Finite Group Databasebeta

← #14770643

Subgroups — #14770643

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×#10623263C211yesmaximal, characteristic
2C2×#10622314C211yesmaximal, characteristic, complemented
3#13071568C211yesmaximal, characteristic, complemented
4#13069545C211yesmaximal, characteristic
5#13069545C211yesmaximal, characteristic
6#13069540C211yesmaximal, characteristic, complemented
7#13069429C211yesmaximal, characteristic
8#13069424C211yesmaximal, characteristic
9#13068629C211yesmaximal, characteristic, complemented
10#13068623C211yesmaximal, characteristic
11#13068619C211yesmaximal, characteristic, complemented
12#13068448C211yesmaximal, characteristic, complemented
13#13068442C211yesmaximal, characteristic
14#103×Dic11C211yesmaximal, characteristic, complemented
15C11×#1960C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×#67000C2211yescharacteristic
18C2×#67000C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21#10623263—24no—
22#10623263C418yescomplemented
23C2×#66951—21no—
24C2×#66951—21no—
25C2×#66950—21no—
26C2×#66945—21no—
27C2×C4×D44C2211yescharacteristic
28C2×C4×Dic22C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#97C2211yescharacteristic
34C11×#382C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×#66885C2211yescharacteristic
41C2×#66879C2211yescharacteristic
42C2×Dic11⋊C8C2211yescharacteristic
43C2×Dic11⋊C8C2211yescharacteristic
44C2×C8×Dic11C2211yescharacteristic
45#10622590C2211yescharacteristic
46#10622589C2211yescharacteristic
47C4⋊C4×Dic11C2211yescharacteristic
48C4⋊C4×Dic11C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C4×C4⋊Dic11C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622314—24no—
54#10622266—21no—
55#10622265—21no—
56#10622262—21no—
57#10622259—21no—
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×Dic22D411yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8C2×C414yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76#67000—22no—
77#67000—22no—
78#67000C2×C414yes—
79#67000C2×C414yes—
80Q8×Dic11—22no—
81Q8×Dic11—22no—
82Q8×Dic11C2×C414yes—
83Q8×Dic11C2×C414yes—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11D411yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4D411yescharacteristic
98C2×Dic11⋊C4D411yescharacteristic
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108#66951—28no—
109#66951—28no—
110#66950—28no—
111#66945—28no—
112C4×D44—22no—
113C4×D44C2×C414yes—
114C4×Dic22C2×C414yes—
115C4×Dic22D414yes—
116C11×#103—22no—
117C11×#103—22no—
118C11×#103—41no—
119C11×#103—41no—
120C11×#97—22no—
121C11×#95—21no—
122C11×#95—21no—
123#66899—22no—
124#66899—22no—
125#66899—41no—
126#66899—41no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132#66885—22no—
133#66885—22no—
134#66879—22no—
135Dic11⋊C8—22no—
136Dic11⋊C8—22no—
137C8×Dic11—22no—
138#66873—41no—
139#66873—41no—
140C4⋊(C11⋊C8)—22no—
141#22548—111nomaximal, Sylow
142C23×D11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11C22×C412yes—
154C2×Q8×C11C22×C412yes—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2411yescharacteristic
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C2×D44—21no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44C22×C412yes—
175C2×C4×D11—24no—
176C2×C4×D11—42no—
177C2×C4×D11—42no—
178C2×Dic22—41no—
179C2×Dic22—41no—
180C2×Dic22C22⋊C414yes—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11#4112yes—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C42×C11C22×C412yes—
194C42×C11C2×D412yes—
195(C2×D11)⋊C4—24no—
196(C2×D11)⋊C4—24no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—24no—
199(C2×D11)⋊C4—24no—
200C4⋊Dic11—24no—
201C4⋊Dic11—24no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11C22⋊C414yes—
207C4⋊Dic11C22×C412yes—
208C4⋊Dic11#4112yes—
209Dic11⋊C4—42no—
210Dic11⋊C4—81no—
211Dic11⋊C4C22⋊C414yes—
212Dic11⋊C4C22⋊C414yes—
213C4×Dic11—24no—
214C4×Dic11—24no—
215C4×Dic11—42no—
216C4×Dic11—81no—
217C4×Dic11—81no—
218C4×Dic11C22×C412yes—
219C4×Dic11C22×C412yes—
220C4×Dic11C2×D412yes—
221C4×Dic11C2×D412yes—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×#556—111no—
229C2×#446—111no—
230#2355—111no—
231#1983—111no—
232#1983—111no—
233#1981—111no—
234#1960D1111yescharacteristic, complemented
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—22no—
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—22no—
255Q8×C11—41no—
256Q8×C11—41no—
257Q8×C11—41no—
258Q8×C11—41no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
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×C11C2×C22⋊C412yes—
276C2×C4×C11C2×C22⋊C412yes—
277C2×C4×C11C23×C411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11H(5,𝔽2)11yescharacteristic
282C2×C4×C112−1+411yescharacteristic
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11C2×C22⋊C412yes—
301C2×Dic11C2×C22⋊C412yes—
302C2×Dic11C2×C22⋊C412yes—
303C2×Dic11C2×C22⋊C412yes—
304D44—22no—
305D44—22no—
306D44—41no—
307D44—41no—
308C4×D11—48no—
309Dic22—44no—
310C8×C11—22no—
311C8×C11—41no—
312C11⋊C8—41no—
313C11⋊C8—41no—
314#556—118no—
315#556—224no—
316C2×C4⋊Q8C2×D1111yescharacteristic
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×Q8—111no—
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×#103C2×D1111yescharacteristic
336C2×#103C2×D1111yescharacteristic
337C2×#103C2×D1111yescharacteristic
338C2×#103C2×D1111yescharacteristic
339C2×#102—111no—
340C2×#102—111no—
341C2×#102—111no—
342C2×#102—111no—
343C2×#97—111no—
344C2×#97C2×D1111yescharacteristic
345C2×C4×C8—111no—
346#391—221no—
347#387—221no—
348#387—221no—
349#384—111no—
350#382—111no—
351#382C2×D1111yescharacteristic
352C4×C4⋊C4—111no—
353C4×C4⋊C4—111no—
354C4×C4⋊C4—111no—
355C4×C4⋊C4—221no—
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—42no—
377C4×C11—42no—
378C4×C11—81no—
379C4×C11—81no—
380C4×C11C4×#4111yescharacteristic
381C4×C11#52011yescharacteristic
382C4×C11#54811yescharacteristic
383C4×C11#55011yescharacteristic
384Dic11—22no—
385Dic11—22no—
386Dic11—22no—
387Dic11—22no—
388Dic11—42no—
389Dic11—42no—
390Dic11—81no—
391C22×Q8—111no—
392C22×Q8C22×D1111yescharacteristic
393C22×Q8C22×D1111yescharacteristic
394C22×D4—111no—
395C23×C4—221no—
396C22×C8—111no—
397C22×C8—111no—
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400C4⋊Q8—22no—
401C4⋊Q8C4×D1114yes—
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—114no—
412C4×Q8—114no—
413C4×Q8—222no—
414C4×Q8—222no—
415C4×D4—114no—
416C4×D4—222no—
417#117—228no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
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—111no—
438C2×C42—111no—
439C2×C42—221no—
440C2×C42—221no—
441C2×C42—221no—
442C2×C42—221no—
443C2×C42—221no—
444C2×C42C22×D1111yescharacteristic
445C4⋊C8—222no—
446C4⋊C8—222no—
447C4⋊C8—222no—
448#103—22no—
449#103—22no—
450#103—41no—
451#103—41no—
452#103—222no—
453#103—222no—
454#103—441no—
455#103—441no—
456#102—222no—
457#102—222no—
458#102—441no—
459#102—441no—
460#97—22no—
461#97—222no—
462C4×C8—222no—
463#95—21no—
464#95—21no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
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—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—114no—
490C2×Q8—441no—
491C2×Q8—441no—
492C2×Q8C2×C4×D1112yes—
493C2×Q8C2×C4×D1112yes—
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—111no—
505C22×C4—111no—
506C22×C4—111no—
507C22×C4—111no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—224no—
511C22×C4—221no—
512C22×C4—442no—
513C22×C4—442no—
514C22×C4D4×D1111yescharacteristic
515C22×C4D4×D1111yescharacteristic
516C22×C4C23×D1111yescharacteristic
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8#434112yes—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—114no—
536C4⋊C4—114no—
537C4⋊C4—114no—
538C4⋊C4—112no—
539C4⋊C4—112no—
540C4⋊C4—224no—
541C4⋊C4—224no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—442no—
547C4⋊C4—881no—
548C22⋊C4—224no—
549C22⋊C4—224no—
550C22⋊C4—224no—
551C22⋊C4—224no—
552C22⋊C4—224no—
553C42—112no—
554C42—112no—
555C42—112no—
556C42—112no—
557C42—224no—
558C42—224no—
559C42—442no—
560C42—881no—
561C42—881no—
562C42C2×C4×D1112yes—
563C42D4×D1112yes—
564C11#2254811yescharacteristic, complemented, Sylow
565C23—222no—
566C23—441no—
567C23—441no—
568C23—441no—
569C23—441no—
570C23—441no—
571C23—441no—
572C23C2×D4×D1111yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—22no—
576Q8—22no—
577Q8—41no—
578Q8—41no—
579Q8—41no—
580Q8—41no—
581Q8—444no—
582D4—222no—
583D4—222no—
584D4—441no—
585D4—441no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—112no—
603C2×C4—112no—
604C2×C4—112no—
605C2×C4—112no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—448no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4C22⋊C4×D1112yes—
625C2×C4C22⋊C4×D1112yes—
626C2×C4C22×C4×D1111yescharacteristic
627C2×C4C2×D4×D1111yescharacteristic
628C2×C4C2×#434111yescharacteristic
629C2×C4#6703711yescharacteristic
630C2×C4#41×D1111yescharacteristic
631C2×C4#6704311yescharacteristic
632C8—22no—
633C8—41no—
634C8—441no—
635C8—441no—
636C22—442no—
637C22—442no—
638C22—442no—
639C22—881no—
640C22—881no—
641C22—881no—
642C22—881no—
643C22C2×C22⋊C4×D1111yescharacteristic
644C22#1062320811yescharacteristic
645C22#1062324911yescharacteristic
646C22#1062330811yescharacteristic
647C22#1062330811yescharacteristic
648C22#1062330911yescharacteristic
649C22#1062331011yescharacteristic
650C4—22no—
651C4—22no—
652C4—42no—
653C4—42no—
654C4—81no—
655C4—81no—
656C4—222no—
657C4—222no—
658C4—222no—
659C4—222no—
660C4—442no—
661C4—442no—
662C4—881no—
663C4C4×#434111yescharacteristic
664C4#1062307711yescharacteristic
665C4#1062312911yescharacteristic
666C4#1062313011yescharacteristic
667C2—882no—
668C2#1307145511yescharacteristic
669C2#1307713411yescharacteristic
670C2#1307714811yescharacteristic
671C2#1308143811yescharacteristic
672C2#1308145311yescharacteristic
673C2#1308168111yescharacteristic
674C2#1308169211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1960C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1960D11
hypocenterC11#22548
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
2. C2×#10622314C2semidirect
3. #13071568C2semidirect
6. #13069540C2semidirect
9. #13068629C2semidirect
11. #13068619C2semidirect
12. #13068448C2semidirect
14. #103×Dic11C2semidirect
15. C11×#1960C2semidirect
22. #10623263C4semidirect
234. #1960D11semidirect
564. C11#22548semidirect

Maximal subgroups

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

subgroupindex
C2×#106232632
C2×#106223142
#130715682
#130695452
#130695402
#130694292
#130694242
#130686292
#130686232
#130686192
#130684482
#130684422
#103×Dic112
C11×#19602
#2254811