Finite Group Databasebeta

← #14803634

Subgroups — #14803634

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622706C211yesmaximal, characteristic, complemented
2C2×#10622632C211yesmaximal, characteristic
3#13071672C211yesmaximal, characteristic, complemented
4#13070025C212yesmaximal, complemented
5#13069933C212yesmaximal
6#13069569C211yesmaximal, characteristic, complemented
7#13069335C211yesmaximal, characteristic, complemented
8#13068974C212yesmaximal
9#13068618C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic
11C11×#2542C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C22⋊Q8—21no—
14C2×C11×C22⋊Q8—21no—
15C2×C4×D4×C11C2211yescharacteristic
16C22×#4324C2212yes—
17C2×#66922C2211yescharacteristic
18C2×C4×Dic22C2212yes—
19C11×#399—22no—
20C11×#390C2212yes—
21C11×#384C2212yes—
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66896C2211yescharacteristic
24C2×#66896C2211yescharacteristic
25#10622706—24no—
26#10622632—24no—
27C4⋊C4×Dic11—21no—
28#10622586—21no—
29C2×#66874C2212yes—
30C2×#66874C2212yes—
31C2×#66874C2212yes—
32C4×C4⋊Dic11C2211yescharacteristic
33#10622542C2212yes—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2212yes—
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622267—22no—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42#10622162C2212yes—
43C22×Q8×C11—21no—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×Dic22C2312yes—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8—22no—
49C11×C22⋊Q8—44no—
50C11×C22⋊Q8—44no—
51C4×D4×C11—22no—
52C4×D4×C11—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C42×C11C2312yes—
64C2×C42×C11C2311yescharacteristic
65C2×#4324—24no—
66C2×#4324—24no—
67C2×#4324—42no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×Dic11⋊C4—22no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11—21no—
75C22×C11⋊C8C2311yescharacteristic
76C22×C11⋊C8C2311yescharacteristic
77C22×C11⋊C8C2312yes—
78#66922—22no—
79#66922D414yes—
80C4×Dic22—24no—
81C4×Dic22—42no—
82C11×#95D412yes—
83#66896—22no—
84#66896—22no—
85C11⋊#95—21no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88#66874—24no—
89#66874—24no—
90#66874—24no—
91C4⋊(C11⋊C8)—22no—
92C4⋊(C11⋊C8)—42no—
93C4×C11⋊C8—22no—
94#25320—111nomaximal, Sylow
95C24×C11—21no—
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11#4112yes—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C22×Dic11—22no—
116C22×Dic11—21no—
117C22×Dic11—21no—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C2×Dic22—22no—
121C2×Dic22—22no—
122C2×Dic22—22no—
123C2×Dic22C2×D414yes—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—44no—
130C11×C4⋊C4—42no—
131C11×C4⋊C4—44no—
132C11×C4⋊C4SD1614yescomplemented
133C11×C22⋊C4—44no—
134C11×C22⋊C4—42no—
135C11×C22⋊C4—44no—
136C42×C11—22no—
137C42×C11—22no—
138C42×C11C2×D412yes—
139C42×C11#4112yes—
140#4324—48no—
141C4⋊Dic11—24no—
142C4⋊Dic11—24no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11#4112yes—
147Dic11⋊C4—44no—
148C4×Dic11—44no—
149C4×Dic11—42no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—21no—
159C2×#487—111no—
160C2×#461—111no—
161#2542D1111yescharacteristic
162#2365—111no—
163#2072—112no—
164#2055—112no—
165#1988—111no—
166#1939—111no—
167#1880—112no—
168#1803—112no—
169C4×#102—111no—
170C23×C11—22no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11C22×D411yescharacteristic
178Q8×C11—84no—
179D4×C11—22no—
180D4×C11—22no—
181D4×C11—41no—
182D4×C11—41no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—84no—
197C2×C4×C11#12112yes—
198C2×C4×C11#12112yes—
199C2×C4×C11C2×SD1614yes—
200C2×C4×C11C2×SD1612yes—
201C2×C4×C11AGL(1,ℤ/8)12yes—
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11H(5,𝔽2)11yescharacteristic
207C2×C4×C112−1+411yescharacteristic
208C2×Dic11—24no—
209C2×Dic11—22no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217Dic22—24no—
218Dic22—24no—
219Dic22—42no—
220Dic22—42no—
221C11⋊C8—41no—
222C11⋊C8—42no—
223C11⋊C8—41no—
224C22×SD16—112no—
225C2×C4⋊Q8—111no—
226C2×C4⋊Q8C2×D1111yescharacteristic
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C4×Q8—112no—
230C2×C4×D4C2×D1111yescharacteristic
231#487—224no—
232#461—224no—
233C2×C4⋊C8—111no—
234C2×C4⋊C8—112no—
235C2×#103—112no—
236C2×#103—112no—
237C2×#103—112no—
238C2×#102—111no—
239C2×#102—111no—
240C2×C4×C8—111no—
241#399—22no—
242#391—112no—
243#390C2×D1112yes—
244#389—221no—
245#387—222no—
246#384C2×D1112yes—
247C4×C4⋊C4—111no—
248C4×C4⋊C4—221no—
249C4×C4⋊C4C2×D1111yescharacteristic
250#340—112no—
251#340—111no—
252#340—112no—
253#340—111no—
254#336—112no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11—81no—
261C22×C11—81no—
262C22×C11C2×#12111yescharacteristic
263C22×C11#54611yescharacteristic
264C22×C11#54811yescharacteristic
265C22×C11C22×SD1611yescharacteristic
266C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
267C22×C11#57811yescharacteristic
268C22×C11#57811yescharacteristic
269C4×C11—24no—
270C4×C11—22no—
271C4×C11—42no—
272C4×C11—81no—
273C4×C11—82no—
274C4×C11#46014yes—
275C4×C11#52911yescharacteristic
276C4×C11#54211yescharacteristic
277C4×C11#54611yescharacteristic
278C4×C11#54711yescharacteristic
279Dic11—42no—
280Dic11—44no—
281Dic11—81no—
282C22×Q8—21no—
283C22×Q8—112no—
284C22×D4C22×D1111yescharacteristic
285C23×C4—21no—
286C2×SD16—224no—
287C2×SD16—224no—
288C2×SD16—442no—
289C22×C8—112no—
290C22×C8—111no—
291C22×C8—111no—
292C4⋊Q8—22no—
293C4⋊Q8—22no—
294C4⋊Q8—114no—
295C4⋊Q8—222no—
296C22⋊Q8—44no—
297C22⋊Q8—44no—
298C4×Q8—224no—
299C4×Q8—442no—
300C4×D4—22no—
301C4×D4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—111no—
306C2×C4⋊C4—111no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4C22⋊D1111yescharacteristic
311C2×C4⋊C4C22⋊D1111yescharacteristic
312C2×C4⋊C4C22×D1111yescharacteristic
313C2×C4⋊C4C22×D1112yes—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C42—222no—
318C2×C42—221no—
319C2×C42C22×D1112yes—
320C2×C42C22×D1111yescharacteristic
321C4⋊C8—222no—
322C4⋊C8—442no—
323#103—224no—
324#103—224no—
325#103—224no—
326#102—222no—
327#102—222no—
328C4×C8—222no—
329#95—221no—
330#95—222no—
331#95—222no—
332#95C22⋊D1112yes—
333C2×C11—82no—
334C2×C11#242711yescharacteristic
335C2×C11C2×#46011yescharacteristic
336C2×C11#304411yescharacteristic
337C2×C11#329811yescharacteristic
338C2×C11#333011yescharacteristic
339C2×C11#335911yescharacteristic
340C2×C11#336711yescharacteristic
341C24—21no—
342C2×Q8—42no—
343C2×Q8—42no—
344C2×Q8—42no—
345C2×Q8—114no—
346C2×Q8—222no—
347C2×Q8—222no—
348C2×Q8—222no—
349C2×Q8—222no—
350C2×Q8—222no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4#434312yes—
357C22×C4—22no—
358C22×C4—21no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—222no—
363C22×C4—221no—
364C22×C4—221no—
365C22×C4C2×C22⋊D1112yes—
366C22×C4C2×C22⋊D1112yes—
367C22×C4C2×C22⋊D1111yescharacteristic
368C22×C4C2×C22⋊D1111yescharacteristic
369C22×C4C23×D1111yescharacteristic
370SD16—448no—
371C2×C8—221no—
372C2×C8—221no—
373C2×C8—222no—
374C2×C8—221no—
375C2×C8—222no—
376C2×C8—221no—
377C2×C8—221no—
378C2×C8—221no—
379C2×C8—222no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—44no—
386C4⋊C4—44no—
387C4⋊C4—42no—
388C4⋊C4—112no—
389C4⋊C4—224no—
390C4⋊C4—224no—
391C4⋊C4—221no—
392C4⋊C4—221no—
393C4⋊C4—221no—
394C4⋊C4—444no—
395C4⋊C4#432414yescomplemented
396C22⋊C4—44no—
397C22⋊C4—44no—
398C22⋊C4—42no—
399C42—22no—
400C42—22no—
401C42—444no—
402C42—442no—
403C42D4×D1112yes—
404C42#434112yes—
405C11#2532011yescharacteristic, complemented, Sylow
406C23—22no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23C22×C22⋊D1111yescharacteristic
414Q8—84no—
415Q8—224no—
416Q8—224no—
417Q8—442no—
418Q8—442no—
419D4—22no—
420D4—22no—
421D4—41no—
422D4—41no—
423C2×C4—22no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—84no—
437C2×C4—224no—
438C2×C4—222no—
439C2×C4—441no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4#6698512yes—
447C2×C4C2×#432414yes—
448C2×C4C2×#432412yes—
449C2×C4#6699112yes—
450C2×C4#6699112yes—
451C2×C4C2×D4×D1111yescharacteristic
452C2×C4C2×#434111yescharacteristic
453C2×C4C2×#434311yescharacteristic
454C2×C4#6704011yescharacteristic
455C2×C4#41×D1111yescharacteristic
456C2×C4#6704211yescharacteristic
457C8—442no—
458C8—441no—
459C8—441no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22C2×#6698511yescharacteristic
468C22C22×#432411yescharacteristic
469C22C2×#6699111yescharacteristic
470C22#1062334811yescharacteristic
471C22#1062336011yescharacteristic
472C22#1062336911yescharacteristic
473C22#1062336911yescharacteristic
474C4—22no—
475C4—24no—
476C4—42no—
477C4—81no—
478C4—82no—
479C4—444no—
480C4—442no—
481C4—881no—
482C4#1062268814yes—
483C4#1062315511yescharacteristic
484C4#1062316111yescharacteristic
485C4#1062316211yescharacteristic
486C4#1062317411yescharacteristic
487C2—82no—
488C2#1307218911yescharacteristic
489C2C2×#1062268811yescharacteristic
490C2#1307814211yescharacteristic
491C2#1308047511yescharacteristic
492C2#1308091511yescharacteristic
493C2#1308125811yescharacteristic
494C2#1308133411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2542C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2542D11
hypocenterC11#25320
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2542

Complements

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

NH ≅ G/Ntype
1. C2×#10622706C2semidirect
3. #13071672C2semidirect
4. #13070025C2semidirect
6. #13069569C2semidirect
7. #13069335C2semidirect
9. #13068618C2semidirect
132. C11×C4⋊C4SD16semidirect
395. C4⋊C4#4324semidirect
405. C11#25320semidirect

Maximal subgroups

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

subgroupindex
C2×#106227062
C2×#106226322
#130716722
#130700252
#130699332
#130695692
#130693352
#130689742
#130686182
C4×#668962
C11×#25422
#2532011