Finite Group Databasebeta

← #14775659

Subgroups — #14775659

Order 2816.

886 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622455C211yesmaximal, characteristic
2#13071705C211yesmaximal, characteristic, complemented
3C4⋊C4×D44C211yesmaximal, characteristic
4#13069577C211yesmaximal, characteristic, complemented
5#13069375C211yesmaximal, characteristic, complemented
6#13069359C212yesmaximal, complemented
7#13069202C212yesmaximal, complemented
8#13068866C212yesmaximal
9#13068442C212yesmaximal
10C4×#66885C211yesmaximal, characteristic
11C11×#1770C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×D11—21no—
13C2×C4×D44C2212yes—
14C2×C4×D44C2211yescharacteristic
15C2×#66922C2211yescharacteristic
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#97C2212yes—
18C2×C4×C8×C11C2211yescharacteristic
19C4×C11×C4⋊C4C2211yescharacteristic
20C2×#66885C2211yescharacteristic
21C2×#66885C2212yes—
22C2×#66885C2211yescharacteristic
23C2×#66882C2212yes—
24C2×#66881C2212yes—
25#10622600—21no—
26C4⋊C4×Dic11—21no—
27#10622586—21no—
28#10622548C2211yescharacteristic
29C4×C4⋊Dic11C2211yescharacteristic
30C4×C4⋊Dic11C2212yes—
31#10622541C2212yes—
32#10622541C2212yes—
33#10622455C418yescomplemented
34#10622281—22no—
35#10622259—22no—
36C11×#336C2212yes—
37#10622189C2212yes—
38#10622189C2212yes—
39#10622189C2211yescharacteristic
40#10622189C2212yes—
41#10622189C2211yescharacteristic
42C22×D44C2311yescharacteristic
43C22×C4×D11—21no—
44C22×C4×D11—22no—
45C22×Dic22—21no—
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2312yes—
48C22×C8×C11C2311yescharacteristic
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C42×C11C2312yes—
52C2×C42×C11C2311yescharacteristic
53C2×(C2×D11)⋊C4—21no—
54C2×(C2×D11)⋊C4—22no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11C2311yescharacteristic
59C2×C4⋊Dic11C2312yes—
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2311yescharacteristic
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11—22no—
67C4⋊C4×D11—44no—
68C4×D44—22no—
69C4×D44—24no—
70C4×D44—42no—
71C4×D44C2×C414yes—
72#66922—22no—
73#66922C2×C414yescomplemented
74C11×C4⋊C8C2×C414yescomplemented
75C11×#97—42no—
76C4×C8×C11—22no—
77C11×#95D412yes—
78C11⋊#95—21no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82#66885—22no—
83#66885C2×C418yes—
84#66885Q814yescomplemented
85#66882—42no—
86#66881C2×C418yescomplemented
87#22969—111nomaximal, Sylow
88C23×D11—21no—
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2411yescharacteristic
94C22×Dic11—21no—
95C22×Dic11—22no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—22no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44C22×C412yes—
103C2×D44C2×Q812yes—
104C2×D44#4112yes—
105C2×C4×D11—24no—
106C2×C4×D11—44no—
107C2×C4×D11—44no—
108C2×C4×D11—42no—
109C2×C4×D11—42no—
110C2×C4×D11—82no—
111C2×Dic22—24no—
112C2×Dic22—81no—
113C2×Dic22—81no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11—22no—
118C2×C8×C11—21no—
119C2×C8×C11—22no—
120C2×C8×C11—21no—
121C2×C8×C11C22×C414yes—
122C2×C8×C11C2×Q812yes—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C42×C11—22no—
126C42×C11—22no—
127C42×C11C22×C412yes—
128C42×C11#4112yes—
129(C2×D11)⋊C4—24no—
130(C2×D11)⋊C4—44no—
131C4⋊Dic11—24no—
132C4⋊Dic11—22no—
133C4⋊Dic11—21no—
134C4⋊Dic11—21no—
135C4⋊Dic11—22no—
136C4⋊Dic11—21no—
137C4⋊Dic11—22no—
138C4⋊Dic11—21no—
139C4⋊Dic11—42no—
140C4⋊Dic11—81no—
141C4⋊Dic11C22×C412yes—
142C4⋊Dic11C22×C414yes—
143C4⋊Dic11C2×Q812yes—
144Dic11⋊C4—44no—
145Dic11⋊C4—82no—
146C4×Dic11—42no—
147C4×Dic11—82no—
148C2×#476—111no—
149#2369—111no—
150D4×C4⋊C4—111no—
151#1990—111no—
152#1947—111no—
153#1944—112no—
154#1920—112no—
155#1862—112no—
156#1770D1111yescharacteristic, complemented
157#1762—112no—
158C4×#102—111no—
159C23×C11C22×D411yescharacteristic
160C22×D11—22no—
161C22×D11—22no—
162C22×D11—22no—
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11C4×D412yes—
176C2×C4×C11C4×D412yes—
177C2×C4×C11AGL(1,ℤ/8)12yes—
178C2×C4×C11#13712yes—
179C2×C4×C11C23×C411yescharacteristic
180C2×C4×C11C22×Q811yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C2×C4×C11H(5,𝔽2)11yescharacteristic
184C2×C4×C112−1+411yescharacteristic
185C2×Dic11—24no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—42no—
192C2×Dic11—41no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—42no—
198C2×Dic11—41no—
199C2×Dic11—42no—
200D44—22no—
201D44—22no—
202D44—22no—
203D44C4×Q814yes—
204C4×D11—48no—
205C4×D11—88no—
206Dic22—84no—
207C8×C11—24no—
208C8×C11—22no—
209C8×C11—41no—
210C2×C4⋊Q8—111no—
211C2×C4×D4—111no—
212C2×C4×D4—112no—
213C22×C4⋊C4—221no—
214#476—118no—
215C2×#107—112no—
216C2×#106—112no—
217C2×C4⋊C8C2×D1111yescharacteristic
218C2×#102—112no—
219C2×#102—111no—
220C2×#102—111no—
221C2×#97C2×D1112yes—
222C2×C4×C8C2×D1111yescharacteristic
223#391—222no—
224#389—112no—
225#389—112no—
226#389—221no—
227#385—222no—
228#384—111no—
229#380—221no—
230C4×C4⋊C4—112no—
231C4×C4⋊C4—111no—
232C4×C4⋊C4—221no—
233C4×C4⋊C4C2×D1111yescharacteristic
234#340—112no—
235#340—111no—
236#340—112no—
237#340—111no—
238#340—112no—
239#336C2×D1112yes—
240C22×C11C2×C4×D411yescharacteristic
241C22×C11#54611yescharacteristic
242C22×C11D4×Q811yescharacteristic
243C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
244C22×C11C2×#13711yescharacteristic
245C22×C11#57611yescharacteristic
246C22×C11#57711yescharacteristic
247C2×D11—24no—
248C2×D11—42no—
249C2×D11—42no—
250C2×D11—42no—
251C2×D11—42no—
252C2×D11—42no—
253C2×D11—42no—
254C4×C11—22no—
255C4×C11—42no—
256C4×C11—42no—
257C4×C11#44014yes—
258C4×C11C2×C4×Q811yescharacteristic
259C4×C11#52011yescharacteristic
260C4×C11#55211yescharacteristic
261C4×C11#55411yescharacteristic
262Dic11—42no—
263Dic11—42no—
264Dic11—44no—
265Dic11—82no—
266Dic11—81no—
267C22×Q8—221no—
268C22×D4—111no—
269C23×C4—221no—
270C23×C4—222no—
271C22×C8C22×D1111yescharacteristic
272C22×C8C22×D1112yes—
273C22×C8C22×D1111yescharacteristic
274C4⋊Q8—114no—
275C4⋊Q8—222no—
276C4×D4—114no—
277C4×D4—224no—
278C4×D4—222no—
279C4×D4—442no—
280C2×C4⋊C4—111no—
281C2×C4⋊C4—112no—
282C2×C4⋊C4—111no—
283C2×C4⋊C4—112no—
284C2×C4⋊C4—111no—
285C2×C4⋊C4—221no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4—222no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4—444no—
291C2×C4⋊C4D4411yescharacteristic
292C2×C4⋊C4D4411yescharacteristic
293C2×C22⋊C4—221no—
294C2×C22⋊C4—222no—
295C2×C42—221no—
296C2×C42—222no—
297C2×C42C22×D1112yes—
298C2×C42C22×D1111yescharacteristic
299#107—442no—
300#106—118no—
301C4⋊C8C4×D1114yescomplemented
302#102—118no—
303#102—114no—
304#102—222no—
305#97—42no—
306C4×C8—22no—
307#95—222no—
308#95—221no—
309#95—222no—
310#95—222no—
311#95D4412yes—
312C2×C11#236011yescharacteristic
313C2×C11C2×#44011yescharacteristic
314C2×C11#294611yescharacteristic
315C2×C11#332511yescharacteristic
316C2×C11#333111yescharacteristic
317C2×C11#338411yescharacteristic
318C2×C11#338511yescharacteristic
319D11—44no—
320C24—221no—
321C2×Q8—224no—
322C2×Q8—881no—
323C2×Q8—881no—
324C2×D4—112no—
325C2×D4—112no—
326C2×D4—112no—
327C2×D4—221no—
328C2×D4—221no—
329C2×D4—221no—
330C22×C4—221no—
331C22×C4—222no—
332C22×C4—221no—
333C22×C4—224no—
334C22×C4—221no—
335C22×C4—222no—
336C22×C4—444no—
337C22×C4—444no—
338C22×C4—442no—
339C22×C4—442no—
340C22×C4—882no—
341C22×C4C2×D4412yes—
342C22×C4C2×D4412yes—
343C22×C4C2×D4411yescharacteristic
344C22×C4C2×D4411yescharacteristic
345C22×C4C23×D1111yescharacteristic
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8C2×C4×D1114yes—
354C2×C8Q8×D1112yes—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—114no—
358C4⋊C4—112no—
359C4⋊C4—112no—
360C4⋊C4—224no—
361C4⋊C4—221no—
362C4⋊C4—222no—
363C4⋊C4—221no—
364C4⋊C4—221no—
365C4⋊C4—222no—
366C4⋊C4—221no—
367C4⋊C4—222no—
368C4⋊C4—444no—
369C4⋊C4—442no—
370C4⋊C4—882no—
371C4⋊C4—881no—
372C22⋊C4—224no—
373C22⋊C4—444no—
374C42—22no—
375C42—22no—
376C42—442no—
377C42—882no—
378C42C2×C4×D1112yes—
379C42#433912yes—
380C11#2296911yescharacteristic, complemented, Sylow
381C23—222no—
382C23—222no—
383C23—222no—
384C23—441no—
385C23—441no—
386C23—441no—
387C23—441no—
388C23C22×D4411yescharacteristic
389Q8—884no—
390D4—114no—
391D4—222no—
392D4—222no—
393D4—222no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—222no—
403C2×C4—224no—
404C2×C4—222no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4—442no—
410C2×C4—442no—
411C2×C4—448no—
412C2×C4—441no—
413C2×C4—442no—
414C2×C4—441no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4—441no—
418C2×C4—888no—
419C2×C4C4×D4412yes—
420C2×C4C4×D4412yes—
421C2×C4#6696112yes—
422C2×C4#6696212yes—
423C2×C4C22×C4×D1111yescharacteristic
424C2×C4C2×#433911yescharacteristic
425C2×C4#6703711yescharacteristic
426C2×C4C2×Q8×D1111yescharacteristic
427C2×C4#41×D1111yescharacteristic
428C2×C4#6704311yescharacteristic
429C8—22no—
430C8—24no—
431C8—41no—
432C22—224no—
433C22—442no—
434C22—442no—
435C22—442no—
436C22—442no—
437C22—442no—
438C22—442no—
439C22C2×C4×D4411yescharacteristic
440C22#1062308511yescharacteristic
441C22Q8×D4411yescharacteristic
442C22C2×#6696111yescharacteristic
443C22C2×#6696211yescharacteristic
444C22#1062328211yescharacteristic
445C22#1062328311yescharacteristic
446C4—22no—
447C4—42no—
448C4—42no—
449C4—442no—
450C4—442no—
451C4—444no—
452C4—882no—
453C4—881no—
454C4#1062232314yes—
455C4#1062304211yescharacteristic
456C4#1062306011yescharacteristic
457C4#1062307711yescharacteristic
458C4C4×Q8×D1111yescharacteristic
459C2—444no—
460C2#1307162311yescharacteristic
461C2C2×#1062232311yescharacteristic
462C2#1307745011yescharacteristic
463C2#1308085911yescharacteristic
464C2#1308093311yescharacteristic
465C2#1308151711yescharacteristic
466C2#1308152811yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1770C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1770D11
hypocenterC11#22969
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1770

Complements

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

NH ≅ G/Ntype
2. #13071705C2semidirect
4. #13069577C2semidirect
5. #13069375C2semidirect
6. #13069359C2semidirect
7. #13069202C2semidirect
11. C11×#1770C2semidirect
33. #10622455C4semidirect
73. #66922C2×C4semidirect
74. C11×C4⋊C8C2×C4semidirect
84. #66885Q8semidirect
86. #66881C2×C4semidirect
156. #1770D11semidirect
301. C4⋊C8C4×D11semidirect
380. C11#22969semidirect

Maximal subgroups

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

subgroupindex
C2×#106224552
#130717052
C4⋊C4×D442
#130695772
#130693752
#130693592
#130692022
#130688662
#130684422
C4×#668852
C11×#17702
#2296911