Finite Group Databasebeta

← #14775650

Subgroups — #14775650

Order 2816.

914 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071676C211yesmaximal, characteristic, complemented
2D4×C4⋊Dic11C211yesmaximal, characteristic
3#13069578C211yesmaximal, characteristic, complemented
4#13069380C211yesmaximal, characteristic, complemented
5#13069355C212yesmaximal, complemented
6#13069210C212yesmaximal, complemented
7#13068879C212yesmaximal
8#13068486C211yesmaximal, characteristic, complemented
9#13068443C212yesmaximal
10C4×#66896C211yesmaximal, characteristic
11C2×C11×#474C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×Q8×Dic11—21no—
15C2×D4×Dic11C2212yes—
16C22×C4⋊Dic11—21no—
17C11×#474C418yescomplemented
18C2×C11×#107C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#102C2212yes—
21#10622843—21no—
22C2×#66896C2211yescharacteristic
23C2×#66896C2211yescharacteristic
24#10622825—21no—
25C2×#66881C2212yes—
26C2×#66879C2212yes—
27#10622598C2212yes—
28#10622598C2212yes—
29#10622594—22no—
30C4⋊C4×Dic11C2212yes—
31#10622563—22no—
32#10622548C2211yescharacteristic
33C4×C4⋊Dic11C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622189C2212yes—
37#10622188C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42C22×Q8×C11—21no—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C23×Dic11—22no—
46C22×C8×C11C2312yes—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8C2×C414yescomplemented
49C4×D4×C11—22no—
50C4×D4×C11C2×C414yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C22⋊C4—21no—
55C2×C42×C11C2311yescharacteristic
56C2×C22⋊Dic11—22no—
57Q8×Dic11—44no—
58D4×Dic11—24no—
59D4×Dic11—42no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—44no—
65C2×C4⋊Dic11D411yescharacteristic
66C2×C4⋊Dic11D411yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4×Dic11—21no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11C2312yes—
73C22×C11⋊C8C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75C11×#107C2×C418yescomplemented
76C11×C4⋊C8C2×C414yescomplemented
77C11×#102C2×C418yes—
78#66896—22no—
79#66896Q814yescomplemented
80C11⋊#95—21no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95D412yes—
85#66881—42no—
86#66879—42no—
87C4×C11⋊C8—22no—
88#22968—111nomaximal, Sylow
89C24×C11—21no—
90C2×Q8×C11—24no—
91C2×Q8×C11—42no—
92C2×Q8×C11—42no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11C22×C412yes—
97C2×D4×C11C2×Q812yes—
98C2×D4×C11#4112yes—
99C22×C4×C11—22no—
100C22×C4×C11—21no—
101C22×C4×C11—24no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11—22no—
110C22×Dic11—44no—
111C22×Dic11—44no—
112C22×Dic11—82no—
113C22×Dic11C2×D412yes—
114C22×Dic11C2×D412yes—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11C22×C414yes—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4C22×C414yes—
122C11×C4⋊C4C22×C412yes—
123C11×C22⋊C4—24no—
124C42×C11C22×C412yes—
125C42×C11#4112yes—
126C22⋊Dic11—44no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—21no—
130C4⋊Dic11—22no—
131C4⋊Dic11—21no—
132C4⋊Dic11—22no—
133C4⋊Dic11—21no—
134C4⋊Dic11—44no—
135C4⋊Dic11—44no—
136C4⋊Dic11—42no—
137C4⋊Dic11—81no—
138C4⋊Dic11C2×Q812yes—
139C4×Dic11—22no—
140C4×Dic11—22no—
141C4×Dic11—44no—
142C4×Dic11—42no—
143C2×C11⋊C8—21no—
144C2×C11⋊C8—21no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8C2×Q812yes—
149C2×#474D1111yescharacteristic
150#2365—111no—
151D4×C4⋊C4—111no—
152#1990—111no—
153#1948—111no—
154#1943—112no—
155#1921—112no—
156#1864—112no—
157#1770—111no—
158#1762—112no—
159C4×#102—111no—
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11C22×D411yescharacteristic
168Q8×C11—48no—
169D4×C11—22no—
170D4×C11—22no—
171D4×C11—22no—
172D4×C11C4×Q814yescomplemented
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—22no—
176C2×C4×C11—24no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—48no—
182C2×C4×C11C4×D412yes—
183C2×C4×C11C4×D412yes—
184C2×C4×C11AGL(1,ℤ/8)12yes—
185C2×C4×C11AGL(1,ℤ/8)12yes—
186C2×C4×C11C23×C411yescharacteristic
187C2×C4×C11C22×Q811yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C2×C4×C11C2×#4111yescharacteristic
190C2×C4×C11H(5,𝔽2)11yescharacteristic
191C2×C4×C112−1+411yescharacteristic
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—42no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—41no—
207C2×Dic11—88no—
208C8×C11—24no—
209C11⋊C8—22no—
210C11⋊C8—41no—
211C2×C4⋊Q8C2×D1111yescharacteristic
212C2×C4×Q8—221no—
213C2×C4×D4—112no—
214C2×C4×D4C2×D1111yescharacteristic
215C22×C4⋊C4—221no—
216#474Dic1118yescomplemented
217C2×#107C2×D1112yes—
218C2×#106—112no—
219C2×C4⋊C8C2×D1111yescharacteristic
220C2×#102—111no—
221C2×#102—111no—
222C2×#102C2×D1112yes—
223C2×#97—112no—
224C2×C4×C8—111no—
225#391—221no—
226#389—112no—
227#389—112no—
228#387—222no—
229#385—222no—
230#384—111no—
231#380—221no—
232C4×C4⋊C4—111no—
233C4×C4⋊C4—112no—
234C4×C4⋊C4—111no—
235#340—112no—
236#340—112no—
237#340—111no—
238#340—111no—
239#340—112no—
240#336—112no—
241C22×C11—24no—
242C22×C11—42no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11C2×C4×D411yescharacteristic
249C22×C11#54611yescharacteristic
250C22×C11D4×Q811yescharacteristic
251C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
252C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
253C22×C11#57711yescharacteristic
254C22×C11#57811yescharacteristic
255C4×C11—22no—
256C4×C11—42no—
257C4×C11—44no—
258C4×C11#44214yes—
259C4×C11C2×C4×Q811yescharacteristic
260C4×C11#52011yescharacteristic
261C4×C11#55211yescharacteristic
262C4×C11#55411yescharacteristic
263Dic11—42no—
264Dic11—42no—
265Dic11—42no—
266Dic11—81no—
267Dic11—82no—
268C22×Q8—21no—
269C22×D4C22×D1111yescharacteristic
270C23×C4—21no—
271C23×C4—222no—
272C22×C8—111no—
273C22×C8—111no—
274C22×C8C22×D1112yes—
275C4⋊Q8—22no—
276C4⋊Q8C2×Dic1114yescomplemented
277C4×Q8—444no—
278C4×D4—22no—
279C4×D4—224no—
280C4×D4—442no—
281C4×D4C2×Dic1114yes—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—111no—
284C2×C4⋊C4—111no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—112no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—222no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4—221no—
292C2×C4⋊C4—444no—
293C2×C4⋊C4C22×D1111yescharacteristic
294C2×C4⋊C4C22×D1112yes—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—222no—
297C2×C42—112no—
298C2×C42—222no—
299C2×C42—221no—
300C2×C42C22×D1111yescharacteristic
301#107C2×Dic1118yescomplemented
302#106—442no—
303C4⋊C8C2×Dic1114yescomplemented
304#102—114no—
305#102—222no—
306#102C2×Dic1118yes—
307#97—442no—
308C4×C8—222no—
309#95—112no—
310#95—222no—
311#95—222no—
312#95—222no—
313#95—221no—
314C2×C11—44no—
315C2×C11#236011yescharacteristic
316C2×C11C2×#44211yescharacteristic
317C2×C11#294711yescharacteristic
318C2×C11#332411yescharacteristic
319C2×C11#333011yescharacteristic
320C2×C11#338411yescharacteristic
321C2×C11#338611yescharacteristic
322C24—21no—
323C2×Q8—24no—
324C2×Q8—42no—
325C2×Q8—42no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4Q8×D1112yes—
330C2×D4#434312yes—
331C2×D4C22×Dic1112yes—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—24no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—112no—
338C22×C4—112no—
339C22×C4—221no—
340C22×C4—221no—
341C22×C4—222no—
342C22×C4—444no—
343C22×C4—444no—
344C22×C4—882no—
345C22×C4D4×D1111yescharacteristic
346C22×C4D4×D1111yescharacteristic
347C22×C4C23×D1111yescharacteristic
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—112no—
351C2×C8—221no—
352C2×C8—221no—
353C2×C8—221no—
354C2×C8—221no—
355C2×C8—221no—
356C2×C8C22×Dic1114yes—
357C4⋊C4—24no—
358C4⋊C4—21no—
359C4⋊C4—22no—
360C4⋊C4—112no—
361C4⋊C4—222no—
362C4⋊C4—222no—
363C4⋊C4—221no—
364C4⋊C4—221no—
365C4⋊C4—222no—
366C4⋊C4—221no—
367C4⋊C4—222no—
368C4⋊C4—444no—
369C4⋊C4—444no—
370C4⋊C4—442no—
371C4⋊C4—881no—
372C4⋊C4C22×Dic1114yes—
373C4⋊C4C22×Dic1112yes—
374C22⋊C4—24no—
375C22⋊C4—444no—
376C42—222no—
377C42—222no—
378C42—444no—
379C42—442no—
380C42#434112yes—
381C42C22×Dic1112yes—
382C11#2296811yescharacteristic, complemented, Sylow
383C23—22no—
384C23—22no—
385C23—22no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23C2×D4×D1111yescharacteristic
391Q8—48no—
392D4—22no—
393D4—22no—
394D4—22no—
395D4Q8×Dic1114yescomplemented
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—22no—
399C2×C4—24no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—48no—
405C2×C4—222no—
406C2×C4—222no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—222no—
410C2×C4—222no—
411C2×C4—222no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4—441no—
418C2×C4—442no—
419C2×C4—441no—
420C2×C4—888no—
421C2×C4#6696412yes—
422C2×C4#6696412yes—
423C2×C4D4×Dic1112yes—
424C2×C4D4×Dic1112yes—
425C2×C4C2×#434111yescharacteristic
426C2×C4C2×Q8×D1111yescharacteristic
427C2×C4C2×#434311yescharacteristic
428C2×C4#6704211yescharacteristic
429C2×C4#6704311yescharacteristic
430C2×C4C23×Dic1111yescharacteristic
431C8—24no—
432C8—222no—
433C8—441no—
434C22—24no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22#1062316111yescharacteristic
442C22#1062316311yescharacteristic
443C22C2×#6696411yescharacteristic
444C22C2×#6696411yescharacteristic
445C22#1062330911yescharacteristic
446C22#1062331011yescharacteristic
447C22C2×D4×Dic1111yescharacteristic
448C4—22no—
449C4—42no—
450C4—44no—
451C4—442no—
452C4—442no—
453C4—442no—
454C4—882no—
455C4—881no—
456C4#1062276514yes—
457C4#1062316611yescharacteristic
458C4#1062317311yescharacteristic
459C4C2×Q8×Dic1111yescharacteristic
460C4#1062335811yescharacteristic
461C2—44no—
462C2#1307162511yescharacteristic
463C2C2×#1062276511yescharacteristic
464C2#1307746011yescharacteristic
465C2#1308084411yescharacteristic
466C2#1308091811yescharacteristic
467C2#1308151911yescharacteristic
468C2#1308154111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC2×#474D11
hypocenterC11#22968
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. #13071676C2semidirect
3. #13069578C2semidirect
4. #13069380C2semidirect
5. #13069355C2semidirect
6. #13069210C2semidirect
8. #13068486C2semidirect
17. C11×#474C4semidirect
48. C11×C4⋊Q8C2×C4semidirect
75. C11×#107C2×C4semidirect
76. C11×C4⋊C8C2×C4semidirect
79. #66896Q8semidirect
172. D4×C11C4×Q8semidirect
216. #474Dic11semidirect
276. C4⋊Q8C2×Dic11semidirect
301. #107C2×Dic11semidirect
303. C4⋊C8C2×Dic11semidirect
382. C11#22968semidirect
395. D4Q8×Dic11semidirect

Maximal subgroups

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

subgroupindex
#130716762
D4×C4⋊Dic112
#130695782
#130693802
#130693552
#130692102
#130688792
#130684862
#130684432
C4×#668962
C2×C11×#4742
#2296811