Finite Group Databasebeta

← #13071985

Subgroups — #13071985

Order 1408.

1246 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D11C211yesmaximal, characteristic, complemented
2C2×#66948C211yesmaximal, characteristic, complemented
3C2×#66937C211yesmaximal, characteristic, complemented
4C2×#66935C211yesmaximal, characteristic, complemented
5C2×#66935C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×D11C211yesmaximal, characteristic, complemented
7C11×#394C211yesmaximal, characteristic, complemented
8#10622836C211yesmaximal, characteristic, complemented
9#10622602C211yesmaximal, characteristic, complemented
10#10622573C211yesmaximal, characteristic, complemented
11#10622572C211yesmaximal, characteristic, complemented
12#10622569C211yesmaximal, characteristic, complemented
13#10622568C211yesmaximal, characteristic, complemented
14#10622278C211yesmaximal, characteristic, complemented
15#10622278C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C24×D11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic, complemented
22C22×C22⋊D11C2211yescharacteristic, complemented
23C2×D4×D11—24no—
24C2×D4×D11—24no—
25C2×D4×D11—24no—
26C22×D44C2211yescharacteristic
27C22×D44C2211yescharacteristic
28C22×D44C2211yescharacteristic, complemented
29C22×D44C2211yescharacteristic, complemented
30C22×C4×D11C2211yescharacteristic
31C22×C4×D11C2211yescharacteristic, complemented
32C22×C4×D11C2211yescharacteristic, complemented
33C2×C11×C4⋊C4C2211yescharacteristic, complemented
34C2×C11×C22⋊C4C2211yescharacteristic, complemented
35C2×C11×C22⋊C4C2211yescharacteristic, complemented
36C2×C11×C22⋊C4C2211yescharacteristic, complemented
37C2×C11×C22⋊C4C2211yescharacteristic, complemented
38C2×C22⋊Dic11C2211yescharacteristic, complemented
39C2×C22⋊Dic11C2211yescharacteristic, complemented
40C2×(C2×D11)⋊C4C2211yescharacteristic
41C2×(C2×D11)⋊C4C2211yescharacteristic
42C2×(C2×D11)⋊C4C2211yescharacteristic
43C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
46C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
47C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
48C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
49C2×Dic11⋊C4C2211yescharacteristic, complemented
50#66948—24no—
51#66937—24no—
52#66935—24no—
53#66935—24no—
54C22⋊C4×D11—24no—
55C11×#95C2211yescharacteristic, complemented
56C11⋊#95C2211yescharacteristic, complemented
57C11⋊#95C2211yescharacteristic, complemented
58C11⋊#95C2211yescharacteristic, complemented
59C24×C11C2311yescharacteristic
60C24×C11C2311yescharacteristic
61C23×D11—22no—
62C23×D11—22no—
63C23×D11—22no—
64C23×D11—22no—
65C23×D11—22no—
66C23×D11—22no—
67C23×D11—22no—
68C23×D11—22no—
69C23×D11—22no—
70C23×D11—41no—
71C23×D11—41no—
72C23×D11—41no—
73C23×D11—41no—
74C23×D11D414yescomplemented
75C23×D11C2311yescharacteristic
76C23×D11C2311yescharacteristic
77C23×D11C2311yescharacteristic
78C23×D11C2311yescharacteristic
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—22no—
82C22×C4×C11C2311yescharacteristic
83C22×C4×C11C2311yescharacteristic
84C22×C4×C11C2311yescharacteristic
85C22×C4×C11C2311yescharacteristic
86C22×C4×C11C2311yescharacteristic
87C2×C22⋊D11—22no—
88C2×C22⋊D11—22no—
89C2×C22⋊D11—22no—
90C2×C22⋊D11—22no—
91C2×C22⋊D11—22no—
92C2×C22⋊D11—22no—
93C2×C22⋊D11—22no—
94C2×C22⋊D11—22no—
95C2×C22⋊D11—41no—
96C2×C22⋊D11—41no—
97C2×C22⋊D11—41no—
98C2×C22⋊D11D414yescomplemented
99C22×Dic11C2311yescharacteristic
100C22×Dic11C2311yescharacteristic
101C22×Dic11C2311yescharacteristic
102C22×Dic11C2311yescharacteristic
103D4×D11—232no—
104C2×D44—22no—
105C2×D44—22no—
106C2×D44—22no—
107C2×D44—22no—
108C2×D44—22no—
109C2×D44—22no—
110C2×D44—22no—
111C2×D44—22no—
112C2×D44—22no—
113C2×D44—22no—
114C2×D44—41no—
115C2×D44D414yescomplemented
116C2×C4×D11—22no—
117C2×C4×D11—22no—
118C2×C4×D11—22no—
119C2×C4×D11—22no—
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—41no—
124C2×C4×D11—41no—
125C11×C4⋊C4—22no—
126C11×C22⋊C4—22no—
127C11×C22⋊C4—22no—
128C11×C22⋊C4—22no—
129C11×C22⋊C4—22no—
130C22⋊Dic11—22no—
131C22⋊Dic11—41no—
132(C2×D11)⋊C4—22no—
133(C2×D11)⋊C4—22no—
134(C2×D11)⋊C4—22no—
135(C2×D11)⋊C4—22no—
136(C2×D11)⋊C4—22no—
137(C2×D11)⋊C4—22no—
138(C2×D11)⋊C4—22no—
139(C2×D11)⋊C4—41no—
140(C2×D11)⋊C4D414yescomplemented
141Dic11⋊C4—22no—
142#2410—111nomaximal, Sylow
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—21no—
155C23×C11C2×D412yes—
156C23×C11C2×D412yes—
157C23×C11C2411yescharacteristic
158C22×D11—21no—
159C22×D11—21no—
160C22×D11—21no—
161C22×D11—21no—
162C22×D11—21no—
163C22×D11—21no—
164C22×D11—21no—
165C22×D11—21no—
166C22×D11—28no—
167C22×D11—21no—
168C22×D11—21no—
169C22×D11—21no—
170C22×D11—21no—
171C22×D11—21no—
172C22×D11—21no—
173C22×D11—28no—
174C22×D11—28no—
175C22×D11—21no—
176C22×D11—21no—
177C22×D11—21no—
178C22×D11—21no—
179C22×D11—21no—
180C22×D11—21no—
181C22×D11—21no—
182C22×D11—44no—
183C22×D11—44no—
184C22×D11—44no—
185C22×D11—44no—
186C22×D11—44no—
187C22×D11—44no—
188C22×D11—44no—
189C22×D11—44no—
190C22×D11—44no—
191C22×D11—44no—
192C22×D11—44no—
193C22×D11C2×D412yes—
194C22×D11C2×D412yes—
195C22×D11C2×D412yes—
196C22×D11C2×D412yes—
197C22×D11C2×D412yes—
198C22×D11C2×D412yes—
199C22×D11#4112yes—
200D4×C11—28no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11C2×D412yes—
215C2×C4×C11C2×D412yescomplemented
216C22⋊D11—28no—
217C22⋊D11—28no—
218C22⋊D11—44no—
219C22⋊D11—44no—
220C2×Dic11—21no—
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—21no—
224C2×Dic11—21no—
225C2×Dic11—21no—
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230C2×Dic11C2×D412yes—
231C2×Dic11C2×D412yescomplemented
232D44—28no—
233D44—44no—
234D44—44no—
235D44—44no—
236C4×D11—28no—
237C4×D11—44no—
238C4×D11—44no—
239C23×D4—111no—
240C2×#121—111no—
241C2×#121—111no—
242C2×#120—111no—
243C2×#120—111no—
244C22×C22⋊C4—111no—
245#394—111no—
246#394D1111yescharacteristic, complemented
247#392—111no—
248#392—111no—
249#386—111no—
250#386—111no—
251#386—111no—
252#385—111no—
253#379—111no—
254C22×C11—22no—
255C22×C11—22no—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—41no—
261C22×C11—41no—
262C22×C11—41no—
263C22×C11—41no—
264C22×C11—41no—
265C22×C11—41no—
266C22×C11—41no—
267C22×C11—41no—
268C22×C11C22×D411yescharacteristic
269C22×C11C22×D411yescharacteristic
270C22×C11C22×D411yescharacteristic
271C22×C11C22×D411yescharacteristic
272C22×C11C2×#4111yescharacteristic
273C22×C11H(5,𝔽2)11yescharacteristic
274C22×C11H(5,𝔽2)11yescharacteristic
275C2×D11—22no—
276C2×D11—22no—
277C2×D11—22no—
278C2×D11—22no—
279C2×D11—22no—
280C2×D11—22no—
281C2×D11—22no—
282C2×D11—22no—
283C2×D11—22no—
284C2×D11—22no—
285C2×D11—22no—
286C2×D11—22no—
287C2×D11—22no—
288C2×D11—22no—
289C2×D11—22no—
290C2×D11—416no—
291C2×D11—416no—
292C2×D11—41no—
293C2×D11—41no—
294C2×D11—41no—
295C2×D11—41no—
296C2×D11—41no—
297C2×D11—41no—
298C2×D11—41no—
299C2×D11—41no—
300C2×D11—41no—
301C2×D11—41no—
302C2×D11—41no—
303C2×D11#12014yescomplemented
304C2×D11#12114yescomplemented
305C4×C11—22no—
306C4×C11—22no—
307C4×C11—41no—
308C4×C11—41no—
309C4×C11—41no—
310Dic11—22no—
311Dic11—22no—
312Dic11—41no—
313Dic11—41no—
314C25—111no—
315C25—111no—
316C22×D4—111no—
317C22×D4—111no—
318C22×D4—111no—
319C22×D4—111no—
320C22×D4—111no—
321C22×D4—111no—
322C22×D4—111no—
323C22×D4—111no—
324C22×D4—224no—
325C22×D4—224no—
326C22×D4—224no—
327C22×D4C2×D1111yescharacteristic
328C23×C4—111no—
329C23×C4—111no—
330C23×C4—111no—
331#121—224no—
332#121—224no—
333#120—224no—
334#120—224no—
335C2×C4⋊C4—111no—
336C2×C4⋊C4C2×D1111yescharacteristic, complemented
337C2×C22⋊C4—111no—
338C2×C22⋊C4—111no—
339C2×C22⋊C4—111no—
340C2×C22⋊C4—111no—
341C2×C22⋊C4—111no—
342C2×C22⋊C4—111no—
343C2×C22⋊C4—111no—
344C2×C22⋊C4—111no—
345C2×C22⋊C4—111no—
346C2×C22⋊C4—111no—
347C2×C22⋊C4—111no—
348C2×C22⋊C4—224no—
349C2×C22⋊C4C2×D1111yescharacteristic, complemented
350C2×C22⋊C4C2×D1111yescharacteristic, complemented
351C2×C22⋊C4C2×D1111yescharacteristic, complemented
352C2×C22⋊C4C2×D1111yescharacteristic, complemented
353#95—111no—
354#95—111no—
355#95—111no—
356#95C2×D1111yescharacteristic, complemented
357C2×C11—42no—
358C2×C11—42no—
359C2×C11C2×#12011yescharacteristic
360C2×C11C2×#12111yescharacteristic
361C2×C11#53411yescharacteristic
362C2×C11D4211yescharacteristic
363C2×C11D4211yescharacteristic
364C2×C11#54611yescharacteristic
365C2×C11#54611yescharacteristic
366D11—24no—
367D11—24no—
368D11—42no—
369D11—81no—
370C24—111no—
371C24—111no—
372C24—111no—
373C24—114no—
374C24—111no—
375C24—222no—
376C24—222no—
377C24—222no—
378C24—222no—
379C24—222no—
380C24—222no—
381C24—222no—
382C24—222no—
383C24—222no—
384C24—441no—
385C24—441no—
386C24—441no—
387C24—441no—
388C24C22×D1111yescharacteristic
389C24C22×D1111yescharacteristic
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—114no—
394C2×D4—114no—
395C2×D4—222no—
396C2×D4—222no—
397C2×D4—222no—
398C2×D4—222no—
399C2×D4—222no—
400C2×D4—222no—
401C2×D4—222no—
402C2×D4—222no—
403C2×D4—222no—
404C2×D4—222no—
405C2×D4—222no—
406C2×D4—2232no—
407C2×D4—222no—
408C2×D4—222no—
409C2×D4—222no—
410C2×D4—222no—
411C2×D4—222no—
412C2×D4—222no—
413C2×D4—222no—
414C2×D4—441no—
415C2×D4—441no—
416C2×D4—441no—
417C2×D4—441no—
418C22×C4—111no—
419C22×C4—111no—
420C22×C4—111no—
421C22×C4—111no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—441no—
430C22×C4—441no—
431C22×C4C22×D1111yescharacteristic
432C22×C4C22×D1111yescharacteristic
433C22×C4C22×D1111yescharacteristic
434C22×C4C22×D1111yescharacteristic
435C22×C4C22×D1111yescharacteristic
436C4⋊C4—22no—
437C4⋊C4—222no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—114no—
443C22⋊C4—222no—
444C22⋊C4—222no—
445C22⋊C4—222no—
446C22⋊C4—222no—
447C22⋊C4—222no—
448C22⋊C4—222no—
449C22⋊C4—222no—
450C22⋊C4—222no—
451C22⋊C4—441no—
452C22⋊C4—441no—
453C11#241011yescharacteristic, complemented, Sylow
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—112no—
467C23—112no—
468C23—112no—
469C23—112no—
470C23—112no—
471C23—112no—
472C23—112no—
473C23—228no—
474C23—228no—
475C23—228no—
476C23—221no—
477C23—221no—
478C23—221no—
479C23—221no—
480C23—221no—
481C23—221no—
482C23—221no—
483C23—221no—
484C23—221no—
485C23—221no—
486C23—221no—
487C23—221no—
488C23—221no—
489C23—221no—
490C23—221no—
491C23—221no—
492C23—221no—
493C23—221no—
494C23—221no—
495C23—221no—
496C23—221no—
497C23—444no—
498C23—444no—
499C23—444no—
500C23—444no—
501C23—444no—
502C23—444no—
503C23—444no—
504C23—444no—
505C23—444no—
506C23—444no—
507C23—444no—
508C23D4×D1112yes—
509C23D4×D1112yes—
510C23C23×D1111yescharacteristic
511D4—28no—
512D4—228no—
513D4—228no—
514D4—228no—
515D4—444no—
516D4—444no—
517D4—444no—
518D4—444no—
519D4—444no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—112no—
534C2×C4—112no—
535C2×C4—228no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—444no—
547C2×C4—444no—
548C2×C4D4×D1112yes—
549C2×C4D4×D1112yescomplemented
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—114no—
565C22—114no—
566C22—222no—
567C22—222no—
568C22—222no—
569C22—222no—
570C22—222no—
571C22—222no—
572C22—222no—
573C22—222no—
574C22—222no—
575C22—222no—
576C22—222no—
577C22—222no—
578C22—222no—
579C22—222no—
580C22—222no—
581C22—4416no—
582C22—4416no—
583C22—441no—
584C22—441no—
585C22—441no—
586C22—441no—
587C22—441no—
588C22—441no—
589C22—441no—
590C22—441no—
591C22—441no—
592C22—441no—
593C22—441no—
594C22C2×D4×D1111yescharacteristic
595C22C2×D4×D1111yescharacteristic
596C22C2×D4×D1111yescharacteristic
597C22C2×D4×D1111yescharacteristic
598C22#41×D1111yescharacteristic
599C22#6704211yescharacteristic
600C22#6704211yescharacteristic
601C4—22no—
602C4—22no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—222no—
607C4—222no—
608C4—441no—
609C4—441no—
610C2—42no—
611C2—42no—
612C2—224no—
613C2—224no—
614C2—442no—
615C2—881no—
616C2D11×#12011yescharacteristic
617C2D11×#12111yescharacteristic
618C2#1062314011yescharacteristic
619C2#1062314011yescharacteristic
620C2#1062318411yescharacteristic
621C2#1062318511yescharacteristic
622C2#1062320711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
hypercenter#394D11
hypocenterC11#2410
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C22×D4×D11C2semidirect
2. C2×#66948C2semidirect
3. C2×#66937C2semidirect
4. C2×#66935C2semidirect
5. C2×#66935C2semidirect
6. C2×C22⋊C4×D11C2semidirect
7. C11×#394C2semidirect
8. #10622836C2semidirect
9. #10622602C2semidirect
10. #10622573C2semidirect
11. #10622572C2semidirect
12. #10622569C2semidirect
13. #10622568C2semidirect
14. #10622278C2semidirect
15. #10622278C2semidirect
21. C22×C22⋊D11C22semidirect
22. C22×C22⋊D11C22semidirect
28. C22×D44C22semidirect
29. C22×D44C22semidirect
31. C22×C4×D11C22semidirect
32. C22×C4×D11C22semidirect
33. C2×C11×C4⋊C4C22semidirect
34. C2×C11×C22⋊C4C22semidirect
35. C2×C11×C22⋊C4C22semidirect
36. C2×C11×C22⋊C4C22semidirect
37. C2×C11×C22⋊C4C22semidirect
38. C2×C22⋊Dic11C22semidirect
39. C2×C22⋊Dic11C22semidirect
43. C2×(C2×D11)⋊C4C22semidirect
44. C2×(C2×D11)⋊C4C22semidirect
45. C2×(C2×D11)⋊C4C22semidirect
46. C2×(C2×D11)⋊C4C22semidirect
47. C2×(C2×D11)⋊C4C22semidirect
48. C2×(C2×D11)⋊C4C22semidirect
49. C2×Dic11⋊C4C22semidirect
55. C11×#95C22semidirect
56. C11⋊#95C22semidirect
57. C11⋊#95C22semidirect
58. C11⋊#95C22semidirect
74. C23×D11D4semidirect
98. C2×C22⋊D11D4semidirect
115. C2×D44D4semidirect
140. (C2×D11)⋊C4D4semidirect
215. C2×C4×C11C2×D4semidirect
231. C2×Dic11C2×D4semidirect
246. #394D11semidirect
303. C2×D11#120semidirect
304. C2×D11#121semidirect
336. C2×C4⋊C4C2×D11semidirect
349. C2×C22⋊C4C2×D11semidirect
350. C2×C22⋊C4C2×D11semidirect
351. C2×C22⋊C4C2×D11semidirect
352. C2×C22⋊C4C2×D11semidirect
356. #95C2×D11semidirect
453. C11#2410semidirect
549. C2×C4D4×D11semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D112
C2×#669482
C2×#669372
C2×#669352
C2×C22⋊C4×D112
C11×#3942
#106228362
#106226022
#106225732
#106225722
#106225692
#106225682
#106222782
#241011