Finite Group Databasebeta

← #14796433

Subgroups — #14796433

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×#10622621C211yesmaximal, characteristic
2C2×C4×#4324C211yesmaximal, characteristic
3#13073824C211yesmaximal, characteristic, complemented
4#13070092C212yesmaximal, complemented
5#13069994C212yesmaximal, complemented
6#13069576C211yesmaximal, characteristic, complemented
7#13069335C211yesmaximal, characteristic, complemented
8#13068950C212yesmaximal
9#13068618C211yesmaximal, characteristic, complemented
10#13068616C212yesmaximal
11D4×C11×C4⋊C4C211yesmaximal, characteristic
12C2×C4×D4×C11C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C22×C11×C4⋊C4—21no—
15C22×#4324C2211yescharacteristic
16C2×#66922C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18C11×#389C2212yes—
19C11×#385—22no—
20C11×#384C2211yescharacteristic
21C11×#380—21no—
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66896C2211yescharacteristic
24C2×#66896C2212yes—
25C4×#4324—24no—
26#10622621—24no—
27#10622598—21no—
28#10622598—21no—
29C2×#66874C2211yescharacteristic
30C2×#66874C2212yes—
31C2×#66872C2211yescharacteristic
32C2×#66872C2212yes—
33#10622548C2212yes—
34#10622542C2212yes—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2212yes—
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622269—22no—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2212yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C23×C4×C11—22no—
46C22×Dic22—21no—
47C22×Dic22C2311yescharacteristic
48C4×D4×C11—24no—
49C4×D4×C11—22no—
50C4×D4×C11—42no—
51C4×D4×C11D414yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—44no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—22no—
62C2×C42×C11C2312yes—
63C2×C42×C11C2311yescharacteristic
64C2×#4324—22no—
65C2×#4324—22no—
66C2×#4324Q814yescomplemented
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2312yes—
72C2×Dic11⋊C4—21no—
73C2×C4×Dic11—21no—
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2312yes—
76C22×C11⋊C8C2311yescharacteristic
77#66922—22no—
78#66922—22no—
79C4×Dic22—22no—
80C4×Dic22—22no—
81C11×#95—22no—
82C11×#95D412yes—
83#66896—24no—
84#66896—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87#66874—22no—
88#66874—42no—
89#66872—24no—
90#66872—22no—
91C4⋊(C11⋊C8)—22no—
92C4⋊(C11⋊C8)—42no—
93C4×C11⋊C8—22no—
94#24815—111nomaximal, Sylow
95C24×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11C2×D412yes—
100C2×D4×C11C2×Q812yes—
101C2×D4×C11#4112yes—
102C22×C4×C11—21no—
103C22×C4×C11—24no—
104C22×C4×C11—22no—
105C22×C4×C11—44no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—44no—
109C22×C4×C11—82no—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C22×Dic11—21no—
116C22×Dic11—22no—
117C22×Dic11—21no—
118C2×Dic22—21no—
119C2×Dic22—21no—
120C2×Dic22—21no—
121C2×Dic22—21no—
122C2×Dic22—21no—
123C2×Dic22—42no—
124C2×Dic22—81no—
125C2×Dic22—81no—
126C2×Dic22C2×Q812yes—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—44no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4—81no—
134C11×C4⋊C4SD1614yescomplemented
135C11×C4⋊C4C2×D412yes—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—44no—
138C42×C11—22no—
139C42×C11—22no—
140C42×C11C2×D412yes—
141C42×C11#4112yes—
142#4324—28no—
143C4⋊Dic11—21no—
144C4⋊Dic11—22no—
145C4⋊Dic11—21no—
146C4⋊Dic11—22no—
147C4⋊Dic11—42no—
148C4⋊Dic11—82no—
149C4⋊Dic11—82no—
150Dic11⋊C4—42no—
151C4×Dic11—42no—
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#2567—111no—
164D4×C4⋊C4D1111yescharacteristic
165#2084—112no—
166#2066—112no—
167#1990—111no—
168#1939—111no—
169#1877—112no—
170#1803—111no—
171#1802—112no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11C22×D411yescharacteristic
180D4×C11—22no—
181D4×C11—22no—
182D4×C11—22no—
183D4×C11C22⋊Q814yes—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—48no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—88no—
199C2×C4×C11#12112yes—
200C2×C4×C11#12112yes—
201C2×C4×C11C2×SD1614yes—
202C2×C4×C11C2×SD1612yes—
203C2×C4×C11#13712yes—
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C22×Q811yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11H(5,𝔽2)11yescharacteristic
209C2×C4×C112−1+411yescharacteristic
210C2×Dic11—22no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—42no—
215C2×Dic11—41no—
216C2×Dic11—42no—
217C2×Dic11—41no—
218C2×Dic11—42no—
219Dic22—22no—
220Dic22—22no—
221Dic22—41no—
222Dic22—41no—
223Dic22—84no—
224C11⋊C8—22no—
225C11⋊C8—41no—
226C11⋊C8—42no—
227C22×SD16—111no—
228C2×C4⋊Q8—111no—
229C2×C4×Q8—111no—
230C2×C4×D4C2×D1112yes—
231C2×C4×D4C2×D1111yescharacteristic
232C22×C4⋊C4—21no—
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—222no—
245#391—112no—
246#389—221no—
247#389—221no—
248#389C2×D1112yes—
249#385—22no—
250#384—112no—
251#384C2×D1111yescharacteristic
252#380—21no—
253C4×C4⋊C4C2×D1111yescharacteristic
254#340—112no—
255#340—112no—
256#340—112no—
257#336—112no—
258C22×C11—24no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11C2×#12111yescharacteristic
266C22×C11#54611yescharacteristic
267C22×C11D4×Q811yescharacteristic
268C22×C11C22×SD1611yescharacteristic
269C22×C11C2×#13711yescharacteristic
270C22×C11#57611yescharacteristic
271C22×C11#57711yescharacteristic
272C4×C11—24no—
273C4×C11—22no—
274C4×C11—42no—
275C4×C11—42no—
276C4×C11—82no—
277C4×C11#46114yes—
278C4×C11C2×C22⋊Q811yescharacteristic
279C4×C11#53711yescharacteristic
280C4×C11#55211yescharacteristic
281C4×C11#55411yescharacteristic
282Dic11—42no—
283Dic11—82no—
284Dic11—81no—
285C22×Q8—111no—
286C22×Q8—221no—
287C22×D4C22×D1111yescharacteristic
288C23×C4—21no—
289C23×C4—22no—
290C2×SD16—114no—
291C2×SD16—222no—
292C2×SD16—222no—
293C22×C8—111no—
294C22×C8—112no—
295C22×C8—111no—
296C4⋊Q8—222no—
297C4⋊Q8—222no—
298C4×Q8—222no—
299C4×Q8—222no—
300C4×D4—24no—
301C4×D4—22no—
302C4×D4—42no—
303C4×D4D4414yes—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—111no—
309C2×C4⋊C4—112no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4C22⋊D1111yescharacteristic
315C2×C4⋊C4C22⋊D1111yescharacteristic
316C2×C4⋊C4C22×D1112yes—
317C2×C4⋊C4C22×D1111yescharacteristic
318C2×C22⋊C4—21no—
319C2×C22⋊C4—22no—
320C2×C42—221no—
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—222no—
334#95—222no—
335#95C22⋊D1112yes—
336C2×C11—44no—
337C2×C11#241711yescharacteristic
338C2×C11C2×#46111yescharacteristic
339C2×C11#304511yescharacteristic
340C2×C11#329511yescharacteristic
341C2×C11#333111yescharacteristic
342C2×C11Q8×SD1611yescharacteristic
343C2×C11#338511yescharacteristic
344C24—21no—
345C2×Q8—112no—
346C2×Q8—221no—
347C2×Q8—221no—
348C2×Q8—221no—
349C2×Q8—221no—
350C2×Q8—221no—
351C2×Q8—442no—
352C2×Q8—881no—
353C2×Q8—881no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4C2×D4412yes—
358C2×D4#434112yes—
359C2×D4Q8×D1112yes—
360C22×C4—21no—
361C22×C4—24no—
362C22×C4—22no—
363C22×C4—44no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—44no—
367C22×C4—82no—
368C22×C4—221no—
369C22×C4—222no—
370C22×C4—221no—
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—22no—
390C4⋊C4—44no—
391C4⋊C4—42no—
392C4⋊C4—81no—
393C4⋊C4—221no—
394C4⋊C4—222no—
395C4⋊C4—221no—
396C4⋊C4—222no—
397C4⋊C4—442no—
398C4⋊C4—442no—
399C4⋊C4—882no—
400C4⋊C4—882no—
401C4⋊C4#432414yescomplemented
402C4⋊C4C2×D4412yes—
403C22⋊C4—24no—
404C22⋊C4—44no—
405C42—22no—
406C42—22no—
407C42—442no—
408C42C2×D4412yes—
409C42#433912yes—
410C11#2481511yescharacteristic, complemented, Sylow
411C23—22no—
412C23—22no—
413C23—22no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23C22×C22⋊D1111yescharacteristic
419Q8—222no—
420Q8—222no—
421Q8—441no—
422Q8—441no—
423Q8—884no—
424D4—22no—
425D4—22no—
426D4—22no—
427D4#6695014yes—
428C2×C4—22no—
429C2×C4—21no—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—48no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—88no—
443C2×C4—222no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—442no—
448C2×C4—441no—
449C2×C4—442no—
450C2×C4—441no—
451C2×C4—442no—
452C2×C4#6698312yes—
453C2×C4#6698312yes—
454C2×C4C2×#432414yes—
455C2×C4C2×#432412yes—
456C2×C4#6700412yes—
457C2×C4C22×D4411yescharacteristic
458C2×C4C2×#433911yescharacteristic
459C2×C4C2×#434111yescharacteristic
460C2×C4#6703711yescharacteristic
461C2×C4C2×Q8×D1111yescharacteristic
462C2×C4#6704011yescharacteristic
463C8—222no—
464C8—441no—
465C8—442no—
466C22—24no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22C2×#6698311yescharacteristic
474C22C22×#432411yescharacteristic
475C22#1062333711yescharacteristic
476C22Q8×C22⋊D1111yescharacteristic
477C22C2×#6700411yescharacteristic
478C22#1062336611yescharacteristic
479C22#1062336811yescharacteristic
480C4—24no—
481C4—22no—
482C4—42no—
483C4—42no—
484C4—82no—
485C4—442no—
486C4—882no—
487C4—881no—
488C4#1062263214yes—
489C4C2×#6695011yescharacteristic
490C4#1062304111yescharacteristic
491C4#1062304211yescharacteristic
492C4#1062304411yescharacteristic
493C2—44no—
494C2#1307206111yescharacteristic
495C2C2×#1062263211yescharacteristic
496C2#1307815511yescharacteristic
497C2#1308044011yescharacteristic
498C2#1308093211yescharacteristic
499C2Q8×#432411yescharacteristic
500C2#1308152611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingD4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterD4×C4⋊C4D11
hypocenterC11#24815
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13073824C2semidirect
4. #13070092C2semidirect
5. #13069994C2semidirect
6. #13069576C2semidirect
7. #13069335C2semidirect
9. #13068618C2semidirect
66. C2×#4324Q8semidirect
134. C11×C4⋊C4SD16semidirect
401. C4⋊C4#4324semidirect
410. C11#24815semidirect

Maximal subgroups

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

subgroupindex
C2×#106226212
C2×C4×#43242
#130738242
#130700922
#130699942
#130695762
#130693352
#130689502
#130686182
#130686162
D4×C11×C4⋊C42
#2481511