—
47C22×Q8×C11—24no—
48C22×Q8×C11—24no—
49C22×Q8×C11—42no—
50C22×Q8×C11—42no—
51C22×Q8×C11C2×C418yes—
52C22×Q8×C11C2312yes—
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11D411yescharacteristic
55C23×C4×C11—22no—
56C23×C4×C11C2312yes—
57C11×C4⋊Q8—28no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8C2×C414yes—
60C11×C22⋊Q8—24no—
61C11×C22⋊Q8—216no—
62C11×C22⋊Q8C2×C418yes—
63C4×Q8×C11—22no—
64C4×Q8×C11C2×C414yes—
65C4×D4×C11—28no—
66C4×D4×C11C2×C414yes—
67C4×D4×C11D414yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4D412yes—
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11—22no—
80#66979—24no—
81#66979—42no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2312yes—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4×Dic11—21no—
88C2×C4×Dic11—22no—
89C2×#4318—24no—
90C2×#4318—24no—
91C2×#4318—42no—
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2312yes—
94C22×C11⋊C8C2311yescharacteristic
95#66899—24no—
96#66899—22no—
97#66899—24no—
98#66899—24no—
99#66899—42no—
100#66899—42no—
101#66899D414yescomplemented
102C11⋊#95—21no—
103C11⋊#95—22no—
104C22⋊(C11⋊C8)—24no—
105C4⋊(C11⋊C8)—22no—
106C4×C11⋊C8—22no—
107#22430—111nomaximal, Sylow
108C24×C11C2×D412yes—
109C2×Q8×C11—28no—
110C2×Q8×C11—21no—
111C2×Q8×C11—22no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—216no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—44no—
120C2×Q8×C11—44no—
121C2×Q8×C11—48no—
122C2×Q8×C11—48no—
123C2×Q8×C11—48no—
124C2×Q8×C11C22×C414yes—
125C2×Q8×C11C22×C412yes—
126C2×Q8×C11C2×D412yes—
127C2×Q8×C11#4112yes—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11C22⋊C414yes—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—28no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—44no—
140C22×C4×C11—44no—
141C22×C4×C11C22×C414yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D414yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—22no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—28no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4C22⋊C414yes—
156C11×C4⋊C4C22×C412yes—
157C11×C22⋊C4—28no—
158C11×C22⋊C4C22⋊C418yes—
159C42×C11—24no—
160C42×C11C22×C412yes—
161C42×C11C2×D412yes—
162C22⋊Dic11—44no—
163C22⋊Dic11—82no—
164C4⋊Dic11—22no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—22no—
169C4⋊Dic11—42no—
170C4⋊Dic11—81no—
171C4⋊Dic11C2×D412yes—
172C4×Dic11—44no—
173C4×Dic11—42no—
174#4318—48no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8C2×D412yes—
184C2×D4×Q8D1111yescharacteristic
185C2×#436—111no—
186C2×#419—112no—
187#2354—111no—
188#1981—111no—
189#1956—111no—
190#1894—112no—
191#1873—112no—
192#1803—111no—
193#1787—112no—
194C4×#103—111no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11C2×C22⋊C414yes—
202C23×C11C22×D411yescharacteristic
203Q8×C11—22no—
204Q8×C11—22no—
205Q8×C11—22no—
206Q8×C11—24no—
207Q8×C11—24no—
208Q8×C11—416no—
209Q8×C11—42no—
210Q8×C11—42no—
211Q8×C11C4×D414yes—
212D4×C11—28no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—416no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11C2×C22⋊C412yes—
232C2×C4×C11C2×C22⋊C414yes—
233C2×C4×C11C2×C22⋊C412yes—
234C2×C4×C11#13712yes—
235C2×C4×C11#13712yes—
236C2×C4×C11C23×C411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11H(5,𝔽2)11yescharacteristic
241C2×C4×C11H(5,𝔽2)11yescharacteristic
242C2×Dic11—22no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—42no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—41no—
251C11⋊C8—22no—
252C11⋊C8—42no—
253C11⋊C8—41no—
254C23×Q8C2×D1112yes—
255C22×M16—112no—
256D4×Q8—24no—
257D4×Q8Dic1118yescomplemented
258C2×C4⋊Q8—21no—
259C2×C4⋊Q8C2×D1111yescharacteristic
260C2×C22⋊Q8—22no—
261C2×C22⋊Q8C2×D1112yes—
262C2×C4×Q8C2×D1111yescharacteristic
263C2×C4×D4—21no—
264C2×C4×D4C2×D1111yescharacteristic
265C2×#117—112no—
266#436—224no—
267C2×C4⋊C8—111no—
268#419—228no—
269C2×#103—111no—
270C2×#103—112no—
271C2×#103—112no—
272C2×#103—112no—
273C2×#103—111no—
274C2×#103—112no—
275C2×#103—112no—
276C2×C22⋊C8—112no—
277C2×C4×C8—111no—
278#390—221no—
279#388—222no—
280#384—111no—
281#380—112no—
282C4×C4⋊C4—111no—
283C4×C4⋊C4—221no—
284#340—112no—
285#340—111no—
286#340—111no—
287C22×C11—24no—
288C22×C11—24no—
289C22×C11—24no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11C22×C22⋊C411yescharacteristic
295C22×C11D4211yescharacteristic
296C22×C11#54611yescharacteristic
297C22×C11C2×#13711yescharacteristic
298C22×C11C2×#13711yescharacteristic
299C22×C11#57711yescharacteristic
300C22×C11#57811yescharacteristic
301C4×C11—24no—
302C4×C11—24no—
303C4×C11—22no—
304C4×C11—44no—
305C4×C11—42no—
306C4×C11#41914yescomplemented
307C4×C11C2×C4×D411yescharacteristic
308C4×C11#51811yescharacteristic
309C4×C11D4211yescharacteristic
310C4×C11#54611yescharacteristic
311Dic11—42no—
312Dic11—81no—
313Dic11—82no—
314C22×Q8—22no—
315C22×Q8—24no—
316C22×Q8—24no—
317C22×Q8—24no—
318C22×Q8—42no—
319C22×Q8—42no—
320C22×Q8C2×Dic1118yes—
321C22×Q8C22×D1112yes—
322C22×Q8C22×D1111yescharacteristic
323C22×D4C22⋊D1111yescharacteristic
324C23×C4—22no—
325C23×C4C22×D1112yes—
326C2×M16—224no—
327C2×M16—224no—
328C2×M16—442no—
329C22×C8—111no—
330C22×C8—112no—
331C22×C8—111no—
332C4⋊Q8—28no—
333C4⋊Q8—22no—
334C4⋊Q8C2×Dic1114yes—
335C22⋊Q8—24no—
336C22⋊Q8—216no—
337C22⋊Q8C2×Dic1118yes—
338C4×Q8—22no—
339C4×Q8C2×Dic1114yes—
340C4×D4—28no—
341C4×D4C2×Dic1114yes—
342C4×D4C22⋊D1114yes—
343#117—224no—
344#117—442no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—111no—
350C2×C4⋊C4—112no—
351C2×C4⋊C4—111no—
352C2×C4⋊C4—221no—
353C2×C4⋊C4—221no—
354C2×C4⋊C4C22⋊D1111yescharacteristic
355C2×C4⋊C4C22×D1111yescharacteristic
356C2×C22⋊C4—22no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4C22⋊D1112yes—
360C2×C42—21no—
361C2×C42—222no—
362C2×C42—221no—
363C2×C42C22×D1111yescharacteristic
364C4⋊C8—222no—
365#103—114no—
366#103—224no—
367#103—224no—
368#103—224no—
369#103—222no—
370#103—442no—
371#103—442no—
372C22⋊C8—224no—
373C4×C8—222no—
374#95—221no—
375#95—222no—
376C2×C11—44no—
377C2×C11D4×C22⋊C411yescharacteristic
378C2×C11C2×#41911yescharacteristic
379C2×C11#289811yescharacteristic
380C2×C11#327611yescharacteristic
381C2×C11#327811yescharacteristic
382C2×C11#332811yescharacteristic
383C2×C11#332911yescharacteristic
384C24C2×C22⋊D1112yes—
385C2×Q8—28no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—22no—
390C2×Q8—216no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—44no—
396C2×Q8—44no—
397C2×Q8—48no—
398C2×Q8—48no—
399C2×Q8—48no—
400C2×Q8D4×D1112yes—
401C2×Q8#434112yes—
402C2×Q8C22×Dic1114yes—
403C2×Q8C22×Dic1112yes—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4C22⋊Dic1114yes—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—28no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—44no—
416C22×C4—44no—
417C22×C4—221no—
418C22×C4—221no—
419C22×C4—222no—
420C22×C4C22×Dic1114yes—
421C22×C4C2×C22⋊D1112yes—
422C22×C4C2×C22⋊D1111yescharacteristic
423C22×C4C2×C22⋊D1114yes—
424C22×C4C2×C22⋊D1111yescharacteristic
425C22×C4C23×D1111yescharacteristic
426M16—448no—
427C2×C8—112no—
428C2×C8—221no—
429C2×C8—221no—
430C2×C8—222no—
431C2×C8—221no—
432C2×C8—221no—
433C2×C8—222no—
434C2×C8—221no—
435C2×C8—222no—
436C4⋊C4—24no—
437C4⋊C4—24no—
438C4⋊C4—24no—
439C4⋊C4—28no—
440C4⋊C4—21no—
441C4⋊C4—112no—
442C4⋊C4—221no—
443C4⋊C4—222no—
444C4⋊C4—221no—
445C4⋊C4—221no—
446C4⋊C4—222no—
447C4⋊C4—442no—
448C4⋊C4—881no—
449C4⋊C4C22⋊Dic1114yes—
450C4⋊C4C22×Dic1112yes—
451C22⋊C4—28no—
452C22⋊C4—444no—
453C22⋊C4—882no—
454C22⋊C4C22⋊Dic1118yes—
455C42—24no—
456C42—444no—
457C42—442no—
458C42C22×Dic1112yes—
459C42C2×C22⋊D1112yes—
460C11#2243011yescharacteristic, complemented, Sylow
461C23—22no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23C2×C22⋊Dic1114yes—
468C23C22×C22⋊D1111yescharacteristic
469Q8—22no—
470Q8—22no—
471Q8—22no—
472Q8—24no—
473Q8—24no—
474Q8—416no—
475Q8—42no—
476Q8—42no—
477Q8D4×Dic1114yes—
478D4—28no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—416no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—222no—
498C2×C4—441no—
499C2×C4—441no—
500C2×C4—442no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4—442no—
504C2×C4—441no—
505C2×C4—442no—
506C2×C4#6699512yes—
507C2×C4#6699512yes—
508C2×C4C2×C22⋊Dic1112yes—
509C2×C4C2×C22⋊Dic1114yes—
510C2×C4C2×C22⋊Dic1112yes—
511C2×C4C2×D4×D1111yescharacteristic
512C2×C4C2×#434111yescharacteristic
513C2×C4#6703711yescharacteristic
514C2×C4#6703711yescharacteristic
515C2×C4C23×Dic1111yescharacteristic
516C2×C4C22×C22⋊D1111yescharacteristic
517C8—222no—
518C8—442no—
519C8—441no—
520C22—24no—
521C22—24no—
522C22—24no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22D4×C22⋊D1111yescharacteristic
528C22#1062333711yescharacteristic
529C22C2×#6699511yescharacteristic
530C22C2×#6699511yescharacteristic
531C22#1062336811yescharacteristic
532C22#1062336911yescharacteristic
533C22C22×C22⋊Dic1111yescharacteristic
534C4—24no—
535C4—24no—
536C4—22no—
537C4—44no—
538C4—42no—
539C4—442no—
540C4—881no—
541C4—882no—
542C4#1062283814yescomplemented
543C4C2×D4×Dic1111yescharacteristic
544C4#1062332911yescharacteristic
545C4D4×C22⋊D1111yescharacteristic
546C4#1062333711yescharacteristic
547C2—44no—
548C2D4×C22⋊Dic1111yescharacteristic
549C2C2×#1062283811yescharacteristic
550C2#1307714911yescharacteristic
551C2#1308026211yescharacteristic
552C2#1308027811yescharacteristic
553C2#1308089911yescharacteristic
554C2#1308091011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×D4×Q8×C11C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
cosocleC22×C4×C11C24
hypercenterC2×D4×Q8D11
hypocenterC11#22430
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#10622838C2semidirect
4. #13069540C2semidirect
5. #13069419C2semidirect
6. #13069050C2semidirect
7. #13068929C2semidirect
8. #13068621C2semidirect
9. #13068551C2semidirect
10. C4×#66899C2semidirect
14. D4×Q8×C11C4semidirect
101. #66899D4semidirect
257. D4×Q8Dic11semidirect
306. C4×C11#419semidirect
460. C11#22430semidirect
542. C4#10622838semidirect

Maximal subgroups

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

subgroupindex
C2×#106226252
C2×#106228382
#130715652
#130695402
#130694192
#130690502
#130689292
#130686212
#130685512
C4×#668992
C2×D4×Q8×C112
#2243011