Finite Group Databasebeta

← #14756217

Subgroups — #14756217

Order 2816.

1238 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622744C211yesmaximal, characteristic
2C22×#66873C211yesmaximal, characteristic
3#13071196C211yesmaximal, characteristic
4#13070973C211yesmaximal, characteristic, complemented
5#13069242C214yesmaximal, complemented
6#13069235C214yesmaximal, complemented
7#13068332C211yesmaximal, characteristic, complemented
8#13068314C211yesmaximal, characteristic, complemented
9C2×C11×#428C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17C11×#428—24no—
18C2×C11×#107C2212yescomplemented
19C2×C11×#106C2212yescomplemented
20C4×C22⋊Dic11—22no—
21#10622744C418yescomplemented
22C2×#66885C2214yes—
23#10622601C2212yes—
24#10622601C2212yes—
25C4⋊C4×Dic11—22no—
26C4⋊C4×Dic11C2214yescomplemented
27C2×#66873—24no—
28C2×#66873C2214yes—
29#10622568—22no—
30#10622552—22no—
31#10622188C2214yescomplemented
32#10622167C2212yescomplemented
33#10622167C2212yescomplemented
34C24×D11—21no—
35C23×C4×C11—21no—
36C23×C4×C11C2311yescharacteristic
37C22×D44—22no—
38C22×D44—22no—
39C22×D44—22no—
40C22×D44—22no—
41C22×D44—21no—
42C22×D44—22no—
43C22×D44C2×C414yes—
44C22×D44C2312yes—
45C2×C11×M16—22no—
46C2×C11×M16—22no—
47C2×C11×M16C2×C414yes—
48C22×C8×C11C2312yes—
49C11×#117—22no—
50C11×#117—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4D414yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C22⋊C4—21no—
58C2×C42×C11—21no—
59C2×C22⋊Dic11—21no—
60C2×C22⋊Dic11D412yes—
61C2×(C2×D11)⋊C4—24no—
62C2×(C2×D11)⋊C4—24no—
63#66979—22no—
64#66979—22no—
65#66979—22no—
66#66979C2×C414yes—
67C2×C4⋊Dic11D412yes—
68C2×C4⋊Dic11C2312yes—
69C2×C4×Dic11—21no—
70C2×C4×Dic11—24no—
71C2×C4×Dic11C2312yes—
72C22×C11⋊C8—22no—
73C22×C11⋊C8—22no—
74C22×C11⋊C8—22no—
75C22×C11⋊C8C2312yes—
76C11×#107—24no—
77C11×#106—24no—
78C11⋊#95—24no—
79#66885C2×C4116yescomplemented
80#66873—28no—
81#21063—111nomaximal, Sylow
82C24×C11C2×D411yescharacteristic
83C23×D11—22no—
84C23×D11—24no—
85C23×D11—42no—
86C23×D11—42no—
87C23×D11—82no—
88C23×D11—82no—
89C22×C4×C11—22no—
90C22×C4×C11—24no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—82no—
94C22×C4×C11C22×C412yes—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D412yes—
97C22×C4×C11#4112yes—
98C22×C4×C11#4112yes—
99C22×C4×C11#4112yes—
100C22×C4×C11#4112yes—
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—22no—
103C22×Dic11C2×D414yes—
104C2×D44—28no—
105C2×D44—24no—
106C2×D44—28no—
107C2×D44—22no—
108C2×D44—22no—
109C2×D44—22no—
110C2×D44—22no—
111C2×D44—22no—
112C2×D44—42no—
113C2×D44—42no—
114C2×D44—44no—
115C2×D44—44no—
116C2×D44C22×C414yes—
117C11×M16—28no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11C22×C414yes—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4C2×D414yes—
128C11×C22⋊C4—42no—
129C42×C11—42no—
130C22⋊Dic11—24no—
131C22⋊Dic11—24no—
132(C2×D11)⋊C4—84no—
133(C2×D11)⋊C4—84no—
134C4⋊Dic11—24no—
135C4⋊Dic11—22no—
136C4⋊Dic11C22×C414yes—
137C4×Dic11—24no—
138C4×Dic11—22no—
139C4×Dic11—22no—
140C4×Dic11—84no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—44no—
145C2×#428D1111yescharacteristic, complemented
146C2×#418—111no—
147C22×#102—111no—
148#2309—111no—
149#2274—111no—
150#1926—114no—
151#1925—114no—
152#1735—111no—
153#1729—111no—
154C23×C11—22no—
155C23×C11—22no—
156C23×C11C4×D412yes—
157C23×C11#12112yes—
158C23×C11#12312yes—
159C23×C11C22×D411yescharacteristic
160C22×D11—24no—
161C22×D11—42no—
162C22×D11—42no—
163C22×D11—44no—
164C22×D11—44no—
165C22×D11—48no—
166C22×D11—88no—
167C22×D11—88no—
168C22×D11—84no—
169C22×D11—84no—
170C2×C4×C11—24no—
171C2×C4×C11—44no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—84no—
177C2×C4×C11#11714yes—
178C2×C4×C11C4×D412yes—
179C2×C4×C11C4×D414yes—
180C2×C4×C11#12112yes—
181C2×C4×C11#12312yes—
182C2×C4×C11#12414yes—
183C2×C4×C11#12614yes—
184C2×C4×C11C23×C411yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C2×C4×C11C2×#4111yescharacteristic
190C2×Dic11—24no—
191C2×Dic11—24no—
192C2×Dic11—24no—
193C2×Dic11—24no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196D44—24no—
197D44—24no—
198D44—42no—
199D44—42no—
200D44—48no—
201C8×C11—24no—
202C11⋊C8—42no—
203C23×D4—111no—
204C22×M16C2×D1111yescharacteristic
205C23×C8—111no—
206C2×#117—111no—
207C2×#117—111no—
208C2×#117C2×D1111yescharacteristic
209C22×C4⋊C4C2×D1111yescharacteristic
210#428—24no—
211C2×#107C2×D1112yescomplemented
212C2×#106C2×D1112yescomplemented
213#418—118no—
214C2×#102—114no—
215C2×#102—114no—
216C2×#102—224no—
217#390—112no—
218#390—112no—
219#390—222no—
220#379—222no—
221C4×C4⋊C4—114no—
222C4×C4⋊C4—222no—
223C4×C22⋊C4—222no—
224#340—112no—
225#340—112no—
226#336—114no—
227C22×C11—24no—
228C22×C11—24no—
229C22×C11—22no—
230C22×C11—22no—
231C22×C11#38814yes—
232C22×C11C2×C4×D411yescharacteristic
233C22×C11C2×#12111yescharacteristic
234C22×C11C2×#12311yescharacteristic
235C22×C11#57612yes—
236C22×C11#57712yes—
237C2×D11—48no—
238C2×D11—44no—
239C2×D11—816no—
240C2×D11—84no—
241C2×D11—82no—
242C2×D11—82no—
243C4×C11—44no—
244C4×C11—81no—
245C4×C11—81no—
246C4×C11#38814yes—
247C4×C11C2×#11711yescharacteristic
248C4×C11C2×C4×D411yescharacteristic
249C4×C11C2×#12411yescharacteristic
250C4×C11C2×#12611yescharacteristic
251Dic11—44no—
252Dic11—44no—
253C25—221no—
254C22×D4—114no—
255C22×D4—112no—
256C22×D4—222no—
257C22×D4—221no—
258C22×D4—222no—
259C22×D4—222no—
260C22×D4—222no—
261C22×D4—222no—
262C23×C4—21no—
263C23×C4C22×D1111yescharacteristic
264C2×M16—22no—
265C2×M16—22no—
266C2×M16C4×D1114yes—
267C22×C8—112no—
268C22×C8—222no—
269C22×C8—222no—
270C22×C8—222no—
271C22×C8C22×D1112yes—
272#117—22no—
273#117—22no—
274#117—114no—
275#117—222no—
276#117—222no—
277#117—222no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—112no—
281C2×C4⋊C4—112no—
282C2×C4⋊C4C22⋊D1114yes—
283C2×C4⋊C4C22×D1111yescharacteristic
284C2×C4⋊C4C22×D1111yescharacteristic
285C2×C4⋊C4C22×D1112yes—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—112no—
288C2×C22⋊C4—221no—
289C2×C22⋊C4—224no—
290C2×C22⋊C4—224no—
291C2×C42—21no—
292C2×C42—112no—
293C2×C42—221no—
294C2×C42—224no—
295#107—24no—
296#106—24no—
297#102—1116no—
298#102—228no—
299#95—224no—
300C2×C11—24no—
301C2×C11C2×#38811yescharacteristic
302C2×C11#294612yes—
303C2×C11#304111yescharacteristic
304C2×C11#304311yescharacteristic
305C2×C11#309612yes—
306D11—84no—
307C24—222no—
308C24—224no—
309C24—442no—
310C24—442no—
311C24—882no—
312C24—882no—
313C24D4×D1111yescharacteristic
314C2×D4—114no—
315C2×D4—228no—
316C2×D4—224no—
317C2×D4—228no—
318C2×D4—222no—
319C2×D4—222no—
320C2×D4—222no—
321C2×D4—222no—
322C2×D4—222no—
323C2×D4—442no—
324C2×D4—444no—
325C2×D4—442no—
326C2×D4—444no—
327C22×C4—22no—
328C22×C4—24no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—82no—
332C22×C4—114no—
333C22×C4—222no—
334C22×C4C2×C4×D1112yes—
335C22×C4#433912yes—
336C22×C4D4×D1111yescharacteristic
337C22×C4#434112yes—
338C22×C4#434312yes—
339C22×C4#434312yes—
340C22×C4C2×C22⋊D1112yes—
341C22×C4C23×D1111yescharacteristic
342M16—28no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—222no—
346C2×C8—222no—
347C2×C8—222no—
348C2×C8—444no—
349C2×C8C2×C4×D1114yes—
350C4⋊C4—24no—
351C4⋊C4—22no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—114no—
357C4⋊C4—224no—
358C4⋊C4—222no—
359C4⋊C4C2×C22⋊D1114yes—
360C22⋊C4—42no—
361C22⋊C4—224no—
362C22⋊C4—224no—
363C22⋊C4—884no—
364C22⋊C4—884no—
365C42—42no—
366C42—224no—
367C42—222no—
368C42—222no—
369C42—884no—
370C11#2106311yescharacteristic, complemented, Sylow
371C23—22no—
372C23—22no—
373C23—224no—
374C23—442no—
375C23—444no—
376C23—444no—
377C23—442no—
378C23—448no—
379C23—888no—
380C23—888no—
381C23—884no—
382C23—884no—
383C23#6694612yes—
384C23#6694712yes—
385C23#6699212yes—
386C23C2×D4×D1111yescharacteristic
387D4—224no—
388D4—224no—
389D4—442no—
390D4—442no—
391D4—448no—
392C2×C4—24no—
393C2×C4—44no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—84no—
399C2×C4—224no—
400C2×C4—224no—
401C2×C4—224no—
402C2×C4—224no—
403C2×C4—442no—
404C2×C4—442no—
405C2×C4#6694514yes—
406C2×C4#6694612yes—
407C2×C4#6694712yes—
408C2×C4#6695114yes—
409C2×C4C4×C22⋊D1114yes—
410C2×C4#6699212yes—
411C2×C4#6700014yes—
412C2×C4C22×C4×D1111yescharacteristic
413C2×C4C2×#433911yescharacteristic
414C2×C4C2×#434111yescharacteristic
415C2×C4C2×#434311yescharacteristic
416C2×C4C2×#434311yescharacteristic
417C2×C4C22×C22⋊D1111yescharacteristic
418C8—24no—
419C8—442no—
420C22—24no—
421C22—22no—
422C22—22no—
423C22—24no—
424C22—448no—
425C22—444no—
426C22—8816no—
427C22—884no—
428C22—882no—
429C22—882no—
430C22#1062260314yes—
431C22C2×#6694611yescharacteristic
432C22C2×#6694711yescharacteristic
433C22#1062330512yes—
434C22#1062330912yes—
435C22C2×#6699211yescharacteristic
436C4—44no—
437C4—81no—
438C4—81no—
439C4—444no—
440C4—444no—
441C4#1062260314yes—
442C4C2×#6694511yescharacteristic
443C4C2×#6695111yescharacteristic
444C4C2×C4×C22⋊D1111yescharacteristic
445C4C2×#6700011yescharacteristic
446C2—24no—
447C2—884no—
448C2C2×#1062260311yescharacteristic
449C2#1307744612yes—
450C2#1307812111yescharacteristic
451C2#1307813911yescharacteristic
452C2#1307857612yes—
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#21063
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. #13070973C2semidirect
5. #13069242C2semidirect
6. #13069235C2semidirect
7. #13068332C2semidirect
8. #13068314C2semidirect
9. C2×C11×#428C2semidirect
18. C2×C11×#107C22semidirect
19. C2×C11×#106C22semidirect
21. #10622744C4semidirect
26. C4⋊C4×Dic11C22semidirect
31. #10622188C22semidirect
32. #10622167C22semidirect
33. #10622167C22semidirect
79. #66885C2×C4semidirect
145. C2×#428D11semidirect
211. C2×#107C2×D11semidirect
212. C2×#106C2×D11semidirect
370. C11#21063semidirect

Maximal subgroups

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

subgroupindex
C2×#106227442
C22×#668732
#130711962
#130709732
#130692422
#130692352
#130683322
#130683142
C2×C11×#4282
#2106311