Finite Group Databasebeta

← #14757135

Subgroups — #14757135

Order 2816.

982 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×#10622493C211yesmaximal, characteristic
2C2×D11×#107C211yesmaximal, characteristic
3C2×#10622302C211yesmaximal, characteristic
4#13071238C212yesmaximal
5#13069358C212yesmaximal, complemented
6#13069356C212yesmaximal, complemented
7#13069350C211yesmaximal, characteristic, complemented
8#13069349C211yesmaximal, characteristic, complemented
9#13069347C211yesmaximal, characteristic, complemented
10#13068334C212yesmaximal
11C11×#1942C211yesmaximal, characteristic, complemented
12C22×#4313C2211yescharacteristic
13C22×C8×D11C2211yescharacteristic
14C2×#66945C2212yes—
15C2×C4⋊C4×D11C2212yes—
16C2×#66925C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19C2×C4×C8×C11C2211yescharacteristic
20C11×#389C2212yes—
21C2×#66882C2211yescharacteristic
22C2×#66882C2211yescharacteristic
23C2×#66879C2211yescharacteristic
24C2×C8×Dic11C2211yescharacteristic
25#10622602—22no—
26#10622598C2212yes—
27#10622589—22no—
28#10622586C2212yes—
29C2×#66872C2212yes—
30C2×#66871C2212yes—
31#10622541C2212yes—
32C2×#66867C2211yescharacteristic
33#10622493C418yescomplemented
34D11×#107—24no—
35#10622302—24no—
36#10622281—22no—
37#10622263—22no—
38C11×#340C2212yes—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×C4×D11—22no—
43C22×C4×D11C2311yescharacteristic
44C22×C8×C11C2311yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C4⋊C4C2312yes—
49C2×C42×C11C2311yescharacteristic
50C2×(C2×D11)⋊C4—22no—
51C2×(C2×D11)⋊C4D411yescharacteristic
52C2×(C2×D11)⋊C4D411yescharacteristic
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11C2312yes—
55C2×C4⋊Dic11C2312yes—
56C2×Dic11⋊C4—22no—
57C2×Dic11⋊C4—22no—
58C2×Dic11⋊C4—22no—
59C2×Dic11⋊C4D411yescharacteristic
60C2×Dic11⋊C4D411yescharacteristic
61C2×C4×Dic11—22no—
62C2×C4×Dic11C2311yescharacteristic
63C22×C11⋊C8C2311yescharacteristic
64C22×C11⋊C8C2311yescharacteristic
65C2×#4313—22no—
66C2×#4313—22no—
67C2×#4313Q814yes—
68C2×C8×D11C2×C414yes—
69C2×C8×D11D414yes—
70C2×C8×D11Q814yes—
71#66945—24no—
72#66945C2×C418yes—
73C4⋊C4×D11—24no—
74C4⋊C4×D11—24no—
75#66925—22no—
76#66925—22no—
77C11×#107—22no—
78C11×#107C2×C414yescomplemented
79C4×C8×C11—22no—
80C11×#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84#66882—22no—
85#66882C2×C414yescomplemented
86#66879—22no—
87C8×Dic11—22no—
88#66872C2×C418yescomplemented
89#66871—24no—
90#66867—22no—
91#21156—111nomaximal, Sylow
92C23×D11C2×D411yescharacteristic
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2411yescharacteristic
98C22×Dic11—22no—
99C22×Dic11—22no—
100C22×Dic11C2×D411yescharacteristic
101C22×Dic11C2×D411yescharacteristic
102C22×Dic11C2×D411yescharacteristic
103C2×C4×D11—44no—
104C2×C4×D11—82no—
105C2×C4×D11—82no—
106C2×C4×D11C22×C412yes—
107C2×C4×D11C2×D412yes—
108C2×C4×D11C2×Q812yes—
109C2×C4×D11C2×Q812yes—
110C2×C4×D11#4112yes—
111C2×C4×D11#4112yes—
112C2×C8×C11—21no—
113C2×C8×C11—21no—
114C2×C8×C11C22×C412yes—
115C2×C8×C11C2×D412yes—
116C2×C8×C11C2×Q812yes—
117C2×C8×C11C2×Q812yes—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—82no—
122C11×C4⋊C4C22×C414yes—
123C42×C11—21no—
124C42×C11—21no—
125(C2×D11)⋊C4—28no—
126(C2×D11)⋊C4—22no—
127(C2×D11)⋊C4—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11—82no—
132C4⋊Dic11C22×C414yes—
133Dic11⋊C4—22no—
134Dic11⋊C4—22no—
135Dic11⋊C4—44no—
136Dic11⋊C4—82no—
137Dic11⋊C4—82no—
138C4×Dic11—28no—
139C4×Dic11—21no—
140C4×Dic11—21no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8C22×C412yes—
144C2×C11⋊C8C2×D412yes—
145C2×C11⋊C8C2×Q812yes—
146C2×C11⋊C8C2×Q812yes—
147#4313—28no—
148C8×D11C4⋊C4116yescomplemented
149C2×#427—111no—
150C22×#107—111no—
151C2×#405—111no—
152#2317—112no—
153#1944—112no—
154#1944—112no—
155#1942—111no—
156#1942—111no—
157#1942—111no—
158#1942D1111yescharacteristic, complemented
159#1736—112no—
160C23×C11C22×D411yescharacteristic
161C22×D11—21no—
162C22×D11—21no—
163C22×D11—21no—
164C22×D11—21no—
165C22×D11C4×D412yes—
166C22×D11#12112yes—
167C22×D11C4⋊Q812yes—
168C2×C4×C11—24no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11C23×C411yescharacteristic
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11C22×Q811yescharacteristic
183C2×C4×C11C22×Q811yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×Dic11—24no—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11C4×D412yes—
199C2×Dic11#12112yes—
200C2×Dic11C4⋊Q812yes—
201C4×D11—88no—
202C4×D11C2×C4⋊C414yes—
203C4×D11C4×Q814yes—
204C4×D11C22⋊Q814yes—
205C4×D11#12514yes—
206C8×C11—22no—
207C8×C11C2×C4⋊C414yes—
208C11⋊C8—22no—
209C11⋊C8C2×C4⋊C414yes—
210C22×M16—111no—
211C23×C8—111no—
212C2×#117—111no—
213C2×#117—112no—
214C22×C4⋊C4—112no—
215#427—118no—
216C2×#107—111no—
217C2×#107—111no—
218C2×#107—112no—
219C2×#107—224no—
220C2×#107C2×D1111yescharacteristic
221C2×#107C2×D1111yescharacteristic
222C2×#106—112no—
223#405—224no—
224C2×#97—111no—
225C2×#97—111no—
226C2×C4×C8—111no—
227C2×C4×C8C2×D1111yescharacteristic
228#389—112no—
229#389—112no—
230#389—112no—
231#389C2×D1112yes—
232#385—222no—
233#385—222no—
234#384—222no—
235#382—222no—
236#340—112no—
237#340—112no—
238#340—112no—
239#340C2×D1112yes—
240C22×C11C2×C4×D411yescharacteristic
241C22×C11C2×#12111yescharacteristic
242C22×C11C2×C4⋊Q811yescharacteristic
243C22×C11#57611yescharacteristic
244C22×C11#57611yescharacteristic
245C22×C11#57811yescharacteristic
246C22×C11#57811yescharacteristic
247C2×D11—22no—
248C2×D11—22no—
249C2×D11—22no—
250C2×D11—22no—
251C2×D11—22no—
252C2×D11—22no—
253C2×D11#38914yes—
254C4×C11—44no—
255C4×C11—41no—
256C4×C11—41no—
257C4×C11—82no—
258C4×C11C22×C4⋊C411yescharacteristic
259C4×C11C2×C4×Q811yescharacteristic
260C4×C11C2×C22⋊Q811yescharacteristic
261C4×C11C2×#12511yescharacteristic
262Dic11—44no—
263Dic11—41no—
264Dic11—41no—
265Dic11—82no—
266Dic11#38914yes—
267C23×C4—111no—
268C23×C4—222no—
269C2×M16—114no—
270C2×M16—222no—
271C2×M16—222no—
272C22×C8—111no—
273C22×C8—114no—
274C22×C8—114no—
275C22×C8—114no—
276C22×C8—111no—
277C22×C8C22×D1111yescharacteristic
278C22×C8C22×D1111yescharacteristic
279#117—118no—
280#117—222no—
281#117—222no—
282#117—224no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—112no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—112no—
288C2×C4⋊C4—224no—
289C2×C4⋊C4—224no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4—222no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4C22×D1112yes—
295C2×C4⋊C4C22×D1112yes—
296C2×C22⋊C4—111no—
297C2×C22⋊C4—111no—
298C2×C22⋊C4—222no—
299C2×C42—111no—
300C2×C42—222no—
301C2×C42C22×D1111yescharacteristic
302#107—22no—
303#107—114no—
304#107—224no—
305#107—222no—
306#107C4×D1114yescomplemented
307#106—118no—
308#97—222no—
309#97—222no—
310C4×C8—22no—
311C4×C8—222no—
312#95—22no—
313#95—222no—
314#95—222no—
315#95—222no—
316C2×C11C2×#38911yescharacteristic
317C2×C11#295111yescharacteristic
318C2×C11#295111yescharacteristic
319C2×C11#305811yescharacteristic
320C2×C11#305911yescharacteristic
321C2×C11#316411yescharacteristic
322C2×C11#316411yescharacteristic
323D11—24no—
324C24—111no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—111no—
328C22×C4—112no—
329C22×C4—112no—
330C22×C4—112no—
331C22×C4—112no—
332C22×C4—112no—
333C22×C4—112no—
334C22×C4—111no—
335C22×C4—111no—
336C22×C4—222no—
337C22×C4—222no—
338C22×C4—444no—
339C22×C4—882no—
340C22×C4—882no—
341C22×C4D4×D1111yescharacteristic
342C22×C4D4×D1111yescharacteristic
343C22×C4C23×D1111yescharacteristic
344M16—228no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—112no—
348C2×C8—112no—
349C2×C8—112no—
350C2×C8—1116no—
351C2×C8—112no—
352C2×C8—221no—
353C2×C8—221no—
354C2×C8C2×C4×D1112yes—
355C2×C8D4×D1112yes—
356C2×C8Q8×D1112yes—
357C2×C8Q8×D1112yes—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—82no—
362C4⋊C4—114no—
363C4⋊C4—222no—
364C4⋊C4—222no—
365C4⋊C4—222no—
366C4⋊C4—222no—
367C4⋊C4—222no—
368C4⋊C4—444no—
369C4⋊C4—882no—
370C4⋊C4—882no—
371C4⋊C4—882no—
372C4⋊C4C2×C4×D1114yes—
373C22⋊C4—222no—
374C22⋊C4—222no—
375C22⋊C4—228no—
376C42—21no—
377C42—21no—
378C42—228no—
379C42—221no—
380C42—221no—
381C11#2115611yescharacteristic, complemented, Sylow
382C23—112no—
383C23—112no—
384C23—112no—
385C23—221no—
386C23—221no—
387C23—221no—
388C23—221no—
389C23C2×D4×D1111yescharacteristic
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—24no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—112no—
403C2×C4—112no—
404C2×C4—112no—
405C2×C4—114no—
406C2×C4—114no—
407C2×C4—114no—
408C2×C4—114no—
409C2×C4—221no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—224no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—442no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—888no—
422C2×C4C22×C4×D1111yescharacteristic
423C2×C4C2×D4×D1111yescharacteristic
424C2×C4C2×Q8×D1111yescharacteristic
425C2×C4C2×Q8×D1111yescharacteristic
426C2×C4#41×D1111yescharacteristic
427C2×C4#41×D1111yescharacteristic
428C8—22no—
429C8—114no—
430C8—222no—
431C8C4⋊C4×D1114yes—
432C22—114no—
433C22—222no—
434C22—222no—
435C22—222no—
436C22—222no—
437C22—222no—
438C22—222no—
439C22C4×D4×D1111yescharacteristic
440C22D11×#12111yescharacteristic
441C22D11×C4⋊Q811yescharacteristic
442C22#1062328811yescharacteristic
443C22#1062329711yescharacteristic
444C22#1062330011yescharacteristic
445C22#1062330211yescharacteristic
446C4—44no—
447C4—41no—
448C4—41no—
449C4—82no—
450C4—114no—
451C4—444no—
452C4—441no—
453C4—441no—
454C4—882no—
455C4C2×C4⋊C4×D1111yescharacteristic
456C4C4×Q8×D1111yescharacteristic
457C4D11×C22⋊Q811yescharacteristic
458C4D11×#12511yescharacteristic
459C2—224no—
460C2D11×#38911yescharacteristic
461C2#1307748611yescharacteristic
462C2#1307749111yescharacteristic
463C2#1307825911yescharacteristic
464C2#1307826611yescharacteristic
465C2#1307914911yescharacteristic
466C2#1307915311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1942C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1942D11
hypocenterC11#21156
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1942

Complements

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

NH ≅ G/Ntype
5. #13069358C2semidirect
6. #13069356C2semidirect
7. #13069350C2semidirect
8. #13069349C2semidirect
9. #13069347C2semidirect
11. C11×#1942C2semidirect
33. #10622493C4semidirect
78. C11×#107C2×C4semidirect
85. #66882C2×C4semidirect
88. #66872C2×C4semidirect
148. C8×D11C4⋊C4semidirect
158. #1942D11semidirect
306. #107C4×D11semidirect
381. C11#21156semidirect

Maximal subgroups

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

subgroupindex
C2×#106224932
C2×D11×#1072
C2×#106223022
#130712382
#130693582
#130693562
#130693502
#130693492
#130693472
#130683342
C11×#19422
#2115611