Finite Group Databasebeta

← #14756189

Subgroups — #14756189

Order 2816.

1342 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622744C211yesmaximal, characteristic
2C2×#10622614C211yesmaximal, characteristic
3C2×#10622601C211yesmaximal, characteristic
4#117×Dic11C211yesmaximal, characteristic, complemented
5#13069242C214yesmaximal, complemented
6#13069235C214yesmaximal, complemented
7#13068335C211yesmaximal, characteristic, complemented
8#13068309C211yesmaximal, characteristic, complemented
9C2×C11×#428C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×(C2×D11)⋊C4—22no—
15C2×#66979C2211yescharacteristic
16C22×C4×Dic11C2211yescharacteristic
17C22×#4318C2211yescharacteristic
18C11×#428—24no—
19C2×C11×#107C2212yescomplemented
20C2×C11×#106C2212yescomplemented
21#10622744C418yescomplemented
22C2×#66885C2214yes—
23#10622614—24no—
24#10622601—21no—
25#10622601—21no—
26#10622601C2214yes—
27C4⋊C4×Dic11C2212yescomplemented
28C4⋊C4×Dic11C2212yescomplemented
29C2×#66873C2212yes—
30C2×#66873C2212yes—
31C22⋊C4×Dic11—22no—
32#10622545—21no—
33C42×Dic11—21no—
34#10622188C2214yescomplemented
35#10622167C2214yescomplemented
36C24×D11—21no—
37C23×C4×C11—21no—
38C23×C4×C11C2311yescharacteristic
39C23×Dic11D412yes—
40C22×D44—22no—
41C22×D44—22no—
42C22×D44—22no—
43C22×D44—22no—
44C22×D44—21no—
45C22×D44—22no—
46C22×D44C2×C414yes—
47C22×D44C2312yes—
48C2×C11×M16—22no—
49C2×C11×M16—22no—
50C2×C11×M16C2×C414yes—
51C22×C8×C11C2312yes—
52C11×#117—22no—
53C11×#117D414yes—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C42×C11—21no—
62C2×C22⋊Dic11—21no—
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—24no—
65C2×(C2×D11)⋊C4—48no—
66#66979—22no—
67#66979C2×C414yes—
68C2×C4⋊Dic11C2312yes—
69C2×C4×Dic11—21no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11D411yescharacteristic
75C2×C4×Dic11D411yescharacteristic
76C2×C4×Dic11C2312yes—
77C2×#4318—22no—
78C2×#4318—22no—
79C2×#4318—22no—
80C22×C11⋊C8C2312yes—
81C11×#107—24no—
82C11×#106—24no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85#66885C2×C4116yescomplemented
86#66873—24no—
87#66873—24no—
88#21060—111nomaximal, Sylow
89C24×C11C2×D411yescharacteristic
90C23×D11—24no—
91C23×D11—22no—
92C23×D11—44no—
93C23×D11—44no—
94C23×D11—42no—
95C23×D11—42no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—44no—
100C22×C4×C11—42no—
101C22×C4×C11C22×C412yes—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D412yes—
104C22×C4×C11#4112yes—
105C22×C4×C11#4112yes—
106C22×C4×C11#4112yes—
107C22×C4×C11#4112yes—
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—24no—
110C22×Dic11—24no—
111C22×Dic11—22no—
112C22×Dic11—42no—
113C22×Dic11C2×D412yes—
114C22×Dic11C2×D412yes—
115C2×D44—28no—
116C2×D44—24no—
117C2×D44—28no—
118C2×D44—22no—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44—42no—
124C2×D44—42no—
125C2×D44—44no—
126C2×D44—44no—
127C2×D44C22×C414yes—
128C11×M16—28no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11C22×C414yes—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—42no—
137C11×C4⋊C4C2×D412yes—
138C11×C4⋊C4C2×D412yes—
139C11×C22⋊C4—24no—
140C42×C11—24no—
141C22⋊Dic11—24no—
142(C2×D11)⋊C4—48no—
143(C2×D11)⋊C4—48no—
144C4⋊Dic11—22no—
145C4⋊Dic11C22×C414yes—
146C4×Dic11—24no—
147C4×Dic11—22no—
148C4×Dic11—22no—
149C4×Dic11—22no—
150C4×Dic11—22no—
151C4×Dic11—44no—
152C4×Dic11—44no—
153#4318—44no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×#428D1111yescharacteristic, complemented
158C2×#418—111no—
159C2×#418—111no—
160C2×#390—111no—
161C4×#117—111no—
162#1926—114no—
163#1925—114no—
164#1736—111no—
165#1728—111no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11C4×D412yes—
169C23×C11#12112yes—
170C23×C11#12312yes—
171C23×C11C22×D411yescharacteristic
172C22×D11—24no—
173C22×D11—416no—
174C22×D11—42no—
175C22×D11—42no—
176C22×D11—44no—
177C22×D11—44no—
178C22×D11—48no—
179C22×D11—88no—
180C22×D11—84no—
181C22×D11—84no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—44no—
188C2×C4×C11—84no—
189C2×C4×C11#11714yes—
190C2×C4×C11C4×D412yes—
191C2×C4×C11C4×D414yes—
192C2×C4×C11#12112yes—
193C2×C4×C11#12312yes—
194C2×C4×C11#12414yes—
195C2×C4×C11#12614yes—
196C2×C4×C11C23×C411yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—24no—
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—48no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11AGL(1,ℤ/8)14yes—
212D44—24no—
213D44—24no—
214D44—42no—
215D44—42no—
216D44—48no—
217C8×C11—24no—
218C11⋊C8—42no—
219C23×D4—111no—
220C22×M16—111no—
221C22×M16C2×D1111yescharacteristic
222C2×#117—111no—
223C2×#117C2×D1111yescharacteristic
224C22×C4⋊C4C2×D1111yescharacteristic
225C22×C22⋊C4—222no—
226C22×C42—111no—
227#428—24no—
228C2×#107C2×D1112yescomplemented
229C2×#106C2×D1112yescomplemented
230#418—118no—
231#418—224no—
232C2×#102—114no—
233C2×#102—112no—
234C2×#102—112no—
235#390—114no—
236#390—221no—
237#390—221no—
238C4×C4⋊C4—112no—
239C4×C4⋊C4—112no—
240C4×C22⋊C4—222no—
241#376—221no—
242C43—221no—
243#340—114no—
244#336—114no—
245C22×C11—24no—
246C22×C11—24no—
247C22×C11—22no—
248C22×C11—22no—
249C22×C11#38814yes—
250C22×C11C2×C4×D411yescharacteristic
251C22×C11C2×#12111yescharacteristic
252C22×C11C2×#12311yescharacteristic
253C22×C11C2×AGL(1,ℤ/8)12yes—
254C22×C11#57512yes—
255C2×D11—48no—
256C2×D11—44no—
257C2×D11—816no—
258C2×D11—84no—
259C2×D11—82no—
260C2×D11—82no—
261C4×C11—42no—
262C4×C11—42no—
263C4×C11—82no—
264C4×C11#38814yes—
265C4×C11C2×#11711yescharacteristic
266C4×C11C2×C4×D411yescharacteristic
267C4×C11C2×#12411yescharacteristic
268C4×C11C2×#12611yescharacteristic
269Dic11—24no—
270Dic11—42no—
271Dic11—44no—
272C25—221no—
273C22×D4—114no—
274C22×D4—112no—
275C22×D4—222no—
276C22×D4—221no—
277C22×D4—222no—
278C22×D4—222no—
279C22×D4—222no—
280C22×D4—222no—
281C23×C4—21no—
282C23×C4—112no—
283C23×C4C22×D1111yescharacteristic
284C2×M16—22no—
285C2×M16—22no—
286C2×M16—222no—
287C2×M16—222no—
288C2×M16—222no—
289C2×M16C4×D1114yes—
290C22×C8—112no—
291C22×C8C22×D1112yes—
292#117—22no—
293#117—114no—
294#117—222no—
295#117C22⋊D1114yes—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—112no—
300C2×C4⋊C4C22×D1112yes—
301C2×C4⋊C4C22×D1111yescharacteristic
302C2×C4⋊C4C22×D1111yescharacteristic
303C2×C22⋊C4—21no—
304C2×C22⋊C4—221no—
305C2×C22⋊C4—224no—
306C2×C22⋊C4—224no—
307C2×C22⋊C4—448no—
308C2×C42—21no—
309C2×C42—111no—
310C2×C42—111no—
311C2×C42—112no—
312C2×C42—222no—
313C2×C42—221no—
314C2×C42—222no—
315C2×C42—222no—
316C2×C42—222no—
317#107—24no—
318#106—24no—
319#102—1116no—
320#102—224no—
321#102—224no—
322#95—222no—
323#95—222no—
324C2×C11—24no—
325C2×C11C2×#38811yescharacteristic
326C2×C11C4×AGL(1,ℤ/8)12yes—
327C2×C11#303811yescharacteristic
328C2×C11#304011yescharacteristic
329C2×C11#309412yes—
330D11—84no—
331C24—224no—
332C24—222no—
333C24—444no—
334C24—444no—
335C24—442no—
336C24—442no—
337C24D4×D1111yescharacteristic
338C2×D4—114no—
339C2×D4—228no—
340C2×D4—224no—
341C2×D4—228no—
342C2×D4—222no—
343C2×D4—222no—
344C2×D4—222no—
345C2×D4—222no—
346C2×D4—222no—
347C2×D4—442no—
348C2×D4—444no—
349C2×D4—442no—
350C2×D4—444no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—44no—
355C22×C4—42no—
356C22×C4—112no—
357C22×C4—112no—
358C22×C4—224no—
359C22×C4—224no—
360C22×C4—222no—
361C22×C4—442no—
362C22×C4C2×C4×D1112yes—
363C22×C4#433912yes—
364C22×C4D4×D1111yescharacteristic
365C22×C4#434112yes—
366C22×C4#434312yes—
367C22×C4#434312yes—
368C22×C4C2×C22⋊D1112yes—
369C22×C4C23×D1111yescharacteristic
370M16—28no—
371M16—444no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—222no—
375C2×C8—222no—
376C2×C8—222no—
377C2×C8C2×C4×D1114yes—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—42no—
383C4⋊C4—114no—
384C4⋊C4—222no—
385C4⋊C4C2×C22⋊D1112yes—
386C4⋊C4C2×C22⋊D1112yes—
387C22⋊C4—24no—
388C22⋊C4—224no—
389C22⋊C4—448no—
390C22⋊C4—448no—
391C42—24no—
392C42—224no—
393C42—222no—
394C42—222no—
395C42—222no—
396C42—222no—
397C42—444no—
398C42—444no—
399C11#2106011yescharacteristic, complemented, Sylow
400C23—22no—
401C23—22no—
402C23—224no—
403C23—4416no—
404C23—442no—
405C23—444no—
406C23—444no—
407C23—442no—
408C23—448no—
409C23—888no—
410C23—884no—
411C23—884no—
412C23#6694612yes—
413C23#6694712yes—
414C23#6699212yes—
415C23C2×D4×D1111yescharacteristic
416D4—224no—
417D4—224no—
418D4—442no—
419D4—442no—
420D4—448no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—44no—
426C2×C4—42no—
427C2×C4—84no—
428C2×C4—114no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—224no—
432C2×C4—222no—
433C2×C4—222no—
434C2×C4—222no—
435C2×C4—448no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4#6694514yes—
439C2×C4#6694612yes—
440C2×C4#6694712yes—
441C2×C4#6695114yes—
442C2×C4C4×C22⋊D1114yes—
443C2×C4#6699212yes—
444C2×C4#6700014yes—
445C2×C4C22×C4×D1111yescharacteristic
446C2×C4C2×#433911yescharacteristic
447C2×C4C2×#434111yescharacteristic
448C2×C4C2×#434311yescharacteristic
449C2×C4C2×#434311yescharacteristic
450C2×C4C22×C22⋊D1111yescharacteristic
451C8—24no—
452C8—442no—
453C22—24no—
454C22—22no—
455C22—22no—
456C22—24no—
457C22—448no—
458C22—444no—
459C22—8816no—
460C22—884no—
461C22—882no—
462C22—882no—
463C22#1062260314yes—
464C22C2×#6694611yescharacteristic
465C22C2×#6694711yescharacteristic
466C22D11×AGL(1,ℤ/8)12yes—
467C22#1062330812yes—
468C22C2×#6699211yescharacteristic
469C4—42no—
470C4—42no—
471C4—82no—
472C4—224no—
473C4—442no—
474C4—444no—
475C4#1062260314yes—
476C4C2×#6694511yescharacteristic
477C4C2×#6695111yescharacteristic
478C4C2×C4×C22⋊D1111yescharacteristic
479C4C2×#6700011yescharacteristic
480C2—24no—
481C2—884no—
482C2C2×#1062260311yescharacteristic
483C2#1307742312yes—
484C2#1307809411yescharacteristic
485C2#1307811211yescharacteristic
486C2#1307855812yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#428C2
socleC23×C11C22×D4
prime radicalC23×D44C22
cosocleC22×C4×C11C24
hypercenterC2×#428D11
hypocenterC11#21060
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
4. #117×Dic11C2semidirect
5. #13069242C2semidirect
6. #13069235C2semidirect
7. #13068335C2semidirect
8. #13068309C2semidirect
9. C2×C11×#428C2semidirect
19. C2×C11×#107C22semidirect
20. C2×C11×#106C22semidirect
21. #10622744C4semidirect
27. C4⋊C4×Dic11C22semidirect
28. C4⋊C4×Dic11C22semidirect
34. #10622188C22semidirect
35. #10622167C22semidirect
85. #66885C2×C4semidirect
157. C2×#428D11semidirect
228. C2×#107C2×D11semidirect
229. C2×#106C2×D11semidirect
399. C11#21060semidirect

Maximal subgroups

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

subgroupindex
C2×#106227442
C2×#106226142
C2×#106226012
#117×Dic112
#130692422
#130692352
#130683352
#130683092
C2×C11×#4282
#2106011