Finite Group Databasebeta

← #14787706

Subgroups — #14787706

Order 2816.

1350 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623086C211yesmaximal, characteristic
2C2×#10622633C211yesmaximal, characteristic, complemented
3C2×C4×#4325C211yesmaximal, characteristic, complemented
4#13069805C212yesmaximal, complemented
5#13069617C212yesmaximal, complemented
6#13069576C211yesmaximal, characteristic, complemented
7#13069411C211yesmaximal, characteristic, complemented
8#13068924C212yesmaximal, complemented
9#13068808C212yesmaximal, complemented
10#13068613C211yesmaximal, characteristic, complemented
11C11×#2538C211yesmaximal, characteristic, complemented
12C22×#4341—21no—
13C2×C11×C22⋊Q8C2212yes—
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C22×#4325C2211yescharacteristic
17C2×#66983C2212yes—
18C22×C4⋊Dic11C2212yes—
19#10623086—24no—
20#10623086—24no—
21C2×#66950—21no—
22C2×#66939—22no—
23C2×C4×D44C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C11×#396—22no—
26C11×#390—21no—
27C11×#389—21no—
28C11×#384C2211yescharacteristic
29C11×#380C2212yes—
30C2×#66899C2212yes—
31C2×#66899C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2212yes—
33C2×C22⋊(C11⋊C8)C2212yes—
34C4×#4325—24no—
35#10622633—24no—
36C2×#66873C2211yescharacteristic
37C2×#66873C2212yes—
38C2×#66872C2211yescharacteristic
39C2×#66872C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11D411yescharacteristic
47C23×C4×C11C2312yes—
48C22×C22⋊D11—22no—
49C23×Dic11—22no—
50C2×#4341—28no—
51C2×#4341—44no—
52C2×#4341—44no—
53C22×D44C2311yescharacteristic
54C22×C4×D11—21no—
55C22×Dic22—21no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—42no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4D412yes—
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74C2×#4325—22no—
75C2×#4325—22no—
76C2×#4325—22no—
77#66983—24no—
78#66983—24no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—22no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—24no—
84C2×C4⋊Dic11—24no—
85C2×C4⋊Dic11C2312yes—
86C2×C4⋊Dic11C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2311yescharacteristic
90#66950—28no—
91#66939—216no—
92C4×D44—22no—
93C4×D44D414yes—
94#66922—22no—
95#66922D414yes—
96C11×#95—22no—
97#66899—24no—
98#66899—22no—
99C22⋊(C11⋊C8)—24no—
100C22⋊(C11⋊C8)—42no—
101#66873—22no—
102#66873—42no—
103#66872—24no—
104#66872—22no—
105C4⋊(C11⋊C8)—22no—
106C4×C11⋊C8—22no—
107#24120—111nomaximal, Sylow
108C24×C11C2×D412yes—
109C23×D11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11#4112yescomplemented
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11SD1614yescomplemented
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C2×C22⋊D11—28no—
133C2×C22⋊D11—44no—
134C2×C22⋊D11—44no—
135C22×Dic11—28no—
136C22×Dic11—22no—
137C22×Dic11—21no—
138C22×Dic11—44no—
139C22×Dic11—44no—
140#4341—432no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44C2×D412yes—
147C2×C4×D11—24no—
148C2×C4×D11—42no—
149C2×C4×D11—42no—
150C2×Dic22—24no—
151C2×Dic22—42no—
152C2×Dic22—42no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—44no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—81no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—44no—
164C11×C22⋊C4—82no—
165C42×C11—42no—
166C42×C11C2×D412yes—
167C42×C11C2×D412yes—
168#4325—28no—
169(C2×D11)⋊C4—28no—
170(C2×D11)⋊C4—24no—
171C4⋊Dic11—28no—
172C4⋊Dic11—24no—
173C4⋊Dic11—22no—
174C4⋊Dic11—21no—
175C4⋊Dic11C2×D414yes—
176C4⋊Dic11C2×D412yes—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8#4112yescomplemented
186C2×#547—111no—
187C2×#475—111no—
188C2×C4×SD16—111no—
189#2538D1111yescharacteristic, complemented
190#2034—112no—
191#2000—112no—
192#1990—111no—
193#1954—111no—
194#1872—112no—
195#1853—112no—
196#1802—111no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11C2×SD1614yes—
204C23×C11C22×D411yescharacteristic
205C22×D11—22no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11—41no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—41no—
212Q8×C11—22no—
213Q8×C11—22no—
214Q8×C11—41no—
215Q8×C11—41no—
216D4×C11—28no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—42no—
234C2×C4×C11—41no—
235C2×C4×C11#12012yes—
236C2×C4×C11#12012yes—
237C2×C4×C11C2×SD1612yes—
238C2×C4×C11AGL(1,ℤ/8)12yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C2×C4×C112−1+411yescharacteristic
245C22⋊D11—416no—
246C2×Dic11—24no—
247C2×Dic11—22no—
248C2×Dic11—416no—
249C2×Dic11—42no—
250C2×Dic11—41no—
251C2×Dic11—42no—
252C2×Dic11—41no—
253D44—22no—
254D44—22no—
255D44—41no—
256D44—41no—
257C4×D11—48no—
258Dic22—48no—
259C11⋊C8—22no—
260C11⋊C8—41no—
261C11⋊C8—42no—
262C22×#41—221no—
263C22×SD16—111no—
264#547—224no—
265#547—224no—
266C2×C4⋊Q8—111no—
267C2×#123—222no—
268C2×C22⋊Q8—221no—
269C2×C22⋊Q8C2×D1112yes—
270C2×#121—112no—
271C2×C4×Q8C2×D1111yescharacteristic
272C2×C4×D4—111no—
273C2×C4×D4C2×D1111yescharacteristic
274C22×C4⋊C4—112no—
275#475—224no—
276C4×SD16—224no—
277C2×#106—112no—
278C2×#106—111no—
279C2×C4⋊C8—111no—
280C2×#103—112no—
281C2×#103—111no—
282C2×#102—111no—
283C2×#102—112no—
284C2×C22⋊C8—112no—
285C2×C22⋊C8—112no—
286C2×C4×C8—111no—
287#396—22no—
288#390—21no—
289#389—21no—
290#384C2×D1111yescharacteristic
291#380C2×D1112yes—
292#340—112no—
293#340—112no—
294#340—112no—
295C22×C11—24no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11C2×#12011yescharacteristic
303C22×C11#54611yescharacteristic
304C22×C11#54711yescharacteristic
305C22×C11C22×SD1611yescharacteristic
306C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C11#57711yescharacteristic
308C22×C11#57811yescharacteristic
309C2×D11—42no—
310C2×D11—42no—
311C2×D11—42no—
312C2×D11—81no—
313C2×D11—81no—
314C2×D11—81no—
315C2×D11—81no—
316C4×C11—22no—
317C4×C11—42no—
318C4×C11—42no—
319C4×C11—82no—
320C4×C11—81no—
321C4×C11#45014yes—
322C4×C11#52511yescharacteristic
323C4×C11#53711yescharacteristic
324C4×C11#54811yescharacteristic
325C4×C11#55011yescharacteristic
326Dic11—44no—
327Dic11—42no—
328C2×#41—228no—
329C2×#41—444no—
330C2×#41—444no—
331C22×Q8—221no—
332C22×Q8C22×D1111yescharacteristic
333C22×D4—111no—
334C22×D4—222no—
335C22×D4C22⋊D1111yescharacteristic
336C23×C4—222no—
337C23×C4—221no—
338C23×C4C22×D1112yes—
339C2×SD16—222no—
340C2×SD16—222no—
341C2×SD16—222no—
342C22×C8—111no—
343C22×C8—111no—
344C22×C8—112no—
345C4⋊Q8—114no—
346C4⋊Q8—222no—
347#123—2216no—
348C22⋊Q8—24no—
349C22⋊Q8—42no—
350C22⋊Q8—228no—
351#121—224no—
352#121—224no—
353C4×Q8—22no—
354C4×Q8—22no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—114no—
358C4×D4—222no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—112no—
365C2×C4⋊C4—224no—
366C2×C4⋊C4—224no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4C22⋊D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C4⋊C4C22×D1112yes—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4C22⋊D1112yes—
377C2×C42—21no—
378C2×C42C22×D1111yescharacteristic
379#106—222no—
380#106—224no—
381C4⋊C8—222no—
382#103—222no—
383#103—224no—
384#102—222no—
385#102—442no—
386C22⋊C8—224no—
387C22⋊C8—442no—
388C4×C8—222no—
389#95—22no—
390C2×C11—44no—
391C2×C11#240711yescharacteristic
392C2×C11C2×#45011yescharacteristic
393C2×C11#301311yescharacteristic
394C2×C11#329811yescharacteristic
395C2×C11#333211yescharacteristic
396C2×C11#333511yescharacteristic
397C2×C11#335311yescharacteristic
398D11—82no—
399C24—221no—
400C24C2×C22⋊D1112yes—
401#41—4432no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—224no—
408C2×Q8—442no—
409C2×Q8—442no—
410C2×Q8#434112yescomplemented
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—112no—
414C2×D4—228no—
415C2×D4—221no—
416C2×D4—221no—
417C2×D4—221no—
418C2×D4—221no—
419C2×D4—221no—
420C2×D4—444no—
421C2×D4—444no—
422C2×D4#432514yescomplemented
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—228no—
433C22×C4—221no—
434C22×C4—222no—
435C22×C4—224no—
436C22×C4—444no—
437C22×C4—444no—
438C22×C4—442no—
439C22×C4—442no—
440C22×C4C2×C22⋊D1112yes—
441C22×C4C2×C22⋊D1111yescharacteristic
442C22×C4C2×C22⋊D1111yescharacteristic
443C22×C4C23×D1111yescharacteristic
444SD16—228no—
445C2×C8—112no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—222no—
450C2×C8—221no—
451C2×C8—222no—
452C2×C8—222no—
453C2×C8—221no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—44no—
460C4⋊C4—42no—
461C4⋊C4—42no—
462C4⋊C4—81no—
463C4⋊C4—112no—
464C4⋊C4—114no—
465C4⋊C4—228no—
466C4⋊C4—224no—
467C4⋊C4—221no—
468C4⋊C4—222no—
469C22⋊C4—24no—
470C22⋊C4—44no—
471C22⋊C4—82no—
472C22⋊C4—228no—
473C22⋊C4—224no—
474C42—42no—
475C42D4×D1112yes—
476C42D4×D1112yes—
477C11#2412011yescharacteristic, complemented, Sylow
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—222no—
485C23—441no—
486C23—441no—
487C23—441no—
488C23—441no—
489C23—441no—
490C23—441no—
491C23C2×#432514yes—
492C23C22×C22⋊D1111yescharacteristic
493Q8—22no—
494Q8—22no—
495Q8—41no—
496Q8—41no—
497Q8—448no—
498D4—28no—
499D4—222no—
500D4—222no—
501D4—4416no—
502D4—441no—
503D4—441no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—222no—
523C2×C4—224no—
524C2×C4—4416no—
525C2×C4—441no—
526C2×C4—442no—
527C2×C4—441no—
528C2×C4—442no—
529C2×C4—448no—
530C2×C4#6699012yes—
531C2×C4#6699012yes—
532C2×C4C2×#432512yes—
533C2×C4#6700212yes—
534C2×C4C2×D4×D1111yescharacteristic
535C2×C4C2×D4×D1111yescharacteristic
536C2×C4C2×#434111yescharacteristic
537C2×C4#6703711yescharacteristic
538C2×C4#41×D1111yescharacteristic
539C2×C4#6704311yescharacteristic
540C8—222no—
541C8—442no—
542C8—441no—
543C22—24no—
544C22—24no—
545C22—24no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—442no—
551C22—442no—
552C22—442no—
553C22—881no—
554C22—881no—
555C22—881no—
556C22—881no—
557C22C2×#6699011yescharacteristic
558C22#1062333711yescharacteristic
559C22C22×#432511yescharacteristic
560C22C2×#6700211yescharacteristic
561C22#1062335511yescharacteristic
562C22#1062336711yescharacteristic
563C22#1062336911yescharacteristic
564C4—22no—
565C4—42no—
566C4—42no—
567C4—82no—
568C4—81no—
569C4—442no—
570C4—444no—
571C4#1062265914yes—
572C4#1062312911yescharacteristic
573C4#1062313011yescharacteristic
574C4#1062313711yescharacteristic
575C4#1062313911yescharacteristic
576C2—44no—
577C2—882no—
578C2#1307195711yescharacteristic
579C2C2×#1062265911yescharacteristic
580C2#1307792811yescharacteristic
581C2#1308048111yescharacteristic
582C2#1308094311yescharacteristic
583C2#1308096711yescharacteristic
584C2#1308119411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2538C2
socleC23×C11C22×D4
prime radicalC2×#10623086C2
hypercenter#2538D11
hypocenterC11#24120
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2538

Complements

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

NH ≅ G/Ntype
2. C2×#10622633C2semidirect
3. C2×C4×#4325C2semidirect
4. #13069805C2semidirect
5. #13069617C2semidirect
6. #13069576C2semidirect
7. #13069411C2semidirect
8. #13068924C2semidirect
9. #13068808C2semidirect
10. #13068613C2semidirect
11. C11×#2538C2semidirect
115. C2×Q8×C11#41semidirect
118. C2×D4×C11SD16semidirect
185. C2×C11⋊C8#41semidirect
189. #2538D11semidirect
410. C2×Q8#4341semidirect
422. C2×D4#4325semidirect
477. C11#24120semidirect

Maximal subgroups

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

subgroupindex
C2×#106230862
C2×#106226332
C2×C4×#43252
#130698052
#130696172
#130695762
#130694112
#130689242
#130688082
#130686132
C11×#25382
#2412011