Finite Group Databasebeta

← #13074996

Subgroups — #13074996

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×#67006C211yesmaximal, characteristic
2C2×#66938C211yesmaximal, characteristic, complemented
3C11×#379C211yesmaximal, characteristic, complemented
4#10622860C211yesmaximal, characteristic, complemented
5#10622574C211yesmaximal, characteristic, complemented
6#10622572C211yesmaximal, characteristic, complemented
7#10622569C211yesmaximal, characteristic, complemented
8#10622569C211yesmaximal, characteristic, complemented
9#10622569C211yesmaximal, characteristic, complemented
10#10622566C211yesmaximal, characteristic, complemented
11#10622565C211yesmaximal, characteristic, complemented
12#10622564C211yesmaximal, characteristic, complemented
13#10622560C211yesmaximal, characteristic, complemented
14#10622560C211yesmaximal, characteristic, complemented
15#10622558C211yesmaximal, characteristic, complemented
16C25×C11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C4×D11C2211yescharacteristic, complemented
21C22×Dic22C2211yescharacteristic, complemented
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic
28#67006—24no—
29C2×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊Dic11C2211yescharacteristic
33C2×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊Dic11C2211yescharacteristic
35C2×C22⋊Dic11C2211yescharacteristic
36C2×C22⋊Dic11C2211yescharacteristic
37C2×C22⋊Dic11C2211yescharacteristic
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#66938—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×C11—22no—
54C24×C11—22no—
55C24×C11—22no—
56C24×C11—41no—
57C24×C11—41no—
58C24×C11—41no—
59C24×C11—41no—
60C24×C11C2311yescharacteristic
61C24×C11C2311yescharacteristic
62C24×C11C2311yescharacteristic
63C23×D11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C2×C22⋊D11—22no—
69C2×C22⋊D11—22no—
70C2×C22⋊D11—22no—
71C2×C22⋊D11—22no—
72C2×C22⋊D11—41no—
73C2×C22⋊D11—41no—
74C2×C22⋊D11—41no—
75C2×C22⋊D11—41no—
76C2×C22⋊D11D414yes—
77C22×Dic11C2311yescharacteristic
78C22×Dic11C2311yescharacteristic
79C22×Dic11C2311yescharacteristic
80C22×Dic11C2311yescharacteristic
81C22×Dic11C2311yescharacteristic
82C22×Dic11C2311yescharacteristic
83C22×Dic11C2311yescharacteristic
84C2×C4×D11—41no—
85C2×C4×D11—41no—
86C2×C4×D11—41no—
87C2×Dic22—22no—
88C2×Dic22—41no—
89C2×Dic22—41no—
90C11×C22⋊C4—22no—
91C11×C22⋊C4—22no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C22⋊Dic11—22no—
97C22⋊Dic11—22no—
98C22⋊Dic11—22no—
99C22⋊Dic11—22no—
100C22⋊Dic11—22no—
101C22⋊Dic11—41no—
102C22⋊Dic11—41no—
103C22⋊Dic11—41no—
104C22⋊Dic11—41no—
105(C2×D11)⋊C4—22no—
106(C2×D11)⋊C4—22no—
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—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×C11—44no—
131C23×C11—44no—
132C23×C11—44no—
133C23×C11—44no—
134C23×C11—44no—
135C23×C11—44no—
136C23×C11—44no—
137C23×C11C2×D412yes—
138C23×C11#4112yes—
139C23×C11#4112yes—
140C23×C11C2411yescharacteristic
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—21no—
144C22×D11—21no—
145C22×D11—21no—
146C22×D11—21no—
147C22×D11C2×D412yes—
148C2×C4×C11—21no—
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—
160C22⋊D11—44no—
161C22⋊D11—44no—
162C22⋊D11—44no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—21no—
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×Dic11C2×D412yes—
184C4×D11—44no—
185Dic22—44no—
186C2×#124—111no—
187C2×#120—111no—
188#397—111no—
189#397—111no—
190#394—111no—
191#394—111no—
192#393—111no—
193#393—111no—
194#388—111no—
195#388—111no—
196#386—111no—
197#386—111no—
198#386—111no—
199#379—111no—
200#379D1111yescharacteristic, complemented
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—416no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
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×C11—41no—
223C22×C11C22×D411yescharacteristic
224C22×C11C2×#4111yescharacteristic
225C22×C11C2×#4111yescharacteristic
226C22×C11H(5,𝔽2)11yescharacteristic
227C22×C11H(5,𝔽2)11yescharacteristic
228C22×C11H(5,𝔽2)11yescharacteristic
229C22×C11H(5,𝔽2)11yescharacteristic
230C2×D11—22no—
231C2×D11—22no—
232C2×D11—22no—
233C2×D11—41no—
234C2×D11—41no—
235C2×D11—41no—
236C2×D11—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—
247Dic11—41no—
248C25C2×D1111yescharacteristic
249C22×Q8—111no—
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⋊C4C2×D1111yescharacteristic
271C2×C22⋊C4C2×D1111yescharacteristic
272C2×C22⋊C4C2×D1111yescharacteristic
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#95—111no—
283#95—111no—
284#95—111no—
285C2×C11—42no—
286C2×C11—42no—
287C2×C11—42no—
288C2×C11#53411yescharacteristic
289C2×C11#53811yescharacteristic
290C2×C11#53811yescharacteristic
291C2×C11#54611yescharacteristic
292C2×C11#54611yescharacteristic
293C2×C11#55111yescharacteristic
294C2×C11H(3,𝔽4)11yescharacteristic
295D11—42no—
296C24—22no—
297C24—22no—
298C24—22no—
299C24—41no—
300C24—41no—
301C24—41no—
302C24—41no—
303C24—111no—
304C24C22×D1111yescharacteristic
305C24C22×D1111yescharacteristic
306C24C22×D1111yescharacteristic
307C2×Q8—222no—
308C2×Q8—441no—
309C2×Q8—441no—
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—111no—
325C22×C4—111no—
326C22×C4—441no—
327C22×C4—441no—
328C22×C4—441no—
329C22×C4C22×D1111yescharacteristic
330C22×C4C22×D1111yescharacteristic
331C22×C4C22×D1111yescharacteristic
332C22×C4C22×D1111yescharacteristic
333C4⋊C4—441no—
334C4⋊C4—441no—
335C22⋊C4—22no—
336C22⋊C4—22no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—222no—
342C22⋊C4—222no—
343C22⋊C4—222no—
344C22⋊C4—222no—
345C22⋊C4—222no—
346C22⋊C4—222no—
347C22⋊C4—222no—
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—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—44no—
374C23—44no—
375C23—44no—
376C23—44no—
377C23—44no—
378C23—44no—
379C23—44no—
380C23—112no—
381C23—221no—
382C23—221no—
383C23—221no—
384C23—221no—
385C23—221no—
386C23—221no—
387C23#433912yes—
388C23D4×D1112yes—
389C23#434112yes—
390C23C23×D1111yescharacteristic
391Q8—444no—
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—112no—
408C2×C4—221no—
409C2×C4—221no—
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—
427C2×C4—221no—
428C2×C4—444no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—416no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—222no—
452C22—222no—
453C22—222no—
454C22—441no—
455C22—441no—
456C22—441no—
457C22—441no—
458C22C2×#433911yescharacteristic
459C22C2×D4×D1111yescharacteristic
460C22C2×#434111yescharacteristic
461C22#6703711yescharacteristic
462C22#6703711yescharacteristic
463C22#6703711yescharacteristic
464C22#6703711yescharacteristic
465C4—41no—
466C4—41no—
467C4—41no—
468C4—41no—
469C4—222no—
470C4—441no—
471C4—441no—
472C4—441no—
473C4—441no—
474C4—441no—
475C4—441no—
476C2—42no—
477C2—42no—
478C2—42no—
479C2—442no—
480C2#1062302111yescharacteristic
481C2#1062302511yescharacteristic
482C2#1062302611yescharacteristic
483C2#1062312011yescharacteristic
484C2#1062312211yescharacteristic
485C2#1062312411yescharacteristic
486C2#1062312511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#379C2
prime radicalC2×#67006C2
hypercenter#379D11
hypocenterC11#2684
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×#66938C2semidirect
3. C11×#379C2semidirect
4. #10622860C2semidirect
5. #10622574C2semidirect
6. #10622572C2semidirect
7. #10622569C2semidirect
8. #10622569C2semidirect
9. #10622569C2semidirect
10. #10622566C2semidirect
11. #10622565C2semidirect
12. #10622564C2semidirect
13. #10622560C2semidirect
14. #10622560C2semidirect
15. #10622558C2semidirect
20. C22×C4×D11C22semidirect
21. C22×Dic22C22semidirect
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
200. #379D11semidirect
354. C11#2684semidirect

Maximal subgroups

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

subgroupindex
C2×#670062
C2×#669382
C11×#3792
#106228602
#106225742
#106225722
#106225692
#106225662
#106225652
#106225642
#106225602
#106225582
#268411