Finite Group Databasebeta

← #14772790

Subgroups — #14772790

Order 2816.

1052 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622446C211yesmaximal, characteristic, complemented
2C42×C22⋊D11C211yesmaximal, characteristic
3#13069221C212yesmaximal, complemented
4#13069170C212yesmaximal, complemented
5#13068908C212yesmaximal
6#13068732C211yesmaximal, characteristic, complemented
7#13068596C211yesmaximal, characteristic, complemented
8#13068593C211yesmaximal, characteristic, complemented
9C4⋊C8×Dic11C211yesmaximal, characteristic, complemented
10C8×C22⋊Dic11C212yesmaximal, complemented
11C22×C11×C4⋊C8C211yesmaximal, characteristic, complemented
12C23×C8×C11C2212yes—
13C22×C42×C11C2211yescharacteristic
14C2×C4×C22⋊D11C411yescharacteristic
15C2×C4×C22⋊D11C411yescharacteristic
16C2×C4×C22⋊D11C2211yescharacteristic
17C2×C42×D11C2211yescharacteristic
18C2×C11×C4⋊C8—24no—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C4×C22⋊Dic11C411yescharacteristic
23C4×C22⋊Dic11C411yescharacteristic
24C4×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2212yes—
26C2×(C2×D11)⋊C8C2212yes—
27C2×(C2×D11)⋊C8C2212yes—
28C2×C8×Dic11C2212yes—
29C2×C8×Dic11C2212yes—
30C4×(C2×D11)⋊C4C411yescharacteristic
31C4×(C2×D11)⋊C4C411yescharacteristic
32C4×(C2×D11)⋊C4C2211yescharacteristic
33C4×Dic11⋊C4C411yescharacteristic
34C4×Dic11⋊C4C411yescharacteristic
35C4×Dic11⋊C4C2211yescharacteristic
36C42×Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622446—24no—
40#10622188C2212yes—
41#10622188C2212yes—
42#10622188C2212yes—
43#10622188C2212yes—
44#10622162C2212yes—
45C23×C4×C11C2×C411yescharacteristic
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11C2×C411yescharacteristic
49C22×C4×D11C2×C411yescharacteristic
50C22×C4×D11C2×C411yescharacteristic
51C22×C4×D11C2311yescharacteristic
52C22×C8×C11—24no—
53C22×C8×C11—24no—
54C22×C8×C11—42no—
55C22×C8×C11C2312yes—
56C22×C8×C11C2312yes—
57C2×C42×C11—22no—
58C2×C42×C11—22no—
59C2×C42×C11C2×C411yescharacteristic
60C2×C42×C11C2×C411yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11C2×C411yescharacteristic
64C2×C22⋊Dic11C2×C411yescharacteristic
65C2×C22⋊Dic11C2×C411yescharacteristic
66C4×C22⋊D11—22no—
67C4×C22⋊D11—22no—
68C4×C22⋊D11—24no—
69C4×C22⋊D11C818yescomplemented
70C2×(C2×D11)⋊C4C2×C411yescharacteristic
71C2×(C2×D11)⋊C4C2×C411yescharacteristic
72C2×(C2×D11)⋊C4C2×C411yescharacteristic
73C2×Dic11⋊C4C2×C411yescharacteristic
74C2×Dic11⋊C4C2×C411yescharacteristic
75C2×Dic11⋊C4C2×C411yescharacteristic
76C2×C4×Dic11C2×C411yescharacteristic
77C2×C4×Dic11C2×C411yescharacteristic
78C2×C4×Dic11C2×C411yescharacteristic
79C2×C4×Dic11C2×C411yescharacteristic
80C2×C4×Dic11C2×C411yescharacteristic
81C2×C4×Dic11C2×C411yescharacteristic
82C2×C4×Dic11C2311yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C22×C11⋊C8C2312yes—
86C22×C11⋊C8C2312yes—
87C42×D11—22no—
88C42×D11—22no—
89C11×C4⋊C8—24no—
90C11×C4⋊C8—22no—
91C11×C4⋊C8D414yescomplemented
92C11⋊#95C2×C411yescharacteristic
93C11⋊#95C2×C411yescharacteristic
94C11⋊#95C2×C411yescharacteristic
95C11⋊#95C2×C411yescharacteristic
96C11⋊#95C2×C411yescharacteristic
97C11⋊#95C2×C411yescharacteristic
98C22⋊(C11⋊C8)—24no—
99(C2×D11)⋊C8—24no—
100(C2×D11)⋊C8—42no—
101C8×Dic11—24no—
102C8×Dic11—42no—
103C4⋊(C11⋊C8)—22no—
104C4⋊(C11⋊C8)—22no—
105#22748—111nomaximal, Sylow
106C24×C11C22×C411yescharacteristic
107C23×D11C22×C411yescharacteristic
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—41no—
117C22×C4×C11C2×C814yes—
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11#4112yes—
124C22×C4×C11#4112yes—
125C22×C4×C11C2411yescharacteristic
126C2×C22⋊D11—22no—
127C2×C22⋊D11—22no—
128C2×C22⋊D11C2×C814yes—
129C22×Dic11C22×C411yescharacteristic
130C22×Dic11C22×C411yescharacteristic
131C22×Dic11C22×C411yescharacteristic
132C22×Dic11C22×C411yescharacteristic
133C22×Dic11C22×C411yescharacteristic
134C22×Dic11C22×C411yescharacteristic
135C22×Dic11C22×C411yescharacteristic
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11—21no—
145C2×C4×D11—21no—
146C2×C4×D11—41no—
147C2×C4×D11C2×C814yescomplemented
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—48no—
154C2×C8×C11C2×D414yes—
155C42×C11—22no—
156C42×C11—22no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11C2×D412yes—
160C42×C11#4112yes—
161C22⋊Dic11—22no—
162C22⋊Dic11C2×C814yes—
163C22⋊Dic11M1614yes—
164(C2×D11)⋊C4—22no—
165(C2×D11)⋊C4—22no—
166(C2×D11)⋊C4C2×C814yescomplemented
167Dic11⋊C4—22no—
168Dic11⋊C4—22no—
169Dic11⋊C4C2×C814yescomplemented
170C4×Dic11—22no—
171C4×Dic11—22no—
172C4×Dic11—22no—
173C4×Dic11—22no—
174C4×Dic11—21no—
175C4×Dic11—21no—
176C4×Dic11—21no—
177C4×Dic11—21no—
178C4×Dic11—21no—
179C4×Dic11—21no—
180C4×Dic11—41no—
181C4×Dic11C2×C814yescomplemented
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×#431—111no—
189C22×C4⋊C8D1111yescharacteristic, complemented
190C42×D4—111no—
191#1923—112no—
192#1916—112no—
193#1869—112no—
194#1831—111no—
195#1797—111no—
196#1797—111no—
197C4×C4⋊C8—111no—
198C8×C22⋊C4—112no—
199C23×C11—21no—
200C23×C11—21no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11#11712yes—
204C23×C11C22×C812yes—
205C23×C11C2×M1612yes—
206C23×C11C23×C411yescharacteristic
207C22×D11—21no—
208C22×D11—21no—
209C22×D11—21no—
210C22×D11—21no—
211C22×D11—21no—
212C22×D11—21no—
213C22×D11C22×C812yes—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—28no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—44no—
229C2×C4×C11#11712yes—
230C2×C4×C11C4×D412yes—
231C2×C4×C11C4×D412yes—
232C2×C4×C11C22×C812yes—
233C2×C4×C11C22×C812yes—
234C2×C4×C11#13112yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11H(5,𝔽2)11yescharacteristic
240C2×C4×C112−1+411yescharacteristic
241C22⋊D11—28no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11C22×C812yes—
259C2×Dic11C22×C812yes—
260C2×Dic11C22×C812yes—
261C2×Dic11C2×M1612yes—
262C2×Dic11C2×M1612yes—
263C4×D11—28no—
264C4×D11—44no—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—41no—
268C4×D11—41no—
269C8×C11—24no—
270C8×C11—42no—
271C11⋊C8—42no—
272C11⋊C8—42no—
273C23×C8C2×D1112yes—
274C2×C4×D4—111no—
275C2×C4×D4—111no—
276C2×C4×D4—111no—
277C22×C42—111no—
278C22×C42C2×D1111yescharacteristic
279#431—224no—
280C2×C4⋊C8—24no—
281C2×C4⋊C8—111no—
282C2×C4⋊C8—111no—
283C2×C4⋊C8C2×D1111yescharacteristic
284C2×C4⋊C8C2×D1112yes—
285C2×C4⋊C8C2×D1111yescharacteristic
286C2×C22⋊C8—112no—
287C2×C22⋊C8—112no—
288C2×C22⋊C8—112no—
289C2×C4×C8—112no—
290C2×C4×C8—112no—
291C4×C4⋊C4—111no—
292C4×C4⋊C4—111no—
293C4×C4⋊C4—111no—
294C4×C22⋊C4—111no—
295C4×C22⋊C4—111no—
296C4×C22⋊C4—111no—
297C4×C22⋊C4—111no—
298C4×C22⋊C4—111no—
299C4×C22⋊C4—111no—
300C43—111no—
301#336—112no—
302#336—112no—
303#336—112no—
304#336—112no—
305#336—112no—
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—22no—
309C22×C11—22no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11#43114yescomplemented
313C22×C11C2×#11711yescharacteristic
314C22×C11C2×C4×D411yescharacteristic
315C22×C11#52011yescharacteristic
316C22×C11C23×C811yescharacteristic
317C22×C11C22×M1611yescharacteristic
318C22×C11C2×#13111yescharacteristic
319C22×C11#56811yescharacteristic
320C2×D11—22no—
321C2×D11—22no—
322C2×D11—22no—
323C2×D11—41no—
324C2×D11—41no—
325C2×D11—41no—
326C2×D11—41no—
327C4×C11—22no—
328C4×C11—22no—
329C4×C11—22no—
330C4×C11—41no—
331C4×C11C8×D414yes—
332C4×C11#54611yescharacteristic
333C4×C11#54811yescharacteristic
334C4×C11#55211yescharacteristic
335C4×C11#55311yescharacteristic
336Dic11—22no—
337Dic11—22no—
338Dic11—22no—
339Dic11—22no—
340Dic11—22no—
341Dic11—41no—
342Dic11—41no—
343C22×D4—111no—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—111no—
347C23×C4C4×D1111yescharacteristic
348C23×C4C4×D1111yescharacteristic
349C23×C4C22×D1111yescharacteristic
350C22×C8—24no—
351C22×C8—24no—
352C22×C8—42no—
353C22×C8—112no—
354C22×C8—112no—
355C22×C8C22×D1112yes—
356C22×C8C22×D1112yes—
357C4×D4—118no—
358C4×D4—224no—
359C4×D4—222no—
360C4×D4—222no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C22⋊C4—111no—
365C2×C22⋊C4—111no—
366C2×C22⋊C4—111no—
367C2×C22⋊C4—111no—
368C2×C22⋊C4—111no—
369C2×C22⋊C4—111no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—111no—
373C2×C42—111no—
374C2×C42—111no—
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—222no—
382C2×C42—222no—
383C2×C42C4×D1111yescharacteristic
384C2×C42C4×D1111yescharacteristic
385C2×C42C22×D1111yescharacteristic
386C2×C42C22×D1111yescharacteristic
387C4⋊C8—24no—
388C4⋊C8—22no—
389C4⋊C8—222no—
390C4⋊C8—222no—
391C4⋊C8C22⋊D1114yescomplemented
392C22⋊C8—224no—
393C22⋊C8—224no—
394C22⋊C8—442no—
395C4×C8—224no—
396C4×C8—442no—
397#95—111no—
398#95—111no—
399#95—111no—
400#95—111no—
401#95—111no—
402#95—111no—
403C2×C11—24no—
404C2×C11#235211yescharacteristic
405C2×C11C2×#43111yescharacteristic
406C2×C11#292511yescharacteristic
407C2×C11C2×C8×D411yescharacteristic
408C2×C11D4×M1611yescharacteristic
409C2×C11#298811yescharacteristic
410C2×C11#299011yescharacteristic
411D11—42no—
412C24—111no—
413C24C2×C4×D1111yescharacteristic
414C2×D4—114no—
415C2×D4—222no—
416C2×D4—222no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—41no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—114no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—441no—
445C22×C4C8×D1114yes—
446C22×C4C2×C4×D1111yescharacteristic
447C22×C4C2×C4×D1111yescharacteristic
448C22×C4C2×C4×D1111yescharacteristic
449C22×C4C2×C4×D1111yescharacteristic
450C22×C4C2×C4×D1111yescharacteristic
451C22×C4#434112yes—
452C22×C4#434312yes—
453C22×C4C23×D1111yescharacteristic
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—48no—
460C2×C8—222no—
461C2×C8—222no—
462C2×C8—222no—
463C2×C8—222no—
464C2×C8—222no—
465C2×C8—222no—
466C2×C8C2×C22⋊D1114yes—
467C4⋊C4—114no—
468C4⋊C4—222no—
469C4⋊C4—222no—
470C22⋊C4—114no—
471C22⋊C4—114no—
472C22⋊C4—114no—
473C22⋊C4—222no—
474C22⋊C4—222no—
475C22⋊C4—222no—
476C42—22no—
477C42—22no—
478C42—21no—
479C42—21no—
480C42—114no—
481C42—222no—
482C42—222no—
483C42—222no—
484C42—222no—
485C42—221no—
486C42—221no—
487C42—221no—
488C42—221no—
489C42—221no—
490C42—221no—
491C42—441no—
492C42#433912yes—
493C42C2×C22⋊D1112yes—
494C11#2274811yescharacteristic, complemented, Sylow
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—112no—
500C23—221no—
501C23—221no—
502C23—221no—
503C23—221no—
504C23—221no—
505C23—221no—
506C23#6694512yes—
507C23C2×C8×D1112yes—
508C23M16×D1112yes—
509C23C22×C4×D1111yescharacteristic
510D4—228no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—28no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—44no—
526C2×C4—112no—
527C2×C4—112no—
528C2×C4—112no—
529C2×C4—112no—
530C2×C4—112no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—228no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—444no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4#6694512yes—
554C2×C4C2×C8×D1112yes—
555C2×C4C2×C8×D1112yes—
556C2×C4#6695412yes—
557C2×C4C4×C22⋊D1112yes—
558C2×C4C4×C22⋊D1112yes—
559C2×C4C2×#433911yescharacteristic
560C2×C4C2×#434111yescharacteristic
561C2×C4#6703711yescharacteristic
562C2×C4C2×#434311yescharacteristic
563C2×C4#6704011yescharacteristic
564C2×C4C22×C22⋊D1111yescharacteristic
565C8—24no—
566C8—42no—
567C8—442no—
568C8—442no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—22no—
575C22—222no—
576C22—222no—
577C22—222no—
578C22—441no—
579C22—441no—
580C22—441no—
581C22—441no—
582C22#1062244614yescomplemented
583C22C2×#6694511yescharacteristic
584C22#1062303511yescharacteristic
585C22C22×C8×D1111yescharacteristic
586C22C2×#6695411yescharacteristic
587C22C2×M16×D1111yescharacteristic
588C22#1062327611yescharacteristic
589C22C2×C4×C22⋊D1111yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—41no—
594C4—222no—
595C4—222no—
596C4—222no—
597C4—222no—
598C4—222no—
599C4—441no—
600C4—441no—
601C4C8×C22⋊D1114yes—
602C4#1062304411yescharacteristic
603C4#1062304511yescharacteristic
604C4#1062333711yescharacteristic
605C4#1062334811yescharacteristic
606C2—24no—
607C2—442no—
608C2#1307154111yescharacteristic
609C2C2×#1062244611yescharacteristic
610C2#1307728111yescharacteristic
611C2C2×C8×C22⋊D1111yescharacteristic
612C2M16×C22⋊D1111yescharacteristic
613C2#1307772511yescharacteristic
614C2#1307773811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C23×C8
FittingC22×C11×C4⋊C8C2
socleC23×C11C23×C4
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenterC22×C4⋊C8D11
hypocenterC11#22748
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#10622446C2semidirect
3. #13069221C2semidirect
4. #13069170C2semidirect
6. #13068732C2semidirect
7. #13068596C2semidirect
8. #13068593C2semidirect
9. C4⋊C8×Dic11C2semidirect
10. C8×C22⋊Dic11C2semidirect
11. C22×C11×C4⋊C8C2semidirect
69. C4×C22⋊D11C8semidirect
91. C11×C4⋊C8D4semidirect
147. C2×C4×D11C2×C8semidirect
166. (C2×D11)⋊C4C2×C8semidirect
169. Dic11⋊C4C2×C8semidirect
181. C4×Dic11C2×C8semidirect
189. C22×C4⋊C8D11semidirect
312. C22×C11#431semidirect
391. C4⋊C8C22⋊D11semidirect
494. C11#22748semidirect
582. C22#10622446semidirect

Maximal subgroups

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

subgroupindex
C2×#106224462
C42×C22⋊D112
#130692212
#130691702
#130689082
#130687322
#130685962
#130685932
C4⋊C8×Dic112
C8×C22⋊Dic112
C22×C11×C4⋊C82
#2274811