Finite Group Databasebeta

← #14675148

Subgroups — #14675148

Order 2816.

1434 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622594C212yesmaximal
2#13066850C212yesmaximal
3#13066848C212yesmaximal
4#13066848C212yesmaximal
5#13066845C212yesmaximal
6#13066843C211yesmaximal, characteristic
7C4×C11⋊#95C211yesmaximal, characteristic
8#95×Dic11C212yesmaximal
9C2×C11×#389C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2212yes—
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2212yes—
15C22×C4×Dic11C2212yes—
16C22×C4×Dic11C2211yescharacteristic
17C22×C4×Dic11C2212yes—
18C22×C4×Dic11C2211yescharacteristic
19C11×#389C418yescomplemented
20C2×C11×#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2211yescharacteristic
25C2×C11⋊#95C2211yescharacteristic
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32#10622594C4116yescomplemented
33C23×C4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C2×C11×C4⋊C4—42no—
43C2×C11×C4⋊C4—42no—
44C2×C11×C4⋊C4—41no—
45C2×C11×C4⋊C4—41no—
46C2×C11×C4⋊C4C2×C418yes—
47C2×C11×C4⋊C4C2×C414yes—
48C2×C11×C4⋊C4C2×C418yes—
49C2×C11×C4⋊C4C2×C414yes—
50C2×C42×C11—41no—
51C2×C42×C11—41no—
52C2×C42×C11C2×C414yes—
53C2×C4⋊Dic11—42no—
54C2×C4⋊Dic11—42no—
55C2×C4⋊Dic11C2×C418yes—
56C2×C4×Dic11—22no—
57C2×C4×Dic11—24no—
58C2×C4×Dic11—42no—
59C2×C4×Dic11—42no—
60C2×C4×Dic11—41no—
61C2×C4×Dic11—41no—
62C2×C4×Dic11—41no—
63C2×C4×Dic11—41no—
64C2×C4×Dic11—42no—
65C2×C4×Dic11—42no—
66C2×C4×Dic11C2×C418yes—
67C2×C4×Dic11Q814yes—
68C11×#95C2×C418yes—
69C11⋊#95—24no—
70C11⋊#95—24no—
71C11⋊#95—24no—
72C11⋊#95—41no—
73C11⋊#95—42no—
74C11⋊#95—41no—
75C11⋊#95—42no—
76C11⋊#95C2×C418yes—
77C11⋊#95C2×C418yes—
78C11⋊#95C2×C418yes—
79C11⋊#95C2×C418yes—
80#13792—111nomaximal, Sylow
81C24×C11C2411yescharacteristic
82C22×C4×C11—21no—
83C22×C4×C11—22no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11C22×C414yes—
104C22×C4×C11C22×C412yes—
105C22×C4×C11C22×C414yes—
106C22×C4×C11C22×C414yes—
107C22×C4×C11C22×C414yes—
108C22×C4×C11C22×C414yes—
109C22×C4×C11C22×C412yes—
110C22×C4×C11C22×C412yes—
111C22×C4×C11C2×Q812yes—
112C22×C4×C11#4112yes—
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×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11C22×C414yes—
136C22×Dic11C22×C414yes—
137C22×Dic11C22×C414yes—
138C22×Dic11C22×C414yes—
139C22×Dic11C2×Q814yes—
140C22×Dic11#4114yes—
141C11×C4⋊C4—44no—
142C11×C4⋊C4—48no—
143C11×C4⋊C4C42116yescomplemented
144C42×C11—44no—
145C4⋊Dic11—48no—
146C4×Dic11—48no—
147C4×Dic11—44no—
148C4×Dic11—44no—
149C4×Dic11—48no—
150C2×#389D1111yescharacteristic
151C2×#387—112no—
152#1436—112no—
153#1436—112no—
154#1436—112no—
155C4⋊#95—112no—
156#1434—111no—
157C4×#95—111no—
158C4×#95—112no—
159C23×C11C23×C412yes—
160C23×C11C23×C411yescharacteristic
161C23×C11C22×Q811yescharacteristic
162C23×C11C2×#4111yescharacteristic
163C23×C11C2×#4112yes—
164C23×C11H(5,𝔽2)12yes—
165C23×C11H(5,𝔽2)11yescharacteristic
166C23×C11H(5,𝔽2)11yescharacteristic
167C23×C11H(5,𝔽2)11yescharacteristic
168C23×C112−1+412yes—
169C23×C112−1+411yescharacteristic
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—24no—
175C2×C4×C11—22no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—22no—
181C2×C4×C11—24no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—24no—
191C2×C4×C11—24no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11C2×C4214yes—
199C2×C4×C11C2×C4218yes—
200C2×C4×C11C4×Q814yes—
201C2×Dic11—24no—
202C2×Dic11—24no—
203C2×Dic11—24no—
204C2×Dic11—24no—
205C2×Dic11—24no—
206C2×Dic11—24no—
207C2×Dic11—24no—
208C2×Dic11—24no—
209C2×Dic11—24no—
210C2×Dic11—24no—
211C2×Dic11—24no—
212C2×Dic11—24no—
213C2×Dic11—24no—
214C2×Dic11—24no—
215C2×Dic11—24no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11C4×Q818yes—
229C22×C4⋊C4—112no—
230C22×C4⋊C4C2×D1112yes—
231C22×C4⋊C4C2×D1111yescharacteristic
232C22×C4⋊C4C2×D1111yescharacteristic
233C22×C42—111no—
234C22×C42—112no—
235C22×C42—112no—
236C22×C42—111no—
237C22×C42C2×D1111yescharacteristic
238#389Dic1118yescomplemented
239#387—1116no—
240C2×#95—112no—
241C2×#95—112no—
242C2×#95—112no—
243C2×#95—112no—
244C2×#95—112no—
245C2×#95—112no—
246C2×#95—112no—
247C2×#95—111no—
248C2×#95—111no—
249C2×#95—112no—
250C2×#95—112no—
251C2×#95C2×D1112yes—
252C22×C11C22×C4211yescharacteristic
253C22×C11C2×C4×Q811yescharacteristic
254C22×C11C2×C4×Q812yes—
255C22×C11C4×#4111yescharacteristic
256C22×C11C4×#4112yes—
257C22×C11#51811yescharacteristic
258C22×C11#51811yescharacteristic
259C22×C11#51812yes—
260C22×C11#51911yescharacteristic
261C22×C11#52012yes—
262C22×C11#52012yes—
263C22×C11#52012yes—
264C22×C11#52011yescharacteristic
265C22×C11#53812yes—
266C22×C11#53811yescharacteristic
267C22×C11#53911yescharacteristic
268C22×C11#53912yes—
269C22×C11#54012yes—
270C22×C11#54112yes—
271C22×C11#54212yes—
272C22×C11#54311yescharacteristic
273C22×C11#54412yes—
274C22×C11#54411yescharacteristic
275C4×C11—24no—
276C4×C11—24no—
277C4×C11—28no—
278C4×C11—42no—
279C4×C11—44no—
280Dic11—28no—
281Dic11—44no—
282Dic11—44no—
283Dic11—44no—
284C23×C4—112no—
285C23×C4—112no—
286C23×C4—112no—
287C23×C4—112no—
288C23×C4C22×D1111yescharacteristic
289C23×C4C22×D1112yes—
290C23×C4C22×D1112yes—
291C23×C4C22×D1111yescharacteristic
292C23×C4C22×D1111yescharacteristic
293C2×C4⋊C4—41no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—118no—
298C2×C4⋊C4—442no—
299C2×C4⋊C4—442no—
300C2×C4⋊C4C4×D1118yes—
301C2×C4⋊C4C2×Dic1114yes—
302C2×C4⋊C4C2×Dic1118yes—
303C2×C4⋊C4C2×Dic1114yes—
304C2×C42—41no—
305C2×C42—41no—
306C2×C42—118no—
307C2×C42—114no—
308C2×C42—224no—
309C2×C42—222no—
310C2×C42—441no—
311C2×C42—442no—
312C2×C42—441no—
313C2×C42—442no—
314C2×C42—441no—
315C2×C42—441no—
316C2×C42—442no—
317C2×C42—442no—
318C2×C42C2×Dic1114yes—
319#95—118no—
320#95—118no—
321#95—118no—
322#95—118no—
323#95—224no—
324#95—224no—
325#95—224no—
326#95—441no—
327#95—441no—
328#95—442no—
329#95—442no—
330#95C2×Dic1118yes—
331C2×C11C42×Q811yescharacteristic
332C2×C11#227411yescharacteristic
333C2×C11#227511yescharacteristic
334C2×C11#232912yes—
335C2×C11#232911yescharacteristic
336C2×C11#233012yes—
337C2×C11#233111yescharacteristic
338C2×C11#233311yescharacteristic
339C2×C11#233412yes—
340C2×C11#233512yes—
341C2×C11#233611yescharacteristic
342C24C23×D1111yescharacteristic
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—114no—
365C22×C4—114no—
366C22×C4—114no—
367C22×C4—114no—
368C22×C4—114no—
369C22×C4—114no—
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×C4—222no—
392C22×C4C2×C4×D1114yes—
393C22×C4C2×C4×D1114yes—
394C22×C4C2×C4×D1114yes—
395C22×C4Q8×D1112yes—
396C22×C4#434312yes—
397C22×C4C22×Dic1114yes—
398C22×C4C22×Dic1112yes—
399C22×C4C22×Dic1114yes—
400C22×C4C22×Dic1112yes—
401C22×C4C22×Dic1112yes—
402C4⋊C4—44no—
403C4⋊C4—48no—
404C4⋊C4—448no—
405C4⋊C4C4×Dic11116yescomplemented
406C42—44no—
407C42—448no—
408C42—444no—
409C42—444no—
410C42—448no—
411C11#1379211yescharacteristic, complemented, Sylow
412C23C22×C4×D1112yes—
413C23#6703712yes—
414C23#6703711yescharacteristic
415C23#6703711yescharacteristic
416C23C2×Q8×D1111yescharacteristic
417C23C2×#434311yescharacteristic
418C23#6704012yes—
419C23#41×D1112yes—
420C23#6704211yescharacteristic
421C23#6704311yescharacteristic
422C23C23×Dic1111yescharacteristic
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—22no—
433C2×C4—24no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—22no—
444C2×C4—24no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—118no—
452C2×C4—224no—
453C2×C4—224no—
454C2×C4—224no—
455C2×C4—224no—
456C2×C4—224no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—224no—
460C2×C4—224no—
461C2×C4—224no—
462C2×C4—224no—
463C2×C4—224no—
464C2×C4—224no—
465C2×C4—224no—
466C2×C4—224no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4C2×C4×Dic1114yes—
480C2×C4C2×C4×Dic1118yes—
481C2×C4Q8×Dic1114yes—
482C22#1062303512yes—
483C22#1062303512yes—
484C22#1062307612yes—
485C22#1062307712yes—
486C22C4×Q8×D1112yes—
487C22C4×#434312yes—
488C22#1062314412yes—
489C22#1062314612yes—
490C22#1062315411yescharacteristic
491C22#1062316511yescharacteristic
492C22#1062317511yescharacteristic
493C22#1062317611yescharacteristic
494C22#1062322312yes—
495C22#1062322712yes—
496C22#1062326012yes—
497C22#1062326412yes—
498C22C22×C4×Dic1111yescharacteristic
499C22#1062332911yescharacteristic
500C22#1062332911yescharacteristic
501C22C2×Q8×Dic1111yescharacteristic
502C22#1062334311yescharacteristic
503C22#41×Dic1111yescharacteristic
504C22#1062335811yescharacteristic
505C4—24no—
506C4—28no—
507C4—24no—
508C4—42no—
509C4—44no—
510C4—228no—
511C4—444no—
512C4—444no—
513C4—444no—
514C2C4×Q8×Dic1111yescharacteristic
515C2#1307097311yescharacteristic
516C2#1307097711yescharacteristic
517C2#1307135012yes—
518C2#1307135111yescharacteristic
519C2#1307135412yes—
520C2#1307136511yescharacteristic
521C2#1307138311yescharacteristic
522C2#1307139012yes—
523C2#1307140912yes—
524C2#1307142211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C11×#389C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#389D11
hypocenterC11#13792
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
19. C11×#389C4semidirect
32. #10622594C4semidirect
143. C11×C4⋊C4C42semidirect
238. #389Dic11semidirect
405. C4⋊C4C4×Dic11semidirect
411. C11#13792semidirect

Maximal subgroups

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

subgroupindex
C2×#106225942
#130668502
#130668482
#130668452
#130668432
C4×C11⋊#952
#95×Dic112
C2×C11×#3892
#1379211