Finite Group Databasebeta

← #14807424

Subgroups — #14807424

Order 2816.

1094 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622699C211yesmaximal, characteristic, complemented
2C2×#10622681C211yesmaximal, characteristic, complemented
3#13074373C211yesmaximal, characteristic
4#13069624C212yesmaximal, complemented
5#13069617C212yesmaximal
6#13069586C211yesmaximal, characteristic, complemented
7#13069419C211yesmaximal, characteristic, complemented
8#13068971C212yesmaximal, complemented
9#13068957C212yesmaximal, complemented
10#13068382C211yesmaximal, characteristic, complemented
11C2×C11×#541C211yesmaximal, characteristic, complemented
12C11×#541—24no—
13C11×#541—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#126—22no—
16C2×C11×#125—22no—
17C2×C11×#125C2211yescharacteristic
18C2×C11×C22⋊Q8C2212yes—
19C2×C4×Q8×C11C2212yes—
20C2×C11×#117C2211yescharacteristic
21C22×#4326C2212yes—
22C22×#4325C2212yes—
23C2×#66983C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66928C2211yescharacteristic
26C2×#66899C2212yes—
27C2×#66899C2212yes—
28C2×C22⋊(C11⋊C8)C2212yes—
29#10622699—24no—
30#10622681—24no—
31#10622607—22no—
32C2×#66874C2212yes—
33C2×#66873C2212yes—
34#10622574—22no—
35#10622552C2211yescharacteristic
36#10622548C2211yescharacteristic
37#10622542C2211yescharacteristic
38C2×#66867C2211yescharacteristic
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2212yes—
43C22×Q8×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C22×C22⋊D11—21no—
46C22×D44C2311yescharacteristic
47C22×Dic22C2311yescharacteristic
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8D414yescomplemented
50C11×#126—216no—
51C11×#125—216no—
52C11×#125—22no—
53C11×#125D414yescomplemented
54C11×C22⋊Q8—24no—
55C11×C22⋊Q8—24no—
56C4×Q8×C11—24no—
57C4×Q8×C11—24no—
58C11×#117—22no—
59C11×#117—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4D412yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4D412yes—
68C2×C42×C11—22no—
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C22⋊Dic11—21no—
72C2×#4326—24no—
73C2×#4326—24no—
74C2×#4326—42no—
75C2×#4325—24no—
76C2×#4325—24no—
77C2×#4325—42no—
78#66983—42no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—22no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85#66977—42no—
86C2×Dic11⋊C4—21no—
87C22×C11⋊C8C2312yes—
88C22×C11⋊C8C2312yes—
89#66928—22no—
90#66928—22no—
91#66899—42no—
92#66899—42no—
93C11⋊#95—22no—
94C22⋊(C11⋊C8)—24no—
95#66874—24no—
96#66873—24no—
97#66867—22no—
98C4×C11⋊C8—22no—
99#25612—111nomaximal, Sylow
100C24×C11C2×D411yescharacteristic
101C23×D11—21no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11C2×D414yes—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2411yescharacteristic
118C2×C22⋊D11—42no—
119C2×C22⋊D11—82no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—22no—
126C2×D44—22no—
127C2×Dic22—21no—
128C2×Dic22—21no—
129C2×Dic22—22no—
130C2×Dic22—22no—
131C11×C4⋊C4—28no—
132C11×C4⋊C4—28no—
133C11×C4⋊C4—28no—
134C11×C4⋊C4—28no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4C2×D414yes—
138C11×C22⋊C4—28no—
139C11×C22⋊C4—24no—
140C42×C11—28no—
141C42×C11—21no—
142C42×C11—21no—
143C42×C11C2×D412yes—
144C42×C11C2×D412yes—
145C22⋊Dic11—42no—
146#4326—48no—
147#4325—48no—
148(C2×D11)⋊C4—42no—
149(C2×D11)⋊C4—44no—
150(C2×D11)⋊C4—82no—
151C4⋊Dic11—22no—
152C4⋊Dic11—22no—
153C4⋊Dic11—82no—
154Dic11⋊C4—42no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8#4114yes—
161C2×#541D1111yescharacteristic, complemented
162C2×#497—111no—
163C2×#488—111no—
164#2620—111no—
165#2001—112no—
166#2000—112no—
167#1992—111no—
168#1956—111no—
169#1880—112no—
170#1878—112no—
171#1750—111no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—21no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11C22×D411yescharacteristic
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—41no—
181C22×D11—42no—
182C22×D11—42no—
183Q8×C11—24no—
184Q8×C11—24no—
185Q8×C11—42no—
186Q8×C11—42no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—24no—
191C2×C4×C11—24no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11#12014yes—
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C2×#4112yes—
207C2×C4×C11H(5,𝔽2)12yes—
208C22⋊D11—84no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216D44—42no—
217D44—42no—
218Dic22—42no—
219Dic22—42no—
220C11⋊C8—24no—
221C11⋊C8—42no—
222C22×Q16—112no—
223C22×SD16—112no—
224#541—24no—
225#541—24no—
226C2×C4⋊Q8C2×D1111yescharacteristic
227C2×#126—22no—
228C2×#125—22no—
229C2×#125C2×D1111yescharacteristic
230C2×#124—111no—
231C2×C22⋊Q8—111no—
232C2×C22⋊Q8C2×D1112yes—
233C2×#121—111no—
234C2×C4×Q8C2×D1112yes—
235C2×#117C2×D1111yescharacteristic
236#497—224no—
237#488—224no—
238C2×#103—112no—
239C2×#103—112no—
240C2×#103—112no—
241C2×#102—112no—
242C2×C22⋊C8—112no—
243C2×#97—111no—
244C2×C4×C8—111no—
245#396—222no—
246#394—222no—
247#391—111no—
248#390—111no—
249#384—111no—
250#340—112no—
251#340—112no—
252#336—112no—
253C22×C11—42no—
254C22×C11—41no—
255C22×C11—41no—
256C22×C11—41no—
257C22×C11—42no—
258C22×C11C2×#12011yescharacteristic
259C22×C11#53211yescharacteristic
260C22×C11#53511yescharacteristic
261C22×C11#57712yes—
262C22×C11#57812yes—
263C2×D11—82no—
264C2×D11—81no—
265C2×D11—81no—
266C2×D11—81no—
267C2×D11—82no—
268C4×C11—24no—
269C4×C11—41no—
270C4×C11—44no—
271C4×C11—42no—
272C4×C11—44no—
273C4×C11#54612yes—
274C4×C11#55012yes—
275Dic11—81no—
276Dic11—81no—
277Dic11—81no—
278C22×Q8—111no—
279C22×Q8C22×D1112yes—
280C22×D4—111no—
281C22×D4—221no—
282C23×C4C22×D1111yescharacteristic
283C2×Q16—224no—
284C2×Q16—224no—
285C2×Q16—442no—
286C2×SD16—224no—
287C2×SD16—224no—
288C2×SD16—442no—
289C22×C8—112no—
290C22×C8—112no—
291C4⋊Q8—22no—
292C4⋊Q8C22⋊D1114yescomplemented
293#126—216no—
294#125—216no—
295#125—22no—
296#125C22⋊D1114yescomplemented
297#124—222no—
298#124—222no—
299C22⋊Q8—24no—
300C22⋊Q8—24no—
301C22⋊Q8—442no—
302#121—442no—
303C4×Q8—24no—
304C4×Q8—24no—
305#117—22no—
306#117—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—111no—
312C2×C4⋊C4—111no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—222no—
315C2×C4⋊C4C22⋊D1112yes—
316C2×C4⋊C4C22×D1112yes—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—221no—
319C2×C22⋊C4—221no—
320C2×C22⋊C4—222no—
321C2×C22⋊C4—222no—
322C2×C22⋊C4C22⋊D1112yes—
323C2×C42—22no—
324C2×C42C22×D1111yescharacteristic
325C2×C42C22×D1111yescharacteristic
326#103—224no—
327#103—442no—
328#103—442no—
329#102—224no—
330C22⋊C8—224no—
331#97—222no—
332C4×C8—222no—
333#95—222no—
334C2×C11—81no—
335C2×C11#243111yescharacteristic
336C2×C11#301312yes—
337C2×C11#317812yes—
338C2×C11#322211yescharacteristic
339C2×C11#322311yescharacteristic
340D11—161no—
341C24—221no—
342C24C2×C22⋊D1111yescharacteristic
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—222no—
349C2×Q8—222no—
350C2×Q8—221no—
351C2×Q8—221no—
352C2×Q8C2×C22⋊D1114yes—
353C2×D4—222no—
354C2×D4—222no—
355C2×D4—221no—
356C2×D4—221no—
357C2×D4—442no—
358C2×D4—882no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—221no—
366C22×C4—221no—
367C22×C4—221no—
368C22×C4C2×C22⋊D1112yes—
369C22×C4C2×C22⋊D1111yescharacteristic
370C22×C4C2×C22⋊D1112yes—
371C22×C4C23×D1111yescharacteristic
372Q16—448no—
373SD16—448no—
374C2×C8—114no—
375C2×C8—222no—
376C2×C8—222no—
377C2×C8—222no—
378C2×C8—222no—
379C2×C8—222no—
380C4⋊C4—28no—
381C4⋊C4—28no—
382C4⋊C4—28no—
383C4⋊C4—28no—
384C4⋊C4—24no—
385C4⋊C4—22no—
386C4⋊C4—222no—
387C4⋊C4—222no—
388C4⋊C4—442no—
389C4⋊C4—882no—
390C4⋊C4C2×C22⋊D1114yes—
391C22⋊C4—28no—
392C22⋊C4—24no—
393C22⋊C4—442no—
394C22⋊C4—442no—
395C22⋊C4—444no—
396C22⋊C4—882no—
397C42—28no—
398C42—21no—
399C42—21no—
400C42C2×C22⋊D1112yes—
401C42C2×C22⋊D1112yes—
402C11#2561211yescharacteristic, complemented, Sylow
403C23—21no—
404C23—21no—
405C23—22no—
406C23—22no—
407C23—21no—
408C23—441no—
409C23—441no—
410C23—442no—
411C23—442no—
412C23—441no—
413C23C22×C22⋊D1111yescharacteristic
414Q8—24no—
415Q8—24no—
416Q8—42no—
417Q8—42no—
418Q8—442no—
419Q8—442no—
420D4—442no—
421D4—442no—
422D4—884no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—21no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—441no—
446C2×C4#6700614yes—
447C2×C4#41×D1112yes—
448C2×C4#6704212yes—
449C2×C4C22×C22⋊D1111yescharacteristic
450C2×C4C22×C22⋊D1111yescharacteristic
451C8—224no—
452C8—442no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—42no—
457C22—42no—
458C22—881no—
459C22—881no—
460C22—881no—
461C22—882no—
462C22—882no—
463C22#1062336111yescharacteristic
464C22#1062336311yescharacteristic
465C22#1062336812yes—
466C22#1062336912yes—
467C22C2×#6700611yescharacteristic
468C4—24no—
469C4—41no—
470C4—44no—
471C4—42no—
472C4—44no—
473C4—881no—
474C4—881no—
475C4—881no—
476C4#1062336012yes—
477C4#1062336512yes—
478C2—81no—
479C2—1761no—
480C2#1307223111yescharacteristic
481C2#1307793112yes—
482C2#1307928612yes—
483C2#1307968211yescharacteristic
484C2#1307969311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#541C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#541D11
hypocenterC11#25612
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. C2×#10622699C2semidirect
2. C2×#10622681C2semidirect
4. #13069624C2semidirect
6. #13069586C2semidirect
7. #13069419C2semidirect
8. #13068971C2semidirect
9. #13068957C2semidirect
10. #13068382C2semidirect
11. C2×C11×#541C2semidirect
49. C11×C4⋊Q8D4semidirect
53. C11×#125D4semidirect
161. C2×#541D11semidirect
292. C4⋊Q8C22⋊D11semidirect
296. #125C22⋊D11semidirect
402. C11#25612semidirect

Maximal subgroups

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

subgroupindex
C2×#106226992
C2×#106226812
#130743732
#130696242
#130696172
#130695862
#130694192
#130689712
#130689572
#130683822
C2×C11×#5412
#2561211