Finite Group Databasebeta

← #14796430

Subgroups — #14796430

Order 2816.

838 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622463C211yesmaximal, characteristic, complemented
2C2×C4×#4324C211yesmaximal, characteristic
3#13073789C211yesmaximal, characteristic
4#13071528C211yesmaximal, characteristic, complemented
5#13070103C212yesmaximal, complemented
6#13070002C212yesmaximal
7#13069576C211yesmaximal, characteristic, complemented
8#13069332C211yesmaximal, characteristic, complemented
9#13068968C212yesmaximal
10#13068630C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C22×#4324C2211yescharacteristic
14C2×#66940C2212yes—
15C2×#66922C2211yescharacteristic
16C2×C4×Dic22C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#102C2212yes—
19C11×#384C2211yescharacteristic
20#10622834C2212yes—
21C2×#66896C2211yescharacteristic
22#10622825—21no—
23#10622825—21no—
24C2×#66882C2212yes—
25C2×#66880C2212yes—
26C2×Dic11⋊C8C2212yes—
27C4×#4324—24no—
28#10622590C2212yes—
29#10622589—21no—
30C4⋊C4×Dic11—21no—
31#10622586C2212yes—
32#10622585—22no—
33C2×#66874C2211yescharacteristic
34C2×#66872C2211yescharacteristic
35#10622560—22no—
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622463—24no—
39C11×#340C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C22×Dic22—21no—
46C22×Dic22C2311yescharacteristic
47C22×C8×C11C2312yes—
48C4×D4×C11—22no—
49C4×D4×C11—22no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C22⋊C4—21no—
55C2×C42×C11C2311yescharacteristic
56C2×C22⋊Dic11—22no—
57C2×C22⋊Dic11—22no—
58C2×#4324—22no—
59C2×#4324—22no—
60C2×#4324Q814yescomplemented
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11D411yescharacteristic
63C2×C4⋊Dic11D411yescharacteristic
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×Dic11⋊C4—21no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×C4×Dic11—21no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11C2312yes—
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74#66940—24no—
75#66940—42no—
76#66922—22no—
77#66922—22no—
78C4×Dic22—22no—
79C4×Dic22D414yes—
80C11×C4⋊C8—22no—
81C11×#102—42no—
82#66896—22no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95D412yes—
87#66882—24no—
88#66880—24no—
89Dic11⋊C8—42no—
90#66874—22no—
91#66872—22no—
92C4×C11⋊C8—22no—
93#24814—111nomaximal, Sylow
94C24×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11C2×Q812yes—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—22no—
112C22×Dic11C2×D412yes—
113C22×Dic11C2×D412yes—
114C2×Dic22—21no—
115C2×Dic22—21no—
116C2×Dic22—21no—
117C2×Dic22—42no—
118C2×Dic22—81no—
119C2×Dic22—81no—
120C2×Dic22C2×D412yes—
121C2×Dic22C2×Q812yes—
122C2×Dic22#4112yes—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—42no—
131C11×C4⋊C4—81no—
132C11×C22⋊C4—42no—
133C42×C11C2×D412yes—
134C42×C11#4112yes—
135C22⋊Dic11—82no—
136C22⋊Dic11—82no—
137#4324—28no—
138C4⋊Dic11—22no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—21no—
142C4⋊Dic11—22no—
143C4⋊Dic11—42no—
144C4⋊Dic11C2×D412yes—
145Dic11⋊C4—24no—
146Dic11⋊C4—44no—
147Dic11⋊C4—82no—
148C4×Dic11—24no—
149C4×Dic11—22no—
150C4×Dic11—22no—
151C4×Dic11—44no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8C2×Q812yes—
158C2×#477—111no—
159C2×C4×SD16—111no—
160#2563—111no—
161Q8×C4⋊C4—111no—
162#2085—112no—
163#2067—112no—
164#1990—111no—
165#1939—111no—
166#1880—112no—
167#1805—112no—
168#1802D1111yescharacteristic
169C23×C11—22no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11C22×D411yescharacteristic
177D4×C11—22no—
178D4×C11—22no—
179D4×C11—41no—
180D4×C11—41no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—84no—
190C2×C4×C11#12112yes—
191C2×C4×C11#12112yes—
192C2×C4×C11#13512yes—
193C2×C4×C11#13712yes—
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C22×Q811yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11H(5,𝔽2)11yescharacteristic
199C2×C4×C112−1+411yescharacteristic
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215Dic22—22no—
216Dic22—22no—
217Dic22—22no—
218Dic22—84no—
219Dic22C22⋊Q814yes—
220C8×C11—42no—
221C11⋊C8—22no—
222C11⋊C8—41no—
223C22×SD16—111no—
224C2×C4⋊Q8—111no—
225C2×C4×Q8—112no—
226C2×C4×Q8—111no—
227C2×C4×D4C2×D1111yescharacteristic
228#477—224no—
229C4×SD16—224no—
230C2×#107—112no—
231C2×#106—111no—
232C2×C4⋊C8—112no—
233C2×C4⋊C8C2×D1111yescharacteristic
234C2×#103—112no—
235C2×#103—111no—
236C2×#102—111no—
237C2×#102C2×D1112yes—
238C2×C4×C8—111no—
239#393—222no—
240#390—112no—
241#389—112no—
242#389—222no—
243#384—221no—
244#384C2×D1111yescharacteristic
245#382—112no—
246#380—221no—
247#380—221no—
248C4×C4⋊C4—111no—
249C4×C4⋊C4—221no—
250#340—112no—
251#340—112no—
252#340C2×D1112yes—
253#336—112no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11—81no—
261C22×C11C2×#12111yescharacteristic
262C22×C11#54611yescharacteristic
263C22×C11D4×Q811yescharacteristic
264C22×C11C2×#13511yescharacteristic
265C22×C11C2×#13711yescharacteristic
266C22×C11#57611yescharacteristic
267C22×C11#57711yescharacteristic
268C4×C11—22no—
269C4×C11—81no—
270C4×C11—82no—
271C4×C11#46414yes—
272C4×C11C2×C22⋊Q811yescharacteristic
273C4×C11#53711yescharacteristic
274C4×C11#55211yescharacteristic
275C4×C11#55411yescharacteristic
276Dic11—24no—
277Dic11—42no—
278Dic11—42no—
279Dic11—42no—
280Dic11—82no—
281C22×Q8—111no—
282C22×Q8—221no—
283C22×D4C22×D1111yescharacteristic
284C23×C4—21no—
285C2×SD16—114no—
286C2×SD16—222no—
287C2×SD16—222no—
288C22×C8—111no—
289C22×C8—111no—
290C22×C8C22×D1112yes—
291C4⋊Q8—222no—
292C4⋊Q8—222no—
293C4×Q8—114no—
294C4×Q8—222no—
295C4×Q8—224no—
296C4×Q8—442no—
297C4×D4—22no—
298C4×D4—22no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—112no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4C22×D1111yescharacteristic
310C2×C4⋊C4C22×D1112yes—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—222no—
313C2×C22⋊C4—222no—
314C2×C42—112no—
315C2×C42—221no—
316C2×C42—222no—
317C2×C42C22×D1111yescharacteristic
318#107—224no—
319#106—222no—
320C4⋊C8—22no—
321C4⋊C8—442no—
322#103—222no—
323#103—224no—
324#102—42no—
325#102—222no—
326C4×C8—222no—
327#95—112no—
328#95—222no—
329#95—222no—
330#95—222no—
331C2×C11—82no—
332C2×C11#241711yescharacteristic
333C2×C11C2×#46411yescharacteristic
334C2×C11#304511yescharacteristic
335C2×C11#330511yescharacteristic
336C2×C11#332911yescharacteristic
337C2×C11#338111yescharacteristic
338C2×C11#338511yescharacteristic
339C24—21no—
340C2×Q8—112no—
341C2×Q8—112no—
342C2×Q8—112no—
343C2×Q8—221no—
344C2×Q8—221no—
345C2×Q8—221no—
346C2×Q8—442no—
347C2×Q8—881no—
348C2×Q8—881no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4Q8×D1112yes—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—112no—
361C22×C4—112no—
362C22×C4—221no—
363C22×C4—221no—
364C22×C4—222no—
365C22×C4D4×D1111yescharacteristic
366C22×C4D4×D1111yescharacteristic
367C22×C4C23×D1111yescharacteristic
368SD16—228no—
369C2×C8—22no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—112no—
373C2×C8—221no—
374C2×C8—221no—
375C2×C8—221no—
376C2×C8—221no—
377C2×C8—221no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—42no—
383C4⋊C4—81no—
384C4⋊C4—112no—
385C4⋊C4—224no—
386C4⋊C4—222no—
387C4⋊C4—222no—
388C4⋊C4—221no—
389C4⋊C4—222no—
390C4⋊C4—222no—
391C4⋊C4—444no—
392C4⋊C4—442no—
393C4⋊C4—882no—
394C22⋊C4—42no—
395C22⋊C4—882no—
396C22⋊C4—882no—
397C42—224no—
398C42—222no—
399C42—222no—
400C42—444no—
401C42#433912yes—
402C42D4×D1112yes—
403C11#2481411yescharacteristic, complemented, Sylow
404C23—22no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23C2×D4×D1111yescharacteristic
412Q8—114no—
413Q8—222no—
414Q8—222no—
415Q8—222no—
416Q8—884no—
417D4—22no—
418D4—22no—
419D4—41no—
420D4—41no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—84no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—222no—
433C2×C4—222no—
434C2×C4—222no—
435C2×C4—222no—
436C2×C4—222no—
437C2×C4—222no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4#6693712yes—
446C2×C4#6693712yes—
447C2×C4#6696512yes—
448C2×C4#6696812yes—
449C2×C4C2×#433911yescharacteristic
450C2×C4C2×D4×D1111yescharacteristic
451C2×C4#6703711yescharacteristic
452C2×C4C2×Q8×D1111yescharacteristic
453C2×C4#41×D1111yescharacteristic
454C2×C4#6704311yescharacteristic
455C8—42no—
456C8—222no—
457C8—441no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22C2×#6693711yescharacteristic
466C22#1062314311yescharacteristic
467C22#1062316311yescharacteristic
468C22C2×#6696511yescharacteristic
469C22C2×#6696811yescharacteristic
470C22#1062330511yescharacteristic
471C22#1062330911yescharacteristic
472C4—22no—
473C4—81no—
474C4—82no—
475C4—224no—
476C4—442no—
477C4—442no—
478C4—442no—
479C4—882no—
480C4#1062238014yes—
481C4#1062304211yescharacteristic
482C4#1062306011yescharacteristic
483C4#1062313911yescharacteristic
484C4D11×C22⋊Q811yescharacteristic
485C2—82no—
486C2#1307206911yescharacteristic
487C2C2×#1062238011yescharacteristic
488C2#1307815411yescharacteristic
489C2#1308056911yescharacteristic
490C2#1308091311yescharacteristic
491C2#1308149511yescharacteristic
492C2#1308153011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1802C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#1802D11
hypocenterC11#24814
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
1. C2×#10622463C2semidirect
4. #13071528C2semidirect
5. #13070103C2semidirect
7. #13069576C2semidirect
8. #13069332C2semidirect
10. #13068630C2semidirect
60. C2×#4324Q8semidirect
403. C11#24814semidirect

Maximal subgroups

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

subgroupindex
C2×#106224632
C2×C4×#43242
#130737892
#130715282
#130701032
#130700022
#130695762
#130693322
#130689682
#130686302
C11×#18022
#2481411