Finite Group Databasebeta

← #14765813

Subgroups — #14765813

Order 2816.

848 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×#10622459C211yesmaximal, characteristic
2C4×#66922C211yesmaximal, characteristic, complemented
3#13071080C211yesmaximal, characteristic
4#13069567C211yesmaximal, characteristic, complemented
5#13069375C211yesmaximal, characteristic, complemented
6#13069349C212yesmaximal, complemented
7#13069299C212yesmaximal
8#13069237C212yesmaximal
9#13069188C212yesmaximal, complemented
10#13068617C211yesmaximal, characteristic
11C4×C11×C4⋊C8C211yesmaximal, characteristic, complemented
12C2×C4×D44C2211yescharacteristic
13C2×#66925—21no—
14C2×#66922C2211yescharacteristic
15C2×C4×Dic22—21no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C4×C8×C11C2212yes—
19C43×C11C2211yescharacteristic
20C2×#66885C2212yes—
21C2×#66885C2212yes—
22C2×#66882C2212yes—
23C2×#66882C2212yes—
24#10622553—21no—
25#10622553—21no—
26#10622552C2211yescharacteristic
27#10622552C2211yescharacteristic
28C4×(C2×D11)⋊C4—21no—
29#10622548C2211yescharacteristic
30C4×C4⋊Dic11—21no—
31C4×C4⋊Dic11C2211yescharacteristic
32C4×C4⋊Dic11C2212yes—
33#10622542—21no—
34#10622541—21no—
35#10622541C2211yescharacteristic
36#10622541C2212yes—
37#10622541C2211yescharacteristic
38#10622459C418yescomplemented
39C11×#336C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42#10622189C2212yes—
43#10622189C2212yes—
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×Dic22—21no—
47C22×C8×C11C2312yes—
48C22×C8×C11C2312yes—
49C2×C42×C11D411yescharacteristic
50C2×C42×C11D411yescharacteristic
51C2×C42×C11D411yescharacteristic
52C2×C42×C11D411yescharacteristic
53C2×C42×C11C2311yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4—21no—
59C2×(C2×D11)⋊C4—21no—
60C2×(C2×D11)⋊C4—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2312yes—
68C2×C4⋊Dic11C2311yescharacteristic
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—21no—
71C2×Dic11⋊C4—21no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11—21no—
74C4×D44—22no—
75C4×D44C2×C414yes—
76#66925—44no—
77#66922—22no—
78#66922C2×C414yes—
79C4×Dic22—44no—
80C11×C4⋊C8—22no—
81C11×C4⋊C8C2×C414yes—
82C4×C8×C11—42no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95—21no—
86C11⋊#95—21no—
87C11⋊#95—21no—
88#66885—42no—
89#66885C2×C418yes—
90#66882—42no—
91#66882C2×C418yes—
92#22110—111nomaximal, Sylow
93C23×D11—21no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—22no—
102C22×Dic11—21no—
103C22×Dic11—22no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44C22×C412yes—
112C2×C4×D11—24no—
113C2×C4×D11—42no—
114C2×C4×D11—42no—
115C2×Dic22—24no—
116C2×Dic22—42no—
117C2×Dic22—42no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11C22×C414yes—
124C42×C11—22no—
125C42×C11—22no—
126C42×C11—21no—
127C42×C11—21no—
128C42×C11—21no—
129C42×C11—21no—
130C42×C11—41no—
131C42×C11D814yes—
132C42×C11C22×C412yes—
133C42×C11#4112yes—
134(C2×D11)⋊C4—24no—
135(C2×D11)⋊C4—42no—
136(C2×D11)⋊C4—42no—
137(C2×D11)⋊C4—42no—
138(C2×D11)⋊C4—42no—
139C4⋊Dic11—24no—
140C4⋊Dic11—22no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—42no—
149C4⋊Dic11—42no—
150C4⋊Dic11C22×C412yes—
151C4⋊Dic11C22×C414yes—
152Dic11⋊C4—44no—
153Dic11⋊C4—42no—
154Dic11⋊C4—42no—
155C4×Dic11—44no—
156C4×Dic11—42no—
157C2×#474—111no—
158C4×C4⋊Q8—111no—
159#2293—111no—
160#1988—111no—
161#1947—111no—
162#1942—112no—
163#1934—112no—
164#1925—112no—
165#1918—112no—
166#1802—111no—
167C4×C4⋊C8D1111yescharacteristic, complemented
168C23×C11C22×D411yescharacteristic
169C22×D11—22no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11C4×D412yes—
188C2×C4×C11C4×D412yes—
189C2×C4×C11C2×D812yes—
190C2×C4×C11C2×D812yes—
191C2×C4×C11C2×D812yes—
192C2×C4×C11#13512yes—
193C2×C4×C11#13712yes—
194C2×C4×C11C23×C411yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11H(5,𝔽2)11yescharacteristic
197C2×C4×C112−1+411yescharacteristic
198C2×C4×C112−1+411yescharacteristic
199C2×C4×C112−1+411yescharacteristic
200C2×Dic11—24no—
201C2×Dic11—22no—
202C2×Dic11—42no—
203C2×Dic11—41no—
204C2×Dic11—42no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—42no—
214C2×Dic11—41no—
215D44—22no—
216D44—22no—
217D44—41no—
218D44—41no—
219C4×D11—48no—
220Dic22—48no—
221C8×C11—24no—
222C8×C11—42no—
223C2×C4⋊Q8—111no—
224C2×C4×Q8—221no—
225C2×C4×D4—111no—
226C2×#117—221no—
227#474—118no—
228C2×#107—112no—
229C2×#107—112no—
230C2×C4⋊C8C2×D1111yescharacteristic
231C2×C4⋊C8C2×D1111yescharacteristic
232C2×#102—112no—
233C2×#102—112no—
234C2×C4×C8C2×D1112yes—
235#391—221no—
236#390—111no—
237#390—111no—
238#389—112no—
239#389—111no—
240#389—111no—
241#389—221no—
242#388—221no—
243#388—221no—
244#384—111no—
245C4×C4⋊C4—112no—
246C4×C4⋊C4—111no—
247C4×C4⋊C4—221no—
248C4×C22⋊C4—221no—
249C43C2×D1111yescharacteristic
250#340—112no—
251#340—112no—
252#340—112no—
253#340—112no—
254#336C2×D1112yes—
255C22×C11C2×C4×D411yescharacteristic
256C22×C11#53611yescharacteristic
257C22×C11#53711yescharacteristic
258C22×C11C22×D811yescharacteristic
259C22×C11C2×#13511yescharacteristic
260C22×C11C2×#13711yescharacteristic
261C22×C11#57511yescharacteristic
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—81no—
266C2×D11—81no—
267C2×D11—81no—
268C2×D11—81no—
269C4×C11—22no—
270C4×C11—22no—
271C4×C11—22no—
272C4×C11—22no—
273C4×C11—41no—
274C4×C11C4×D814yes—
275C4×C11#51911yescharacteristic
276C4×C11#52011yescharacteristic
277C4×C11#54111yescharacteristic
278C4×C11#54211yescharacteristic
279Dic11—44no—
280Dic11—42no—
281Dic11—81no—
282Dic11—82no—
283Dic11—81no—
284C22×Q8—221no—
285C22×D4—111no—
286C23×C4—221no—
287C22×C8C22×D1112yes—
288C22×C8C22×D1112yes—
289C4⋊Q8—114no—
290C4⋊Q8—222no—
291C4×Q8—444no—
292C4×D4—114no—
293C4×D4—222no—
294#117—444no—
295C2×C4⋊C4—111no—
296C2×C4⋊C4—112no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—112no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—221no—
306C2×C22⋊C4—221no—
307C2×C22⋊C4—221no—
308C2×C22⋊C4—221no—
309C2×C22⋊C4—221no—
310C2×C22⋊C4—221no—
311C2×C42—221no—
312C2×C42—222no—
313C2×C42D4411yescharacteristic
314C2×C42D4411yescharacteristic
315C2×C42D4411yescharacteristic
316C2×C42D4411yescharacteristic
317C2×C42C22×D1111yescharacteristic
318C2×C42C22×D1111yescharacteristic
319C2×C42C22×D1111yescharacteristic
320#107—118no—
321#107—442no—
322C4⋊C8—22no—
323C4⋊C8C4×D1114yes—
324#102—118no—
325#102—442no—
326C4×C8—42no—
327#95—221no—
328#95—221no—
329#95—221no—
330#95—222no—
331#95—222no—
332C2×C11#232311yescharacteristic
333C2×C11C2×C4×D811yescharacteristic
334C2×C11C4×#13711yescharacteristic
335C2×C11#322611yescharacteristic
336C2×C11#323311yescharacteristic
337C2×C11#324511yescharacteristic
338C2×C11#324811yescharacteristic
339D11—82no—
340C24—221no—
341C2×Q8—224no—
342C2×Q8—442no—
343C2×Q8—442no—
344C2×D4—112no—
345C2×D4—221no—
346C2×D4—221no—
347C2×D4—221no—
348C2×D4—221no—
349C2×D4—221no—
350C22×C4—222no—
351C22×C4—221no—
352C22×C4—224no—
353C22×C4—221no—
354C22×C4—221no—
355C22×C4—222no—
356C22×C4—442no—
357C22×C4—442no—
358C22×C4C2×D4411yescharacteristic
359C22×C4C2×D4411yescharacteristic
360C22×C4C2×D4411yescharacteristic
361C22×C4C2×D4411yescharacteristic
362C22×C4C2×D4411yescharacteristic
363C22×C4C2×D4411yescharacteristic
364C22×C4C23×D1111yescharacteristic
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8C2×C4×D1114yes—
371C4⋊C4—114no—
372C4⋊C4—112no—
373C4⋊C4—224no—
374C4⋊C4—221no—
375C4⋊C4—222no—
376C4⋊C4—222no—
377C4⋊C4—221no—
378C4⋊C4—222no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—442no—
383C4⋊C4—442no—
384C4⋊C4—442no—
385C4⋊C4—444no—
386C4⋊C4—442no—
387C22⋊C4—224no—
388C22⋊C4—442no—
389C22⋊C4—442no—
390C22⋊C4—442no—
391C22⋊C4—442no—
392C42—22no—
393C42—22no—
394C42—21no—
395C42—21no—
396C42—21no—
397C42—21no—
398C42—41no—
399C42—442no—
400C42—444no—
401C42D8814yes—
402C42C2×C4×D1112yes—
403C42#433912yes—
404C11#2211011yescharacteristic, complemented, Sylow
405C23—222no—
406C23—441no—
407C23—441no—
408C23—441no—
409C23—441no—
410C23—441no—
411C23—441no—
412C23C22×D4411yescharacteristic
413Q8—448no—
414D4—222no—
415D4—222no—
416D4—441no—
417D4—441no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—222no—
430C2×C4—224no—
431C2×C4—442no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—442no—
435C2×C4—448no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—442no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4C4×D4412yes—
446C2×C4C4×D4412yes—
447C2×C4C2×D8812yes—
448C2×C4C2×D8812yes—
449C2×C4C2×D8812yes—
450C2×C4#6695712yes—
451C2×C4#6696212yes—
452C2×C4C22×C4×D1111yescharacteristic
453C2×C4C2×#433911yescharacteristic
454C2×C4#6703711yescharacteristic
455C2×C4#6704011yescharacteristic
456C2×C4#6704311yescharacteristic
457C2×C4#6704311yescharacteristic
458C8—24no—
459C8—42no—
460C22—442no—
461C22—442no—
462C22—442no—
463C22—881no—
464C22—881no—
465C22—881no—
466C22—881no—
467C22C2×C4×D4411yescharacteristic
468C22#1062304111yescharacteristic
469C22#1062305711yescharacteristic
470C22C22×D8811yescharacteristic
471C22C2×#6695711yescharacteristic
472C22C2×#6696211yescharacteristic
473C22#1062327911yescharacteristic
474C4—22no—
475C4—22no—
476C4—22no—
477C4—22no—
478C4—41no—
479C4—442no—
480C4—444no—
481C4—881no—
482C4—882no—
483C4—881no—
484C4C4×D8814yes—
485C4#1062307711yescharacteristic
486C4#1062309211yescharacteristic
487C4#1062310311yescharacteristic
488C4#1062311411yescharacteristic
489C2—882no—
490C2#1307129911yescharacteristic
491C2C2×C4×D8811yescharacteristic
492C2C4×#6696211yescharacteristic
493C2#1307973911yescharacteristic
494C2#1307979711yescharacteristic
495C2#1307992611yescharacteristic
496C2#1307995411yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×C4⋊C8C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenterC4×C4⋊C8D11
hypocenterC11#22110
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×#66922C2semidirect
4. #13069567C2semidirect
5. #13069375C2semidirect
6. #13069349C2semidirect
9. #13069188C2semidirect
11. C4×C11×C4⋊C8C2semidirect
38. #10622459C4semidirect
167. C4×C4⋊C8D11semidirect
404. C11#22110semidirect

Maximal subgroups

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

subgroupindex
C2×#106224592
C4×#669222
#130710802
#130695672
#130693752
#130693492
#130692992
#130692372
#130691882
#130686172
C4×C11×C4⋊C82
#2211011