Finite Group Databasebeta

← #14770601

Subgroups — #14770601

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623202C211yesmaximal, characteristic
2C2×#10622441C211yesmaximal, characteristic, complemented
3C4⋊C4×Dic22C211yesmaximal, characteristic, complemented
4#13069547C211yesmaximal, characteristic
5#13069537C211yesmaximal, characteristic, complemented
6#13069433C211yesmaximal, characteristic
7#13069431C211yesmaximal, characteristic
8#13069416C211yesmaximal, characteristic, complemented
9#13068622C211yesmaximal, characteristic, complemented
10#13068619C211yesmaximal, characteristic, complemented
11#13068614C211yesmaximal, characteristic
12#13068449C211yesmaximal, characteristic, complemented
13#13068448C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, characteristic
15C11×#1983C211yesmaximal, characteristic
16C2×C11×#124C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×#66997C2211yescharacteristic
19C2×#66989C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21#10623202—24no—
22#10623202C418yescomplemented
23C2×#66932—21no—
24C2×#66932—21no—
25C2×#66931—21no—
26C2×#66930—21no—
27C2×C4×Dic22—21no—
28C2×C4×Dic22C2211yescharacteristic
29C2×C4×Dic22C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C4×C11×C4⋊C4C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66880C2211yescharacteristic
41C2×#66880C2211yescharacteristic
42C2×#66879C2211yescharacteristic
43C2×Dic11⋊C8C2211yescharacteristic
44C2×Dic11⋊C8C2211yescharacteristic
45C2×C8×Dic11C2211yescharacteristic
46#10622589C2211yescharacteristic
47#10622589C2211yescharacteristic
48C4⋊C4×Dic11C2211yescharacteristic
49C4⋊C4×Dic11C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×#66874C2211yescharacteristic
52#10622548C2211yescharacteristic
53#10622541—21no—
54C2×#66867C2211yescharacteristic
55#10622441—24no—
56#10622260—21no—
57#10622260—21no—
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C22×Dic22D411yescharacteristic
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×#124—22no—
70C11×#124C2×C414yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80Q8×Dic11—22no—
81Q8×Dic11C2×C414yes—
82#66997—22no—
83#66997C2×C414yes—
84#66989—22no—
85#66989C2×C414yes—
86D4×Dic11—22no—
87D4×Dic11C2×C414yes—
88C2×C4⋊Dic11—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⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4D411yescharacteristic
103C2×Dic11⋊C4D411yescharacteristic
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112#66932—28no—
113#66932—28no—
114#66931—28no—
115#66930—28no—
116C4×Dic22—22no—
117C4×Dic22—44no—
118C4×Dic22C2×C414yes—
119C4×Dic22C2×C414yes—
120C4×Dic22D414yes—
121C11×C4⋊C8—22no—
122C11×#103—22no—
123C11×#103—41no—
124C11×#102—22no—
125C11×#102—41no—
126C11×#95—21no—
127#66899—22no—
128#66899—41no—
129#66896—22no—
130#66896—41no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133#66880—41no—
134#66880—41no—
135#66879—22no—
136Dic11⋊C8—22no—
137Dic11⋊C8—22no—
138C8×Dic11—22no—
139#66874—22no—
140#66874—22no—
141#66867—22no—
142#22544—111nomaximal, Sylow
143C24×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C22×C412yes—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11C22×C412yes—
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—24no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—42no—
168C22×Dic11—42no—
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D411yescharacteristic
173C2×Dic22—22no—
174C2×Dic22—22no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22—21no—
180C2×Dic22C22⋊C414yes—
181C2×Dic22C22×C412yes—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4#4112yes—
192C11×C22⋊C4—24no—
193C11×C22⋊C4—24no—
194C42×C11—42no—
195C42×C11C22×C412yes—
196C42×C11C2×D412yes—
197C22⋊Dic11—24no—
198C22⋊Dic11—24no—
199C22⋊Dic11—24no—
200C4⋊Dic11—24no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—42no—
207C4⋊Dic11—81no—
208C4⋊Dic11C22⋊C414yes—
209C4⋊Dic11C22×C412yes—
210Dic11⋊C4—24no—
211Dic11⋊C4—24no—
212Dic11⋊C4—24no—
213Dic11⋊C4—42no—
214Dic11⋊C4—42no—
215Dic11⋊C4—81no—
216Dic11⋊C4—81no—
217Dic11⋊C4C22⋊C414yes—
218Dic11⋊C4C22⋊C414yes—
219C4×Dic11—24no—
220C4×Dic11—24no—
221C4×Dic11—42no—
222C4×Dic11—42no—
223C4×Dic11C22×C412yes—
224C4×Dic11C22×C412yes—
225C4×Dic11C2×D412yes—
226C4×Dic11C2×D412yes—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8#4112yes—
233C2×#556—111no—
234C2×#446—111no—
235Q8×C4⋊C4—111no—
236#1983—111no—
237#1983D1111yescharacteristic
238#1981—111no—
239#1959—111no—
240#1959—111no—
241#1956—111no—
242#1803—111no—
243#1803—111no—
244#1802—111no—
245#1763—111no—
246#1763—111no—
247C4×#102—111no—
248C23×C11—22no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11C22×D411yescharacteristic
256Q8×C11—22no—
257Q8×C11—22no—
258Q8×C11—41no—
259Q8×C11—41no—
260D4×C11—22no—
261D4×C11—22no—
262D4×C11—41no—
263D4×C11—41no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
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×C11—41no—
277C2×C4×C11C2×C22⋊C412yes—
278C2×C4×C11C2×C22⋊C412yes—
279C2×C4×C11C23×C411yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×C4×C112−1+411yescharacteristic
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—48no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11C2×C22⋊C412yes—
305C2×Dic11C2×C22⋊C412yes—
306C2×Dic11C2×C22⋊C412yes—
307C2×Dic11C2×C22⋊C412yes—
308C2×Dic11AGL(1,ℤ/8)12yes—
309C2×Dic11#13712yes—
310Dic22—28no—
311Dic22—22no—
312Dic22—22no—
313Dic22—41no—
314Dic22—41no—
315C8×C11—41no—
316C8×C11—41no—
317C11⋊C8—22no—
318C11⋊C8—41no—
319#556—118no—
320#556—224no—
321C2×C4⋊Q8—111no—
322C2×#126—221no—
323C2×#126—221no—
324C2×#124—111no—
325C2×#124C2×D1111yescharacteristic
326C2×C22⋊Q8—221no—
327C2×C4×Q8—111no—
328C2×C4×Q8—111no—
329C2×C4×Q8—111no—
330C2×C4×Q8—221no—
331C2×C4×D4—111no—
332C2×#117—221no—
333#446—224no—
334C2×C4⋊C8—111no—
335C2×C4⋊C8—111no—
336C2×C4⋊C8C2×D1111yescharacteristic
337C2×#103—111no—
338C2×#103—111no—
339C2×#103—111no—
340C2×#103—111no—
341C2×#103—111no—
342C2×#103—111no—
343C2×#103C2×D1111yescharacteristic
344C2×#103C2×D1111yescharacteristic
345C2×#102—111no—
346C2×#102—111no—
347C2×#102C2×D1111yescharacteristic
348C2×#102C2×D1111yescharacteristic
349C2×#97—111no—
350C2×#97—111no—
351C2×C4×C8—111no—
352#389—221no—
353#389—221no—
354#389—221no—
355#384—111no—
356#384—111no—
357#384—111no—
358C4×C4⋊C4—111no—
359C4×C4⋊C4—111no—
360C4×C4⋊C4C2×D1111yescharacteristic
361#340—111no—
362#340—111no—
363#340—111no—
364#340—111no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11—81no—
372C22×C11C22×C22⋊C411yescharacteristic
373C22×C11#54811yescharacteristic
374C22×C11#55011yescharacteristic
375C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C11C2×#13711yescharacteristic
377C22×C11#57711yescharacteristic
378C22×C11#57811yescharacteristic
379C4×C11—22no—
380C4×C11—22no—
381C4×C11—42no—
382C4×C11—42no—
383C4×C11—81no—
384C4×C11C4×#4111yescharacteristic
385C4×C11#52011yescharacteristic
386C4×C11#54811yescharacteristic
387C4×C11#55011yescharacteristic
388Dic11—22no—
389Dic11—22no—
390Dic11—22no—
391Dic11—42no—
392Dic11—42no—
393Dic11—81no—
394Dic11—81no—
395Dic11#41714yes—
396C22×Q8—111no—
397C22×Q8—111no—
398C22×Q8C22×D1111yescharacteristic
399C22×D4C22×D1111yescharacteristic
400C23×C4—221no—
401C22×C8—111no—
402C22×C8—111no—
403C22×C8C22×D1111yescharacteristic
404C22×C8C22×D1111yescharacteristic
405C4⋊Q8—114no—
406C4⋊Q8—222no—
407#126—228no—
408#126—228no—
409#124—22no—
410#124—114no—
411#124—222no—
412#124C4×D1114yes—
413C22⋊Q8—228no—
414C4×Q8—114no—
415C4×Q8—114no—
416C4×Q8—114no—
417C4×Q8—114no—
418C4×Q8—222no—
419C4×Q8—222no—
420C4×Q8—444no—
421C4×D4—114no—
422C4×D4—222no—
423#117—228no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C42—21no—
448C2×C42—111no—
449C2×C42—111no—
450C2×C42—221no—
451C2×C42—221no—
452C2×C42—221no—
453C2×C42—221no—
454C2×C42C22×D1111yescharacteristic
455C4⋊C8—22no—
456C4⋊C8—222no—
457C4⋊C8—222no—
458#103—22no—
459#103—41no—
460#103—222no—
461#103—222no—
462#103—222no—
463#103—441no—
464#103—441no—
465#103—441no—
466#102—22no—
467#102—41no—
468#102—222no—
469#102—441no—
470#97—222no—
471#97—222no—
472C4×C8—222no—
473#95—21no—
474#95—221no—
475#95—221no—
476C2×C11—82no—
477C2×C11#234111yescharacteristic
478C2×C11C2×#41711yescharacteristic
479C2×C11#289811yescharacteristic
480C2×C11#336711yescharacteristic
481C2×C11#336911yescharacteristic
482C2×C11#339711yescharacteristic
483C2×C11#339811yescharacteristic
484C24—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—114no—
491C2×Q8—112no—
492C2×Q8—222no—
493C2×Q8—222no—
494C2×Q8—221no—
495C2×Q8—221no—
496C2×Q8—221no—
497C2×Q8—221no—
498C2×Q8—221no—
499C2×Q8C2×C4×D1112yes—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4C2×C4×D1112yes—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—111no—
510C22×C4—111no—
511C22×C4—111no—
512C22×C4—111no—
513C22×C4—224no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—442no—
519C22×C4—442no—
520C22×C4D4×D1111yescharacteristic
521C22×C4D4×D1111yescharacteristic
522C22×C4C23×D1111yescharacteristic
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—112no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—114no—
539C4⋊C4—114no—
540C4⋊C4—114no—
541C4⋊C4—112no—
542C4⋊C4—224no—
543C4⋊C4—224no—
544C4⋊C4—224no—
545C4⋊C4—224no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—442no—
552C4⋊C4—442no—
553C4⋊C4—442no—
554C4⋊C4—881no—
555C4⋊C4—881no—
556C4⋊C4—881no—
557C4⋊C4#434112yes—
558C22⋊C4—24no—
559C22⋊C4—24no—
560C22⋊C4—224no—
561C22⋊C4—224no—
562C22⋊C4—224no—
563C42—42no—
564C42—112no—
565C42—112no—
566C42—112no—
567C42—112no—
568C42—224no—
569C42—224no—
570C42—442no—
571C42—442no—
572C42C2×C4×D1112yes—
573C42D4×D1112yes—
574C11#2254411yescharacteristic, complemented, Sylow
575C23—22no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23C2×D4×D1111yescharacteristic
583Q8—22no—
584Q8—22no—
585Q8—41no—
586Q8—41no—
587Q8—228no—
588Q8—222no—
589Q8—222no—
590Q8—441no—
591Q8—441no—
592D4—22no—
593D4—22no—
594D4—41no—
595D4—41no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—112no—
610C2×C4—112no—
611C2×C4—112no—
612C2×C4—112no—
613C2×C4—112no—
614C2×C4—112no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—448no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4C22⋊C4×D1112yes—
635C2×C4C22⋊C4×D1112yes—
636C2×C4C22×C4×D1111yescharacteristic
637C2×C4C2×D4×D1111yescharacteristic
638C2×C4C2×#434111yescharacteristic
639C2×C4#6703711yescharacteristic
640C2×C4#41×D1111yescharacteristic
641C2×C4#6704311yescharacteristic
642C8—41no—
643C8—41no—
644C8—222no—
645C8—441no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22C2×C22⋊C4×D1111yescharacteristic
654C22#1062312911yescharacteristic
655C22#1062313011yescharacteristic
656C22#1062330111yescharacteristic
657C22#1062330211yescharacteristic
658C22D11×AGL(1,ℤ/8)11yescharacteristic
659C22D11×#13711yescharacteristic
660C4—22no—
661C4—22no—
662C4—42no—
663C4—42no—
664C4—81no—
665C4—114no—
666C4—222no—
667C4—222no—
668C4—222no—
669C4—442no—
670C4—442no—
671C4—881no—
672C4—881no—
673C4C4×#434111yescharacteristic
674C4#1062307711yescharacteristic
675C4#1062320811yescharacteristic
676C4#1062324911yescharacteristic
677C2—82no—
678C2#1307145511yescharacteristic
679C2D11×#41711yescharacteristic
680C2#1307714511yescharacteristic
681C2#1308132911yescharacteristic
682C2#1308135111yescharacteristic
683C2#1308163911yescharacteristic
684C2#1308165011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1983C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1983D11
hypocenterC11#22544
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1983

Complements

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

NH ≅ G/Ntype
2. C2×#10622441C2semidirect
3. C4⋊C4×Dic22C2semidirect
5. #13069537C2semidirect
8. #13069416C2semidirect
9. #13068622C2semidirect
10. #13068619C2semidirect
12. #13068449C2semidirect
13. #13068448C2semidirect
22. #10623202C4semidirect
574. C11#22544semidirect

Maximal subgroups

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

subgroupindex
C2×#106232022
C2×#106224412
C4⋊C4×Dic222
#130695472
#130695372
#130694332
#130694312
#130694162
#130686222
#130686192
#130686142
#130684492
#130684482
#102×Dic112
C11×#19832
#2254411