Finite Group Databasebeta

← #14759121

Subgroups — #14759121

Order 2816.

1222 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic
2C4×#66979C211yesmaximal, characteristic, complemented
3#13069600C212yesmaximal, complemented
4#13069451C212yesmaximal
5#13069072C214yesmaximal, complemented
6C4×#66870C214yesmaximal, complemented
7C11×#2283C211yesmaximal, characteristic, complemented
8C22×C42×C11C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C2×#66982C2212yes—
11C2×C4×C22⋊D11C2212yes—
12C2×#66979C2212yes—
13C2×#66977C2211yescharacteristic
14#10623010—21no—
15#10623010—21no—
16#10623010—21no—
17#10623010—21no—
18#10623010—21no—
19#10623010—21no—
20#10623010—21no—
21#10623010—21no—
22C2×#66929C412yescomplemented
23C2×#66928C411yescharacteristic, complemented
24C2×C4×D44C411yescharacteristic, complemented
25C2×#66925C412yescomplemented
26C2×#66923C411yescharacteristic, complemented
27C2×C4×Dic22C411yescharacteristic, complemented
28C11×#383—21no—
29C11×#382—21no—
30C11×#381C2212yes—
31C11×#380C2212yes—
32C4×C11×C4⋊C4—21no—
33C4×C11×C22⋊C4C2212yes—
34C11×#376—21no—
35C4×C22⋊Dic11C2212yes—
36C4×C22⋊Dic11C2212yes—
37C2×#66870C2218yes—
38C4×C4⋊Dic11—21no—
39C4×C4⋊Dic11—21no—
40#10622545—21no—
41C42×Dic11—21no—
42#10622165C2218yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11C2312yes—
47C22×D44C2×C411yescharacteristic
48C22×C4×D11C2×C412yes—
49C22×Dic22C2×C411yescharacteristic
50C2×C11×C4⋊C4—22no—
51C2×C11×C22⋊C4C2314yes—
52C2×C42×C11—22no—
53C2×C42×C11C2×C411yescharacteristic
54C2×C42×C11C2×C411yescharacteristic
55C2×C42×C11C2×C411yescharacteristic
56C2×C42×C11C2×C411yescharacteristic
57C2×C42×C11D411yescharacteristic
58C2×C42×C11D411yescharacteristic
59C2×C42×C11D411yescharacteristic
60C2×C42×C11D411yescharacteristic
61C2×C42×C11D411yescharacteristic
62C2×C42×C11D411yescharacteristic
63C2×C42×C11D411yescharacteristic
64C2×C42×C11D411yescharacteristic
65C2×C22⋊Dic11C2312yes—
66C2×C22⋊Dic11C2314yes—
67#66983—21no—
68#66983—21no—
69#66983—21no—
70#66983—21no—
71#66982—22no—
72#66982—22no—
73#66982—22no—
74#66982—22no—
75C4×C22⋊D11—22no—
76C4×C22⋊D11—22no—
77C4×C22⋊D11—22no—
78C4×C22⋊D11—22no—
79C2×(C2×D11)⋊C4C2×C412yes—
80C2×(C2×D11)⋊C4C2×C412yes—
81C2×(C2×D11)⋊C4C2×C412yes—
82C2×(C2×D11)⋊C4C2×C412yes—
83#66979—28no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11C2×C411yescharacteristic
86C2×C4⋊Dic11C2×C411yescharacteristic
87#66977—21no—
88#66977—21no—
89#66977—21no—
90#66977—21no—
91C2×Dic11⋊C4C2×C412yes—
92C2×Dic11⋊C4C2×C412yes—
93C2×Dic11⋊C4C2×C412yes—
94C2×Dic11⋊C4C2×C412yes—
95C2×C4×Dic11—22no—
96C2×C4×Dic11—22no—
97C2×C4×Dic11—22no—
98C2×C4×Dic11C2×C412yes—
99#66929—22no—
100#66929—22no—
101#66929—22no—
102#66929—22no—
103#66928—21no—
104#66928—21no—
105#66928—21no—
106#66928—21no—
107C4×D44—21no—
108C4×D44—21no—
109C4×D44—21no—
110C4×D44—21no—
111#66925—22no—
112#66925—22no—
113#66925—22no—
114#66925—22no—
115#66923—21no—
116#66923—21no—
117#66923—21no—
118#66923—21no—
119C4×Dic22—21no—
120C4×Dic22—21no—
121C4×Dic22—21no—
122C4×Dic22—21no—
123C11×#95—22no—
124C11×#95—22no—
125C11×#95—22no—
126C11×#95—22no—
127C11⋊#95—22no—
128C11⋊#95—22no—
129#66870—216no—
130#21421—111nomaximal, Sylow
131C24×C11C2411yescharacteristic
132C23×D11C22×C412yes—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C22×C411yescharacteristic
141C22×C4×C11C22×C411yescharacteristic
142C22×C4×C11C22×C411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C2×C22⋊D11—22no—
156C2×C22⋊D11—22no—
157C2×C22⋊D11—28no—
158C22×Dic11—24no—
159C22×Dic11C22×C412yes—
160C22×Dic11C22×C412yes—
161C22×Dic11C22×C412yes—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—42no—
165C2×C4×D11—22no—
166C2×C4×D11—22no—
167C2×C4×D11—44no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—42no—
171C11×C4⋊C4—44no—
172C11×C22⋊C4—28no—
173C42×C11—44no—
174C42×C11C22⋊C411yescharacteristic
175C42×C11C22⋊C411yescharacteristic
176C42×C11C22⋊C411yescharacteristic
177C42×C11C22⋊C411yescharacteristic
178C42×C11C22⋊C411yescharacteristic
179C42×C11C22⋊C411yescharacteristic
180C42×C11C22⋊C411yescharacteristic
181C42×C11C22⋊C411yescharacteristic
182C42×C11C22⋊C411yescharacteristic
183C42×C11C22⋊C411yescharacteristic
184C42×C11C22⋊C411yescharacteristic
185C42×C11C22⋊C411yescharacteristic
186C42×C11C22⋊C411yescharacteristic
187C42×C11C22⋊C411yescharacteristic
188C42×C11C22⋊C411yescharacteristic
189C42×C11C22⋊C411yescharacteristic
190C22⋊Dic11—22no—
191C22⋊Dic11—22no—
192C22⋊Dic11—24no—
193C22⋊Dic11#4118yes—
194(C2×D11)⋊C4—22no—
195(C2×D11)⋊C4—22no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—22no—
199(C2×D11)⋊C4—22no—
200(C2×D11)⋊C4—22no—
201(C2×D11)⋊C4—22no—
202C4⋊Dic11—28no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4—22no—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215C4×Dic11—28no—
216C4×Dic11—22no—
217C4×Dic11—22no—
218C4×Dic11—44no—
219C4×Dic11—44no—
220C2×#529—111no—
221#2283D1111yescharacteristic, complemented
222C4×#117—111no—
223#1996—112no—
224#1964—112no—
225#1899—114no—
226C4×#99—114no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11C23×C411yescharacteristic
230C23×C11C22×D411yescharacteristic
231C23×C11C22×D411yescharacteristic
232C23×C11C2×#4114yes—
233C22×D11—22no—
234C22×D11—24no—
235C22×D11—42no—
236C22×D11—42no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—44no—
256C2×C4×C11—44no—
257C2×C4×C11—44no—
258C2×C4×C11C2×C22⋊C411yescharacteristic
259C2×C4×C11C2×C22⋊C411yescharacteristic
260C2×C4×C11C2×C22⋊C411yescharacteristic
261C2×C4×C11C2×C22⋊C411yescharacteristic
262C2×C4×C11C2×C22⋊C411yescharacteristic
263C2×C4×C11C2×C22⋊C411yescharacteristic
264C2×C4×C11C2×C22⋊C411yescharacteristic
265C2×C4×C11C2×C22⋊C411yescharacteristic
266C2×C4×C11C2×C22⋊C411yescharacteristic
267C2×C4×C11C2×C22⋊C411yescharacteristic
268C2×C4×C11C2×C22⋊C411yescharacteristic
269C2×C4×C11C2×C22⋊C411yescharacteristic
270C22⋊D11—44no—
271C22⋊D11—44no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—28no—
277C2×Dic11—44no—
278C2×Dic11—44no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281D44—42no—
282D44—42no—
283C4×D11—44no—
284C4×D11—44no—
285Dic22—42no—
286Dic22—42no—
287#529—221no—
288#529—221no—
289#529—221no—
290#529—221no—
291#529—221no—
292#529—221no—
293#529—221no—
294#529—221no—
295C2×#126—112no—
296C2×#125—111no—
297C2×#124—111no—
298C2×#123—112no—
299C2×C22⋊Q8—111no—
300C2×#121—111no—
301C2×C4×Q8—111no—
302C2×C4×D4—112no—
303C2×C4×D4—111no—
304C2×#117—112no—
305C2×#117—112no—
306C22×C42C2×D1111yescharacteristic
307C2×#99—118no—
308#383—21no—
309#382—21no—
310#381C2×D1112yes—
311#380C2×D1112yes—
312C4×C4⋊C4—21no—
313C4×C4⋊C4—221no—
314C4×C4⋊C4—221no—
315C4×C22⋊C4—112no—
316C4×C22⋊C4—112no—
317C4×C22⋊C4C2×D1112yes—
318#376—21no—
319#376—221no—
320C43—221no—
321#342—118no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—44no—
329C22×C11C22×C22⋊C411yescharacteristic
330C22×C11C4×#4112yes—
331C22×C11#52512yes—
332C22×C11#53212yes—
333C2×D11—42no—
334C2×D11—42no—
335C2×D11—42no—
336C2×D11—84no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—21no—
347C4×C11—84no—
348C4×C11#41012yes—
349C4×C11#41012yes—
350Dic11—48no—
351Dic11—42no—
352Dic11—42no—
353Dic11—42no—
354C22×Q8—111no—
355C22×D4—112no—
356C22×D4—111no—
357C23×C4—112no—
358C23×C4C22×D1111yescharacteristic
359C23×C4C22×D1111yescharacteristic
360C23×C4C22×D1111yescharacteristic
361#126—222no—
362#126—222no—
363#126—222no—
364#126—222no—
365#125—221no—
366#125—221no—
367#125—221no—
368#125—221no—
369#124—221no—
370#124—221no—
371#124—221no—
372#124—221no—
373#123—222no—
374#123—222no—
375#123—222no—
376#123—222no—
377C22⋊Q8—221no—
378C22⋊Q8—221no—
379C22⋊Q8—221no—
380C22⋊Q8—221no—
381#121—221no—
382#121—221no—
383#121—221no—
384#121—221no—
385C4×Q8—221no—
386C4×Q8—221no—
387C4×Q8—221no—
388C4×Q8—221no—
389C4×D4—222no—
390C4×D4—222no—
391C4×D4—222no—
392C4×D4—222no—
393C4×D4—221no—
394C4×D4—221no—
395C4×D4—221no—
396C4×D4—221no—
397#117—228no—
398#117—222no—
399#117—222no—
400#117—222no—
401#117—222no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—112no—
404C2×C4⋊C4—112no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—112no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—112no—
409C2×C4⋊C4—222no—
410C2×C22⋊C4—114no—
411C2×C22⋊C4—112no—
412C2×C22⋊C4—112no—
413C2×C22⋊C4—112no—
414C2×C22⋊C4—112no—
415C2×C22⋊C4—112no—
416C2×C22⋊C4C22×D1114yes—
417C2×C42—22no—
418C2×C42—112no—
419C2×C42—222no—
420C2×C42—222no—
421C2×C42—222no—
422C2×C42C4×D1111yescharacteristic
423C2×C42C4×D1111yescharacteristic
424C2×C42C4×D1111yescharacteristic
425C2×C42C4×D1111yescharacteristic
426C2×C42D4411yescharacteristic
427C2×C42D4411yescharacteristic
428C2×C42D4411yescharacteristic
429C2×C42D4411yescharacteristic
430C2×C42C22⋊D1111yescharacteristic
431C2×C42C22⋊D1111yescharacteristic
432C2×C42C22⋊D1111yescharacteristic
433C2×C42C22⋊D1111yescharacteristic
434#99—2216no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—222no—
440#95—222no—
441C2×C11—22no—
442C2×C11—22no—
443C2×C11—22no—
444C2×C11#229711yescharacteristic
445C2×C11C2×#41011yescharacteristic
446C2×C11C2×#41011yescharacteristic
447D11—82no—
448C24—112no—
449C24C23×D1111yescharacteristic
450C2×Q8—221no—
451C2×Q8—221no—
452C2×Q8—442no—
453C2×D4—222no—
454C2×D4—228no—
455C2×D4—222no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—442no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—112no—
464C22×C4—112no—
465C22×C4—112no—
466C22×C4—224no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—444no—
470C22×C4C2×C4×D1111yescharacteristic
471C22×C4C2×C4×D1111yescharacteristic
472C22×C4C2×C4×D1111yescharacteristic
473C22×C4C2×C4×D1111yescharacteristic
474C22×C4C2×C4×D1111yescharacteristic
475C22×C4C2×C4×D1111yescharacteristic
476C22×C4C2×D4411yescharacteristic
477C22×C4C2×D4411yescharacteristic
478C22×C4C2×D4411yescharacteristic
479C22×C4C2×D4411yescharacteristic
480C22×C4C2×D4411yescharacteristic
481C22×C4C2×D4411yescharacteristic
482C22×C4C2×C22⋊D1111yescharacteristic
483C22×C4C2×C22⋊D1111yescharacteristic
484C22×C4C2×C22⋊D1111yescharacteristic
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C2×C22⋊D1111yescharacteristic
488C4⋊C4—44no—
489C4⋊C4—228no—
490C4⋊C4—222no—
491C4⋊C4—222no—
492C4⋊C4—222no—
493C4⋊C4—222no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—222no—
497C4⋊C4—222no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—222no—
501C4⋊C4—222no—
502C22⋊C4—28no—
503C22⋊C4—118no—
504C22⋊C4—222no—
505C22⋊C4—224no—
506C22⋊C4—222no—
507C22⋊C4—222no—
508C22⋊C4—222no—
509C22⋊C4—222no—
510C22⋊C4—222no—
511C22⋊C4—222no—
512C22⋊C4—222no—
513C22⋊C4—222no—
514C22⋊C4—222no—
515C42—44no—
516C42—228no—
517C42—222no—
518C42—222no—
519C42—444no—
520C42—444no—
521C42(C2×D11)⋊C411yescharacteristic
522C42(C2×D11)⋊C411yescharacteristic
523C42(C2×D11)⋊C411yescharacteristic
524C42(C2×D11)⋊C411yescharacteristic
525C42(C2×D11)⋊C411yescharacteristic
526C42(C2×D11)⋊C411yescharacteristic
527C42(C2×D11)⋊C411yescharacteristic
528C42(C2×D11)⋊C411yescharacteristic
529C42(C2×D11)⋊C411yescharacteristic
530C42(C2×D11)⋊C411yescharacteristic
531C42(C2×D11)⋊C411yescharacteristic
532C42(C2×D11)⋊C411yescharacteristic
533C42(C2×D11)⋊C411yescharacteristic
534C42(C2×D11)⋊C411yescharacteristic
535C42(C2×D11)⋊C411yescharacteristic
536C42(C2×D11)⋊C411yescharacteristic
537C11#2142111yescharacteristic, complemented, Sylow
538C23—41no—
539C23—41no—
540C23—222no—
541C23—224no—
542C23—442no—
543C23—442no—
544C23C22×C4×D1111yescharacteristic
545C23C22×D4411yescharacteristic
546C23#41×D1114yes—
547C23C22×C22⋊D1111yescharacteristic
548Q8—442no—
549Q8—442no—
550D4—442no—
551D4—444no—
552D4—444no—
553D4—442no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—224no—
576C2×C4—228no—
577C2×C4—222no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—444no—
581C2×C4—444no—
582C2×C4—444no—
583C2×C4—444no—
584C2×C4—442no—
585C2×C4—442no—
586C2×C4C2×(C2×D11)⋊C411yescharacteristic
587C2×C4C2×(C2×D11)⋊C411yescharacteristic
588C2×C4C2×(C2×D11)⋊C411yescharacteristic
589C2×C4C2×(C2×D11)⋊C411yescharacteristic
590C2×C4C2×(C2×D11)⋊C411yescharacteristic
591C2×C4C2×(C2×D11)⋊C411yescharacteristic
592C2×C4C2×(C2×D11)⋊C411yescharacteristic
593C2×C4C2×(C2×D11)⋊C411yescharacteristic
594C2×C4C2×(C2×D11)⋊C411yescharacteristic
595C2×C4C2×(C2×D11)⋊C411yescharacteristic
596C2×C4C2×(C2×D11)⋊C411yescharacteristic
597C2×C4C2×(C2×D11)⋊C411yescharacteristic
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—44no—
605C22—442no—
606C22—442no—
607C22—442no—
608C22—884no—
609C22#1062305312yes—
610C22#1062305512yes—
611C22C22×(C2×D11)⋊C411yescharacteristic
612C22#1062336312yes—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—21no—
623C4—84no—
624C4—448no—
625C4—442no—
626C4—442no—
627C4—442no—
628C4#1062261912yes—
629C4#1062261912yes—
630C2—22no—
631C2—22no—
632C2—22no—
633C2—882no—
634C2#1307110411yescharacteristic
635C2C2×#1062261911yescharacteristic
636C2C2×#1062261911yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#2283C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66983C22
cosocleC24×C11C24
hypercenter#2283D11
hypocenterC11#21421
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2283

Complements

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

NH ≅ G/Ntype
2. C4×#66979C2semidirect
3. #13069600C2semidirect
5. #13069072C2semidirect
6. C4×#66870C2semidirect
7. C11×#2283C2semidirect
22. C2×#66929C4semidirect
23. C2×#66928C4semidirect
24. C2×C4×D44C4semidirect
25. C2×#66925C4semidirect
26. C2×#66923C4semidirect
27. C2×C4×Dic22C4semidirect
221. #2283D11semidirect
537. C11#21421semidirect

Maximal subgroups

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

subgroupindex
C2×#106230102
C4×#669792
#130696002
#130694512
#130690722
C4×#668702
C11×#22832
#2142111