Finite Group Databasebeta

← #13072159

Subgroups — #13072159

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×#66990C211yesmaximal, characteristic, complemented
2C2×#66937C211yesmaximal, characteristic, complemented
3C2×#66937C211yesmaximal, characteristic, complemented
4C2×#66935C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D11C211yesmaximal, characteristic, complemented
6C2×C4×D44C211yesmaximal, characteristic, complemented
7C11×#390C211yesmaximal, characteristic, complemented
8#10622836C211yesmaximal, characteristic, complemented
9#10622604C211yesmaximal, characteristic, complemented
10#10622602C211yesmaximal, characteristic, complemented
11#10622574C211yesmaximal, characteristic, complemented
12#10622569C211yesmaximal, characteristic, complemented
13#10622569C211yesmaximal, characteristic, complemented
14#10622561C211yesmaximal, characteristic, complemented
15#10622553C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic, complemented
22C22×D44C2211yescharacteristic
23C22×D44C2211yescharacteristic
24C22×C4×D11C2211yescharacteristic
25C22×C4×D11C2211yescharacteristic
26C22×C4×D11C2211yescharacteristic, complemented
27C2×C11×C4⋊C4C2211yescharacteristic, complemented
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic, complemented
31C2×C11×C22⋊C4C2211yescharacteristic, complemented
32C2×C42×C11C2211yescharacteristic, complemented
33C2×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊Dic11C2211yescharacteristic
35C2×C22⋊Dic11C2211yescharacteristic, complemented
36#66990—24no—
37C2×(C2×D11)⋊C4C2211yescharacteristic
38C2×(C2×D11)⋊C4C2211yescharacteristic
39C2×(C2×D11)⋊C4C2211yescharacteristic
40C2×(C2×D11)⋊C4C2211yescharacteristic
41C2×(C2×D11)⋊C4C2211yescharacteristic
42C2×(C2×D11)⋊C4C2211yescharacteristic
43C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
45C2×C4⋊Dic11C2211yescharacteristic, complemented
46C2×Dic11⋊C4C2211yescharacteristic, complemented
47C2×Dic11⋊C4C2211yescharacteristic, complemented
48#66937—24no—
49#66937—24no—
50#66935—24no—
51C22⋊C4×D11—24no—
52C4×D44—24no—
53C11⋊#95C2211yescharacteristic, complemented
54C11⋊#95C2211yescharacteristic, complemented
55C11⋊#95C2211yescharacteristic, complemented
56C11⋊#95C2211yescharacteristic, complemented
57C24×C11C2311yescharacteristic
58C24×C11C2311yescharacteristic
59C23×D11—22no—
60C23×D11—22no—
61C23×D11—22no—
62C23×D11—22no—
63C23×D11—22no—
64C23×D11—41no—
65C23×D11—41no—
66C23×D11C2311yescharacteristic
67C23×D11C2311yescharacteristic
68C23×D11C2311yescharacteristic
69C2×D4×C11—22no—
70C2×D4×C11—22no—
71C2×D4×C11—41no—
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C22×C4×C11C2311yescharacteristic
76C22×C4×C11C2311yescharacteristic
77C2×C22⋊D11—22no—
78C2×C22⋊D11—22no—
79C2×C22⋊D11—22no—
80C2×C22⋊D11—22no—
81C2×C22⋊D11—22no—
82C2×C22⋊D11—22no—
83C2×C22⋊D11—22no—
84C2×C22⋊D11—22no—
85C2×C22⋊D11—22no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C2×C22⋊D11—41no—
89C22×Dic11C2311yescharacteristic
90C22×Dic11C2311yescharacteristic
91C22×Dic11C2311yescharacteristic
92C22×Dic11C2311yescharacteristic
93C22×Dic11C2311yescharacteristic
94C2×D44—22no—
95C2×D44—22no—
96C2×D44—22no—
97C2×D44—22no—
98C2×D44—41no—
99C2×D44D414yescomplemented
100C2×C4×D11—22no—
101C2×C4×D11—22no—
102C2×C4×D11—22no—
103C2×C4×D11—22no—
104C2×C4×D11—22no—
105C2×C4×D11—22no—
106C2×C4×D11—41no—
107C2×C4×D11—41no—
108C2×C4×D11—41no—
109C11×C4⋊C4—41no—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—22no—
112C11×C22⋊C4—22no—
113C11×C22⋊C4—22no—
114C42×C11—22no—
115C22⋊Dic11—22no—
116C22⋊Dic11—22no—
117C22⋊Dic11—41no—
118(C2×D11)⋊C4—22no—
119(C2×D11)⋊C4—22no—
120(C2×D11)⋊C4—22no—
121(C2×D11)⋊C4—22no—
122(C2×D11)⋊C4—22no—
123(C2×D11)⋊C4—22no—
124(C2×D11)⋊C4D414yescomplemented
125(C2×D11)⋊C4D414yescomplemented
126C4⋊Dic11—22no—
127Dic11⋊C4—22no—
128Dic11⋊C4—22no—
129#2424—111nomaximal, Sylow
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
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#4112yes—
144C23×C11C2411yescharacteristic
145C22×D11—21no—
146C22×D11—21no—
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—28no—
150C22×D11—21no—
151C22×D11—21no—
152C22×D11—21no—
153C22×D11—21no—
154C22×D11—21no—
155C22×D11—21no—
156C22×D11—21no—
157C22×D11—21no—
158C22×D11—21no—
159C22×D11—21no—
160C22×D11—21no—
161C22×D11—21no—
162C22×D11—44no—
163C22×D11—44no—
164C22×D11—44no—
165C22×D11—44no—
166C22×D11—44no—
167C22×D11—44no—
168C22×D11C2×D412yes—
169C22×D11C2×D412yes—
170C22×D11C2×D412yes—
171C22×D11C2×D412yes—
172C22×D11#4112yes—
173D4×C11—44no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
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×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11C2×D412yes—
187C2×C4×C11C2×D412yes—
188C2×C4×C11C2×D412yes—
189C22⋊D11—44no—
190C22⋊D11—44no—
191C22⋊D11—44no—
192C22⋊D11—44no—
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×Dic11C2×D412yes—
207C2×Dic11C2×D412yes—
208D44—28no—
209D44—44no—
210C4×D11—44no—
211C4×D11—44no—
212C4×D11—44no—
213C2×#121—111no—
214C2×#121—111no—
215C2×#120—111no—
216C2×#120—111no—
217C2×C4×D4—111no—
218C22×C22⋊C4—111no—
219#396—111no—
220#394—111no—
221#394—111no—
222#392—111no—
223#390D1111yescharacteristic, complemented
224#388—111no—
225#386—111no—
226#386—111no—
227#385—111no—
228C22×C11—22no—
229C22×C11—22no—
230C22×C11—22no—
231C22×C11—41no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11—41no—
242C22×C11C22×D411yescharacteristic
243C22×C11C22×D411yescharacteristic
244C22×C11C22×D411yescharacteristic
245C22×C11C2×#4111yescharacteristic
246C22×C11C2×#4111yescharacteristic
247C22×C11H(5,𝔽2)11yescharacteristic
248C22×C11H(5,𝔽2)11yescharacteristic
249C2×D11—22no—
250C2×D11—22no—
251C2×D11—22no—
252C2×D11—22no—
253C2×D11—22no—
254C2×D11—22no—
255C2×D11—22no—
256C2×D11—22no—
257C2×D11—22no—
258C2×D11—22no—
259C2×D11—22no—
260C2×D11—22no—
261C2×D11—416no—
262C2×D11—41no—
263C2×D11—41no—
264C2×D11—41no—
265C2×D11—41no—
266C2×D11—41no—
267C2×D11—41no—
268C2×D11—41no—
269C2×D11—41no—
270C2×D11#12114yescomplemented
271C4×C11—22no—
272C4×C11—22no—
273C4×C11—22no—
274C4×C11—41no—
275C4×C11—41no—
276Dic11—22no—
277Dic11—22no—
278Dic11—41no—
279Dic11—41no—
280Dic11—41no—
281C25—111no—
282C22×D4—111no—
283C22×D4—111no—
284C22×D4—111no—
285C22×D4—111no—
286C22×D4—111no—
287C22×D4—111no—
288C22×D4C2×D1111yescharacteristic
289C23×C4—111no—
290C23×C4—111no—
291C23×C4—111no—
292#121—224no—
293#121—224no—
294#120—224no—
295#120—224no—
296C4×D4—224no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4C2×D1111yescharacteristic, complemented
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—224no—
313C2×C22⋊C4C2×D1111yescharacteristic
314C2×C22⋊C4C2×D1111yescharacteristic
315C2×C22⋊C4C2×D1111yescharacteristic, complemented
316C2×C22⋊C4C2×D1111yescharacteristic, complemented
317C2×C42C2×D1111yescharacteristic, complemented
318#95—111no—
319#95—111no—
320#95—111no—
321#95—111no—
322C2×C11—42no—
323C2×C11—81no—
324C2×C11C2×#12111yescharacteristic
325C2×C11#52511yescharacteristic
326C2×C11#53811yescharacteristic
327C2×C11D4211yescharacteristic
328C2×C11D4211yescharacteristic
329C2×C11#54611yescharacteristic
330C2×C11#54611yescharacteristic
331D11—24no—
332D11—42no—
333D11—42no—
334C24—111no—
335C24—111no—
336C24—111no—
337C24—222no—
338C24—222no—
339C24—222no—
340C24—222no—
341C24—222no—
342C24—441no—
343C24—441no—
344C24C22×D1111yescharacteristic
345C24C22×D1111yescharacteristic
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—41no—
349C2×D4—114no—
350C2×D4—222no—
351C2×D4—222no—
352C2×D4—222no—
353C2×D4—222no—
354C2×D4—222no—
355C2×D4—222no—
356C2×D4—222no—
357C2×D4—222no—
358C2×D4—222no—
359C2×D4—222no—
360C2×D4—222no—
361C2×D4—222no—
362C2×D4—222no—
363C2×D4—441no—
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—222no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—441no—
379C22×C4—441no—
380C22×C4—441no—
381C22×C4C22×D1111yescharacteristic
382C22×C4C22×D1111yescharacteristic
383C22×C4C22×D1111yescharacteristic
384C22×C4C22×D1111yescharacteristic
385C22×C4C22×D1111yescharacteristic
386C4⋊C4—41no—
387C4⋊C4—222no—
388C4⋊C4—222no—
389C4⋊C4—222no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—22no—
394C22⋊C4—114no—
395C22⋊C4—114no—
396C22⋊C4—222no—
397C22⋊C4—222no—
398C22⋊C4—222no—
399C22⋊C4—222no—
400C22⋊C4—222no—
401C22⋊C4—222no—
402C22⋊C4—222no—
403C22⋊C4—222no—
404C22⋊C4—441no—
405C42—22no—
406C11#242411yescharacteristic, complemented, Sylow
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—112no—
421C23—112no—
422C23—112no—
423C23—112no—
424C23—112no—
425C23—228no—
426C23—221no—
427C23—221no—
428C23—221no—
429C23—221no—
430C23—221no—
431C23—221no—
432C23—221no—
433C23—221no—
434C23—221no—
435C23—221no—
436C23—221no—
437C23—221no—
438C23—221no—
439C23—221no—
440C23—221no—
441C23—221no—
442C23—444no—
443C23—444no—
444C23—444no—
445C23—444no—
446C23—444no—
447C23—444no—
448C23#433912yes—
449C23C23×D1111yescharacteristic
450D4—44no—
451D4—228no—
452D4—444no—
453D4—444no—
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—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—112no—
470C2×C4—112no—
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—444no—
485C2×C4—444no—
486C2×C4—444no—
487C2×C4D4×D1112yes—
488C2×C4D4×D1112yes—
489C2×C4D4×D1112yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—114no—
505C22—222no—
506C22—222no—
507C22—222no—
508C22—222no—
509C22—222no—
510C22—222no—
511C22—222no—
512C22—222no—
513C22—222no—
514C22—222no—
515C22—222no—
516C22—222no—
517C22—4416no—
518C22—441no—
519C22—441no—
520C22—441no—
521C22—441no—
522C22—441no—
523C22—441no—
524C22—441no—
525C22—441no—
526C22C2×#433911yescharacteristic
527C22C2×D4×D1111yescharacteristic
528C22C2×D4×D1111yescharacteristic
529C22C2×D4×D1111yescharacteristic
530C22#6703711yescharacteristic
531C22#41×D1111yescharacteristic
532C22#6704211yescharacteristic
533C4—22no—
534C4—22no—
535C4—22no—
536C4—41no—
537C4—41no—
538C4—222no—
539C4—222no—
540C4—441no—
541C4—441no—
542C4—441no—
543C2—42no—
544C2—81no—
545C2—224no—
546C2—442no—
547C2—442no—
548C2#1062302111yescharacteristic
549C2#1062307811yescharacteristic
550C2#1062308111yescharacteristic
551C2D11×#12111yescharacteristic
552C2#1062314011yescharacteristic
553C2#1062320911yescharacteristic
554C2#1062324811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
hypercenter#390D11
hypocenterC11#2424
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#66990C2semidirect
2. C2×#66937C2semidirect
3. C2×#66937C2semidirect
4. C2×#66935C2semidirect
5. C2×C22⋊C4×D11C2semidirect
6. C2×C4×D44C2semidirect
7. C11×#390C2semidirect
8. #10622836C2semidirect
9. #10622604C2semidirect
10. #10622602C2semidirect
11. #10622574C2semidirect
12. #10622569C2semidirect
13. #10622569C2semidirect
14. #10622561C2semidirect
15. #10622553C2semidirect
21. C22×C22⋊D11C22semidirect
26. C22×C4×D11C22semidirect
27. C2×C11×C4⋊C4C22semidirect
30. C2×C11×C22⋊C4C22semidirect
31. C2×C11×C22⋊C4C22semidirect
32. C2×C42×C11C22semidirect
35. C2×C22⋊Dic11C22semidirect
43. C2×(C2×D11)⋊C4C22semidirect
44. C2×(C2×D11)⋊C4C22semidirect
45. C2×C4⋊Dic11C22semidirect
46. C2×Dic11⋊C4C22semidirect
47. C2×Dic11⋊C4C22semidirect
53. C11⋊#95C22semidirect
54. C11⋊#95C22semidirect
55. C11⋊#95C22semidirect
56. C11⋊#95C22semidirect
99. C2×D44D4semidirect
124. (C2×D11)⋊C4D4semidirect
125. (C2×D11)⋊C4D4semidirect
223. #390D11semidirect
270. C2×D11#121semidirect
300. C2×C4⋊C4C2×D11semidirect
315. C2×C22⋊C4C2×D11semidirect
316. C2×C22⋊C4C2×D11semidirect
317. C2×C42C2×D11semidirect
406. C11#2424semidirect

Maximal subgroups

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

subgroupindex
C2×#669902
C2×#669372
C2×#669352
C2×C22⋊C4×D112
C2×C4×D442
C11×#3902
#106228362
#106226042
#106226022
#106225742
#106225692
#106225612
#106225532
#242411