Finite Group Databasebeta

← #14675998

Subgroups — #14675998

Order 2816.

3526 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622824C212yesmaximal, complemented
2C2×#10622825C211yesmaximal, characteristic, complemented
3C2×#10622860C212yesmaximal
4C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
5#13066861C214yesmaximal, complemented
6#13066853C214yesmaximal, complemented
7C23×C11×C22⋊C4C211yesmaximal, characteristic
8C26×C11C2211yescharacteristic
9C24×C4×C11C2211yescharacteristic
10C24×C4×C11C2211yescharacteristic
11C22×C11×C22⋊C4—24no—
12C22×C11×C22⋊C4—24no—
13C22×C11×C22⋊C4C418yescomplemented
14C22×C11×C22⋊C4C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2218yes—
18C22×C22⋊Dic11C2212yes—
19C22×C4⋊Dic11C2212yescomplemented
20C22×C4×Dic11C2212yescomplemented
21#10622860—28no—
22#10622825—24no—
23#10622824—28no—
24C4×C22⋊Dic11—24no—
25C2×C11⋊#95C2212yescomplemented
26C2×C11⋊#95C2212yescomplemented
27C2×C11⋊#95C2218yescomplemented
28C25×C11—22no—
29C25×C11—22no—
30C25×C11—28no—
31C25×C11—24no—
32C25×C11—24no—
33C25×C11—44no—
34C25×C11C2×C414yes—
35C25×C11C2312yes—
36C25×C11C2311yescharacteristic
37C23×C4×C11—24no—
38C23×C4×C11—22no—
39C23×C4×C11—22no—
40C23×C4×C11—24no—
41C23×C4×C11—44no—
42C23×C4×C11C2×C414yes—
43C23×C4×C11C2×C414yes—
44C23×C4×C11D414yes—
45C23×C4×C11D414yes—
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×Dic11C2314yes—
50C23×Dic11C2314yes—
51C2×C11×C22⋊C4—232no—
52C2×C11×C22⋊C4—24no—
53C2×C11×C22⋊C4—24no—
54C2×C11×C22⋊C4—24no—
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4C2×C418yes—
57C2×C11×C22⋊C4C2×C418yes—
58C2×C22⋊Dic11—24no—
59C2×C22⋊Dic11—24no—
60C2×C22⋊Dic11—24no—
61C2×C22⋊Dic11—24no—
62C2×C22⋊Dic11—24no—
63C2×C22⋊Dic11—216no—
64C2×C22⋊Dic11—216no—
65C2×C22⋊Dic11—48no—
66C2×C22⋊Dic11D418yes—
67C2×C4⋊Dic11—24no—
68C2×C4⋊Dic11—44no—
69C2×C4×Dic11—24no—
70C2×C4×Dic11—44no—
71C11⋊#95—24no—
72C11⋊#95—24no—
73C11⋊#95—216no—
74#13903—111nomaximal, Sylow
75C24×C11—24no—
76C24×C11—24no—
77C24×C11—216no—
78C24×C11—216no—
79C24×C11—28no—
80C24×C11—216no—
81C24×C11—24no—
82C24×C11—22no—
83C24×C11—22no—
84C24×C11—24no—
85C24×C11—24no—
86C24×C11—28no—
87C24×C11—216no—
88C24×C11—48no—
89C24×C11—432no—
90C24×C11—432no—
91C24×C11—48no—
92C24×C11—48no—
93C24×C11—48no—
94C24×C11—44no—
95C24×C11—44no—
96C24×C11C22×C414yes—
97C24×C11C22×C412yes—
98C24×C11C2×D412yes—
99C24×C11C2×D412yes—
100C24×C11C2×D414yes—
101C24×C11#4118yes—
102C24×C11#4114yes—
103C24×C11C2411yescharacteristic
104C22×C4×C11—24no—
105C22×C4×C11—24no—
106C22×C4×C11—28no—
107C22×C4×C11—216no—
108C22×C4×C11—24no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—24no—
112C22×C4×C11—48no—
113C22×C4×C11—48no—
114C22×C4×C11—48no—
115C22×C4×C11—48no—
116C22×C4×C11—44no—
117C22×C4×C11—44no—
118C22×C4×C11C22⋊C4116yescomplemented
119C22×C4×C11C22×C414yes—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×Dic11—24no—
127C22×Dic11—24no—
128C22×Dic11—24no—
129C22×Dic11—24no—
130C22×Dic11—28no—
131C22×Dic11—24no—
132C22×Dic11—28no—
133C22×Dic11—28no—
134C22×Dic11—28no—
135C22×Dic11C2×D418yes—
136C11×C22⋊C4—216no—
137C11×C22⋊C4—216no—
138C22⋊Dic11—216no—
139C22⋊Dic11—432no—
140C22⋊Dic11—48no—
141C4⋊Dic11—48no—
142C4×Dic11—48no—
143C23×C22⋊C4D1111yescharacteristic
144C2×#381—112no—
145C2×#380—111no—
146C2×#379—112no—
147C2×C4×C22⋊C4—111no—
148#1439—114no—
149#1437—114no—
150C23×C11—24no—
151C23×C11—24no—
152C23×C11—24no—
153C23×C11—24no—
154C23×C11—24no—
155C23×C11—24no—
156C23×C11—216no—
157C23×C11—216no—
158C23×C11—232no—
159C23×C11—24no—
160C23×C11—24no—
161C23×C11—28no—
162C23×C11—28no—
163C23×C11—28no—
164C23×C11—28no—
165C23×C11—216no—
166C23×C11—216no—
167C23×C11—464no—
168C23×C11—432no—
169C23×C11—416no—
170C23×C11—464no—
171C23×C11—432no—
172C23×C11—44no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—44no—
176C23×C11—44no—
177C23×C11—48no—
178C23×C11—48no—
179C23×C11—416no—
180C23×C11C2×C22⋊C414yes—
181C23×C11#11718yes—
182C23×C11C4×D418yes—
183C23×C11#12118yes—
184C23×C11#12414yes—
185C23×C11#12714yes—
186C23×C11C23×C411yescharacteristic
187C23×C11C22×D412yes—
188C23×C11C22×D411yescharacteristic
189C23×C11C22×D411yescharacteristic
190C23×C11C2×#4114yes—
191C23×C11C2×#4112yes—
192C23×C11H(5,𝔽2)14yes—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—28no—
201C2×C4×C11—416no—
202C2×C4×C11—44no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—416no—
206C2×C4×C11C2×C22⋊C414yes—
207C2×C4×C11C2×C22⋊C414yes—
208C2×Dic11—28no—
209C2×Dic11—216no—
210C2×Dic11—44no—
211C2×Dic11—44no—
212C2×Dic11—48no—
213C2×Dic11—44no—
214C2×Dic11—44no—
215C2×Dic11—44no—
216C2×Dic11—48no—
217C2×Dic11—48no—
218C26C2×D1111yescharacteristic
219C24×C4C2×D1111yescharacteristic
220C24×C4C2×D1111yescharacteristic
221C22×C4⋊C4—112no—
222C22×C22⋊C4—24no—
223C22×C22⋊C4—24no—
224C22×C22⋊C4—112no—
225C22×C22⋊C4—112no—
226C22×C22⋊C4—118no—
227C22×C22⋊C4Dic1118yescomplemented
228C22×C22⋊C4C2×D1112yes—
229C22×C22⋊C4C2×D1112yes—
230C22×C42—112no—
231#381—228no—
232#380—224no—
233#379—228no—
234C4×C22⋊C4—224no—
235C2×#95—112no—
236C2×#95—118no—
237C2×#95—112no—
238C22×C11—28no—
239C22×C11—24no—
240C22×C11—216no—
241C22×C11—216no—
242C22×C11—24no—
243C22×C11—28no—
244C22×C11—216no—
245C22×C11—28no—
246C22×C11—464no—
247C22×C11—48no—
248C22×C11—44no—
249C22×C11—48no—
250C22×C11—416no—
251C22×C11—48no—
252C22×C11—44no—
253C22×C11#39018yes—
254C22×C11C22×C22⋊C411yescharacteristic
255C22×C11C2×#11712yes—
256C22×C11C2×C4×D412yes—
257C22×C11#51812yes—
258C22×C11C2×#12112yes—
259C22×C11#52512yes—
260C22×C11#52512yes—
261C22×C11C2×#12411yescharacteristic
262C22×C11C2×#12711yescharacteristic
263C22×C11#53412yes—
264C22×C11#53412yes—
265C22×C11#54618yes—
266C22×C11#55118yes—
267C4×C11—24no—
268C4×C11—24no—
269C4×C11—44no—
270Dic11—48no—
271Dic11—84no—
272C25—28no—
273C25—22no—
274C25—22no—
275C25—24no—
276C25—24no—
277C25—44no—
278C25C2×Dic1114yes—
279C25C22×D1112yes—
280C25C22×D1111yescharacteristic
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—44no—
286C23×C4—114no—
287C23×C4—114no—
288C23×C4C2×Dic1114yes—
289C23×C4C2×Dic1114yes—
290C23×C4C22⋊D1114yes—
291C23×C4C22⋊D1114yes—
292C23×C4C22×D1112yes—
293C23×C4C22×D1111yescharacteristic
294C23×C4C22×D1111yescharacteristic
295C2×C4⋊C4—224no—
296C2×C4⋊C4—444no—
297C2×C22⋊C4—232no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—118no—
303C2×C22⋊C4—224no—
304C2×C22⋊C4—224no—
305C2×C22⋊C4—2216no—
306C2×C22⋊C4—2216no—
307C2×C22⋊C4—224no—
308C2×C22⋊C4—224no—
309C2×C22⋊C4—224no—
310C2×C22⋊C4—448no—
311C2×C22⋊C4C2×Dic1118yes—
312C2×C22⋊C4C2×Dic1118yes—
313C2×C42—224no—
314C2×C42—444no—
315#95—2216no—
316#95—224no—
317#95—224no—
318C2×C11—28no—
319C2×C11—48no—
320C2×C11#228011yescharacteristic
321C2×C11C2×#39011yescharacteristic
322C2×C11#230811yescharacteristic
323C2×C11#234214yes—
324C2×C11#253414yes—
325C2×C11#253912yes—
326C2×C11#256112yes—
327C24—24no—
328C24—24no—
329C24—216no—
330C24—216no—
331C24—216no—
332C24—28no—
333C24—24no—
334C24—24no—
335C24—24no—
336C24—28no—
337C24—22no—
338C24—22no—
339C24—216no—
340C24—48no—
341C24—432no—
342C24—432no—
343C24—48no—
344C24—48no—
345C24—44no—
346C24—48no—
347C24—44no—
348C24#433918yes—
349C24D4×D1114yes—
350C24#434114yes—
351C24C22×Dic1114yes—
352C24C22×Dic1112yes—
353C24C2×C22⋊D1112yes—
354C24C2×C22⋊D1112yes—
355C24C23×D1111yescharacteristic
356C22×C4—24no—
357C22×C4—24no—
358C22×C4—216no—
359C22×C4—28no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—48no—
365C22×C4—48no—
366C22×C4—48no—
367C22×C4—44no—
368C22×C4—48no—
369C22×C4—44no—
370C22×C4—118no—
371C22×C4—228no—
372C22×C4—224no—
373C22×C4—228no—
374C22×C4—224no—
375C22×C4—228no—
376C22×C4—224no—
377C22×C4—224no—
378C22×C4—228no—
379C22×C4—224no—
380C22×C4C22⋊Dic11116yescomplemented
381C22×C4C22×Dic1114yes—
382C22×C4C22×Dic1112yes—
383C22×C4C22×Dic1112yes—
384C22×C4C2×C22⋊D1112yes—
385C22×C4C2×C22⋊D1112yes—
386C22×C4C2×C22⋊D1112yes—
387C22×C4C2×C22⋊D1112yes—
388C4⋊C4—448no—
389C22⋊C4—216no—
390C22⋊C4—216no—
391C22⋊C4—2216no—
392C22⋊C4—4432no—
393C22⋊C4—448no—
394C42—448no—
395C11#1390311yescharacteristic, complemented, Sylow
396C23—216no—
397C23—216no—
398C23—24no—
399C23—24no—
400C23—24no—
401C23—24no—
402C23—24no—
403C23—24no—
404C23—232no—
405C23—216no—
406C23—216no—
407C23—24no—
408C23—28no—
409C23—28no—
410C23—28no—
411C23—28no—
412C23—24no—
413C23—464no—
414C23—416no—
415C23—464no—
416C23—432no—
417C23—432no—
418C23—48no—
419C23—48no—
420C23—42no—
421C23—44no—
422C23—42no—
423C23—44no—
424C23—44no—
425C23—416no—
426C23#6697918yes—
427C23D4×Dic1118yes—
428C23#6698914yes—
429C23#6699118yes—
430C23#6699314yes—
431C23C2×C22⋊Dic1114yes—
432C23C2×#433914yes—
433C23C2×D4×D1112yes—
434C23C2×#434112yes—
435C23#6703714yes—
436C23C23×Dic1111yescharacteristic
437C23C22×C22⋊D1111yescharacteristic
438C23C22×C22⋊D1111yescharacteristic
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—28no—
446C2×C4—24no—
447C2×C4—416no—
448C2×C4—42no—
449C2×C4—44no—
450C2×C4—42no—
451C2×C4—416no—
452C2×C4—2216no—
453C2×C4—228no—
454C2×C4—448no—
455C2×C4—444no—
456C2×C4—444no—
457C2×C4—448no—
458C2×C4—448no—
459C2×C4—444no—
460C2×C4—444no—
461C2×C4—444no—
462C2×C4C2×C22⋊Dic1114yes—
463C2×C4C2×C22⋊Dic1114yes—
464C22—24no—
465C22—216no—
466C22—216no—
467C22—28no—
468C22—28no—
469C22—24no—
470C22—216no—
471C22—28no—
472C22—464no—
473C22—44no—
474C22—416no—
475C22—48no—
476C22—48no—
477C22—48no—
478C22—44no—
479C22#1062283418yes—
480C22#1062302118yes—
481C22#1062302618yes—
482C22C2×#6697912yes—
483C22#1062332212yes—
484C22#1062332212yes—
485C22C2×D4×Dic1112yes—
486C22C2×#6698911yescharacteristic
487C22#1062332912yes—
488C22C2×#6699112yes—
489C22C2×#6699311yescharacteristic
490C22#1062333512yes—
491C22#1062333512yes—
492C22C22×C22⋊Dic1111yescharacteristic
493C4—24no—
494C4—24no—
495C4—44no—
496C4—448no—
497C4—884no—
498C2—28no—
499C2—48no—
500C2#1307099911yescharacteristic
501C2C2×#1062283411yescharacteristic
502C2#1307119411yescharacteristic
503C2#1307146514yes—
504C2#1307350614yes—
505C2#1307354712yes—
506C2#1307377412yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC23×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC26×C11C22
hypercenterC23×C22⋊C4D11
hypocenterC11#13903
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622824C2semidirect
2. C2×#10622825C2semidirect
4. C2×C4×C22⋊Dic11C2semidirect
5. #13066861C2semidirect
6. #13066853C2semidirect
13. C22×C11×C22⋊C4C4semidirect
19. C22×C4⋊Dic11C22semidirect
20. C22×C4×Dic11C22semidirect
25. C2×C11⋊#95C22semidirect
26. C2×C11⋊#95C22semidirect
27. C2×C11⋊#95C22semidirect
118. C22×C4×C11C22⋊C4semidirect
227. C22×C22⋊C4Dic11semidirect
380. C22×C4C22⋊Dic11semidirect
395. C11#13903semidirect

Maximal subgroups

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

subgroupindex
C2×#106228242
C2×#106228252
C2×#106228602
C2×C4×C22⋊Dic112
#130668612
#130668532
C23×C11×C22⋊C42
#1390311