Finite Group Databasebeta

← #14770401

Subgroups — #14770401

Order 2816.

1110 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623221C211yesmaximal, characteristic
2C2×#10622441C211yesmaximal, characteristic, complemented
3C4⋊C4×Dic22C211yesmaximal, characteristic, complemented
4#13069586C211yesmaximal, characteristic, complemented
5#13069583C211yesmaximal, characteristic, complemented
6#13069575C211yesmaximal, characteristic, complemented
7#13069570C211yesmaximal, characteristic, complemented
8#13069562C211yesmaximal, characteristic, complemented
9#13068617C211yesmaximal, characteristic
10#13068615C211yesmaximal, characteristic
11#13068615C211yesmaximal, characteristic
12#13068444C211yesmaximal, characteristic
13#13068440C211yesmaximal, characteristic
14#13068430C211yesmaximal, characteristic
15C11×#1989C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17#10623221—24no—
18#10623221C418yescomplemented
19C2×#66950—21no—
20C2×#66949—21no—
21C2×#66949—21no—
22C2×#66946C2211yescharacteristic
23C2×#66946C2211yescharacteristic
24C2×C4⋊C4×D11—21no—
25C2×#66943C2211yescharacteristic
26C2×#66941C2211yescharacteristic
27C2×C4×D44C2211yescharacteristic
28C2×C4×Dic22—21no—
29C2×C4×Dic22C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C4×C11×C4⋊C4C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622589C2211yescharacteristic
39#10622589C2211yescharacteristic
40C4⋊C4×Dic11C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44#10622548C2211yescharacteristic
45#10622541—21no—
46C2×#66867C2211yescharacteristic
47#10622441—24no—
48#10622260—21no—
49#10622260—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×Dic22—21no—
67C22×Dic22D411yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×#125—22no—
71C11×#125C2×C414yes—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11D411yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4D411yescharacteristic
97C2×Dic11⋊C4D411yescharacteristic
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66950—28no—
105#66949—28no—
106#66949—28no—
107#66946—22no—
108#66946—22no—
109#66946C2×C414yes—
110#66946C2×C414yes—
111C4⋊C4×D11—28no—
112#66943—22no—
113#66943C2×C414yes—
114#66941—22no—
115#66941C2×C414yes—
116C4×D44—22no—
117C4×D44C2×C414yes—
118C4×Dic22—44no—
119C4×Dic22C2×C414yes—
120C4×Dic22D414yes—
121C11×C4⋊C8—22no—
122C11×#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125#66885—22no—
126#66885—22no—
127#66879—22no—
128Dic11⋊C8—22no—
129Dic11⋊C8—22no—
130C8×Dic11—22no—
131#66873—22no—
132#66873Q814yescomplemented
133#66867—22no—
134#22522—111nomaximal, Sylow
135C23×D11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44C22×C412yes—
154C2×D44C2×Q812yes—
155C2×D44#4112yes—
156C2×C4×D11—24no—
157C2×C4×D11—24no—
158C2×C4×D11—24no—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11—81no—
162C2×C4×D11—81no—
163C2×C4×D11—81no—
164C2×C4×D11—81no—
165C2×Dic22—22no—
166C2×Dic22—22no—
167C2×Dic22—24no—
168C2×Dic22—81no—
169C2×Dic22—81no—
170C2×Dic22C22⋊C414yes—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4C22×C412yes—
185C11×C4⋊C4C22×C412yes—
186C11×C4⋊C4C2×Q812yes—
187C42×C11—42no—
188C42×C11C22×C412yes—
189C42×C11C2×D412yes—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—24no—
193C4⋊Dic11—24no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—42no—
200C4⋊Dic11—81no—
201C4⋊Dic11C22⋊C414yes—
202C4⋊Dic11C22×C412yes—
203Dic11⋊C4—24no—
204Dic11⋊C4—24no—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207Dic11⋊C4—81no—
208Dic11⋊C4—81no—
209Dic11⋊C4C22⋊C414yes—
210Dic11⋊C4C22⋊C414yes—
211C4×Dic11—42no—
212C4×Dic11—42no—
213C4×Dic11C22×C412yes—
214C4×Dic11C22×C412yes—
215C4×Dic11C2×D412yes—
216C4×Dic11C2×D412yes—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8C2×Q812yes—
223C2×#554—111no—
224C2×#446—111no—
225Q8×C4⋊C4—111no—
226#1992—111no—
227#1992—111no—
228#1990—111no—
229#1989—111no—
230#1989D1111yescharacteristic, complemented
231#1987—111no—
232#1802—111no—
233#1802—111no—
234#1802—111no—
235#1762—111no—
236#1762—111no—
237C4×#102—111no—
238C23×C11C22×D411yescharacteristic
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11C2×C22⋊C412yes—
263C2×C4×C11C2×C22⋊C412yes—
264C2×C4×C11C23×C411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×Q811yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C112−1+411yescharacteristic
269C2×C4×C112−1+411yescharacteristic
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—22no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11C2×C22⋊C412yes—
286C2×Dic11C2×C22⋊C412yes—
287C2×Dic11C2×C22⋊C412yes—
288C2×Dic11C2×C22⋊C412yes—
289C2×Dic11AGL(1,ℤ/8)12yes—
290C2×Dic11#13712yes—
291D44—22no—
292D44—22no—
293D44—22no—
294D44C4×Q814yescomplemented
295C4×D11—48no—
296C4×D11—84no—
297C4×D11—84no—
298Dic22—28no—
299Dic22—84no—
300C8×C11—41no—
301C8×C11—41no—
302C11⋊C8—22no—
303C11⋊C8—41no—
304#554—118no—
305#554—224no—
306C2×C4⋊Q8—111no—
307C2×#125—111no—
308C2×#125C2×D1111yescharacteristic
309C2×C22⋊Q8—221no—
310C2×C22⋊Q8—221no—
311C2×C22⋊Q8—221no—
312C2×C4×Q8—111no—
313C2×C4×Q8—221no—
314C2×C4×D4—111no—
315C2×C4×D4—111no—
316C2×C4×D4—111no—
317C22×C4⋊C4—221no—
318#446—224no—
319C2×C4⋊C8—111no—
320C2×C4⋊C8—111no—
321C2×C4⋊C8C2×D1111yescharacteristic
322C2×#102—111no—
323C2×#102—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×#97—111no—
327C2×#97—111no—
328C2×C4×C8—111no—
329#389—221no—
330#389—221no—
331#389—221no—
332#384—111no—
333#384—111no—
334#384—111no—
335C4×C4⋊C4—111no—
336C4×C4⋊C4—111no—
337C4×C4⋊C4C2×D1111yescharacteristic
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340C2×D1111yescharacteristic
347#340C2×D1111yescharacteristic
348#340C2×D1111yescharacteristic
349#340C2×D1111yescharacteristic
350C22×C11C22×C22⋊C411yescharacteristic
351C22×C11#54811yescharacteristic
352C22×C11D4×Q811yescharacteristic
353C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C11C2×#13711yescharacteristic
355C22×C11#57611yescharacteristic
356C22×C11#57711yescharacteristic
357C2×D11—24no—
358C2×D11—42no—
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—42no—
363C2×D11—42no—
364C4×C11—22no—
365C4×C11—22no—
366C4×C11—42no—
367C4×C11—42no—
368C4×C11—42no—
369C4×C11—81no—
370C4×C11C2×C4×Q811yescharacteristic
371C4×C11#51911yescharacteristic
372C4×C11#54811yescharacteristic
373C4×C11D4×Q811yescharacteristic
374Dic11—22no—
375Dic11—22no—
376Dic11—22no—
377Dic11—42no—
378Dic11—81no—
379Dic11—81no—
380Dic11#41714yes—
381C22×Q8—111no—
382C22×Q8—221no—
383C22×D4—111no—
384C23×C4—221no—
385C23×C4—221no—
386C23×C4—221no—
387C22×C8—111no—
388C22×C8—111no—
389C22×C8C22×D1111yescharacteristic
390C22×C8C22×D1111yescharacteristic
391C4⋊Q8—114no—
392C4⋊Q8—222no—
393#125—22no—
394#125—114no—
395#125—222no—
396#125C4×D1114yes—
397C22⋊Q8—228no—
398C22⋊Q8—228no—
399C22⋊Q8—228no—
400C4×Q8—114no—
401C4×Q8—114no—
402C4×Q8—444no—
403C4×D4—114no—
404C4×D4—114no—
405C4×D4—114no—
406C4×D4—222no—
407C4×D4—222no—
408C4×D4—222no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—228no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C42—21no—
435C2×C42—111no—
436C2×C42—111no—
437C2×C42—221no—
438C2×C42—221no—
439C2×C42C22×D1111yescharacteristic
440C4⋊C8—22no—
441C4⋊C8—222no—
442C4⋊C8—222no—
443#102—114no—
444#102—222no—
445#102—222no—
446#102—222no—
447#97—222no—
448#97—222no—
449C4×C8—222no—
450#95—21no—
451#95—221no—
452#95—221no—
453C2×C11Q8×C22⋊C411yescharacteristic
454C2×C11C2×#41711yescharacteristic
455C2×C11#289711yescharacteristic
456C2×C11#336611yescharacteristic
457C2×C11#337211yescharacteristic
458C2×C11#338411yescharacteristic
459C2×C11#338511yescharacteristic
460D11—44no—
461C24—221no—
462C2×Q8—114no—
463C2×Q8—222no—
464C2×Q8—222no—
465C2×Q8—224no—
466C2×Q8—881no—
467C2×Q8—881no—
468C2×D4—112no—
469C2×D4—112no—
470C2×D4—112no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—221no—
485C22×C4—224no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4—881no—
491C22×C4—881no—
492C22×C4—881no—
493C22×C4—881no—
494C22×C4D4×D1111yescharacteristic
495C22×C4D4×D1111yescharacteristic
496C22×C4C23×D1111yescharacteristic
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—112no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C4⋊C4—24no—
510C4⋊C4—24no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—114no—
517C4⋊C4—114no—
518C4⋊C4—114no—
519C4⋊C4—112no—
520C4⋊C4—224no—
521C4⋊C4—224no—
522C4⋊C4—224no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—442no—
529C4⋊C4—442no—
530C4⋊C4—442no—
531C4⋊C4—881no—
532C4⋊C4—881no—
533C4⋊C4—881no—
534C4⋊C4C2×C4×D1112yes—
535C4⋊C4C2×C4×D1112yes—
536C4⋊C4Q8×D1112yes—
537C22⋊C4—224no—
538C22⋊C4—224no—
539C22⋊C4—224no—
540C42—42no—
541C42—112no—
542C42—112no—
543C42—112no—
544C42—112no—
545C42—442no—
546C42—442no—
547C42C2×C4×D1112yes—
548C42D4×D1112yes—
549C11#2252211yescharacteristic, complemented, Sylow
550C23—222no—
551C23—222no—
552C23—222no—
553C23—441no—
554C23—441no—
555C23—441no—
556C23—441no—
557C23C2×D4×D1111yescharacteristic
558Q8—228no—
559Q8—884no—
560D4—114no—
561D4—222no—
562D4—222no—
563D4—222no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—112no—
581C2×C4—112no—
582C2×C4—112no—
583C2×C4—112no—
584C2×C4—112no—
585C2×C4—112no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—222no—
593C2×C4—448no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—884no—
603C2×C4—884no—
604C2×C4C22⋊C4×D1112yes—
605C2×C4C22⋊C4×D1112yes—
606C2×C4C22×C4×D1111yescharacteristic
607C2×C4C2×D4×D1111yescharacteristic
608C2×C4C2×Q8×D1111yescharacteristic
609C2×C4#6704011yescharacteristic
610C2×C4#41×D1111yescharacteristic
611C2×C4#6704311yescharacteristic
612C8—41no—
613C8—41no—
614C8—222no—
615C8—441no—
616C22—224no—
617C22—442no—
618C22—442no—
619C22—442no—
620C22—442no—
621C22—442no—
622C22—442no—
623C22C2×C22⋊C4×D1111yescharacteristic
624C22#1062316311yescharacteristic
625C22#1062316411yescharacteristic
626C22#1062330011yescharacteristic
627C22#1062330111yescharacteristic
628C22D11×AGL(1,ℤ/8)11yescharacteristic
629C22D11×#13711yescharacteristic
630C4—22no—
631C4—22no—
632C4—42no—
633C4—42no—
634C4—42no—
635C4—81no—
636C4—114no—
637C4—222no—
638C4—222no—
639C4—222no—
640C4—442no—
641C4—881no—
642C4—881no—
643C4C4×Q8×D1111yescharacteristic
644C4#1062310311yescharacteristic
645C4#1062320811yescharacteristic
646C4#1062325811yescharacteristic
647C2—444no—
648C2#1307145011yescharacteristic
649C2D11×#41711yescharacteristic
650C2#1307713811yescharacteristic
651C2#1308132611yescharacteristic
652C2#1308140011yescharacteristic
653C2#1308151811yescharacteristic
654C2#1308152911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1989C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1989D11
hypocenterC11#22522
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1989

Complements

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

NH ≅ G/Ntype
2. C2×#10622441C2semidirect
3. C4⋊C4×Dic22C2semidirect
4. #13069586C2semidirect
5. #13069583C2semidirect
6. #13069575C2semidirect
7. #13069570C2semidirect
8. #13069562C2semidirect
15. C11×#1989C2semidirect
18. #10623221C4semidirect
132. #66873Q8semidirect
230. #1989D11semidirect
294. D44C4×Q8semidirect
549. C11#22522semidirect

Maximal subgroups

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

subgroupindex
C2×#106232212
C2×#106224412
C4⋊C4×Dic222
#130695862
#130695832
#130695752
#130695702
#130695622
#130686172
#130686152
#130684442
#130684402
#130684302
C11×#19892
#2252211