Finite Group Databasebeta

← #14767635

Subgroups — #14767635

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622673C211yesmaximal, characteristic
2#13071333C211yesmaximal, characteristic, complemented
3#13071329C211yesmaximal, characteristic
4#13069418C211yesmaximal, characteristic, complemented
5#13068968C212yesmaximal
6#13068955C212yesmaximal, complemented
7#13068954C212yesmaximal, complemented
8#13068948C212yesmaximal
9#13068749C211yesmaximal, characteristic, complemented
10#13068367C211yesmaximal, characteristic, complemented
11C11×#1958C211yesmaximal, characteristic
12C2×C11×#124C2211yescharacteristic
13C2×Q8×Dic11C2211yescharacteristic
14C22×#4326C2212yes—
15C2×D4×Dic11C2211yescharacteristic
16C22×#4324C2212yes—
17C2×#66940C2212yes—
18C2×#66922C2211yescharacteristic
19C2×C11×#103C2212yes—
20C2×C11×#102C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22C11×#382C2211yescharacteristic
23#10622843C2211yescharacteristic
24#10622834C2211yescharacteristic
25C2×#66880C2212yes—
26C2×#66880C2212yes—
27#10622673C418yescomplemented
28#10622587C2212yes—
29#10622564—22no—
30#10622563—22no—
31#10622548C2211yescharacteristic
32#10622545C2211yescharacteristic
33C2×#66867C2211yescharacteristic
34#10622267—22no—
35#10622267—22no—
36#10622188C2212yes—
37#10622188C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40C22×Q8×C11C2311yescharacteristic
41C22×D4×C11C2311yescharacteristic
42C23×Dic11—21no—
43C22×Dic22C2312yes—
44C22×C8×C11C2312yes—
45C11×#124—22no—
46C11×#124C2×C414yes—
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C22⋊C4—22no—
49C2×C42×C11C2311yescharacteristic
50C2×C22⋊Dic11—21no—
51C2×C22⋊Dic11—22no—
52Q8×Dic11—42no—
53C2×#4326—42no—
54C2×#4326—42no—
55C2×#4326C2×C418yescomplemented
56D4×Dic11—42no—
57C2×#4324—42no—
58C2×#4324—42no—
59C2×#4324C2×C418yes—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4⋊Dic11C2311yescharacteristic
65C2×Dic11⋊C4—22no—
66C2×C4×Dic11—22no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11C2311yescharacteristic
69C2×C4×Dic11C2311yescharacteristic
70C22×C11⋊C8C2312yes—
71#66940—42no—
72#66940—42no—
73#66922—22no—
74#66922C2×C414yescomplemented
75C11×#103—42no—
76C11×#102—42no—
77C4×C8×C11—22no—
78C11×#95—22no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95D412yes—
83C11⋊#95D412yes—
84#66880—42no—
85#66880—42no—
86#66867C2×C414yescomplemented
87#22278—111nomaximal, Sylow
88C24×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11C22×C412yes—
93C2×D4×C11—21no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11C22×C412yes—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—22no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—42no—
105C22×Dic11—82no—
106C22×Dic11C2×D411yescharacteristic
107C22×Dic11C2×D411yescharacteristic
108C22×Dic11C2×D412yes—
109C2×Dic22—22no—
110C2×Dic22—22no—
111C2×Dic22—22no—
112C2×Dic22—22no—
113C2×Dic22—22no—
114C2×Dic22C22×C414yes—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C22⋊C4—28no—
121C42×C11C22×C412yes—
122C42×C11#4112yes—
123C22⋊Dic11—42no—
124C22⋊Dic11—82no—
125#4326—48no—
126#4324—48no—
127C4⋊Dic11—28no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11—42no—
131C4⋊Dic11—82no—
132Dic11⋊C4—44no—
133C4×Dic11—22no—
134C4×Dic11—22no—
135C4×Dic11—44no—
136C4×Dic11—42no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8C22×C414yes—
140C2×#497—111no—
141#2327—111no—
142#2326—111no—
143#1958D1111yescharacteristic
144#1956—111no—
145#1880—112no—
146#1878—112no—
147#1878—112no—
148#1877—112no—
149#1836—111no—
150#1746—111no—
151C23×C11—22no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—42no—
155C23×C11—42no—
156C23×C11C22×D411yescharacteristic
157Q8×C11—24no—
158Q8×C11—42no—
159D4×C11—24no—
160D4×C11—42no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11C4×D414yes—
170C2×C4×C11C23×C411yescharacteristic
171C2×C4×C11C2×#4111yescharacteristic
172C2×C4×C11H(5,𝔽2)12yes—
173C2×C4×C11H(5,𝔽2)12yes—
174C2×Dic11—24no—
175C2×Dic11—22no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—22no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—84no—
189Dic22—24no—
190Dic22—24no—
191Dic22—42no—
192Dic22—42no—
193C8×C11—42no—
194C11⋊C8—24no—
195C22×Q16—112no—
196C22×SD16—112no—
197C2×C4⋊Q8—111no—
198C2×#124C2×D1111yescharacteristic
199C2×C4×Q8—111no—
200C2×C4×Q8—112no—
201C2×C4×D4—111no—
202#497—118no—
203C2×#103—112no—
204C2×#103—112no—
205C2×#103C2×D1112yes—
206C2×#102C2×D1112yes—
207C2×#97—111no—
208C2×C4×C8C2×D1111yescharacteristic
209#391—111no—
210#391—112no—
211#390—111no—
212#388—222no—
213#387—222no—
214#387—222no—
215#385—222no—
216#384—111no—
217#382C2×D1111yescharacteristic
218#376—111no—
219#340—112no—
220#340—112no—
221#336—112no—
222#336—112no—
223C22×C11—42no—
224C22×C11—44no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11—82no—
228C22×C11C2×C4×D411yescharacteristic
229C22×C11#53511yescharacteristic
230C22×C11#53511yescharacteristic
231C22×C11#57712yes—
232C22×C11#57812yes—
233C4×C11—24no—
234C4×C11—42no—
235C4×C11—82no—
236C4×C11#51812yes—
237C4×C11#54012yes—
238Dic11—44no—
239Dic11—41no—
240Dic11—41no—
241Dic11—42no—
242Dic11—81no—
243Dic11—81no—
244C22×Q8—112no—
245C22×Q8C22×D1111yescharacteristic
246C22×D4C22×D1111yescharacteristic
247C23×C4—221no—
248C2×Q16—118no—
249C2×Q16—442no—
250C2×Q16—442no—
251C2×SD16—118no—
252C2×SD16—442no—
253C2×SD16—442no—
254C22×C8—112no—
255C22×C8C22×D1112yes—
256C4⋊Q8—114no—
257C4⋊Q8—222no—
258#124—22no—
259#124C4×D1114yes—
260C4×Q8—442no—
261C4×Q8—442no—
262C4×Q8—442no—
263C4×D4—442no—
264C2×C4⋊C4—111no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—222no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—222no—
269C2×C4⋊C4—222no—
270C2×C4⋊C4C22×D1112yes—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—221no—
273C2×C22⋊C4—222no—
274C2×C42—111no—
275C2×C42—111no—
276C2×C42—222no—
277C2×C42—221no—
278C2×C42C22×D1111yescharacteristic
279#103—42no—
280#103—442no—
281#103—442no—
282#102—42no—
283#97—114no—
284C4×C8—22no—
285#95—22no—
286#95—112no—
287#95—112no—
288#95—222no—
289#95—222no—
290#95—222no—
291C2×C11—82no—
292C2×C11#232811yescharacteristic
293C2×C11#294712yes—
294C2×C11#322211yescharacteristic
295C2×C11#322311yescharacteristic
296C2×C11#322512yes—
297C24—21no—
298C2×Q8—21no—
299C2×Q8—22no—
300C2×Q8—22no—
301C2×Q8—114no—
302C2×Q8—222no—
303C2×Q8—222no—
304C2×Q8—222no—
305C2×Q8—222no—
306C2×Q8—222no—
307C2×Q8C2×C4×D1112yes—
308C2×D4—21no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4C2×C4×D1112yes—
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—111no—
315C22×C4—111no—
316C22×C4—112no—
317C22×C4—222no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—442no—
321C22×C4—882no—
322C22×C4D4×D1112yes—
323C22×C4C23×D1111yescharacteristic
324Q16—448no—
325SD16—448no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—114no—
330C2×C8—222no—
331C2×C8—222no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—228no—
335C4⋊C4—222no—
336C4⋊C4—222no—
337C4⋊C4—444no—
338C4⋊C4—442no—
339C4⋊C4—882no—
340C22⋊C4—28no—
341C22⋊C4—442no—
342C22⋊C4—882no—
343C42—222no—
344C42—222no—
345C42—442no—
346C42—444no—
347C42C2×C4×D1112yes—
348C42#434112yes—
349C11#2227811yescharacteristic, complemented, Sylow
350C23—22no—
351C23—41no—
352C23—42no—
353C23—42no—
354C23—41no—
355C23C2×D4×D1111yescharacteristic
356Q8—24no—
357Q8—42no—
358Q8—224no—
359Q8—224no—
360Q8—442no—
361Q8—442no—
362D4—24no—
363D4—42no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—222no—
373C2×C4—224no—
374C2×C4—222no—
375C2×C4—222no—
376C2×C4—222no—
377C2×C4—222no—
378C2×C4—221no—
379C2×C4—221no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4—442no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—884no—
387C2×C4(C22⋊D11)⋊C414yes—
388C2×C4C22×C4×D1111yescharacteristic
389C2×C4C2×#434111yescharacteristic
390C2×C4#6703712yes—
391C2×C4#6704212yes—
392C8—42no—
393C8—224no—
394C22—44no—
395C22—42no—
396C22—81no—
397C22—81no—
398C22—82no—
399C22C2×(C22⋊D11)⋊C411yescharacteristic
400C22#1062320511yescharacteristic
401C22#1062324611yescharacteristic
402C22#1062330112yes—
403C22#1062330212yes—
404C4—24no—
405C4—42no—
406C4—82no—
407C4—441no—
408C4—441no—
409C4—442no—
410C4—444no—
411C4—881no—
412C4—881no—
413C4#1062307612yes—
414C4#1062315012yes—
415C2—82no—
416C2#1307134011yescharacteristic
417C2#1307746212yes—
418C2#1307969111yescharacteristic
419C2#1307970211yescharacteristic
420C2#1307971812yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1958C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1958D11
hypocenterC11#22278
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1958

Complements

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

NH ≅ G/Ntype
2. #13071333C2semidirect
4. #13069418C2semidirect
6. #13068955C2semidirect
7. #13068954C2semidirect
9. #13068749C2semidirect
10. #13068367C2semidirect
27. #10622673C4semidirect
55. C2×#4326C2×C4semidirect
74. #66922C2×C4semidirect
86. #66867C2×C4semidirect
349. C11#22278semidirect

Maximal subgroups

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

subgroupindex
C2×#106226732
#130713332
#130713292
#130694182
#130689682
#130689552
#130689542
#130689482
#130687492
#130683672
C11×#19582
#2227811