Finite Group Databasebeta

← #14719922

Subgroups — #14719922

Order 2816.

952 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623223C211yesmaximal, characteristic
2#13077656C211yesmaximal, characteristic, complemented
3#13077644C211yesmaximal, characteristic, complemented
4#13066986C211yesmaximal, characteristic, complemented
5#13066983C211yesmaximal, characteristic, complemented
6#13066978C212yesmaximal, complemented
7#13066972C211yesmaximal, characteristic, complemented
8#13066963C212yesmaximal, complemented
9#13066953C212yesmaximal, complemented
10#13066944C212yesmaximal, complemented
11C11×#1470C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13#10623223—22no—
14#10623223—22no—
15#10623223—22no—
16#10623223—22no—
17C2×#66951C411yescharacteristic
18C2×#66950C411yescharacteristic
19C2×#66949C411yescharacteristic
20C2×#66949C2211yescharacteristic
21C2×#66948C411yescharacteristic
22C2×#66947C411yescharacteristic
23C2×#66947C411yescharacteristic
24C2×#66947C411yescharacteristic
25C2×#66947C2211yescharacteristic
26C2×#66946C2211yescharacteristic
27C2×C4⋊C4×D11C2211yescharacteristic
28C2×#66942C411yescharacteristic
29C2×#66929C2211yescharacteristic
30C2×C4×D44C2211yescharacteristic
31C11×#432C2211yescharacteristic
32C11×#431C2211yescharacteristic
33#10622539C2211yescharacteristic
34#10622538C2211yescharacteristic
35#10622451—22no—
36#10622449—22no—
37#10622339C2212yes—
38#10622339C2212yes—
39#10622339C2212yes—
40D11×C22⋊C8C2212yes—
41#10622319—22no—
42#10622301—22no—
43C11×#324C2212yes—
44C11×#324C2212yes—
45#10622166C2212yes—
46#10622166C2212yes—
47#10622107C2212yes—
48#10622107C2212yes—
49#10622106C2212yes—
50#10622106C2212yes—
51C22×D44C2×C411yescharacteristic
52C22×D44C2×C411yescharacteristic
53C22×D44C2×C411yescharacteristic
54C22×C4×D11C2×C411yescharacteristic
55C22×C4×D11C2×C411yescharacteristic
56C22×C4×D11C2×C411yescharacteristic
57C22×C4×D11C2311yescharacteristic
58C22×C4×D11C2311yescharacteristic
59C22×Dic22C2×C411yescharacteristic
60C11×#125—21no—
61C11×#125—21no—
62C11×#125—21no—
63C11×#125—21no—
64C2×C11×C4⋊C4C2×C411yescharacteristic
65C2×C11×C4⋊C4C2×C411yescharacteristic
66C2×C11×C4⋊C4C2×C411yescharacteristic
67C2×C11×C4⋊C4C2×C411yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4C2×C411yescharacteristic
72C2×(C2×D11)⋊C4C2×C411yescharacteristic
73C2×(C2×D11)⋊C4C2×C411yescharacteristic
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2×C411yescharacteristic
77C2×(C2×D11)⋊C4C2×C411yescharacteristic
78C2×(C2×D11)⋊C4C2×C411yescharacteristic
79C2×(C2×D11)⋊C4C2×C411yescharacteristic
80C2×(C2×D11)⋊C4C2311yescharacteristic
81C2×C4⋊Dic11C2×C411yescharacteristic
82C2×C4⋊Dic11C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×Dic11⋊C4C2×C411yescharacteristic
87C2×Dic11⋊C4C2×C411yescharacteristic
88C2×Dic11⋊C4C2311yescharacteristic
89C2×C4×Dic11C2×C411yescharacteristic
90C2×#4313—22no—
91C2×#4313—22no—
92C2×#4313—22no—
93C2×C8×D11—22no—
94#66951—22no—
95#66951—22no—
96#66950—22no—
97#66950—22no—
98#66949—22no—
99#66949—22no—
100#66949—22no—
101#66949—22no—
102#66948—22no—
103#66948—22no—
104#66947—22no—
105#66947—22no—
106#66947—22no—
107#66947—22no—
108#66947—22no—
109#66947—22no—
110#66947—22no—
111#66947—22no—
112#66946—22no—
113#66946—22no—
114C4⋊C4×D11—22no—
115C4⋊C4×D11—22no—
116#66942—22no—
117#66942—22no—
118#66929—21no—
119#66929—21no—
120#66929—21no—
121#66929—21no—
122C4×D44D412yes—
123C4×D44D412yes—
124C4×D44D412yes—
125C4×D44D412yes—
126C11×C4⋊C8—21no—
127C11×C4⋊C8—21no—
128C11×C22⋊C8C2312yes—
129C11×C22⋊C8C2312yes—
130C11×#97—21no—
131C4×C8×C11—21no—
132C22⋊(C11⋊C8)C2312yes—
133C22⋊(C11⋊C8)C2312yes—
134(C2×D11)⋊C8—22no—
135(C2×D11)⋊C8—22no—
136(C2×D11)⋊C8—22no—
137(C2×D11)⋊C8—22no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)—21no—
140#66867—21no—
141C4×C11⋊C8—21no—
142#17406—111nomaximal, Sylow
143C23×D11C22×C411yescharacteristic
144C23×D11C22×C411yescharacteristic
145C23×D11C22×C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11C22×C411yescharacteristic
154C22×Dic11C22×C411yescharacteristic
155C22×Dic11C22×C411yescharacteristic
156C22×Dic11C22×C411yescharacteristic
157C22×Dic11C22×C411yescharacteristic
158C2×D44—22no—
159C2×D44—22no—
160C2×D44—42no—
161C2×D44—42no—
162C2×D44—81no—
163C2×D44C22⋊C412yes—
164C2×D44C22⋊C412yes—
165C2×C4×D11—22no—
166C2×C4×D11—22no—
167C2×C4×D11—22no—
168C2×C4×D11—42no—
169C2×C4×D11—81no—
170C2×C4×D11—81no—
171C2×C4×D11—81no—
172C2×C4×D11—81no—
173C2×C4×D11C2×D412yes—
174C2×C4×D11C2×D412yes—
175C2×C4×D11C2×D412yes—
176C2×C4×D11C2×D412yes—
177C2×Dic22—22no—
178C2×Dic22—81no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C42×C11C2×D411yescharacteristic
194C42×C11C2×D411yescharacteristic
195C42×C11C2×D411yescharacteristic
196C42×C11C2×D411yescharacteristic
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—
202(C2×D11)⋊C4—21no—
203(C2×D11)⋊C4—21no—
204(C2×D11)⋊C4—21no—
205(C2×D11)⋊C4—21no—
206(C2×D11)⋊C4—21no—
207(C2×D11)⋊C4—21no—
208(C2×D11)⋊C4C22⋊C412yes—
209(C2×D11)⋊C4C22⋊C412yes—
210(C2×D11)⋊C4C22⋊C412yes—
211(C2×D11)⋊C4C22⋊C412yes—
212C4⋊Dic11—22no—
213C4⋊Dic11C22⋊C412yes—
214C4⋊Dic11C22⋊C412yes—
215Dic11⋊C4—22no—
216Dic11⋊C4—22no—
217Dic11⋊C4—22no—
218Dic11⋊C4—21no—
219Dic11⋊C4—21no—
220Dic11⋊C4—21no—
221Dic11⋊C4—21no—
222Dic11⋊C4—21no—
223Dic11⋊C4—21no—
224C4×Dic11—22no—
225C2×C11⋊C8—22no—
226C2×C11⋊C8—22no—
227#4313—82no—
228#4313—82no—
229#4313—82no—
230C8×D11—82no—
231C2×#539—111no—
232#2975—111no—
233#2973—111no—
234#1473—111no—
235#1473—111no—
236#1472—112no—
237#1470—111no—
238#1470D1111yescharacteristic, complemented
239#1468—112no—
240#1465—112no—
241#1463—112no—
242C23×C11C23×C411yescharacteristic
243C22×D11—22no—
244C22×D11—22no—
245C22×D11—21no—
246C22×D11—22no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11C2×C22⋊C412yes—
254C22×D11C2×C22⋊C412yes—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11C2×C22⋊C411yescharacteristic
267C2×C4×C11C2×C22⋊C411yescharacteristic
268C2×C4×C11C2×C22⋊C411yescharacteristic
269C2×C4×C11C2×C22⋊C411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—22no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11C2×C22⋊C412yes—
281C2×Dic11C2×C22⋊C412yes—
282D44—42no—
283D44—42no—
284D44—44no—
285D44—82no—
286C4×D11—42no—
287C4×D11—42no—
288C4×D11—42no—
289C4×D11—42no—
290C4×D11—44no—
291C4×D11—82no—
292C4×D11—82no—
293Dic22—82no—
294C8×C11—42no—
295C8×C11—42no—
296C11⋊C8—42no—
297C11⋊C8—42no—
298#539—222no—
299#539—222no—
300#539—222no—
301#539—222no—
302C2×#126—111no—
303C2×#126—111no—
304C2×#125—111no—
305C2×#125C2×D1111yescharacteristic
306C2×#123—111no—
307C2×#123—111no—
308C2×#123—111no—
309C2×#123—111no—
310C2×C22⋊Q8—111no—
311C2×C22⋊Q8—111no—
312C2×C22⋊Q8—111no—
313C2×#121—111no—
314C2×C4×D4—111no—
315C2×C4×D4—111no—
316C22×C4⋊C4—111no—
317#436—222no—
318#436—222no—
319#435—222no—
320#435—222no—
321#432—111no—
322#432C2×D1111yescharacteristic
323#431—111no—
324#431C2×D1111yescharacteristic
325#407—112no—
326#407—112no—
327#407—112no—
328C2×C22⋊C8—112no—
329#324—112no—
330#324—112no—
331#324—112no—
332#324—112no—
333#324C2×D1112yes—
334#324C2×D1112yes—
335#323—112no—
336#323—112no—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11C22×C22⋊C411yescharacteristic
340C22×C11#56812yes—
341C2×D11—22no—
342C2×D11—22no—
343C2×D11—22no—
344C2×D11—22no—
345C2×D11—22no—
346C2×D11—22no—
347C2×D11—44no—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—82no—
352C2×D11—82no—
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—21no—
358C4×C11—21no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—41no—
363Dic11—22no—
364Dic11—22no—
365Dic11—41no—
366Dic11—41no—
367Dic11—41no—
368C22×Q8—111no—
369C22×D4—111no—
370C22×D4—111no—
371C22×D4—111no—
372C23×C4—111no—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—111no—
376C23×C4—111no—
377C2×M16—222no—
378C2×M16—222no—
379C2×M16—222no—
380C22×C8—222no—
381#126—222no—
382#126—222no—
383#126—221no—
384#126—221no—
385#126—221no—
386#126—221no—
387#125—21no—
388#125—21no—
389#125—21no—
390#125—21no—
391#125—222no—
392#125—222no—
393#123—222no—
394#123—222no—
395#123—222no—
396#123—222no—
397#123—222no—
398#123—222no—
399#123—222no—
400#123—222no—
401C22⋊Q8—222no—
402C22⋊Q8—222no—
403C22⋊Q8—222no—
404C22⋊Q8—222no—
405C22⋊Q8—222no—
406C22⋊Q8—222no—
407#121—222no—
408#121—222no—
409C4×D4—112no—
410C4×D4—112no—
411C4×D4—112no—
412C4×D4—112no—
413C4×D4—222no—
414C4×D4—222no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—222no—
424C2×C4⋊C4—222no—
425C2×C4⋊C4C4×D1111yescharacteristic
426C2×C4⋊C4C4×D1111yescharacteristic
427C2×C4⋊C4C4×D1111yescharacteristic
428C2×C4⋊C4C4×D1111yescharacteristic
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C22⋊C4—111no—
432C2×C22⋊C4—111no—
433C2×C22⋊C4—111no—
434C2×C22⋊C4—111no—
435C2×C22⋊C4—111no—
436C2×C22⋊C4—111no—
437C2×C22⋊C4—111no—
438C2×C22⋊C4—111no—
439C2×C22⋊C4—111no—
440C2×C22⋊C4—111no—
441C2×C42—111no—
442C2×C42C22×D1111yescharacteristic
443C4⋊C8—21no—
444C4⋊C8—21no—
445C4⋊C8—221no—
446C4⋊C8—221no—
447C22⋊C8—112no—
448C22⋊C8—112no—
449C22⋊C8—222no—
450C22⋊C8—222no—
451C22⋊C8—222no—
452C22⋊C8—222no—
453C22⋊C8C22×D1112yes—
454C22⋊C8C22×D1112yes—
455#97—21no—
456#97—221no—
457C4×C8—21no—
458C4×C8—221no—
459C2×C11—22no—
460C2×C11#287911yescharacteristic
461C2×C11#288311yescharacteristic
462C2×C11#288911yescharacteristic
463D11—42no—
464D11—42no—
465D11—81no—
466C24—111no—
467C24—111no—
468C24—111no—
469C2×Q8—222no—
470C2×Q8—881no—
471C2×D4—112no—
472C2×D4—112no—
473C2×D4—222no—
474C2×D4—222no—
475C2×D4—442no—
476C2×D4—442no—
477C2×D4—881no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—112no—
481C22×C4—112no—
482C22×C4—112no—
483C22×C4—112no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—442no—
491C22×C4—881no—
492C22×C4—881no—
493C22×C4—881no—
494C22×C4—881no—
495C22×C4C2×C4×D1111yescharacteristic
496C22×C4C2×C4×D1111yescharacteristic
497C22×C4C2×C4×D1111yescharacteristic
498C22×C4C2×C4×D1111yescharacteristic
499C22×C4C2×C4×D1111yescharacteristic
500C22×C4C2×C4×D1111yescharacteristic
501C22×C4C23×D1111yescharacteristic
502M16—882no—
503M16—882no—
504M16—882no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—222no—
508C2×C8—222no—
509C2×C8—882no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—112no—
523C4⋊C4—112no—
524C4⋊C4—222no—
525C4⋊C4—222no—
526C4⋊C4—222no—
527C4⋊C4—222no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C22⋊C4—112no—
535C22⋊C4—112no—
536C22⋊C4—112no—
537C22⋊C4—112no—
538C22⋊C4—222no—
539C22⋊C4—222no—
540C22⋊C4—222no—
541C22⋊C4—222no—
542C22⋊C4—222no—
543C22⋊C4—221no—
544C22⋊C4—221no—
545C22⋊C4—221no—
546C22⋊C4—221no—
547C22⋊C4—221no—
548C22⋊C4—221no—
549C42—222no—
550C42D4×D1111yescharacteristic
551C42D4×D1111yescharacteristic
552C42D4×D1111yescharacteristic
553C42D4×D1111yescharacteristic
554C11#1740611yescharacteristic, complemented, Sylow
555C23—112no—
556C23—112no—
557C23—222no—
558C23—222no—
559C23—221no—
560C23—222no—
561C23—441no—
562C23—441no—
563C23—441no—
564C23—441no—
565C23—441no—
566C23—441no—
567C23C22×C4×D1111yescharacteristic
568Q8—882no—
569D4—442no—
570D4—442no—
571D4—444no—
572D4—882no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—112no—
585C2×C4—112no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—222no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—444no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—882no—
600C2×C4—882no—
601C2×C4C22⋊C4×D1111yescharacteristic
602C2×C4C22⋊C4×D1111yescharacteristic
603C2×C4C22⋊C4×D1111yescharacteristic
604C2×C4C22⋊C4×D1111yescharacteristic
605C2×C4C2×D4×D1111yescharacteristic
606C2×C4C2×D4×D1111yescharacteristic
607C8—42no—
608C8—42no—
609C8—442no—
610C8—442no—
611C22—21no—
612C22—21no—
613C22—222no—
614C22—222no—
615C22—222no—
616C22—222no—
617C22—222no—
618C22—222no—
619C22—444no—
620C22—441no—
621C22—441no—
622C22—441no—
623C22—882no—
624C22—882no—
625C22C2×C22⋊C4×D1111yescharacteristic
626C22#1062328112yes—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—222no—
638C4—222no—
639C4—441no—
640C4—441no—
641C4—441no—
642C2—22no—
643C2—442no—
644C2—442no—
645C2—881no—
646C2#1307705811yescharacteristic
647C2#1307707511yescharacteristic
648C2#1307709611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1470C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66948C4
cosocleC22×C4×C11C24
hypercenter#1470D11
hypocenterC11#17406
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1470

Complements

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

NH ≅ G/Ntype
2. #13077656C2semidirect
3. #13077644C2semidirect
4. #13066986C2semidirect
5. #13066983C2semidirect
6. #13066978C2semidirect
7. #13066972C2semidirect
8. #13066963C2semidirect
9. #13066953C2semidirect
10. #13066944C2semidirect
11. C11×#1470C2semidirect
238. #1470D11semidirect
554. C11#17406semidirect

Maximal subgroups

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

subgroupindex
C2×#106232232
#130776562
#130776442
#130669862
#130669832
#130669782
#130669722
#130669632
#130669532
#130669442
C11×#14702
#1740611