Finite Group Databasebeta

← #14796417

Subgroups — #14796417

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622633C211yesmaximal, characteristic, complemented
2#13073569C211yesmaximal, characteristic
3Q8×C4⋊Dic11C211yesmaximal, characteristic, complemented
4#13070095C212yesmaximal, complemented
5#13069986C212yesmaximal
6#13069577C211yesmaximal, characteristic, complemented
7#13069334C211yesmaximal, characteristic, complemented
8#13068973C212yesmaximal
9#13068619C212yesmaximal, complemented
10#13068616C211yesmaximal, characteristic
11C2×C4×C11×SD16C211yesmaximal, characteristic
12C22×C11×SD16C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×Q8×Dic11C2212yes—
16C2×#66977—21no—
17C2×#66977—21no—
18C2×#66922C2211yescharacteristic
19C4×C11×SD16—24no—
20C2×C11×#106C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C2×#66899C2212yes—
25#10622834C2212yes—
26C2×#66896C2212yes—
27C2×Dic11⋊C8C2212yes—
28#10622633—24no—
29#10622598—22no—
30#10622598C2212yes—
31#10622589C2212yes—
32C2×#66872C2212yes—
33#10622562—22no—
34#10622548—21no—
35#10622548C2211yescharacteristic
36C4×C4⋊Dic11—21no—
37C4×C4⋊Dic11C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622189C2212yes—
40#10622189C2212yes—
41#10622188C2212yes—
42#10622167C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×Dic22—21no—
47C2×C11×SD16—22no—
48C2×C11×SD16—22no—
49C2×C11×SD16Q814yescomplemented
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C4×Q8×C11—22no—
53C4×Q8×C11D414yes—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64Q8×Dic11—24no—
65Q8×Dic11—42no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11D411yescharacteristic
72C2×C4⋊Dic11D411yescharacteristic
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2312yes—
75#66977—44no—
76#66977—44no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×C4×Dic11—22no—
80C2×C4×Dic11C2312yes—
81C22×C11⋊C8C2312yes—
82#66922—22no—
83#66922—22no—
84C11×#106—22no—
85C11×#103—22no—
86C11×#102—22no—
87C4×C8×C11—22no—
88#66899—24no—
89#66896—42no—
90C11⋊#95—22no—
91C11⋊#95D412yes—
92Dic11⋊C8—42no—
93#66872—24no—
94C4⋊(C11⋊C8)—22no—
95#24813—111nomaximal, Sylow
96C24×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11C2×D412yes—
101C2×Q8×C11C2×Q812yes—
102C2×Q8×C11#4112yes—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11C2×Q812yes—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11C2×D412yes—
121C22×Dic11C2×D412yes—
122C2×Dic22—42no—
123C2×Dic22—42no—
124C2×Dic22—42no—
125C11×SD16—28no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11C2×Q812yes—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4C2×D412yes—
137C11×C22⋊C4—42no—
138C42×C11—24no—
139C42×C11C2×D412yes—
140C42×C11#4112yes—
141C22⋊Dic11—44no—
142C22⋊Dic11—44no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—44no—
149C4⋊Dic11—42no—
150C4⋊Dic11—42no—
151C4⋊Dic11—81no—
152C4⋊Dic11—82no—
153C4⋊Dic11SD1614yescomplemented
154Dic11⋊C4—44no—
155Dic11⋊C4—44no—
156C4×Dic11—22no—
157C4×Dic11—22no—
158C4×Dic11—44no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×#475—111no—
163C2×C4×SD16D1111yescharacteristic
164#2542—111no—
165Q8×C4⋊C4—111no—
166#2084—112no—
167#2065—112no—
168#1990—111no—
169#1939—111no—
170#1880—112no—
171#1803—112no—
172#1802—111no—
173C23×C11—22no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11C22×D411yescharacteristic
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11—22no—
184Q8×C11C22⋊Q814yescomplemented
185D4×C11—22no—
186D4×C11—22no—
187D4×C11—41no—
188D4×C11—41no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—22no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—84no—
201C2×C4×C11#12112yes—
202C2×C4×C11#12112yes—
203C2×C4×C11C2×SD1612yes—
204C2×C4×C11AGL(1,ℤ/8)12yes—
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×Q811yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11H(5,𝔽2)11yescharacteristic
210C2×C4×C112−1+411yescharacteristic
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11C2×SD1614yes—
223Dic22—84no—
224C8×C11—22no—
225C8×C11—41no—
226C11⋊C8—42no—
227C22×SD16C2×D1111yescharacteristic
228C2×C4⋊Q8—111no—
229C2×C22⋊Q8—221no—
230C2×C22⋊Q8—221no—
231C2×C4×Q8—112no—
232C2×C4×Q8C2×D1111yescharacteristic
233C2×C4×D4C2×D1111yescharacteristic
234#475—224no—
235C4×SD16—24no—
236C2×#106—112no—
237C2×#106C2×D1111yescharacteristic
238C2×C4⋊C8—111no—
239C2×C4⋊C8—112no—
240C2×#103—112no—
241C2×#103C2×D1111yescharacteristic
242C2×#102—112no—
243C2×#102C2×D1111yescharacteristic
244C2×C4×C8C2×D1111yescharacteristic
245#399—222no—
246#390—112no—
247#389—112no—
248#389—222no—
249#384—112no—
250#384—111no—
251#384—221no—
252C4×C4⋊C4—111no—
253C4×C4⋊C4—221no—
254#340—112no—
255#340—112no—
256#340—112no—
257#336—112no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11—81no—
265C22×C11C2×#12111yescharacteristic
266C22×C11#54611yescharacteristic
267C22×C11D4×Q811yescharacteristic
268C22×C11C22×SD1611yescharacteristic
269C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C11#57711yescharacteristic
271C22×C11#57811yescharacteristic
272C4×C11—24no—
273C4×C11—22no—
274C4×C11—42no—
275C4×C11—81no—
276C4×C11#46014yes—
277C4×C11C2×C22⋊Q811yescharacteristic
278C4×C11#53711yescharacteristic
279C4×C11#55211yescharacteristic
280C4×C11#55411yescharacteristic
281Dic11—24no—
282Dic11—42no—
283Dic11—82no—
284Dic11—82no—
285C22×Q8—221no—
286C22×Q8C22×D1111yescharacteristic
287C22×D4C22×D1111yescharacteristic
288C23×C4—21no—
289C2×SD16—22no—
290C2×SD16—22no—
291C2×SD16Dic2214yescomplemented
292C22×C8—112no—
293C22×C8C22×D1111yescharacteristic
294C22×C8C22×D1111yescharacteristic
295C4⋊Q8—222no—
296C4⋊Q8—222no—
297C22⋊Q8—444no—
298C22⋊Q8—444no—
299C4×Q8—22no—
300C4×Q8—224no—
301C4×Q8—442no—
302C4×Q8C22⋊D1114yes—
303C4×D4—22no—
304C4×D4—22no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—111no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—112no—
309C2×C4⋊C4—112no—
310C2×C4⋊C4—222no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4C22×D1111yescharacteristic
318C2×C4⋊C4C22×D1111yescharacteristic
319C2×C22⋊C4—21no—
320C2×C22⋊C4—222no—
321C2×C22⋊C4—222no—
322C2×C42—21no—
323C2×C42—112no—
324C2×C42—222no—
325C2×C42C22×D1111yescharacteristic
326#106—22no—
327#106—224no—
328C4⋊C8—222no—
329C4⋊C8—442no—
330#103—22no—
331#103—224no—
332#102—22no—
333#102—442no—
334C4×C8—22no—
335#95—112no—
336#95—222no—
337C2×C11—82no—
338C2×C11#241711yescharacteristic
339C2×C11C2×#46011yescharacteristic
340C2×C11#304611yescharacteristic
341C2×C11#329811yescharacteristic
342C2×C11#333211yescharacteristic
343C2×C11Q8×SD1611yescharacteristic
344C2×C11#338611yescharacteristic
345C24—21no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—442no—
350C2×Q8—442no—
351C2×Q8—442no—
352C2×Q8C2×Dic2212yes—
353C2×Q8#433912yes—
354C2×Q8C2×C22⋊D1112yes—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4C2×Dic2212yes—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—112no—
368C22×C4—112no—
369C22×C4—222no—
370C22×C4—222no—
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—24no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—114no—
389C4⋊C4—222no—
390C4⋊C4—222no—
391C4⋊C4—222no—
392C4⋊C4—222no—
393C4⋊C4—222no—
394C4⋊C4—444no—
395C4⋊C4—444no—
396C4⋊C4—444no—
397C4⋊C4—442no—
398C4⋊C4—442no—
399C4⋊C4—881no—
400C4⋊C4—882no—
401C4⋊C4C2×C22⋊D1112yes—
402C22⋊C4—42no—
403C22⋊C4—444no—
404C22⋊C4—444no—
405C42—24no—
406C42—222no—
407C42—222no—
408C42—444no—
409C42#434112yes—
410C42C2×C22⋊D1112yes—
411C11#2481311yescharacteristic, complemented, Sylow
412C23—22no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23C2×D4×D1111yescharacteristic
420Q8—22no—
421Q8—22no—
422Q8—22no—
423Q8—884no—
424Q8#6697714yescomplemented
425D4—22no—
426D4—22no—
427D4—41no—
428D4—41no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—84no—
441C2×C4—114no—
442C2×C4—222no—
443C2×C4—222no—
444C2×C4—222no—
445C2×C4—222no—
446C2×C4—222no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4SD16×D1112yes—
454C2×C4#6696712yes—
455C2×C4#6699212yes—
456C2×C4#6699212yes—
457C2×C4C22×Dic2211yescharacteristic
458C2×C4C2×#433911yescharacteristic
459C2×C4C2×#434111yescharacteristic
460C2×C4#6704211yescharacteristic
461C2×C4#6704311yescharacteristic
462C2×C4C22×C22⋊D1111yescharacteristic
463C8—22no—
464C8—41no—
465C8—442no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22D4×Dic2211yescharacteristic
474C22#1062308111yescharacteristic
475C22C2×SD16×D1111yescharacteristic
476C22C2×#6696711yescharacteristic
477C22#1062330111yescharacteristic
478C22#1062330211yescharacteristic
479C22C2×#6699211yescharacteristic
480C4—22no—
481C4—24no—
482C4—42no—
483C4—81no—
484C4—224no—
485C4—442no—
486C4—882no—
487C4—882no—
488C4#1062277614yes—
489C4#1062307211yescharacteristic
490C4#1062307411yescharacteristic
491C4C2×#6697711yescharacteristic
492C4#1062336411yescharacteristic
493C2—82no—
494C2#1307206711yescharacteristic
495C2C2×#1062277611yescharacteristic
496C2#1307816411yescharacteristic
497C2#1308048311yescharacteristic
498C2#1308094511yescharacteristic
499C2SD16×Dic2211yescharacteristic
500C2#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#24813
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
1. C2×#10622633C2semidirect
3. Q8×C4⋊Dic11C2semidirect
4. #13070095C2semidirect
6. #13069577C2semidirect
7. #13069334C2semidirect
9. #13068619C2semidirect
49. C2×C11×SD16Q8semidirect
153. C4⋊Dic11SD16semidirect
184. Q8×C11C22⋊Q8semidirect
291. C2×SD16Dic22semidirect
411. C11#24813semidirect
424. Q8#66977semidirect

Maximal subgroups

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

subgroupindex
C2×#106226332
#130735692
Q8×C4⋊Dic112
#130700952
#130699862
#130695772
#130693342
#130689732
#130686192
#130686162
C2×C4×C11×SD162
#2481311