Finite Group Databasebeta

← #14682482

Subgroups — #14682482

Order 2816.

1290 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622594C212yesmaximal
2#13066881C212yesmaximal
3#13066869C212yesmaximal
4#13066869C212yesmaximal
5#13066850C212yesmaximal
6#13066846C211yesmaximal, characteristic
7#13066845C212yesmaximal
8#13066843C211yesmaximal, characteristic
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⋊Dic11C2212yes—
17C22×C4×Dic11C2212yes—
18C11×#389C418yescomplemented
19C2×C11×#95C2212yes—
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2211yescharacteristic
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32#10622594—28no—
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—42no—
45C2×C11×C4⋊C4C2×C414yes—
46C2×C11×C4⋊C4C2×C418yes—
47C2×C11×C4⋊C4C2×C414yes—
48C2×C11×C4⋊C4D414yes—
49C2×C11×C4⋊C4Q814yes—
50C2×C42×C11—42no—
51C2×C42×C11C2×C414yes—
52C2×C4⋊Dic11—24no—
53C2×C4⋊Dic11—24no—
54C2×C4⋊Dic11—24no—
55C2×C4⋊Dic11—24no—
56C2×C4⋊Dic11—42no—
57C2×C4⋊Dic11—42no—
58C2×C4⋊Dic11—42no—
59C2×C4⋊Dic11—42no—
60C2×C4⋊Dic11—42no—
61C2×C4×Dic11—24no—
62C2×C4×Dic11—24no—
63C2×C4×Dic11—42no—
64C11×#95C2×C418yes—
65C11⋊#95—24no—
66C11⋊#95—24no—
67C11⋊#95—24no—
68C11⋊#95—24no—
69C11⋊#95—22no—
70C11⋊#95—41no—
71C11⋊#95—42no—
72C11⋊#95—42no—
73C11⋊#95—42no—
74C11⋊#95—42no—
75C11⋊#95—41no—
76C11⋊#95Q814yes—
77#14465—111nomaximal, Sylow
78C24×C11C2411yescharacteristic
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11C22×C414yes—
98C22×C4×C11C22×C412yes—
99C22×C4×C11C22×C414yes—
100C22×C4×C11C22×C412yes—
101C22×C4×C11C22×C412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D414yes—
104C22×C4×C11C2×Q812yes—
105C22×C4×C11C2×Q814yes—
106C22×C4×C11C2×Q812yes—
107C22×C4×C11#4112yes—
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×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11C2×Q814yes—
135C22×Dic11#4114yes—
136C11×C4⋊C4—44no—
137C11×C4⋊C4—48no—
138C11×C4⋊C4C4⋊C4116yescomplemented
139C42×C11—44no—
140C4⋊Dic11—48no—
141C4⋊Dic11—48no—
142C4⋊Dic11—48no—
143C4×Dic11—48no—
144C2×#389D1111yescharacteristic
145C2×#387—112no—
146#1444—112no—
147#1441—112no—
148#1441—112no—
149#1436—112no—
150C4⋊#95—111no—
151C4⋊#95—112no—
152#1434—111no—
153C23×C11C23×C411yescharacteristic
154C23×C11C22×D411yescharacteristic
155C23×C11C22×Q811yescharacteristic
156C23×C11C22×Q811yescharacteristic
157C23×C11C2×#4111yescharacteristic
158C23×C11C2×#4112yes—
159C23×C11H(5,𝔽2)12yes—
160C23×C11H(5,𝔽2)12yes—
161C23×C11H(5,𝔽2)11yescharacteristic
162C23×C112−1+412yes—
163C23×C112−1+411yescharacteristic
164C2×C4×C11—24no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—24no—
169C2×C4×C11—22no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—22no—
183C2×C4×C11—24no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11C2×C4⋊C414yes—
191C2×C4×C11C2×C4⋊C418yes—
192C2×C4×C11C4×Q814yes—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—24no—
197C2×Dic11—24no—
198C2×Dic11—24no—
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—
220C2×Dic11—42no—
221C22×C4⋊C4—112no—
222C22×C4⋊C4—112no—
223C22×C4⋊C4—112no—
224C22×C4⋊C4C2×D1112yes—
225C22×C4⋊C4C2×D1111yescharacteristic
226C22×C4⋊C4C2×D1111yescharacteristic
227C22×C42—112no—
228C22×C42C2×D1111yescharacteristic
229#389Dic1118yescomplemented
230#387—228no—
231C2×#95—111no—
232C2×#95—112no—
233C2×#95—111no—
234C2×#95—112no—
235C2×#95—112no—
236C2×#95—112no—
237C2×#95—112no—
238C2×#95—111no—
239C2×#95—112no—
240C2×#95—111no—
241C2×#95—112no—
242C2×#95—112no—
243C2×#95C2×D1112yes—
244C22×C11C22×C4⋊C411yescharacteristic
245C22×C11C2×C4×Q811yescharacteristic
246C22×C11C4×#4111yescharacteristic
247C22×C11#51811yescharacteristic
248C22×C11#51811yescharacteristic
249C22×C11#51911yescharacteristic
250C22×C11#52011yescharacteristic
251C22×C11#53712yes—
252C22×C11#53912yes—
253C22×C11#54112yes—
254C22×C11#54212yes—
255C22×C11#54412yes—
256C22×C11#54412yes—
257C22×C11#54612yes—
258C22×C11D4×Q811yescharacteristic
259C22×C11#55011yescharacteristic
260C22×C11#55112yes—
261C22×C11#55412yes—
262C22×C11#55412yes—
263C22×C11#55711yescharacteristic
264C22×C11Q8211yescharacteristic
265C22×C11#56012yes—
266C22×C11#56212yes—
267C4×C11—24no—
268C4×C11—28no—
269C4×C11—24no—
270C4×C11—42no—
271C4×C11—44no—
272Dic11—44no—
273Dic11—44no—
274Dic11—82no—
275Dic11—82no—
276C23×C4—112no—
277C23×C4—112no—
278C23×C4—112no—
279C23×C4—112no—
280C23×C4C22×D1112yes—
281C23×C4C22×D1111yescharacteristic
282C23×C4C22×D1112yes—
283C23×C4C22×D1111yescharacteristic
284C23×C4C22×D1111yescharacteristic
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—224no—
289C2×C4⋊C4—224no—
290C2×C4⋊C4—224no—
291C2×C4⋊C4—224no—
292C2×C4⋊C4—442no—
293C2×C4⋊C4—442no—
294C2×C4⋊C4—442no—
295C2×C4⋊C4—442no—
296C2×C4⋊C4—442no—
297C2×C4⋊C4Dic2214yes—
298C2×C4⋊C4D4414yes—
299C2×C4⋊C4C2×Dic1114yes—
300C2×C4⋊C4C2×Dic1118yes—
301C2×C4⋊C4C2×Dic1114yes—
302C2×C42—42no—
303C2×C42—224no—
304C2×C42—224no—
305C2×C42—442no—
306C2×C42C2×Dic1114yes—
307#95—114no—
308#95—224no—
309#95—224no—
310#95—224no—
311#95—224no—
312#95—222no—
313#95—442no—
314#95—442no—
315#95—442no—
316#95—441no—
317#95—441no—
318#95—442no—
319#95C2×Dic1118yes—
320C2×C11#231611yescharacteristic
321C2×C11#233111yescharacteristic
322C2×C11#233611yescharacteristic
323C2×C11#234911yescharacteristic
324C2×C11Q8×C4⋊C411yescharacteristic
325C2×C11#236811yescharacteristic
326C2×C11#237711yescharacteristic
327C2×C11#270412yes—
328C2×C11#270512yes—
329C2×C11#275512yes—
330C2×C11#279212yes—
331C24C23×D1111yescharacteristic
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—114no—
351C22×C4—114no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—222no—
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×C4C2×Dic2212yes—
379C22×C4C2×Dic2214yes—
380C22×C4C2×D4412yes—
381C22×C4C2×D4414yes—
382C22×C4Q8×D1112yes—
383C22×C4#434312yes—
384C22×C4C22×Dic1114yes—
385C22×C4C22×Dic1112yes—
386C22×C4C22×Dic1114yes—
387C22×C4C22×Dic1112yes—
388C22×C4C22×Dic1112yes—
389C4⋊C4—44no—
390C4⋊C4—48no—
391C4⋊C4—448no—
392C4⋊C4—448no—
393C4⋊C4—448no—
394C4⋊C4C4⋊Dic11116yescomplemented
395C42—44no—
396C42—448no—
397C11#1446511yescharacteristic, complemented, Sylow
398C23C22×Dic2211yescharacteristic
399C23C22×D4411yescharacteristic
400C23#6703712yes—
401C23#6703712yes—
402C23C2×Q8×D1111yescharacteristic
403C23C2×#434311yescharacteristic
404C23#6704012yes—
405C23#41×D1112yes—
406C23#6704211yescharacteristic
407C23#6704311yescharacteristic
408C23C23×Dic1111yescharacteristic
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—22no—
428C2×C4—24no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—224no—
436C2×C4—224no—
437C2×C4—224no—
438C2×C4—224no—
439C2×C4—224no—
440C2×C4—224no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
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×C4C2×C4⋊Dic1114yes—
464C2×C4C2×C4⋊Dic1118yes—
465C2×C4Q8×Dic1114yes—
466C22#1062303112yes—
467C22#1062304112yes—
468C22#1062307012yes—
469C22#1062308512yes—
470C22Q8×Dic2211yescharacteristic
471C22#1062310111yescharacteristic
472C22Q8×D4411yescharacteristic
473C22#1062310811yescharacteristic
474C22#1062315112yes—
475C22#1062315212yes—
476C22#1062316712yes—
477C22#1062316812yes—
478C22#1062322312yes—
479C22#1062322712yes—
480C22#1062326012yes—
481C22#1062326412yes—
482C22C22×C4⋊Dic1111yescharacteristic
483C22#1062332911yescharacteristic
484C22#1062332911yescharacteristic
485C22C2×Q8×Dic1111yescharacteristic
486C22#1062334311yescharacteristic
487C22#41×Dic1111yescharacteristic
488C22#1062335811yescharacteristic
489C4—24no—
490C4—24no—
491C4—28no—
492C4—42no—
493C4—44no—
494C4—444no—
495C4—444no—
496C4—882no—
497C4—882no—
498C2#1307123411yescharacteristic
499C2#1307136511yescharacteristic
500C2#1307142211yescharacteristic
501C2#1307152611yescharacteristic
502C2Q8×C4⋊Dic1111yescharacteristic
503C2#1307170111yescharacteristic
504C2#1307177311yescharacteristic
505C2#1307527212yes—
506C2#1307528712yes—
507C2#1307592412yes—
508C2#1307641112yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#389C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#389D11
hypocenterC11#14465
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
18. C11×#389C4semidirect
138. C11×C4⋊C4C4⋊C4semidirect
229. #389Dic11semidirect
394. C4⋊C4C4⋊Dic11semidirect
397. C11#14465semidirect

Maximal subgroups

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

subgroupindex
C2×#106225942
#130668812
#130668692
#130668502
#130668462
#130668452
#130668432
C2×C11×#3892
#1446511