Finite Group Databasebeta

← #13072148

Subgroups — #13072148

Order 1408.

922 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#120C211yesmaximal, characteristic, complemented
2C2×#67006C211yesmaximal, characteristic, complemented
3C22×C22⋊Dic11C211yesmaximal, characteristic, complemented
4C2×#66992C211yesmaximal, characteristic, complemented
5C2×#66991C211yesmaximal, characteristic, complemented
6C2×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
7#10622836C211yesmaximal, characteristic, complemented
8#10622835C211yesmaximal, characteristic, complemented
9#10622834C211yesmaximal, characteristic, complemented
10#10622833C211yesmaximal, characteristic, complemented
11#10622574C211yesmaximal, characteristic, complemented
12#10622569C211yesmaximal, characteristic, complemented
13#10622563C211yesmaximal, characteristic, complemented
14#10622561C211yesmaximal, characteristic, complemented
15#10622557C211yesmaximal, characteristic, complemented
16C25×C11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C22×D4×C11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C22×C22⋊D11C2211yescharacteristic
23C22×C22⋊D11C2211yescharacteristic, complemented
24C23×Dic11C2211yescharacteristic
25C23×Dic11C2211yescharacteristic
26C22×C4×D11C2211yescharacteristic, complemented
27C11×#120—24no—
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31#67006—24no—
32C2×C22⋊Dic11—24no—
33C2×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊Dic11C2211yescharacteristic
35C2×C22⋊Dic11C2211yescharacteristic
36C2×C22⋊Dic11C2211yescharacteristic
37C2×C22⋊Dic11C2211yescharacteristic
38C2×C22⋊Dic11C2211yescharacteristic
39C2×C22⋊Dic11C2211yescharacteristic
40C2×C22⋊Dic11C2211yescharacteristic, complemented
41C2×C22⋊Dic11C2211yescharacteristic, complemented
42C2×C22⋊Dic11C2211yescharacteristic, complemented
43#66992—24no—
44#66991—24no—
45C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
46C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
47C2×C4⋊Dic11C2211yescharacteristic, complemented
48C2×C4⋊Dic11C2211yescharacteristic, complemented
49C2×Dic11⋊C4C2211yescharacteristic, complemented
50C2×Dic11⋊C4C2211yescharacteristic, complemented
51C2×C4×Dic11C2211yescharacteristic, complemented
52(C22⋊D11)⋊C4—24no—
53C11⋊#95C2211yescharacteristic, complemented
54C11⋊#95C2211yescharacteristic, complemented
55C11⋊#95C2211yescharacteristic, complemented
56C11⋊#95C2211yescharacteristic, complemented
57C24×C11—22no—
58C24×C11—22no—
59C24×C11—22no—
60C24×C11—22no—
61C24×C11—22no—
62C24×C11—41no—
63C24×C11—41no—
64C24×C11C2311yescharacteristic
65C24×C11C2311yescharacteristic
66C24×C11C2311yescharacteristic
67C24×C11C2311yescharacteristic
68C23×D11C2311yescharacteristic
69C2×D4×C11—22no—
70C2×D4×C11—22no—
71C2×D4×C11—22no—
72C2×D4×C11—22no—
73C2×D4×C11—22no—
74C2×D4×C11—22no—
75C2×D4×C11—22no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C22×C4×C11C2311yescharacteristic
79C22×C4×C11C2311yescharacteristic
80C22×C4×C11C2311yescharacteristic
81C2×C22⋊D11—22no—
82C2×C22⋊D11—22no—
83C2×C22⋊D11—22no—
84C2×C22⋊D11—22no—
85C2×C22⋊D11—22no—
86C2×C22⋊D11—22no—
87C2×C22⋊D11—22no—
88C2×C22⋊D11—22no—
89C2×C22⋊D11—41no—
90C2×C22⋊D11—41no—
91C2×C22⋊D11—41no—
92C2×C22⋊D11D414yescomplemented
93C22×Dic11—22no—
94C22×Dic11—22no—
95C22×Dic11—22no—
96C22×Dic11—22no—
97C22×Dic11—41no—
98C22×Dic11—41no—
99C22×Dic11C2311yescharacteristic
100C22×Dic11C2311yescharacteristic
101C22×Dic11C2311yescharacteristic
102C22×Dic11C2311yescharacteristic
103C22×Dic11C2311yescharacteristic
104C22×Dic11C2311yescharacteristic
105C22×Dic11C2311yescharacteristic
106C2×C4×D11—22no—
107C2×C4×D11—22no—
108C2×C4×D11—41no—
109C11×C22⋊C4—22no—
110C11×C22⋊C4—22no—
111C11×C22⋊C4D414yescomplemented
112C22⋊Dic11—22no—
113C22⋊Dic11—22no—
114C22⋊Dic11—22no—
115C22⋊Dic11—22no—
116C22⋊Dic11—22no—
117C22⋊Dic11—22no—
118C22⋊Dic11—22no—
119C22⋊Dic11—22no—
120C22⋊Dic11—41no—
121C22⋊Dic11D414yescomplemented
122(C2×D11)⋊C4—22no—
123(C2×D11)⋊C4—22no—
124C4⋊Dic11—22no—
125C4⋊Dic11—41no—
126Dic11⋊C4—22no—
127Dic11⋊C4—22no—
128C4×Dic11—22no—
129#2424—111nomaximal, Sylow
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—28no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—21no—
154C23×C11—44no—
155C23×C11—44no—
156C23×C11—44no—
157C23×C11—44no—
158C23×C11—44no—
159C23×C11—44no—
160C23×C11C2×D412yes—
161C23×C11C2×D412yes—
162C23×C11C2×D412yes—
163C23×C11#4112yes—
164C23×C11#4112yes—
165C23×C11C2411yescharacteristic
166C22×D11—21no—
167C22×D11—21no—
168C22×D11—21no—
169C22×D11—21no—
170C22×D11—21no—
171C22×D11—21no—
172C22×D11C2×D412yes—
173D4×C11—44no—
174D4×C11—44no—
175D4×C11—44no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11C2×D412yes—
184C2×C4×C11C2×D412yes—
185C22⋊D11—28no—
186C22⋊D11—44no—
187C22⋊D11—44no—
188C22⋊D11—44no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—44no—
208C2×Dic11—44no—
209C2×Dic11C2×D412yes—
210C2×Dic11C2×D412yes—
211C2×Dic11C2×D412yes—
212C4×D11—44no—
213C2×#121—111no—
214C2×#121—111no—
215C2×#120—111no—
216C2×#120D1111yescharacteristic, complemented
217C2×C4×D4—111no—
218C22×C22⋊C4—111no—
219#396—111no—
220#394—111no—
221#394—111no—
222#392—111no—
223#390—111no—
224#388—111no—
225#386—111no—
226#386—111no—
227#385—111no—
228C22×C11—22no—
229C22×C11—22no—
230C22×C11—22no—
231C22×C11—22no—
232C22×C11—22no—
233C22×C11—22no—
234C22×C11—22no—
235C22×C11—22no—
236C22×C11—22no—
237C22×C11—22no—
238C22×C11—22no—
239C22×C11—22no—
240C22×C11—416no—
241C22×C11—41no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11—41no—
246C22×C11—41no—
247C22×C11—41no—
248C22×C11—41no—
249C22×C11—41no—
250C22×C11—41no—
251C22×C11—41no—
252C22×C11—41no—
253C22×C11—41no—
254C22×C11—41no—
255C22×C11—41no—
256C22×C11#12114yescomplemented
257C22×C11C22×D411yescharacteristic
258C22×C11C22×D411yescharacteristic
259C22×C11C22×D411yescharacteristic
260C22×C11C2×#4111yescharacteristic
261C22×C11C2×#4111yescharacteristic
262C22×C11H(5,𝔽2)11yescharacteristic
263C22×C11H(5,𝔽2)11yescharacteristic
264C2×D11—22no—
265C2×D11—22no—
266C2×D11—22no—
267C2×D11—41no—
268C2×D11—41no—
269C2×D11—41no—
270C2×D11—41no—
271C4×C11—22no—
272C4×C11—22no—
273C4×C11—41no—
274Dic11—22no—
275Dic11—22no—
276Dic11—22no—
277Dic11—41no—
278Dic11—41no—
279Dic11—41no—
280Dic11—41no—
281C25C2×D1111yescharacteristic
282C22×D4—111no—
283C22×D4—111no—
284C22×D4—111no—
285C22×D4—111no—
286C22×D4C2×D1111yescharacteristic
287C22×D4C2×D1111yescharacteristic
288C22×D4C2×D1111yescharacteristic
289C23×C4—111no—
290C23×C4—111no—
291C23×C4—111no—
292#121—224no—
293#121—224no—
294#120—24no—
295#120—224no—
296C4×D4—224no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—111no—
301C2×C22⋊C4—111no—
302C2×C22⋊C4—111no—
303C2×C22⋊C4—111no—
304C2×C22⋊C4—111no—
305C2×C22⋊C4—111no—
306C2×C22⋊C4—111no—
307C2×C22⋊C4—111no—
308C2×C22⋊C4—111no—
309C2×C22⋊C4—111no—
310C2×C22⋊C4—111no—
311C2×C22⋊C4—111no—
312C2×C22⋊C4—111no—
313C2×C22⋊C4—224no—
314C2×C22⋊C4C2×D1111yescharacteristic
315C2×C22⋊C4C2×D1111yescharacteristic
316C2×C22⋊C4C2×D1111yescharacteristic
317C2×C42—111no—
318#95—111no—
319#95—111no—
320#95—111no—
321#95—111no—
322C2×C11—24no—
323C2×C11—42no—
324C2×C11—42no—
325C2×C11—81no—
326C2×C11C2×#12111yescharacteristic
327C2×C11#52511yescharacteristic
328C2×C11#53811yescharacteristic
329C2×C11D4211yescharacteristic
330C2×C11D4211yescharacteristic
331C2×C11#54611yescharacteristic
332C2×C11#54611yescharacteristic
333D11—42no—
334C24—22no—
335C24—22no—
336C24—22no—
337C24—22no—
338C24—22no—
339C24—41no—
340C24—41no—
341C24—111no—
342C24C22×D1111yescharacteristic
343C24C22×D1111yescharacteristic
344C24C22×D1111yescharacteristic
345C24C22×D1111yescharacteristic
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—114no—
356C2×D4—222no—
357C2×D4—222no—
358C2×D4—222no—
359C2×D4—222no—
360C2×D4—222no—
361C2×D4—222no—
362C2×D4—222no—
363C2×D4—222no—
364C2×D4—441no—
365C2×D4—441no—
366C2×D4—441no—
367C22×C4—111no—
368C22×C4—111no—
369C22×C4—111no—
370C22×C4—111no—
371C22×C4—111no—
372C22×C4—111no—
373C22×C4—111no—
374C22×C4—222no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—441no—
381C22×C4—441no—
382C22×C4—441no—
383C22×C4C22×D1111yescharacteristic
384C22×C4C22×D1111yescharacteristic
385C22×C4C22×D1111yescharacteristic
386C4⋊C4—222no—
387C4⋊C4—222no—
388C4⋊C4—222no—
389C4⋊C4—441no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—114no—
393C22⋊C4—222no—
394C22⋊C4—222no—
395C22⋊C4—222no—
396C22⋊C4—222no—
397C22⋊C4—222no—
398C22⋊C4—222no—
399C22⋊C4—222no—
400C22⋊C4—222no—
401C22⋊C4—222no—
402C22⋊C4—222no—
403C22⋊C4—441no—
404C22⋊C4C22⋊D1114yescomplemented
405C42—222no—
406C11#242411yescharacteristic, complemented, Sylow
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—28no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—44no—
435C23—44no—
436C23—44no—
437C23—112no—
438C23—221no—
439C23—221no—
440C23—221no—
441C23—221no—
442C23—221no—
443C23—221no—
444C23D4×D1112yes—
445C23D4×D1112yes—
446C23#434112yes—
447C23#434112yes—
448C23C2×C22⋊D1112yes—
449C23C23×D1111yescharacteristic
450D4—44no—
451D4—44no—
452D4—44no—
453D4—228no—
454D4—444no—
455D4—444no—
456D4—444no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—112no—
465C2×C4—112no—
466C2×C4—112no—
467C2×C4—221no—
468C2×C4—221no—
469C2×C4—221no—
470C2×C4—221no—
471C2×C4—221no—
472C2×C4—221no—
473C2×C4—221no—
474C2×C4—221no—
475C2×C4—221no—
476C2×C4—221no—
477C2×C4—221no—
478C2×C4—221no—
479C2×C4—221no—
480C2×C4—221no—
481C2×C4—221no—
482C2×C4—221no—
483C2×C4—221no—
484C2×C4—221no—
485C2×C4—444no—
486C2×C4—444no—
487C2×C4—444no—
488C2×C4C2×C22⋊D1112yes—
489C2×C4C2×C22⋊D1112yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—22no—
501C22—22no—
502C22—416no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—222no—
519C22—222no—
520C22—222no—
521C22—441no—
522C22—441no—
523C22—441no—
524C22—441no—
525C22#6699114yescomplemented
526C22C2×D4×D1111yescharacteristic
527C22C2×D4×D1111yescharacteristic
528C22C2×#434111yescharacteristic
529C22C2×#434111yescharacteristic
530C22#6703711yescharacteristic
531C22#6703711yescharacteristic
532C22C22×C22⋊D1111yescharacteristic
533C4—22no—
534C4—22no—
535C4—41no—
536C4—222no—
537C4—222no—
538C4—222no—
539C4—441no—
540C4—441no—
541C4—441no—
542C4—441no—
543C2—24no—
544C2—42no—
545C2—42no—
546C2—81no—
547C2—442no—
548C2#1062311711yescharacteristic
549C2#1062312111yescharacteristic
550C2#1062312211yescharacteristic
551C2#1062312411yescharacteristic
552C2C2×#6699111yescharacteristic
553C2D4×C22⋊D1111yescharacteristic
554C2#1062333711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#120C2
hypercenterC2×#120D11
hypocenterC11#2424
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×C11×#120C2semidirect
2. C2×#67006C2semidirect
3. C22×C22⋊Dic11C2semidirect
4. C2×#66992C2semidirect
5. C2×#66991C2semidirect
6. C2×(C22⋊D11)⋊C4C2semidirect
7. #10622836C2semidirect
8. #10622835C2semidirect
9. #10622834C2semidirect
10. #10622833C2semidirect
11. #10622574C2semidirect
12. #10622569C2semidirect
13. #10622563C2semidirect
14. #10622561C2semidirect
15. #10622557C2semidirect
23. C22×C22⋊D11C22semidirect
26. C22×C4×D11C22semidirect
40. C2×C22⋊Dic11C22semidirect
41. C2×C22⋊Dic11C22semidirect
42. C2×C22⋊Dic11C22semidirect
45. C2×(C2×D11)⋊C4C22semidirect
46. C2×(C2×D11)⋊C4C22semidirect
47. C2×C4⋊Dic11C22semidirect
48. C2×C4⋊Dic11C22semidirect
49. C2×Dic11⋊C4C22semidirect
50. C2×Dic11⋊C4C22semidirect
51. C2×C4×Dic11C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
55. C11⋊#95C22semidirect
56. C11⋊#95C22semidirect
92. C2×C22⋊D11D4semidirect
111. C11×C22⋊C4D4semidirect
121. C22⋊Dic11D4semidirect
216. C2×#120D11semidirect
256. C22×C11#121semidirect
404. C22⋊C4C22⋊D11semidirect
406. C11#2424semidirect
525. C22#66991semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1202
C2×#670062
C22×C22⋊Dic112
C2×#669922
C2×#669912
C2×(C22⋊D11)⋊C42
#106228362
#106228352
#106228342
#106228332
#106225742
#106225692
#106225632
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