Finite Group Databasebeta

← #14787739

Subgroups — #14787739

Order 2816.

1090 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623073C211yesmaximal, characteristic
2C2×#10622633C211yesmaximal, characteristic, complemented
3C2×C4×#4326C211yesmaximal, characteristic, complemented
4#13069812C212yesmaximal, complemented
5#13069624C212yesmaximal, complemented
6#13069576C211yesmaximal, characteristic, complemented
7#13069411C211yesmaximal, characteristic
8#13068929C212yesmaximal, complemented
9#13068813C212yesmaximal, complemented
10#13068618C211yesmaximal, characteristic, complemented
11C11×#2538C211yesmaximal, characteristic
12C2×C11×C22⋊Q8C2212yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C22×#4326C2211yescharacteristic
16C2×#66989—21no—
17C2×#66979C2212yes—
18C2×#66977C2212yes—
19#10623073—24no—
20#10623073—24no—
21C2×#66940—21no—
22C2×#66932—22no—
23C2×#66922C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
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×#4326—24no—
35#10622633—24no—
36C2×#66874C2211yescharacteristic
37C2×#66874C2212yes—
38C2×#66872C2212yes—
39C2×#66871C2211yescharacteristic
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×Dic22—21no—
49C22×Dic22C2311yescharacteristic
50C11×C22⋊Q8—24no—
51C11×C22⋊Q8—42no—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4D412yes—
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11—22no—
70C2×#4326—22no—
71C2×#4326—22no—
72C2×#4326—22no—
73#66989—28no—
74#66979—24no—
75#66979—24no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2312yes—
79#66977—24no—
80#66977—24no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—22no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11—22no—
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2312yes—
87C22×C11⋊C8C2311yescharacteristic
88#66940—28no—
89#66932—216no—
90#66922—22no—
91#66922D414yes—
92C4×Dic22—22no—
93C4×Dic22D414yes—
94C11×#95—22no—
95#66899—24no—
96#66899—22no—
97C22⋊(C11⋊C8)—24no—
98C22⋊(C11⋊C8)—42no—
99#66874—22no—
100#66874—42no—
101#66872—24no—
102#66871—22no—
103C4⋊(C11⋊C8)—22no—
104C4×C11⋊C8—22no—
105#24123—111nomaximal, Sylow
106C24×C11C2×D412yes—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11#4112yes—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—22no—
132C2×Dic22—24no—
133C2×Dic22—21no—
134C2×Dic22—21no—
135C2×Dic22—21no—
136C2×Dic22—21no—
137C2×Dic22—21no—
138C2×Dic22—42no—
139C2×Dic22—42no—
140C2×Dic22C2×D412yes—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—44no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4—81no—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—44no—
152C11×C22⋊C4—82no—
153C42×C11—42no—
154C42×C11C2×D412yes—
155C42×C11C2×D412yes—
156C22⋊Dic11—28no—
157C22⋊Dic11—28no—
158#4326—28no—
159C4⋊Dic11—24no—
160C4⋊Dic11—21no—
161C4⋊Dic11—22no—
162C4⋊Dic11C2×D412yes—
163C4⋊Dic11C2×D414yes—
164Dic11⋊C4—28no—
165Dic11⋊C4—24no—
166C4×Dic11—28no—
167C4×Dic11—24no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8#4112yes—
177C2×#556—111no—
178C2×#475—111no—
179C2×C4×Q16—111no—
180#2538D1111yescharacteristic
181#2035—112no—
182#2001—112no—
183#1990—111no—
184#1954—111no—
185#1873—112no—
186#1854—112no—
187#1803—111no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11C22×D411yescharacteristic
196Q8×C11—22no—
197Q8×C11—22no—
198Q8×C11—41no—
199Q8×C11—41no—
200D4×C11—44no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11#12012yes—
220C2×C4×C11#12012yes—
221C2×C4×C11#13512yes—
222C2×C4×C11#13712yes—
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11H(5,𝔽2)11yescharacteristic
228C2×C4×C112−1+411yescharacteristic
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—24no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238Dic22—22no—
239Dic22—22no—
240Dic22—41no—
241Dic22—41no—
242Dic22—48no—
243C11⋊C8—22no—
244C11⋊C8—41no—
245C11⋊C8—42no—
246C22×Q16—111no—
247#556—224no—
248#556—224no—
249C2×C4⋊Q8—111no—
250C2×#126—222no—
251C2×#124—221no—
252C2×C22⋊Q8—112no—
253C2×C22⋊Q8C2×D1112yes—
254C2×C4×Q8—111no—
255C2×C4×Q8—221no—
256C2×C4×Q8C2×D1111yescharacteristic
257C2×C4×D4C2×D1111yescharacteristic
258C2×#117—112no—
259#475—224no—
260C4×Q16—224no—
261C2×#107—111no—
262C2×#106—112no—
263C2×C4⋊C8—111no—
264C2×#103—112no—
265C2×#103—111no—
266C2×#103—111no—
267C2×#103—112no—
268C2×C22⋊C8—112no—
269C2×C22⋊C8—112no—
270C2×C4×C8—111no—
271#396—22no—
272#390—21no—
273#389—21no—
274#384C2×D1111yescharacteristic
275#380C2×D1112yes—
276#340—112no—
277#340—112no—
278#340—112no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11C2×#12011yescharacteristic
287C22×C11#54611yescharacteristic
288C22×C11#54711yescharacteristic
289C22×C11C2×#13511yescharacteristic
290C22×C11C2×#13711yescharacteristic
291C22×C11#57711yescharacteristic
292C22×C11#57811yescharacteristic
293C4×C11—22no—
294C4×C11—42no—
295C4×C11—42no—
296C4×C11—81no—
297C4×C11—82no—
298C4×C11#45214yes—
299C4×C11#52511yescharacteristic
300C4×C11#53711yescharacteristic
301C4×C11#54811yescharacteristic
302C4×C11#55011yescharacteristic
303Dic11—42no—
304Dic11—44no—
305Dic11—42no—
306C22×Q8—111no—
307C22×Q8—221no—
308C22×Q8C22×D1111yescharacteristic
309C22×D4C22⋊D1111yescharacteristic
310C23×C4C22×D1112yes—
311C2×Q16—222no—
312C2×Q16—222no—
313C2×Q16—222no—
314C22×C8—111no—
315C22×C8—111no—
316C22×C8—112no—
317C4⋊Q8—114no—
318C4⋊Q8—222no—
319#126—2216no—
320#124—228no—
321C22⋊Q8—24no—
322C22⋊Q8—42no—
323C22⋊Q8—224no—
324C22⋊Q8—224no—
325C4×Q8—22no—
326C4×Q8—22no—
327C4×Q8—114no—
328C4×Q8—228no—
329C4×Q8—222no—
330C4×D4—22no—
331C4×D4—22no—
332#117—224no—
333#117—224no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—111no—
339C2×C4⋊C4—112no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—222no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4C22⋊D1111yescharacteristic
344C2×C4⋊C4C22×D1111yescharacteristic
345C2×C4⋊C4C22×D1112yes—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—222no—
349C2×C22⋊C4—222no—
350C2×C22⋊C4C22⋊D1112yes—
351C2×C42—21no—
352C2×C42—222no—
353C2×C42—221no—
354C2×C42C22×D1111yescharacteristic
355#107—222no—
356#106—224no—
357C4⋊C8—222no—
358#103—222no—
359#103—222no—
360#103—224no—
361#103—442no—
362C22⋊C8—224no—
363C22⋊C8—442no—
364C4×C8—222no—
365#95—22no—
366C2×C11—82no—
367C2×C11#240711yescharacteristic
368C2×C11C2×#45211yescharacteristic
369C2×C11#301311yescharacteristic
370C2×C11#330411yescharacteristic
371C2×C11#332811yescharacteristic
372C2×C11#334211yescharacteristic
373C2×C11#335611yescharacteristic
374C24C2×C22⋊D1112yes—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—112no—
381C2×Q8—224no—
382C2×Q8—221no—
383C2×Q8—221no—
384C2×Q8—221no—
385C2×Q8—221no—
386C2×Q8—221no—
387C2×Q8—442no—
388C2×Q8—442no—
389C2×Q8#434112yes—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—221no—
403C22×C4—222no—
404C22×C4—221no—
405C22×C4C2×C22⋊D1112yes—
406C22×C4C2×C22⋊D1111yescharacteristic
407C22×C4C2×C22⋊D1111yescharacteristic
408C22×C4C23×D1111yescharacteristic
409Q16—228no—
410C2×C8—112no—
411C2×C8—221no—
412C2×C8—221no—
413C2×C8—221no—
414C2×C8—222no—
415C2×C8—221no—
416C2×C8—222no—
417C2×C8—222no—
418C2×C8—221no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—44no—
425C4⋊C4—42no—
426C4⋊C4—42no—
427C4⋊C4—81no—
428C4⋊C4—114no—
429C4⋊C4—112no—
430C4⋊C4—228no—
431C4⋊C4—224no—
432C4⋊C4—224no—
433C4⋊C4—221no—
434C4⋊C4—222no—
435C22⋊C4—24no—
436C22⋊C4—44no—
437C22⋊C4—82no—
438C22⋊C4—228no—
439C22⋊C4—228no—
440C42—42no—
441C42—228no—
442C42—224no—
443C42D4×D1112yes—
444C42D4×D1112yes—
445C11#2412311yescharacteristic, complemented, Sylow
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—22no—
452C23—22no—
453C23C22×C22⋊D1111yescharacteristic
454Q8—22no—
455Q8—22no—
456Q8—41no—
457Q8—41no—
458Q8—222no—
459Q8—222no—
460Q8—441no—
461Q8—441no—
462Q8—448no—
463D4—44no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—222no—
483C2×C4—224no—
484C2×C4—222no—
485C2×C4—441no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4—441no—
489C2×C4—441no—
490C2×C4—441no—
491C2×C4#6699012yes—
492C2×C4#6699012yes—
493C2×C4#6699512yes—
494C2×C4#6700312yes—
495C2×C4C2×D4×D1111yescharacteristic
496C2×C4C2×D4×D1111yescharacteristic
497C2×C4C2×#434111yescharacteristic
498C2×C4#6703711yescharacteristic
499C2×C4#41×D1111yescharacteristic
500C2×C4#6704311yescharacteristic
501C8—222no—
502C8—442no—
503C8—441no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22C2×#6699011yescharacteristic
512C22#1062333711yescharacteristic
513C22C2×#6699511yescharacteristic
514C22C2×#6700311yescharacteristic
515C22#1062335511yescharacteristic
516C22#1062336711yescharacteristic
517C22#1062336911yescharacteristic
518C4—22no—
519C4—42no—
520C4—42no—
521C4—81no—
522C4—82no—
523C4—444no—
524C4—442no—
525C4—442no—
526C4#1062266014yes—
527C4#1062312911yescharacteristic
528C4#1062313011yescharacteristic
529C4#1062313711yescharacteristic
530C4#1062313911yescharacteristic
531C2—82no—
532C2#1307195711yescharacteristic
533C2C2×#1062266011yescharacteristic
534C2#1307792811yescharacteristic
535C2#1308055511yescharacteristic
536C2#1308089911yescharacteristic
537C2#1308104211yescharacteristic
538C2#1308123111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2538C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2538D11
hypocenterC11#24123
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×#4326C2semidirect
4. #13069812C2semidirect
5. #13069624C2semidirect
6. #13069576C2semidirect
8. #13068929C2semidirect
9. #13068813C2semidirect
10. #13068618C2semidirect
445. C11#24123semidirect

Maximal subgroups

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

subgroupindex
C2×#106230732
C2×#106226332
C2×C4×#43262
#130698122
#130696242
#130695762
#130694112
#130689292
#130688132
#130686182
C11×#25382
#2412311