Finite Group Databasebeta

← #14769827

Subgroups — #14769827

Order 2816.

1500 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4343C211yesmaximal, characteristic
2C2×C8×D44C211yesmaximal, characteristic, complemented
3C2×#10622447C211yesmaximal, characteristic, complemented
4#13069553C211yesmaximal, characteristic, complemented
5#13068907C212yesmaximal, complemented
6#13068907C212yesmaximal, complemented
7#13068683C212yesmaximal, complemented
8#13068593C211yesmaximal, characteristic, complemented
9C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
10D11×#336C212yesmaximal, complemented
11C11×#1984C211yesmaximal, characteristic, complemented
12C22×#4343C411yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×Q8×Dic11C411yescharacteristic
15C22×C8×D11C2212yes—
16C22×C8×D11C2212yes—
17C4×#4343—24no—
18C4×#4343—24no—
19C2×#66946C411yescharacteristic
20C2×#66946C412yes—
21C2×#66945C412yes—
22C2×#66945C411yescharacteristic
23C2×C4×D44C2212yes—
24C2×C4×D44C2211yescharacteristic
25C2×C42×D11C2212yes—
26C2×C42×D11C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C4×C8×C11C2211yescharacteristic
29C2×(C2×D11)⋊C8C2212yes—
30C2×(C2×D11)⋊C8C2212yes—
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2212yes—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622447—24no—
37C8×D44—24no—
38C11×#336C2212yes—
39C11×#336C2212yes—
40#10622188C2211yescharacteristic
41#10622188C2212yes—
42#10622188C2211yescharacteristic
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11C2×C411yescharacteristic
46C2×#4343—24no—
47C2×#4343—24no—
48C2×#4343C818yescomplemented
49C22×D44C2×C412yes—
50C22×D44C2×C411yescharacteristic
51C22×C4×D11C2×C412yes—
52C22×C4×D11C2×C411yescharacteristic
53C22×C4×D11C2×C412yes—
54C22×C4×D11C2×C411yescharacteristic
55C22×C4×D11C2311yescharacteristic
56C22×C4×D11C2312yes—
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2312yes—
59C22×C8×C11C2311yescharacteristic
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C2×C11×C4⋊C4C2×C411yescharacteristic
63C2×C11×C4⋊C4C2×C412yes—
64C2×C42×C11C2312yes—
65C2×C42×C11C2311yescharacteristic
66Q8×Dic11—24no—
67C2×(C2×D11)⋊C4C2×C412yes—
68C2×(C2×D11)⋊C4C2×C412yes—
69C2×(C2×D11)⋊C4C2×C412yes—
70C2×C4⋊Dic11C2×C412yes—
71C2×C4⋊Dic11C2×C411yescharacteristic
72C2×C4×Dic11C2×C412yes—
73C2×C4×Dic11C2×C411yescharacteristic
74C2×C4×Dic11C2×C412yes—
75C2×C4×Dic11C2×C411yescharacteristic
76C2×C4×Dic11C2311yescharacteristic
77C22×C11⋊C8C2311yescharacteristic
78C22×C11⋊C8C2312yes—
79C22×C11⋊C8C2311yescharacteristic
80C2×C8×D11—24no—
81C2×C8×D11—24no—
82C2×C8×D11—24no—
83C2×C8×D11—24no—
84C2×C8×D11—42no—
85C2×C8×D11—42no—
86#66946—24no—
87#66946—28no—
88#66945—28no—
89#66945—24no—
90C4×D44—24no—
91C4×D44—24no—
92C4×D44D414yes—
93C4×D44D414yes—
94C42×D11—24no—
95C42×D11—24no—
96C42×D11—22no—
97C42×D11—22no—
98C11×C4⋊C8—22no—
99C4×C8×C11—22no—
100(C2×D11)⋊C8—24no—
101(C2×D11)⋊C8—24no—
102(C2×D11)⋊C8—22no—
103(C2×D11)⋊C8—22no—
104(C2×D11)⋊C8—42no—
105C4⋊(C11⋊C8)—22no—
106C4×C11⋊C8—22no—
107#22469—111nomaximal, Sylow
108C23×D11C22×C411yescharacteristic
109C23×D11C22×C412yes—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11C2×C814yescomplemented
113C22×C4×C11C22×C412yes—
114C22×C4×C11C22×C411yescharacteristic
115C22×C4×C11C22×C412yes—
116C22×C4×C11C22×C411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C22×Dic11C22×C411yescharacteristic
119C22×Dic11C22×C412yes—
120C22×Dic11C22×C411yescharacteristic
121C22×Dic11C22×C411yescharacteristic
122#4343—232no—
123C2×D44—24no—
124C2×D44—24no—
125C2×D44C22⋊C414yes—
126C2×D44C2×C814yes—
127C2×D44C2×C818yescomplemented
128C2×D44M1614yes—
129C2×C4×D11—22no—
130C2×C4×D11—24no—
131C2×C4×D11—24no—
132C2×C4×D11—24no—
133C2×C4×D11—24no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11—22no—
144C2×C4×D11—21no—
145C2×C4×D11—22no—
146C2×C4×D11—21no—
147C2×C4×D11—41no—
148C2×C4×D11—42no—
149C2×C4×D11C2×C818yescomplemented
150C2×C4×D11C2×C814yescomplemented
151C2×C4×D11C2×D414yes—
152C2×C4×D11C2×D414yes—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—22no—
156C2×C8×C11—21no—
157C2×C8×C11—22no—
158C2×C8×C11—21no—
159C2×C8×C11—22no—
160C2×C8×C11—21no—
161C2×C8×C11#4112yescomplemented
162C11×C4⋊C4—24no—
163C11×C4⋊C4—22no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11C2×D412yes—
167C42×C11C2×D412yes—
168(C2×D11)⋊C4—24no—
169(C2×D11)⋊C4—24no—
170(C2×D11)⋊C4C22⋊C418yes—
171C4⋊Dic11—24no—
172C4⋊Dic11C22⋊C414yes—
173C4×Dic11—24no—
174C4×Dic11—24no—
175C4×Dic11—22no—
176C4×Dic11—22no—
177C4×Dic11—21no—
178C4×Dic11—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8#4112yescomplemented
188C8×D11—48no—
189C8×D11—48no—
190C2×C4×#41—111no—
191C2×C8×D4—111no—
192C2×C8×D4—111no—
193#1984—111no—
194#1984D1111yescharacteristic, complemented
195#1869—112no—
196#1869—112no—
197#1817—112no—
198#1797—111no—
199C4×C22⋊C8—111no—
200C2×#336—112no—
201C23×C11C23×C411yescharacteristic
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—21no—
207C22×D11—21no—
208C22×D11—21no—
209C22×D11—21no—
210C22×D11—21no—
211C22×D11—21no—
212C22×D11C2×C22⋊C414yes—
213C22×D11C22×C812yes—
214C22×D11C22×C814yes—
215C22×D11C2×M1614yes—
216Q8×C11—28no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11C2×C22⋊C412yes—
225C2×C4×C11C2×C22⋊C412yes—
226C2×C4×C11C22×C814yes—
227C2×C4×C11C22×C812yes—
228C2×C4×C11C2×M1612yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11H(5,𝔽2)11yescharacteristic
234C2×C4×C112−1+411yescharacteristic
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11C2×C22⋊C414yes—
245C2×Dic11C22×C812yes—
246C2×Dic11#13112yes—
247D44—216no—
248D44C22⋊C8116yescomplemented
249C4×D11—216no—
250C4×D11—24no—
251C4×D11—24no—
252C4×D11—24no—
253C4×D11—24no—
254C4×D11—28no—
255C4×D11—44no—
256C4×D11—48no—
257C4×D11—41no—
258C4×D11—41no—
259C4×D11—41no—
260C4×D11—41no—
261C8×C11—22no—
262C8×C11—42no—
263C8×C11—41no—
264C11⋊C8—22no—
265C11⋊C8—42no—
266C11⋊C8—41no—
267C22×#41—111no—
268C23×C8—112no—
269C23×C8—112no—
270C4×#41—224no—
271C4×#41—224no—
272C2×C4×Q8—111no—
273C2×C4×Q8C2×D1111yescharacteristic
274C2×C4×D4—112no—
275C2×C4×D4—111no—
276C2×C4×D4—111no—
277C2×C4×D4—112no—
278C2×#117—112no—
279C2×#117—111no—
280C22×C42—111no—
281C22×C42—112no—
282C8×D4—224no—
283C8×D4—224no—
284C2×C4⋊C8—111no—
285C2×C4⋊C8C2×D1111yescharacteristic
286C2×C22⋊C8—112no—
287C2×C22⋊C8—112no—
288C2×C22⋊C8—111no—
289C2×C22⋊C8—111no—
290C2×C22⋊C8—112no—
291C2×C4×C8—111no—
292C2×C4×C8C2×D1111yescharacteristic
293#336—112no—
294#336—111no—
295#336—111no—
296#336—112no—
297#336—112no—
298#336C2×D1112yes—
299#336C2×D1112yes—
300C22×C11C22×C22⋊C411yescharacteristic
301C22×C11C4×#4111yescharacteristic
302C22×C11#52011yescharacteristic
303C22×C11C23×C811yescharacteristic
304C22×C11C22×M1611yescharacteristic
305C22×C11C2×#13111yescharacteristic
306C22×C11#56811yescharacteristic
307C2×D11—24no—
308C2×D11—24no—
309C2×D11—24no—
310C2×D11—24no—
311C2×D11—24no—
312C2×D11—24no—
313C2×D11—22no—
314C2×D11—22no—
315C2×D11—22no—
316C2×D11—41no—
317C2×D11—41no—
318C2×D11—41no—
319C2×D11—41no—
320C2×D11C2×C22⋊C818yes—
321C4×C11—24no—
322C4×C11—22no—
323C4×C11—42no—
324C4×C11C2×C22⋊C814yes—
325C4×C11#54611yescharacteristic
326C4×C11#54611yescharacteristic
327C4×C11#54711yescharacteristic
328C4×C11#54711yescharacteristic
329Dic11—24no—
330Dic11—22no—
331Dic11—22no—
332Dic11—41no—
333C2×#41—118no—
334C2×#41—224no—
335C2×#41—224no—
336C22×Q8C4×D1111yescharacteristic
337C22×D4—111no—
338C22×D4—112no—
339C23×C4—112no—
340C23×C4—111no—
341C23×C4—112no—
342C23×C4—111no—
343C23×C4—112no—
344C23×C4—111no—
345C22×C8—111no—
346C22×C8—112no—
347C22×C8—111no—
348C22×C8—224no—
349C22×C8—224no—
350C22×C8—224no—
351C22×C8—224no—
352C22×C8—442no—
353C22×C8—442no—
354C22×C8C22×D1112yes—
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
357C4×Q8—22no—
358C4×Q8—22no—
359C4×Q8—224no—
360C4×D4—114no—
361C4×D4—114no—
362C4×D4—224no—
363C4×D4—224no—
364C4×D4—228no—
365C4×D4—224no—
366#117—228no—
367#117—224no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—112no—
370C2×C4⋊C4C4×D1111yescharacteristic
371C2×C4⋊C4C4×D1112yes—
372C2×C22⋊C4—112no—
373C2×C22⋊C4—112no—
374C2×C22⋊C4—112no—
375C2×C42—112no—
376C2×C42—111no—
377C2×C42—112no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—224no—
381C2×C42—224no—
382C2×C42—222no—
383C2×C42—222no—
384C2×C42C22×D1112yes—
385C2×C42C22×D1111yescharacteristic
386C4⋊C8—22no—
387C4⋊C8—222no—
388C22⋊C8—222no—
389C22⋊C8—224no—
390C22⋊C8—224no—
391C22⋊C8—222no—
392C22⋊C8—442no—
393C4×C8—22no—
394C4×C8—222no—
395C2×C11#233911yescharacteristic
396C2×C11C22×C22⋊C811yescharacteristic
397C2×C11#288011yescharacteristic
398C2×C11C8×#4111yescharacteristic
399C2×C11#297011yescharacteristic
400C2×C11#298811yescharacteristic
401C2×C11#299011yescharacteristic
402D11—28no—
403D11—42no—
404C24—112no—
405C24—111no—
406#41—2232no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8C8×D1114yescomplemented
410C2×D4—114no—
411C2×D4—114no—
412C2×D4—118no—
413C2×D4—114no—
414C2×D4—224no—
415C2×D4—224no—
416C22×C4—111no—
417C22×C4—111no—
418C22×C4—112no—
419C22×C4—118no—
420C22×C4—114no—
421C22×C4—114no—
422C22×C4—114no—
423C22×C4—111no—
424C22×C4—222no—
425C22×C4—224no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—224no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—441no—
443C22×C4—442no—
444C22×C4C2×C4×D1112yes—
445C22×C4C2×C4×D1111yescharacteristic
446C22×C4C2×C4×D1112yes—
447C22×C4C2×C4×D1111yescharacteristic
448C22×C4C23×D1111yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—22no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—112no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—222no—
462C2×C8—221no—
463C2×C8—222no—
464C2×C8—221no—
465C2×C8—222no—
466C2×C8—448no—
467C2×C8—448no—
468C2×C8#434312yescomplemented
469C4⋊C4—24no—
470C4⋊C4—22no—
471C4⋊C4—114no—
472C4⋊C4—224no—
473C22⋊C4—118no—
474C22⋊C4—224no—
475C22⋊C4—224no—
476C42—22no—
477C42—22no—
478C42—224no—
479C42—224no—
480C42—222no—
481C42—222no—
482C42—221no—
483C42—221no—
484C42D4×D1112yes—
485C42D4×D1112yes—
486C11#2246911yescharacteristic, complemented, Sylow
487C23—114no—
488C23—114no—
489C23—114no—
490C23—112no—
491C23—222no—
492C23—222no—
493C23—222no—
494C23—222no—
495C23—221no—
496C23—221no—
497C23—221no—
498C23—221no—
499C23—221no—
500C23—221no—
501C23C22×C4×D1111yescharacteristic
502Q8—28no—
503D4—1116no—
504D4—2216no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—112no—
513C2×C4—114no—
514C2×C4—112no—
515C2×C4—2216no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—224no—
523C2×C4—228no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—444no—
531C2×C4—448no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4C22⋊C4×D1112yes—
537C2×C4C22⋊C4×D1112yes—
538C2×C4C2×C8×D1114yes—
539C2×C4C2×C8×D1112yes—
540C2×C4M16×D1112yes—
541C2×C4C2×D4×D1111yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4C2×#434311yescharacteristic
544C2×C4#6704011yescharacteristic
545C2×C4#41×D1111yescharacteristic
546C2×C4#6704211yescharacteristic
547C8—22no—
548C8—41no—
549C8—42no—
550C8—222no—
551C8—441no—
552C8—442no—
553C22—118no—
554C22—224no—
555C22—224no—
556C22—224no—
557C22—224no—
558C22—224no—
559C22—224no—
560C22—222no—
561C22—222no—
562C22—222no—
563C22—441no—
564C22—441no—
565C22—441no—
566C22—441no—
567C22C2×C22⋊C4×D1111yescharacteristic
568C22C4×#434311yescharacteristic
569C22#1062310511yescharacteristic
570C22C22×C8×D1111yescharacteristic
571C22C2×M16×D1111yescharacteristic
572C22D11×#13111yescharacteristic
573C22#1062328111yescharacteristic
574C4—24no—
575C4—22no—
576C4—42no—
577C4—222no—
578C4—222no—
579C4—224no—
580C4—441no—
581C4D11×C22⋊C814yes—
582C4#1062316111yescharacteristic
583C4#1062316211yescharacteristic
584C4#1062320711yescharacteristic
585C4#1062325711yescharacteristic
586C2—228no—
587C2—442no—
588C2#1307144511yescharacteristic
589C2C2×D11×C22⋊C811yescharacteristic
590C2#1307706411yescharacteristic
591C2C8×#434311yescharacteristic
592C2#1307762911yescharacteristic
593C2#1307772611yescharacteristic
594C2#1307774011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C23×C8
FittingC11×#1984C2
socleC23×C11C23×C4
prime radicalC22×#4343C4
cosocleC22×C4×C11C24
hypercenter#1984D11
hypocenterC11#22469
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1984

Complements

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

NH ≅ G/Ntype
2. C2×C8×D44C2semidirect
3. C2×#10622447C2semidirect
4. #13069553C2semidirect
5. #13068907C2semidirect
6. #13068907C2semidirect
7. #13068683C2semidirect
8. #13068593C2semidirect
9. C4×(C2×D11)⋊C8C2semidirect
10. D11×#336C2semidirect
11. C11×#1984C2semidirect
48. C2×#4343C8semidirect
112. C2×Q8×C11C2×C8semidirect
127. C2×D44C2×C8semidirect
149. C2×C4×D11C2×C8semidirect
150. C2×C4×D11C2×C8semidirect
161. C2×C8×C11#41semidirect
187. C2×C11⋊C8#41semidirect
194. #1984D11semidirect
248. D44C22⋊C8semidirect
409. C2×Q8C8×D11semidirect
468. C2×C8#4343semidirect
486. C11#22469semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43432
C2×C8×D442
C2×#106224472
#130695532
#130689072
#130686832
#130685932
C4×(C2×D11)⋊C82
D11×#3362
C11×#19842
#2246911