Finite Group Databasebeta

← #14756911

Subgroups — #14756911

Order 2816.

938 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071259C211yesmaximal, characteristic, complemented
2#13070977C211yesmaximal, characteristic, complemented
3#13069238C212yesmaximal, complemented
4#13069210C212yesmaximal, complemented
5#13068966C212yesmaximal
6#13068865C212yesmaximal, complemented
7C4×#66882C211yesmaximal, characteristic, complemented
8#13068441C211yesmaximal, characteristic, complemented
9#13068441C211yesmaximal, characteristic, complemented
10#13068367C211yesmaximal, characteristic, complemented
11C2×C4×C11×D8C211yesmaximal, characteristic
12C22×C11×D8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×D4×Dic11C2212yes—
16C4×C11×D8C418yescomplemented
17C2×C11×#107C2211yescharacteristic
18C2×C11×#102C2211yescharacteristic
19C2×C11×#102C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21#10622834C2212yes—
22C2×#66896C2212yes—
23C2×#66896C2212yes—
24#10622825—21no—
25#10622824—21no—
26C4×C22⋊Dic11—21no—
27C2×C11⋊#95—21no—
28C2×#66882C2212yes—
29#10622598C2212yes—
30C4⋊C4×Dic11C2212yes—
31#10622564—22no—
32C22⋊C4×Dic11—22no—
33C4×C4⋊Dic11C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35#10622545C2211yescharacteristic
36C2×#66867C2211yescharacteristic
37#10622189C2212yes—
38#10622188C2212yes—
39#10622188C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×D4×C11C2311yescharacteristic
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C23×C4×C11—21no—
46C23×Dic11—22no—
47C2×C11×D8—24no—
48C2×C11×D8C2×C414yes—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C4×D4×C11—22no—
52C4×D4×C11—22no—
53C4×D4×C11C2×C414yes—
54C4×D4×C11C2×C414yescomplemented
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—21no—
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63D4×Dic11—24no—
64D4×Dic11—24no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2312yes—
68C2×C4×Dic11—21no—
69C2×C4×Dic11—21no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11C2312yes—
72C22×C11⋊C8C2312yes—
73C11×#107C2×C414yescomplemented
74C11×#102C2×C414yes—
75C11×#102C2×C414yescomplemented
76C4×C8×C11C2×C414yescomplemented
77#66896—24no—
78#66896—24no—
79C11⋊#95—21no—
80C11⋊#95—21no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95D412yes—
84C11⋊#95D411yescharacteristic
85C11⋊#95D411yescharacteristic
86#66882—24no—
87#66867—22no—
88#21129—111nomaximal, Sylow
89C24×C11—21no—
90C24×C11—21no—
91C2×D4×C11—22no—
92C2×D4×C11—21no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—21no—
96C2×D4×C11C22×C412yes—
97C2×D4×C11C22×C412yes—
98C2×D4×C11#4114yes—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—24no—
102C22×C4×C11—24no—
103C22×C4×C11—82no—
104C22×C4×C11—82no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2411yescharacteristic
108C22×Dic11—28no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—82no—
112C22×Dic11—82no—
113C22×Dic11C2×D412yes—
114C22×Dic11C2×D412yes—
115C11×D8—28no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11C22×C412yes—
119C2×C8×C11C22×C412yes—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4C22×C412yes—
123C11×C4⋊C4C22×C412yes—
124C11×C22⋊C4—24no—
125C11×C22⋊C4—24no—
126C42×C11C22×C412yes—
127C42×C11#4112yes—
128C22⋊Dic11—28no—
129C22⋊Dic11—82no—
130C22⋊Dic11—82no—
131C4⋊Dic11—22no—
132C4⋊Dic11—22no—
133C4⋊Dic11—22no—
134C4⋊Dic11—82no—
135C4⋊Dic11#4114yes—
136C4×Dic11—22no—
137C4×Dic11—22no—
138C4×Dic11—81no—
139C4×Dic11—81no—
140C4×Dic11—82no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×C4×D8D1111yescharacteristic
145#2319—111no—
146#2275—111no—
147#1925—112no—
148#1921—112no—
149#1879—112no—
150#1862—112no—
151C4×#107—111no—
152#1762—111no—
153#1762—111no—
154#1746—111no—
155C23×C11—22no—
156C23×C11—24no—
157C23×C11—22no—
158C23×C11—41no—
159C23×C11—42no—
160C23×C11—41no—
161C23×C11—42no—
162C23×C11—41no—
163C23×C11—42no—
164C23×C11—41no—
165C23×C11C22×D411yescharacteristic
166D4×C11—22no—
167D4×C11—22no—
168D4×C11—22no—
169D4×C11—24no—
170D4×C11—42no—
171D4×C11#11714yes—
172C2×C4×C11—21no—
173C2×C4×C11—22no—
174C2×C4×C11—21no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—84no—
180C2×C4×C11—84no—
181C2×C4×C11C4×D412yes—
182C2×C4×C11C4×D412yes—
183C2×C4×C11C23×C411yescharacteristic
184C2×C4×C11C2×#4112yes—
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C11C2×#4112yes—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—24no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—88no—
200C8×C11—22no—
201C8×C11—22no—
202C11⋊C8—42no—
203C22×D8C2×D1111yescharacteristic
204C2×C4×D4—112no—
205C2×C4×D4C2×D1111yescharacteristic
206C2×C4×D4C2×D1111yescharacteristic
207C4×D8Dic1118yescomplemented
208C2×#107—112no—
209C2×#107C2×D1111yescharacteristic
210C2×#102—112no—
211C2×#102—112no—
212C2×#102C2×D1111yescharacteristic
213C2×#102C2×D1111yescharacteristic
214C2×#97—111no—
215C2×C4×C8C2×D1111yescharacteristic
216#390—112no—
217#389—112no—
218#388—222no—
219#381—221no—
220#380—221no—
221C4×C4⋊C4—112no—
222C4×C4⋊C4—111no—
223C4×C4⋊C4—111no—
224C4×C22⋊C4—222no—
225C4×C22⋊C4—221no—
226#376—111no—
227C2×#95—221no—
228#340—112no—
229#340—112no—
230#340—112no—
231#336—112no—
232#336—112no—
233C22×C11—24no—
234C22×C11—44no—
235C22×C11—44no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11—82no—
242C22×C11—82no—
243C22×C11C2×C4×D411yescharacteristic
244C22×C11#52512yes—
245C22×C11#57612yes—
246C22×C11#57611yescharacteristic
247C22×C11#57811yescharacteristic
248C4×C11—22no—
249C4×C11—22no—
250C4×C11—42no—
251C4×C11—42no—
252C4×C11C2×#11711yescharacteristic
253C4×C11C4×#4111yescharacteristic
254C4×C11#52912yes—
255Dic11—42no—
256Dic11—44no—
257Dic11—42no—
258Dic11—82no—
259C22×D4C22×D1111yescharacteristic
260C22×D4C22×D1111yescharacteristic
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—222no—
264C2×D8—24no—
265C2×D8C2×Dic1114yes—
266C22×C8—112no—
267C22×C8C22×D1111yescharacteristic
268C22×C8C22×D1111yescharacteristic
269C4×D4—22no—
270C4×D4—22no—
271C4×D4—224no—
272C4×D4—224no—
273C4×D4C2×Dic1114yes—
274C4×D4C2×Dic1114yescomplemented
275C2×C4⋊C4—112no—
276C2×C4⋊C4—112no—
277C2×C4⋊C4—222no—
278C2×C4⋊C4C22×D1111yescharacteristic
279C2×C4⋊C4C22×D1111yescharacteristic
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—222no—
283C2×C22⋊C4—222no—
284C2×C22⋊C4—222no—
285C2×C42—112no—
286C2×C42—222no—
287C2×C42—221no—
288C2×C42—221no—
289C2×C42C22×D1111yescharacteristic
290#107—224no—
291#107C2×Dic1114yescomplemented
292#102—224no—
293#102—224no—
294#102C2×Dic1114yes—
295#102C2×Dic1114yescomplemented
296#97—222no—
297C4×C8C2×Dic1114yescomplemented
298#95—111no—
299#95—111no—
300#95—112no—
301#95—222no—
302#95—222no—
303#95—221no—
304#95—221no—
305C2×C11—44no—
306C2×C11—82no—
307C2×C11#229011yescharacteristic
308C2×C11#294811yescharacteristic
309C2×C11#295111yescharacteristic
310C2×C11#312212yes—
311C2×C11#312412yes—
312C24—21no—
313C24—21no—
314C2×D4—22no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—22no—
318C2×D4—22no—
319C2×D4#433914yes—
320C2×D4C22×Dic1112yes—
321C2×D4C22×Dic1112yes—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—24no—
325C22×C4—24no—
326C22×C4—82no—
327C22×C4—82no—
328C22×C4—112no—
329C22×C4—112no—
330C22×C4—222no—
331C22×C4—228no—
332C22×C4—222no—
333C22×C4—882no—
334C22×C4—882no—
335C22×C4D4×D1111yescharacteristic
336C22×C4D4×D1111yescharacteristic
337C22×C4C23×D1111yescharacteristic
338D8—28no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—222no—
342C2×C8—222no—
343C2×C8—222no—
344C2×C8C22×Dic1112yes—
345C2×C8C22×Dic1112yes—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—114no—
349C4⋊C4—222no—
350C4⋊C4—222no—
351C4⋊C4—222no—
352C4⋊C4—882no—
353C4⋊C4C22×Dic1112yes—
354C4⋊C4C22×Dic1112yes—
355C22⋊C4—24no—
356C22⋊C4—24no—
357C22⋊C4—228no—
358C22⋊C4—882no—
359C22⋊C4—882no—
360C42—222no—
361C42—222no—
362C42—881no—
363C42—881no—
364C42—882no—
365C42#434112yes—
366C42C22×Dic1112yes—
367C11#2112911yescharacteristic, complemented, Sylow
368C23—22no—
369C23—24no—
370C23—22no—
371C23—42no—
372C23—41no—
373C23—41no—
374C23—42no—
375C23—41no—
376C23—41no—
377C23—42no—
378C23C2×D4×D1111yescharacteristic
379D4—22no—
380D4—24no—
381D4—22no—
382D4—22no—
383D4—42no—
384D4#6697914yes—
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—84no—
393C2×C4—84no—
394C2×C4—222no—
395C2×C4—222no—
396C2×C4—222no—
397C2×C4—222no—
398C2×C4—222no—
399C2×C4—222no—
400C2×C4—224no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—442no—
404C2×C4—442no—
405C2×C4—442no—
406C2×C4—888no—
407C2×C4D4×Dic1112yes—
408C2×C4D4×Dic1112yes—
409C2×C4C2×#433912yes—
410C2×C4C2×#434111yescharacteristic
411C2×C4#41×D1112yes—
412C2×C4C23×Dic1111yescharacteristic
413C8—22no—
414C8—22no—
415C8—442no—
416C22—24no—
417C22—44no—
418C22—44no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22—42no—
424C22—82no—
425C22—82no—
426C22#1062307812yes—
427C22#1062328812yes—
428C22#1062330011yescharacteristic
429C22#1062330211yescharacteristic
430C22C2×D4×Dic1111yescharacteristic
431C4—22no—
432C4—22no—
433C4—42no—
434C4—42no—
435C4—442no—
436C4—444no—
437C4—442no—
438C4—882no—
439C4#1062306912yes—
440C4C2×#6697911yescharacteristic
441C4#41×Dic1111yescharacteristic
442C2—44no—
443C2—82no—
444C2#1307106111yescharacteristic
445C2#1307746811yescharacteristic
446C2#1307749211yescharacteristic
447C2#1307885612yes—
448C2#1307887412yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×D8C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
cosocleC22×C4×C11C24
hypercenterC2×C4×D8D11
hypocenterC11#21129
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. #13071259C2semidirect
2. #13070977C2semidirect
3. #13069238C2semidirect
4. #13069210C2semidirect
6. #13068865C2semidirect
7. C4×#66882C2semidirect
8. #13068441C2semidirect
9. #13068441C2semidirect
10. #13068367C2semidirect
16. C4×C11×D8C4semidirect
54. C4×D4×C11C2×C4semidirect
73. C11×#107C2×C4semidirect
75. C11×#102C2×C4semidirect
76. C4×C8×C11C2×C4semidirect
207. C4×D8Dic11semidirect
274. C4×D4C2×Dic11semidirect
291. #107C2×Dic11semidirect
295. #102C2×Dic11semidirect
297. C4×C8C2×Dic11semidirect
367. C11#21129semidirect

Maximal subgroups

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

subgroupindex
#130712592
#130709772
#130692382
#130692102
#130689662
#130688652
C4×#668822
#130684412
#130683672
C2×C4×C11×D82
#2112911