Finite Group Databasebeta

← #14770849

Subgroups — #14770849

Order 2816.

994 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622615C211yesmaximal, characteristic
2#13071447C211yesmaximal, characteristic
3#13069305C212yesmaximal, complemented
4#13069257C212yesmaximal, complemented
5#13068862C212yesmaximal, complemented
6#13068711C211yesmaximal, characteristic, complemented
7#13068643C211yesmaximal, characteristic, complemented
8#13068554C211yesmaximal, characteristic
9#13068444C212yesmaximal, complemented
10#13068394C211yesmaximal, characteristic, complemented
11C11×#2346C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C23×C11⋊C8C2211yescharacteristic
15C2×C4×D44C2212yes—
16C11×#389C2212yes—
17C11×#388—22no—
18C11×#382—21no—
19C11×#380C2211yescharacteristic
20C4×C11×C4⋊C4C2212yes—
21C4×C11×C22⋊C4C2211yescharacteristic
22C11×#376—21no—
23#10622825C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25#10622615C418yescomplemented
26C2×#66874C2212yes—
27C2×#66874C2211yescharacteristic
28C2×#66874C2211yescharacteristic
29C2×#66873C2212yes—
30C2×#66873C2211yescharacteristic
31C2×#66873C2211yescharacteristic
32C2×#66871C2212yes—
33#10622569—22no—
34#10622542C2212yes—
35C2×#66867C2212yes—
36#10622277—21no—
37D11×#95—21no—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622162C2212yes—
42C23×C4×C11C2311yescharacteristic
43C22×C22⋊D11—21no—
44C2×#4339—22no—
45C2×#4339—24no—
46C2×#4339—42no—
47C2×#4339C2×C414yes—
48C22×D44C2311yescharacteristic
49C22×C4×D11—21no—
50C22×C4×D11—22no—
51C22×Dic22C2311yescharacteristic
52C11×#117—22no—
53C11×#117C2×C414yescomplemented
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4D412yes—
61C2×C42×C11—21no—
62C2×C42×C11—22no—
63C2×C42×C11C2312yes—
64C2×C22⋊Dic11—21no—
65C2×(C2×D11)⋊C4—22no—
66C2×C4⋊Dic11C2312yes—
67C22×C11⋊C8—42no—
68C22×C11⋊C8C2×C414yescomplemented
69C22×C11⋊C8C2312yes—
70C22×C11⋊C8C2311yescharacteristic
71C22×C11⋊C8C2311yescharacteristic
72C4×D44—24no—
73C4×D44—42no—
74C11×#95—21no—
75C11×#95—22no—
76C11×#95—22no—
77C11×#95D411yescharacteristic
78C11×#95D411yescharacteristic
79C11⋊#95—21no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C22⋊(C11⋊C8)—22no—
83#66874—42no—
84#66874C2×C414yescomplemented
85#66874C2×C414yescomplemented
86#66873—24no—
87#66873C2×C414yes—
88#66873C2×C414yes—
89#66871—42no—
90#66867—42no—
91#22564—111nomaximal, Sylow
92C24×C11C2×D411yescharacteristic
93C23×D11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11C22×C412yes—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11#4112yes—
104C22×C4×C11C2411yescharacteristic
105C2×C22⋊D11—24no—
106C2×C22⋊D11—44no—
107C22×Dic11—21no—
108C22×Dic11—22no—
109#4339—28no—
110#4339—44no—
111#4339—48no—
112C2×D44—21no—
113C2×D44—22no—
114C2×D44C22×C412yes—
115C2×D44#4114yes—
116C2×C4×D11—24no—
117C2×C4×D11—44no—
118C2×C4×D11—44no—
119C2×C4×D11—44no—
120C2×C4×D11—82no—
121C2×Dic22—22no—
122C2×Dic22—21no—
123C2×Dic22—22no—
124C2×Dic22C22×C412yes—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—82no—
130C11×C4⋊C4C22×C412yes—
131C11×C4⋊C4C22×C412yes—
132C11×C22⋊C4—24no—
133C11×C22⋊C4—42no—
134C11×C22⋊C4—81no—
135C42×C11—24no—
136C42×C11—22no—
137C42×C11—22no—
138C42×C11—44no—
139C22⋊Dic11—81no—
140(C2×D11)⋊C4—44no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—44no—
149C2×C11⋊C8C22×C412yes—
150C2×C11⋊C8C22×C412yes—
151C2×#416—111no—
152#2346D1111yescharacteristic, complemented
153#2339—111no—
154#1935—112no—
155#1928—112no—
156#1862—112no—
157#1825—111no—
158#1808—111no—
159#1788—111no—
160#1762—112no—
161#1752—111no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11C4×D412yes—
167C23×C11C22×D411yescharacteristic
168C22×D11—22no—
169C22×D11—24no—
170C22×D11—42no—
171C22×D11—41no—
172C22×D11—41no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—24no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—42no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11C4×D412yes—
192C2×C4×C11C23×C411yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11C2×#4112yes—
195C2×C4×C11H(5,𝔽2)12yes—
196C22⋊D11—48no—
197C2×Dic11—22no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202D44—22no—
203D44—24no—
204D44#11714yes—
205C4×D11—48no—
206C4×D11—88no—
207Dic22—22no—
208Dic22—22no—
209Dic22—42no—
210C11⋊C8—22no—
211C11⋊C8—22no—
212C11⋊C8—42no—
213C22×#41—111no—
214C23×C8—111no—
215C2×C4×D4—112no—
216C2×#117C2×D1111yescharacteristic
217C2×#107—112no—
218#416—118no—
219C2×#103—111no—
220C2×#103—111no—
221C2×#103—112no—
222C2×#102—111no—
223C2×#102—111no—
224C2×#102—112no—
225C2×C22⋊C8—111no—
226C2×#97—112no—
227#391—112no—
228#389C2×D1112yes—
229#388—22no—
230#386—222no—
231#382—21no—
232#381—221no—
233#380—111no—
234#380C2×D1111yescharacteristic
235C4×C4⋊C4C2×D1112yes—
236C4×C22⋊C4C2×D1111yescharacteristic
237#376—21no—
238C2×#95—221no—
239#340—112no—
240#340—112no—
241#340—112no—
242#336—112no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—22no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11C2×C4×D411yescharacteristic
249C22×C11#54612yes—
250C22×C11#57512yes—
251C22×C11#57611yescharacteristic
252C22×C11#57811yescharacteristic
253C2×D11—24no—
254C2×D11—42no—
255C2×D11—42no—
256C2×D11—44no—
257C2×D11—44no—
258C4×C11—22no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—42no—
263C4×C11—82no—
264C4×C11C2×#11711yescharacteristic
265C4×C11#51811yescharacteristic
266C4×C11#55112yes—
267Dic11—42no—
268Dic11—82no—
269C2×#41—114no—
270C2×#41—224no—
271C2×#41—222no—
272C2×#41—442no—
273C22×Q8—111no—
274C22×D4—111no—
275C22×D4—221no—
276C23×C4—221no—
277C23×C4—222no—
278C23×C4C22×D1111yescharacteristic
279C22×C8—111no—
280C22×C8—111no—
281C22×C8—114no—
282C22×C8—112no—
283C22×C8—442no—
284C4×D4—224no—
285C4×D4—442no—
286#117—22no—
287#117C4×D1114yescomplemented
288C2×C4⋊C4—22no—
289C2×C4⋊C4—112no—
290C2×C4⋊C4C22×D1112yes—
291C2×C4⋊C4C22×D1111yescharacteristic
292C2×C4⋊C4C22×D1111yescharacteristic
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—222no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4C22⋊D1112yes—
298C2×C42—21no—
299C2×C42—22no—
300C2×C42C22×D1112yes—
301#107—442no—
302#103—114no—
303#103—114no—
304#103—442no—
305#102—114no—
306#102—114no—
307#102—224no—
308C22⋊C8—222no—
309#97—442no—
310#95—21no—
311#95—22no—
312#95—22no—
313#95—221no—
314#95—222no—
315#95—222no—
316#95C22⋊D1111yescharacteristic
317#95C22⋊D1111yescharacteristic
318C2×C11—42no—
319C2×C11#234211yescharacteristic
320C2×C11#294311yescharacteristic
321C2×C11#295111yescharacteristic
322C2×C11#331512yes—
323C2×C11#331912yes—
324D11—44no—
325C24—221no—
326C24C2×C22⋊D1111yescharacteristic
327#41—228no—
328#41—444no—
329#41—448no—
330C2×Q8—112no—
331C2×Q8—221no—
332C2×Q8—222no—
333C2×Q8—222no—
334C2×D4—112no—
335C2×D4—114no—
336C2×D4—224no—
337C2×D4—221no—
338C2×D4—222no—
339C2×D4—444no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—221no—
346C22×C4—224no—
347C22×C4—222no—
348C22×C4—444no—
349C22×C4—444no—
350C22×C4—444no—
351C22×C4—882no—
352C22×C4C2×C4×D1112yes—
353C22×C4#433912yes—
354C22×C4C2×C22⋊D1112yes—
355C22×C4C2×C22⋊D1112yes—
356C22×C4C2×C22⋊D1111yescharacteristic
357C22×C4C23×D1111yescharacteristic
358C2×C8—112no—
359C2×C8—112no—
360C2×C8—222no—
361C2×C8—222no—
362C2×C8—222no—
363C2×C8—222no—
364C2×C8—222no—
365C2×C8—444no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—82no—
371C4⋊C4—222no—
372C4⋊C4—222no—
373C4⋊C4C2×C4×D1112yes—
374C4⋊C4C2×C4×D1112yes—
375C22⋊C4—24no—
376C22⋊C4—42no—
377C22⋊C4—81no—
378C22⋊C4—444no—
379C22⋊C4—881no—
380C42—24no—
381C42—22no—
382C42—22no—
383C42—44no—
384C11#2256411yescharacteristic, complemented, Sylow
385C23—22no—
386C23—22no—
387C23—21no—
388C23—21no—
389C23—222no—
390C23—224no—
391C23—442no—
392C23—441no—
393C23—441no—
394C23C4×C22⋊D1112yes—
395C23C22×C22⋊D1111yescharacteristic
396Q8—222no—
397Q8—222no—
398Q8—442no—
399D4—114no—
400D4—222no—
401D4—224no—
402D4—448no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—222no—
422C2×C4—448no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4—442no—
427C2×C4—888no—
428C2×C4C4×C22⋊D1112yes—
429C2×C4C22×C4×D1111yescharacteristic
430C2×C4C2×#433911yescharacteristic
431C2×C4#41×D1112yes—
432C2×C4#6704212yes—
433C8—222no—
434C8—222no—
435C8—442no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—42no—
440C22—42no—
441C22—224no—
442C22—444no—
443C22—442no—
444C22—444no—
445C22—442no—
446C22C2×C4×C22⋊D1111yescharacteristic
447C22#1062335312yes—
448C22#1062336012yes—
449C22#1062336611yescharacteristic
450C22#1062336911yescharacteristic
451C4—22no—
452C4—42no—
453C4—42no—
454C4—42no—
455C4—42no—
456C4—82no—
457C4—442no—
458C4—882no—
459C4D11×#11711yescharacteristic
460C4#1062305211yescharacteristic
461C4#1062305812yes—
462C2—42no—
463C2—444no—
464C2#1307146611yescharacteristic
465C2#1307741411yescharacteristic
466C2#1307748911yescharacteristic
467C2#1308070612yes—
468C2#1308076612yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2346C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#2346D11
hypocenterC11#22564
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2346

Complements

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

NH ≅ G/Ntype
3. #13069305C2semidirect
4. #13069257C2semidirect
5. #13068862C2semidirect
6. #13068711C2semidirect
7. #13068643C2semidirect
9. #13068444C2semidirect
10. #13068394C2semidirect
11. C11×#2346C2semidirect
25. #10622615C4semidirect
53. C11×#117C2×C4semidirect
68. C22×C11⋊C8C2×C4semidirect
84. #66874C2×C4semidirect
85. #66874C2×C4semidirect
152. #2346D11semidirect
287. #117C4×D11semidirect
384. C11#22564semidirect

Maximal subgroups

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

subgroupindex
C2×#106226152
#130714472
#130693052
#130692572
#130688622
#130687112
#130686432
#130685542
#130684442
#130683942
C11×#23462
#2256411