Finite Group Databasebeta

← #13072745

Subgroups — #13072745

Order 1408.

786 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×#67000C211yesmaximal, characteristic, complemented
2C2×#66999C211yesmaximal, characteristic, complemented
3C2×#66935C211yesmaximal, characteristic
4C2×C22⋊C4×D11C211yesmaximal, characteristic, complemented
5C11×#393C211yesmaximal, characteristic, complemented
6#10622574C211yesmaximal, characteristic, complemented
7#10622570C211yesmaximal, characteristic, complemented
8#10622568C211yesmaximal, characteristic, complemented
9#10622558C211yesmaximal, characteristic, complemented
10#10622288C211yesmaximal, characteristic, complemented
11#10622285C211yesmaximal, characteristic, complemented
12#10622283C211yesmaximal, characteristic, complemented
13#10622279C211yesmaximal, characteristic, complemented
14#10622278C211yesmaximal, characteristic, complemented
15#10622278C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×Q8×C11C2211yescharacteristic, complemented
18C22×C22⋊D11C2211yescharacteristic
19C22×D44C2211yescharacteristic
20C22×D44C2211yescharacteristic
21C22×C4×D11C2211yescharacteristic
22C22×C4×D11C2211yescharacteristic
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28#67000—24no—
29#66999—24no—
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×(C2×D11)⋊C4C2211yescharacteristic
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×(C2×D11)⋊C4C2211yescharacteristic
37C2×(C2×D11)⋊C4C2211yescharacteristic
38C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
42C2×C4⋊Dic11C2211yescharacteristic, complemented
43C2×Dic11⋊C4C2211yescharacteristic, complemented
44C2×Dic11⋊C4C2211yescharacteristic, complemented
45C2×C4×Dic11C2211yescharacteristic, complemented
46C2×C4×Dic11C2211yescharacteristic, complemented
47#66935—24no—
48C22⋊C4×D11—24no—
49C11×#95C2211yescharacteristic, complemented
50C11×#95C2211yescharacteristic, complemented
51C11×#95C2211yescharacteristic, complemented
52C11⋊#95C2211yescharacteristic, complemented
53C11⋊#95C2211yescharacteristic, complemented
54C11⋊#95C2211yescharacteristic, complemented
55C24×C11C2311yescharacteristic
56C23×D11—22no—
57C23×D11—22no—
58C23×D11—22no—
59C23×D11—22no—
60C23×D11—22no—
61C23×D11—41no—
62C23×D11—41no—
63C23×D11C2311yescharacteristic
64C23×D11C2311yescharacteristic
65C23×D11C2311yescharacteristic
66C2×Q8×C11—22no—
67C2×Q8×C11—22no—
68C2×Q8×C11—41no—
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C2×C22⋊D11—22no—
76C2×C22⋊D11—22no—
77C2×C22⋊D11—41no—
78C22×Dic11C2311yescharacteristic
79C22×Dic11C2311yescharacteristic
80C22×Dic11C2311yescharacteristic
81C22×Dic11C2311yescharacteristic
82C22×Dic11C2311yescharacteristic
83C2×D44—22no—
84C2×D44—22no—
85C2×D44—22no—
86C2×D44—22no—
87C2×D44—22no—
88C2×D44—41no—
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×C22⋊C4—22no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—41no—
98C22⋊Dic11—22no—
99C22⋊Dic11—22no—
100(C2×D11)⋊C4—22no—
101(C2×D11)⋊C4—22no—
102(C2×D11)⋊C4—22no—
103(C2×D11)⋊C4—22no—
104(C2×D11)⋊C4—22no—
105(C2×D11)⋊C4—22no—
106(C2×D11)⋊C4—22no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4D414yes—
111(C2×D11)⋊C4D414yescomplemented
112C4⋊Dic11—22no—
113Dic11⋊C4—22no—
114Dic11⋊C4—22no—
115C4×Dic11—22no—
116C4×Dic11—41no—
117#2472—111nomaximal, Sylow
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11#4112yes—
125C23×C11C2411yescharacteristic
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—28no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—21no—
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×D11C2×D412yes—
152C22×D11#4112yes—
153C22×D11#4112yes—
154Q8×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—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11C2×D412yes—
172C2×C4×C11C2×D412yes—
173C22⋊D11—44no—
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×Dic11C2×D412yes—
188C2×Dic11C2×D412yes—
189D44—44no—
190D44—44no—
191C4×D11—44no—
192C4×D11—44no—
193C2×#124—111no—
194C2×C22⋊Q8—111no—
195C2×#120—111no—
196C22×C22⋊C4—111no—
197#397—111no—
198#394—111no—
199#394—111no—
200#393D1111yescharacteristic, complemented
201#390—111no—
202#388—111no—
203#388—111no—
204#386—111no—
205#386—111no—
206#379—111no—
207C4×C22⋊C4—111no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—22no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11C22×D411yescharacteristic
216C22×C11C22×D411yescharacteristic
217C22×C11C2×#4111yescharacteristic
218C22×C11C2×#4111yescharacteristic
219C22×C11C2×#4111yescharacteristic
220C22×C11H(5,𝔽2)11yescharacteristic
221C22×C11H(5,𝔽2)11yescharacteristic
222C2×D11—22no—
223C2×D11—22no—
224C2×D11—22no—
225C2×D11—22no—
226C2×D11—22no—
227C2×D11—22no—
228C2×D11—22no—
229C2×D11—22no—
230C2×D11—22no—
231C2×D11—416no—
232C2×D11—41no—
233C2×D11—41no—
234C2×D11—41no—
235C2×D11—41no—
236C2×D11—41no—
237C2×D11—41no—
238C2×D11—41no—
239C2×D11—41no—
240C2×D11—41no—
241C2×D11—41no—
242C2×D11—41no—
243C2×D11#12414yescomplemented
244C4×C11—22no—
245C4×C11—22no—
246C4×C11—41no—
247C4×C11—41no—
248C4×C11—41no—
249C4×C11—41no—
250Dic11—22no—
251Dic11—22no—
252Dic11—41no—
253Dic11—41no—
254Dic11—41no—
255C25—111no—
256C22×Q8C2×D1111yescharacteristic, complemented
257C22×D4—111no—
258C22×D4—111no—
259C22×D4—111no—
260C23×C4—111no—
261C23×C4—111no—
262#124—224no—
263C22⋊Q8—224no—
264#120—224no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—111no—
268C2×C22⋊C4—111no—
269C2×C22⋊C4—111no—
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—224no—
283C2×C22⋊C4C2×D1111yescharacteristic
284C2×C22⋊C4C2×D1111yescharacteristic
285C2×C22⋊C4C2×D1111yescharacteristic
286C2×C42—111no—
287C2×C42—111no—
288#95—111no—
289#95—111no—
290#95—111no—
291#95C2×D1111yescharacteristic, complemented
292#95C2×D1111yescharacteristic, complemented
293#95C2×D1111yescharacteristic, complemented
294C2×C11—42no—
295C2×C11#52511yescharacteristic
296C2×C11C2×#12411yescharacteristic
297C2×C11#53811yescharacteristic
298C2×C11D4211yescharacteristic
299C2×C11#54611yescharacteristic
300C2×C11#54611yescharacteristic
301C2×C11#55111yescharacteristic
302D11—24no—
303D11—42no—
304D11—81no—
305C24—111no—
306C24—111no—
307C24—111no—
308C24—222no—
309C24—222no—
310C24—222no—
311C24—222no—
312C24—222no—
313C24—441no—
314C24—441no—
315C24C22×D1111yescharacteristic
316C2×Q8—22no—
317C2×Q8—22no—
318C2×Q8—41no—
319C2×D4—222no—
320C2×D4—222no—
321C2×D4—222no—
322C2×D4—222no—
323C2×D4—222no—
324C2×D4—222no—
325C2×D4—222no—
326C2×D4—441no—
327C2×D4—441no—
328C22×C4—111no—
329C22×C4—111no—
330C22×C4—111no—
331C22×C4—111no—
332C22×C4—111no—
333C22×C4—222no—
334C22×C4—222no—
335C22×C4—222no—
336C22×C4—222no—
337C22×C4—441no—
338C22×C4—441no—
339C22×C4C22×D1111yescharacteristic
340C22×C4C22×D1111yescharacteristic
341C22×C4C22×D1111yescharacteristic
342C22×C4C22×D1111yescharacteristic
343C22×C4C22×D1111yescharacteristic
344C22×C4C22×D1111yescharacteristic
345C4⋊C4—222no—
346C4⋊C4—222no—
347C4⋊C4—222no—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—41no—
351C22⋊C4—114no—
352C22⋊C4—114no—
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—
365C42—222no—
366C42—441no—
367C11#247211yescharacteristic, complemented, Sylow
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—112no—
375C23—112no—
376C23—112no—
377C23—112no—
378C23—228no—
379C23—221no—
380C23—221no—
381C23—221no—
382C23—221no—
383C23—221no—
384C23—221no—
385C23—221no—
386C23—221no—
387C23—221no—
388C23—221no—
389C23—221no—
390C23—221no—
391C23—221no—
392C23—221no—
393C23—221no—
394C23—221no—
395C23—221no—
396C23—444no—
397C23—444no—
398C23—444no—
399C23—444no—
400C23—444no—
401C23—444no—
402C23#434312yes—
403C23C23×D1111yescharacteristic
404Q8—44no—
405D4—444no—
406D4—444no—
407D4—444no—
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—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—112no—
425C2×C4—112no—
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×C4D4×D1112yes—
442C2×C4D4×D1112yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—114no—
451C22—222no—
452C22—222no—
453C22—222no—
454C22—222no—
455C22—222no—
456C22—222no—
457C22—222no—
458C22—222no—
459C22—222no—
460C22—4416no—
461C22—441no—
462C22—441no—
463C22—441no—
464C22—441no—
465C22—441no—
466C22—441no—
467C22—441no—
468C22—441no—
469C22—441no—
470C22—441no—
471C22—441no—
472C22C2×D4×D1111yescharacteristic
473C22C2×D4×D1111yescharacteristic
474C22#6703711yescharacteristic
475C22C2×#434311yescharacteristic
476C22#41×D1111yescharacteristic
477C22#41×D1111yescharacteristic
478C22#6704211yescharacteristic
479C4—22no—
480C4—22no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—222no—
486C4—222no—
487C4—441no—
488C4—441no—
489C4—441no—
490C2—42no—
491C2—224no—
492C2—442no—
493C2—881no—
494C2#1062312111yescharacteristic
495C2#1062315811yescharacteristic
496C2#1062316111yescharacteristic
497C2#1062316811yescharacteristic
498C2D11×#12411yescharacteristic
499C2#1062320711yescharacteristic
500C2#1062320911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#393C2
prime radicalC2×#66935C2
hypercenter#393D11
hypocenterC11#2472
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#67000C2semidirect
2. C2×#66999C2semidirect
4. C2×C22⋊C4×D11C2semidirect
5. C11×#393C2semidirect
6. #10622574C2semidirect
7. #10622570C2semidirect
8. #10622568C2semidirect
9. #10622558C2semidirect
10. #10622288C2semidirect
11. #10622285C2semidirect
12. #10622283C2semidirect
13. #10622279C2semidirect
14. #10622278C2semidirect
15. #10622278C2semidirect
17. C22×Q8×C11C22semidirect
38. C2×(C2×D11)⋊C4C22semidirect
39. C2×(C2×D11)⋊C4C22semidirect
40. C2×(C2×D11)⋊C4C22semidirect
41. C2×(C2×D11)⋊C4C22semidirect
42. C2×C4⋊Dic11C22semidirect
43. C2×Dic11⋊C4C22semidirect
44. C2×Dic11⋊C4C22semidirect
45. C2×C4×Dic11C22semidirect
46. C2×C4×Dic11C22semidirect
49. C11×#95C22semidirect
50. C11×#95C22semidirect
51. C11×#95C22semidirect
52. C11⋊#95C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
111. (C2×D11)⋊C4D4semidirect
200. #393D11semidirect
243. C2×D11#124semidirect
256. C22×Q8C2×D11semidirect
291. #95C2×D11semidirect
292. #95C2×D11semidirect
293. #95C2×D11semidirect
367. C11#2472semidirect

Maximal subgroups

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

subgroupindex
C2×#670002
C2×#669992
C2×#669352
C2×C22⋊C4×D112
C11×#3932
#106225742
#106225702
#106225682
#106225582
#106222882
#106222852
#106222832
#106222792
#106222782
#247211