Finite Group Databasebeta

← #14763785

Subgroups — #14763785

Order 2816.

1106 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077249C211yesmaximal, characteristic, complemented
2#13071023C211yesmaximal, characteristic, complemented
3#13069561C212yesmaximal, complemented
4#13069536C212yesmaximal, complemented
5#13069065C214yesmaximal, complemented
6#13068636C214yesmaximal, complemented
7C11×#3444C211yesmaximal, characteristic
8C11×#533C411yescharacteristic, complemented
9C11×#533C411yescharacteristic, complemented
10C11×#533C2211yescharacteristic
11C11×#532C411yescharacteristic, complemented
12C11×#532C411yescharacteristic, complemented
13C11×#532C2211yescharacteristic
14C11×#529—21no—
15C11×#529—21no—
16C11×#529—21no—
17C11×#529—21no—
18C11×#529C412yescomplemented
19C11×#529C412yescomplemented
20C11×#525—21no—
21C11×#525—21no—
22C11×#525C2212yes—
23C4×C11×#41—21no—
24C4×C11×#41—21no—
25C4×C11×#41C2212yes—
26C22×C42×C11C2211yescharacteristic
27C2×#66979C2212yes—
28C2×#66901C2218yes—
29#10622825—21no—
30#10622825—21no—
31#10622820C2212yes—
32#10622549—21no—
33#10622548—21no—
34C4×C4⋊Dic11C2212yes—
35C4×C4⋊Dic11C2212yes—
36#10622539—21no—
37#10622539—21no—
38#10622538—21no—
39#10622538—21no—
40#10622537C2212yes—
41C4×#4318C2212yes—
42#10622170C2218yes—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41C2312yes—
46C23×C4×C11D411yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C11×C4⋊Q8C2×C411yescharacteristic
50C11×C4⋊Q8C2×C411yescharacteristic
51C11×C4⋊Q8C2×C411yescharacteristic
52C11×#127C2×C411yescharacteristic
53C11×#126—22no—
54C11×#126—22no—
55C11×#125—21no—
56C11×#125—21no—
57C11×#125C2×C412yes—
58C11×#124—21no—
59C11×#124—21no—
60C11×#124C2×C412yes—
61C11×#123—22no—
62C11×#123—22no—
63C11×#123—22no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8—21no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8C2×C412yes—
69C11×C22⋊Q8C2×C412yes—
70C11×#121—21no—
71C11×#121—21no—
72C11×#121—21no—
73C11×#121—21no—
74C11×#121C2×C412yes—
75C11×#121C2×C412yes—
76C11×#120—22no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11C2×C412yes—
82C4×Q8×C11C2×C412yes—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—21no—
90C4×D4×C11—21no—
91C4×D4×C11—21no—
92C4×D4×C11—21no—
93C4×D4×C11C2×C412yes—
94C4×D4×C11C2×C412yes—
95C11×#117—21no—
96C11×#117—21no—
97C11×#117—22no—
98C11×#117—22no—
99C11×#117—22no—
100C11×#117C2312yes—
101C2×C42×C11—22no—
102C2×C42×C11C2×C411yescharacteristic
103C2×C42×C11C2×C411yescharacteristic
104C2×C42×C11C2×C411yescharacteristic
105C2×C42×C11C2×C411yescharacteristic
106C2×C42×C11D411yescharacteristic
107C2×C42×C11D411yescharacteristic
108C2×C42×C11D411yescharacteristic
109C2×C42×C11D411yescharacteristic
110C2×C42×C11D411yescharacteristic
111C2×C42×C11D411yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C2×C22⋊Dic11—22no—
115#66979—44no—
116C2×C4⋊Dic11—22no—
117C2×C4⋊Dic11—22no—
118C2×C4⋊Dic11—22no—
119C2×C4×Dic11C2314yes—
120C2×#4318C2314yes—
121#66901—48no—
122C11⋊#95—22no—
123C11⋊#95—22no—
124C22⋊(C11⋊C8)—22no—
125C22⋊(C11⋊C8)—22no—
126C4⋊(C11⋊C8)—22no—
127C4⋊(C11⋊C8)—22no—
128#66867—22no—
129C4×C11⋊C8—22no—
130#21900—111nomaximal, Sylow
131C24×C11C2×D411yescharacteristic
132C11×#41—24no—
133C11×#41—24no—
134C11×#41—44no—
135C11×#41—44no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11C22×C412yes—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11C22×C412yes—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11C22⋊C411yescharacteristic
153C22×C4×C11C22⋊C411yescharacteristic
154C22×C4×C11C22⋊C411yescharacteristic
155C22×C4×C11C22⋊C411yescharacteristic
156C22×C4×C11C22⋊C411yescharacteristic
157C22×C4×C11C22⋊C411yescharacteristic
158C22×C4×C11C22⋊C411yescharacteristic
159C22×C4×C11C22⋊C411yescharacteristic
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2411yescharacteristic
170C22×Dic11—24no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4C22×C412yes—
182C11×C4⋊C4C22×C412yes—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C42×C11—22no—
193C42×C11—22no—
194C42×C11—22no—
195C42×C11C22⋊C411yescharacteristic
196C42×C11C22⋊C411yescharacteristic
197C42×C11C22⋊C411yescharacteristic
198C42×C11C22⋊C411yescharacteristic
199C42×C11C22⋊C411yescharacteristic
200C42×C11C22⋊C411yescharacteristic
201C42×C11C22⋊C411yescharacteristic
202C42×C11C22⋊C411yescharacteristic
203C42×C11C22×C411yescharacteristic
204C42×C11C22×C411yescharacteristic
205C42×C11C22×C411yescharacteristic
206C42×C11C22×C411yescharacteristic
207C42×C11C2×D411yescharacteristic
208C42×C11C2×D411yescharacteristic
209C42×C11C2×D411yescharacteristic
210C42×C11C2×D411yescharacteristic
211C22⋊Dic11—44no—
212C4⋊Dic11—44no—
213C4⋊Dic11—44no—
214C4⋊Dic11—44no—
215C4×Dic11—28no—
216#4318—24no—
217#4318—24no—
218C2×C11⋊C8—24no—
219#3444D1111yescharacteristic
220#2920—111no—
221#2285—111no—
222#1986—112no—
223#1980—112no—
224#1897—114no—
225#1806—114no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—22no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11C2×C22⋊C411yescharacteristic
232C23×C11C2×C22⋊C411yescharacteristic
233C23×C11C22×D411yescharacteristic
234Q8×C11—24no—
235Q8×C11—42no—
236Q8×C11—42no—
237D4×C11—24no—
238D4×C11—42no—
239D4×C11—44no—
240D4×C11—44no—
241D4×C11—42no—
242D4×C11—42no—
243D4×C11—42no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—44no—
266C2×C4×C11—44no—
267C2×C4×C11—44no—
268C2×C4×C11C2×C22⋊C411yescharacteristic
269C2×C4×C11C2×C22⋊C411yescharacteristic
270C2×C4×C11C2×C22⋊C411yescharacteristic
271C2×C4×C11C2×C22⋊C411yescharacteristic
272C2×C4×C11C2×C22⋊C411yescharacteristic
273C2×C4×C11C2×C22⋊C411yescharacteristic
274C2×C4×C11C2×C22⋊C411yescharacteristic
275C2×C4×C11C2×C22⋊C411yescharacteristic
276C2×C4×C11C2×C22⋊C411yescharacteristic
277C2×C4×C11C2×C22⋊C411yescharacteristic
278C2×C4×C11C23×C411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11H(5,𝔽2)12yes—
281C2×C4×C112−1+412yes—
282C2×Dic11—44no—
283C2×Dic11—44no—
284C2×Dic11—44no—
285C11⋊C8—44no—
286#533Dic1111yescharacteristic, complemented
287#533Dic1111yescharacteristic, complemented
288#533C2×D1111yescharacteristic
289#532Dic1111yescharacteristic, complemented
290#532Dic1111yescharacteristic, complemented
291#532C2×D1111yescharacteristic
292#529—21no—
293#529—21no—
294#529—21no—
295#529—21no—
296#529Dic1112yescomplemented
297#529Dic1112yescomplemented
298#525—21no—
299#525—21no—
300#525C2×D1112yes—
301C4×#41—21no—
302C4×#41—21no—
303C4×#41C2×D1112yes—
304C2×#117—112no—
305C22×C42C2×D1111yescharacteristic
306#432—221no—
307#432—221no—
308#431—221no—
309#431—221no—
310#423—112no—
311C2×#104—118no—
312#407—112no—
313C4×M16—112no—
314#384—221no—
315#382—221no—
316#380—221no—
317#380—221no—
318C4×C4⋊C4—112no—
319C4×C4⋊C4—112no—
320#339—118no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11C22×C22⋊C411yescharacteristic
335C22×C11#53511yescharacteristic
336C22×C11#53611yescharacteristic
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11—42no—
348C4×C11#42112yes—
349C4×C11#42112yes—
350C4×C11#52012yes—
351C4×C11#53712yes—
352Dic11—84no—
353C2×#41—21no—
354C2×#41—21no—
355C2×#41C22×D1112yes—
356C23×C4C22⋊D1111yescharacteristic
357C23×C4C22⋊D1111yescharacteristic
358C23×C4C22×D1111yescharacteristic
359C2×M16—114no—
360C4⋊Q8C2×Dic1111yescharacteristic
361C4⋊Q8C2×Dic1111yescharacteristic
362C4⋊Q8C2×Dic1111yescharacteristic
363#127C2×Dic1111yescharacteristic
364#126—22no—
365#126—22no—
366#125—21no—
367#125—21no—
368#125C2×Dic1112yes—
369#124—21no—
370#124—21no—
371#124C2×Dic1112yes—
372#123—22no—
373#123—22no—
374#123—22no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8C2×Dic1112yes—
380C22⋊Q8C2×Dic1112yes—
381#121—21no—
382#121—21no—
383#121—21no—
384#121—21no—
385#121C2×Dic1112yes—
386#121C2×Dic1112yes—
387#120—22no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8C2×Dic1112yes—
393C4×Q8C2×Dic1112yes—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4C2×Dic1112yes—
405C4×D4C2×Dic1112yes—
406#117—21no—
407#117—21no—
408#117—22no—
409#117—22no—
410#117—22no—
411#117—444no—
412#117C22×D1112yes—
413C2×C4⋊C4—222no—
414C2×C4⋊C4—222no—
415C2×C4⋊C4—222no—
416C2×C22⋊C4—222no—
417C2×C42—22no—
418C2×C42—114no—
419C2×C42C2×Dic1111yescharacteristic
420C2×C42C2×Dic1111yescharacteristic
421C2×C42C2×Dic1111yescharacteristic
422C2×C42C2×Dic1111yescharacteristic
423C2×C42C22⋊D1111yescharacteristic
424C2×C42C22⋊D1111yescharacteristic
425C2×C42C22⋊D1111yescharacteristic
426C2×C42C22⋊D1111yescharacteristic
427C2×C42C22⋊D1111yescharacteristic
428C2×C42C22⋊D1111yescharacteristic
429C2×C42C22×D1111yescharacteristic
430C2×C42C22×D1111yescharacteristic
431C4⋊C8—222no—
432C4⋊C8—222no—
433#104—448no—
434C22⋊C8—222no—
435C22⋊C8—222no—
436#97—222no—
437C4×C8—222no—
438#95—222no—
439#95—222no—
440C2×C11—21no—
441C2×C11—21no—
442C2×C11—41no—
443C2×C11—41no—
444C2×C11—82no—
445C2×C11#231111yescharacteristic
446C2×C11C2×#42111yescharacteristic
447C2×C11C2×#42111yescharacteristic
448C24C2×C22⋊D1111yescharacteristic
449#41—24no—
450#41—24no—
451#41—44no—
452#41—44no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8C22×Dic1112yes—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4C22×Dic1112yes—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—224no—
470C22×C4C22⋊Dic1111yescharacteristic
471C22×C4C22⋊Dic1111yescharacteristic
472C22×C4C22⋊Dic1111yescharacteristic
473C22×C4C22⋊Dic1111yescharacteristic
474C22×C4C22⋊Dic1111yescharacteristic
475C22×C4C22⋊Dic1111yescharacteristic
476C22×C4C22⋊Dic1111yescharacteristic
477C22×C4C22⋊Dic1111yescharacteristic
478C22×C4C22×Dic1111yescharacteristic
479C22×C4C22×Dic1111yescharacteristic
480C22×C4C2×C22⋊D1111yescharacteristic
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C2×C22⋊D1111yescharacteristic
483C22×C4C2×C22⋊D1111yescharacteristic
484C22×C4C2×C22⋊D1111yescharacteristic
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C23×D1111yescharacteristic
488M16—224no—
489M16—224no—
490C2×C8—224no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—444no—
502C4⋊C4—444no—
503C4⋊C4—444no—
504C4⋊C4C22×Dic1112yes—
505C4⋊C4C22×Dic1112yes—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—444no—
516C42—22no—
517C42—22no—
518C42—22no—
519C42—228no—
520C42C22⋊Dic1111yescharacteristic
521C42C22⋊Dic1111yescharacteristic
522C42C22⋊Dic1111yescharacteristic
523C42C22⋊Dic1111yescharacteristic
524C42C22⋊Dic1111yescharacteristic
525C42C22⋊Dic1111yescharacteristic
526C42C22⋊Dic1111yescharacteristic
527C42C22⋊Dic1111yescharacteristic
528C42C22×Dic1111yescharacteristic
529C42C22×Dic1111yescharacteristic
530C42C22×Dic1111yescharacteristic
531C42C22×Dic1111yescharacteristic
532C42C2×C22⋊D1111yescharacteristic
533C42C2×C22⋊D1111yescharacteristic
534C42C2×C22⋊D1111yescharacteristic
535C42C2×C22⋊D1111yescharacteristic
536C11#2190011yescharacteristic, complemented, Sylow
537C23—21no—
538C23—21no—
539C23—22no—
540C23—41no—
541C23—41no—
542C23C2×C22⋊Dic1111yescharacteristic
543C23C2×C22⋊Dic1111yescharacteristic
544C23C22×C22⋊D1111yescharacteristic
545Q8—24no—
546Q8—42no—
547Q8—42no—
548D4—24no—
549D4—42no—
550D4—44no—
551D4—44no—
552D4—42no—
553D4—42no—
554D4—42no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—444no—
580C2×C4—444no—
581C2×C4—444no—
582C2×C4C2×C22⋊Dic1111yescharacteristic
583C2×C4C2×C22⋊Dic1111yescharacteristic
584C2×C4C2×C22⋊Dic1111yescharacteristic
585C2×C4C2×C22⋊Dic1111yescharacteristic
586C2×C4C2×C22⋊Dic1111yescharacteristic
587C2×C4C2×C22⋊Dic1111yescharacteristic
588C2×C4C2×C22⋊Dic1111yescharacteristic
589C2×C4C2×C22⋊Dic1111yescharacteristic
590C2×C4C2×C22⋊Dic1111yescharacteristic
591C2×C4C2×C22⋊Dic1111yescharacteristic
592C2×C4#6704212yes—
593C2×C4#6704312yes—
594C2×C4C23×Dic1111yescharacteristic
595C2×C4C22×C22⋊D1111yescharacteristic
596C8—444no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22#1062335611yescharacteristic
611C22#1062336111yescharacteristic
612C22C22×C22⋊Dic1111yescharacteristic
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—21no—
621C4—42no—
622C4—42no—
623C4—42no—
624C4—884no—
625C4#1062284912yes—
626C4#1062284912yes—
627C4#1062335812yes—
628C4#1062336412yes—
629C2—21no—
630C2—21no—
631C2—41no—
632C2—41no—
633C2—82no—
634C2#1307120811yescharacteristic
635C2C2×#1062284911yescharacteristic
636C2C2×#1062284911yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3444C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenter#3444D11
hypocenterC11#21900
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #13077249C2semidirect
2. #13071023C2semidirect
3. #13069561C2semidirect
4. #13069536C2semidirect
5. #13069065C2semidirect
6. #13068636C2semidirect
8. C11×#533C4semidirect
9. C11×#533C4semidirect
11. C11×#532C4semidirect
12. C11×#532C4semidirect
18. C11×#529C4semidirect
19. C11×#529C4semidirect
286. #533Dic11semidirect
287. #533Dic11semidirect
289. #532Dic11semidirect
290. #532Dic11semidirect
296. #529Dic11semidirect
297. #529Dic11semidirect
536. C11#21900semidirect

Maximal subgroups

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

subgroupindex
#130772492
#130710232
#130695612
#130695362
#130690652
#130686362
C11×#34442
#2190011