Finite Group Databasebeta

← #14755944

Subgroups — #14755944

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622734C211yesmaximal, characteristic
2#13071098C211yesmaximal, characteristic
3C2×C4⋊C4×Dic11C211yesmaximal, characteristic
4#13069207C212yesmaximal, complemented
5#13069200C212yesmaximal, complemented
6#13069193C212yesmaximal, complemented
7#13069186C212yesmaximal, complemented
8#13068337C211yesmaximal, characteristic
9#13068335C211yesmaximal, characteristic
10#13068309C211yesmaximal, characteristic
11C11×#1736C211yesmaximal, characteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4×Dic11—21no—
18C22×C4×Dic11C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C2×C11⋊#95—21no—
21#10622734C418yescomplemented
22C2×#66882C2212yes—
23C2×#66881C2212yes—
24C4⋊C4×Dic11—21no—
25C4⋊C4×Dic11—21no—
26C4⋊C4×Dic11C2212yes—
27C4⋊C4×Dic11C2212yes—
28#10622586C2211yescharacteristic
29#10622586C2211yescharacteristic
30#10622586C2211yescharacteristic
31#10622586C2211yescharacteristic
32#10622559—21no—
33#10622559—21no—
34C4×Dic11⋊C4—21no—
35C4×Dic11⋊C4—21no—
36C11×#340C2212yes—
37C11×#340C2212yes—
38#10622188C2212yes—
39#10622188C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C23×C4×C11—21no—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11—21no—
47C23×Dic11D411yescharacteristic
48C23×Dic11D411yescharacteristic
49C2×C11×M16—22no—
50C2×C11×M16—22no—
51C2×C11×M16C2×C414yes—
52C22×C8×C11C2312yes—
53C11×#117—22no—
54C11×#117—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4Q814yes—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C22⋊C4—21no—
62C2×C42×C11—21no—
63C2×C22⋊Dic11—21no—
64#66979—22no—
65#66979C2×C414yes—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11C2×C414yes—
69C2×C4⋊Dic11C2312yes—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×Dic11⋊C4—21no—
73C2×Dic11⋊C4—21no—
74C2×Dic11⋊C4—21no—
75C2×Dic11⋊C4—21no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—22no—
78C2×C4×Dic11—22no—
79C2×C4×Dic11—22no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11—44no—
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C2×C4×Dic11C2311yescharacteristic
86C2×#4318—22no—
87C2×#4318—22no—
88C2×#4318—22no—
89C22×C11⋊C8C2312yes—
90C11⋊#95—21no—
91C11⋊#95—21no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94C11⋊#95—22no—
95C11⋊#95—22no—
96#66882C2×C418yescomplemented
97#66881C2×C418yescomplemented
98#21033—111nomaximal, Sylow
99C24×C11C2×D411yescharacteristic
100C22×C4×C11—24no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11C22×C412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×Q812yes—
109C22×C4×C11#4112yes—
110C22×C4×C11#4112yes—
111C22×C4×C11#4112yes—
112C22×C4×C11#4112yes—
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—24no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—41no—
123C22×Dic11—41no—
124C22×Dic11—42no—
125C22×Dic11—42no—
126C22×Dic11C2×D411yescharacteristic
127C22×Dic11C2×D411yescharacteristic
128C22×Dic11C2×D411yescharacteristic
129C22×Dic11C2×D411yescharacteristic
130C11×M16—28no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11C22×C414yes—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4C2×Q814yes—
141C11×C22⋊C4—42no—
142C42×C11—42no—
143C22⋊Dic11—24no—
144C4⋊Dic11—24no—
145C4⋊Dic11—22no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11C22×C412yes—
149C4⋊Dic11C22×C414yes—
150C4⋊Dic11C22×C412yes—
151Dic11⋊C4—42no—
152Dic11⋊C4—42no—
153Dic11⋊C4—42no—
154Dic11⋊C4—42no—
155C4×Dic11—24no—
156C4×Dic11—22no—
157C4×Dic11—22no—
158C4×Dic11—21no—
159C4×Dic11—21no—
160C4×Dic11—21no—
161C4×Dic11—21no—
162C4×Dic11—44no—
163C4×Dic11—44no—
164#4318—44no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×#428—111no—
169#2296—111no—
170C2×C4×C4⋊C4—111no—
171#1921—112no—
172#1920—112no—
173#1919—112no—
174#1918—112no—
175#1736—111no—
176#1736—111no—
177#1736D1111yescharacteristic
178#1728—111no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11C4×D412yes—
184C23×C11C22⋊Q812yes—
185C23×C11#12312yes—
186C23×C11C22×D411yescharacteristic
187C2×C4×C11—24no—
188C2×C4×C11—48no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11#11714yes—
198C2×C4×C11C4×D412yes—
199C2×C4×C11C4×Q814yes—
200C2×C4×C11C22⋊Q812yes—
201C2×C4×C11#12312yes—
202C2×C4×C11#12514yes—
203C2×C4×C11#12614yes—
204C2×C4×C11C23×C411yescharacteristic
205C2×C4×C11C22×Q811yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×Dic11—28no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—24no—
218C2×Dic11—21no—
219C2×Dic11—21no—
220C2×Dic11—21no—
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—21no—
224C2×Dic11—44no—
225C2×Dic11—48no—
226C2×Dic11—42no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—42no—
232C2×Dic11AGL(1,ℤ/8)12yes—
233C2×Dic11#13712yes—
234C8×C11—24no—
235C11⋊C8—42no—
236C22×M16—111no—
237C22×M16C2×D1111yescharacteristic
238C2×#117—111no—
239C2×#117C2×D1111yescharacteristic
240C22×C4⋊C4—111no—
241C22×C4⋊C4C2×D1111yescharacteristic
242C22×C42—111no—
243C22×C42—221no—
244#428—118no—
245C2×#107—112no—
246C2×#106—112no—
247#389—111no—
248#389—111no—
249#389—111no—
250#389—111no—
251#385—221no—
252#385—221no—
253C4×C4⋊C4—112no—
254C4×C4⋊C4—112no—
255C4×C4⋊C4—221no—
256C4×C4⋊C4—221no—
257C4×C4⋊C4—221no—
258C4×C4⋊C4—221no—
259C2×#95—221no—
260#340—112no—
261#340—112no—
262#340—112no—
263#340—112no—
264#340C2×D1112yes—
265#340C2×D1112yes—
266#336—112no—
267#336—112no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11#38714yes—
275C22×C11C2×C4×D411yescharacteristic
276C22×C11C2×C22⋊Q811yescharacteristic
277C22×C11C2×#12311yescharacteristic
278C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C11C2×#13711yescharacteristic
280C22×C11#57511yescharacteristic
281C22×C11#57511yescharacteristic
282C4×C11—44no—
283C4×C11—81no—
284C4×C11—81no—
285C4×C11#38714yes—
286C4×C11C2×#11711yescharacteristic
287C4×C11C2×C4×Q811yescharacteristic
288C4×C11C2×#12511yescharacteristic
289C4×C11C2×#12611yescharacteristic
290Dic11—22no—
291Dic11—22no—
292Dic11—41no—
293Dic11—41no—
294Dic11—42no—
295Dic11—44no—
296Dic11—42no—
297C23×C4—21no—
298C23×C4—111no—
299C23×C4—111no—
300C23×C4—221no—
301C23×C4C22×D1111yescharacteristic
302C2×M16—22no—
303C2×M16—22no—
304C2×M16—222no—
305C2×M16—222no—
306C2×M16—222no—
307C2×M16C4×D1114yes—
308C22×C8—112no—
309C22×C8C22×D1112yes—
310#117—22no—
311#117—22no—
312#117—114no—
313#117—222no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—114no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—111no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4—222no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4Dic2214yes—
327C2×C4⋊C4C22×D1111yescharacteristic
328C2×C4⋊C4C22×D1111yescharacteristic
329C2×C4⋊C4C22×D1112yes—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—221no—
332C2×C42—21no—
333C2×C42—111no—
334C2×C42—111no—
335C2×C42—111no—
336C2×C42—111no—
337C2×C42—222no—
338C2×C42—221no—
339C2×C42—222no—
340C2×C42—222no—
341C2×C42—222no—
342C2×C42—444no—
343#107—118no—
344#106—118no—
345#95—222no—
346#95—222no—
347#95—221no—
348#95—221no—
349#95—221no—
350#95—221no—
351C2×C11—24no—
352C2×C11C2×#38711yescharacteristic
353C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
354C2×C11C4×#13711yescharacteristic
355C2×C11#307711yescharacteristic
356C2×C11#307811yescharacteristic
357C2×C11#309211yescharacteristic
358C2×C11#309311yescharacteristic
359C24D4×D1111yescharacteristic
360C22×C4—24no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—111no—
367C22×C4—111no—
368C22×C4—111no—
369C22×C4—111no—
370C22×C4—222no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—224no—
375C22×C4—222no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4—441no—
379C22×C4—441no—
380C22×C4—442no—
381C22×C4—442no—
382C22×C4C2×Dic2212yes—
383C22×C4C2×C4×D1112yes—
384C22×C4#433912yes—
385C22×C4D4×D1111yescharacteristic
386C22×C4#434112yes—
387C22×C4#434112yes—
388C22×C4#434312yes—
389C22×C4C23×D1111yescharacteristic
390M16—28no—
391M16—444no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—222no—
395C2×C8—222no—
396C2×C8—222no—
397C2×C8C2×C4×D1114yes—
398C4⋊C4—24no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—112no—
405C4⋊C4—114no—
406C4⋊C4—112no—
407C4⋊C4—224no—
408C4⋊C4—222no—
409C4⋊C4—221no—
410C4⋊C4—221no—
411C4⋊C4—442no—
412C4⋊C4—442no—
413C4⋊C4—442no—
414C4⋊C4—442no—
415C4⋊C4C2×Dic2214yes—
416C22⋊C4—42no—
417C22⋊C4—224no—
418C42—42no—
419C42—222no—
420C42—222no—
421C42—224no—
422C42—221no—
423C42—221no—
424C42—221no—
425C42—221no—
426C42—444no—
427C42—444no—
428C11#2103311yescharacteristic, complemented, Sylow
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23#6693112yes—
434C23#6693612yes—
435C23#6694612yes—
436C23C2×D4×D1111yescharacteristic
437C2×C4—24no—
438C2×C4—48no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—112no—
448C2×C4—112no—
449C2×C4—228no—
450C2×C4—221no—
451C2×C4—221no—
452C2×C4—221no—
453C2×C4—221no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—222no—
457C2×C4—222no—
458C2×C4—224no—
459C2×C4—221no—
460C2×C4—221no—
461C2×C4—221no—
462C2×C4—221no—
463C2×C4—444no—
464C2×C4—448no—
465C2×C4—442no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—442no—
471C2×C4C4×Dic2214yes—
472C2×C4#6693014yes—
473C2×C4#6693112yes—
474C2×C4#6693612yes—
475C2×C4#6694314yes—
476C2×C4#6694612yes—
477C2×C4#6695114yes—
478C2×C4C22×Dic2211yescharacteristic
479C2×C4C22×C4×D1111yescharacteristic
480C2×C4C2×#433911yescharacteristic
481C2×C4C2×#434111yescharacteristic
482C2×C4C2×#434111yescharacteristic
483C2×C4C2×#434311yescharacteristic
484C8—24no—
485C8—442no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22#1062226714yes—
493C22C2×#6693111yescharacteristic
494C22C2×#6693611yescharacteristic
495C22C2×#6694611yescharacteristic
496C22D11×AGL(1,ℤ/8)11yescharacteristic
497C22#1062330411yescharacteristic
498C22D11×#13711yescharacteristic
499C22#1062330811yescharacteristic
500C4—44no—
501C4—81no—
502C4—81no—
503C4—222no—
504C4—222no—
505C4—441no—
506C4—441no—
507C4—444no—
508C4—442no—
509C4—442no—
510C4#1062226714yes—
511C4C2×C4×Dic2211yescharacteristic
512C4C2×#6693011yescharacteristic
513C4C2×#6694311yescharacteristic
514C4C2×#6695111yescharacteristic
515C2—24no—
516C2C2×#1062226711yescharacteristic
517C2#1307742311yescharacteristic
518C2#1307743411yescharacteristic
519C2#1307841011yescharacteristic
520C2#1307841811yescharacteristic
521C2#1307853711yescharacteristic
522C2#1307854611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1736D11
hypocenterC11#21033
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. #13069207C2semidirect
5. #13069200C2semidirect
6. #13069193C2semidirect
7. #13069186C2semidirect
21. #10622734C4semidirect
96. #66882C2×C4semidirect
97. #66881C2×C4semidirect
428. C11#21033semidirect

Maximal subgroups

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

subgroupindex
C2×#106227342
#130710982
C2×C4⋊C4×Dic112
#130692072
#130692002
#130691932
#130691862
#130683372
#130683352
#130683092
C11×#17362
#2103311