Finite Group Databasebeta

← #14853517

Subgroups — #14853517

Order 2816.

742 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66928C211yesmaximal, characteristic
2#13070184C212yesmaximal, complemented
3#13069857C212yesmaximal
4#13069312C212yesmaximal
5#13069305C212yesmaximal, complemented
6#13068618C211yesmaximal, characteristic, complemented
7#13068618C211yesmaximal, characteristic, complemented
8#13068613C211yesmaximal, characteristic
9#13068613C211yesmaximal, characteristic
10#13068469C211yesmaximal, characteristic, complemented
11C11×#2859C211yesmaximal, characteristic, complemented
12C2×C11×#125—21no—
13C2×#66928C2211yescharacteristic
14C2×C4×D44C2211yescharacteristic
15C2×C4×Dic22C2211yescharacteristic
16C11×#389—21no—
17C11×#389—21no—
18C11×#389C2212yes—
19C11×#389C2212yes—
20C11×#384C2211yescharacteristic
21C11×#384C2211yescharacteristic
22C11×#382—21no—
23C43×C11C2211yescharacteristic
24C2×#66874C2212yes—
25C2×#66874C2212yes—
26C2×#66873C2212yes—
27C2×#66873C2212yes—
28#10622553—21no—
29#10622553—21no—
30#10622552C2211yescharacteristic
31C4×(C2×D11)⋊C4—21no—
32C4×(C2×D11)⋊C4—21no—
33#10622549C2211yescharacteristic
34#10622542C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×#66867C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2212yes—
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C22×Dic22C2311yescharacteristic
46C11×#125—44no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2312yes—
55C2×C42×C11D411yescharacteristic
56C2×C42×C11D411yescharacteristic
57C2×C42×C11D411yescharacteristic
58C2×C42×C11D411yescharacteristic
59C2×C42×C11C2311yescharacteristic
60C2×C42×C11C2311yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C2×(C2×D11)⋊C4—21no—
63C2×(C2×D11)⋊C4—21no—
64C2×(C2×D11)⋊C4—21no—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—21no—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×Dic11⋊C4—21no—
70C2×C4×Dic11—21no—
71C22×C11⋊C8C2312yes—
72C22×C11⋊C8C2312yes—
73#66928—22no—
74#66928—22no—
75C4×D44—22no—
76C4×D44—22no—
77C4×Dic22—22no—
78C4×Dic22—22no—
79C11×#95—22no—
80C11×#95—22no—
81C11⋊#95—21no—
82C11⋊#95—21no—
83C11⋊#95—21no—
84C11⋊#95—21no—
85#66874—24no—
86#66874—42no—
87#66873—24no—
88#66873—42no—
89C4⋊(C11⋊C8)—22no—
90C4⋊(C11⋊C8)—22no—
91#66867—42no—
92#29131—111nomaximal, Sylow
93C23×D11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44#4112yes—
112C2×C4×D11—42no—
113C2×C4×D11—42no—
114C2×C4×D11—42no—
115C2×Dic22—21no—
116C2×Dic22—21no—
117C2×Dic22—21no—
118C2×Dic22—21no—
119C2×Dic22—21no—
120C2×Dic22#4112yes—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—42no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4—44no—
128C11×C4⋊C4—44no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4—42no—
131C42×C11—22no—
132C42×C11—22no—
133C42×C11—21no—
134C42×C11—21no—
135C42×C11—21no—
136C42×C11—21no—
137C42×C11—41no—
138C42×C11—41no—
139C42×C11#4112yes—
140C42×C11#4112yes—
141(C2×D11)⋊C4—24no—
142(C2×D11)⋊C4—24no—
143(C2×D11)⋊C4—42no—
144(C2×D11)⋊C4—42no—
145(C2×D11)⋊C4—42no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150Dic11⋊C4—42no—
151C4×Dic11—42no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158#2859D1111yescharacteristic, complemented
159C4×#124—111no—
160#2101—112no—
161#2042—112no—
162#1936—112no—
163#1935—112no—
164#1803—111no—
165#1803—111no—
166#1802—111no—
167#1802—111no—
168#1767—111no—
169C23×C11C22×D411yescharacteristic
170C22×D11—22no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—41no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11#12412yes—
198C2×C4×C11#12412yes—
199C2×C4×C11AGL(1,ℤ/8)12yes—
200C2×C4×C11#13712yes—
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11H(5,𝔽2)11yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C2×Dic11—22no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216D44—22no—
217D44—22no—
218D44—41no—
219D44—41no—
220C4×D11—84no—
221Dic22—22no—
222Dic22—22no—
223Dic22—41no—
224Dic22—41no—
225C11⋊C8—42no—
226C11⋊C8—42no—
227C2×#125—21no—
228C2×#124—111no—
229C2×C4×Q8—111no—
230C2×C4×D4—111no—
231C2×C4⋊C8—111no—
232C2×C4⋊C8—111no—
233C2×#103—112no—
234C2×#103—112no—
235C2×#102—112no—
236C2×#102—112no—
237C2×#97—112no—
238#391—111no—
239#390—111no—
240#389—21no—
241#389—21no—
242#389C2×D1112yes—
243#389C2×D1112yes—
244#388—221no—
245#388—221no—
246#384C2×D1111yescharacteristic
247#384C2×D1111yescharacteristic
248#382—21no—
249#382—111no—
250C4×C22⋊C4—221no—
251C4×C22⋊C4—221no—
252C43C2×D1111yescharacteristic
253#340—112no—
254#340—112no—
255#340—112no—
256#340—112no—
257#336—112no—
258C22×C11#52511yescharacteristic
259C22×C11C2×#12411yescharacteristic
260C22×C11#53711yescharacteristic
261C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
262C22×C11C2×#13711yescharacteristic
263C22×C11#57511yescharacteristic
264C22×C11#57511yescharacteristic
265C2×D11—42no—
266C2×D11—42no—
267C2×D11—42no—
268C2×D11—81no—
269C2×D11—81no—
270C2×D11—81no—
271C2×D11—81no—
272C4×C11—22no—
273C4×C11—41no—
274C4×C11—41no—
275C4×C11—41no—
276C4×C11—41no—
277C4×C11—82no—
278C4×C11—82no—
279C4×C11#48914yes—
280C4×C11#55211yescharacteristic
281C4×C11#55211yescharacteristic
282C4×C11#55311yescharacteristic
283C4×C11#55311yescharacteristic
284Dic11—42no—
285Dic11—81no—
286Dic11—81no—
287C22×Q8—111no—
288C22×D4—111no—
289C23×C4—221no—
290C22×C8—112no—
291C22×C8—112no—
292#125—44no—
293#124—222no—
294#124—222no—
295C4×Q8—222no—
296C4×Q8—222no—
297C4×D4—222no—
298C4×D4—222no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—111no—
306C2×C4⋊C4—111no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4C22×D1112yes—
309C2×C4⋊C4C22×D1112yes—
310C2×C22⋊C4—221no—
311C2×C22⋊C4—221no—
312C2×C22⋊C4—221no—
313C2×C22⋊C4—221no—
314C2×C22⋊C4—221no—
315C2×C42—221no—
316C2×C42C22⋊D1111yescharacteristic
317C2×C42C22⋊D1111yescharacteristic
318C2×C42C22⋊D1111yescharacteristic
319C2×C42C22⋊D1111yescharacteristic
320C2×C42C22×D1111yescharacteristic
321C2×C42C22×D1111yescharacteristic
322C2×C42C22×D1111yescharacteristic
323C4⋊C8—222no—
324C4⋊C8—222no—
325#103—224no—
326#103—442no—
327#102—224no—
328#102—442no—
329#97—442no—
330#95—22no—
331#95—22no—
332#95—221no—
333#95—221no—
334#95—221no—
335#95—221no—
336C2×C11#256211yescharacteristic
337C2×C11#311511yescharacteristic
338C2×C11#311611yescharacteristic
339C2×C11C2×#48911yescharacteristic
340C2×C11#314211yescharacteristic
341C2×C11#325111yescharacteristic
342C2×C11#325211yescharacteristic
343D11—82no—
344C24—221no—
345C2×Q8—112no—
346C2×Q8—221no—
347C2×Q8—221no—
348C2×Q8—221no—
349C2×Q8—221no—
350C2×Q8—221no—
351C2×D4—112no—
352C2×D4—221no—
353C2×D4—221no—
354C2×D4—221no—
355C2×D4—221no—
356C2×D4—221no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—221no—
360C22×C4—221no—
361C22×C4—221no—
362C22×C4—442no—
363C22×C4—442no—
364C22×C4—442no—
365C22×C4C2×C22⋊D1111yescharacteristic
366C22×C4C2×C22⋊D1111yescharacteristic
367C22×C4C2×C22⋊D1111yescharacteristic
368C22×C4C2×C22⋊D1111yescharacteristic
369C22×C4C2×C22⋊D1111yescharacteristic
370C22×C4C2×C22⋊D1111yescharacteristic
371C22×C4C23×D1111yescharacteristic
372C2×C8—222no—
373C2×C8—222no—
374C2×C8—222no—
375C2×C8—222no—
376C2×C8—222no—
377C2×C8—222no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—44no—
383C4⋊C4—44no—
384C4⋊C4—42no—
385C4⋊C4—42no—
386C4⋊C4—42no—
387C4⋊C4—42no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4—442no—
393C22⋊C4—224no—
394C22⋊C4—224no—
395C22⋊C4—442no—
396C22⋊C4—442no—
397C22⋊C4—442no—
398C42—22no—
399C42—22no—
400C42—21no—
401C42—21no—
402C42—21no—
403C42—21no—
404C42—41no—
405C42—41no—
406C42—442no—
407C42#434312yes—
408C42#434312yes—
409C11#2913111yescharacteristic, complemented, Sylow
410C23—222no—
411C23—441no—
412C23—441no—
413C23—441no—
414C23—441no—
415C23—441no—
416C23—441no—
417C23C22×C22⋊D1111yescharacteristic
418Q8—222no—
419Q8—222no—
420Q8—441no—
421Q8—441no—
422D4—222no—
423D4—222no—
424D4—441no—
425D4—441no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—222no—
447C2×C4—441no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—884no—
456C2×C4#6698512yes—
457C2×C4#6699512yes—
458C2×C4#6700012yes—
459C2×C4#6700012yes—
460C2×C4C2×#434311yescharacteristic
461C2×C4C2×#434311yescharacteristic
462C2×C4#41×D1111yescharacteristic
463C2×C4#41×D1111yescharacteristic
464C2×C4#6704211yescharacteristic
465C2×C4#6704311yescharacteristic
466C8—442no—
467C8—442no—
468C22—442no—
469C22—442no—
470C22—442no—
471C22—881no—
472C22—881no—
473C22—881no—
474C22—881no—
475C22C2×#6698511yescharacteristic
476C22C2×#6699511yescharacteristic
477C22C2×#6700011yescharacteristic
478C22#1062335311yescharacteristic
479C22#1062335311yescharacteristic
480C22#1062335911yescharacteristic
481C22#1062336411yescharacteristic
482C4—22no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—82no—
488C4—82no—
489C4—442no—
490C4—881no—
491C4—881no—
492C4#1062270214yes—
493C4#1062322511yescharacteristic
494C4#1062322511yescharacteristic
495C4#1062322611yescharacteristic
496C4#1062322611yescharacteristic
497C2—882no—
498C2#1307378311yescharacteristic
499C2#1307876111yescharacteristic
500C2#1307877211yescharacteristic
501C2C2×#1062270211yescharacteristic
502C2#1307901911yescharacteristic
503C2#1307997211yescharacteristic
504C2#1307998311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2859C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2859D11
hypocenterC11#29131
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #2859

Complements

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

NH ≅ G/Ntype
2. #13070184C2semidirect
5. #13069305C2semidirect
6. #13068618C2semidirect
7. #13068618C2semidirect
10. #13068469C2semidirect
11. C11×#2859C2semidirect
158. #2859D11semidirect
409. C11#29131semidirect

Maximal subgroups

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

subgroupindex
C4×#669282
#130701842
#130698572
#130693122
#130693052
#130686182
#130686132
#130684692
C11×#28592
#2913111