Finite Group Databasebeta

← #13072749

Subgroups — #13072749

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×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#67000C211yesmaximal, characteristic, complemented
3C22×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
4C2×#66935C211yesmaximal, characteristic
5#10622844C211yesmaximal, characteristic, complemented
6#10622826C211yesmaximal, characteristic, complemented
7#10622606C211yesmaximal, characteristic, complemented
8#10622604C211yesmaximal, characteristic, complemented
9#10622604C211yesmaximal, characteristic, complemented
10#10622603C211yesmaximal, characteristic, complemented
11#10622603C211yesmaximal, characteristic, complemented
12#10622601C211yesmaximal, characteristic, complemented
13#10622571C211yesmaximal, characteristic, complemented
14#10622568C211yesmaximal, characteristic, complemented
15C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×Q8×C11C2211yescharacteristic, complemented
18C23×C4×C11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C23×Dic11C2211yescharacteristic
21C22×D44C2211yescharacteristic
22C22×D44C2211yescharacteristic
23C11×C22⋊Q8—24no—
24C2×C11×C4⋊C4C2211yescharacteristic, complemented
25C2×C11×C4⋊C4C2211yescharacteristic, complemented
26C2×C11×C4⋊C4C2211yescharacteristic, complemented
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic
30#67000—24no—
31C2×(C2×D11)⋊C4—24no—
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
39C2×(C2×D11)⋊C4C2211yescharacteristic
40C2×(C2×D11)⋊C4C2211yescharacteristic
41C2×(C2×D11)⋊C4C2211yescharacteristic
42C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
46C2×C4×Dic11C2211yescharacteristic, complemented
47C2×C4×Dic11C2211yescharacteristic, complemented
48#66935—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×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
77C22×C4×C11C2311yescharacteristic
78C2×C22⋊D11—22no—
79C2×C22⋊D11—22no—
80C2×C22⋊D11—22no—
81C22×Dic11—22no—
82C22×Dic11—22no—
83C22×Dic11—41no—
84C22×Dic11C2311yescharacteristic
85C22×Dic11C2311yescharacteristic
86C22×Dic11C2311yescharacteristic
87C22×Dic11C2311yescharacteristic
88C22×Dic11C2311yescharacteristic
89C2×D44—22no—
90C2×D44—22no—
91C2×D44—22no—
92C2×D44—22no—
93C2×D44—41no—
94C2×D44—41no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C22⋊C4—22no—
99C11×C22⋊C4D414yes—
100C22⋊Dic11—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—22no—
108(C2×D11)⋊C4—22no—
109(C2×D11)⋊C4—22no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4D414yescomplemented
115C4×Dic11—22no—
116C4×Dic11—41no—
117#2472—111nomaximal, Sylow
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11C2×D412yes—
123C23×C11#4112yes—
124C23×C11#4112yes—
125C23×C11C2411yescharacteristic
126C22×D11—28no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
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—21no—
145C22×D11—21no—
146C22×D11—44no—
147C22×D11—44no—
148C22×D11—44no—
149C22×D11—44no—
150C22×D11—44no—
151C22×D11—44no—
152C22×D11C2×D412yes—
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—44no—
171C2×C4×C11C2×D412yes—
172C2×C4×C11C2×D412yes—
173C2×C4×C11C2×D412yes—
174C22⋊D11—44no—
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—44no—
190C2×Dic11C2×D412yes—
191D44—44no—
192D44—44no—
193C2×#124—111no—
194C2×C22⋊Q8D1111yescharacteristic, complemented
195C2×#120—111no—
196C22×C22⋊C4—111no—
197#397—111no—
198#394—111no—
199#394—111no—
200#393—111no—
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—22no—
212C22×C11—22no—
213C22×C11—22no—
214C22×C11#12414yescomplemented
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—416no—
229C2×D11—41no—
230C2×D11—41no—
231C2×D11—41no—
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—41no—
244C4×C11—22no—
245C4×C11—22no—
246C4×C11—22no—
247C4×C11—41no—
248C4×C11—41no—
249C4×C11—41no—
250Dic11—22no—
251Dic11—41no—
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×C4C2×D1111yescharacteristic
262#124—224no—
263C22⋊Q8—24no—
264#120—224no—
265C2×C4⋊C4C2×D1111yescharacteristic, complemented
266C2×C4⋊C4C2×D1111yescharacteristic, complemented
267C2×C4⋊C4C2×D1111yescharacteristic, complemented
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—111no—
283C2×C22⋊C4—224no—
284C2×C22⋊C4C2×D1111yescharacteristic
285C2×C22⋊C4C2×D1111yescharacteristic
286C2×C42—111no—
287C2×C42—111no—
288#95—111no—
289#95—111no—
290#95—111no—
291#95—111no—
292#95—111no—
293#95—111no—
294C2×C11—24no—
295C2×C11#52511yescharacteristic
296C2×C11C2×#12411yescharacteristic
297C2×C11#53811yescharacteristic
298C2×C11D4211yescharacteristic
299C2×C11#54611yescharacteristic
300C2×C11#54611yescharacteristic
301C2×C11#55111yescharacteristic
302D11—42no—
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—22no—
329C22×C4—22no—
330C22×C4—41no—
331C22×C4—111no—
332C22×C4—111no—
333C22×C4—111no—
334C22×C4—111no—
335C22×C4—111no—
336C22×C4—222no—
337C22×C4—222no—
338C22×C4—441no—
339C22×C4C22×D1111yescharacteristic
340C22×C4C22×D1111yescharacteristic
341C22×C4C22×D1111yescharacteristic
342C22×C4C22×D1111yescharacteristic
343C22×C4C22×D1111yescharacteristic
344C22×C4C22×D1111yescharacteristic
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—114no—
350C22⋊C4—222no—
351C22⋊C4—222no—
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—441no—
361C22⋊C4—441no—
362C22⋊C4—441no—
363C22⋊C4—441no—
364C22⋊C4C22⋊D1114yes—
365C42—222no—
366C42—441no—
367C11#247211yescharacteristic, complemented, Sylow
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—112no—
373C23—112no—
374C23—228no—
375C23—221no—
376C23—221no—
377C23—221no—
378C23—221no—
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—444no—
395C23—444no—
396C23—444no—
397C23—444no—
398C23—444no—
399C23—444no—
400C23#434312yes—
401C23#434312yes—
402C23C2×C22⋊D1112yes—
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—44no—
424C2×C4—112no—
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×C4D4×D1112yes—
441C2×C4C2×C22⋊D1112yes—
442C2×C4C2×C22⋊D1112yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—222no—
450C22—222no—
451C22—222no—
452C22—222no—
453C22—222no—
454C22—222no—
455C22—4416no—
456C22—441no—
457C22—441no—
458C22—441no—
459C22—441no—
460C22—441no—
461C22—441no—
462C22—441no—
463C22—441no—
464C22—441no—
465C22—441no—
466C22—441no—
467C22—441no—
468C22—441no—
469C22—441no—
470C22—441no—
471C22#6700014yescomplemented
472C22C2×D4×D1111yescharacteristic
473C22#6703711yescharacteristic
474C22C2×#434311yescharacteristic
475C22C2×#434311yescharacteristic
476C22#41×D1111yescharacteristic
477C22#6704211yescharacteristic
478C22C22×C22⋊D1111yescharacteristic
479C4—22no—
480C4—22no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—222no—
486C4—441no—
487C4—441no—
488C4—441no—
489C4—441no—
490C2—24no—
491C2—442no—
492C2—442no—
493C2—881no—
494C2#1062315811yescharacteristic
495C2#1062316111yescharacteristic
496C2#1062316811yescharacteristic
497C2#1062317511yescharacteristic
498C2D4×C22⋊D1111yescharacteristic
499C2C2×#6700011yescharacteristic
500C2#1062336011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C22⋊Q8C2
prime radicalC2×#66935C2
hypercenterC2×C22⋊Q8D11
hypocenterC11#2472
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C11×C22⋊Q8C2semidirect
2. C2×#67000C2semidirect
3. C22×(C2×D11)⋊C4C2semidirect
5. #10622844C2semidirect
6. #10622826C2semidirect
7. #10622606C2semidirect
8. #10622604C2semidirect
9. #10622604C2semidirect
10. #10622603C2semidirect
11. #10622603C2semidirect
12. #10622601C2semidirect
13. #10622571C2semidirect
14. #10622568C2semidirect
15. C22⋊C4×Dic11C2semidirect
17. C22×Q8×C11C22semidirect
24. C2×C11×C4⋊C4C22semidirect
25. C2×C11×C4⋊C4C22semidirect
26. C2×C11×C4⋊C4C22semidirect
42. C2×(C2×D11)⋊C4C22semidirect
43. C2×(C2×D11)⋊C4C22semidirect
44. C2×(C2×D11)⋊C4C22semidirect
45. C2×(C2×D11)⋊C4C22semidirect
46. C2×C4×Dic11C22semidirect
47. C2×C4×Dic11C22semidirect
49. C11⋊#95C22semidirect
50. C11⋊#95C22semidirect
51. C11⋊#95C22semidirect
52. C11⋊#95C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
114. (C2×D11)⋊C4D4semidirect
194. C2×C22⋊Q8D11semidirect
214. C22×C11#124semidirect
256. C22×Q8C2×D11semidirect
265. C2×C4⋊C4C2×D11semidirect
266. C2×C4⋊C4C2×D11semidirect
267. C2×C4⋊C4C2×D11semidirect
367. C11#2472semidirect
471. C22#67000semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊Q82
C2×#670002
C22×(C2×D11)⋊C42
C2×#669352
#106228442
#106228262
#106226062
#106226042
#106226032
#106226012
#106225712
#106225682
C22⋊C4×Dic112
#247211