Finite Group Databasebeta

← #13074999

Subgroups — #13074999

Order 1408.

688 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#67000C211yesmaximal, characteristic, complemented
2C2×#66935C211yesmaximal, characteristic
3C11×#393C211yesmaximal, characteristic, complemented
4#10622844C211yesmaximal, characteristic, complemented
5#10622574C211yesmaximal, characteristic, complemented
6#10622569C211yesmaximal, characteristic, complemented
7#10622568C211yesmaximal, characteristic, complemented
8#10622568C211yesmaximal, characteristic, complemented
9#10622557C211yesmaximal, characteristic, complemented
10#10622288C211yesmaximal, characteristic, complemented
11#10622287C211yesmaximal, characteristic, complemented
12#10622285C211yesmaximal, characteristic, complemented
13#10622283C211yesmaximal, 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, complemented
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27#67000—24no—
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic, complemented
42C2×Dic11⋊C4C2211yescharacteristic, complemented
43C2×C4×Dic11C2211yescharacteristic, complemented
44#66935—24no—
45C11×#95C2211yescharacteristic, complemented
46C11×#95C2211yescharacteristic, complemented
47C11×#95C2211yescharacteristic, complemented
48C11⋊#95C2211yescharacteristic, complemented
49C11⋊#95C2211yescharacteristic, complemented
50C11⋊#95C2211yescharacteristic, complemented
51C11⋊#95C2211yescharacteristic, complemented
52C11⋊#95C2211yescharacteristic, complemented
53C24×C11C2311yescharacteristic
54C23×D11—22no—
55C23×D11—22no—
56C23×D11—22no—
57C23×D11—41no—
58C23×D11—41no—
59C23×D11—41no—
60C23×D11—41no—
61C23×D11C2311yescharacteristic
62C23×D11C2311yescharacteristic
63C23×D11C2311yescharacteristic
64C2×Q8×C11—22no—
65C2×Q8×C11—41no—
66C2×Q8×C11—41no—
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C22×C4×C11C2311yescharacteristic
73C2×C22⋊D11—22no—
74C2×C22⋊D11—22no—
75C2×C22⋊D11—41no—
76C22×Dic11C2311yescharacteristic
77C22×Dic11C2311yescharacteristic
78C22×Dic11C2311yescharacteristic
79C22×Dic11C2311yescharacteristic
80C22×Dic11C2311yescharacteristic
81C2×D44—22no—
82C2×D44—22no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44D414yes—
87C2×C4×D11—41no—
88C2×C4×D11—41no—
89C2×C4×D11—41no—
90C11×C22⋊C4—22no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C22⋊Dic11—22no—
94C22⋊Dic11—41no—
95(C2×D11)⋊C4—22no—
96(C2×D11)⋊C4—22no—
97(C2×D11)⋊C4—22no—
98(C2×D11)⋊C4—22no—
99(C2×D11)⋊C4—22no—
100(C2×D11)⋊C4—22no—
101(C2×D11)⋊C4—22no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108C4⋊Dic11—41no—
109Dic11⋊C4—41no—
110C4×Dic11—22no—
111#2684—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11#4112yes—
119C23×C11C2411yescharacteristic
120C22×D11—21no—
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—21no—
125C22×D11—21no—
126C22×D11—21no—
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—44no—
139C22×D11—44no—
140C22×D11—44no—
141C22×D11—44no—
142C22×D11—44no—
143C22×D11—44no—
144C22×D11—44no—
145C22×D11C2×D412yes—
146C22×D11C2×D412yes—
147C22×D11#4112yes—
148Q8×C11—44no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
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×C11C2×D412yes—
167C22⋊D11—44no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
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—
183D44—44no—
184D44—44no—
185C4×D11—44no—
186C2×#124—111no—
187C2×#120—111no—
188#397—111no—
189#397—111no—
190#394—111no—
191#394—111no—
192#393—111no—
193#393D1111yescharacteristic, complemented
194#388—111no—
195#388—111no—
196#386—111no—
197#386—111no—
198#386—111no—
199#379—111no—
200#379—111no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11C22×D411yescharacteristic
209C22×C11C2×#4111yescharacteristic
210C22×C11C2×#4111yescharacteristic
211C22×C11H(5,𝔽2)11yescharacteristic
212C22×C11H(5,𝔽2)11yescharacteristic
213C22×C11H(5,𝔽2)11yescharacteristic
214C22×C11H(5,𝔽2)11yescharacteristic
215C2×D11—22no—
216C2×D11—22no—
217C2×D11—22no—
218C2×D11—22no—
219C2×D11—22no—
220C2×D11—22no—
221C2×D11—22no—
222C2×D11—22no—
223C2×D11—22no—
224C2×D11—416no—
225C2×D11—41no—
226C2×D11—41no—
227C2×D11—41no—
228C2×D11—41no—
229C2×D11—41no—
230C2×D11—41no—
231C2×D11—41no—
232C2×D11—41no—
233C2×D11—41no—
234C2×D11—41no—
235C2×D11—41no—
236C2×D11—41no—
237C4×C11—22no—
238C4×C11—41no—
239C4×C11—41no—
240C4×C11—41no—
241C4×C11—41no—
242C4×C11—41no—
243Dic11—41no—
244Dic11—41no—
245Dic11—41no—
246Dic11—41no—
247Dic11—41no—
248C25—111no—
249C22×Q8C2×D1111yescharacteristic, complemented
250C22×D4—111no—
251C22×D4—111no—
252C22×D4—111no—
253C23×C4—111no—
254#124—224no—
255#120—224no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—111no—
258C2×C22⋊C4—111no—
259C2×C22⋊C4—111no—
260C2×C22⋊C4—111no—
261C2×C22⋊C4—111no—
262C2×C22⋊C4—111no—
263C2×C22⋊C4—111no—
264C2×C22⋊C4—111no—
265C2×C22⋊C4—111no—
266C2×C22⋊C4—111no—
267C2×C22⋊C4—111no—
268C2×C22⋊C4—111no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4—111no—
271C2×C22⋊C4—111no—
272C2×C22⋊C4—111no—
273C2×C22⋊C4C2×D1111yescharacteristic
274C2×C22⋊C4C2×D1111yescharacteristic
275C2×C22⋊C4C2×D1111yescharacteristic
276C2×C42—111no—
277#95—111no—
278#95—111no—
279#95—111no—
280#95—111no—
281#95—111no—
282#95C2×D1111yescharacteristic, complemented
283#95C2×D1111yescharacteristic, complemented
284#95C2×D1111yescharacteristic, complemented
285C2×C11—42no—
286C2×C11#53411yescharacteristic
287C2×C11#53811yescharacteristic
288C2×C11#53811yescharacteristic
289C2×C11#54611yescharacteristic
290C2×C11#54611yescharacteristic
291C2×C11#55111yescharacteristic
292C2×C11H(3,𝔽4)11yescharacteristic
293D11—42no—
294D11—42no—
295D11—42no—
296C24—111no—
297C24—111no—
298C24—111no—
299C24—222no—
300C24—222no—
301C24—222no—
302C24—441no—
303C24—441no—
304C24—441no—
305C24—441no—
306C24C22×D1111yescharacteristic
307C2×Q8—22no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×D4—114no—
311C2×D4—222no—
312C2×D4—222no—
313C2×D4—222no—
314C2×D4—222no—
315C2×D4—441no—
316C2×D4—441no—
317C2×D4—441no—
318C2×D4—441no—
319C22×C4—111no—
320C22×C4—111no—
321C22×C4—111no—
322C22×C4—111no—
323C22×C4—111no—
324C22×C4—441no—
325C22×C4—441no—
326C22×C4—441no—
327C22×C4C22×D1111yescharacteristic
328C22×C4C22×D1111yescharacteristic
329C22×C4C22×D1111yescharacteristic
330C22×C4C22×D1111yescharacteristic
331C22×C4C22×D1111yescharacteristic
332C22×C4C22×D1111yescharacteristic
333C4⋊C4—441no—
334C4⋊C4—441no—
335C22⋊C4—22no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—222no—
339C22⋊C4—222no—
340C22⋊C4—222no—
341C22⋊C4—222no—
342C22⋊C4—222no—
343C22⋊C4—222no—
344C22⋊C4—222no—
345C22⋊C4—222no—
346C22⋊C4—441no—
347C22⋊C4—441no—
348C22⋊C4—441no—
349C22⋊C4—441no—
350C22⋊C4—441no—
351C22⋊C4—441no—
352C22⋊C4—441no—
353C42—222no—
354C11#268411yescharacteristic, complemented, Sylow
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—112no—
362C23—112no—
363C23—112no—
364C23—221no—
365C23—221no—
366C23—221no—
367C23—221no—
368C23—221no—
369C23—221no—
370C23—221no—
371C23—221no—
372C23—221no—
373C23—221no—
374C23—221no—
375C23—221no—
376C23—221no—
377C23—221no—
378C23—221no—
379C23—221no—
380C23—221no—
381C23—221no—
382C23—444no—
383C23—444no—
384C23—444no—
385C23—444no—
386C23—444no—
387C23—444no—
388C23—444no—
389C23#434312yes—
390C23C23×D1111yescharacteristic
391Q8—44no—
392D4—444no—
393D4—444no—
394D4—444no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—221no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—221no—
420C2×C4—221no—
421C2×C4—221no—
422C2×C4—221no—
423C2×C4—221no—
424C2×C4—221no—
425C2×C4—221no—
426C2×C4—221no—
427C2×C4—444no—
428C2×C4D4×D1112yes—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—222no—
437C22—222no—
438C22—222no—
439C22—222no—
440C22—222no—
441C22—222no—
442C22—222no—
443C22—222no—
444C22—222no—
445C22—4416no—
446C22—441no—
447C22—441no—
448C22—441no—
449C22—441no—
450C22—441no—
451C22—441no—
452C22—441no—
453C22—441no—
454C22—441no—
455C22—441no—
456C22—441no—
457C22—441no—
458C22C2×D4×D1111yescharacteristic
459C22#6703711yescharacteristic
460C22#6703711yescharacteristic
461C22C2×#434311yescharacteristic
462C22#41×D1111yescharacteristic
463C22#6704211yescharacteristic
464C22#6704211yescharacteristic
465C4—22no—
466C4—41no—
467C4—41no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—441no—
472C4—441no—
473C4—441no—
474C4—441no—
475C4—441no—
476C2—42no—
477C2—442no—
478C2—442no—
479C2—442no—
480C2#1062312011yescharacteristic
481C2#1062316111yescharacteristic
482C2#1062316811yescharacteristic
483C2#1062317511yescharacteristic
484C2#1062320711yescharacteristic
485C2#1062320911yescharacteristic
486C2#1062321411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#393C2
prime radicalC2×#66935C2
hypercenter#393D11
hypocenterC11#2684
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#67000C2semidirect
3. C11×#393C2semidirect
4. #10622844C2semidirect
5. #10622574C2semidirect
6. #10622569C2semidirect
7. #10622568C2semidirect
8. #10622568C2semidirect
9. #10622557C2semidirect
10. #10622288C2semidirect
11. #10622287C2semidirect
12. #10622285C2semidirect
13. #10622283C2semidirect
14. #10622278C2semidirect
15. #10622278C2semidirect
17. C22×Q8×C11C22semidirect
21. C22×C4×D11C22semidirect
38. C2×(C2×D11)⋊C4C22semidirect
39. C2×(C2×D11)⋊C4C22semidirect
40. C2×(C2×D11)⋊C4C22semidirect
41. C2×C4⋊Dic11C22semidirect
42. C2×Dic11⋊C4C22semidirect
43. C2×C4×Dic11C22semidirect
45. C11×#95C22semidirect
46. C11×#95C22semidirect
47. C11×#95C22semidirect
48. C11⋊#95C22semidirect
49. C11⋊#95C22semidirect
50. C11⋊#95C22semidirect
51. C11⋊#95C22semidirect
52. C11⋊#95C22semidirect
193. #393D11semidirect
249. C22×Q8C2×D11semidirect
282. #95C2×D11semidirect
283. #95C2×D11semidirect
284. #95C2×D11semidirect
354. C11#2684semidirect

Maximal subgroups

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

subgroupindex
C2×#670002
C2×#669352
C11×#3932
#106228442
#106225742
#106225692
#106225682
#106225572
#106222882
#106222872
#106222852
#106222832
#106222782
#268411