Finite Group Databasebeta

← #14644657

Subgroups — #14644657

Order 2816.

712 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068378C211yesmaximal, characteristic, complemented
2C2×#10622175C212yesmaximal
3#13066843C211yesmaximal, characteristic, complemented
4#13066494C212yesmaximal, complemented
5C4×C11×#121C211yesmaximal, characteristic
6C2×C11×#121C2211yescharacteristic
7C2×C4×D4×C11—21no—
8C2×C4×D4×C11C411yescharacteristic, complemented
9C22×C42×C11C2211yescharacteristic
10C11×#390C411yescharacteristic, complemented
11C11×#389C411yescharacteristic, complemented
12C11×#388—21no—
13C11×#386—21no—
14C11×#380C2211yescharacteristic
15C4×C11×C4⋊C4C411yescharacteristic, complemented
16C4×C11×C22⋊C4—21no—
17C2×C11⋊#95—21no—
18C2×C11⋊#95—21no—
19C2×C11⋊#95C2212yes—
20C2×C22⋊(C11⋊C8)C2212yes—
21C2×#66867—21no—
22#10622175C418yescomplemented
23#10622162—21no—
24C22×D4×C11—21no—
25C22×D4×C11C2×C411yescharacteristic
26C23×C4×C11—21no—
27C23×C4×C11D411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C23×Dic11—22no—
31C11×#121—22no—
32C11×#121C2×C414yes—
33C4×D4×C11—42no—
34C4×D4×C11—44no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C42×C11—21no—
45C2×C42×C11—42no—
46C2×C42×C11C2×C411yescharacteristic
47C2×C42×C11C2×C411yescharacteristic
48C2×C42×C11D411yescharacteristic
49C2×C42×C11D411yescharacteristic
50C22×C11⋊C8—22no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11⋊#95—22no—
55C11⋊#95—42no—
56C11⋊#95—42no—
57C11⋊#95C2×C414yescomplemented
58C22⋊(C11⋊C8)—22no—
59C22⋊(C11⋊C8)C2×C414yescomplemented
60#66867—42no—
61#8216—111nomaximal, Sylow
62C24×C11—21no—
63C24×C11C2×D411yescharacteristic
64C2×D4×C11—24no—
65C2×D4×C11—21no—
66C2×D4×C11—41no—
67C2×D4×C11—41no—
68C2×D4×C11—42no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11C4212yes—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—22no—
75C22×C4×C11—21no—
76C22×C4×C11—22no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—42no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11C22⋊C411yescharacteristic
88C22×C4×C11C22⋊C411yescharacteristic
89C22×C4×C11C22⋊C411yescharacteristic
90C22×C4×C11C22⋊C411yescharacteristic
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C22×C412yes—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4112yes—
95C22×Dic11—24no—
96C22×Dic11—42no—
97C22×Dic11—42no—
98C22×Dic11—42no—
99C22×Dic11—42no—
100C22×Dic11—42no—
101C22×Dic11—42no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—42no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4C4212yes—
107C11×C22⋊C4—24no—
108C11×C22⋊C4—42no—
109C11×C22⋊C4—42no—
110C11×C22⋊C4—42no—
111C11×C22⋊C4—42no—
112C42×C11—22no—
113C42×C11—22no—
114C42×C11—41no—
115C42×C11—41no—
116C42×C11—42no—
117C2×C11⋊C8—24no—
118C2×C11⋊C8—42no—
119C2×C11⋊C8—42no—
120C4×#121D1111yescharacteristic
121#1749—111no—
122C2×#327—112no—
123#1434—111no—
124#1294—112no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—22no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11C2×C22⋊C411yescharacteristic
137C23×C11C4×D412yes—
138C23×C11AGL(1,ℤ/8)12yes—
139C23×C11AGL(1,ℤ/8)11yescharacteristic
140C23×C11#13711yescharacteristic
141D4×C11—42no—
142D4×C11—42no—
143D4×C11—44no—
144D4×C11—44no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—22no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—44no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—84no—
175C2×C4×C11#9912yes—
176C2×C4×C11C2×C4211yescharacteristic
177C2×C4×C11#11711yescharacteristic
178C2×C4×C11C4×D412yes—
179C2×Dic11—44no—
180C2×Dic11—44no—
181C2×Dic11—44no—
182C2×Dic11—82no—
183C2×Dic11—82no—
184C2×Dic11—82no—
185C2×Dic11—82no—
186C11⋊C8—44no—
187C2×#121C2×D1111yescharacteristic
188C2×C4×D4—21no—
189C2×C4×D4Dic1111yescharacteristic, complemented
190C22×C42C2×D1111yescharacteristic
191C2×C22⋊C8—112no—
192C2×#97—221no—
193#390Dic1111yescharacteristic, complemented
194#389Dic1111yescharacteristic, complemented
195#388—21no—
196#386—21no—
197#380C2×D1111yescharacteristic
198C4×C4⋊C4Dic1111yescharacteristic, complemented
199C4×C22⋊C4—21no—
200C2×#95—112no—
201C2×#95—221no—
202C2×#95—221no—
203#336—221no—
204#327—118no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—22no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11—42no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11C4×C22⋊C411yescharacteristic
221C22×C11C2×#9911yescharacteristic
222C22×C11#41011yescharacteristic
223C22×C11#41711yescharacteristic
224C22×C11#41811yescharacteristic
225C22×C11#42111yescharacteristic
226C22×C11#42111yescharacteristic
227C22×C11#44012yes—
228C22×C11#44212yes—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—22no—
232C4×C11—22no—
233C4×C11—42no—
234C4×C11—41no—
235C4×C11—41no—
236C4×C11—41no—
237C4×C11—81no—
238C4×C11—81no—
239Dic11—84no—
240C22×D4—21no—
241C22×D4C2×Dic1111yescharacteristic
242C23×C4—21no—
243C23×C4—222no—
244C23×C4C22⋊D1111yescharacteristic
245C23×C4C22⋊D1111yescharacteristic
246C23×C4C22×D1111yescharacteristic
247C22×C8—222no—
248#121—22no—
249#121C4×D1114yes—
250C4×D4—42no—
251C4×D4—44no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4C2×Dic1111yescharacteristic
254C2×C4⋊C4C2×Dic1111yescharacteristic
255C2×C4⋊C4C2×Dic1111yescharacteristic
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C42—21no—
262C2×C42—42no—
263C2×C42C2×Dic1111yescharacteristic
264C2×C42C2×Dic1111yescharacteristic
265C2×C42C22⋊D1111yescharacteristic
266C2×C42C22⋊D1111yescharacteristic
267C22⋊C8—114no—
268C22⋊C8—222no—
269#97—442no—
270#95—21no—
271#95—21no—
272#95—21no—
273#95—114no—
274#95—222no—
275#95—442no—
276#95—442no—
277C2×C11—22no—
278C2×C11—22no—
279C2×C11—82no—
280C2×C11#151011yescharacteristic
281C2×C11#151211yescharacteristic
282C2×C11#151311yescharacteristic
283C2×C11#151411yescharacteristic
284C2×C11C4×#9911yescharacteristic
285C2×C11#175911yescharacteristic
286C2×C11#176211yescharacteristic
287C24—21no—
288C24C2×C22⋊D1111yescharacteristic
289C2×D4—24no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—42no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4C4×Dic1112yes—
297C22×C4—22no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—224no—
313C22×C4—442no—
314C22×C4—442no—
315C22×C4—442no—
316C22×C4—442no—
317C22×C4—442no—
318C22×C4—442no—
319C22×C4C22⋊Dic1111yescharacteristic
320C22×C4C22⋊Dic1111yescharacteristic
321C22×C4C22⋊Dic1111yescharacteristic
322C22×C4C22⋊Dic1111yescharacteristic
323C22×C4C2×C4×D1112yes—
324C22×C4#433912yes—
325C22×C4C22×Dic1111yescharacteristic
326C22×C4C2×C22⋊D1111yescharacteristic
327C2×C8—224no—
328C2×C8—442no—
329C2×C8—442no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—42no—
334C4⋊C4C4×Dic1112yes—
335C22⋊C4—24no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C42—22no—
341C42—22no—
342C42—41no—
343C42—41no—
344C42—42no—
345C11#821611yescharacteristic, complemented, Sylow
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—22no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23C4×C22⋊D1112yes—
358C23#6698512yes—
359C23#6700211yescharacteristic
360C23#6700411yescharacteristic
361C23C2×C22⋊Dic1111yescharacteristic
362D4—42no—
363D4—42no—
364D4—44no—
365D4—44no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—84no—
396C2×C4—444no—
397C2×C4—444no—
398C2×C4—444no—
399C2×C4—882no—
400C2×C4—882no—
401C2×C4—882no—
402C2×C4—882no—
403C2×C4#6689812yes—
404C2×C4C2×C4×Dic1111yescharacteristic
405C2×C4#6697911yescharacteristic
406C2×C4C4×C22⋊D1112yes—
407C8—444no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—22no—
416C22—42no—
417C22—42no—
418C22—42no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22#1062262712yes—
424C22#1062263112yes—
425C22C4×C22⋊Dic1111yescharacteristic
426C22#1062282811yescharacteristic
427C22C2×#6689811yescharacteristic
428C22#1062284511yescharacteristic
429C22#1062284911yescharacteristic
430C22#1062284911yescharacteristic
431C22#1062285311yescharacteristic
432C4—22no—
433C4—21no—
434C4—21no—
435C4—22no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—42no—
440C4—81no—
441C4—81no—
442C4—884no—
443C2—22no—
444C2—22no—
445C2—82no—
446C2#1306714511yescharacteristic
447C2#1306715411yescharacteristic
448C2#1306715911yescharacteristic
449C2#1306716311yescharacteristic
450C2C4×#6689811yescharacteristic
451C2#1306842611yescharacteristic
452C2#1306844111yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC4×C11×#121C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenterC4×#121D11
hypocenterC11#8216
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. #13068378C2semidirect
3. #13066843C2semidirect
4. #13066494C2semidirect
8. C2×C4×D4×C11C4semidirect
10. C11×#390C4semidirect
11. C11×#389C4semidirect
15. C4×C11×C4⋊C4C4semidirect
22. #10622175C4semidirect
57. C11⋊#95C2×C4semidirect
59. C22⋊(C11⋊C8)C2×C4semidirect
189. C2×C4×D4Dic11semidirect
193. #390Dic11semidirect
194. #389Dic11semidirect
198. C4×C4⋊C4Dic11semidirect
345. C11#8216semidirect

Maximal subgroups

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

subgroupindex
#130683782
C2×#106221752
#130668432
#130664942
C4×C11×#1212
#821611