Finite Group Databasebeta

← #14805631

Subgroups — #14805631

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×#10622697C211yesmaximal, characteristic
2C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
3#13073534C211yesmaximal, characteristic
4#13070118C212yesmaximal, complemented
5#13069987C212yesmaximal
6#13069578C211yesmaximal, characteristic, complemented
7#13069379C211yesmaximal, characteristic, complemented
8#13069341C212yesmaximal, complemented
9#13069298C212yesmaximal
10C4×#66873C211yesmaximal, characteristic
11C11×#2567C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×#66999—21no—
15C2×C4×D44C2211yescharacteristic
16C11×#395—22no—
17C11×#391—21no—
18C11×#389C2212yes—
19C11×#389C2212yes—
20C11×#384—21no—
21C4×C11×C4⋊C4C2211yescharacteristic
22#10622697—24no—
23Q8×C11⋊C8—24no—
24#10622607—22no—
25#10622600—21no—
26C2×#66873C2212yes—
27C2×#66873C2211yescharacteristic
28C2×#66873C2211yescharacteristic
29C2×#66872C2212yes—
30C2×#66872C2212yes—
31#10622552C2212yes—
32#10622548C2211yescharacteristic
33#10622541C2212yes—
34C2×C4⋊(C11⋊C8)C2212yes—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37C2×C4×C11⋊C8C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42#10622167C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11D411yescharacteristic
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8—22no—
49C4×Q8×C11—22no—
50C4×Q8×C11—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C42×C11—21no—
60C2×C42×C11C2312yes—
61C2×C42×C11C2311yescharacteristic
62#66999—44no—
63C2×(C2×D11)⋊C4—21no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2312yes—
70C2×Dic11⋊C4—22no—
71C22×C11⋊C8C2311yescharacteristic
72C22×C11⋊C8C2312yes—
73C22×C11⋊C8C2311yescharacteristic
74C4×D44—22no—
75C4×D44—22no—
76C11×#95—21no—
77C11×#95—22no—
78C11×#95—22no—
79C11⋊#95—22no—
80#66873—22no—
81#66873—24no—
82#66873Q814yescomplemented
83#66872—24no—
84#66872—24no—
85C4⋊(C11⋊C8)—24no—
86C4⋊(C11⋊C8)D414yes—
87C4×C11⋊C8—22no—
88C4×C11⋊C8—24no—
89#25470—111nomaximal, Sylow
90C23×D11—21no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11—42no—
94C2×Q8×C11—81no—
95C2×Q8×C11—81no—
96C2×Q8×C11SD1614yes—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—21no—
106C22×Dic11—22no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44C2×Q812yes—
113C2×C4×D11—42no—
114C2×C4×D11—42no—
115C2×C4×D11—42no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—42no—
123C11×C4⋊C4—82no—
124C11×C4⋊C4—82no—
125C11×C4⋊C4C2×Q812yes—
126C11×C4⋊C4#4112yes—
127C42×C11—22no—
128C42×C11—22no—
129C42×C11—42no—
130C42×C11C2×D412yes—
131C42×C11#4112yes—
132(C2×D11)⋊C4—42no—
133(C2×D11)⋊C4—44no—
134(C2×D11)⋊C4—82no—
135C4⋊Dic11—21no—
136C4⋊Dic11—22no—
137C4⋊Dic11—21no—
138C4⋊Dic11—22no—
139C4⋊Dic11—42no—
140C4⋊Dic11—81no—
141Dic11⋊C4—44no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—21no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8C2×D414yes—
150C2×C11⋊C8C2×Q812yes—
151C2×#476—111no—
152C2×C8×Q8—111no—
153#2567D1111yescharacteristic, complemented
154#2538—111no—
155#2088—112no—
156#2065—112no—
157#1990—111no—
158#1948—111no—
159#1941—112no—
160#1934—112no—
161C4×#102—111no—
162C23×C11C22×D411yescharacteristic
163C22×D11—22no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—41no—
168C22×D11—41no—
169C22×D11—41no—
170Q8×C11—28no—
171Q8×C11—84no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11#12112yes—
189C2×C4×C11#12112yes—
190C2×C4×C11C2×SD1614yes—
191C2×C4×C11C2×SD1612yes—
192C2×C4×C11#13512yes—
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×Q811yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C112−1+411yescharacteristic
198C2×C4×C112−1+411yescharacteristic
199C2×Dic11—41no—
200C2×Dic11—42no—
201C2×Dic11—41no—
202C2×Dic11—42no—
203C2×Dic11—41no—
204C2×Dic11—42no—
205D44—22no—
206D44—22no—
207D44—41no—
208D44—41no—
209C4×D11—84no—
210C11⋊C8—24no—
211C11⋊C8—22no—
212C11⋊C8—41no—
213C2×C4⋊Q8C2×D1111yescharacteristic
214C2×C22⋊Q8—221no—
215C2×C4×Q8C2×D1111yescharacteristic
216C2×C4×D4—111no—
217#476—224no—
218C8×Q8—224no—
219C2×#106—112no—
220C2×#106—112no—
221C2×C4⋊C8—111no—
222C2×C4⋊C8—112no—
223C2×#102—111no—
224C2×#102—111no—
225C2×#102—112no—
226C2×C4×C8—112no—
227C2×C4×C8—111no—
228#396—222no—
229#395—22no—
230#391—21no—
231#390—112no—
232#389—112no—
233#389C2×D1112yes—
234#389C2×D1112yes—
235#384—21no—
236#384—111no—
237#380—221no—
238C4×C4⋊C4C2×D1111yescharacteristic
239#340—112no—
240#340—111no—
241#340—112no—
242#340—112no—
243#340—111no—
244C22×C11C2×#12111yescharacteristic
245C22×C11#54811yescharacteristic
246C22×C11D4×Q811yescharacteristic
247C22×C11C22×SD1611yescharacteristic
248C22×C11C2×#13511yescharacteristic
249C22×C11#57611yescharacteristic
250C22×C11#57711yescharacteristic
251C2×D11—42no—
252C2×D11—42no—
253C2×D11—42no—
254C2×D11—81no—
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—81no—
258C4×C11—24no—
259C4×C11—22no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—42no—
263C4×C11—82no—
264C4×C11#46514yes—
265C4×C11#53311yescharacteristic
266C4×C11#54111yescharacteristic
267C4×C11#54711yescharacteristic
268C4×C11D4×Q811yescharacteristic
269Dic11—82no—
270Dic11—81no—
271C22×Q8—21no—
272C22×Q8C22⋊D1111yescharacteristic
273C22×D4—111no—
274C23×C4—221no—
275C22×C8—111no—
276C22×C8—112no—
277C22×C8—111no—
278C4⋊Q8—22no—
279C4⋊Q8—22no—
280C22⋊Q8—444no—
281C4×Q8—22no—
282C4×Q8—22no—
283C4×D4—222no—
284C4×D4—222no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—112no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4C22⋊D1111yescharacteristic
294C2×C4⋊C4C22⋊D1112yes—
295C2×C4⋊C4C22×D1112yes—
296C2×C4⋊C4C22×D1111yescharacteristic
297C2×C4⋊C4C22×D1111yescharacteristic
298C2×C22⋊C4—221no—
299C2×C22⋊C4—222no—
300C2×C22⋊C4—222no—
301C2×C42—21no—
302C2×C42C22×D1112yes—
303C2×C42C22×D1111yescharacteristic
304#106—224no—
305#106—224no—
306C4⋊C8—114no—
307C4⋊C8—224no—
308#102—114no—
309#102—224no—
310#102—222no—
311C4×C8—224no—
312C4×C8—222no—
313#95—21no—
314#95—22no—
315#95—22no—
316#95—222no—
317C2×C11#242911yescharacteristic
318C2×C11C2×#46511yescharacteristic
319C2×C11#306211yescharacteristic
320C2×C11#336011yescharacteristic
321C2×C11#336211yescharacteristic
322C2×C11Q8×SD1611yescharacteristic
323C2×C11#338011yescharacteristic
324D11—82no—
325C24—221no—
326C2×Q8—22no—
327C2×Q8—22no—
328C2×Q8—42no—
329C2×Q8—81no—
330C2×Q8—81no—
331C2×Q8#432514yes—
332C2×D4—112no—
333C2×D4—221no—
334C2×D4—221no—
335C2×D4—221no—
336C2×D4—221no—
337C2×D4—221no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—221no—
342C22×C4—222no—
343C22×C4—442no—
344C22×C4—442no—
345C22×C4—442no—
346C22×C4C2×C22⋊D1112yes—
347C22×C4C2×C22⋊D1111yescharacteristic
348C22×C4C2×C22⋊D1112yes—
349C22×C4C2×C22⋊D1111yescharacteristic
350C22×C4C23×D1111yescharacteristic
351C2×C8—114no—
352C2×C8—112no—
353C2×C8—221no—
354C2×C8—222no—
355C2×C8—222no—
356C2×C8—221no—
357C2×C8—221no—
358C2×C8—221no—
359C2×C8—221no—
360C4⋊C4—24no—
361C4⋊C4—22no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—42no—
367C4⋊C4—82no—
368C4⋊C4—82no—
369C4⋊C4—221no—
370C4⋊C4—221no—
371C4⋊C4—222no—
372C4⋊C4—222no—
373C4⋊C4—444no—
374C4⋊C4—442no—
375C4⋊C4—881no—
376C4⋊C4Q8×D1112yes—
377C4⋊C4#434312yes—
378C22⋊C4—442no—
379C22⋊C4—444no—
380C22⋊C4—882no—
381C42—22no—
382C42—22no—
383C42—42no—
384C42D4×D1112yes—
385C42#434112yes—
386C11#2547011yescharacteristic, complemented, Sylow
387C23—222no—
388C23—441no—
389C23—441no—
390C23—441no—
391C23—441no—
392C23—441no—
393C23—441no—
394C23C22×C22⋊D1111yescharacteristic
395Q8—28no—
396Q8—84no—
397D4—222no—
398D4—222no—
399D4—441no—
400D4—441no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—441no—
418C2×C4—442no—
419C2×C4—441no—
420C2×C4—442no—
421C2×C4—441no—
422C2×C4—442no—
423C2×C4—884no—
424C2×C4#6699212yes—
425C2×C4#6699212yes—
426C2×C4C2×#432514yes—
427C2×C4C2×#432512yes—
428C2×C4#6700312yes—
429C2×C4C2×D4×D1111yescharacteristic
430C2×C4C2×#434111yescharacteristic
431C2×C4C2×Q8×D1111yescharacteristic
432C2×C4C2×#434311yescharacteristic
433C2×C4#6704011yescharacteristic
434C2×C4#6704011yescharacteristic
435C8—224no—
436C8—222no—
437C8—441no—
438C22—442no—
439C22—442no—
440C22—442no—
441C22—881no—
442C22—881no—
443C22—881no—
444C22—881no—
445C22C2×#6699211yescharacteristic
446C22C22×#432511yescharacteristic
447C22Q8×C22⋊D1111yescharacteristic
448C22#1062334811yescharacteristic
449C22C2×#6700311yescharacteristic
450C22#1062336611yescharacteristic
451C22#1062336711yescharacteristic
452C4—22no—
453C4—24no—
454C4—42no—
455C4—42no—
456C4—42no—
457C4—82no—
458C4—881no—
459C4—882no—
460C4#1062266114yes—
461C4#1062325711yescharacteristic
462C4#1062325811yescharacteristic
463C4#1062325911yescharacteristic
464C4#1062326211yescharacteristic
465C2—882no—
466C2#1307221811yescharacteristic
467C2C2×#1062266111yescharacteristic
468C2#1307829211yescharacteristic
469C2#1308126511yescharacteristic
470C2#1308128711yescharacteristic
471C2Q8×#432511yescharacteristic
472C2#1308147911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2567C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2567D11
hypocenterC11#25470
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2567

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C11⋊C8C2semidirect
4. #13070118C2semidirect
6. #13069578C2semidirect
7. #13069379C2semidirect
8. #13069341C2semidirect
11. C11×#2567C2semidirect
82. #66873Q8semidirect
153. #2567D11semidirect
386. C11#25470semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
C2×Q8×C11⋊C82
#130735342
#130701182
#130699872
#130695782
#130693792
#130693412
#130692982
C4×#668732
C11×#25672
#2547011