Finite Group Databasebeta

← #14719808

Subgroups — #14719808

Order 2816.

984 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077645C211yesmaximal, characteristic, complemented
2#13077640C211yesmaximal, characteristic, complemented
3#13066985C212yesmaximal, complemented
4#13066980C212yesmaximal, complemented
5#13066972C212yesmaximal, complemented
6#13066964C212yesmaximal, complemented
7#13066934C212yesmaximal, complemented
8C2×#10622166C212yesmaximal, complemented
9C2×C11×#539C211yesmaximal, characteristic
10C11×#539—24no—
11C11×#539—24no—
12C2×C11×#126C411yescharacteristic
13C2×C11×#126C2211yescharacteristic
14C2×C11×#125C411yescharacteristic
15C2×C11×#125C2211yescharacteristic
16C2×C11×#123C411yescharacteristic
17C2×C11×#123C411yescharacteristic
18C2×C11×#123C411yescharacteristic
19C2×C11×#123C2211yescharacteristic
20C2×C11×C22⋊Q8C411yescharacteristic
21C2×C11×C22⋊Q8C411yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121C411yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27#10622820C2212yes—
28C2×C22⋊(C11⋊C8)C2212yes—
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×C22⋊(C11⋊C8)C2212yes—
31#10622624—24no—
32D4×C11⋊C8—24no—
33#10622539C2212yes—
34#10622538C2212yes—
35#10622166C2214yes—
36#10622166C2214yes—
37#10622166C2214yes—
38#10622163C2214yes—
39C22×Q8×C11C2×C411yescharacteristic
40C22×D4×C11C2×C411yescharacteristic
41C22×D4×C11C2×C411yescharacteristic
42C22×D4×C11C2×C411yescharacteristic
43C23×C4×C11C2×C411yescharacteristic
44C23×C4×C11C2×C411yescharacteristic
45C23×C4×C11C2×C411yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C11×#126—24no—
49C11×#126—22no—
50C11×#126—22no—
51C11×#125—24no—
52C11×#125—22no—
53C11×#125—22no—
54C11×#123—24no—
55C11×#123—22no—
56C11×#123—22no—
57C11×#123—24no—
58C11×#123—24no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—24no—
63C11×#121—24no—
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C4×D4×C11D414yes—
67C4×D4×C11D414yes—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4C2×C411yescharacteristic
71C2×C11×C4⋊C4C2×C411yescharacteristic
72C2×C11×C4⋊C4C2×C411yescharacteristic
73C2×C11×C4⋊C4C2×C411yescharacteristic
74C2×C11×C4⋊C4C2×C411yescharacteristic
75C2×C11×C4⋊C4C2×C411yescharacteristic
76C2×C11×C4⋊C4C2×C411yescharacteristic
77C2×C11×C4⋊C4C2×C411yescharacteristic
78C2×C11×C4⋊C4C2×C411yescharacteristic
79C2×C11×C4⋊C4C2×C411yescharacteristic
80C2×C11×C4⋊C4C2×C411yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4C2×C411yescharacteristic
85C2×C11×C22⋊C4C2×C411yescharacteristic
86C2×C11×C22⋊C4C2×C411yescharacteristic
87C2×C11×C22⋊C4C2×C411yescharacteristic
88C2×C11×C22⋊C4C2×C411yescharacteristic
89C2×C11×C22⋊C4C2×C411yescharacteristic
90C2×C11×C22⋊C4C2×C411yescharacteristic
91C2×C11×C22⋊C4C2×C411yescharacteristic
92C2×C11×C22⋊C4C2×C411yescharacteristic
93C2×C11×C22⋊C4C2311yescharacteristic
94C2×C42×C11C2×C411yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×#4318—22no—
97C22×C11⋊C8—22no—
98C22×C11⋊C8—22no—
99C22×C11⋊C8—22no—
100C22⋊(C11⋊C8)—22no—
101C22⋊(C11⋊C8)—22no—
102C22⋊(C11⋊C8)—22no—
103C22⋊(C11⋊C8)—22no—
104C22⋊(C11⋊C8)C2314yes—
105C22⋊(C11⋊C8)C2314yes—
106C4⋊(C11⋊C8)—22no—
107C4⋊(C11⋊C8)—22no—
108#66867—22no—
109C4×C11⋊C8—22no—
110#17387—111nomaximal, Sylow
111C24×C11C22×C411yescharacteristic
112C24×C11C22×C411yescharacteristic
113C24×C11C22×C411yescharacteristic
114C2×Q8×C11—22no—
115C2×Q8×C11—81no—
116C2×D4×C11—24no—
117C2×D4×C11—22no—
118C2×D4×C11—24no—
119C2×D4×C11—22no—
120C2×D4×C11—81no—
121C2×D4×C11C22⋊C414yes—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—81no—
127C22×C4×C11—81no—
128C22×C4×C11—81no—
129C22×C4×C11—81no—
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C22×C411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2411yescharacteristic
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4C22⋊C414yes—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—21no—
171C11×C22⋊C4—21no—
172C11×C22⋊C4C22⋊C414yes—
173C11×C22⋊C4C22⋊C414yes—
174C42×C11—22no—
175C42×C11C2×D412yes—
176C42×C11C2×D412yes—
177#4318—82no—
178C2×C11⋊C8—24no—
179C2×C11⋊C8—24no—
180C2×C11⋊C8—82no—
181C2×C11⋊C8—82no—
182C2×C11⋊C8—82no—
183C2×#539D1111yescharacteristic
184#2973—111no—
185#2972—111no—
186#1473—112no—
187#1472—112no—
188#1470—112no—
189#1468—112no—
190#1459—112no—
191C2×#324—112no—
192C23×C11—22no—
193C23×C11—21no—
194C23×C11—22no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11C2×C22⋊C412yes—
202C23×C11C2×C22⋊C412yes—
203C23×C11#13114yes—
204C23×C11C23×C411yescharacteristic
205Q8×C11—82no—
206D4×C11—28no—
207D4×C11—44no—
208D4×C11—82no—
209C2×C4×C11—22no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—44no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—82no—
234C2×C4×C11—82no—
235C2×C4×C11C2×C22⋊C412yes—
236C2×C4×C11C2×C22⋊C412yes—
237C2×C4×C11C2×C22⋊C412yes—
238C2×C4×C11C2×C22⋊C412yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C11⋊C8—44no—
242C11⋊C8—44no—
243#539—24no—
244#539—24no—
245C2×#126Dic1111yescharacteristic
246C2×#126C2×D1111yescharacteristic
247C2×#125Dic1111yescharacteristic
248C2×#125C2×D1111yescharacteristic
249C2×#123Dic1111yescharacteristic
250C2×#123Dic1111yescharacteristic
251C2×#123Dic1111yescharacteristic
252C2×#123C2×D1111yescharacteristic
253C2×C22⋊Q8Dic1111yescharacteristic
254C2×C22⋊Q8Dic1111yescharacteristic
255C2×C22⋊Q8C2×D1111yescharacteristic
256C2×#121Dic1111yescharacteristic
257C2×C4×D4C2×D1111yescharacteristic
258C2×C4×D4C2×D1111yescharacteristic
259C22×C4⋊C4C2×D1111yescharacteristic
260#435—224no—
261C8×D4—224no—
262#432—112no—
263#431—112no—
264#407—112no—
265C2×C22⋊C8—112no—
266C2×C22⋊C8—112no—
267C2×C22⋊C8—112no—
268#324—114no—
269#324—114no—
270#324—114no—
271#323—114no—
272C22×C11—21no—
273C22×C11—22no—
274C22×C11—21no—
275C22×C11—22no—
276C22×C11—22no—
277C22×C11—22no—
278C22×C11—22no—
279C22×C11—44no—
280C22×C11—41no—
281C22×C11—41no—
282C22×C11—41no—
283C22×C11—82no—
284C22×C11—82no—
285C22×C11#40814yes—
286C22×C11C22×C22⋊C411yescharacteristic
287C22×C11C2×#13112yes—
288C4×C11—22no—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—22no—
292C4×C11—22no—
293C4×C11—22no—
294C4×C11—41no—
295C4×C11—41no—
296C4×C11—41no—
297C4×C11—41no—
298C4×C11—41no—
299C4×C11—41no—
300C4×C11—41no—
301C22×Q8C2×Dic1111yescharacteristic
302C22×D4C2×Dic1111yescharacteristic
303C22×D4C2×Dic1111yescharacteristic
304C22×D4C2×Dic1111yescharacteristic
305C23×C4C2×Dic1111yescharacteristic
306C23×C4C2×Dic1111yescharacteristic
307C23×C4C2×Dic1111yescharacteristic
308C23×C4C22×D1111yescharacteristic
309C23×C4C22×D1111yescharacteristic
310C2×M16—222no—
311C22×C8—222no—
312C22×C8—222no—
313C22×C8—222no—
314#126—24no—
315#126—22no—
316#126—22no—
317#125—24no—
318#125—22no—
319#125—22no—
320#123—24no—
321#123—22no—
322#123—22no—
323#123—24no—
324#123—24no—
325C22⋊Q8—22no—
326C22⋊Q8—22no—
327C22⋊Q8—24no—
328C22⋊Q8—24no—
329#121—24no—
330C4×D4—22no—
331C4×D4—22no—
332C4×D4C22⋊D1114yes—
333C4×D4C22⋊D1114yes—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4C2×Dic1111yescharacteristic
337C2×C4⋊C4C2×Dic1111yescharacteristic
338C2×C4⋊C4C2×Dic1111yescharacteristic
339C2×C4⋊C4C2×Dic1111yescharacteristic
340C2×C4⋊C4C2×Dic1111yescharacteristic
341C2×C4⋊C4C2×Dic1111yescharacteristic
342C2×C4⋊C4C2×Dic1111yescharacteristic
343C2×C4⋊C4C2×Dic1111yescharacteristic
344C2×C4⋊C4C2×Dic1111yescharacteristic
345C2×C4⋊C4C2×Dic1111yescharacteristic
346C2×C4⋊C4C2×Dic1111yescharacteristic
347C2×C4⋊C4C22×D1111yescharacteristic
348C2×C4⋊C4C22×D1111yescharacteristic
349C2×C4⋊C4C22×D1111yescharacteristic
350C2×C22⋊C4C2×Dic1111yescharacteristic
351C2×C22⋊C4C2×Dic1111yescharacteristic
352C2×C22⋊C4C2×Dic1111yescharacteristic
353C2×C22⋊C4C2×Dic1111yescharacteristic
354C2×C22⋊C4C2×Dic1111yescharacteristic
355C2×C22⋊C4C2×Dic1111yescharacteristic
356C2×C22⋊C4C2×Dic1111yescharacteristic
357C2×C22⋊C4C2×Dic1111yescharacteristic
358C2×C22⋊C4C2×Dic1111yescharacteristic
359C2×C22⋊C4C22×D1111yescharacteristic
360C2×C42C2×Dic1111yescharacteristic
361C2×C42C22×D1111yescharacteristic
362C4⋊C8—222no—
363C4⋊C8—222no—
364C22⋊C8—114no—
365C22⋊C8—114no—
366C22⋊C8—222no—
367C22⋊C8—222no—
368C22⋊C8—222no—
369C22⋊C8—222no—
370#97—222no—
371C4×C8—222no—
372C2×C11—22no—
373C2×C11—24no—
374C2×C11—42no—
375C2×C11—81no—
376C2×C11C2×#40811yescharacteristic
377C2×C11#288311yescharacteristic
378C2×C11#288911yescharacteristic
379C24C22×Dic1111yescharacteristic
380C24C22×Dic1111yescharacteristic
381C24C22×Dic1111yescharacteristic
382C2×Q8—22no—
383C2×Q8—81no—
384C2×D4—24no—
385C2×D4—24no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—81no—
389C2×D4C22⋊Dic1114yes—
390C22×C4—24no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—81no—
395C22×C4—81no—
396C22×C4—81no—
397C22×C4—81no—
398C22×C4C22×Dic1111yescharacteristic
399C22×C4C22×Dic1111yescharacteristic
400C22×C4C22×Dic1111yescharacteristic
401C22×C4C22×Dic1111yescharacteristic
402C22×C4C22×Dic1111yescharacteristic
403C22×C4C22×Dic1111yescharacteristic
404C22×C4C22×Dic1111yescharacteristic
405C22×C4C22×Dic1111yescharacteristic
406C22×C4C22×Dic1111yescharacteristic
407C22×C4C22×Dic1111yescharacteristic
408C22×C4C22×Dic1111yescharacteristic
409C22×C4C2×C22⋊D1112yes—
410C22×C4C2×C22⋊D1112yes—
411C22×C4C2×C22⋊D1112yes—
412C22×C4C2×C22⋊D1112yes—
413C22×C4C23×D1111yescharacteristic
414M16—882no—
415C2×C8—224no—
416C2×C8—224no—
417C2×C8—882no—
418C2×C8—882no—
419C2×C8—882no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4C22⋊Dic1114yes—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—21no—
445C22⋊C4—21no—
446C22⋊C4C22⋊Dic1114yes—
447C22⋊C4C22⋊Dic1114yes—
448C42—22no—
449C42C2×C22⋊D1112yes—
450C42C2×C22⋊D1112yes—
451C11#1738711yescharacteristic, complemented, Sylow
452C23—22no—
453C23—21no—
454C23—22no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23#6700114yes—
462C23C2×C22⋊Dic1112yes—
463C23C2×C22⋊Dic1112yes—
464C23C23×Dic1111yescharacteristic
465Q8—82no—
466D4—28no—
467D4—44no—
468D4—82no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—44no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—82no—
494C2×C4—82no—
495C2×C4C2×C22⋊Dic1112yes—
496C2×C4C2×C22⋊Dic1112yes—
497C2×C4C2×C22⋊Dic1112yes—
498C2×C4C2×C22⋊Dic1112yes—
499C2×C4C22×C22⋊D1111yescharacteristic
500C2×C4C22×C22⋊D1111yescharacteristic
501C8—444no—
502C8—444no—
503C22—21no—
504C22—22no—
505C22—21no—
506C22—22no—
507C22—22no—
508C22—22no—
509C22—22no—
510C22—44no—
511C22—41no—
512C22—41no—
513C22—41no—
514C22—82no—
515C22—82no—
516C22#1062284714yes—
517C22C2×#6700112yes—
518C22C22×C22⋊Dic1111yescharacteristic
519C4—22no—
520C4—21no—
521C4—21no—
522C4—22no—
523C4—22no—
524C4—22no—
525C4—41no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—41no—
532C2—22no—
533C2—24no—
534C2—42no—
535C2—81no—
536C2C2×#1062284711yescharacteristic
537C2#1307707711yescharacteristic
538C2#1307709911yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#539C2
socleC22×C11C22×C22⋊C4
prime radicalC2×C11×#121C4
cosocleC22×C4×C11C24
hypercenterC2×#539D11
hypocenterC11#17387
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#539

Complements

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

NH ≅ G/Ntype
1. #13077645C2semidirect
2. #13077640C2semidirect
3. #13066985C2semidirect
4. #13066980C2semidirect
5. #13066972C2semidirect
6. #13066964C2semidirect
7. #13066934C2semidirect
8. C2×#10622166C2semidirect
451. C11#17387semidirect

Maximal subgroups

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

subgroupindex
#130776452
#130776402
#130669852
#130669802
#130669722
#130669642
#130669342
C2×#106221662
C2×C11×#5392
#1738711