Finite Group Databasebeta

← #14803309

Subgroups — #14803309

Order 2816.

886 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622640C211yesmaximal, characteristic
2C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
3#13073615C211yesmaximal, characteristic
4#13069987C212yesmaximal, complemented
5#13069931C212yesmaximal, complemented
6#13069473C212yesmaximal, complemented
7#13069421C211yesmaximal, characteristic
8#13069377C211yesmaximal, characteristic, complemented
9#13069298C212yesmaximal, complemented
10C4×#66899C211yesmaximal, characteristic, complemented
11C11×#2582C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×#67000—21no—
15C22×#4325C2212yes—
16C2×#66927C2211yescharacteristic
17C11×#398—22no—
18C11×#391—21no—
19C11×#391C2212yes—
20C11×#389—21no—
21C11×#389C2212yes—
22C11×#384C2211yescharacteristic
23C2×#66899C2211yescharacteristic
24C2×#66899C2211yescharacteristic
25#10622640—24no—
26Q8×C11⋊C8—24no—
27#10622604—22no—
28#10622601—21no—
29C2×#66873C2212yes—
30C2×#66873C2212yes—
31C2×#66873C2212yes—
32C2×#66872C2212yes—
33#10622552C2212yes—
34#10622552C2212yes—
35C4×C4⋊Dic11C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2212yes—
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39C2×C4×C11⋊C8C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11D411yescharacteristic
44C22×Q8×C11C2311yescharacteristic
45C22×D44—21no—
46C22×D44—21no—
47C22×D44C2312yes—
48C4×Q8×C11—22no—
49C4×Q8×C11—22no—
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4D412yes—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11C2312yes—
62C2×C42×C11C2311yescharacteristic
63#67000—44no—
64C2×#4325—24no—
65C2×#4325—24no—
66C2×#4325—42no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4⋊Dic11C2311yescharacteristic
73C2×C4×Dic11—21no—
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2312yes—
76C22×C11⋊C8C2311yescharacteristic
77#66927—22no—
78#66927—22no—
79C11×#95—22no—
80C11×#95—22no—
81C11×#95—22no—
82#66899—22no—
83#66899—22no—
84C11⋊#95—21no—
85#66873—24no—
86#66873—24no—
87#66873—42no—
88#66872—42no—
89C4⋊(C11⋊C8)—24no—
90C4⋊(C11⋊C8)D414yes—
91C4×C11⋊C8—22no—
92C4×C11⋊C8—24no—
93#25295—111nomaximal, Sylow
94C23×D11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11SD1614yescomplemented
103C2×Q8×C11#4112yes—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2411yescharacteristic
112C22×Dic11—21no—
113C22×Dic11—21no—
114C2×D44—22no—
115C2×D44—22no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—22no—
119C2×D44—22no—
120C2×D44—42no—
121C2×D44—42no—
122C2×D44—42no—
123C2×D44—42no—
124C2×D44—81no—
125C2×D44—81no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4—81no—
135C11×C4⋊C4—82no—
136C42×C11—22no—
137C42×C11—22no—
138C42×C11—42no—
139C42×C11C2×D412yes—
140C42×C11#4112yes—
141#4325—48no—
142(C2×D11)⋊C4—44no—
143(C2×D11)⋊C4—44no—
144(C2×D11)⋊C4—82no—
145(C2×D11)⋊C4—82no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4×Dic11—42no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8C2×D414yes—
159C2×C11⋊C8#4112yes—
160C2×#460—111no—
161C2×C8×Q8—111no—
162#2582D1111yescharacteristic, complemented
163#2548—111no—
164#2065—112no—
165#2055—112no—
166#1968—112no—
167#1957—111no—
168#1948—111no—
169#1934—112no—
170C4×#103—111no—
171C23×C11C22×D411yescharacteristic
172C22×D11—42no—
173C22×D11—42no—
174C22×D11—42no—
175C22×D11—42no—
176C22×D11—42no—
177C22×D11—42no—
178C22×D11—42no—
179Q8×C11—28no—
180Q8×C11—22no—
181Q8×C11—22no—
182Q8×C11—41no—
183Q8×C11—41no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11#12112yes—
201C2×C4×C11#12112yes—
202C2×C4×C11C2×SD1614yes—
203C2×C4×C11C2×SD1612yes—
204C2×C4×C11#13512yes—
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11H(5,𝔽2)11yescharacteristic
210C2×C4×C112−1+411yescharacteristic
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217D44—42no—
218D44—42no—
219D44—42no—
220D44—42no—
221D44—84no—
222D44—84no—
223C11⋊C8—24no—
224C11⋊C8—22no—
225C11⋊C8—41no—
226C22×SD16—112no—
227C2×#127—111no—
228C2×#124—221no—
229C2×C4×Q8C2×D1111yescharacteristic
230C2×C4×Q8C2×D1111yescharacteristic
231#460—224no—
232C8×Q8—224no—
233C2×#106—112no—
234C2×C4⋊C8—111no—
235C2×C4⋊C8—112no—
236C2×#103—111no—
237C2×#103—111no—
238C2×#102—112no—
239C2×#102—112no—
240C2×#102—112no—
241C2×C4×C8—112no—
242C2×C4×C8—111no—
243#398—22no—
244#394—222no—
245#391—21no—
246#391C2×D1112yes—
247#390—112no—
248#390—112no—
249#390—221no—
250#389—21no—
251#389C2×D1112yes—
252#384C2×D1111yescharacteristic
253C4×C4⋊C4—111no—
254#340—112no—
255#340—111no—
256#340—111no—
257C22×C11C2×#12111yescharacteristic
258C22×C11#54811yescharacteristic
259C22×C11#55011yescharacteristic
260C22×C11C22×SD1611yescharacteristic
261C22×C11C2×#13511yescharacteristic
262C22×C11#57611yescharacteristic
263C22×C11#57711yescharacteristic
264C2×D11—82no—
265C2×D11—82no—
266C2×D11—82no—
267C2×D11—82no—
268C2×D11—82no—
269C2×D11—82no—
270C2×D11—82no—
271C4×C11—24no—
272C4×C11—22no—
273C4×C11—42no—
274C4×C11—42no—
275C4×C11—82no—
276C4×C11—81no—
277C4×C11#46514yes—
278C4×C11#52911yescharacteristic
279C4×C11#54211yescharacteristic
280C4×C11#54611yescharacteristic
281C4×C11#54811yescharacteristic
282Dic11—81no—
283Dic11—81no—
284C22×Q8C22⋊D1111yescharacteristic
285C22×Q8C22×D1111yescharacteristic
286C22×D4—112no—
287C22×D4—221no—
288C22×D4—221no—
289C2×SD16—224no—
290C2×SD16—224no—
291C2×SD16—442no—
292C22×C8—112no—
293C22×C8—111no—
294C22×C8—111no—
295#127—222no—
296#127—222no—
297#124—444no—
298C4×Q8—22no—
299C4×Q8—22no—
300C4×Q8—22no—
301C4×Q8—22no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—111no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4C22⋊D1111yescharacteristic
309C2×C4⋊C4C22⋊D1112yes—
310C2×C4⋊C4C22×D1111yescharacteristic
311C2×C4⋊C4C22×D1112yes—
312C2×C22⋊C4—222no—
313C2×C22⋊C4—222no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4—222no—
316C2×C42—21no—
317C2×C42—221no—
318C2×C42C22×D1112yes—
319C2×C42C22×D1111yescharacteristic
320#106—442no—
321C4⋊C8—114no—
322C4⋊C8—224no—
323#103—222no—
324#103—222no—
325#102—224no—
326#102—224no—
327#102—442no—
328C4×C8—224no—
329C4×C8—222no—
330#95—22no—
331#95—22no—
332#95—22no—
333#95—221no—
334C2×C11#242611yescharacteristic
335C2×C11C2×#46511yescharacteristic
336C2×C11#306211yescharacteristic
337C2×C11#336211yescharacteristic
338C2×C11#336511yescharacteristic
339C2×C11#339211yescharacteristic
340C2×C11#339611yescharacteristic
341D11—162no—
342C24—222no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8#432514yescomplemented
351C2×Q8#434312yes—
352C2×D4—222no—
353C2×D4—222no—
354C2×D4—222no—
355C2×D4—222no—
356C2×D4—222no—
357C2×D4—222no—
358C2×D4—442no—
359C2×D4—442no—
360C2×D4—442no—
361C2×D4—442no—
362C2×D4—881no—
363C2×D4—881no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—221no—
368C22×C4—221no—
369C22×C4C2×C22⋊D1112yes—
370C22×C4C2×C22⋊D1111yescharacteristic
371C22×C4C2×C22⋊D1112yes—
372C22×C4C2×C22⋊D1111yescharacteristic
373C22×C4C23×D1111yescharacteristic
374SD16—448no—
375C2×C8—114no—
376C2×C8—112no—
377C2×C8—221no—
378C2×C8—222no—
379C2×C8—221no—
380C2×C8—222no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8—221no—
384C4⋊C4—24no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—42no—
391C4⋊C4—42no—
392C4⋊C4—81no—
393C4⋊C4—82no—
394C4⋊C4—221no—
395C4⋊C4—221no—
396C4⋊C4—221no—
397C4⋊C4—221no—
398C22⋊C4—444no—
399C22⋊C4—444no—
400C22⋊C4—882no—
401C22⋊C4—882no—
402C42—22no—
403C42—22no—
404C42—42no—
405C42—442no—
406C42D4×D1112yes—
407C42#434112yes—
408C11#2529511yescharacteristic, complemented, Sylow
409C23—442no—
410C23—442no—
411C23—442no—
412C23—442no—
413C23—442no—
414C23—442no—
415C23—442no—
416C23C22×C22⋊D1111yescharacteristic
417Q8—28no—
418Q8—22no—
419Q8—22no—
420Q8—41no—
421Q8—41no—
422D4—442no—
423D4—442no—
424D4—442no—
425D4—442no—
426D4—884no—
427D4—884no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4#6699212yes—
451C2×C4#6699212yes—
452C2×C4C2×#432514yes—
453C2×C4C2×#432512yes—
454C2×C4#6700312yes—
455C2×C4C2×D4×D1111yescharacteristic
456C2×C4C2×#434111yescharacteristic
457C2×C4C2×#434311yescharacteristic
458C2×C4#6704011yescharacteristic
459C2×C4#41×D1111yescharacteristic
460C2×C4#6704211yescharacteristic
461C8—224no—
462C8—222no—
463C8—441no—
464C22—882no—
465C22—882no—
466C22—882no—
467C22—882no—
468C22—882no—
469C22—882no—
470C22—882no—
471C22C2×#6699211yescharacteristic
472C22C22×#432511yescharacteristic
473C22#1062334811yescharacteristic
474C22C2×#6700311yescharacteristic
475C22#1062336511yescharacteristic
476C22#1062336611yescharacteristic
477C22#1062336811yescharacteristic
478C4—22no—
479C4—24no—
480C4—42no—
481C4—42no—
482C4—82no—
483C4—81no—
484C4—881no—
485C4—881no—
486C4#1062266114yes—
487C4#1062315511yescharacteristic
488C4#1062316111yescharacteristic
489C4#1062316411yescharacteristic
490C4#1062317411yescharacteristic
491C2—1762no—
492C2#1307218411yescharacteristic
493C2C2×#1062266111yescharacteristic
494C2#1307829811yescharacteristic
495C2#1308128711yescharacteristic
496C2#1308131211yescharacteristic
497C2#1308159311yescharacteristic
498C2#1308162411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2582C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#2582D11
hypocenterC11#25295
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2582

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C11⋊C8C2semidirect
4. #13069987C2semidirect
5. #13069931C2semidirect
6. #13069473C2semidirect
8. #13069377C2semidirect
9. #13069298C2semidirect
10. C4×#66899C2semidirect
11. C11×#2582C2semidirect
102. C2×Q8×C11SD16semidirect
162. #2582D11semidirect
350. C2×Q8#4325semidirect
408. C11#25295semidirect

Maximal subgroups

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

subgroupindex
C2×#106226402
C2×Q8×C11⋊C82
#130736152
#130699872
#130699312
#130694732
#130694212
#130693772
#130692982
C4×#668992
C11×#25822
#2529511