Finite Group Databasebeta

← #13075180

Subgroups — #13075180

Order 1408.

680 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66990C211yesmaximal, characteristic
2C2×#66982C211yesmaximal, characteristic, complemented
3C11×#386C211yesmaximal, characteristic, complemented
4#10622835C211yesmaximal, characteristic, complemented
5#10622826C211yesmaximal, characteristic, complemented
6#10622574C211yesmaximal, characteristic, complemented
7#10622570C211yesmaximal, characteristic, complemented
8#10622568C211yesmaximal, characteristic, complemented
9#10622568C211yesmaximal, characteristic, complemented
10#10622561C211yesmaximal, characteristic, complemented
11#10622557C211yesmaximal, characteristic, complemented
12#10622289C211yesmaximal, characteristic, complemented
13#10622288C211yesmaximal, characteristic, complemented
14#10622287C211yesmaximal, characteristic, complemented
15#10622282C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C23×C4×C11C2211yescharacteristic, complemented
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C11×C22⋊C4C2211yescharacteristic, complemented
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic, complemented
28C2×C22⋊Dic11C2211yescharacteristic, complemented
29#66990—24no—
30#66982—24no—
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
39C2×(C2×D11)⋊C4C2211yescharacteristic
40C2×(C2×D11)⋊C4C2211yescharacteristic
41C2×C4⋊Dic11C2211yescharacteristic, complemented
42C2×Dic11⋊C4C2211yescharacteristic, complemented
43C2×Dic11⋊C4C2211yescharacteristic, complemented
44C2×Dic11⋊C4C2211yescharacteristic, complemented
45C2×Dic11⋊C4C2211yescharacteristic, complemented
46C2×C4×Dic11C2211yescharacteristic, complemented
47C11×#95C2211yescharacteristic, complemented
48C11×#95C2211yescharacteristic, complemented
49C11⋊#95C2211yescharacteristic, complemented
50C11⋊#95C2211yescharacteristic, complemented
51C11⋊#95C2211yescharacteristic, complemented
52C11⋊#95C2211yescharacteristic, complemented
53C24×C11C2311yescharacteristic
54C24×C11C2311yescharacteristic
55C23×D11—22no—
56C23×D11—22no—
57C23×D11—22no—
58C23×D11—41no—
59C23×D11—41no—
60C23×D11—41no—
61C23×D11—41no—
62C23×D11C2311yescharacteristic
63C23×D11C2311yescharacteristic
64C2×D4×C11—22no—
65C2×D4×C11—22no—
66C2×D4×C11—41no—
67C22×C4×C11—22no—
68C22×C4×C11—41no—
69C22×C4×C11—41no—
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—
78C2×C22⋊D11—41no—
79C2×C22⋊D11—41no—
80C2×C22⋊D11D414yes—
81C22×Dic11C2311yescharacteristic
82C22×Dic11C2311yescharacteristic
83C22×Dic11C2311yescharacteristic
84C22×Dic11C2311yescharacteristic
85C22×Dic11C2311yescharacteristic
86C22×Dic11C2311yescharacteristic
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C22⋊Dic11—22no—
91C22⋊Dic11—22no—
92C22⋊Dic11—22no—
93C22⋊Dic11—41no—
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—41no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105C4⋊Dic11—41no—
106Dic11⋊C4—22no—
107Dic11⋊C4—22no—
108Dic11⋊C4—41no—
109Dic11⋊C4—41no—
110C4×Dic11—41no—
111#2697—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11C2×D412yes—
125C23×C11#4112yes—
126C23×C11C2411yescharacteristic
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—44no—
140C22×D11—44no—
141C22×D11—44no—
142C22×D11—44no—
143C22×D11—44no—
144C22×D11—44no—
145C22×D11—44no—
146C22×D11C2×D412yes—
147C22×D11#4112yes—
148D4×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—44no—
165C22⋊D11—44no—
166C22⋊D11—44no—
167C2×Dic11—21no—
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—
183C2×Dic11—21no—
184C2×Dic11C2×D412yes—
185C2×#123—111no—
186C2×#120—111no—
187#397—111no—
188#397—111no—
189#396—111no—
190#396—111no—
191#394—111no—
192#394—111no—
193#390—111no—
194#388—111no—
195#388—111no—
196#386—111no—
197#386D1111yescharacteristic, complemented
198#379—111no—
199#379—111no—
200C22×C11—22no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11—22no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11C22×D411yescharacteristic
215C22×C11C2×#4111yescharacteristic
216C22×C11C2×#4111yescharacteristic
217C22×C11H(5,𝔽2)11yescharacteristic
218C22×C11H(5,𝔽2)11yescharacteristic
219C22×C11H(5,𝔽2)11yescharacteristic
220C22×C11H(5,𝔽2)11yescharacteristic
221C2×D11—22no—
222C2×D11—22no—
223C2×D11—22no—
224C2×D11—22no—
225C2×D11—22no—
226C2×D11—22no—
227C2×D11—416no—
228C2×D11—41no—
229C2×D11—41no—
230C2×D11—41no—
231C2×D11—41no—
232C2×D11—41no—
233C2×D11—41no—
234C2×D11—41no—
235C2×D11—41no—
236C4×C11—41no—
237C4×C11—41no—
238C4×C11—41no—
239C4×C11—41no—
240C4×C11—41no—
241Dic11—22no—
242Dic11—41no—
243Dic11—41no—
244Dic11—41no—
245Dic11—41no—
246Dic11—41no—
247C25—111no—
248C22×D4—111no—
249C22×D4—111no—
250C22×D4C2×D1111yescharacteristic
251C23×C4C2×D1111yescharacteristic, complemented
252#123—224no—
253#120—224no—
254C2×C4⋊C4—111no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—111no—
258C2×C4⋊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⋊C4—111no—
274C2×C22⋊C4C2×D1111yescharacteristic
275C2×C22⋊C4C2×D1111yescharacteristic
276C2×C22⋊C4C2×D1111yescharacteristic, complemented
277C2×C42—111no—
278#95—111no—
279#95—111no—
280#95—111no—
281#95—111no—
282#95C2×D1111yescharacteristic, complemented
283#95C2×D1111yescharacteristic, complemented
284C2×C11—42no—
285C2×C11—42no—
286C2×C11#53411yescharacteristic
287C2×C11#53811yescharacteristic
288C2×C11#53811yescharacteristic
289C2×C11#54611yescharacteristic
290C2×C11#54611yescharacteristic
291C2×C11#55111yescharacteristic
292C2×C11#56011yescharacteristic
293D11—42no—
294D11—42no—
295C24—111no—
296C24—111no—
297C24—222no—
298C24—222no—
299C24—222no—
300C24—441no—
301C24—441no—
302C24—441no—
303C24—441no—
304C24C22×D1111yescharacteristic
305C24C22×D1111yescharacteristic
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—41no—
309C2×D4—114no—
310C2×D4—222no—
311C2×D4—222no—
312C2×D4—441no—
313C2×D4—441no—
314C2×D4—441no—
315C22×C4—22no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—111no—
319C22×C4—111no—
320C22×C4—111no—
321C22×C4—111no—
322C22×C4—111no—
323C22×C4—111no—
324C22×C4C22×D1111yescharacteristic
325C22×C4C22×D1111yescharacteristic
326C22×C4C22×D1111yescharacteristic
327C22×C4C22×D1111yescharacteristic
328C22×C4C22×D1111yescharacteristic
329C4⋊C4—222no—
330C4⋊C4—222no—
331C4⋊C4—441no—
332C4⋊C4—441no—
333C4⋊C4—441no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—222no—
338C22⋊C4—222no—
339C22⋊C4—222no—
340C22⋊C4—222no—
341C22⋊C4—222no—
342C22⋊C4—222no—
343C22⋊C4—222no—
344C22⋊C4—222no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C22⋊C4—441no—
348C22⋊C4—441no—
349C22⋊C4—441no—
350C22⋊C4—441no—
351C22⋊C4—441no—
352C42—441no—
353C11#269711yescharacteristic, complemented, Sylow
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—112no—
367C23—112no—
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—444no—
381C23—444no—
382C23—444no—
383C23—444no—
384C23—444no—
385C23—444no—
386C23—444no—
387C23#433912yes—
388C23D4×D1112yes—
389C23C23×D1111yescharacteristic
390D4—44no—
391D4—444no—
392D4—444no—
393C2×C4—21no—
394C2×C4—21no—
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—44no—
409C2×C4—112no—
410C2×C4—221no—
411C2×C4—221no—
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—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—222no—
442C22—222no—
443C22—222no—
444C22—222no—
445C22—222no—
446C22—222no—
447C22—4416no—
448C22—441no—
449C22—441no—
450C22—441no—
451C22—441no—
452C22—441no—
453C22—441no—
454C22—441no—
455C22—441no—
456C22C2×#433911yescharacteristic
457C22C2×D4×D1111yescharacteristic
458C22#6703711yescharacteristic
459C22#6703711yescharacteristic
460C22#6703711yescharacteristic
461C22#41×D1111yescharacteristic
462C22#6704211yescharacteristic
463C4—41no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—41no—
468C4—222no—
469C4—441no—
470C4—441no—
471C4—441no—
472C4—441no—
473C4—441no—
474C2—42no—
475C2—42no—
476C2—442no—
477C2—442no—
478C2#1062302111yescharacteristic
479C2#1062308711yescharacteristic
480C2#1062309111yescharacteristic
481C2#1062312011yescharacteristic
482C2#1062314411yescharacteristic
483C2#1062315111yescharacteristic
484C2#1062318511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#386C2
prime radicalC2×#66990C2
hypercenter#386D11
hypocenterC11#2697
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×#66982C2semidirect
3. C11×#386C2semidirect
4. #10622835C2semidirect
5. #10622826C2semidirect
6. #10622574C2semidirect
7. #10622570C2semidirect
8. #10622568C2semidirect
9. #10622568C2semidirect
10. #10622561C2semidirect
11. #10622557C2semidirect
12. #10622289C2semidirect
13. #10622288C2semidirect
14. #10622287C2semidirect
15. #10622282C2semidirect
18. C23×C4×C11C22semidirect
23. C2×C11×C22⋊C4C22semidirect
27. C2×C22⋊Dic11C22semidirect
28. C2×C22⋊Dic11C22semidirect
41. C2×C4⋊Dic11C22semidirect
42. C2×Dic11⋊C4C22semidirect
43. C2×Dic11⋊C4C22semidirect
44. C2×Dic11⋊C4C22semidirect
45. C2×Dic11⋊C4C22semidirect
46. C2×C4×Dic11C22semidirect
47. C11×#95C22semidirect
48. C11×#95C22semidirect
49. C11⋊#95C22semidirect
50. C11⋊#95C22semidirect
51. C11⋊#95C22semidirect
52. C11⋊#95C22semidirect
197. #386D11semidirect
251. C23×C4C2×D11semidirect
276. C2×C22⋊C4C2×D11semidirect
282. #95C2×D11semidirect
283. #95C2×D11semidirect
353. C11#2697semidirect

Maximal subgroups

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

subgroupindex
C2×#669902
C2×#669822
C11×#3862
#106228352
#106228262
#106225742
#106225702
#106225682
#106225612
#106225572
#106222892
#106222882
#106222872
#106222822
#269711