Finite Group Databasebeta

← #14719027

Subgroups — #14719027

Order 2816.

1142 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066886C212yesmaximal
2#13066886C211yesmaximal, characteristic
3#13066886C211yesmaximal, characteristic
4#13066886C212yesmaximal
5#13066875C212yesmaximal
6#13066873C212yesmaximal
7#13066873C212yesmaximal
8#13066872C212yesmaximal
9C11×#1442C211yesmaximal, characteristic
10C23×Dic22C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C4⋊Dic11C2212yes—
14C2×C11×#95C2212yes—
15C2×C11×#95C2212yes—
16C2×C11×#95C2211yescharacteristic
17C2×C11×#95C2211yescharacteristic
18C2×C11⋊#95C2212yes—
19C2×C11⋊#95C2212yes—
20C2×C11⋊#95C2211yescharacteristic
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C23×C4×C11C2312yes—
32C23×C4×C11C2312yes—
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×Dic11C2312yes—
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C22×Dic22—22no—
41C22×Dic22—24no—
42C22×Dic22—42no—
43C22×Dic22—41no—
44C22×Dic22—41no—
45C22×Dic22—42no—
46C22×Dic22—42no—
47C22×Dic22—41no—
48C22×Dic22—41no—
49C22×Dic22Q814yescomplemented
50C2×C11×C4⋊C4—42no—
51C2×C11×C4⋊C4—41no—
52C2×C4⋊Dic11—42no—
53C2×C4⋊Dic11—42no—
54C2×C4⋊Dic11—42no—
55C11×#95—24no—
56C11×#95—42no—
57C11×#95—41no—
58C11×#95Q814yescomplemented
59C11⋊#95—24no—
60C11⋊#95—24no—
61C11⋊#95—42no—
62C11⋊#95—42no—
63C11⋊#95—42no—
64C11⋊#95—42no—
65C11⋊#95—42no—
66C11⋊#95—42no—
67C11⋊#95—42no—
68C11⋊#95—42no—
69C11⋊#95—41no—
70C11⋊#95—42no—
71C11⋊#95—41no—
72#17281—111nomaximal, Sylow
73C24×C11C2411yescharacteristic
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—21no—
82C22×C4×C11—22no—
83C22×C4×C11—21no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11C2×Q814yes—
100C22×C4×C11C2×Q812yes—
101C22×C4×C11C2×Q812yes—
102C22×C4×C11#4112yes—
103C22×Dic11—22no—
104C22×Dic11—22no—
105C22×Dic11—22no—
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11C2×Q814yes—
130C22×Dic11#4114yes—
131C2×Dic22—48no—
132C2×Dic22—44no—
133C2×Dic22—48no—
134C2×Dic22—44no—
135C2×Dic22—44no—
136C2×Dic22—48no—
137C2×Dic22—44no—
138C2×Dic22—48no—
139C2×Dic22—44no—
140C2×Dic22—44no—
141C11×C4⋊C4—44no—
142C4⋊Dic11—48no—
143#1446—111no—
144#1446—112no—
145#1446—111no—
146#1446—112no—
147#1442—112no—
148#1442—112no—
149#1442—112no—
150#1442—112no—
151#1442D1111yescharacteristic
152C23×C11C22×Q811yescharacteristic
153C23×C11C22×Q811yescharacteristic
154C23×C11C2×#4111yescharacteristic
155C23×C11C2×#4112yes—
156C23×C11H(5,𝔽2)11yescharacteristic
157C23×C11H(5,𝔽2)12yes—
158C23×C11H(5,𝔽2)11yescharacteristic
159C23×C11H(5,𝔽2)12yes—
160C23×C11H(5,𝔽2)11yescharacteristic
161C23×C112−1+411yescharacteristic
162C23×C112−1+412yes—
163C2×C4×C11—22no—
164C2×C4×C11—24no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×Dic11—24no—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—24no—
197C2×Dic11—24no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220Dic22—416no—
221Dic22—416no—
222C23×Q8—111no—
223C23×Q8—111no—
224C22×C4⋊C4—112no—
225C22×C4⋊C4C2×D1111yescharacteristic
226C2×#95—112no—
227C2×#95—112no—
228C2×#95—112no—
229C2×#95—112no—
230C2×#95—112no—
231C2×#95—112no—
232C2×#95—112no—
233C2×#95—111no—
234C2×#95—111no—
235C2×#95—112no—
236C2×#95—112no—
237C2×#95—112no—
238C2×#95—112no—
239C2×#95C2×D1112yes—
240C2×#95C2×D1112yes—
241C2×#95C2×D1111yescharacteristic
242C2×#95C2×D1111yescharacteristic
243C22×C11#53812yes—
244C22×C11#53811yescharacteristic
245C22×C11#54212yes—
246C22×C11#54212yes—
247C22×C11#54212yes—
248C22×C11#54312yes—
249C22×C11#54311yescharacteristic
250C22×C11#54411yescharacteristic
251C22×C11#54412yes—
252C22×C11#55112yes—
253C22×C11#55111yescharacteristic
254C22×C11#55412yes—
255C22×C11#55411yescharacteristic
256C22×C11#55711yescharacteristic
257C22×C11#55712yes—
258C22×C11Q8211yescharacteristic
259C22×C11H(3,𝔽4)11yescharacteristic
260C22×C11H(3,𝔽4)12yes—
261C22×C11H(3,𝔽4)11yescharacteristic
262C22×C11#56212yes—
263C22×C11#56211yescharacteristic
264C22×C11#56311yescharacteristic
265C22×C11#56312yes—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11—42no—
269C4×C11—44no—
270C4×C11—82no—
271Dic11—44no—
272Dic11—44no—
273Dic11—82no—
274Dic11—82no—
275C22×Q8—114no—
276C22×Q8—224no—
277C22×Q8—222no—
278C22×Q8—441no—
279C22×Q8—442no—
280C22×Q8—441no—
281C22×Q8—442no—
282C22×Q8—441no—
283C22×Q8—442no—
284C22×Q8—441no—
285C23×C4—112no—
286C23×C4—112no—
287C23×C4—112no—
288C23×C4—112no—
289C23×C4C22×D1112yes—
290C23×C4C22×D1112yes—
291C23×C4C22×D1111yescharacteristic
292C23×C4C22×D1111yescharacteristic
293C23×C4C22×D1111yescharacteristic
294C2×C4⋊C4—41no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—442no—
297C2×C4⋊C4—442no—
298C2×C4⋊C4—442no—
299#95—24no—
300#95—41no—
301#95—42no—
302#95—224no—
303#95—224no—
304#95—442no—
305#95—442no—
306#95—442no—
307#95—442no—
308#95—442no—
309#95—441no—
310#95—441no—
311#95—442no—
312#95—442no—
313#95—442no—
314#95—442no—
315#95Dic2214yescomplemented
316C2×C11#273611yescharacteristic
317C2×C11#276311yescharacteristic
318C2×C11#276312yes—
319C2×C11#279912yes—
320C2×C11#279911yescharacteristic
321C2×C11#280612yes—
322C2×C11#280611yescharacteristic
323C2×C11#283212yes—
324C2×C11#283211yescharacteristic
325C2×C11#284011yescharacteristic
326C2×C11#284411yescharacteristic
327C24C23×D1111yescharacteristic
328C2×Q8—448no—
329C2×Q8—444no—
330C2×Q8—448no—
331C2×Q8—444no—
332C2×Q8—444no—
333C2×Q8—448no—
334C2×Q8—444no—
335C2×Q8—448no—
336C2×Q8—444no—
337C2×Q8—444no—
338C22×C4—22no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—114no—
364C22×C4—114no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—222no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4—222no—
390C22×C4—222no—
391C22×C4C2×Dic2212yes—
392C22×C4C2×Dic2214yes—
393C22×C4#434112yes—
394C22×C4Q8×D1112yes—
395C4⋊C4—44no—
396C4⋊C4—448no—
397C11#1728111yescharacteristic, complemented, Sylow
398C23C22×Dic2211yescharacteristic
399C23C2×#434111yescharacteristic
400C23#6703711yescharacteristic
401C23#6703712yes—
402C23C2×Q8×D1111yescharacteristic
403C23#6704011yescharacteristic
404C23#41×D1112yes—
405C23#6704211yescharacteristic
406C23#6704212yes—
407C23#6704211yescharacteristic
408C23#6704312yes—
409Q8—4416no—
410Q8—4416no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—22no—
419C2×C4—24no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—224no—
441C2×C4—224no—
442C2×C4—224no—
443C2×C4—224no—
444C2×C4—224no—
445C2×C4—224no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—442no—
468C22#1062303111yescharacteristic
469C22#1062305012yes—
470C22#1062307012yes—
471C22#1062307411yescharacteristic
472C22Q8×Dic2211yescharacteristic
473C22#1062312511yescharacteristic
474C22#1062313412yes—
475C22#1062314811yescharacteristic
476C22#1062316512yes—
477C22#1062316511yescharacteristic
478C22#1062317112yes—
479C22#1062318912yes—
480C22#1062319011yescharacteristic
481C22#1062319812yes—
482C22#1062320311yescharacteristic
483C22#1062321412yes—
484C22#1062321411yescharacteristic
485C22#1062321612yes—
486C22#1062323012yes—
487C22#1062323111yescharacteristic
488C22#1062323512yes—
489C22#1062324112yes—
490C22#1062325211yescharacteristic
491C4—42no—
492C4—44no—
493C4—42no—
494C4—42no—
495C4—82no—
496C4—444no—
497C4—444no—
498C4—882no—
499C4—882no—
500C2#1307566311yescharacteristic
501C2#1307603011yescharacteristic
502C2#1307603212yes—
503C2#1307649612yes—
504C2#1307650411yescharacteristic
505C2#1307657412yes—
506C2#1307657811yescharacteristic
507C2#1307678512yes—
508C2#1307678711yescharacteristic
509C2#1307686811yescharacteristic
510C2#1307688811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, prime radical, cosocleC24×C11C24
FittingC11×#1442C2
hypercenter#1442D11
hypocenterC11#17281
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
49. C22×Dic22Q8semidirect
58. C11×#95Q8semidirect
315. #95Dic22semidirect
397. C11#17281semidirect

Maximal subgroups

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

subgroupindex
#130668862
#130668752
#130668732
#130668722
C11×#14422
#1728111