Finite Group Databasebeta

← #14787741

Subgroups — #14787741

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×#10622464C211yesmaximal, characteristic, complemented
3C2×C4×Dic44C211yesmaximal, characteristic, complemented
4#13073538C211yesmaximal, characteristic
5#13069813C212yesmaximal, complemented
6#13069626C212yesmaximal, complemented
7#13069577C211yesmaximal, characteristic, complemented
8#13068926C212yesmaximal, complemented
9#13068817C212yesmaximal, complemented
10#13068622C211yesmaximal, characteristic, complemented
11C11×#1954C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66989—21no—
14C2×#66979C2212yes—
15C2×#66977C2212yes—
16C2×#66977C2212yes—
17C22×Dic44C2211yescharacteristic
18#10623073—24no—
19#10623073—24no—
20C2×#66940—21no—
21C2×#66932—22no—
22C2×#66922C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2212yes—
27C2×C11×C22⋊C8C2212yes—
28C2×C4×C8×C11C2211yescharacteristic
29#10622834—21no—
30#10622825C2212yes—
31C2×#66882C2211yescharacteristic
32C2×#66881C2212yes—
33C2×#66880C2212yes—
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2212yes—
37#10622586—21no—
38#10622561—22no—
39#10622548C2211yescharacteristic
40#10622464—24no—
41C4×Dic44—24no—
42#10622189C2212yes—
43#10622189C2212yes—
44#10622189C2212yes—
45C22×D4×C11D411yescharacteristic
46C23×C4×C11C2312yes—
47C22×Dic22—21no—
48C22×Dic22C2311yescharacteristic
49C22×Dic22C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C22×C8×C11C2311yescharacteristic
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C22⋊C4D412yes—
57C2×C42×C11C2311yescharacteristic
58C2×C22⋊Dic11—22no—
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62#66989—28no—
63#66979—24no—
64#66979—24no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2312yes—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2312yes—
72#66977—24no—
73#66977—24no—
74#66977—24no—
75#66977—42no—
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—22no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11—22no—
82C2×C4×Dic11—21no—
83C2×Dic44—22no—
84C2×Dic44—22no—
85C2×Dic44—22no—
86#66940—28no—
87#66932—216no—
88#66922—22no—
89#66922D414yes—
90C4×Dic22—22no—
91C4×Dic22—22no—
92C4×Dic22—22no—
93C4×Dic22D414yes—
94C11×C4⋊C8—22no—
95C11×C22⋊C8—24no—
96C11×C22⋊C8—42no—
97C4×C8×C11—22no—
98C11⋊#95—22no—
99#66882—22no—
100#66881—24no—
101#66880—22no—
102#66880—24no—
103#66880—22no—
104#66880—42no—
105#24123—111nomaximal, Sylow
106C24×C11C2×D412yes—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2411yescharacteristic
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—22no—
124C22×Dic11—21no—
125C22×Dic11—22no—
126C2×Dic22—24no—
127C2×Dic22—21no—
128C2×Dic22—21no—
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—42no—
138C2×Dic22—42no—
139C2×Dic22C2×D412yes—
140C2×Dic22#4112yes—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—22no—
144C2×C8×C11—21no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11#4112yes—
150C11×C4⋊C4—22no—
151C11×C22⋊C4—24no—
152C42×C11C2×D412yes—
153C42×C11C2×D412yes—
154C22⋊Dic11—28no—
155C22⋊Dic11—28no—
156C22⋊Dic11—44no—
157C22⋊Dic11—82no—
158C4⋊Dic11—24no—
159C4⋊Dic11—21no—
160C4⋊Dic11—22no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165C4⋊Dic11—42no—
166C4⋊Dic11—81no—
167C4⋊Dic11C2×D414yes—
168C4⋊Dic11C2×D412yes—
169Dic11⋊C4—28no—
170Dic11⋊C4—24no—
171Dic11⋊C4—44no—
172Dic11⋊C4—42no—
173C4×Dic11—28no—
174C4×Dic11—24no—
175C4×Dic11—42no—
176Dic44—28no—
177C2×#556—111no—
178C2×#475—111no—
179C2×C4×Q16—111no—
180#2538—111no—
181#2035—112no—
182#2001—112no—
183#1990—111no—
184#1954D1111yescharacteristic
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
196D4×C11—44no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11#12012yes—
207C2×C4×C11#12012yes—
208C2×C4×C11#13512yes—
209C2×C4×C11#13712yes—
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11H(5,𝔽2)11yescharacteristic
215C2×C4×C112−1+411yescharacteristic
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—24no—
219C2×Dic11—22no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234Dic22—22no—
235Dic22—22no—
236Dic22—22no—
237Dic22—22no—
238Dic22—41no—
239Dic22—41no—
240Dic22—41no—
241Dic22—41no—
242Dic22—48no—
243C8×C11—22no—
244C8×C11—41no—
245C8×C11—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⋊Q8—112no—
254C2×C4×Q8—111no—
255C2×C4×Q8—111no—
256C2×C4×Q8—221no—
257C2×C4×D4C2×D1111yescharacteristic
258C2×#117—112no—
259#475—224no—
260C4×Q16—224no—
261C2×#107—111no—
262C2×#106—112no—
263C2×C4⋊C8C2×D1111yescharacteristic
264C2×#103—112no—
265C2×#103—111no—
266C2×#103—111no—
267C2×#103—112no—
268C2×C22⋊C8C2×D1112yes—
269C2×C22⋊C8C2×D1112yes—
270C2×C4×C8C2×D1111yescharacteristic
271#396—222no—
272#390—221no—
273#389—221no—
274#384—111no—
275#380—112no—
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#45214yes—
296C4×C11#52511yescharacteristic
297C4×C11#53711yescharacteristic
298C4×C11#54811yescharacteristic
299C4×C11#55011yescharacteristic
300Dic11—42no—
301Dic11—42no—
302Dic11—44no—
303Dic11—42no—
304Dic11—81no—
305Dic11—82no—
306C22×Q8—111no—
307C22×Q8—111no—
308C22×Q8—221no—
309C22×D4D4411yescharacteristic
310C23×C4C22×D1112yes—
311C2×Q16—222no—
312C2×Q16—222no—
313C2×Q16—222no—
314C22×C8C22×D1111yescharacteristic
315C22×C8C22×D1112yes—
316C22×C8C22×D1111yescharacteristic
317C4⋊Q8—114no—
318C4⋊Q8—222no—
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—22no—
331C4×D4—22no—
332#117—224no—
333#117—224no—
334C2×C4⋊C4—111no—
335C2×C4⋊C4—112no—
336C2×C4⋊C4—111no—
337C2×C4⋊C4—112no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4—222no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4—222no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4D4411yescharacteristic
346C2×C22⋊C4—222no—
347C2×C22⋊C4—222no—
348C2×C22⋊C4—222no—
349C2×C22⋊C4—222no—
350C2×C22⋊C4D4412yes—
351C2×C42—222no—
352C2×C42—221no—
353C2×C42—221no—
354C2×C42C22×D1111yescharacteristic
355#107—222no—
356#106—224no—
357C4⋊C8—22no—
358#103—222no—
359#103—224no—
360#103—222no—
361#103—442no—
362C22⋊C8—24no—
363C22⋊C8—42no—
364C4×C8—22no—
365#95—222no—
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×D4412yes—
375C2×Q8—112no—
376C2×Q8—112no—
377C2×Q8—224no—
378C2×Q8—221no—
379C2×Q8—221no—
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—442no—
389C2×Q8—442no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—221no—
400C22×C4—222no—
401C22×C4—221no—
402C22×C4—221no—
403C22×C4—221no—
404C22×C4—222no—
405C22×C4C2×D4412yes—
406C22×C4C2×D4411yescharacteristic
407C22×C4C2×D4411yescharacteristic
408C22×C4C23×D1111yescharacteristic
409Q16—228no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—21no—
416C2×C8—22no—
417C2×C8—21no—
418C2×C8#434112yes—
419C4⋊C4—22no—
420C4⋊C4—114no—
421C4⋊C4—112no—
422C4⋊C4—228no—
423C4⋊C4—224no—
424C4⋊C4—224no—
425C4⋊C4—221no—
426C4⋊C4—222no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—222no—
430C4⋊C4—222no—
431C4⋊C4—444no—
432C4⋊C4—442no—
433C4⋊C4—442no—
434C4⋊C4—881no—
435C22⋊C4—24no—
436C22⋊C4—228no—
437C22⋊C4—228no—
438C22⋊C4—444no—
439C22⋊C4—882no—
440C42—228no—
441C42—224no—
442C42—442no—
443C42D4×D1112yes—
444C42D4×D1112yes—
445C11#2412311yescharacteristic, complemented, Sylow
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—22no—
452C23—22no—
453C23C22×D4411yescharacteristic
454Q8—222no—
455Q8—222no—
456Q8—222no—
457Q8—222no—
458Q8—441no—
459Q8—441no—
460Q8—448no—
461Q8—441no—
462Q8—441no—
463D4—44no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—222no—
474C2×C4—224no—
475C2×C4—222no—
476C2×C4—222no—
477C2×C4—442no—
478C2×C4—441no—
479C2×C4—442no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4—442no—
486C2×C4—441no—
487C2×C4—441no—
488C2×C4—442no—
489C2×C4—441no—
490C2×C4—442no—
491C2×C4#6693512yes—
492C2×C4#6693512yes—
493C2×C4#6695712yes—
494C2×C4#6696212yes—
495C2×C4C2×D4×D1111yescharacteristic
496C2×C4C2×D4×D1111yescharacteristic
497C2×C4C2×#434111yescharacteristic
498C2×C4#6703711yescharacteristic
499C2×C4#41×D1111yescharacteristic
500C2×C4#6704311yescharacteristic
501C8—22no—
502C8—42no—
503C8—41no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22C2×#6693511yescharacteristic
512C22#1062308511yescharacteristic
513C22#1062308611yescharacteristic
514C22C2×#6695711yescharacteristic
515C22C2×#6696211yescharacteristic
516C22#1062328211yescharacteristic
517C22#1062328411yescharacteristic
518C4—22no—
519C4—42no—
520C4—444no—
521C4—442no—
522C4—442no—
523C4—442no—
524C4—881no—
525C4—882no—
526C4#1062234614yes—
527C4#1062313711yescharacteristic
528C4#1062313911yescharacteristic
529C4#1062320811yescharacteristic
530C4#1062324911yescharacteristic
531C2—82no—
532C2#1307195911yescharacteristic
533C2C2×#1062234611yescharacteristic
534C2#1307793411yescharacteristic
535C2#1308055611yescharacteristic
536C2#1308090011yescharacteristic
537C2#1308104711yescharacteristic
538C2#1308123211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1954C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#1954D11
hypocenterC11#24123
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. C2×#10622464C2semidirect
3. C2×C4×Dic44C2semidirect
5. #13069813C2semidirect
6. #13069626C2semidirect
7. #13069577C2semidirect
8. #13068926C2semidirect
9. #13068817C2semidirect
10. #13068622C2semidirect
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×#106224642
C2×C4×Dic442
#130735382
#130698132
#130696262
#130695772
#130689262
#130688172
#130686222
C11×#19542
#2412311