Finite Group Databasebeta

← #14770503

Subgroups — #14770503

Order 2816.

1364 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4341C211yesmaximal, characteristic
2C2×#10622292C211yesmaximal, characteristic, complemented
3C2×#10622444C211yesmaximal, characteristic, complemented
4#13069412C212yesmaximal, complemented
5#13069412C212yesmaximal, complemented
6#13069411C211yesmaximal, characteristic, complemented
7#13068594C212yesmaximal, complemented
8#13068593C211yesmaximal, characteristic, complemented
9#13068380C212yesmaximal, complemented
10C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
11C11×#1954C211yesmaximal, characteristic, complemented
12C22×#4341C411yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×D4×Dic11C411yescharacteristic
15C2×C4×C22⋊D11C2212yes—
16C22×C4×Dic11C2212yes—
17C4×#4341—24no—
18C4×#4341—24no—
19C2×#66945C411yescharacteristic
20C2×#66940C411yescharacteristic
21C2×(C22⋊D11)⋊C4C412yes—
22C2×#66930C412yes—
23C2×C42×D11C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2212yes—
27C2×C11×C22⋊C8C2212yes—
28C2×C4×C8×C11C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×C22⋊(C11⋊C8)C2212yes—
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2212yes—
34C2×#66879C2212yes—
35C2×#66879C2212yes—
36C2×Dic11⋊C8C2212yes—
37C2×Dic11⋊C8C2212yes—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622444—24no—
41#10622292—24no—
42#10622188C2212yes—
43#10622188C2211yescharacteristic
44#10622188C2211yescharacteristic
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
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2312yes—
59C22×C8×C11C2311yescharacteristic
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C2×C11×C4⋊C4C2×C411yescharacteristic
63C2×C11×C22⋊C4C2×C412yes—
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11C2×C412yes—
66D4×Dic11—24no—
67C4×C22⋊D11—24no—
68C4×C22⋊D11—24no—
69C2×(C2×D11)⋊C4C2×C412yes—
70C2×C4⋊Dic11C2×C411yescharacteristic
71C2×Dic11⋊C4C2×C412yes—
72C2×Dic11⋊C4C2×C412yes—
73C2×C4×Dic11—24no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11C2×C411yescharacteristic
76C2×C4×Dic11C2×C411yescharacteristic
77C2×C4×Dic11C2×C412yes—
78C2×C4×Dic11C2×C412yes—
79C2×C4×Dic11C2311yescharacteristic
80C2×C4×Dic11C2312yes—
81C22×C11⋊C8C2311yescharacteristic
82C22×C11⋊C8C2312yes—
83C22×C11⋊C8C2311yescharacteristic
84#66945—24no—
85#66940—24no—
86(C22⋊D11)⋊C4—28no—
87#66930—28no—
88C42×D11—22no—
89C42×D11—22no—
90C4×Dic22D414yes—
91C4×Dic22D414yes—
92C11×C4⋊C8—22no—
93C11×C22⋊C8—24no—
94C11×C22⋊C8—42no—
95C4×C8×C11—22no—
96C22⋊(C11⋊C8)—24no—
97C22⋊(C11⋊C8)—42no—
98(C2×D11)⋊C8—22no—
99(C2×D11)⋊C8—22no—
100(C2×D11)⋊C8—42no—
101#66879—24no—
102#66879—24no—
103Dic11⋊C8—24no—
104Dic11⋊C8—24no—
105C4⋊(C11⋊C8)—22no—
106C4×C11⋊C8—22no—
107#22532—111nomaximal, Sylow
108C24×C11C22×C412yes—
109C23×D11C22×C411yescharacteristic
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11M1614yes—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C411yescharacteristic
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×C412yes—
135C22×Dic11C22×C411yescharacteristic
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×D11M1614yes—
150C2×Dic22—22no—
151C2×Dic22—22no—
152C2×Dic22C22⋊C414yes—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—22no—
156C2×C8×C11—21no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11#4112yescomplemented
162C11×C4⋊C4—22no—
163C11×C22⋊C4—24no—
164C42×C11C2×D412yes—
165C42×C11C2×D412yes—
166C22⋊Dic11—24no—
167(C2×D11)⋊C4—24no—
168C4⋊Dic11C22⋊C414yes—
169Dic11⋊C4—24no—
170Dic11⋊C4C22⋊C418yes—
171C4×Dic11—24no—
172C4×Dic11—24no—
173C4×Dic11—22no—
174C4×Dic11—22no—
175C4×Dic11—21no—
176C4×Dic11—21no—
177C4×Dic11C2×D414yes—
178C4×Dic11C2×D414yes—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8#4112yescomplemented
188C2×C4×#41—111no—
189C2×#446—111no—
190C2×#446—111no—
191#1955—112no—
192#1955—112no—
193#1954—111no—
194#1954D1111yescharacteristic, complemented
195#1797—111no—
196#1797—112no—
197#1749—112no—
198C4×C22⋊C8—111no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11C2×M1614yes—
206C23×C11C23×C411yescharacteristic
207C22×D11—21no—
208C22×D11—21no—
209C22×D11—21no—
210C22×D11—21no—
211C22×D11—21no—
212C22×D11—21no—
213C22×D11C2×M1612yes—
214D4×C11—28no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11C2×C22⋊C412yes—
225C2×C4×C11C2×C22⋊C412yes—
226C2×C4×C11C2×M1612yes—
227C2×C4×C11C2×M1612yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11H(5,𝔽2)11yescharacteristic
233C2×C4×C112−1+411yescharacteristic
234C22⋊D11—216no—
235C2×Dic11—216no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—21no—
241C2×Dic11—22no—
242C2×Dic11—21no—
243C2×Dic11—22no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—48no—
248C2×Dic11C2×C22⋊C414yes—
249C2×Dic11C2×C22⋊C414yes—
250C2×Dic11C2×M1612yes—
251C2×Dic11#13112yes—
252C4×D11—28no—
253C4×D11—44no—
254C4×D11—41no—
255C4×D11—41no—
256C4×D11—41no—
257C4×D11—41no—
258Dic22—28no—
259C8×C11—22no—
260C8×C11—42no—
261C8×C11—41no—
262C11⋊C8—22no—
263C11⋊C8—41no—
264C11⋊C8—42no—
265C22×#41—111no—
266C4×#41—224no—
267C4×#41—224no—
268C2×C4×Q8—111no—
269C2×C4×Q8—111no—
270C2×C4×D4—111no—
271C2×C4×D4—112no—
272C2×C4×D4—112no—
273C2×C4×D4C2×D1111yescharacteristic
274C2×#117—111no—
275C2×#117—112no—
276C22×C42—112no—
277C22×C42—111no—
278#446—224no—
279#446—224no—
280C2×C4⋊C8—112no—
281C2×C4⋊C8—112no—
282C2×C4⋊C8—111no—
283C2×C4⋊C8C2×D1111yescharacteristic
284C2×C22⋊C8—112no—
285C2×C22⋊C8—111no—
286C2×C22⋊C8—111no—
287C2×C22⋊C8—112no—
288C2×C22⋊C8—112no—
289C2×C22⋊C8C2×D1112yes—
290C2×C22⋊C8C2×D1112yes—
291C2×#97—112no—
292C2×#97—112no—
293C2×C4×C8—111no—
294C2×C4×C8C2×D1111yescharacteristic
295#336—111no—
296#336—112no—
297#336—111no—
298C22×C11—24no—
299C22×C11—24no—
300C22×C11—24no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11C22×C22⋊C411yescharacteristic
306C22×C11C4×#4111yescharacteristic
307C22×C11#52011yescharacteristic
308C22×C11C22×M1611yescharacteristic
309C22×C11C22×M1611yescharacteristic
310C22×C11C2×#13111yescharacteristic
311C22×C11#56811yescharacteristic
312C2×D11—22no—
313C2×D11—22no—
314C2×D11—22no—
315C2×D11—41no—
316C2×D11—41no—
317C2×D11—41no—
318C2×D11—41no—
319C4×C11—22no—
320C4×C11—42no—
321C4×C11#40714yes—
322C4×C11#54811yescharacteristic
323C4×C11#54811yescharacteristic
324C4×C11#55011yescharacteristic
325C4×C11#55011yescharacteristic
326Dic11—24no—
327Dic11—22no—
328Dic11—22no—
329Dic11—24no—
330Dic11—41no—
331C2×#41—224no—
332C2×#41—224no—
333C2×#41—224no—
334C22×Q8—111no—
335C22×D4—112no—
336C22×D4C4×D1111yescharacteristic
337C23×C4—111no—
338C23×C4—112no—
339C23×C4—112no—
340C23×C4—111no—
341C23×C4—111no—
342C23×C4C22×D1112yes—
343C22×C8—111no—
344C22×C8—111no—
345C22×C8—112no—
346C22×C8C22×D1111yescharacteristic
347C22×C8C22×D1112yes—
348C22×C8C22×D1111yescharacteristic
349C4×Q8—114no—
350C4×Q8—114no—
351C4×Q8—224no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—224no—
355C4×D4—224no—
356C4×D4—228no—
357C4×D4—224no—
358#117—228no—
359#117—224no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4C4×D1111yescharacteristic
364C2×C22⋊C4—112no—
365C2×C22⋊C4—112no—
366C2×C22⋊C4C4×D1112yes—
367C2×C42—112no—
368C2×C42—112no—
369C2×C42—111no—
370C2×C42—112no—
371C2×C42—111no—
372C2×C42—111no—
373C2×C42—224no—
374C2×C42—224no—
375C2×C42—222no—
376C2×C42—222no—
377C2×C42C22×D1111yescharacteristic
378C4⋊C8—22no—
379C4⋊C8—224no—
380C4⋊C8—224no—
381C4⋊C8—222no—
382C22⋊C8—24no—
383C22⋊C8—42no—
384C22⋊C8—222no—
385C22⋊C8—224no—
386C22⋊C8—222no—
387C22⋊C8—442no—
388C22⋊C8—442no—
389#97—224no—
390#97—224no—
391C4×C8—22no—
392C4×C8—222no—
393C2×C11—44no—
394C2×C11#234111yescharacteristic
395C2×C11C2×#40711yescharacteristic
396C2×C11#288011yescharacteristic
397C2×C11#296511yescharacteristic
398C2×C11#297011yescharacteristic
399C2×C11#298911yescharacteristic
400C2×C11#299011yescharacteristic
401D11—42no—
402C24—111no—
403C24C2×C4×D1112yes—
404#41—2232no—
405C2×Q8—114no—
406C2×Q8—222no—
407C2×Q8—222no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—224no—
411C2×D4—224no—
412C2×D4—224no—
413C2×D4#431314yes—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—111no—
421C22×C4—111no—
422C22×C4—112no—
423C22×C4—112no—
424C22×C4—114no—
425C22×C4—111no—
426C22×C4—222no—
427C22×C4—224no—
428C22×C4—224no—
429C22×C4—224no—
430C22×C4—224no—
431C22×C4—224no—
432C22×C4—222no—
433C22×C4—222no—
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×C4C23×D1111yescharacteristic
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—21no—
453C2×C8—22no—
454C2×C8—21no—
455C2×C8—112no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—222no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—222no—
463C2×C8—222no—
464C2×C8#434112yescomplemented
465C4⋊C4—22no—
466C4⋊C4—118no—
467C4⋊C4—114no—
468C4⋊C4—224no—
469C22⋊C4—24no—
470C22⋊C4—224no—
471C22⋊C4—224no—
472C42—114no—
473C42—114no—
474C42—224no—
475C42—224no—
476C42—222no—
477C42—222no—
478C42—221no—
479C42—221no—
480C42D4×D1112yes—
481C42D4×D1112yes—
482C11#2253211yescharacteristic, complemented, Sylow
483C23—22no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—112no—
490C23—221no—
491C23—221no—
492C23—221no—
493C23—221no—
494C23—221no—
495C23—221no—
496C23C2×#431314yes—
497C23C22×C4×D1111yescharacteristic
498Q8—228no—
499D4—28no—
500D4—2216no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—114no—
511C2×C4—114no—
512C2×C4—112no—
513C2×C4—112no—
514C2×C4—2216no—
515C2×C4—221no—
516C2×C4—222no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—221no—
522C2×C4—222no—
523C2×C4—228no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—444no—
528C2×C4—448no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4C22⋊C4×D1112yes—
534C2×C4C22⋊C4×D1112yes—
535C2×C4C2×#431312yes—
536C2×C4M16×D1112yes—
537C2×C4C2×D4×D1111yescharacteristic
538C2×C4C2×D4×D1111yescharacteristic
539C2×C4C2×#434111yescharacteristic
540C2×C4#6703711yescharacteristic
541C2×C4#41×D1111yescharacteristic
542C2×C4#6704311yescharacteristic
543C8—22no—
544C8—42no—
545C8—41no—
546C8—222no—
547C8—441no—
548C8—442no—
549C22—24no—
550C22—24no—
551C22—24no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—222no—
557C22—222no—
558C22—222no—
559C22—441no—
560C22—441no—
561C22—441no—
562C22—441no—
563C22C2×C22⋊C4×D1111yescharacteristic
564C22C4×#434111yescharacteristic
565C22#1062307711yescharacteristic
566C22C22×#431311yescharacteristic
567C22C2×M16×D1111yescharacteristic
568C22D11×#13111yescharacteristic
569C22#1062328111yescharacteristic
570C4—22no—
571C4—42no—
572C4—222no—
573C4—224no—
574C4—222no—
575C4—224no—
576C4—441no—
577C4#1062233914yes—
578C4#1062312911yescharacteristic
579C4#1062313011yescharacteristic
580C4#1062320811yescharacteristic
581C4#1062324911yescharacteristic
582C2—44no—
583C2—442no—
584C2#1307145511yescharacteristic
585C2C2×#1062233911yescharacteristic
586C2#1307706411yescharacteristic
587C2#1307757911yescharacteristic
588C2#1307762411yescharacteristic
589C2#1307773111yescharacteristic
590C2#1307773911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1954C2
prime radicalC22×#4341C4
cosocleC22×C4×C11C24
hypercenter#1954D11
hypocenterC11#22532
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. C2×#10622292C2semidirect
3. C2×#10622444C2semidirect
4. #13069412C2semidirect
5. #13069412C2semidirect
6. #13069411C2semidirect
7. #13068594C2semidirect
8. #13068593C2semidirect
9. #13068380C2semidirect
10. C4×(C2×D11)⋊C8C2semidirect
11. C11×#1954C2semidirect
161. C2×C8×C11#41semidirect
187. C2×C11⋊C8#41semidirect
194. #1954D11semidirect
464. C2×C8#4341semidirect
482. C11#22532semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43412
C2×#106222922
C2×#106224442
#130694122
#130694112
#130685942
#130685932
#130683802
C4×(C2×D11)⋊C82
C11×#19542
#2253211