Finite Group Databasebeta

← #14789016

Subgroups — #14789016

Order 2816.

1430 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078084C212yesmaximal, complemented
2C2×#10622855C212yesmaximal, complemented
3#13071328C211yesmaximal, characteristic, complemented
4#13069837C212yesmaximal, complemented
5#13069663C212yesmaximal, complemented
6#13069449C212yesmaximal, complemented
7#13068608C211yesmaximal, characteristic, complemented
8#13068570C212yesmaximal, complemented
9C11×#3496C211yesmaximal, characteristic
10C2×C11×H(5,𝔽2)C2212yes—
11C11×#547—22no—
12C11×#546—24no—
13D42×C11—22no—
14C11×#537C2212yes—
15C11×#534—22no—
16C11×#532C2212yes—
17C2×C11×#121—22no—
18C2×C4×D4×C11C2211yescharacteristic
19C2×#67004C2214yescomplemented
20C2×#66989C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic, complemented
22#10622855—28no—
23C2×#66901C2214yescomplemented
24C2×#66901C2214yescomplemented
25#10622845C2214yescomplemented
26#10622834C2211yescharacteristic
27C2×#66897C2212yes—
28#10622823—22no—
29#10622703—22no—
30#10622688—22no—
31#10622667—24no—
32#10622589C2211yescharacteristic, complemented
33#10622587C2211yescharacteristic, complemented
34#10622557—22no—
35#10622545C2211yescharacteristic, complemented
36#10622537C2212yescomplemented
37#10622168C2212yescomplemented
38C11×H(5,𝔽2)—24no—
39C11×H(5,𝔽2)—24no—
40C11×H(5,𝔽2)—44no—
41C2×C11×#41—24no—
42C2×C11×#41C2314yes—
43C22×D4×C11—24no—
44C22×D4×C11—22no—
45C22×D4×C11—24no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11D412yes—
48C22×Dic22C2311yescharacteristic
49C11×C4⋊Q8D412yes—
50C11×#127D412yes—
51C11×#124D414yes—
52C11×#123—28no—
53C11×C22⋊Q8—24no—
54C11×#121—24no—
55C11×#121—24no—
56C11×#121—24no—
57C11×#121—22no—
58C11×#121—24no—
59C11×#121—22no—
60C11×#120—28no—
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C4×D4×C11—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4D412yes—
69C2×C42×C11C2311yescharacteristic
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—22no—
72#67004—28no—
73#67004—44no—
74C2×#4326—24no—
75#66989—22no—
76#66989D414yescomplemented
77C2×#4324—24no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—22no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11C2311yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C2×#4318C2314yes—
85C4×Dic22—22no—
86C4×Dic22—22no—
87#66901—28no—
88#66901—44no—
89#66899—24no—
90#66897—24no—
91#66896—24no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94C11⋊#95—22no—
95C4⋊(C11⋊C8)—22no—
96C4⋊(C11⋊C8)—22no—
97#24228—111nomaximal, Sylow
98C24×C11—24no—
99C24×C11C2×D412yes—
100C11×#41—24no—
101C11×#41—24no—
102C11×#41—24no—
103C11×#41—24no—
104C11×#41—48no—
105C11×#41—48no—
106C2×Q8×C11C2×D414yes—
107C2×D4×C11—28no—
108C2×D4×C11—24no—
109C2×D4×C11—24no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—48no—
115C2×D4×C11—48no—
116C2×D4×C11—48no—
117C2×D4×C11—48no—
118C2×D4×C11—84no—
119C2×D4×C11C2×D414yes—
120C2×D4×C11C2×D412yes—
121C2×D4×C11#4112yes—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—82no—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C2×Dic22—22no—
136C2×Dic22—21no—
137C2×Dic22—22no—
138C2×Dic22C2×D412yescomplemented
139C11×C4⋊C4—24no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C22⋊C4—28no—
144C11×C22⋊C4—24no—
145C11×C22⋊C4—24no—
146C11×C22⋊C4—24no—
147C42×C11C2×D412yes—
148C42×C11C2×D412yes—
149C22⋊Dic11—28no—
150C22⋊Dic11—82no—
151#4326—48no—
152#4324—48no—
153C4⋊Dic11—22no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—82no—
157C4×Dic11—21no—
158C4×Dic11—22no—
159C4×Dic11—42no—
160C4×Dic11C2×D412yescomplemented
161#4318—24no—
162#4318—24no—
163C2×C11⋊C8—24no—
164#3496D1111yescharacteristic
165#3037—112no—
166C2×#455—112no—
167#2326—111no—
168#2039—112no—
169#2007—112no—
170#1963—112no—
171#1800—111no—
172#1792—112no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—24no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—48no—
179C23×C11—84no—
180C23×C11—84no—
181C23×C11#12114yes—
182C23×C11C22×D411yescharacteristic
183Q8×C11—24no—
184Q8×C11—24no—
185D4×C11—24no—
186D4×C11—24no—
187D4×C11—24no—
188D4×C11—24no—
189D4×C11—44no—
190D4×C11—416no—
191D4×C11—44no—
192D4×C11—44no—
193D4×C11—82no—
194D4×C11—84no—
195C2×C4×C11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—44no—
200C2×C4×C11—48no—
201C2×C4×C11—44no—
202C2×C4×C11—44no—
203C2×C4×C11—42no—
204C2×C4×C11—82no—
205C2×C4×C11#12012yes—
206C2×C4×C11#12011yescharacteristic
207C2×C4×C11#12011yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D412yes—
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11H(5,𝔽2)12yes—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—42no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223Dic22—24no—
224Dic22—42no—
225C11⋊C8—44no—
226C2×H(5,𝔽2)C2×D1112yes—
227C2×#137—114no—
228#547—22no—
229#546—24no—
230D42—22no—
231#537C2×D1112yes—
232#534—22no—
233#532C2×D1112yes—
234C2×#124—111no—
235C2×#121—22no—
236C2×C4×Q8—111no—
237C2×C4×D4C2×D1111yescharacteristic
238#464—224no—
239#462—222no—
240#460—222no—
241#455—228no—
242#423—112no—
243C2×#104—114no—
244C2×#104—114no—
245#417—114no—
246C2×#100—112no—
247#391—111no—
248#390—111no—
249#388—222no—
250#385—222no—
251#384—111no—
252#376—111no—
253#343—112no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—24no—
257C22×C11—44no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—44no—
261C22×C11—44no—
262C22×C11—44no—
263C22×C11—82no—
264C22×C11—168no—
265C22×C11C2×#12011yescharacteristic
266C22×C11C2×#12111yescharacteristic
267C22×C11#53511yescharacteristic
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—22no—
271C4×C11—44no—
272C4×C11—42no—
273C4×C11D4212yes—
274C4×C11#54612yes—
275Dic11—42no—
276Dic11—42no—
277Dic11—81no—
278Dic11—81no—
279H(5,𝔽2)—24no—
280H(5,𝔽2)—24no—
281H(5,𝔽2)—44no—
282C2×#41—24no—
283C2×#41C22×D1114yes—
284C22×Q8—111no—
285C22×D4—24no—
286C22×D4—22no—
287C22×D4—24no—
288C22×D4C22×D1111yescharacteristic
289C23×C4C22⋊D1112yes—
290#137—228no—
291#137—444no—
292C2×Q16—224no—
293C2×SD16—224no—
294C2×M16—114no—
295C4⋊Q8C22⋊D1112yes—
296#127C22⋊D1112yes—
297#124—114no—
298#124—222no—
299#124C22⋊D1114yes—
300#123—28no—
301C22⋊Q8—24no—
302#121—24no—
303#121—24no—
304#121—24no—
305#121—22no—
306#121—24no—
307#121—22no—
308#120—28no—
309C4×Q8—222no—
310C4×Q8—222no—
311C4×D4—22no—
312C4×D4—22no—
313C4×D4—22no—
314C4×D4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—111no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4C22×D1111yescharacteristic
320C2×C22⋊C4—24no—
321C2×C22⋊C4—222no—
322C2×C22⋊C4—222no—
323C2×C22⋊C4C22⋊D1112yes—
324C2×C42—111no—
325C2×C42—111no—
326C2×C42—221no—
327C2×C42C22×D1111yescharacteristic
328C4⋊C8—222no—
329C4⋊C8—222no—
330#104—228no—
331#104—444no—
332#103—224no—
333#102—224no—
334#100—224no—
335#95—221no—
336#95—221no—
337#95—222no—
338C2×C11—21no—
339C2×C11—21no—
340C2×C11—44no—
341C2×C11—84no—
342C2×C11#240811yescharacteristic
343C2×C11#301911yescharacteristic
344C2×C11#302211yescharacteristic
345C24—24no—
346C24C2×C22⋊D1112yes—
347#41—24no—
348#41—24no—
349#41—24no—
350#41—24no—
351#41—48no—
352#41—48no—
353C2×Q8—112no—
354C2×Q8—221no—
355C2×Q8—222no—
356C2×Q8—222no—
357C2×Q8C2×C22⋊D1114yes—
358C2×D4—28no—
359C2×D4—24no—
360C2×D4—24no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—48no—
366C2×D4—48no—
367C2×D4—48no—
368C2×D4—48no—
369C2×D4—84no—
370C2×D4D4×D1112yes—
371C2×D4#434112yes—
372C2×D4C2×C22⋊D1114yes—
373C22×C4—24no—
374C22×C4—22no—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—82no—
378C22×C4—221no—
379C22×C4—221no—
380C22×C4—221no—
381C22×C4—221no—
382C22×C4C2×C22⋊D1112yes—
383C22×C4C2×C22⋊D1111yescharacteristic
384C22×C4C2×C22⋊D1111yescharacteristic
385C22×C4C23×D1111yescharacteristic
386Q16—448no—
387SD16—448no—
388M16—224no—
389M16—224no—
390C2×C8—224no—
391C4⋊C4—24no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—222no—
396C4⋊C4—441no—
397C4⋊C4—441no—
398C4⋊C4—882no—
399C22⋊C4—28no—
400C22⋊C4—24no—
401C22⋊C4—24no—
402C22⋊C4—24no—
403C22⋊C4—228no—
404C22⋊C4—882no—
405C42—112no—
406C42—221no—
407C42—222no—
408C42—442no—
409C42C2×C22⋊D1112yes—
410C42C2×C22⋊D1112yes—
411C11#2422811yescharacteristic, complemented, Sylow
412C23—22no—
413C23—22no—
414C23—24no—
415C23—42no—
416C23—42no—
417C23—48no—
418C23—84no—
419C23—84no—
420C23#6699114yes—
421C23C22×C22⋊D1111yescharacteristic
422Q8—24no—
423Q8—24no—
424Q8—224no—
425Q8—442no—
426D4—24no—
427D4—24no—
428D4—24no—
429D4—24no—
430D4—44no—
431D4—416no—
432D4—44no—
433D4—44no—
434D4—82no—
435D4—84no—
436C2×C4—22no—
437C2×C4—24no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—44no—
441C2×C4—48no—
442C2×C4—44no—
443C2×C4—44no—
444C2×C4—42no—
445C2×C4—82no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—442no—
454C2×C4—441no—
455C2×C4—441no—
456C2×C4—441no—
457C2×C4#6700612yes—
458C2×C4#6700611yescharacteristic
459C2×C4#6700611yescharacteristic
460C2×C4C2×D4×D1111yescharacteristic
461C2×C4C2×#434111yescharacteristic
462C2×C4#6703712yes—
463C2×C4C22×C22⋊D1112yes—
464C8—444no—
465C22—21no—
466C22—21no—
467C22—24no—
468C22—44no—
469C22—42no—
470C22—42no—
471C22—44no—
472C22—44no—
473C22—44no—
474C22—82no—
475C22—168no—
476C22C2×#6699111yescharacteristic
477C22#1062333611yescharacteristic
478C22C2×#6700611yescharacteristic
479C4—21no—
480C4—21no—
481C4—22no—
482C4—44no—
483C4—42no—
484C4—442no—
485C4—442no—
486C4—881no—
487C4—881no—
488C4D4×C22⋊D1112yes—
489C4#1062333712yes—
490C2—21no—
491C2—21no—
492C2—44no—
493C2—84no—
494C2#1307196611yescharacteristic
495C2#1307797311yescharacteristic
496C2#1307799511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3496C2
socleC22×C11C2×#120
hypercenter#3496D11
hypocenterC11#24228
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. #13078084C2semidirect
2. C2×#10622855C2semidirect
3. #13071328C2semidirect
4. #13069837C2semidirect
5. #13069663C2semidirect
6. #13069449C2semidirect
7. #13068608C2semidirect
8. #13068570C2semidirect
19. C2×#67004C22semidirect
21. C2×C4×Dic22C22semidirect
23. C2×#66901C22semidirect
24. C2×#66901C22semidirect
25. #10622845C22semidirect
32. #10622589C22semidirect
33. #10622587C22semidirect
35. #10622545C22semidirect
36. #10622537C22semidirect
37. #10622168C22semidirect
76. #66989D4semidirect
138. C2×Dic22C2×D4semidirect
160. C4×Dic11C2×D4semidirect
411. C11#24228semidirect

Maximal subgroups

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

subgroupindex
#130780842
C2×#106228552
#130713282
#130698372
#130696632
#130694492
#130686082
#130685702
C11×#34962
#2422811