Finite Group Databasebeta

← #14787746

Subgroups — #14787746

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×#10623263C211yesmaximal, characteristic
2C2×#10622707C211yesmaximal, characteristic, complemented
3C2×C4×Dic44C211yesmaximal, characteristic, complemented
4#13073539C211yesmaximal, characteristic
5#13069815C212yesmaximal, complemented
6#13069627C212yesmaximal, complemented
7#13069410C211yesmaximal, characteristic
8#13068927C212yesmaximal, complemented
9#13068818C212yesmaximal, complemented
10#13068618C211yesmaximal, characteristic, complemented
11C11×#1990C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#67000—21no—
14C2×Q8×Dic11—21no—
15C22×Dic44C2211yescharacteristic
16#10623263—24no—
17#10623263—24no—
18C2×#66951—22no—
19C2×#66950C2212yes—
20C2×#66950C2212yes—
21C2×#66945C2212yes—
22C2×C4×D44C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#384C2211yescharacteristic
27C2×(C2×D11)⋊C8C2212yes—
28C2×(C2×D11)⋊C8C2212yes—
29C2×#66882C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32#10622707—24no—
33#10622607—22no—
34#10622601—21no—
35#10622600C2212yes—
36#10622598—21no—
37C2×#66874C2212yes—
38C2×#66874C2212yes—
39C2×#66872C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C4×Dic44—24no—
42C11×#340C2212yes—
43C11×#340C2212yes—
44#10622167C2212yes—
45C22×Q8×C11—21no—
46C22×D44D411yescharacteristic
47C22×C4×D11C2312yes—
48C22×Dic22C2311yescharacteristic
49C22×Dic22C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8D414yes—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2312yes—
59C2×C42×C11C2311yescharacteristic
60#67000—28no—
61Q8×Dic11—28no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4D412yes—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11D411yescharacteristic
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×Dic11⋊C4—21no—
73C2×Dic11⋊C4—21no—
74C2×C4×Dic11—21no—
75C2×C4×Dic11—22no—
76C2×C4×Dic11—21no—
77C22×C11⋊C8C2312yes—
78C2×Dic44—22no—
79C2×Dic44—22no—
80C2×Dic44—22no—
81#66951—216no—
82#66950—24no—
83#66950—24no—
84#66950—24no—
85#66950—42no—
86#66945—24no—
87#66945—24no—
88C4×D44—22no—
89C4×D44—22no—
90C4×Dic22—22no—
91C4×Dic22—22no—
92C4×Dic22—22no—
93C4×Dic22D414yes—
94C4×C8×C11—22no—
95C11⋊#95—22no—
96(C2×D11)⋊C8—24no—
97(C2×D11)⋊C8—42no—
98#66882—22no—
99#66880—22no—
100#66880—22no—
101#66874—24no—
102#66874—42no—
103#66872—24no—
104C4⋊(C11⋊C8)—22no—
105#24123—111nomaximal, Sylow
106C23×D11C2×D412yes—
107C2×Q8×C11—24no—
108C2×Q8×C11—42no—
109C2×Q8×C11—42no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C22×Dic11—21no—
116C22×Dic11—21no—
117C22×Dic11—21no—
118C22×Dic11—21no—
119C22×Dic11C2×D412yes—
120C2×D44—22no—
121C2×D44—22no—
122C2×D44—22no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×C4×D11—22no—
129C2×Dic22—21no—
130C2×Dic22—21no—
131C2×Dic22—21no—
132C2×Dic22—21no—
133C2×Dic22—21no—
134C2×Dic22—21no—
135C2×Dic22—21no—
136C2×Dic22—21no—
137C2×Dic22—21no—
138C2×Dic22—21no—
139C2×Dic22C2×D412yes—
140C2×Dic22#4112yes—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11#4112yes—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—81no—
153C11×C4⋊C4C2×D414yes—
154C42×C11C2×D412yes—
155C42×C11C2×D412yes—
156(C2×D11)⋊C4—28no—
157(C2×D11)⋊C4—28no—
158(C2×D11)⋊C4—24no—
159(C2×D11)⋊C4—44no—
160(C2×D11)⋊C4—82no—
161C4⋊Dic11—28no—
162C4⋊Dic11—22no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—44no—
167C4⋊Dic11C2×D412yes—
168Dic11⋊C4—24no—
169Dic11⋊C4—42no—
170C4×Dic11—28no—
171C4×Dic11—24no—
172C4×Dic11—42no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176Dic44—28no—
177C2×#556—111no—
178C2×#475—111no—
179C2×C4×Q16—111no—
180#2538—111no—
181#2035—112no—
182#2001—112no—
183#1990D1111yescharacteristic, complemented
184#1954—111no—
185#1873—112no—
186#1854—112no—
187#1803—111no—
188C23×C11C22×D411yescharacteristic
189C22×D11—22no—
190C22×D11—22no—
191C22×D11—22no—
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—22no—
196Q8×C11—48no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—24no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11#12012yes—
206C2×C4×C11#12012yes—
207C2×C4×C11#13512yes—
208C2×C4×C11#13712yes—
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11H(5,𝔽2)11yescharacteristic
214C2×C4×C112−1+411yescharacteristic
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230D44—44no—
231C4×D11—42no—
232C4×D11—42no—
233C4×D11—42no—
234C4×D11—42no—
235Dic22—22no—
236Dic22—22no—
237Dic22—22no—
238Dic22—22no—
239Dic22—41no—
240Dic22—41no—
241Dic22—41no—
242Dic22—41no—
243C8×C11—22no—
244C8×C11—41no—
245C11⋊C8—42no—
246C22×Q16—111no—
247#556—224no—
248#556—224no—
249C2×C4⋊Q8C2×D1111yescharacteristic
250C2×#126—222no—
251C2×#124—221no—
252C2×C22⋊Q8—112no—
253C2×C22⋊Q8—112no—
254C2×C4×Q8—111no—
255C2×C4×Q8—111no—
256C2×C4×Q8—221no—
257C2×C4×D4—111no—
258C2×#117—112no—
259#475—224no—
260C4×Q16—224no—
261C2×#107—111no—
262C2×#106—112no—
263C2×C4⋊C8—111no—
264C2×#103—111no—
265C2×#103—111no—
266C2×#103—112no—
267C2×#103—112no—
268C2×C22⋊C8—112no—
269C2×C22⋊C8—112no—
270C2×C4×C8C2×D1111yescharacteristic
271#396—222no—
272#390—221no—
273#389—221no—
274#384C2×D1111yescharacteristic
275#380—112no—
276#340—112no—
277#340C2×D1112yes—
278#340C2×D1112yes—
279C22×C11C2×#12011yescharacteristic
280C22×C11#54611yescharacteristic
281C22×C11#54711yescharacteristic
282C22×C11C2×#13511yescharacteristic
283C22×C11C2×#13711yescharacteristic
284C22×C11#57711yescharacteristic
285C22×C11#57811yescharacteristic
286C2×D11—42no—
287C2×D11—42no—
288C2×D11—42no—
289C2×D11—42no—
290C2×D11—42no—
291C2×D11—42no—
292C2×D11—42no—
293C4×C11—22no—
294C4×C11—44no—
295C4×C11—82no—
296C4×C11#45214yes—
297C4×C11#52511yescharacteristic
298C4×C11#53711yescharacteristic
299C4×C11#54811yescharacteristic
300C4×C11#55011yescharacteristic
301Dic11—42no—
302Dic11—42no—
303Dic11—42no—
304Dic11—42no—
305Dic11—81no—
306C22×Q8—21no—
307C22×Q8—111no—
308C22×Q8—111no—
309C22×D4—111no—
310C23×C4—112no—
311C2×Q16—222no—
312C2×Q16—222no—
313C2×Q16—222no—
314C22×C8—112no—
315C22×C8C22×D1111yescharacteristic
316C22×C8C22×D1111yescharacteristic
317C4⋊Q8—22no—
318C4⋊Q8D4414yes—
319#126—2216no—
320#124—228no—
321C22⋊Q8—224no—
322C22⋊Q8—224no—
323C22⋊Q8—224no—
324C22⋊Q8—442no—
325C4×Q8—114no—
326C4×Q8—228no—
327C4×Q8—222no—
328C4×Q8—222no—
329C4×Q8—222no—
330C4×D4—222no—
331C4×D4—222no—
332#117—224no—
333#117—224no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—111no—
338C2×C4⋊C4—111no—
339C2×C4⋊C4—111no—
340C2×C4⋊C4—222no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4—222no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4C22×D1112yes—
345C2×C4⋊C4C22×D1112yes—
346C2×C22⋊C4—112no—
347C2×C22⋊C4—222no—
348C2×C22⋊C4—222no—
349C2×C22⋊C4—222no—
350C2×C22⋊C4—222no—
351C2×C42—222no—
352C2×C42—221no—
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—22no—
365#95—222no—
366C2×C11#240711yescharacteristic
367C2×C11C2×#45211yescharacteristic
368C2×C11#301311yescharacteristic
369C2×C11#330411yescharacteristic
370C2×C11#332811yescharacteristic
371C2×C11#334211yescharacteristic
372C2×C11#335611yescharacteristic
373D11—82no—
374C24—112no—
375C2×Q8—24no—
376C2×Q8—42no—
377C2×Q8—42no—
378C2×Q8—112no—
379C2×Q8—112no—
380C2×Q8—221no—
381C2×Q8—221no—
382C2×Q8—221no—
383C2×Q8—221no—
384C2×Q8—221no—
385C2×Q8—221no—
386C2×Q8—221no—
387C2×Q8—221no—
388C2×Q8—221no—
389C2×Q8—221no—
390C2×D4—222no—
391C2×D4—222no—
392C2×D4—222no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—112no—
396C22×C4—221no—
397C22×C4—221no—
398C22×C4—221no—
399C22×C4—222no—
400C22×C4—222no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4—222no—
405C22×C4—221no—
406C22×C4D4×D1111yescharacteristic
407C22×C4D4×D1111yescharacteristic
408C22×C4C23×D1111yescharacteristic
409Q16—228no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—21no—
415C2×C8—222no—
416C2×C8—222no—
417C2×C8—222no—
418C2×C8#434312yes—
419C4⋊C4—24no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—42no—
424C4⋊C4—81no—
425C4⋊C4—112no—
426C4⋊C4—228no—
427C4⋊C4—222no—
428C4⋊C4—224no—
429C4⋊C4—221no—
430C4⋊C4—221no—
431C4⋊C4—221no—
432C4⋊C4—444no—
433C4⋊C4—442no—
434C4⋊C4C2×D4414yes—
435C22⋊C4—228no—
436C22⋊C4—228no—
437C22⋊C4—224no—
438C22⋊C4—444no—
439C22⋊C4—882no—
440C42—228no—
441C42—224no—
442C42—442no—
443C42C2×D4412yes—
444C42D4×D1112yes—
445C11#2412311yescharacteristic, complemented, Sylow
446C23—222no—
447C23—222no—
448C23—222no—
449C23—222no—
450C23—222no—
451C23—222no—
452C23—222no—
453C23C2×D4×D1111yescharacteristic
454Q8—48no—
455Q8—222no—
456Q8—222no—
457Q8—222no—
458Q8—222no—
459Q8—441no—
460Q8—441no—
461Q8—441no—
462Q8—441no—
463D4—444no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—24no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—222no—
476C2×C4—222no—
477C2×C4—222no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4—441no—
489C2×C4—441no—
490C2×C4—441no—
491C2×C4#6693512yes—
492C2×C4#6693512yes—
493C2×C4#6696512yes—
494C2×C4#6696812yes—
495C2×C4C22×D4411yescharacteristic
496C2×C4C2×D4×D1111yescharacteristic
497C2×C4C2×#434311yescharacteristic
498C2×C4#6704011yescharacteristic
499C2×C4#41×D1111yescharacteristic
500C2×C4#6704211yescharacteristic
501C8—22no—
502C8—41no—
503C8—442no—
504C22—442no—
505C22—442no—
506C22—442no—
507C22—442no—
508C22—442no—
509C22—442no—
510C22—442no—
511C22C2×#6693511yescharacteristic
512C22#1062320711yescharacteristic
513C22#1062325711yescharacteristic
514C22C2×#6696511yescharacteristic
515C22C2×#6696811yescharacteristic
516C22#1062329311yescharacteristic
517C22#1062329711yescharacteristic
518C4—22no—
519C4—44no—
520C4—82no—
521C4—442no—
522C4—442no—
523C4—442no—
524C4—442no—
525C4—881no—
526C4#1062239614yes—
527C4#1062310711yescharacteristic
528C4#1062310811yescharacteristic
529C4#1062315811yescharacteristic
530C4#1062316011yescharacteristic
531C2—882no—
532C2#1307196411yescharacteristic
533C2C2×#1062239611yescharacteristic
534C2#1307793611yescharacteristic
535C2#1308055411yescharacteristic
536C2#1308089811yescharacteristic
537C2#1308104611yescharacteristic
538C2#1308123011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenter#1990D11
hypocenterC11#24123
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
2. C2×#10622707C2semidirect
3. C2×C4×Dic44C2semidirect
5. #13069815C2semidirect
6. #13069627C2semidirect
8. #13068927C2semidirect
9. #13068818C2semidirect
10. #13068618C2semidirect
11. C11×#1990C2semidirect
183. #1990D11semidirect
445. C11#24123semidirect

Maximal subgroups

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

subgroupindex
C2×#106232632
C2×#106227072
C2×C4×Dic442
#130735392
#130698152
#130696272
#130694102
#130689272
#130688182
#130686182
C11×#19902
#2412311