Finite Group Databasebeta

← #14769872

Subgroups — #14769872

Order 2816.

1412 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×#4341C211yesmaximal, characteristic
2C2×#10622625C211yesmaximal, characteristic, complemented
3#13069552C211yesmaximal, characteristic, complemented
4#13069551C211yesmaximal, characteristic, complemented
5#13068913C212yesmaximal, complemented
6#13068911C212yesmaximal, complemented
7#13068682C212yesmaximal, complemented
8#13068593C211yesmaximal, characteristic, complemented
9C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
10#13068309C212yesmaximal, complemented
11C2×C11×#436C211yesmaximal, characteristic, complemented
12C22×#4341C411yescharacteristic
13C22×C11×M16C2212yes—
14C2×C4×D4×C11C2211yescharacteristic
15C2×D4×Dic11C411yescharacteristic
16C2×C4×C22⋊D11C2212yes—
17C22×C4×Dic11C2212yes—
18C22×#4318C2212yes—
19C4×#4341—24no—
20C4×#4341—24no—
21C2×#66945C411yescharacteristic
22C2×#66940C411yescharacteristic
23C2×(C22⋊D11)⋊C4C412yes—
24C2×#66930C412yes—
25C2×C42×D11C2211yescharacteristic
26C2×C4×Dic22C2211yescharacteristic
27C11×#436—24no—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C22⋊C8C2212yes—
30C2×C4×C8×C11C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2212yes—
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2212yes—
35#10622625—24no—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622188C2211yescharacteristic
39#10622188C2212yes—
40#10622188C2212yes—
41#10622188C2212yes—
42#10622188C2211yescharacteristic
43#10622188C2212yes—
44#10622188C2212yes—
45C22×D4×C11C2×C411yescharacteristic
46C23×C4×C11C2312yes—
47C22×C22⋊D11C2×C412yes—
48C23×Dic11C2×C412yes—
49C23×Dic11C2×C412yes—
50C2×#4341—24no—
51C2×#4341—24no—
52C2×#4341—24no—
53C22×C4×D11C2×C411yescharacteristic
54C22×C4×D11C2×C411yescharacteristic
55C22×C4×D11C2311yescharacteristic
56C22×Dic22C2×C411yescharacteristic
57C2×C11×M16—24no—
58C2×C11×M16—24no—
59C2×C11×M16—42no—
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2312yes—
62C22×C8×C11C2311yescharacteristic
63C4×D4×C11D414yes—
64C4×D4×C11D414yes—
65C2×C11×C4⋊C4C2×C411yescharacteristic
66C2×C11×C22⋊C4C2×C412yes—
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11C2×C412yes—
69D4×Dic11—24no—
70C4×C22⋊D11—24no—
71C4×C22⋊D11—24no—
72C2×(C2×D11)⋊C4C2×C412yes—
73C2×C4⋊Dic11C2×C411yescharacteristic
74C2×Dic11⋊C4C2×C412yes—
75C2×Dic11⋊C4C2×C412yes—
76C2×C4×Dic11—24no—
77C2×C4×Dic11—24no—
78C2×C4×Dic11C2×C411yescharacteristic
79C2×C4×Dic11C2×C411yescharacteristic
80C2×C4×Dic11C2×C412yes—
81C2×C4×Dic11C2×C412yes—
82C2×C4×Dic11C2312yes—
83C2×C4×Dic11C2311yescharacteristic
84C2×#4318—24no—
85C2×#4318—24no—
86C2×#4318—42no—
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2311yescharacteristic
90#66945—24no—
91#66940—24no—
92(C22⋊D11)⋊C4—28no—
93#66930—28no—
94C42×D11—22no—
95C42×D11—22no—
96C4×Dic22—22no—
97C4×Dic22—22no—
98C11×C4⋊C8—22no—
99C11×C22⋊C8—24no—
100C4×C8×C11—22no—
101C22⋊(C11⋊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#22473—111nomaximal, Sylow
108C24×C11C22×C412yes—
109C23×D11C22×C411yescharacteristic
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11C22⋊C414yes—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11C22×C412yes—
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C2×D414yes—
121C22×C4×C11C2×D414yes—
122C22×C4×C11C2411yescharacteristic
123C2×C22⋊D11—24no—
124C2×C22⋊D11—24no—
125C2×C22⋊D11—24no—
126C22×Dic11—24no—
127C22×Dic11—24no—
128C22×Dic11—24no—
129C22×Dic11—24no—
130C22×Dic11—24no—
131C22×Dic11—42no—
132C22×Dic11C22×C411yescharacteristic
133C22×Dic11C22×C412yes—
134C22×Dic11C22×C411yescharacteristic
135C22×Dic11C22×C412yes—
136C22×Dic11C22×C411yescharacteristic
137#4341—232no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11—21no—
145C2×C4×D11—21no—
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×C4×D11—41no—
149C2×C4×D11M1614yescomplemented
150C2×Dic22—22no—
151C2×Dic22—22no—
152C2×Dic22M1614yescomplemented
153C11×M16—48no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—22no—
157C2×C8×C11—21no—
158C2×C8×C11—22no—
159C2×C8×C11—21no—
160C2×C8×C11—22no—
161C2×C8×C11—21no—
162C2×C8×C11#4112yescomplemented
163C11×C4⋊C4C22⋊C414yes—
164C11×C22⋊C4C22⋊C418yes—
165C42×C11C2×D412yes—
166C42×C11C2×D412yes—
167C22⋊Dic11—24no—
168(C2×D11)⋊C4—24no—
169C4⋊Dic11—22no—
170Dic11⋊C4—24no—
171Dic11⋊C4—24no—
172C4×Dic11—22no—
173C4×Dic11—22no—
174C4×Dic11—24no—
175C4×Dic11—24no—
176C4×Dic11—22no—
177C4×Dic11—22no—
178C4×Dic11—21no—
179C4×Dic11—21no—
180#4318—48no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8#4112yescomplemented
190C2×C4×#41—111no—
191C2×#436—111no—
192C2×#436D1111yescharacteristic, complemented
193#1984—111no—
194#1984—111no—
195#1870—112no—
196#1870—112no—
197#1817—112no—
198#1797—111no—
199C4×C22⋊C8—111no—
200#1728—112no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11C2×C22⋊C414yes—
208C23×C11C23×C411yescharacteristic
209C22×D11—21no—
210C22×D11—21no—
211C22×D11—21no—
212C22×D11—21no—
213C22×D11—21no—
214C22×D11—21no—
215C22×D11C2×M1612yes—
216D4×C11—28no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11C2×C22⋊C414yes—
226C2×C4×C11C2×C22⋊C412yes—
227C2×C4×C11C2×C22⋊C412yes—
228C2×C4×C11C2×M1612yes—
229C2×C4×C11C2×M1612yes—
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11H(5,𝔽2)11yescharacteristic
235C2×C4×C112−1+411yescharacteristic
236C22⋊D11—216no—
237C2×Dic11—216no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—22no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—48no—
251C2×Dic11C2×M1614yes—
252C2×Dic11C2×M1612yes—
253C2×Dic11#13112yes—
254C4×D11—28no—
255C4×D11—44no—
256C4×D11—41no—
257C4×D11—41no—
258C4×D11—41no—
259C4×D11—41no—
260Dic22—28no—
261C8×C11—22no—
262C8×C11—42no—
263C8×C11—41no—
264C11⋊C8—22no—
265C11⋊C8—42no—
266C11⋊C8—41no—
267C22×#41—111no—
268C22×M16—112no—
269C22×M16C2×D1112yes—
270C4×#41—224no—
271C4×#41—224no—
272C2×C4×Q8—111no—
273C2×C4×Q8—111no—
274C2×C4×D4—111no—
275C2×C4×D4—112no—
276C2×C4×D4—112no—
277C2×C4×D4C2×D1111yescharacteristic
278C2×#117—111no—
279C2×#117—112no—
280C22×C42—112no—
281C22×C42—111no—
282#436—24no—
283#436—224no—
284C2×C4⋊C8—111no—
285C2×C4⋊C8C2×D1111yescharacteristic
286C2×C22⋊C8—112no—
287C2×C22⋊C8—111no—
288C2×C22⋊C8—111no—
289C2×C22⋊C8—112no—
290C2×C22⋊C8C2×D1112yes—
291C2×C4×C8—111no—
292C2×C4×C8C2×D1111yescharacteristic
293#336—112no—
294#336—111no—
295#336—112no—
296#336—112no—
297#336—112no—
298#336—112no—
299#336—111no—
300C22×C11—24no—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11C22×C22⋊C411yescharacteristic
308C22×C11C4×#4111yescharacteristic
309C22×C11#52011yescharacteristic
310C22×C11C22×M1611yescharacteristic
311C22×C11C22×M1611yescharacteristic
312C22×C11C2×#13111yescharacteristic
313C22×C11#56811yescharacteristic
314C2×D11—22no—
315C2×D11—22no—
316C2×D11—22no—
317C2×D11—41no—
318C2×D11—41no—
319C2×D11—41no—
320C2×D11—41no—
321C4×C11—24no—
322C4×C11—22no—
323C4×C11#40714yes—
324C4×C11#54611yescharacteristic
325C4×C11#54611yescharacteristic
326C4×C11#54711yescharacteristic
327C4×C11#54711yescharacteristic
328Dic11—24no—
329Dic11—22no—
330Dic11—22no—
331Dic11—41no—
332Dic11—42no—
333C2×#41—224no—
334C2×#41—224no—
335C2×#41—224no—
336C22×Q8—111no—
337C22×D4—112no—
338C22×D4C4×D1111yescharacteristic
339C23×C4—111no—
340C23×C4—112no—
341C23×C4—112no—
342C23×C4—111no—
343C23×C4—111no—
344C23×C4C22×D1112yes—
345C2×M16—24no—
346C2×M16—24no—
347C2×M16—42no—
348C2×M16—224no—
349C2×M16—224no—
350C2×M16—442no—
351C22×C8—111no—
352C22×C8—112no—
353C22×C8—111no—
354C22×C8C22×D1112yes—
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
357C4×Q8—224no—
358C4×Q8—222no—
359C4×Q8—222no—
360C4×D4—224no—
361C4×D4—224no—
362C4×D4—224no—
363C4×D4—228no—
364C4×D4D4414yes—
365C4×D4C22⋊D1114yes—
366#117—224no—
367#117—228no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—112no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4C4×D1111yescharacteristic
372C2×C22⋊C4—112no—
373C2×C22⋊C4—112no—
374C2×C22⋊C4C4×D1112yes—
375C2×C42—112no—
376C2×C42—111no—
377C2×C42—112no—
378C2×C42—111no—
379C2×C42—112no—
380C2×C42—111no—
381C2×C42—224no—
382C2×C42—224no—
383C2×C42—222no—
384C2×C42—222no—
385C2×C42C22×D1111yescharacteristic
386C4⋊C8—22no—
387C4⋊C8—222no—
388C22⋊C8—24no—
389C22⋊C8—222no—
390C22⋊C8—224no—
391C22⋊C8—222no—
392C22⋊C8—442no—
393C4×C8—22no—
394C4×C8—222no—
395C2×C11—44no—
396C2×C11#233911yescharacteristic
397C2×C11C2×#40711yescharacteristic
398C2×C11#288011yescharacteristic
399C2×C11#296511yescharacteristic
400C2×C11#297111yescharacteristic
401C2×C11#298911yescharacteristic
402C2×C11#299111yescharacteristic
403D11—42no—
404C24—111no—
405C24C2×C4×D1112yes—
406#41—2232no—
407C2×Q8—114no—
408C2×Q8—222no—
409C2×Q8—222no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—224no—
413C2×D4—224no—
414C2×D4—224no—
415C2×D4(C2×D11)⋊C414yes—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—111no—
421C22×C4—111no—
422C22×C4—112no—
423C22×C4—114no—
424C22×C4—112no—
425C22×C4—111no—
426C22×C4—222no—
427C22×C4—224no—
428C22×C4—224no—
429C22×C4—224no—
430C22×C4—224no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—224no—
434C22×C4—222no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—441no—
442C22×C4—442no—
443C22×C4C2×C4×D1112yes—
444C22×C4C2×C4×D1111yescharacteristic
445C22×C4C2×C4×D1111yescharacteristic
446C22×C4C2×D4414yes—
447C22×C4C2×C22⋊D1114yes—
448C22×C4C23×D1111yescharacteristic
449M16—48no—
450M16—448no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—22no—
459C2×C8—112no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—222no—
464C2×C8—221no—
465C2×C8—222no—
466C2×C8—222no—
467C2×C8—221no—
468C2×C8#434112yescomplemented
469C4⋊C4—224no—
470C4⋊C4—224no—
471C4⋊C4—222no—
472C4⋊C4(C2×D11)⋊C414yes—
473C22⋊C4—224no—
474C22⋊C4—224no—
475C22⋊C4(C2×D11)⋊C418yes—
476C42—224no—
477C42—222no—
478C42—224no—
479C42—222no—
480C42—221no—
481C42—222no—
482C42—221no—
483C42—222no—
484C42C2×D4412yes—
485C42C2×C22⋊D1112yes—
486C11#2247311yescharacteristic, complemented, Sylow
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—112no—
494C23—221no—
495C23—221no—
496C23—221no—
497C23—221no—
498C23—221no—
499C23—221no—
500C23C2×(C2×D11)⋊C414yes—
501C23C22×C4×D1111yescharacteristic
502Q8—228no—
503D4—28no—
504D4—2216no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—112no—
514C2×C4—114no—
515C2×C4—112no—
516C2×C4—2216no—
517C2×C4—221no—
518C2×C4—222no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—222no—
523C2×C4—228no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—222no—
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×C4M16×D1112yes—
537C2×C4M16×D1112yes—
538C2×C4C2×(C2×D11)⋊C414yes—
539C2×C4C2×(C2×D11)⋊C412yes—
540C2×C4C2×(C2×D11)⋊C412yes—
541C2×C4C22×D4411yescharacteristic
542C2×C4C2×#434111yescharacteristic
543C2×C4#6703711yescharacteristic
544C2×C4#41×D1111yescharacteristic
545C2×C4#6704311yescharacteristic
546C2×C4C22×C22⋊D1111yescharacteristic
547C8—22no—
548C8—42no—
549C8—41no—
550C8—222no—
551C8—442no—
552C8—441no—
553C22—24no—
554C22—24no—
555C22—24no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—222no—
561C22—222no—
562C22—222no—
563C22—441no—
564C22—441no—
565C22—441no—
566C22—441no—
567C22C4×#434111yescharacteristic
568C22#1062307711yescharacteristic
569C22C2×M16×D1111yescharacteristic
570C22C2×M16×D1111yescharacteristic
571C22D11×#13111yescharacteristic
572C22#1062328111yescharacteristic
573C22C22×(C2×D11)⋊C411yescharacteristic
574C4—22no—
575C4—24no—
576C4—222no—
577C4—224no—
578C4—222no—
579C4—442no—
580C4—441no—
581C4#1062273914yes—
582C4#1062308511yescharacteristic
583C4#1062308611yescharacteristic
584C4#1062333711yescharacteristic
585C4#1062335511yescharacteristic
586C2—44no—
587C2—442no—
588C2#1307144111yescharacteristic
589C2C2×#1062273911yescharacteristic
590C2#1307706311yescharacteristic
591C2#1307757911yescharacteristic
592C2#1307763211yescharacteristic
593C2#1307773111yescharacteristic
594C2#1307774411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#436C2
prime radicalC22×#4341C4
cosocleC22×C4×C11C24
hypercenterC2×#436D11
hypocenterC11#22473
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
2. C2×#10622625C2semidirect
3. #13069552C2semidirect
4. #13069551C2semidirect
5. #13068913C2semidirect
6. #13068911C2semidirect
7. #13068682C2semidirect
8. #13068593C2semidirect
9. C4×(C2×D11)⋊C8C2semidirect
10. #13068309C2semidirect
11. C2×C11×#436C2semidirect
149. C2×C4×D11M16semidirect
152. C2×Dic22M16semidirect
162. C2×C8×C11#41semidirect
189. C2×C11⋊C8#41semidirect
192. C2×#436D11semidirect
468. C2×C8#4341semidirect
486. C11#22473semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43412
C2×#106226252
#130695522
#130695512
#130689132
#130689112
#130686822
#130685932
C4×(C2×D11)⋊C82
#130683092
C2×C11×#4362
#2247311