Finite Group Databasebeta

← #13076612

Subgroups — #13076612

Order 1408.

712 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66990C211yesmaximal, characteristic, complemented
2C2×#66935C211yesmaximal, characteristic, complemented
3C11×#394C211yesmaximal, characteristic, complemented
4#10622836C211yesmaximal, characteristic, complemented
5#10622606C211yesmaximal, characteristic, complemented
6#10622604C211yesmaximal, characteristic, complemented
7#10622574C211yesmaximal, characteristic, complemented
8#10622574C211yesmaximal, characteristic, complemented
9#10622573C211yesmaximal, characteristic, complemented
10#10622573C211yesmaximal, characteristic, complemented
11#10622572C211yesmaximal, characteristic, complemented
12#10622568C211yesmaximal, characteristic, complemented
13#10622565C211yesmaximal, characteristic, complemented
14#10622287C211yesmaximal, characteristic, complemented
15#10622285C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic, complemented
22C22×D44C2211yescharacteristic
23C22×D44C2211yescharacteristic
24C2×C11×C4⋊C4C2211yescharacteristic, complemented
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic, complemented
28C2×C11×C22⋊C4C2211yescharacteristic, complemented
29C2×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊Dic11C2211yescharacteristic, complemented
32#66990—24no—
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, complemented
42C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
44C2×C4⋊Dic11C2211yescharacteristic, complemented
45C2×Dic11⋊C4C2211yescharacteristic, complemented
46#66935—24no—
47C11×#95C2211yescharacteristic, complemented
48C11⋊#95C2211yescharacteristic, complemented
49C11⋊#95C2211yescharacteristic, complemented
50C11⋊#95C2211yescharacteristic, complemented
51C11⋊#95C2211yescharacteristic, complemented
52C11⋊#95C2211yescharacteristic, complemented
53C24×C11C2311yescharacteristic
54C24×C11C2311yescharacteristic
55C23×D11—41no—
56C23×D11—41no—
57C23×D11—41no—
58C23×D11—41no—
59C23×D11—41no—
60C23×D11—41no—
61C23×D11D414yescomplemented
62C23×D11C2311yescharacteristic
63C23×D11C2311yescharacteristic
64C23×D11C2311yescharacteristic
65C2×D4×C11—22no—
66C2×D4×C11—41no—
67C2×D4×C11—41no—
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—22no—
76C2×C22⋊D11—41no—
77C2×C22⋊D11—41no—
78C2×C22⋊D11—41no—
79C2×C22⋊D11—41no—
80C2×C22⋊D11—41no—
81C2×C22⋊D11—41no—
82C2×C22⋊D11—41no—
83C2×C22⋊D11—41no—
84C2×C22⋊D11—41no—
85C22×Dic11C2311yescharacteristic
86C22×Dic11C2311yescharacteristic
87C22×Dic11C2311yescharacteristic
88C22×Dic11C2311yescharacteristic
89C22×Dic11C2311yescharacteristic
90C2×D44—22no—
91C2×D44—22no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—41no—
95C2×D44—41no—
96C11×C4⋊C4—41no—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C22⋊Dic11—22no—
102C22⋊Dic11—41no—
103C22⋊Dic11—41no—
104(C2×D11)⋊C4—22no—
105(C2×D11)⋊C4—22no—
106(C2×D11)⋊C4—22no—
107(C2×D11)⋊C4—22no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—41no—
115C4⋊Dic11—41no—
116Dic11⋊C4—41no—
117#2812—111nomaximal, Sylow
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—21no—
131C23×C11C2×D412yes—
132C23×C11C2411yescharacteristic
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—21no—
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—21no—
151C22×D11—21no—
152C22×D11—44no—
153C22×D11—44no—
154C22×D11—44no—
155C22×D11—44no—
156C22×D11—44no—
157C22×D11—44no—
158C22×D11—44no—
159C22×D11C2×D412yes—
160C22×D11C2×D412yes—
161D4×C11—44no—
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×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C22⋊D11—44no—
178C22⋊D11—44no—
179C22⋊D11—44no—
180C22⋊D11—44no—
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—21no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196D44—44no—
197D44—44no—
198C2×#120—111no—
199C2×#120—111no—
200#397—111no—
201#397—111no—
202#397—111no—
203#394—111no—
204#394—111no—
205#394—111no—
206#394—111no—
207#394—111no—
208#394D1111yescharacteristic, complemented
209#392—111no—
210#392—111no—
211#392—111no—
212#379—111no—
213C22×C11—22no—
214C22×C11—22no—
215C22×C11—22no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11—41no—
227C22×C11C22×D411yescharacteristic
228C22×C11H(5,𝔽2)11yescharacteristic
229C22×C11H(5,𝔽2)11yescharacteristic
230C22×C11H(5,𝔽2)11yescharacteristic
231C22×C11H(5,𝔽2)11yescharacteristic
232C22×C11H(5,𝔽2)11yescharacteristic
233C22×C11H(5,𝔽2)11yescharacteristic
234C2×D11—22no—
235C2×D11—22no—
236C2×D11—22no—
237C2×D11—22no—
238C2×D11—22no—
239C2×D11—22no—
240C2×D11—416no—
241C2×D11—41no—
242C2×D11—41no—
243C2×D11—41no—
244C2×D11—41no—
245C2×D11—41no—
246C2×D11—41no—
247C2×D11—41no—
248C2×D11—41no—
249C2×D11—41no—
250C2×D11—41no—
251C2×D11—41no—
252C2×D11—41no—
253C2×D11—41no—
254C2×D11—41no—
255C2×D11—41no—
256C4×C11—41no—
257C4×C11—41no—
258C4×C11—41no—
259C4×C11—41no—
260C4×C11—41no—
261Dic11—41no—
262Dic11—41no—
263Dic11—41no—
264Dic11—41no—
265Dic11—41no—
266C25—111no—
267C22×D4—111no—
268C22×D4—111no—
269C22×D4—111no—
270C22×D4—111no—
271C22×D4—111no—
272C22×D4—111no—
273C22×D4C2×D1111yescharacteristic
274#120—224no—
275#120—224no—
276C2×C4⋊C4—111no—
277C2×C4⋊C4—111no—
278C2×C4⋊C4C2×D1111yescharacteristic, complemented
279C2×C22⋊C4—111no—
280C2×C22⋊C4—111no—
281C2×C22⋊C4—111no—
282C2×C22⋊C4—111no—
283C2×C22⋊C4—111no—
284C2×C22⋊C4—111no—
285C2×C22⋊C4—111no—
286C2×C22⋊C4—111no—
287C2×C22⋊C4—111no—
288C2×C22⋊C4—111no—
289C2×C22⋊C4—111no—
290C2×C22⋊C4—111no—
291C2×C22⋊C4—111no—
292C2×C22⋊C4—111no—
293C2×C22⋊C4C2×D1111yescharacteristic
294C2×C22⋊C4C2×D1111yescharacteristic
295C2×C22⋊C4C2×D1111yescharacteristic, complemented
296C2×C22⋊C4C2×D1111yescharacteristic, complemented
297#95—111no—
298#95—111no—
299#95—111no—
300#95—111no—
301#95—111no—
302#95C2×D1111yescharacteristic, complemented
303C2×C11—42no—
304C2×C11—81no—
305C2×C11#53411yescharacteristic
306C2×C11#53411yescharacteristic
307C2×C11#53411yescharacteristic
308C2×C11#56011yescharacteristic
309C2×C11#56011yescharacteristic
310C2×C11#56011yescharacteristic
311C2×C11H(3,𝔽4)11yescharacteristic
312D11—42no—
313D11—42no—
314D11—81no—
315C24—111no—
316C24—111no—
317C24—114no—
318C24—111no—
319C24—441no—
320C24—441no—
321C24—441no—
322C24—441no—
323C24—441no—
324C24—441no—
325C24C22×D1111yescharacteristic
326C24C22×D1111yescharacteristic
327C2×D4—22no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—222no—
331C2×D4—222no—
332C2×D4—222no—
333C2×D4—222no—
334C2×D4—222no—
335C2×D4—441no—
336C2×D4—441no—
337C2×D4—441no—
338C2×D4—441no—
339C2×D4—441no—
340C2×D4—441no—
341C2×D4—441no—
342C2×D4—441no—
343C2×D4—441no—
344C2×D4—441no—
345C2×D4—441no—
346C2×D4—441no—
347C2×D4—441no—
348C22×C4—111no—
349C22×C4—111no—
350C22×C4—111no—
351C22×C4—111no—
352C22×C4—111no—
353C22×C4C22×D1111yescharacteristic
354C22×C4C22×D1111yescharacteristic
355C22×C4C22×D1111yescharacteristic
356C22×C4C22×D1111yescharacteristic
357C22×C4C22×D1111yescharacteristic
358C4⋊C4—41no—
359C4⋊C4—441no—
360C4⋊C4—441no—
361C22⋊C4—22no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—222no—
366C22⋊C4—222no—
367C22⋊C4—222no—
368C22⋊C4—222no—
369C22⋊C4—222no—
370C22⋊C4—441no—
371C22⋊C4—441no—
372C22⋊C4—441no—
373C22⋊C4—441no—
374C22⋊C4—441no—
375C22⋊C4—441no—
376C22⋊C4—441no—
377C22⋊C4—441no—
378C22⋊C4—441no—
379C11#281211yescharacteristic, complemented, Sylow
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—112no—
394C23—112no—
395C23—221no—
396C23—221no—
397C23—221no—
398C23—221no—
399C23—221no—
400C23—221no—
401C23—221no—
402C23—221no—
403C23—221no—
404C23—221no—
405C23—221no—
406C23—221no—
407C23—221no—
408C23—221no—
409C23—221no—
410C23—221no—
411C23—221no—
412C23—221no—
413C23—221no—
414C23—444no—
415C23—444no—
416C23—444no—
417C23—444no—
418C23—444no—
419C23—444no—
420C23—444no—
421C23D4×D1112yes—
422C23C23×D1111yescharacteristic
423D4—44no—
424D4—444no—
425D4—444no—
426D4—444no—
427D4—444no—
428D4—444no—
429D4—444no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—221no—
448C2×C4—221no—
449C2×C4—221no—
450C2×C4—221no—
451C2×C4—221no—
452C2×C4—221no—
453C2×C4—221no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—221no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—221no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—222no—
475C22—222no—
476C22—222no—
477C22—222no—
478C22—222no—
479C22—222no—
480C22—4416no—
481C22—441no—
482C22—441no—
483C22—441no—
484C22—441no—
485C22—441no—
486C22—441no—
487C22—441no—
488C22—441no—
489C22—441no—
490C22—441no—
491C22—441no—
492C22—441no—
493C22—441no—
494C22—441no—
495C22—441no—
496C22C2×D4×D1111yescharacteristic
497C22#6703711yescharacteristic
498C22#6703711yescharacteristic
499C22#6703711yescharacteristic
500C22#6704211yescharacteristic
501C22#6704211yescharacteristic
502C22#6704211yescharacteristic
503C4—41no—
504C4—41no—
505C4—41no—
506C4—41no—
507C4—41no—
508C4—441no—
509C4—441no—
510C4—441no—
511C4—441no—
512C4—441no—
513C2—42no—
514C2—81no—
515C2—442no—
516C2—442no—
517C2—881no—
518C2#1062312011yescharacteristic
519C2#1062313611yescharacteristic
520C2#1062315111yescharacteristic
521C2#1062315111yescharacteristic
522C2#1062318411yescharacteristic
523C2#1062319711yescharacteristic
524C2#1062321411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
hypercenter#394D11
hypocenterC11#2812
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#66990C2semidirect
2. C2×#66935C2semidirect
3. C11×#394C2semidirect
4. #10622836C2semidirect
5. #10622606C2semidirect
6. #10622604C2semidirect
7. #10622574C2semidirect
8. #10622574C2semidirect
9. #10622573C2semidirect
10. #10622573C2semidirect
11. #10622572C2semidirect
12. #10622568C2semidirect
13. #10622565C2semidirect
14. #10622287C2semidirect
15. #10622285C2semidirect
21. C22×C22⋊D11C22semidirect
24. C2×C11×C4⋊C4C22semidirect
27. C2×C11×C22⋊C4C22semidirect
28. C2×C11×C22⋊C4C22semidirect
31. C2×C22⋊Dic11C22semidirect
41. C2×(C2×D11)⋊C4C22semidirect
42. C2×(C2×D11)⋊C4C22semidirect
43. C2×(C2×D11)⋊C4C22semidirect
44. C2×C4⋊Dic11C22semidirect
45. C2×Dic11⋊C4C22semidirect
47. C11×#95C22semidirect
48. C11⋊#95C22semidirect
49. C11⋊#95C22semidirect
50. C11⋊#95C22semidirect
51. C11⋊#95C22semidirect
52. C11⋊#95C22semidirect
61. C23×D11D4semidirect
208. #394D11semidirect
278. C2×C4⋊C4C2×D11semidirect
295. C2×C22⋊C4C2×D11semidirect
296. C2×C22⋊C4C2×D11semidirect
302. #95C2×D11semidirect
379. C11#2812semidirect

Maximal subgroups

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

subgroupindex
C2×#669902
C2×#669352
C11×#3942
#106228362
#106226062
#106226042
#106225742
#106225732
#106225722
#106225682
#106225652
#106222872
#106222852
#281211