Finite Group Databasebeta

← #14770638

Subgroups — #14770638

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic
2C2×#10622637C211yesmaximal, characteristic, complemented
3#13069548C211yesmaximal, characteristic
4#13069548C211yesmaximal, characteristic
5#13069539C211yesmaximal, characteristic, complemented
6#13069435C211yesmaximal, characteristic, complemented
7#13069430C211yesmaximal, characteristic
8#13069425C211yesmaximal, characteristic
9#13068628C211yesmaximal, characteristic, complemented
10#13068623C211yesmaximal, characteristic
11#13068618C211yesmaximal, characteristic, complemented
12#13068449C211yesmaximal, characteristic, complemented
13#13068444C211yesmaximal, characteristic
14C4×#66874C211yesmaximal, characteristic, complemented
15C11×#2355C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999—21no—
18#10623115—24no—
19#10623115C418yescomplemented
20C2×#66951—21no—
21C2×#66951—21no—
22C2×#66945—21no—
23C2×#66928C2211yescharacteristic
24C2×#66928C2211yescharacteristic
25C2×C4×D44C2211yescharacteristic
26C2×#66922C2211yescharacteristic
27C2×C4×Dic22C2211yescharacteristic
28C2×C4×Dic22C2211yescharacteristic
29C11×#391—21no—
30C11×#387—21no—
31C11×#387—21no—
32C11×#384C2211yescharacteristic
33C11×#382C2211yescharacteristic
34C11×#382C2211yescharacteristic
35C4×C11×C4⋊C4—21no—
36C4×C11×C4⋊C4C2211yescharacteristic
37C4×C11×C4⋊C4C2211yescharacteristic
38C4×C11×C4⋊C4C2211yescharacteristic
39#10622637—24no—
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C2×#66873C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55C2×#66867C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57C2×C4×C11⋊C8C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11D411yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×Dic22C2311yescharacteristic
66C22×Dic22C2311yescharacteristic
67C4×Q8×C11C2×C414yes—
68C4×Q8×C11D414yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84#66999—28no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66951—28no—
102#66951—28no—
103#66945—28no—
104#66928—22no—
105#66928—22no—
106#66928C2×C414yes—
107#66928C2×C414yes—
108C4×D44—22no—
109C4×D44C2×C414yes—
110#66922—22no—
111#66922C2×C414yes—
112C4×Dic22—22no—
113C4×Dic22—22no—
114C4×Dic22C2×C414yes—
115C4×Dic22C2×C414yes—
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119C11×#95—21no—
120C11×#95—21no—
121C11×#95—21no—
122C11×#95—21no—
123#66874—22no—
124#66874—22no—
125#66874—22no—
126#66874—22no—
127#66874—41no—
128#66874—41no—
129#66874—41no—
130#66874—41no—
131#66873—22no—
132#66873—22no—
133#66873—41no—
134#66873—41no—
135C4⋊(C11⋊C8)—22no—
136C4⋊(C11⋊C8)—22no—
137C4⋊(C11⋊C8)—22no—
138#66867—22no—
139#66867—22no—
140C4×C11⋊C8—22no—
141#22548—111nomaximal, Sylow
142C23×D11—21no—
143C2×Q8×C11—41no—
144C2×Q8×C11—41no—
145C2×Q8×C11C22⋊C414yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44C22×C412yes—
166C2×C4×D11—24no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22C22×C412yes—
180C2×Dic22C22×C412yes—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4—81no—
190C11×C4⋊C4C22⋊C414yes—
191C11×C4⋊C4C22⋊C414yes—
192C11×C4⋊C4C22⋊C414yes—
193C11×C4⋊C4#4112yes—
194C42×C11—42no—
195C42×C11—81no—
196C42×C11—81no—
197C42×C11C22×C412yes—
198C42×C11C22×C412yes—
199C42×C11C22×C412yes—
200C42×C11C2×D412yes—
201C42×C11C2×D412yes—
202C42×C11C2×D412yes—
203(C2×D11)⋊C4—24no—
204(C2×D11)⋊C4—24no—
205(C2×D11)⋊C4—24no—
206(C2×D11)⋊C4—24no—
207(C2×D11)⋊C4—24no—
208C4⋊Dic11—24no—
209C4⋊Dic11—24no—
210C4⋊Dic11—21no—
211C4⋊Dic11C22×C412yes—
212Dic11⋊C4—24no—
213Dic11⋊C4—24no—
214C4×Dic11—24no—
215C4×Dic11—24no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8#4112yes—
228C2×#556—111no—
229C2×#446—111no—
230#2355D1111yescharacteristic, complemented
231#1983—111no—
232#1983—111no—
233#1981—111no—
234#1960—111no—
235#1959—111no—
236#1958—111no—
237#1805—111no—
238#1804—111no—
239#1803—111no—
240#1763—111no—
241#1762—111no—
242C4×#103—111no—
243C23×C11C22×D411yescharacteristic
244C22×D11—22no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251Q8×C11—44no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11C2×C22⋊C412yes—
277C2×C4×C11C2×C22⋊C412yes—
278C2×C4×C11C2×C22⋊C412yes—
279C2×C4×C11C2×C22⋊C412yes—
280C2×C4×C11C2×C22⋊C412yes—
281C2×C4×C11C2×C22⋊C412yes—
282C2×C4×C11C23×C411yescharacteristic
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C2×C4×C112−1+411yescharacteristic
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297D44—22no—
298D44—22no—
299D44—41no—
300D44—41no—
301C4×D11—48no—
302Dic22—22no—
303Dic22—22no—
304Dic22—22no—
305Dic22—22no—
306Dic22—41no—
307Dic22—41no—
308Dic22—41no—
309Dic22—41no—
310C11⋊C8—22no—
311C11⋊C8—41no—
312C11⋊C8—41no—
313C11⋊C8—41no—
314#556—118no—
315#556—224no—
316C2×C4⋊Q8—111no—
317C2×#126—221no—
318C2×#126—221no—
319C2×#124—111no—
320C2×#124—111no—
321C2×C22⋊Q8—221no—
322C2×C4×Q8—111no—
323C2×C4×Q8—111no—
324C2×C4×Q8C2×D1111yescharacteristic
325C2×C4×D4—111no—
326C2×#117—221no—
327#446—224no—
328C2×C4⋊C8—111no—
329C2×C4⋊C8—111no—
330C2×C4⋊C8—111no—
331C2×#103—111no—
332C2×#103—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103—111no—
339C2×#102—111no—
340C2×#102—111no—
341C2×#102—111no—
342C2×#102—111no—
343C2×#97—111no—
344C2×#97—111no—
345C2×C4×C8—111no—
346#391—21no—
347#387—21no—
348#387—21no—
349#384C2×D1111yescharacteristic
350#382C2×D1111yescharacteristic
351#382C2×D1111yescharacteristic
352C4×C4⋊C4—21no—
353C4×C4⋊C4C2×D1111yescharacteristic
354C4×C4⋊C4C2×D1111yescharacteristic
355C4×C4⋊C4C2×D1111yescharacteristic
356#340—111no—
357#340—111no—
358#340—111no—
359#340—111no—
360C22×C11C22×C22⋊C411yescharacteristic
361C22×C11#54811yescharacteristic
362C22×C11#55011yescharacteristic
363C22×C11#57511yescharacteristic
364C22×C11#57511yescharacteristic
365C22×C11#57711yescharacteristic
366C22×C11#57811yescharacteristic
367C2×D11—42no—
368C2×D11—42no—
369C2×D11—42no—
370C2×D11—81no—
371C2×D11—81no—
372C2×D11—81no—
373C2×D11—81no—
374C4×C11—22no—
375C4×C11—22no—
376C4×C11—22no—
377C4×C11—22no—
378C4×C11—22no—
379C4×C11—22no—
380C4×C11—42no—
381C4×C11—81no—
382C4×C11—81no—
383C4×C11—81no—
384C4×C11C4×#4111yescharacteristic
385C4×C11#52011yescharacteristic
386C4×C11#54811yescharacteristic
387C4×C11#55011yescharacteristic
388Dic11—42no—
389Dic11—42no—
390Dic11—42no—
391C22×Q8—111no—
392C22×Q8—111no—
393C22×Q8C22⋊D1111yescharacteristic
394C22×D4—111no—
395C23×C4—221no—
396C22×C8—111no—
397C22×C8—111no—
398C22×C8—111no—
399C22×C8—111no—
400C4⋊Q8—114no—
401C4⋊Q8—222no—
402#126—228no—
403#126—228no—
404#124—114no—
405#124—114no—
406#124—222no—
407#124—222no—
408C22⋊Q8—228no—
409C4×Q8—114no—
410C4×Q8—114no—
411C4×Q8—222no—
412C4×Q8—222no—
413C4×Q8C4×D1114yes—
414C4×Q8D4414yes—
415C4×D4—114no—
416C4×D4—222no—
417#117—228no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4C22⋊D1111yescharacteristic
426C2×C4⋊C4C22⋊D1111yescharacteristic
427C2×C4⋊C4C22⋊D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—221no—
441C2×C42—221no—
442C2×C42C22×D1111yescharacteristic
443C2×C42C22×D1111yescharacteristic
444C2×C42C22×D1111yescharacteristic
445C4⋊C8—222no—
446C4⋊C8—222no—
447C4⋊C8—222no—
448#103—222no—
449#103—222no—
450#103—222no—
451#103—222no—
452#103—441no—
453#103—441no—
454#103—441no—
455#103—441no—
456#102—222no—
457#102—222no—
458#102—441no—
459#102—441no—
460#97—222no—
461#97—222no—
462C4×C8—222no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470C2×C11#234111yescharacteristic
471C2×C11#289611yescharacteristic
472C2×C11#289811yescharacteristic
473C2×C11#337611yescharacteristic
474C2×C11#337711yescharacteristic
475C2×C11#340111yescharacteristic
476C2×C11#340211yescharacteristic
477D11—82no—
478C24—221no—
479C2×Q8—41no—
480C2×Q8—41no—
481C2×Q8—112no—
482C2×Q8—112no—
483C2×Q8—221no—
484C2×Q8—221no—
485C2×Q8—221no—
486C2×Q8—221no—
487C2×Q8—221no—
488C2×Q8—221no—
489C2×Q8—221no—
490C2×Q8—221no—
491C2×Q8—221no—
492C2×Q8—221no—
493C2×Q8(C2×D11)⋊C414yes—
494C2×D4—112no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—221no—
498C2×D4—221no—
499C2×D4—221no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—224no—
508C22×C4—442no—
509C22×C4—442no—
510C22×C4C2×C22⋊D1111yescharacteristic
511C22×C4C2×C22⋊D1111yescharacteristic
512C22×C4C2×C22⋊D1111yescharacteristic
513C22×C4C2×C22⋊D1111yescharacteristic
514C22×C4C2×C22⋊D1111yescharacteristic
515C22×C4C2×C22⋊D1111yescharacteristic
516C22×C4C23×D1111yescharacteristic
517C2×C8—112no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—42no—
537C4⋊C4—81no—
538C4⋊C4—112no—
539C4⋊C4—224no—
540C4⋊C4—224no—
541C4⋊C4—224no—
542C4⋊C4—224no—
543C4⋊C4—221no—
544C4⋊C4(C2×D11)⋊C414yes—
545C4⋊C4(C2×D11)⋊C414yes—
546C4⋊C4(C2×D11)⋊C414yes—
547C4⋊C4#434312yes—
548C22⋊C4—224no—
549C22⋊C4—224no—
550C22⋊C4—224no—
551C22⋊C4—224no—
552C22⋊C4—224no—
553C42—42no—
554C42—81no—
555C42—81no—
556C42—224no—
557C42—224no—
558C42C2×C4×D1112yes—
559C42C2×C4×D1112yes—
560C42C2×C4×D1112yes—
561C42C2×D4412yes—
562C42C2×D4412yes—
563C42C2×D4412yes—
564C11#2254811yescharacteristic, complemented, Sylow
565C23—222no—
566C23—441no—
567C23—441no—
568C23—441no—
569C23—441no—
570C23—441no—
571C23—441no—
572C23C22×C22⋊D1111yescharacteristic
573Q8—44no—
574Q8—222no—
575Q8—222no—
576Q8—222no—
577Q8—222no—
578Q8—441no—
579Q8—441no—
580Q8—441no—
581Q8—441no—
582D4—222no—
583D4—222no—
584D4—441no—
585D4—441no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—448no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4C2×(C2×D11)⋊C412yes—
621C2×C4C2×(C2×D11)⋊C412yes—
622C2×C4C2×(C2×D11)⋊C412yes—
623C2×C4C2×(C2×D11)⋊C412yes—
624C2×C4C2×(C2×D11)⋊C412yes—
625C2×C4C2×(C2×D11)⋊C412yes—
626C2×C4C22×C4×D1111yescharacteristic
627C2×C4C22×D4411yescharacteristic
628C2×C4C2×#434311yescharacteristic
629C2×C4#6704011yescharacteristic
630C2×C4#41×D1111yescharacteristic
631C2×C4#6704211yescharacteristic
632C8—222no—
633C8—441no—
634C8—441no—
635C8—441no—
636C22—442no—
637C22—442no—
638C22—442no—
639C22—881no—
640C22—881no—
641C22—881no—
642C22—881no—
643C22C22×(C2×D11)⋊C411yescharacteristic
644C22#1062334811yescharacteristic
645C22#1062335311yescharacteristic
646C22#1062335311yescharacteristic
647C22#1062336511yescharacteristic
648C22#1062336711yescharacteristic
649C22#1062336911yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—22no—
654C4—22no—
655C4—22no—
656C4—42no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4—442no—
661C4—442no—
662C4—442no—
663C4C4×#434311yescharacteristic
664C4#1062310511yescharacteristic
665C4#1062310711yescharacteristic
666C4#1062310811yescharacteristic
667C2—882no—
668C2#1307145411yescharacteristic
669C2#1307713311yescharacteristic
670C2#1307714611yescharacteristic
671C2#1308144311yescharacteristic
672C2#1308145811yescharacteristic
673C2#1308167611yescharacteristic
674C2#1308169111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2355C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#2355D11
hypocenterC11#22548
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2355

Complements

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

NH ≅ G/Ntype
2. C2×#10622637C2semidirect
5. #13069539C2semidirect
6. #13069435C2semidirect
9. #13068628C2semidirect
11. #13068618C2semidirect
12. #13068449C2semidirect
14. C4×#66874C2semidirect
15. C11×#2355C2semidirect
19. #10623115C4semidirect
230. #2355D11semidirect
564. C11#22548semidirect

Maximal subgroups

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

subgroupindex
C2×#106231152
C2×#106226372
#130695482
#130695392
#130694352
#130694302
#130694252
#130686282
#130686232
#130686182
#130684492
#130684442
C4×#668742
C11×#23552
#2254811