Finite Group Databasebeta

← #14770502

Subgroups — #14770502

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×#4343C211yesmaximal, characteristic
2C2×#10622637C211yesmaximal, characteristic, complemented
3#13069414C212yesmaximal, complemented
4#13069413C212yesmaximal, complemented
5#13069410C211yesmaximal, characteristic, complemented
6#13069409C211yesmaximal, characteristic, complemented
7#13068593C212yesmaximal, complemented
8#13068593C211yesmaximal, characteristic, complemented
9#13068379C212yesmaximal, complemented
10C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
11C2×C11×#446C211yesmaximal, characteristic, complemented
12C22×#4343C411yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×Q8×Dic11C411yescharacteristic
15C4×#4343—24no—
16C4×#4343—24no—
17C2×#66946C412yes—
18C2×#66946C411yescharacteristic
19C2×#66945C412yes—
20C2×#66945C411yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C4×D44C2212yes—
23C2×C42×D11C2211yescharacteristic
24C2×C42×D11C2212yes—
25C11×#446—24no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2212yes—
28C2×C11×#97C2212yes—
29C2×C4×C8×C11C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2212yes—
33C2×(C2×D11)⋊C8C2212yes—
34C2×(C2×D11)⋊C8C2212yes—
35C2×(C2×D11)⋊C8C2212yes—
36C2×(C2×D11)⋊C8C2212yes—
37#10622637—24no—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2212yes—
40C2×#66867C2212yes—
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622188C2211yescharacteristic
43#10622188C2212yes—
44#10622188C2211yescharacteristic
45C22×Q8×C11C2×C411yescharacteristic
46C2×#4343—24no—
47C2×#4343—24no—
48C2×#4343—24no—
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×C11D414yes—
61C4×Q8×C11D414yes—
62C2×C11×C4⋊C4C2×C412yes—
63C2×C11×C4⋊C4C2×C411yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2312yes—
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×C411yescharacteristic
73C2×C4×Dic11C2×C412yes—
74C2×C4×Dic11C2×C412yes—
75C2×C4×Dic11C2×C411yescharacteristic
76C2×C4×Dic11C2311yescharacteristic
77C22×C11⋊C8C2311yescharacteristic
78C22×C11⋊C8C2312yes—
79C22×C11⋊C8C2311yescharacteristic
80#66946—28no—
81#66946—24no—
82#66945—28no—
83#66945—24no—
84C4×D44—22no—
85C4×D44—24no—
86C4×D44—22no—
87C4×D44—24no—
88C42×D11—22no—
89C42×D11—24no—
90C42×D11—22no—
91C42×D11—24no—
92C11×C4⋊C8—22no—
93C11×C4⋊C8—24no—
94C11×#97—24no—
95C4×C8×C11—22no—
96(C2×D11)⋊C8—22no—
97(C2×D11)⋊C8—24no—
98(C2×D11)⋊C8—22no—
99(C2×D11)⋊C8—24no—
100(C2×D11)⋊C8—42no—
101(C2×D11)⋊C8—42no—
102(C2×D11)⋊C8—42no—
103C4⋊(C11⋊C8)—24no—
104C4⋊(C11⋊C8)—22no—
105#66867—24no—
106C4×C11⋊C8—22no—
107#22532—111nomaximal, Sylow
108C23×D11C22×C412yes—
109C23×D11C22×C411yescharacteristic
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11C22⋊C414yes—
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×D44—24no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44M1614yes—
129C2×C4×D11—24no—
130C2×C4×D11—22no—
131C2×C4×D11—24no—
132C2×C4×D11—24no—
133C2×C4×D11—24no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—24no—
137C2×C4×D11—22no—
138C2×C4×D11—21no—
139C2×C4×D11—22no—
140C2×C4×D11—21no—
141C2×C4×D11—22no—
142C2×C4×D11—21no—
143C2×C4×D11—22no—
144C2×C4×D11—21no—
145C2×C4×D11—22no—
146C2×C4×D11—21no—
147C2×C4×D11—22no—
148C2×C4×D11—21no—
149C2×C4×D11—22no—
150C2×C4×D11—42no—
151C2×C4×D11—41no—
152C2×C4×D11M1614yes—
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⋊C4C22⋊C418yes—
163C11×C4⋊C4C22⋊C414yes—
164C42×C11C2×D412yes—
165C42×C11C2×D414yes—
166C42×C11C2×D412yes—
167C42×C11C2×D414yes—
168(C2×D11)⋊C4—24no—
169(C2×D11)⋊C4—24no—
170(C2×D11)⋊C4—24no—
171C4⋊Dic11—24no—
172C4⋊Dic11—22no—
173C4×Dic11—22no—
174C4×Dic11—24no—
175C4×Dic11—24no—
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
188C2×C4×#41—111no—
189C2×#446—111no—
190C2×#446D1111yescharacteristic, complemented
191#1955—112no—
192#1955—112no—
193#1954—111no—
194#1954—111no—
195#1797—112no—
196#1797—111no—
197#1749—112no—
198C4×C22⋊C8—111no—
199C23×C11C23×C411yescharacteristic
200C22×D11—22no—
201C22×D11—21no—
202C22×D11—21no—
203C22×D11—22no—
204C22×D11—21no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—21no—
208C22×D11—21no—
209C22×D11—22no—
210C22×D11—22no—
211C22×D11—21no—
212C22×D11C2×M1614yes—
213C22×D11C2×M1612yes—
214Q8×C11—28no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11C2×C22⋊C414yes—
222C2×C4×C11C2×C22⋊C412yes—
223C2×C4×C11C2×C22⋊C414yes—
224C2×C4×C11C2×C22⋊C412yes—
225C2×C4×C11C2×M1612yes—
226C2×C4×C11C2×M1612yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11H(5,𝔽2)11yescharacteristic
232C2×C4×C112−1+411yescharacteristic
233C2×Dic11—21no—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—22no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—22no—
241C2×Dic11—21no—
242C2×Dic11—22no—
243C2×Dic11C2×M1612yes—
244C2×Dic11#13112yes—
245D44—216no—
246D44—28no—
247C4×D11—216no—
248C4×D11—28no—
249C4×D11—44no—
250C4×D11—48no—
251C4×D11—41no—
252C4×D11—42no—
253C4×D11—41no—
254C4×D11—42no—
255C4×D11—41no—
256C4×D11—42no—
257C4×D11—41no—
258C4×D11—42no—
259C8×C11—22no—
260C8×C11—41no—
261C8×C11—42no—
262C11⋊C8—22no—
263C11⋊C8—41no—
264C11⋊C8—42no—
265C22×#41—111no—
266C4×#41—224no—
267C4×#41—224no—
268C2×C4×Q8—111no—
269C2×C4×Q8C2×D1111yescharacteristic
270C2×C4×D4—111no—
271C2×C4×D4—112no—
272C2×C4×D4—111no—
273C2×C4×D4—112no—
274C2×#117—111no—
275C2×#117—112no—
276C22×C42—111no—
277C22×C42—112no—
278#446—24no—
279#446—224no—
280C2×C4⋊C8—111no—
281C2×C4⋊C8—112no—
282C2×C4⋊C8C2×D1111yescharacteristic
283C2×C4⋊C8C2×D1112yes—
284C2×C22⋊C8—112no—
285C2×C22⋊C8—112no—
286C2×C22⋊C8—111no—
287C2×C22⋊C8—111no—
288C2×C22⋊C8—112no—
289C2×C22⋊C8—112no—
290C2×C22⋊C8—112no—
291C2×#97—112no—
292C2×#97C2×D1112yes—
293C2×C4×C8—111no—
294C2×C4×C8C2×D1111yescharacteristic
295#336—111no—
296#336—112no—
297#336—111no—
298C22×C11C22×C22⋊C411yescharacteristic
299C22×C11C4×#4111yescharacteristic
300C22×C11#52011yescharacteristic
301C22×C11C22×M1611yescharacteristic
302C22×C11C22×M1611yescharacteristic
303C22×C11C2×#13111yescharacteristic
304C22×C11#56811yescharacteristic
305C2×D11—24no—
306C2×D11—22no—
307C2×D11—22no—
308C2×D11—24no—
309C2×D11—22no—
310C2×D11—24no—
311C2×D11—41no—
312C2×D11—42no—
313C2×D11—41no—
314C2×D11—42no—
315C2×D11—42no—
316C2×D11—41no—
317C2×D11—42no—
318C2×D11—41no—
319C4×C11—24no—
320C4×C11—22no—
321C4×C11—24no—
322C4×C11#40714yes—
323C4×C11#54811yescharacteristic
324C4×C11#54811yescharacteristic
325C4×C11#55011yescharacteristic
326C4×C11#55011yescharacteristic
327Dic11—22no—
328Dic11—22no—
329Dic11—42no—
330Dic11—41no—
331C2×#41—224no—
332C2×#41—224no—
333C2×#41—224no—
334C22×Q8C4×D1111yescharacteristic
335C22×D4—111no—
336C22×D4—112no—
337C23×C4—111no—
338C23×C4—112no—
339C23×C4—112no—
340C23×C4—111no—
341C23×C4—111no—
342C23×C4—112no—
343C22×C8—111no—
344C22×C8—111no—
345C22×C8—112no—
346C22×C8C22×D1111yescharacteristic
347C22×C8C22×D1112yes—
348C22×C8C22×D1111yescharacteristic
349C4×Q8—224no—
350C4×Q8D4414yes—
351C4×Q8C22⋊D1114yes—
352C4×D4—228no—
353C4×D4—224no—
354C4×D4—222no—
355C4×D4—224no—
356C4×D4—222no—
357C4×D4—224no—
358#117—228no—
359#117—224no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4C4×D1112yes—
363C2×C4⋊C4C4×D1111yescharacteristic
364C2×C22⋊C4—112no—
365C2×C22⋊C4—112no—
366C2×C22⋊C4—112no—
367C2×C42—111no—
368C2×C42—112no—
369C2×C42—112no—
370C2×C42—111no—
371C2×C42—111no—
372C2×C42—222no—
373C2×C42—224no—
374C2×C42—222no—
375C2×C42—224no—
376C2×C42C22×D1111yescharacteristic
377C2×C42C22×D1112yes—
378C4⋊C8—22no—
379C4⋊C8—24no—
380C4⋊C8—222no—
381C4⋊C8—224no—
382C22⋊C8—224no—
383C22⋊C8—222no—
384C22⋊C8—224no—
385C22⋊C8—222no—
386C22⋊C8—442no—
387C22⋊C8—442no—
388C22⋊C8—442no—
389#97—24no—
390#97—224no—
391C4×C8—22no—
392C4×C8—222no—
393C2×C11#234111yescharacteristic
394C2×C11C2×#40711yescharacteristic
395C2×C11#288011yescharacteristic
396C2×C11#296511yescharacteristic
397C2×C11#297011yescharacteristic
398C2×C11#298911yescharacteristic
399C2×C11#299011yescharacteristic
400D11—42no—
401D11—44no—
402C24—111no—
403C24—112no—
404#41—2232no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8(C2×D11)⋊C414yes—
408C2×D4—114no—
409C2×D4—224no—
410C2×D4—224no—
411C2×D4—222no—
412C2×D4—224no—
413C2×D4—222no—
414C22×C4—111no—
415C22×C4—111no—
416C22×C4—114no—
417C22×C4—111no—
418C22×C4—112no—
419C22×C4—224no—
420C22×C4—222no—
421C22×C4—224no—
422C22×C4—224no—
423C22×C4—222no—
424C22×C4—224no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—224no—
428C22×C4—221no—
429C22×C4—222no—
430C22×C4—221no—
431C22×C4—222no—
432C22×C4—221no—
433C22×C4—222no—
434C22×C4—221no—
435C22×C4—222no—
436C22×C4—221no—
437C22×C4—222no—
438C22×C4—221no—
439C22×C4—222no—
440C22×C4—442no—
441C22×C4—441no—
442C22×C4C2×C4×D1111yescharacteristic
443C22×C4C2×C4×D1112yes—
444C22×C4C2×C4×D1112yes—
445C22×C4C2×C4×D1111yescharacteristic
446C22×C4C23×D1111yescharacteristic
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—22no—
451C2×C8—21no—
452C2×C8—22no—
453C2×C8—21no—
454C2×C8—22no—
455C2×C8—112no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—222no—
460C2×C8—221no—
461C2×C8—222no—
462C2×C8—221no—
463C2×C8—222no—
464C2×C8#434312yescomplemented
465C4⋊C4—224no—
466C4⋊C4—222no—
467C4⋊C4(C2×D11)⋊C418yes—
468C4⋊C4(C2×D11)⋊C414yes—
469C22⋊C4—224no—
470C22⋊C4—224no—
471C22⋊C4—224no—
472C42—222no—
473C42—224no—
474C42—224no—
475C42—222no—
476C42—221no—
477C42—221no—
478C42C2×D4412yes—
479C42C2×D4414yes—
480C42C2×C22⋊D1112yes—
481C42C2×C22⋊D1114yes—
482C11#2253211yescharacteristic, complemented, Sylow
483C23—112no—
484C23—114no—
485C23—222no—
486C23—221no—
487C23—221no—
488C23—222no—
489C23—222no—
490C23—221no—
491C23—222no—
492C23—221no—
493C23—221no—
494C23—222no—
495C23—221no—
496C23—222no—
497C23C22×C4×D1111yescharacteristic
498Q8—28no—
499D4—2216no—
500D4—228no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—112no—
508C2×C4—112no—
509C2×C4—2216no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—228no—
515C2×C4—222no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—222no—
519C2×C4—221no—
520C2×C4—222no—
521C2×C4—444no—
522C2×C4—448no—
523C2×C4—441no—
524C2×C4—442no—
525C2×C4—441no—
526C2×C4—442no—
527C2×C4—441no—
528C2×C4—442no—
529C2×C4—441no—
530C2×C4—442no—
531C2×C4M16×D1112yes—
532C2×C4M16×D1112yes—
533C2×C4C2×(C2×D11)⋊C412yes—
534C2×C4C2×(C2×D11)⋊C414yes—
535C2×C4C2×(C2×D11)⋊C414yes—
536C2×C4C2×(C2×D11)⋊C412yes—
537C2×C4C22×D4411yescharacteristic
538C2×C4C2×#434311yescharacteristic
539C2×C4#6704011yescharacteristic
540C2×C4#41×D1111yescharacteristic
541C2×C4#6704211yescharacteristic
542C2×C4C22×C22⋊D1111yescharacteristic
543C8—22no—
544C8—41no—
545C8—42no—
546C8—222no—
547C8—441no—
548C8—442no—
549C22—224no—
550C22—222no—
551C22—222no—
552C22—224no—
553C22—222no—
554C22—224no—
555C22—441no—
556C22—442no—
557C22—442no—
558C22—441no—
559C22—442no—
560C22—441no—
561C22—442no—
562C22—441no—
563C22C4×#434311yescharacteristic
564C22#1062310511yescharacteristic
565C22C2×M16×D1111yescharacteristic
566C22C2×M16×D1111yescharacteristic
567C22D11×#13111yescharacteristic
568C22#1062328111yescharacteristic
569C22C22×(C2×D11)⋊C411yescharacteristic
570C4—24no—
571C4—22no—
572C4—24no—
573C4—222no—
574C4—222no—
575C4—442no—
576C4—441no—
577C4#1062273914yes—
578C4#1062310711yescharacteristic
579C4#1062310811yescharacteristic
580C4#1062334811yescharacteristic
581C4#1062336511yescharacteristic
582C2—442no—
583C2—444no—
584C2#1307145411yescharacteristic
585C2C2×#1062273911yescharacteristic
586C2#1307706311yescharacteristic
587C2#1307758111yescharacteristic
588C2#1307762911yescharacteristic
589C2#1307773211yescharacteristic
590C2#1307774011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#446C2
prime radicalC22×#4343C4
cosocleC22×C4×C11C24
hypercenterC2×#446D11
hypocenterC11#22532
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. C2×#10622637C2semidirect
3. #13069414C2semidirect
4. #13069413C2semidirect
5. #13069410C2semidirect
6. #13069409C2semidirect
7. #13068593C2semidirect
8. #13068593C2semidirect
9. #13068379C2semidirect
10. C4×(C2×D11)⋊C8C2semidirect
11. C2×C11×#446C2semidirect
161. C2×C8×C11#41semidirect
187. C2×C11⋊C8#41semidirect
190. C2×#446D11semidirect
464. C2×C8#4343semidirect
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×#43432
C2×#106226372
#130694142
#130694132
#130694102
#130694092
#130685932
#130683792
C4×(C2×D11)⋊C82
C2×C11×#4462
#2253211