Finite Group Databasebeta

← #14803301

Subgroups — #14803301

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×#10622461C211yesmaximal, characteristic
2#13073986C211yesmaximal, characteristic, complemented
3#13073615C211yesmaximal, characteristic
4#13069989C212yesmaximal, complemented
5#13069934C212yesmaximal, complemented
6#13069470C212yesmaximal, complemented
7#13069422C211yesmaximal, characteristic
8#13069380C211yesmaximal, characteristic, complemented
9#13069299C212yesmaximal, complemented
10C4×#66880C211yesmaximal, characteristic, complemented
11C2×C8×Q8×C11C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#67000—21no—
14C22×#4314C2212yes—
15C2×#66927C2211yescharacteristic
16C2×C4×Dic22C2211yescharacteristic
17C8×Q8×C11—24no—
18C2×C11×C4⋊C8C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21C2×C4×C8×C11C2212yes—
22#10622843—21no—
23C2×#66885C2212yes—
24C2×#66885C2212yes—
25C2×#66885C2212yes—
26C2×#66881C2212yes—
27C2×#66880C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29#10622604—22no—
30#10622601—21no—
31#10622597—22no—
32#10622586—21no—
33#10622552C2212yes—
34#10622552C2212yes—
35#10622548C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37#10622542C2212yes—
38#10622541C2212yes—
39#10622461—24no—
40#10622189C2212yes—
41#10622189C2211yescharacteristic
42#10622189C2211yescharacteristic
43C22×Q8×C11D411yescharacteristic
44C22×D44—21no—
45C22×D44—21no—
46C22×D44C2312yes—
47C22×Dic22C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2312yes—
50C22×C8×C11C2311yescharacteristic
51C4×Q8×C11—22no—
52C4×Q8×C11—22no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C4⋊C4D412yes—
55C2×C42×C11C2312yes—
56C2×C42×C11C2311yescharacteristic
57#67000—44no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2312yes—
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×Dic11⋊C4—21no—
69C2×Dic11⋊C4—22no—
70C2×C4×Dic11—21no—
71C2×C4×Dic11—21no—
72C2×#4314—24no—
73C2×#4314—24no—
74C2×#4314—42no—
75#66927—22no—
76#66927—22no—
77C4×Dic22—22no—
78C4×Dic22—22no—
79C11×C4⋊C8—24no—
80C11×C4⋊C8D414yes—
81C4×C8×C11—24no—
82C4×C8×C11—22no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—21no—
87#66885—24no—
88#66885—24no—
89#66885—42no—
90#66881—42no—
91#66880—22no—
92#66880—22no—
93#25295—111nomaximal, Sylow
94C23×D11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11SD1614yescomplemented
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—21no—
104C22×Dic11—22no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C2×D44—22no—
109C2×D44—22no—
110C2×D44—22no—
111C2×D44—22no—
112C2×D44—22no—
113C2×D44—22no—
114C2×D44—42no—
115C2×D44—42no—
116C2×D44—42no—
117C2×D44—42no—
118C2×D44—81no—
119C2×D44—81no—
120C2×Dic22—21no—
121C2×Dic22—21no—
122C2×Dic22—21no—
123C2×Dic22—21no—
124C2×Dic22—21no—
125C2×Dic22#4112yes—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—22no—
129C2×C8×C11—21no—
130C2×C8×C11—22no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11C2×D414yes—
134C2×C8×C11#4112yes—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—22no—
137C42×C11—22no—
138C42×C11—22no—
139C42×C11C2×D412yes—
140C42×C11#4112yes—
141(C2×D11)⋊C4—44no—
142(C2×D11)⋊C4—44no—
143(C2×D11)⋊C4—82no—
144(C2×D11)⋊C4—82no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—22no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—22no—
152C4⋊Dic11—21no—
153C4⋊Dic11—42no—
154C4⋊Dic11—81no—
155Dic11⋊C4—42no—
156Dic11⋊C4—82no—
157C4×Dic11—42no—
158C4×Dic11—42no—
159#4314—48no—
160C2×#460—111no—
161C2×C8×Q8D1111yescharacteristic, complemented
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×#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—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11#12112yes—
188C2×C4×C11#12112yes—
189C2×C4×C11C2×SD1614yes—
190C2×C4×C11C2×SD1612yes—
191C2×C4×C11#13512yes—
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11H(5,𝔽2)11yescharacteristic
197C2×C4×C112−1+411yescharacteristic
198C2×Dic11—22no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—42no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—41no—
209C2×Dic11—42no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213D44—42no—
214D44—42no—
215D44—42no—
216D44—42no—
217D44—84no—
218D44—84no—
219Dic22—22no—
220Dic22—22no—
221Dic22—41no—
222Dic22—41no—
223C8×C11—24no—
224C8×C11—22no—
225C8×C11—41no—
226C22×SD16—112no—
227C2×#127—111no—
228C2×#124—221no—
229C2×C4×Q8—111no—
230C2×C4×Q8C2×D1111yescharacteristic
231#460—224no—
232C8×Q8—24no—
233C2×#106—112no—
234C2×C4⋊C8C2×D1112yes—
235C2×C4⋊C8C2×D1111yescharacteristic
236C2×#103—111no—
237C2×#103—111no—
238C2×#102—112no—
239C2×#102—112no—
240C2×#102—112no—
241C2×C4×C8C2×D1112yes—
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⋊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#46514yes—
275C4×C11#52911yescharacteristic
276C4×C11#54211yescharacteristic
277C4×C11#54611yescharacteristic
278C4×C11#54811yescharacteristic
279Dic11—42no—
280Dic11—81no—
281Dic11—81no—
282Dic11—82no—
283Dic11—81no—
284C22×Q8—111no—
285C22×Q8D4411yescharacteristic
286C22×D4—112no—
287C22×D4—221no—
288C22×D4—221no—
289C2×SD16—224no—
290C2×SD16—224no—
291C2×SD16—442no—
292C22×C8C22×D1111yescharacteristic
293C22×C8C22×D1111yescharacteristic
294C22×C8C22×D1112yes—
295#127—222no—
296#127—222no—
297#124—444no—
298C4×Q8—22no—
299C4×Q8—22no—
300C4×Q8—222no—
301C4×Q8—222no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—111no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4D4411yescharacteristic
311C2×C4⋊C4D4412yes—
312C2×C22⋊C4—222no—
313C2×C22⋊C4—222no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4—222no—
316C2×C42—221no—
317C2×C42—221no—
318C2×C42C22×D1112yes—
319C2×C42C22×D1111yescharacteristic
320#106—442no—
321C4⋊C8—24no—
322C4⋊C8C22⋊D1114yes—
323#103—222no—
324#103—222no—
325#102—224no—
326#102—224no—
327#102—442no—
328C4×C8—24no—
329C4×C8—22no—
330#95—221no—
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—22no—
344C2×Q8—22no—
345C2×Q8—112no—
346C2×Q8—221no—
347C2×Q8—221no—
348C2×Q8—221no—
349C2×Q8—221no—
350C2×Q8—221no—
351C2×Q8#431414yescomplemented
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—221no—
365C22×C4—222no—
366C22×C4—221no—
367C22×C4—221no—
368C22×C4—221no—
369C22×C4C2×D4412yes—
370C22×C4C2×D4412yes—
371C22×C4C2×D4411yescharacteristic
372C22×C4C2×D4411yescharacteristic
373C22×C4C23×D1111yescharacteristic
374SD16—448no—
375C2×C8—21no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8#434312yes—
383C2×C8C2×C22⋊D1114yes—
384C4⋊C4—24no—
385C4⋊C4—22no—
386C4⋊C4—221no—
387C4⋊C4—222no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C4⋊C4—222no—
392C4⋊C4—221no—
393C4⋊C4—221no—
394C4⋊C4—442no—
395C4⋊C4—442no—
396C4⋊C4—882no—
397C4⋊C4—881no—
398C22⋊C4—444no—
399C22⋊C4—444no—
400C22⋊C4—882no—
401C22⋊C4—882no—
402C42—22no—
403C42—22no—
404C42—442no—
405C42—442no—
406C42#433912yes—
407C42C2×C22⋊D1112yes—
408C11#2529511yescharacteristic, complemented, Sylow
409C23—442no—
410C23—442no—
411C23—442no—
412C23—442no—
413C23—442no—
414C23—442no—
415C23—442no—
416C23C22×D4411yescharacteristic
417Q8—28no—
418Q8—222no—
419Q8—222no—
420Q8—441no—
421Q8—441no—
422D4—442no—
423D4—442no—
424D4—442no—
425D4—442no—
426D4—884no—
427D4—884no—
428C2×C4—22no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—222no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—442no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—442no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—442no—
449C2×C4—441no—
450C2×C4C2×#431414yes—
451C2×C4C2×#431412yes—
452C2×C4#6695712yes—
453C2×C4#6698312yes—
454C2×C4#6698312yes—
455C2×C4C2×#433911yescharacteristic
456C2×C4C2×#434311yescharacteristic
457C2×C4#6704011yescharacteristic
458C2×C4#41×D1111yescharacteristic
459C2×C4#6704211yescharacteristic
460C2×C4C22×C22⋊D1111yescharacteristic
461C8—22no—
462C8—24no—
463C8—41no—
464C22—882no—
465C22—882no—
466C22—882no—
467C22—882no—
468C22—882no—
469C22—882no—
470C22—882no—
471C22#1062310711yescharacteristic
472C22#1062310811yescharacteristic
473C22C22×#431411yescharacteristic
474C22C2×#6695711yescharacteristic
475C22#1062328211yescharacteristic
476C22#1062328311yescharacteristic
477C22C2×#6698311yescharacteristic
478C4—22no—
479C4—24no—
480C4—42no—
481C4—442no—
482C4—881no—
483C4—882no—
484C4—881no—
485C4—881no—
486C4#1062272714yes—
487C4#1062311111yescharacteristic
488C4#1062311311yescharacteristic
489C4#1062334811yescharacteristic
490C4#1062336011yescharacteristic
491C2—1762no—
492C2#1307217611yescharacteristic
493C2C2×#1062272711yescharacteristic
494C2#1307829611yescharacteristic
495C2#1308128811yescharacteristic
496C2#1308131411yescharacteristic
497C2#1308159811yescharacteristic
498C2#1308162911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C8×Q8×C11C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenterC2×C8×Q8D11
hypocenterC11#25295
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
2. #13073986C2semidirect
4. #13069989C2semidirect
5. #13069934C2semidirect
6. #13069470C2semidirect
8. #13069380C2semidirect
9. #13069299C2semidirect
10. C4×#66880C2semidirect
11. C2×C8×Q8×C11C2semidirect
97. C2×Q8×C11SD16semidirect
161. C2×C8×Q8D11semidirect
351. C2×Q8#4314semidirect
408. C11#25295semidirect

Maximal subgroups

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

subgroupindex
C2×#106224612
#130739862
#130736152
#130699892
#130699342
#130694702
#130694222
#130693802
#130692992
C4×#668802
C2×C8×Q8×C112
#2529511