Finite Group Databasebeta

← #14810735

Subgroups — #14810735

Order 2816.

1022 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×#10622702C211yesmaximal, characteristic
2C2×#10622641C211yesmaximal, characteristic
3#13074104C211yesmaximal, characteristic
4#13069764C212yesmaximal, complemented
5#13069759C212yesmaximal
6#13069565C211yesmaximal, characteristic, complemented
7#13069557C211yesmaximal, characteristic, complemented
8#13068971C212yesmaximal
9#13068957C212yesmaximal, complemented
10#13068446C211yesmaximal, characteristic, complemented
11C2×C11×#557C211yesmaximal, characteristic, complemented
12C11×#557—24no—
13C11×#557—24no—
14C2×C11×C4⋊Q8—21no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125—22no—
17C2×C11×#125C2212yes—
18C2×C4×Q8×C11—21no—
19C2×C4×Q8×C11C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C22×#4325C2211yescharacteristic
24C2×#66928C2211yescharacteristic
25#10622844—21no—
26C2×#66899C2212yes—
27#10622702—24no—
28#10622641—24no—
29#10622606—21no—
30#10622603—22no—
31C2×#66874C2211yescharacteristic
32C2×#66874C2212yes—
33C2×#66873C2211yescharacteristic
34C2×#66873C2212yes—
35#10622552C2212yes—
36C4×C4⋊Dic11C2211yescharacteristic
37#10622542C2212yes—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×#66867C2211yescharacteristic
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11D411yescharacteristic
47C22×Q8×C11C2311yescharacteristic
48C22×D44C2311yescharacteristic
49C22×Dic22C2311yescharacteristic
50C11×C4⋊Q8—28no—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8D414yes—
53C11×#125—216no—
54C11×#125—24no—
55C11×#125—24no—
56C4×Q8×C11—28no—
57C4×Q8×C11—24no—
58C4×Q8×C11—24no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×Q8×C11D414yes—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4D412yes—
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2312yes—
72C2×C42×C11—22no—
73C2×C42×C11—21no—
74C2×C42×C11C2312yes—
75C2×C42×C11C2311yescharacteristic
76C2×#4326—22no—
77C2×#4326—24no—
78C2×#4325—22no—
79C2×#4325—24no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×C4⋊Dic11C2312yes—
85C2×C4×Dic11—21no—
86C22×C11⋊C8C2312yes—
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89#66928—22no—
90#66928—22no—
91#66899—24no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94C11⋊#95—21no—
95#66874—22no—
96#66874—24no—
97#66873—22no—
98#66873—24no—
99C4⋊(C11⋊C8)—22no—
100#66867—22no—
101#25941—111nomaximal, Sylow
102C23×D11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—24no—
105C2×Q8×C11—21no—
106C2×Q8×C11—22no—
107C2×Q8×C11—42no—
108C2×Q8×C11—44no—
109C2×Q8×C11C2×D412yes—
110C2×Q8×C11#4114yes—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2411yescharacteristic
119C22×Dic11—21no—
120C22×Dic11—22no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44—22no—
124C2×D44—22no—
125C2×Dic22—21no—
126C2×Dic22—21no—
127C2×Dic22—22no—
128C2×Dic22—22no—
129C11×C4⋊C4—28no—
130C11×C4⋊C4—28no—
131C11×C4⋊C4—28no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4C2×D414yes—
139C11×C4⋊C4C2×D412yes—
140C42×C11—28no—
141C42×C11—24no—
142C42×C11—22no—
143C42×C11—22no—
144C42×C11C2×D412yes—
145C42×C11C2×D412yes—
146#4326—44no—
147#4325—44no—
148(C2×D11)⋊C4—44no—
149(C2×D11)⋊C4—42no—
150(C2×D11)⋊C4—42no—
151(C2×D11)⋊C4—82no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4×Dic11—81no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×#557D1111yescharacteristic, complemented
163C2×#489—111no—
164C2×#464—111no—
165#2592—111no—
166#2026—112no—
167#2025—112no—
168#1987—111no—
169#1985—111no—
170#1880—112no—
171#1878—112no—
172#1763—111no—
173C23×C11C22×D411yescharacteristic
174C22×D11—41no—
175C22×D11—42no—
176C22×D11—42no—
177C22×D11—41no—
178C22×D11—41no—
179Q8×C11—22no—
180Q8×C11—24no—
181Q8×C11—44no—
182Q8×C11—48no—
183Q8×C11#12414yes—
184C2×C4×C11—22no—
185C2×C4×C11—24no—
186C2×C4×C11—22no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—24no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—44no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11#12012yes—
201C2×C4×C11#12012yes—
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C2×#4112yes—
205C2×C4×C112−1+412yes—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211D44—41no—
212D44—41no—
213D44—42no—
214Dic22—41no—
215Dic22—41no—
216Dic22—42no—
217C11⋊C8—41no—
218C11⋊C8—41no—
219C11⋊C8—42no—
220C22×Q16—111no—
221C22×SD16—111no—
222#557—24no—
223#557—24no—
224C2×C4⋊Q8—21no—
225C2×C4⋊Q8C2×D1111yescharacteristic
226C2×#125—22no—
227C2×#125C2×D1112yes—
228C2×#124—111no—
229C2×C4×Q8—21no—
230C2×C4×Q8C2×D1112yes—
231C2×C4×Q8C2×D1111yescharacteristic
232C2×C4×Q8C2×D1111yescharacteristic
233#489—224no—
234#464—224no—
235C2×C4⋊C8—111no—
236C2×#103—112no—
237C2×#103—112no—
238C2×#103—111no—
239C2×#102—112no—
240C2×#102—111no—
241C2×#97—111no—
242#397—221no—
243#393—221no—
244#391—112no—
245#390—112no—
246#388—222no—
247C4×C4⋊C4—111no—
248#340—112no—
249#340—112no—
250#340—112no—
251#336—112no—
252#336—112no—
253C22×C11C2×#12011yescharacteristic
254C22×C11#54812yes—
255C22×C11#57512yes—
256C22×C11#57711yescharacteristic
257C22×C11#57811yescharacteristic
258C2×D11—82no—
259C2×D11—82no—
260C2×D11—81no—
261C2×D11—81no—
262C2×D11—81no—
263C4×C11—24no—
264C4×C11—22no—
265C4×C11—22no—
266C4×C11—42no—
267C4×C11—44no—
268C4×C11—42no—
269C4×C11—42no—
270C4×C11C2×#12411yescharacteristic
271C4×C11#53611yescharacteristic
272C4×C11#54812yes—
273Dic11—82no—
274Dic11—81no—
275C22×Q8—21no—
276C22×Q8—111no—
277C22×Q8C22⋊D1111yescharacteristic
278C22×Q8C22×D1111yescharacteristic
279C22×D4—111no—
280C2×Q16—224no—
281C2×Q16—222no—
282C2×SD16—224no—
283C2×SD16—222no—
284C22×C8—111no—
285C22×C8—111no—
286C22×C8—112no—
287C4⋊Q8—28no—
288C4⋊Q8—22no—
289C4⋊Q8C22⋊D1114yes—
290#125—216no—
291#125—24no—
292#125—24no—
293#124—222no—
294#124—222no—
295C4×Q8—28no—
296C4×Q8—24no—
297C4×Q8—24no—
298C4×Q8—22no—
299C4×Q8—22no—
300C4×Q8—22no—
301C4×Q8C22⋊D1114yes—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—112no—
308C2×C4⋊C4C22⋊D1111yescharacteristic
309C2×C4⋊C4C22⋊D1112yes—
310C2×C4⋊C4C22×D1111yescharacteristic
311C2×C4⋊C4C22×D1112yes—
312C2×C22⋊C4—221no—
313C2×C22⋊C4—221no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4—222no—
316C2×C42—22no—
317C2×C42—21no—
318C2×C42—221no—
319C2×C42C22×D1112yes—
320C2×C42C22×D1111yescharacteristic
321C4⋊C8—222no—
322#103—224no—
323#103—222no—
324#103—224no—
325#102—222no—
326#102—224no—
327#97—222no—
328#95—221no—
329#95—222no—
330#95—222no—
331C2×C11#243611yescharacteristic
332C2×C11#300511yescharacteristic
333C2×C11#301311yescharacteristic
334C2×C11#337112yes—
335C2×C11#337712yes—
336D11—161no—
337C24—221no—
338C2×Q8—22no—
339C2×Q8—24no—
340C2×Q8—22no—
341C2×Q8—21no—
342C2×Q8—42no—
343C2×Q8—44no—
344C2×Q8—222no—
345C2×Q8—222no—
346C2×Q8—221no—
347C2×Q8—221no—
348C2×Q8#434314yes—
349C2×Q8C2×C22⋊D1112yes—
350C2×D4—222no—
351C2×D4—222no—
352C2×D4—221no—
353C2×D4—221no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—221no—
358C22×C4—222no—
359C22×C4C2×C22⋊D1112yes—
360C22×C4C2×C22⋊D1112yes—
361C22×C4C2×C22⋊D1111yescharacteristic
362C22×C4C2×C22⋊D1111yescharacteristic
363C22×C4C23×D1111yescharacteristic
364Q16—444no—
365SD16—444no—
366C2×C8—222no—
367C2×C8—222no—
368C2×C8—222no—
369C2×C8—222no—
370C2×C8—222no—
371C2×C8—221no—
372C2×C8—221no—
373C4⋊C4—28no—
374C4⋊C4—28no—
375C4⋊C4—28no—
376C4⋊C4—24no—
377C4⋊C4—24no—
378C4⋊C4—22no—
379C4⋊C4—24no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—222no—
383C4⋊C4—222no—
384C4⋊C4C2×C22⋊D1114yes—
385C4⋊C4C2×C22⋊D1112yes—
386C22⋊C4—444no—
387C22⋊C4—442no—
388C22⋊C4—442no—
389C22⋊C4—882no—
390C42—28no—
391C42—24no—
392C42—22no—
393C42—22no—
394C42—881no—
395C42C2×C22⋊D1112yes—
396C42C2×C22⋊D1112yes—
397C11#2594111yescharacteristic, complemented, Sylow
398C23—442no—
399C23—442no—
400C23—441no—
401C23—441no—
402C23—441no—
403C23C22×C22⋊D1111yescharacteristic
404Q8—22no—
405Q8—24no—
406Q8—44no—
407Q8—48no—
408Q8—441no—
409Q8—441no—
410Q8—442no—
411Q8#6700014yes—
412D4—441no—
413D4—441no—
414D4—442no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—44no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—441no—
436C2×C4#6700612yes—
437C2×C4#6700612yes—
438C2×C4C2×#434312yes—
439C2×C4#6704012yes—
440C2×C4C22×C22⋊D1111yescharacteristic
441C2×C4C22×C22⋊D1111yescharacteristic
442C8—441no—
443C8—441no—
444C8—442no—
445C22—882no—
446C22—881no—
447C22—882no—
448C22—881no—
449C22—881no—
450C22#1062334812yes—
451C22#1062335312yes—
452C22#1062336811yescharacteristic
453C22#1062336911yescharacteristic
454C22C2×#6700611yescharacteristic
455C4—22no—
456C4—24no—
457C4—22no—
458C4—42no—
459C4—44no—
460C4—42no—
461C4—42no—
462C4—882no—
463C4—881no—
464C4C2×#6700011yescharacteristic
465C4#1062334711yescharacteristic
466C4#1062334812yes—
467C2—1761no—
468C2#1307227011yescharacteristic
469C2#1307785811yescharacteristic
470C2#1307793111yescharacteristic
471C2#1308138412yes—
472C2#1308145812yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#557C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#557D11
hypocenterC11#25941
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
4. #13069764C2semidirect
6. #13069565C2semidirect
7. #13069557C2semidirect
9. #13068957C2semidirect
10. #13068446C2semidirect
11. C2×C11×#557C2semidirect
162. C2×#557D11semidirect
397. C11#25941semidirect

Maximal subgroups

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

subgroupindex
C2×#106227022
C2×#106226412
#130741042
#130697642
#130697592
#130695652
#130695572
#130689712
#130689572
#130684462
C2×C11×#5572
#2594111