Finite Group Databasebeta

← #13072075

Subgroups — #13072075

Order 1408.

800 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#123C211yesmaximal, characteristic, complemented
2C2×#66990C211yesmaximal, characteristic
3C2×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D11C211yesmaximal, characteristic, complemented
5#10622835C211yesmaximal, characteristic, complemented
6#10622826C211yesmaximal, characteristic, complemented
7#10622605C211yesmaximal, characteristic, complemented
8#10622603C211yesmaximal, characteristic, complemented
9#10622602C211yesmaximal, characteristic, complemented
10#10622600C211yesmaximal, characteristic, complemented
11#10622574C211yesmaximal, characteristic, complemented
12#10622569C211yesmaximal, characteristic, complemented
13#10622568C211yesmaximal, characteristic, complemented
14#10622565C211yesmaximal, characteristic, complemented
15#10622564C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C23×C4×C11C2211yescharacteristic, complemented
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C4×D11C2211yescharacteristic
22C22×C4×D11C2211yescharacteristic
23C11×#123—24no—
24C2×C11×C4⋊C4C2211yescharacteristic, complemented
25C2×C11×C4⋊C4C2211yescharacteristic, complemented
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic, complemented
29C2×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊Dic11C2211yescharacteristic, complemented
33C2×C22⋊Dic11C2211yescharacteristic, complemented
34#66990—24no—
35C4×C22⋊D11—24no—
36C2×(C2×D11)⋊C4C2211yescharacteristic
37C2×(C2×D11)⋊C4C2211yescharacteristic
38C2×(C2×D11)⋊C4C2211yescharacteristic
39C2×(C2×D11)⋊C4C2211yescharacteristic
40C2×(C2×D11)⋊C4C2211yescharacteristic
41C2×(C2×D11)⋊C4C2211yescharacteristic
42C2×(C2×D11)⋊C4C2211yescharacteristic
43C2×(C2×D11)⋊C4C2211yescharacteristic
44C2×C4⋊Dic11C2211yescharacteristic, complemented
45C2×Dic11⋊C4C2211yescharacteristic, complemented
46C2×Dic11⋊C4C2211yescharacteristic, complemented
47C2×C4×Dic11C2211yescharacteristic, complemented
48C22⋊C4×D11—24no—
49C11⋊#95C2211yescharacteristic, complemented
50C11⋊#95C2211yescharacteristic, complemented
51C11⋊#95C2211yescharacteristic, complemented
52C11⋊#95C2211yescharacteristic, complemented
53C11⋊#95C2211yescharacteristic, complemented
54C11⋊#95C2211yescharacteristic, complemented
55C24×C11C2311yescharacteristic
56C24×C11C2311yescharacteristic
57C23×D11—22no—
58C23×D11—22no—
59C23×D11—22no—
60C23×D11—22no—
61C23×D11—22no—
62C23×D11—41no—
63C23×D11—41no—
64C23×D11C2311yescharacteristic
65C23×D11C2311yescharacteristic
66C2×D4×C11—22no—
67C2×D4×C11—22no—
68C2×D4×C11—41no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—41no—
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C22×C4×C11C2311yescharacteristic
76C22×C4×C11C2311yescharacteristic
77C2×C22⋊D11—22no—
78C2×C22⋊D11—22no—
79C2×C22⋊D11—22no—
80C2×C22⋊D11—22no—
81C2×C22⋊D11—41no—
82C2×C22⋊D11D414yes—
83C22×Dic11C2311yescharacteristic
84C22×Dic11C2311yescharacteristic
85C22×Dic11C2311yescharacteristic
86C22×Dic11C2311yescharacteristic
87C22×Dic11C2311yescharacteristic
88C22×Dic11C2311yescharacteristic
89C2×C4×D11—22no—
90C2×C4×D11—22no—
91C2×C4×D11—22no—
92C2×C4×D11—22no—
93C2×C4×D11—41no—
94C2×C4×D11—41no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—22no—
99C11×C22⋊C4D414yescomplemented
100C22⋊Dic11—22no—
101C22⋊Dic11—22no—
102C22⋊Dic11—22no—
103C22⋊Dic11—41no—
104C22⋊Dic11—41no—
105(C2×D11)⋊C4—22no—
106(C2×D11)⋊C4—22no—
107(C2×D11)⋊C4—22no—
108(C2×D11)⋊C4—22no—
109(C2×D11)⋊C4—22no—
110(C2×D11)⋊C4—22no—
111(C2×D11)⋊C4—22no—
112(C2×D11)⋊C4—41no—
113C4⋊Dic11—41no—
114Dic11⋊C4—22no—
115Dic11⋊C4—41no—
116C4×Dic11—22no—
117#2418—111nomaximal, Sylow
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11C2×D412yes—
131C23×C11C2×D412yes—
132C23×C11C2411yescharacteristic
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—28no—
138C22×D11—21no—
139C22×D11—21no—
140C22×D11—21no—
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—21no—
144C22×D11—44no—
145C22×D11—44no—
146C22×D11—44no—
147C22×D11—44no—
148C22×D11—44no—
149C22×D11—44no—
150C22×D11C2×D412yes—
151C22×D11#4112yes—
152C22×D11#4112yes—
153C22×D11#4112yes—
154D4×C11—44no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—44no—
169C2×C4×C11C2×D412yes—
170C2×C4×C11C2×D412yes—
171C22⋊D11—28no—
172C22⋊D11—44no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—21no—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11C2×D412yes—
191C4×D11—44no—
192C4×D11—44no—
193C2×#123D1111yescharacteristic, complemented
194C2×#120—111no—
195C2×C4×D4—111no—
196C22×C22⋊C4—111no—
197#399—111no—
198#397—111no—
199#394—111no—
200#394—111no—
201#388—111no—
202#388—111no—
203#386—111no—
204#386—111no—
205#385—111no—
206#380—111no—
207#379—111no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—22no—
211C22×C11—22no—
212C22×C11—22no—
213C22×C11—22no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11C22×D411yescharacteristic
223C22×C11C22×D411yescharacteristic
224C22×C11C2×#4111yescharacteristic
225C22×C11C2×#4111yescharacteristic
226C22×C11C2×#4111yescharacteristic
227C22×C11H(5,𝔽2)11yescharacteristic
228C22×C11H(5,𝔽2)11yescharacteristic
229C2×D11—22no—
230C2×D11—22no—
231C2×D11—22no—
232C2×D11—22no—
233C2×D11—22no—
234C2×D11—22no—
235C2×D11—22no—
236C2×D11—22no—
237C2×D11—22no—
238C2×D11—416no—
239C2×D11—41no—
240C2×D11—41no—
241C2×D11—41no—
242C2×D11—41no—
243C2×D11#12314yescomplemented
244C4×C11—22no—
245C4×C11—22no—
246C4×C11—41no—
247C4×C11—41no—
248C4×C11—41no—
249Dic11—22no—
250Dic11—41no—
251Dic11—41no—
252Dic11—41no—
253Dic11—41no—
254Dic11—41no—
255C25—111no—
256C22×D4—111no—
257C22×D4—111no—
258C22×D4C2×D1111yescharacteristic
259C23×C4—111no—
260C23×C4—111no—
261C23×C4C2×D1111yescharacteristic, complemented
262#123—24no—
263#120—224no—
264C4×D4—224no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—111no—
268C2×C4⋊C4C2×D1111yescharacteristic, complemented
269C2×C4⋊C4C2×D1111yescharacteristic, complemented
270C2×C22⋊C4—111no—
271C2×C22⋊C4—111no—
272C2×C22⋊C4—111no—
273C2×C22⋊C4—111no—
274C2×C22⋊C4—111no—
275C2×C22⋊C4—111no—
276C2×C22⋊C4—111no—
277C2×C22⋊C4—111no—
278C2×C22⋊C4—111no—
279C2×C22⋊C4—111no—
280C2×C22⋊C4—111no—
281C2×C22⋊C4—111no—
282C2×C22⋊C4—111no—
283C2×C22⋊C4—224no—
284C2×C22⋊C4C2×D1111yescharacteristic
285C2×C22⋊C4C2×D1111yescharacteristic
286C2×C22⋊C4C2×D1111yescharacteristic, complemented
287C2×C42—111no—
288#95—111no—
289#95—111no—
290#95—111no—
291#95—111no—
292#95—111no—
293#95—111no—
294C2×C11—42no—
295C2×C11—42no—
296C2×C11C2×#12311yescharacteristic
297C2×C11#52511yescharacteristic
298C2×C11#53811yescharacteristic
299C2×C11D4211yescharacteristic
300C2×C11#54611yescharacteristic
301C2×C11#54611yescharacteristic
302C2×C11#55111yescharacteristic
303D11—24no—
304D11—42no—
305C24—111no—
306C24—111no—
307C24—222no—
308C24—222no—
309C24—222no—
310C24—222no—
311C24—222no—
312C24—441no—
313C24—441no—
314C24C22×D1111yescharacteristic
315C24C22×D1111yescharacteristic
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—41no—
319C2×D4—114no—
320C2×D4—222no—
321C2×D4—222no—
322C2×D4—222no—
323C2×D4—222no—
324C2×D4—441no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—41no—
328C22×C4—111no—
329C22×C4—111no—
330C22×C4—111no—
331C22×C4—111no—
332C22×C4—111no—
333C22×C4—111no—
334C22×C4—222no—
335C22×C4—222no—
336C22×C4—222no—
337C22×C4—222no—
338C22×C4—441no—
339C22×C4—441no—
340C22×C4C22×D1111yescharacteristic
341C22×C4C22×D1111yescharacteristic
342C22×C4C22×D1111yescharacteristic
343C22×C4C22×D1111yescharacteristic
344C22×C4C22×D1111yescharacteristic
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—222no—
348C4⋊C4—441no—
349C4⋊C4—441no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—222no—
353C22⋊C4—222no—
354C22⋊C4—222no—
355C22⋊C4—222no—
356C22⋊C4—222no—
357C22⋊C4—222no—
358C22⋊C4—222no—
359C22⋊C4—222no—
360C22⋊C4—222no—
361C22⋊C4—222no—
362C22⋊C4—441no—
363C22⋊C4—441no—
364C22⋊C4—441no—
365C22⋊C4C22⋊D1114yescomplemented
366C42—222no—
367C11#241811yescharacteristic, complemented, Sylow
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—112no—
381C23—112no—
382C23—112no—
383C23—112no—
384C23—228no—
385C23—221no—
386C23—221no—
387C23—221no—
388C23—221no—
389C23—221no—
390C23—221no—
391C23—221no—
392C23—221no—
393C23—221no—
394C23—221no—
395C23—444no—
396C23—444no—
397C23—444no—
398C23—444no—
399C23—444no—
400C23—444no—
401C23D4×D1112yes—
402C23C2×C22⋊D1112yes—
403C23C23×D1111yescharacteristic
404D4—44no—
405D4—228no—
406D4—444no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—44no—
421C2×C4—112no—
422C2×C4—221no—
423C2×C4—221no—
424C2×C4—221no—
425C2×C4—221no—
426C2×C4—221no—
427C2×C4—221no—
428C2×C4—221no—
429C2×C4—221no—
430C2×C4—221no—
431C2×C4—221no—
432C2×C4—221no—
433C2×C4—221no—
434C2×C4—221no—
435C2×C4—221no—
436C2×C4—221no—
437C2×C4—221no—
438C2×C4—221no—
439C2×C4—444no—
440C2×C4—444no—
441C2×C4C2×C22⋊D1112yes—
442C2×C4C2×C22⋊D1112yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—114no—
458C22—222no—
459C22—222no—
460C22—222no—
461C22—222no—
462C22—222no—
463C22—222no—
464C22—222no—
465C22—222no—
466C22—222no—
467C22—4416no—
468C22—441no—
469C22—441no—
470C22—441no—
471C22—441no—
472C22C2×D4×D1111yescharacteristic
473C22#6703711yescharacteristic
474C22#41×D1111yescharacteristic
475C22#41×D1111yescharacteristic
476C22#41×D1111yescharacteristic
477C22#6704211yescharacteristic
478C22C22×C22⋊D1111yescharacteristic
479C4—22no—
480C4—22no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—222no—
485C4—441no—
486C4—441no—
487C4—441no—
488C4—441no—
489C4—441no—
490C2—42no—
491C2—42no—
492C2—224no—
493C2—442no—
494C2D11×#12311yescharacteristic
495C2#1062318511yescharacteristic
496C2#1062318811yescharacteristic
497C2#1062319011yescharacteristic
498C2D4×C22⋊D1111yescharacteristic
499C2#1062335911yescharacteristic
500C2#1062336011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#123C2
prime radicalC2×#66990C2
hypercenterC2×#123D11
hypocenterC11#2418
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×C11×#123C2semidirect
3. C2×C4×C22⋊D11C2semidirect
4. C2×C22⋊C4×D11C2semidirect
5. #10622835C2semidirect
6. #10622826C2semidirect
7. #10622605C2semidirect
8. #10622603C2semidirect
9. #10622602C2semidirect
10. #10622600C2semidirect
11. #10622574C2semidirect
12. #10622569C2semidirect
13. #10622568C2semidirect
14. #10622565C2semidirect
15. #10622564C2semidirect
18. C23×C4×C11C22semidirect
24. C2×C11×C4⋊C4C22semidirect
25. C2×C11×C4⋊C4C22semidirect
28. C2×C11×C22⋊C4C22semidirect
32. C2×C22⋊Dic11C22semidirect
33. C2×C22⋊Dic11C22semidirect
44. C2×C4⋊Dic11C22semidirect
45. C2×Dic11⋊C4C22semidirect
46. C2×Dic11⋊C4C22semidirect
47. C2×C4×Dic11C22semidirect
49. C11⋊#95C22semidirect
50. C11⋊#95C22semidirect
51. C11⋊#95C22semidirect
52. C11⋊#95C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
99. C11×C22⋊C4D4semidirect
193. C2×#123D11semidirect
243. C2×D11#123semidirect
261. C23×C4C2×D11semidirect
268. C2×C4⋊C4C2×D11semidirect
269. C2×C4⋊C4C2×D11semidirect
286. C2×C22⋊C4C2×D11semidirect
365. C22⋊C4C22⋊D11semidirect
367. C11#2418semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1232
C2×#669902
C2×C4×C22⋊D112
C2×C22⋊C4×D112
#106228352
#106228262
#106226052
#106226032
#106226022
#106226002
#106225742
#106225692
#106225682
#106225652
#106225642
#241811