Finite Group Databasebeta

← #14803307

Subgroups — #14803307

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×C8×Dic22C211yesmaximal, characteristic, complemented
3#13073986C211yesmaximal, characteristic, complemented
4#13073618C211yesmaximal, characteristic
5#13069991C212yesmaximal, complemented
6#13069930C212yesmaximal, complemented
7#13069467C212yesmaximal, complemented
8#13069422C211yesmaximal, characteristic
9#13069379C211yesmaximal, characteristic, complemented
10#13069297C212yesmaximal, complemented
11C4×C11×#103C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C22×#4325C2212yes—
14C2×#66928—21no—
15C2×#66927C2211yescharacteristic
16C2×C4×Dic22C2211yescharacteristic
17C2×C11×#103C2211yescharacteristic
18C2×C11×#103C2211yescharacteristic
19C2×C4×C8×C11C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21#10622843C2212yes—
22C2×#66885C2212yes—
23C2×#66885C2212yes—
24C2×Dic11⋊C8C2212yes—
25C2×C8×Dic11C2212yes—
26#10622640—24no—
27#10622601C2212yes—
28#10622601C2212yes—
29#10622597—22no—
30#10622586C2212yes—
31C2×#66873C2212yes—
32C2×#66872C2212yes—
33#10622552—21no—
34#10622548C2211yescharacteristic
35#10622542—21no—
36#10622541—21no—
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C8×Dic22—24no—
39#10622285—22no—
40C11×#340C2211yescharacteristic
41C11×#340C2211yescharacteristic
42#10622167C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D44—21no—
45C22×D44—21no—
46C22×D44C2312yes—
47C22×Dic22D411yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C42×C11—21no—
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59C2×#4325—24no—
60C2×#4325—24no—
61C2×#4325—42no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11D411yescharacteristic
69C2×C4⋊Dic11C2312yes—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4D412yes—
72C2×C4×Dic11C2312yes—
73C22×C11⋊C8C2312yes—
74#66928—44no—
75#66927—22no—
76#66927—22no—
77C4×Dic22—22no—
78C4×Dic22—22no—
79C11×#103—22no—
80C11×#103—22no—
81C4×C8×C11—22no—
82C11×#95—21no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86#66885—24no—
87#66885—42no—
88Dic11⋊C8—24no—
89C8×Dic11—24no—
90#66873—24no—
91#66872—42no—
92C4⋊(C11⋊C8)D414yes—
93#25295—111nomaximal, Sylow
94C23×D11—22no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11#4112yes—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2411yescharacteristic
108C22×Dic11—22no—
109C22×Dic11C2×D412yes—
110C22×Dic11C2×D412yes—
111C2×D44—22no—
112C2×D44—22no—
113C2×D44—22no—
114C2×D44—22no—
115C2×D44—22no—
116C2×D44—22no—
117C2×D44—42no—
118C2×D44—42no—
119C2×D44—42no—
120C2×D44—42no—
121C2×D44—81no—
122C2×D44—81no—
123C2×Dic22—22no—
124C2×Dic22—22no—
125C2×Dic22SD1614yescomplemented
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11#4112yes—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—42no—
139C42×C11—42no—
140C42×C11—42no—
141C42×C11C2×D412yes—
142C42×C11#4112yes—
143#4325—48no—
144(C2×D11)⋊C4—44no—
145(C2×D11)⋊C4—44no—
146(C2×D11)⋊C4—82no—
147(C2×D11)⋊C4—82no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11—42no—
152C4⋊Dic11—81no—
153Dic11⋊C4—24no—
154Dic11⋊C4—82no—
155C4×Dic11—22no—
156C4×Dic11—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8C2×D414yes—
160C2×#460—111no—
161C2×C8×Q8—111no—
162#2582—111no—
163#2548—111no—
164#2065—112no—
165#2055—112no—
166#1968—112no—
167#1957—111no—
168#1948—111no—
169#1934—112no—
170C4×#103D1111yescharacteristic, complemented
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—22no—
180Q8×C11—22no—
181Q8×C11—41no—
182Q8×C11—41no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—22no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11#12112yes—
198C2×C4×C11#12112yes—
199C2×C4×C11C2×SD1612yes—
200C2×C4×C11#13512yes—
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11H(5,𝔽2)11yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11C2×SD1614yes—
216D44—42no—
217D44—42no—
218D44—42no—
219D44—42no—
220D44—84no—
221D44—84no—
222Dic22—28no—
223C8×C11—22no—
224C8×C11—41no—
225C11⋊C8—24no—
226C22×SD16—112no—
227C2×#127—111no—
228C2×#124—221no—
229C2×C4×Q8—111no—
230C2×C4×Q8C2×D1111yescharacteristic
231#460—224no—
232C8×Q8—224no—
233C2×#106—112no—
234C2×C4⋊C8—111no—
235C2×C4⋊C8—112no—
236C2×#103C2×D1111yescharacteristic
237C2×#103C2×D1111yescharacteristic
238C2×#102—112no—
239C2×#102—112no—
240C2×#102—112no—
241C2×C4×C8—112no—
242C2×C4×C8C2×D1111yescharacteristic
243#398—222no—
244#394—222no—
245#391—112no—
246#391—221no—
247#390—112no—
248#390—112no—
249#390—221no—
250#389—112no—
251#389—221no—
252#384—111no—
253C4×C4⋊C4C2×D1111yescharacteristic
254#340—112no—
255#340C2×D1111yescharacteristic
256#340C2×D1111yescharacteristic
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—22no—
272C4×C11—42no—
273C4×C11—81no—
274C4×C11—81no—
275C4×C11—81no—
276C4×C11#46514yes—
277C4×C11#52911yescharacteristic
278C4×C11#54211yescharacteristic
279C4×C11#54611yescharacteristic
280C4×C11#54811yescharacteristic
281Dic11—24no—
282Dic11—42no—
283Dic11—82no—
284C22×Q8—111no—
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×C8C22×D1111yescharacteristic
294C22×C8C22×D1111yescharacteristic
295#127—222no—
296#127—222no—
297#124—444no—
298C4×Q8—22no—
299C4×Q8—22no—
300C4×Q8—222no—
301C4×Q8—222no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—112no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4C22×D1111yescharacteristic
310C2×C4⋊C4C22×D1111yescharacteristic
311C2×C4⋊C4C22×D1111yescharacteristic
312C2×C22⋊C4—222no—
313C2×C22⋊C4—222no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4—222no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—112no—
319C2×C42C22×D1111yescharacteristic
320#106—442no—
321C4⋊C8—114no—
322C4⋊C8—224no—
323#103—22no—
324#103—22no—
325#102—224no—
326#102—224no—
327#102—442no—
328C4×C8—22no—
329C4×C8—224no—
330#95—21no—
331#95—222no—
332#95—222no—
333#95—222no—
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—21no—
344C2×Q8—21no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—114no—
349C2×Q8—222no—
350C2×Q8—222no—
351C2×Q8#433912yes—
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—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—112no—
369C22×C4—112no—
370C22×C4—222no—
371C22×C4D4×D1111yescharacteristic
372C22×C4D4×D1111yescharacteristic
373C22×C4C23×D1111yescharacteristic
374SD16—448no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—114no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8#433912yes—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—42no—
391C4⋊C4—224no—
392C4⋊C4—222no—
393C4⋊C4—222no—
394C4⋊C4—222no—
395C4⋊C4—442no—
396C4⋊C4—881no—
397C4⋊C4—882no—
398C22⋊C4—444no—
399C22⋊C4—444no—
400C22⋊C4—882no—
401C22⋊C4—882no—
402C42—42no—
403C42—42no—
404C42—222no—
405C42—222no—
406C42#433912yes—
407C42D4×D1112yes—
408C11#2529511yescharacteristic, complemented, Sylow
409C23—442no—
410C23—442no—
411C23—442no—
412C23—442no—
413C23—442no—
414C23—442no—
415C23—442no—
416C23C2×D4×D1111yescharacteristic
417Q8—22no—
418Q8—22no—
419Q8—41no—
420Q8—41no—
421Q8—228no—
422D4—442no—
423D4—442no—
424D4—442no—
425D4—442no—
426D4—884no—
427D4—884no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—114no—
443C2×C4—222no—
444C2×C4—222no—
445C2×C4—222no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4#6693712yes—
452C2×C4#6693712yes—
453C2×C4SD16×D1112yes—
454C2×C4#6697212yes—
455C2×C4C2×#433911yescharacteristic
456C2×C4C2×#433911yescharacteristic
457C2×C4C2×#433911yescharacteristic
458C2×C4C2×D4×D1111yescharacteristic
459C2×C4#6704211yescharacteristic
460C2×C4#6704311yescharacteristic
461C8—22no—
462C8—41no—
463C8—224no—
464C22—882no—
465C22—882no—
466C22—882no—
467C22—882no—
468C22—882no—
469C22—882no—
470C22—882no—
471C22C2×#6693711yescharacteristic
472C22#1062308311yescharacteristic
473C22#1062308411yescharacteristic
474C22C2×SD16×D1111yescharacteristic
475C22C2×#6697211yescharacteristic
476C22#1062330011yescharacteristic
477C22#1062330111yescharacteristic
478C4—22no—
479C4—42no—
480C4—81no—
481C4—81no—
482C4—81no—
483C4—224no—
484C4—442no—
485C4—882no—
486C4#1062242014yes—
487C4#1062301011yescharacteristic
488C4#1062306511yescharacteristic
489C4#1062308111yescharacteristic
490C4#1062308311yescharacteristic
491C2—1762no—
492C2#1307218211yescharacteristic
493C2C2×#1062242011yescharacteristic
494C2#1307829911yescharacteristic
495C2#1308128511yescharacteristic
496C2#1308131011yescharacteristic
497C2#1308159511yescharacteristic
498C2#1308162611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#103C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenterC4×#103D11
hypocenterC11#25295
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic22C2semidirect
3. #13073986C2semidirect
5. #13069991C2semidirect
6. #13069930C2semidirect
7. #13069467C2semidirect
9. #13069379C2semidirect
10. #13069297C2semidirect
11. C4×C11×#103C2semidirect
125. C2×Dic22SD16semidirect
170. C4×#103D11semidirect
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×C8×Dic222
#130739862
#130736182
#130699912
#130699302
#130694672
#130694222
#130693792
#130692972
C4×C11×#1032
#2529511