Finite Group Databasebeta

← #14796450

Subgroups — #14796450

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622620C211yesmaximal, characteristic
2#13073828C211yesmaximal, characteristic, complemented
3D4×C4⋊Dic11C211yesmaximal, characteristic
4#13070101C212yesmaximal, complemented
5#13070007C212yesmaximal, complemented
6#13069577C211yesmaximal, characteristic, complemented
7#13069334C211yesmaximal, characteristic, complemented
8#13068952C212yesmaximal
9#13068624C212yesmaximal
10#13068621C211yesmaximal, characteristic, complemented
11C2×C4×C11×SD16C211yesmaximal, characteristic
12C22×C11×SD16C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×D4×Dic11C2212yes—
16C22×C4⋊Dic11—21no—
17C2×#66922C2211yescharacteristic
18C4×C11×SD16—24no—
19C2×C11×#106C2211yescharacteristic
20C2×C11×#103C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23#10622843C2212yes—
24C2×#66899C2212yes—
25C2×#66896C2212yes—
26#10622825—21no—
27C2×Dic11⋊C8C2212yes—
28#10622620—24no—
29#10622599—22no—
30#10622598C2212yes—
31#10622590C2212yes—
32C2×#66871C2212yes—
33#10622563—22no—
34#10622548C2211yescharacteristic
35C4×C4⋊Dic11C2211yescharacteristic
36#10622542—21no—
37#10622542—21no—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622189C2212yes—
40#10622189C2212yes—
41#10622188C2212yes—
42#10622167C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C23×Dic11—22no—
47C22×Dic22—21no—
48C2×C11×SD16—22no—
49C2×C11×SD16—22no—
50C2×C11×SD16Q814yescomplemented
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C4×Q8×C11—22no—
54C4×Q8×C11—22no—
55C4×D4×C11—22no—
56C4×D4×C11D414yes—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11—22no—
64D4×Dic11—24no—
65D4×Dic11—42no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—44no—
71C2×C4⋊Dic11D411yescharacteristic
72C2×C4⋊Dic11D411yescharacteristic
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2312yes—
75C2×C4×Dic11C2312yes—
76C22×C11⋊C8C2312yes—
77#66922—22no—
78#66922—22no—
79C11×#106—22no—
80C11×#103—22no—
81C11×#102—22no—
82C4×C8×C11—22no—
83#66899—42no—
84#66896—24no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C11⋊#95D412yes—
91Dic11⋊C8—42no—
92#66871—24no—
93C4⋊(C11⋊C8)—22no—
94#24816—111nomaximal, Sylow
95C24×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11C2×Q812yes—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11C2×D412yes—
106C2×D4×C11C2×Q812yes—
107C2×D4×C11#4112yes—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—24no—
111C22×C4×C11—21no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2411yescharacteristic
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—44no—
120C22×Dic11—44no—
121C22×Dic11—82no—
122C22×Dic11C2×D412yes—
123C22×Dic11C2×D412yes—
124C2×Dic22—42no—
125C2×Dic22—42no—
126C2×Dic22—42no—
127C11×SD16—28no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11C2×Q812yes—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4C2×D412yes—
139C11×C22⋊C4—24no—
140C42×C11—42no—
141C42×C11C2×D412yes—
142C42×C11#4112yes—
143C22⋊Dic11—44no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—44no—
151C4⋊Dic11—42no—
152C4⋊Dic11—42no—
153C4⋊Dic11—81no—
154C4×Dic11—22no—
155C4×Dic11—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×#474—111no—
160C2×C4×SD16D1111yescharacteristic
161#2568—111no—
162D4×C4⋊C4—111no—
163#2085—112no—
164#2068—112no—
165#1990—111no—
166#1939—111no—
167#1877—112no—
168#1804—112no—
169#1803—111no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11C22×D411yescharacteristic
178Q8×C11—22no—
179Q8×C11—22no—
180Q8×C11—41no—
181Q8×C11—41no—
182D4×C11—22no—
183D4×C11—22no—
184D4×C11—22no—
185D4×C11C22⋊Q814yes—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—48no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11#12112yes—
199C2×C4×C11#12112yes—
200C2×C4×C11#13512yes—
201C2×C4×C11AGL(1,ℤ/8)12yes—
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C22×Q811yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11H(5,𝔽2)11yescharacteristic
207C2×C4×C112−1+411yescharacteristic
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—88no—
221Dic22—84no—
222C8×C11—22no—
223C8×C11—41no—
224C11⋊C8—42no—
225C22×SD16C2×D1111yescharacteristic
226C2×C4⋊Q8—111no—
227C2×C4×Q8C2×D1111yescharacteristic
228C2×C4×D4—112no—
229C2×C4×D4C2×D1111yescharacteristic
230C22×C4⋊C4—221no—
231#474—224no—
232C4×SD16—24no—
233C2×#107—112no—
234C2×#106C2×D1111yescharacteristic
235C2×C4⋊C8—111no—
236C2×C4⋊C8—112no—
237C2×#103—112no—
238C2×#103C2×D1111yescharacteristic
239C2×#102—112no—
240C2×#102C2×D1111yescharacteristic
241C2×C4×C8C2×D1111yescharacteristic
242#400—222no—
243#391—112no—
244#391—221no—
245#391—221no—
246#389—112no—
247#385—222no—
248#384—111no—
249#382—112no—
250#380—221no—
251C4×C4⋊C4—111no—
252#340—112no—
253#340—112no—
254#340—112no—
255#336—112no—
256C22×C11—24no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11C2×#12111yescharacteristic
264C22×C11#54611yescharacteristic
265C22×C11D4×Q811yescharacteristic
266C22×C11C2×#13511yescharacteristic
267C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
268C22×C11#57711yescharacteristic
269C22×C11#57811yescharacteristic
270C4×C11—22no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—81no—
274C4×C11#46314yes—
275C4×C11C2×C22⋊Q811yescharacteristic
276C4×C11#53711yescharacteristic
277C4×C11#55211yescharacteristic
278C4×C11#55411yescharacteristic
279Dic11—42no—
280Dic11—42no—
281Dic11—82no—
282Dic11—82no—
283C22×Q8—221no—
284C22×Q8C22×D1111yescharacteristic
285C22×D4C22×D1111yescharacteristic
286C23×C4—21no—
287C23×C4—222no—
288C2×SD16—22no—
289C2×SD16—22no—
290C2×SD16Dic2214yescomplemented
291C22×C8—112no—
292C22×C8C22×D1111yescharacteristic
293C22×C8C22×D1111yescharacteristic
294C4⋊Q8—222no—
295C4⋊Q8—222no—
296C4×Q8—22no—
297C4×Q8—22no—
298C4×D4—22no—
299C4×D4—224no—
300C4×D4—442no—
301C4×D4C22⋊D1114yes—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—111no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—112no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—444no—
312C2×C4⋊C4C22×D1111yescharacteristic
313C2×C4⋊C4C22×D1111yescharacteristic
314C2×C22⋊C4—21no—
315C2×C22⋊C4—222no—
316C2×C42—21no—
317C2×C42—112no—
318C2×C42C22×D1111yescharacteristic
319#107—224no—
320#106—22no—
321C4⋊C8—222no—
322C4⋊C8—442no—
323#103—22no—
324#103—442no—
325#102—22no—
326#102—224no—
327C4×C8—22no—
328#95—112no—
329#95—222no—
330#95—222no—
331#95—222no—
332#95—222no—
333#95—222no—
334C2×C11—44no—
335C2×C11#241711yescharacteristic
336C2×C11C2×#46311yescharacteristic
337C2×C11#304611yescharacteristic
338C2×C11#330211yescharacteristic
339C2×C11#332411yescharacteristic
340C2×C11#338111yescharacteristic
341C2×C11#338611yescharacteristic
342C24—21no—
343C2×Q8—21no—
344C2×Q8—21no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—442no—
349C2×Q8—442no—
350C2×Q8—442no—
351C2×Q8C2×Dic2212yes—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4C2×Dic2212yes—
356C2×D4#433912yes—
357C2×D4C2×C22⋊D1112yes—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—24no—
361C22×C4—21no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—112no—
365C22×C4—112no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—444no—
369C22×C4—444no—
370C22×C4—882no—
371C22×C4D4×D1111yescharacteristic
372C22×C4D4×D1111yescharacteristic
373C22×C4C23×D1111yescharacteristic
374SD16—28no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—222no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8C2×Dic2212yes—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—42no—
388C4⋊C4—222no—
389C4⋊C4—222no—
390C4⋊C4—222no—
391C4⋊C4—222no—
392C4⋊C4—222no—
393C4⋊C4—222no—
394C4⋊C4—444no—
395C4⋊C4—442no—
396C4⋊C4—442no—
397C4⋊C4—881no—
398C4⋊C4C2×C22⋊D1112yes—
399C22⋊C4—24no—
400C22⋊C4—444no—
401C42—42no—
402C42—222no—
403C42—222no—
404C42#434112yes—
405C42C2×C22⋊D1112yes—
406C11#2481611yescharacteristic, complemented, Sylow
407C23—22no—
408C23—22no—
409C23—22no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23C2×D4×D1111yescharacteristic
415Q8—22no—
416Q8—22no—
417Q8—41no—
418Q8—41no—
419Q8—884no—
420D4—22no—
421D4—22no—
422D4—22no—
423D4#6697714yes—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—48no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—222no—
437C2×C4—222no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—888no—
449C2×C4#6696712yes—
450C2×C4#6696912yes—
451C2×C4#6699212yes—
452C2×C4#6699212yes—
453C2×C4C22×Dic2211yescharacteristic
454C2×C4C2×#433911yescharacteristic
455C2×C4C2×#434111yescharacteristic
456C2×C4#6704211yescharacteristic
457C2×C4#6704311yescharacteristic
458C2×C4C22×C22⋊D1111yescharacteristic
459C8—22no—
460C8—41no—
461C8—442no—
462C22—24no—
463C22—42no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22D4×Dic2211yescharacteristic
470C22#1062308111yescharacteristic
471C22C2×#6696711yescharacteristic
472C22C2×#6696911yescharacteristic
473C22#1062330111yescharacteristic
474C22#1062330211yescharacteristic
475C22C2×#6699211yescharacteristic
476C4—22no—
477C4—42no—
478C4—42no—
479C4—81no—
480C4—442no—
481C4—442no—
482C4—882no—
483C4—882no—
484C4#1062277814yes—
485C4#1062307211yescharacteristic
486C4#1062307411yescharacteristic
487C4C2×#6697711yescharacteristic
488C4#1062336411yescharacteristic
489C2—44no—
490C2#1307206711yescharacteristic
491C2C2×#1062277811yescharacteristic
492C2#1307816411yescharacteristic
493C2#1308053511yescharacteristic
494C2#1308084911yescharacteristic
495C2#1308148911yescharacteristic
496C2#1308153511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×C4×SD16D11
hypocenterC11#24816
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. #13073828C2semidirect
4. #13070101C2semidirect
5. #13070007C2semidirect
6. #13069577C2semidirect
7. #13069334C2semidirect
10. #13068621C2semidirect
50. C2×C11×SD16Q8semidirect
290. C2×SD16Dic22semidirect
406. C11#24816semidirect

Maximal subgroups

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

subgroupindex
C2×#106226202
#130738282
D4×C4⋊Dic112
#130701012
#130700072
#130695772
#130693342
#130689522
#130686242
#130686212
C2×C4×C11×SD162
#2481611