Finite Group Databasebeta

← #14788567

Subgroups — #14788567

Order 2816.

1082 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic
2C2×#10622644C211yesmaximal, characteristic, complemented
3C2×C4×#4325C211yesmaximal, characteristic
4#13069857C212yesmaximal
5#13069709C212yesmaximal
6#13069553C211yesmaximal, characteristic, complemented
7#13069417C211yesmaximal, characteristic, complemented
8#13068960C212yesmaximal, complemented
9#13068883C212yesmaximal, complemented
10#13068613C211yesmaximal, characteristic
11C11×#2582C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×#66999—21no—
15C22×#4326C2212yes—
16C22×#4325C2211yescharacteristic
17#10623115—24no—
18#10623115—24no—
19C2×#66951—22no—
20C2×#66945—21no—
21C2×#66928C2212yes—
22C2×C4×D44C2211yescharacteristic
23C2×#66922C2211yescharacteristic
24C2×C4×Dic22C2212yes—
25C11×#398—22no—
26C11×#391—21no—
27C11×#391C2212yes—
28C11×#389—21no—
29C11×#389C2212yes—
30C11×#384C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622644—24no—
33C4×#4325—24no—
34C2×#66874C2212yes—
35C2×#66874C2212yes—
36C2×#66874C2212yes—
37C2×#66873C2211yescharacteristic
38C2×#66873C2212yes—
39C2×#66872C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C22×Dic22C2312yes—
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4D412yes—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2312yes—
62C2×C42×C11—21no—
63C2×C42×C11C2312yes—
64C2×C42×C11C2311yescharacteristic
65#66999—28no—
66C2×#4326—24no—
67C2×#4326—24no—
68C2×#4326—42no—
69C2×#4325—22no—
70C2×#4325—22no—
71C2×#4325—22no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×Dic11⋊C4—22no—
79C2×C4×Dic11—22no—
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2312yes—
82C22×C11⋊C8C2311yescharacteristic
83#66951—216no—
84#66945—28no—
85#66928—24no—
86#66928—24no—
87C4×D44—22no—
88C4×D44D414yes—
89#66922—22no—
90#66922D414yes—
91C4×Dic22—24no—
92C4×Dic22—24no—
93C11×#95—22no—
94C11×#95—22no—
95C11×#95—22no—
96#66899—22no—
97#66874—24no—
98#66874—24no—
99#66874—42no—
100#66873—22no—
101#66873—42no—
102#66872—22no—
103C4⋊(C11⋊C8)—22no—
104C4×C11⋊C8—22no—
105#24189—111nomaximal, Sylow
106C23×D11—21no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11#4112yes—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C22×Dic11—21no—
125C22×Dic11—22no—
126C2×D44—21no—
127C2×D44—21no—
128C2×D44—21no—
129C2×D44—21no—
130C2×D44—21no—
131C2×D44C2×D412yes—
132C2×C4×D11—24no—
133C2×C4×D11—42no—
134C2×C4×D11—42no—
135C2×Dic22—22no—
136C2×Dic22—22no—
137C2×Dic22—22no—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C2×Dic22C2×D414yes—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4—81no—
150C11×C4⋊C4—82no—
151C42×C11—22no—
152C42×C11—22no—
153C42×C11—42no—
154C42×C11C2×D412yes—
155C42×C11C2×D412yes—
156#4326—48no—
157#4325—28no—
158(C2×D11)⋊C4—28no—
159(C2×D11)⋊C4—28no—
160(C2×D11)⋊C4—24no—
161C4⋊Dic11—24no—
162C4⋊Dic11—24no—
163C4⋊Dic11—21no—
164C4⋊Dic11C2×D412yes—
165Dic11⋊C4—28no—
166C4×Dic11—28no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8#4112yes—
176C2×#556—111no—
177C2×#462—111no—
178C2×C4×SD16—111no—
179#2582D1111yescharacteristic, complemented
180#2042—112no—
181#2015—112no—
182#1984—111no—
183#1956—111no—
184#1878—112no—
185#1865—112no—
186#1802—111no—
187C23×C11C22×D411yescharacteristic
188C22×D11—22no—
189C22×D11—41no—
190C22×D11—41no—
191C22×D11—41no—
192C22×D11—41no—
193C22×D11—41no—
194C22×D11—41no—
195Q8×C11—22no—
196Q8×C11—22no—
197Q8×C11—41no—
198Q8×C11—41no—
199Q8×C11—44no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11#12012yes—
218C2×C4×C11#12012yes—
219C2×C4×C11#13512yes—
220C2×C4×C11#13712yes—
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11H(5,𝔽2)11yescharacteristic
226C2×C4×C112−1+411yescharacteristic
227C2×Dic11—22no—
228C2×Dic11—24no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233D44—22no—
234D44—22no—
235D44—41no—
236D44—41no—
237C4×D11—48no—
238Dic22—24no—
239Dic22—24no—
240Dic22—42no—
241Dic22—42no—
242C11⋊C8—22no—
243C11⋊C8—41no—
244C11⋊C8—42no—
245C22×Q16—112no—
246C22×SD16—111no—
247#556—224no—
248#556—224no—
249C2×C4⋊Q8—111no—
250C2×#126—222no—
251C2×#124—112no—
252C2×C22⋊Q8—221no—
253C2×C4×Q8—112no—
254C2×C4×Q8C2×D1111yescharacteristic
255C2×C4×Q8C2×D1111yescharacteristic
256C2×C4×D4—111no—
257C2×#117—221no—
258#462—224no—
259C4×SD16—224no—
260C2×#106—111no—
261C2×C4⋊C8—111no—
262C2×#103—111no—
263C2×#103—112no—
264C2×#103—112no—
265C2×#103—112no—
266C2×#102—111no—
267C2×#102—112no—
268C2×C4×C8—111no—
269#398—22no—
270#391—21no—
271#391C2×D1112yes—
272#389—21no—
273#389C2×D1112yes—
274#384C2×D1111yescharacteristic
275#340—112no—
276#336—112no—
277#336—112no—
278C22×C11C2×#12011yescharacteristic
279C22×C11#54811yescharacteristic
280C22×C11#55011yescharacteristic
281C22×C11C2×#13511yescharacteristic
282C22×C11C2×#13711yescharacteristic
283C22×C11#57711yescharacteristic
284C22×C11#57811yescharacteristic
285C2×D11—42no—
286C2×D11—42no—
287C2×D11—42no—
288C2×D11—81no—
289C2×D11—81no—
290C2×D11—81no—
291C2×D11—81no—
292C4×C11—22no—
293C4×C11—42no—
294C4×C11—42no—
295C4×C11—42no—
296C4×C11—82no—
297C4×C11—81no—
298C4×C11#45214yes—
299C4×C11#52511yescharacteristic
300C4×C11#53711yescharacteristic
301C4×C11#54611yescharacteristic
302C4×C11#54711yescharacteristic
303Dic11—44no—
304Dic11—42no—
305C22×Q8—112no—
306C22×Q8C22⋊D1111yescharacteristic
307C22×Q8C22×D1111yescharacteristic
308C22×D4—111no—
309C23×C4—221no—
310C2×Q16—224no—
311C2×Q16—224no—
312C2×Q16—442no—
313C2×SD16—222no—
314C2×SD16—222no—
315C2×SD16—222no—
316C22×C8—111no—
317C22×C8—112no—
318C22×C8—111no—
319C4⋊Q8—114no—
320C4⋊Q8—222no—
321#126—2216no—
322#124—224no—
323#124—224no—
324C22⋊Q8—228no—
325C4×Q8—22no—
326C4×Q8—22no—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×Q8—224no—
330C4×Q8—224no—
331C4×D4—114no—
332C4×D4—222no—
333#117—228no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—111no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4—222no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4C22⋊D1111yescharacteristic
343C2×C4⋊C4C22⋊D1112yes—
344C2×C4⋊C4C22×D1111yescharacteristic
345C2×C4⋊C4C22×D1112yes—
346C2×C22⋊C4—222no—
347C2×C22⋊C4—221no—
348C2×C22⋊C4—222no—
349C2×C42—21no—
350C2×C42—222no—
351C2×C42C22×D1112yes—
352C2×C42C22×D1111yescharacteristic
353#106—222no—
354C4⋊C8—222no—
355#103—224no—
356#103—224no—
357#103—222no—
358#103—442no—
359#102—222no—
360#102—442no—
361C4×C8—222no—
362#95—22no—
363#95—22no—
364#95—22no—
365C2×C11#240711yescharacteristic
366C2×C11C2×#45211yescharacteristic
367C2×C11#301311yescharacteristic
368C2×C11#336411yescharacteristic
369C2×C11#336911yescharacteristic
370C2×C11#339411yescharacteristic
371C2×C11#339811yescharacteristic
372D11—82no—
373C24—221no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—114no—
383C2×Q8—222no—
384C2×Q8—222no—
385C2×Q8—222no—
386C2×Q8—222no—
387C2×Q8—222no—
388C2×Q8#434312yes—
389C2×D4—112no—
390C2×D4—221no—
391C2×D4—221no—
392C2×D4—221no—
393C2×D4—221no—
394C2×D4—221no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—221no—
399C22×C4—222no—
400C22×C4—224no—
401C22×C4—442no—
402C22×C4—442no—
403C22×C4C2×C22⋊D1112yes—
404C22×C4C2×C22⋊D1112yes—
405C22×C4C2×C22⋊D1111yescharacteristic
406C22×C4C2×C22⋊D1111yescharacteristic
407C22×C4C23×D1111yescharacteristic
408Q16—448no—
409SD16—228no—
410C2×C8—112no—
411C2×C8—221no—
412C2×C8—221no—
413C2×C8—221no—
414C2×C8—222no—
415C2×C8—222no—
416C2×C8—221no—
417C2×C8—222no—
418C2×C8—221no—
419C4⋊C4—22no—
420C4⋊C4—24no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—42no—
426C4⋊C4—42no—
427C4⋊C4—81no—
428C4⋊C4—82no—
429C4⋊C4—112no—
430C4⋊C4—228no—
431C4⋊C4—224no—
432C4⋊C4—224no—
433C4⋊C4—221no—
434C22⋊C4—228no—
435C22⋊C4—228no—
436C22⋊C4—224no—
437C42—22no—
438C42—22no—
439C42—42no—
440C42—228no—
441C42D4×D1112yes—
442C42D4×D1112yes—
443C11#2418911yescharacteristic, complemented, Sylow
444C23—222no—
445C23—441no—
446C23—441no—
447C23—441no—
448C23—441no—
449C23—441no—
450C23—441no—
451C23C22×C22⋊D1111yescharacteristic
452Q8—22no—
453Q8—22no—
454Q8—41no—
455Q8—41no—
456Q8—44no—
457Q8—224no—
458Q8—224no—
459Q8—442no—
460Q8—442no—
461D4—222no—
462D4—222no—
463D4—441no—
464D4—441no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—222no—
483C2×C4—224no—
484C2×C4—441no—
485C2×C4—442no—
486C2×C4—441no—
487C2×C4—442no—
488C2×C4—448no—
489C2×C4#6699012yes—
490C2×C4#6699012yes—
491C2×C4#6699512yes—
492C2×C4#6700312yes—
493C2×C4C2×D4×D1111yescharacteristic
494C2×C4C2×D4×D1111yescharacteristic
495C2×C4C2×#434311yescharacteristic
496C2×C4#6704011yescharacteristic
497C2×C4#41×D1111yescharacteristic
498C2×C4#6704211yescharacteristic
499C8—222no—
500C8—441no—
501C8—442no—
502C22—442no—
503C22—442no—
504C22—442no—
505C22—881no—
506C22—881no—
507C22—881no—
508C22—881no—
509C22C2×#6699011yescharacteristic
510C22C2×#6699511yescharacteristic
511C22#1062334811yescharacteristic
512C22C2×#6700311yescharacteristic
513C22#1062336511yescharacteristic
514C22#1062336711yescharacteristic
515C22#1062336911yescharacteristic
516C4—22no—
517C4—42no—
518C4—42no—
519C4—42no—
520C4—82no—
521C4—81no—
522C4—442no—
523C4—444no—
524C4#1062266014yes—
525C4#1062315811yescharacteristic
526C4#1062316011yescharacteristic
527C4#1062316111yescharacteristic
528C4#1062316211yescharacteristic
529C2—882no—
530C2#1307196311yescharacteristic
531C2C2×#1062266011yescharacteristic
532C2#1307792811yescharacteristic
533C2#1308130111yescharacteristic
534C2#1308135611yescharacteristic
535C2#1308160811yescharacteristic
536C2#1308164311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2582C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2582D11
hypocenterC11#24189
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2582

Complements

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

NH ≅ G/Ntype
2. C2×#10622644C2semidirect
6. #13069553C2semidirect
7. #13069417C2semidirect
8. #13068960C2semidirect
9. #13068883C2semidirect
11. C11×#2582C2semidirect
179. #2582D11semidirect
443. C11#24189semidirect

Maximal subgroups

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

subgroupindex
C2×#106231152
C2×#106226442
C2×C4×#43252
#130698572
#130697092
#130695532
#130694172
#130689602
#130688832
#130686132
C11×#25822
#2418911