Finite Group Databasebeta

← #14805628

Subgroups — #14805628

Order 2816.

818 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622621C211yesmaximal, characteristic
2C2×C8×Dic22C211yesmaximal, characteristic, complemented
3#13073824C211yesmaximal, characteristic, complemented
4#13073538C211yesmaximal, characteristic
5#13070119C212yesmaximal, complemented
6#13069986C212yesmaximal
7#13069577C211yesmaximal, characteristic, complemented
8#13069379C211yesmaximal, characteristic, complemented
9#13069343C212yesmaximal, complemented
10#13069301C212yesmaximal
11C4×C11×#102C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66977—21no—
14C2×#66922C2211yescharacteristic
15C2×C4×Dic22C2211yescharacteristic
16C2×C11×#102C2211yescharacteristic
17C2×C11×#102C2211yescharacteristic
18C2×C4×C8×C11C2211yescharacteristic
19C4×C11×C4⋊C4C2211yescharacteristic
20#10622834C2212yes—
21C2×#66896C2212yes—
22#10622825—21no—
23C2×Dic11⋊C8C2212yes—
24C2×C8×Dic11C2212yes—
25#10622621—24no—
26#10622598C2212yes—
27#10622598C2212yes—
28#10622586C2212yes—
29C2×#66872C2212yes—
30C2×#66872C2212yes—
31#10622561—22no—
32#10622548—21no—
33#10622548C2211yescharacteristic
34#10622542—21no—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C8×Dic22—24no—
37#10622269—22no—
38C11×#340C2211yescharacteristic
39C11×#340C2211yescharacteristic
40#10622189C2212yes—
41#10622189C2212yes—
42#10622167C2212yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C22×Dic22—21no—
46C22×Dic22D411yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C4×D4×C11—22no—
50C4×D4×C11—22no—
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C22⋊C4—21no—
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11D411yescharacteristic
65C2×C4⋊Dic11C2312yes—
66C2×C4⋊Dic11C2312yes—
67#66977—44no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4D412yes—
70C2×C4×Dic11C2312yes—
71C22×C11⋊C8C2312yes—
72#66922—22no—
73#66922—22no—
74C4×Dic22—22no—
75C4×Dic22—22no—
76C11×#102—22no—
77C11×#102Q814yescomplemented
78C4×C8×C11—22no—
79C11×#95—21no—
80#66896—24no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84Dic11⋊C8—24no—
85C8×Dic11—24no—
86#66872—24no—
87#66872—24no—
88C4⋊(C11⋊C8)D414yes—
89#25470—111nomaximal, Sylow
90C24×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11C2×Q812yes—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—42no—
101C22×C4×C11—42no—
102C22×C4×C11—42no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2411yescharacteristic
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11C2×D412yes—
109C22×Dic11C2×D412yes—
110C2×Dic22—22no—
111C2×Dic22—22no—
112C2×Dic22—42no—
113C2×Dic22—81no—
114C2×Dic22—81no—
115C2×Dic22SD1614yes—
116C2×C8×C11—21no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11C2×Q812yes—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4C2×Q812yes—
127C11×C4⋊C4#4112yes—
128C11×C22⋊C4—42no—
129C42×C11—42no—
130C42×C11C2×D412yes—
131C42×C11#4112yes—
132C22⋊Dic11—44no—
133C22⋊Dic11—82no—
134C4⋊Dic11—22no—
135C4⋊Dic11—22no—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139C4⋊Dic11—42no—
140C4⋊Dic11—42no—
141C4⋊Dic11—81no—
142C4⋊Dic11—82no—
143C4⋊Dic11—82no—
144Dic11⋊C4—24no—
145Dic11⋊C4—44no—
146C4×Dic11—22no—
147C4×Dic11—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8C2×D414yes—
151C2×#476—111no—
152C2×C8×Q8—111no—
153#2567—111no—
154#2538—111no—
155#2088—112no—
156#2065—112no—
157#1990—111no—
158#1948—111no—
159#1941—112no—
160#1934—112no—
161C4×#102D1111yescharacteristic
162C23×C11—22no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11C22×D411yescharacteristic
170D4×C11—22no—
171D4×C11—22no—
172D4×C11—41no—
173D4×C11—41no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—84no—
186C2×C4×C11#12112yes—
187C2×C4×C11#12112yes—
188C2×C4×C11C2×SD1612yes—
189C2×C4×C11#13512yes—
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C22×Q811yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C112−1+411yescharacteristic
195C2×C4×C112−1+411yescharacteristic
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11C2×SD1614yes—
208Dic22—28no—
209Dic22—84no—
210C8×C11—22no—
211C8×C11—41no—
212C11⋊C8—24no—
213C2×C4⋊Q8—111no—
214C2×C22⋊Q8—221no—
215C2×C4×Q8—111no—
216C2×C4×D4C2×D1111yescharacteristic
217#476—224no—
218C8×Q8—224no—
219C2×#106—112no—
220C2×#106—112no—
221C2×C4⋊C8—111no—
222C2×C4⋊C8—112no—
223C2×#102—112no—
224C2×#102C2×D1111yescharacteristic
225C2×#102C2×D1111yescharacteristic
226C2×C4×C8—112no—
227C2×C4×C8C2×D1111yescharacteristic
228#396—222no—
229#395—222no—
230#391—221no—
231#390—112no—
232#389—112no—
233#389—112no—
234#389—112no—
235#384—111no—
236#384—221no—
237#380—221no—
238C4×C4⋊C4C2×D1111yescharacteristic
239#340—112no—
240#340—112no—
241#340—112no—
242#340C2×D1111yescharacteristic
243#340C2×D1111yescharacteristic
244C22×C11—42no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11C2×#12111yescharacteristic
252C22×C11#54811yescharacteristic
253C22×C11D4×Q811yescharacteristic
254C22×C11C22×SD1611yescharacteristic
255C22×C11C2×#13511yescharacteristic
256C22×C11#57611yescharacteristic
257C22×C11#57711yescharacteristic
258C4×C11—22no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—81no—
262C4×C11#46514yes—
263C4×C11#53311yescharacteristic
264C4×C11#54111yescharacteristic
265C4×C11#54711yescharacteristic
266C4×C11D4×Q811yescharacteristic
267Dic11—24no—
268Dic11—42no—
269Dic11—82no—
270Dic11—82no—
271C22×Q8—111no—
272C22×Q8—221no—
273C22×D4C22×D1111yescharacteristic
274C23×C4—21no—
275C22×C8—112no—
276C22×C8C22×D1111yescharacteristic
277C22×C8C22×D1111yescharacteristic
278C4⋊Q8—222no—
279C4⋊Q8—222no—
280C22⋊Q8—444no—
281C4×Q8—222no—
282C4×Q8—222no—
283C4×D4—22no—
284C4×D4—22no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—112no—
287C2×C4⋊C4—112no—
288C2×C4⋊C4—112no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4—221no—
292C2×C4⋊C4—222no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4C22×D1111yescharacteristic
296C2×C4⋊C4C22×D1111yescharacteristic
297C2×C4⋊C4C22×D1111yescharacteristic
298C2×C22⋊C4—21no—
299C2×C22⋊C4—222no—
300C2×C22⋊C4—222no—
301C2×C42—21no—
302C2×C42—112no—
303C2×C42C22×D1111yescharacteristic
304#106—224no—
305#106—224no—
306C4⋊C8—114no—
307C4⋊C8—224no—
308#102—22no—
309#102—224no—
310#102Dic2214yescomplemented
311C4×C8—22no—
312C4×C8—224no—
313#95—21no—
314#95—222no—
315#95—222no—
316#95—222no—
317C2×C11—82no—
318C2×C11#242911yescharacteristic
319C2×C11C2×#46511yescharacteristic
320C2×C11#306211yescharacteristic
321C2×C11#336011yescharacteristic
322C2×C11#336211yescharacteristic
323C2×C11Q8×SD1611yescharacteristic
324C2×C11#338011yescharacteristic
325C24—21no—
326C2×Q8—114no—
327C2×Q8—222no—
328C2×Q8—222no—
329C2×Q8—442no—
330C2×Q8—881no—
331C2×Q8—881no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4C2×Dic2212yes—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—112no—
345C22×C4—112no—
346C22×C4—222no—
347C22×C4—222no—
348C22×C4D4×D1111yescharacteristic
349C22×C4D4×D1111yescharacteristic
350C22×C4C23×D1111yescharacteristic
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—114no—
357C2×C8—222no—
358C2×C8—222no—
359C2×C8C2×Dic2212yes—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—224no—
365C4⋊C4—222no—
366C4⋊C4—222no—
367C4⋊C4—222no—
368C4⋊C4—222no—
369C4⋊C4—222no—
370C4⋊C4—444no—
371C4⋊C4—442no—
372C4⋊C4—442no—
373C4⋊C4—881no—
374C4⋊C4—882no—
375C4⋊C4—882no—
376C4⋊C4C2×Dic2212yes—
377C4⋊C4#433912yes—
378C22⋊C4—42no—
379C22⋊C4—444no—
380C22⋊C4—882no—
381C42—42no—
382C42—222no—
383C42—222no—
384C42#433912yes—
385C42D4×D1112yes—
386C11#2547011yescharacteristic, complemented, Sylow
387C23—22no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23C2×D4×D1111yescharacteristic
395Q8—228no—
396Q8—884no—
397D4—22no—
398D4—22no—
399D4—41no—
400D4—41no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—84no—
413C2×C4—114no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—222no—
418C2×C4—222no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4—442no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4#6693712yes—
426C2×C4#6693712yes—
427C2×C4#6696512yes—
428C2×C4SD16×D1112yes—
429C2×C4C22×Dic2211yescharacteristic
430C2×C4C2×#433911yescharacteristic
431C2×C4C2×#433911yescharacteristic
432C2×C4C2×D4×D1111yescharacteristic
433C2×C4#6704311yescharacteristic
434C2×C4#6704311yescharacteristic
435C8—22no—
436C8—41no—
437C8—224no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22—81no—
445C22C2×#6693711yescharacteristic
446C22D4×Dic2211yescharacteristic
447C22#1062308311yescharacteristic
448C22C2×#6696511yescharacteristic
449C22C2×SD16×D1111yescharacteristic
450C22#1062330011yescharacteristic
451C22#1062330111yescharacteristic
452C4—22no—
453C4—42no—
454C4—42no—
455C4—81no—
456C4—224no—
457C4—442no—
458C4—882no—
459C4—882no—
460C4#1062239114yes—
461C4#1062300111yescharacteristic
462C4#1062304911yescharacteristic
463C4D4×Dic2211yescharacteristic
464C4#1062308211yescharacteristic
465C2—82no—
466C2#1307221511yescharacteristic
467C2C2×#1062239111yescharacteristic
468C2#1307829911yescharacteristic
469C2#1308126311yescharacteristic
470C2#1308128511yescharacteristic
471C2SD16×Dic2211yescharacteristic
472C2#1308148111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC4×#102D11
hypocenterC11#25470
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic22C2semidirect
3. #13073824C2semidirect
5. #13070119C2semidirect
7. #13069577C2semidirect
8. #13069379C2semidirect
9. #13069343C2semidirect
77. C11×#102Q8semidirect
310. #102Dic22semidirect
386. C11#25470semidirect

Maximal subgroups

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

subgroupindex
C2×#106226212
C2×C8×Dic222
#130738242
#130735382
#130701192
#130699862
#130695772
#130693792
#130693432
#130693012
C4×C11×#1022
#2547011