Finite Group Databasebeta

← #14796435

Subgroups — #14796435

Order 2816.

910 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622697C211yesmaximal, characteristic
2C2×C4×#4325C211yesmaximal, characteristic
3C4⋊C4×D44C211yesmaximal, characteristic
4#13070093C212yesmaximal, complemented
5#13069997C212yesmaximal, complemented
6#13069578C211yesmaximal, characteristic, complemented
7#13069335C211yesmaximal, characteristic, complemented
8#13068953C212yesmaximal
9#13068621C211yesmaximal, characteristic, complemented
10#13068613C212yesmaximal
11C11×#2567C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C22×#4325C2211yescharacteristic
15C2×C4⋊C4×D11—21no—
16C2×C4×D44C2212yes—
17C2×C4×D44C2211yescharacteristic
18C11×#395—22no—
19C11×#391C2212yes—
20C11×#389—21no—
21C11×#389—21no—
22C11×#384C2212yes—
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66899C2211yescharacteristic
25C2×#66899C2212yes—
26#10622697—24no—
27C4×#4325—24no—
28#10622600—21no—
29C2×#66873C2211yescharacteristic
30C2×#66873C2212yes—
31C2×#66872C2211yescharacteristic
32C2×#66872C2212yes—
33#10622548C2211yescharacteristic
34#10622541C2212yes—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2212yes—
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622281—22no—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C22×C4×D11—22no—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8—22no—
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C42×C11—21no—
61C2×C42×C11C2312yes—
62C2×C42×C11C2311yescharacteristic
63C2×#4325—22no—
64C2×#4325—22no—
65C2×#4325Q814yescomplemented
66C2×(C2×D11)⋊C4—21no—
67C2×(C2×D11)⋊C4—22no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2311yescharacteristic
72C2×Dic11⋊C4—22no—
73C22×C11⋊C8C2311yescharacteristic
74C22×C11⋊C8C2312yes—
75C22×C11⋊C8C2311yescharacteristic
76C4⋊C4×D11—44no—
77C4×D44—22no—
78C4×D44—24no—
79C4×D44—42no—
80C4×D44D414yes—
81C11×#95—22no—
82C11×#95—22no—
83C11×#95D412yes—
84#66899—22no—
85#66899—42no—
86C11⋊#95—22no—
87#66873—22no—
88#66873—24no—
89#66872—22no—
90#66872—24no—
91C4⋊(C11⋊C8)—22no—
92C4⋊(C11⋊C8)—42no—
93C4×C11⋊C8—22no—
94#24815—111nomaximal, Sylow
95C23×D11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—42no—
102C2×Q8×C11—81no—
103C2×Q8×C11—81no—
104C2×Q8×C11C2×Q812yes—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C22×Dic11—21no—
114C22×Dic11—22no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44C2×D412yes—
119C2×D44C2×Q812yes—
120C2×D44#4112yes—
121C2×C4×D11—24no—
122C2×C4×D11—44no—
123C2×C4×D11—42no—
124C2×C4×D11—44no—
125C2×C4×D11—42no—
126C2×C4×D11—82no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4—82no—
135C11×C4⋊C4—82no—
136C11×C4⋊C4SD1614yescomplemented
137C42×C11—22no—
138C42×C11—22no—
139C42×C11—42no—
140C42×C11C2×D412yes—
141C42×C11#4112yes—
142#4325—28no—
143(C2×D11)⋊C4—24no—
144(C2×D11)⋊C4—44no—
145C4⋊Dic11—21no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—42no—
149C4⋊Dic11—81no—
150C4⋊Dic11C2×D412yes—
151Dic11⋊C4—44no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8C2×Q812yes—
161C2×#476—111no—
162C2×C4×SD16—111no—
163#2567D1111yescharacteristic, complemented
164D4×C4⋊C4—111no—
165#2084—112no—
166#2066—112no—
167#1990—111no—
168#1939—111no—
169#1877—112no—
170#1803—111no—
171#1802—112no—
172C23×C11C22×D411yescharacteristic
173C22×D11—22no—
174C22×D11—22no—
175C22×D11—22no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—41no—
180Q8×C11—22no—
181Q8×C11—22no—
182Q8×C11—41no—
183Q8×C11—41no—
184Q8×C11—84no—
185C2×C4×C11—22no—
186C2×C4×C11—21no—
187C2×C4×C11—22no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11#12112yes—
202C2×C4×C11#12112yes—
203C2×C4×C11C2×SD1614yes—
204C2×C4×C11C2×SD1612yes—
205C2×C4×C11#13712yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×Q811yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11H(5,𝔽2)11yescharacteristic
211C2×C4×C112−1+411yescharacteristic
212C2×Dic11—22no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218D44—22no—
219D44—22no—
220D44—22no—
221D44C22⋊Q814yes—
222C4×D11—48no—
223C4×D11—88no—
224C11⋊C8—22no—
225C11⋊C8—41no—
226C11⋊C8—42no—
227C22×SD16—111no—
228C2×C4⋊Q8C2×D1111yescharacteristic
229C2×C4×Q8C2×D1111yescharacteristic
230C2×C4×D4—111no—
231C2×C4×D4—112no—
232C22×C4⋊C4—221no—
233#476—224no—
234C4×SD16—224no—
235C2×#106—112no—
236C2×#106—111no—
237C2×C4⋊C8—111no—
238C2×C4⋊C8—112no—
239C2×#103—111no—
240C2×#103—112no—
241C2×#102—111no—
242C2×#102—112no—
243C2×C4×C8—111no—
244#395—22no—
245#391C2×D1112yes—
246#389—21no—
247#389—21no—
248#389—112no—
249#385—222no—
250#384—111no—
251#384C2×D1112yes—
252#380—221no—
253C4×C4⋊C4C2×D1111yescharacteristic
254#340—112no—
255#340—112no—
256#340—112no—
257#336—112no—
258C22×C11C2×#12111yescharacteristic
259C22×C11#54611yescharacteristic
260C22×C11D4×Q811yescharacteristic
261C22×C11C22×SD1611yescharacteristic
262C22×C11C2×#13711yescharacteristic
263C22×C11#57611yescharacteristic
264C22×C11#57711yescharacteristic
265C2×D11—24no—
266C2×D11—42no—
267C2×D11—42no—
268C2×D11—42no—
269C2×D11—42no—
270C2×D11—42no—
271C2×D11—42no—
272C4×C11—24no—
273C4×C11—22no—
274C4×C11—42no—
275C4×C11—42no—
276C4×C11—81no—
277C4×C11—82no—
278C4×C11#46114yes—
279C4×C11C2×C22⋊Q811yescharacteristic
280C4×C11#53711yescharacteristic
281C4×C11#55211yescharacteristic
282C4×C11#55411yescharacteristic
283Dic11—42no—
284Dic11—82no—
285C22×Q8—21no—
286C22×Q8C22×D1111yescharacteristic
287C22×D4—111no—
288C23×C4—221no—
289C23×C4—222no—
290C2×SD16—114no—
291C2×SD16—222no—
292C2×SD16—222no—
293C22×C8—111no—
294C22×C8—112no—
295C22×C8—111no—
296C4⋊Q8—22no—
297C4⋊Q8—22no—
298C4×Q8—22no—
299C4×Q8—22no—
300C4×D4—114no—
301C4×D4—224no—
302C4×D4—222no—
303C4×D4—442no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—111no—
309C2×C4⋊C4—112no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—444no—
314C2×C4⋊C4C22⋊D1111yescharacteristic
315C2×C4⋊C4C22⋊D1111yescharacteristic
316C2×C4⋊C4C22×D1111yescharacteristic
317C2×C4⋊C4C22×D1112yes—
318C2×C22⋊C4—221no—
319C2×C22⋊C4—222no—
320C2×C42—21no—
321C2×C42C22×D1112yes—
322C2×C42C22×D1111yescharacteristic
323#106—222no—
324#106—224no—
325C4⋊C8—222no—
326C4⋊C8—442no—
327#103—222no—
328#103—442no—
329#102—222no—
330#102—224no—
331C4×C8—222no—
332#95—22no—
333#95—22no—
334#95—222no—
335#95C22⋊D1112yes—
336C2×C11#241711yescharacteristic
337C2×C11C2×#46111yescharacteristic
338C2×C11#304511yescharacteristic
339C2×C11#329511yescharacteristic
340C2×C11#333111yescharacteristic
341C2×C11Q8×SD1611yescharacteristic
342C2×C11#338511yescharacteristic
343D11—44no—
344C24—221no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—42no—
351C2×Q8—81no—
352C2×Q8—81no—
353C2×Q8Q8×D1112yes—
354C2×D4—112no—
355C2×D4—112no—
356C2×D4—112no—
357C2×D4—221no—
358C2×D4—221no—
359C2×D4—221no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—221no—
364C22×C4—224no—
365C22×C4—222no—
366C22×C4—444no—
367C22×C4—442no—
368C22×C4—442no—
369C22×C4—444no—
370C22×C4—882no—
371C22×C4C2×C22⋊D1112yes—
372C22×C4C2×C22⋊D1111yescharacteristic
373C22×C4C2×C22⋊D1112yes—
374C22×C4C2×C22⋊D1111yescharacteristic
375C22×C4C23×D1111yescharacteristic
376SD16—228no—
377C2×C8—112no—
378C2×C8—221no—
379C2×C8—221no—
380C2×C8—221no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—221no—
384C2×C8—222no—
385C2×C8—221no—
386C4⋊C4—22no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—42no—
392C4⋊C4—42no—
393C4⋊C4—82no—
394C4⋊C4—82no—
395C4⋊C4—112no—
396C4⋊C4—221no—
397C4⋊C4—222no—
398C4⋊C4—222no—
399C4⋊C4—444no—
400C4⋊C4—442no—
401C4⋊C4—881no—
402C4⋊C4#432514yescomplemented
403C22⋊C4—224no—
404C22⋊C4—444no—
405C42—22no—
406C42—22no—
407C42—42no—
408C42D4×D1112yes—
409C42#434112yes—
410C11#2481511yescharacteristic, complemented, Sylow
411C23—222no—
412C23—222no—
413C23—222no—
414C23—441no—
415C23—441no—
416C23—441no—
417C23—441no—
418C23C22×C22⋊D1111yescharacteristic
419Q8—22no—
420Q8—22no—
421Q8—41no—
422Q8—41no—
423Q8—84no—
424D4—114no—
425D4—222no—
426D4—222no—
427D4—222no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—222no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—448no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—888no—
452C2×C4#6699112yes—
453C2×C4#6699112yes—
454C2×C4C2×#432514yes—
455C2×C4C2×#432512yes—
456C2×C4#6699512yes—
457C2×C4C2×D4×D1111yescharacteristic
458C2×C4C2×#434111yescharacteristic
459C2×C4C2×Q8×D1111yescharacteristic
460C2×C4#6704011yescharacteristic
461C2×C4#41×D1111yescharacteristic
462C2×C4#6704211yescharacteristic
463C8—222no—
464C8—441no—
465C8—442no—
466C22—224no—
467C22—442no—
468C22—442no—
469C22—442no—
470C22—442no—
471C22—442no—
472C22—442no—
473C22C2×#6699111yescharacteristic
474C22C22×#432511yescharacteristic
475C22C2×#6699511yescharacteristic
476C22Q8×C22⋊D1111yescharacteristic
477C22#1062336011yescharacteristic
478C22#1062336611yescharacteristic
479C22#1062336711yescharacteristic
480C4—24no—
481C4—22no—
482C4—42no—
483C4—42no—
484C4—82no—
485C4—81no—
486C4—442no—
487C4—882no—
488C4#1062269614yes—
489C4D11×C22⋊Q811yescharacteristic
490C4#1062316011yescharacteristic
491C4#1062316611yescharacteristic
492C4#1062317011yescharacteristic
493C2—444no—
494C2#1307206311yescharacteristic
495C2C2×#1062269611yescharacteristic
496C2#1307815111yescharacteristic
497C2#1308043411yescharacteristic
498C2#1308092611yescharacteristic
499C2Q8×#432511yescharacteristic
500C2#1308152211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2567C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2567D11
hypocenterC11#24815
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2567

Complements

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

NH ≅ G/Ntype
4. #13070093C2semidirect
5. #13069997C2semidirect
6. #13069578C2semidirect
7. #13069335C2semidirect
9. #13068621C2semidirect
11. C11×#2567C2semidirect
65. C2×#4325Q8semidirect
136. C11×C4⋊C4SD16semidirect
163. #2567D11semidirect
402. C4⋊C4#4325semidirect
410. C11#24815semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
C2×C4×#43252
C4⋊C4×D442
#130700932
#130699972
#130695782
#130693352
#130689532
#130686212
#130686132
C11×#25672
#2481511