Finite Group Databasebeta

← #14664226

Subgroups — #14664226

Order 2816.

778 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 778 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071930C211yesmaximal, characteristic
2D11×#342C211yesmaximal, characteristic, complemented
3#13066941C211yesmaximal, characteristic, complemented
4#13066638C211yesmaximal, characteristic, complemented
5#13066636C211yesmaximal, characteristic, complemented
6#13066613C211yesmaximal, characteristic, complemented
7C11×#1343C211yesmaximal, characteristic, complemented
8C22×#4341C411yescharacteristic, complemented
9C2×#66990—21no—
10C2×C22⋊C4×D11—21no—
11C2×C22⋊C4×D11C2211yescharacteristic
12C11×#392C2211yescharacteristic
13#10622836C411yescharacteristic, complemented
14#10622833—21no—
15#10622571—21no—
16#10622569—21no—
17#10622560C2211yescharacteristic
18#10622339—21no—
19#10622286C411yescharacteristic, complemented
20#10622277C411yescharacteristic, complemented
21C11×#342C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622165—21no—
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622106—21no—
27C24×D11D411yescharacteristic
28C22×D4×C11—21no—
29C22×D4×C11C2×C411yescharacteristic, complemented
30C22×C22⋊D11—21no—
31C22×C22⋊D11—21no—
32C23×Dic11—21no—
33C2×#4341—41no—
34C2×#4341—41no—
35C2×#4341—44no—
36C22×C4×D11—41no—
37C22×C4×D11C2×C411yescharacteristic
38C22×C4×D11D411yescharacteristic
39C22×Dic22C2×C411yescharacteristic, complemented
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4C2311yescharacteristic
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11D411yescharacteristic
47#66990—44no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—21no—
50C2×(C2×D11)⋊C4—41no—
51C2×(C2×D11)⋊C4C2×C411yescharacteristic
52C2×(C2×D11)⋊C4D411yescharacteristic
53C2×#4313—41no—
54C22⋊C4×D11—24no—
55C22⋊C4×D11—41no—
56C22⋊C4×D11—41no—
57C22⋊C4×D11—42no—
58C11×C22⋊C8—21no—
59C11×#95C2×C411yescharacteristic, complemented
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95C2×C411yescharacteristic, complemented
64C22⋊(C11⋊C8)—21no—
65(C2×D11)⋊C8—41no—
66#11753—111nomaximal, Sylow
67C24×C11—21no—
68C24×C11C2×D411yescharacteristic
69C23×D11—21no—
70C23×D11—21no—
71C23×D11—21no—
72C23×D11—21no—
73C23×D11—22no—
74C23×D11—42no—
75C23×D11—81no—
76C23×D11C22⋊C411yescharacteristic
77C23×D11C22⋊C411yescharacteristic
78C2×D4×C11—41no—
79C2×D4×C11—42no—
80C2×D4×C11—42no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—81no—
84C22×C4×C11—21no—
85C22×C4×C11—41no—
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C2×C22⋊D11—24no—
89C2×C22⋊D11—42no—
90C2×C22⋊D11—42no—
91C2×C22⋊D11—41no—
92C2×C22⋊D11—41no—
93C2×C22⋊D11—42no—
94C2×C22⋊D11—81no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—42no—
98C22×Dic11—41no—
99C22×Dic11—42no—
100C22×Dic11—42no—
101C22×Dic11C22⋊C411yescharacteristic
102C22×Dic11C22⋊C411yescharacteristic
103#4341—44no—
104#4341—44no—
105#4341—44no—
106#4341—44no—
107C2×C4×D11—21no—
108C2×C4×D11—21no—
109C2×C4×D11—21no—
110C2×C4×D11—21no—
111C2×C4×D11—42no—
112C2×C4×D11—44no—
113C2×C4×D11—81no—
114C2×C4×D11—82no—
115C2×C4×D11—82no—
116C2×Dic22—41no—
117C2×Dic22—42no—
118C2×C8×C11—41no—
119C11×C22⋊C4—22no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—81no—
123C22⋊Dic11—22no—
124C22⋊Dic11—41no—
125C22⋊Dic11—42no—
126C22⋊Dic11—41no—
127C22⋊Dic11—81no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—41no—
130(C2×D11)⋊C4—44no—
131(C2×D11)⋊C4—42no—
132(C2×D11)⋊C4—42no—
133C2×C11⋊C8—41no—
134#4313—82no—
135#2404—111no—
136C2×#342—111no—
137#1462—111no—
138#1351—111no—
139#1351—111no—
140#1343—111no—
141#1343D1111yescharacteristic, complemented
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—22no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11C2×C22⋊C411yescharacteristic
154C23×C11AGL(1,ℤ/8)11yescharacteristic
155C23×C11#13711yescharacteristic
156C22×D11—22no—
157C22×D11—22no—
158C22×D11—21no—
159C22×D11—21no—
160C22×D11—21no—
161C22×D11—22no—
162C22×D11—22no—
163C22×D11—21no—
164C22×D11—22no—
165C22×D11—41no—
166C22×D11—42no—
167C22×D11—42no—
168C22×D11—41no—
169C22×D11—41no—
170C22×D11—81no—
171C22×D11—81no—
172C22×D11—84no—
173C22×D11—82no—
174C22×D11—82no—
175C22×D11#9911yescharacteristic
176C22×D11#9911yescharacteristic
177C22×D11#10412yes—
178D4×C11—42no—
179D4×C11—42no—
180D4×C11—82no—
181D4×C11—82no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—81no—
191C2×C4×C11—81no—
192C22⋊D11—44no—
193C22⋊D11—44no—
194C22⋊D11—84no—
195C2×Dic11—22no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—41no—
199C2×Dic11—48no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—42no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—81no—
208C2×Dic11—81no—
209C4×D11—42no—
210C4×D11—42no—
211C4×D11—42no—
212C4×D11—81no—
213C4×D11—88no—
214Dic22—42no—
215Dic22—42no—
216C8×C11—81no—
217C11⋊C8—81no—
218C22×#41—111no—
219C2×#120—221no—
220C22×C22⋊C4—111no—
221C22×C22⋊C4—221no—
222#407—221no—
223#393—111no—
224#393—111no—
225#392—111no—
226#392C2×D1111yescharacteristic
227#386—221no—
228#386—221no—
229#386—221no—
230#381—111no—
231#342—111no—
232#342—221no—
233#342C2×D1111yescharacteristic
234#323—111no—
235#323—221no—
236#323C2×D1111yescharacteristic
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—41no—
242C22×C11—41no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—41no—
246C22×C11—41no—
247C22×C11—42no—
248C22×C11—81no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11—81no—
252C22×C11—81no—
253C22×C11C2×#9911yescharacteristic
254C22×C11#41711yescharacteristic
255C22×C11C2×#10411yescharacteristic
256C2×D11—21no—
257C2×D11—21no—
258C2×D11—21no—
259C2×D11—21no—
260C2×D11—21no—
261C2×D11—22no—
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—44no—
265C2×D11—44no—
266C2×D11—41no—
267C2×D11—41no—
268C2×D11—42no—
269C2×D11—81no—
270C2×D11—82no—
271C2×D11—82no—
272C2×D11AΣL(1,𝔽16)12yes—
273C4×C11—41no—
274C4×C11—41no—
275C4×C11—81no—
276C4×C11—82no—
277Dic11—42no—
278Dic11—41no—
279Dic11—41no—
280Dic11—81no—
281Dic11—82no—
282C25—111no—
283C2×#41—441no—
284C2×#41—441no—
285C2×#41—444no—
286C22×Q8—111no—
287C22×D4—21no—
288C22×D4—221no—
289C22×D4—221no—
290C22×D4C4×D1111yescharacteristic, complemented
291C23×C4—111no—
292C23×C4—111no—
293C23×C4—221no—
294C23×C4—441no—
295C2×M16—441no—
296#120—444no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—111no—
300C2×C22⋊C4—111no—
301C2×C22⋊C4—111no—
302C2×C22⋊C4—224no—
303C2×C22⋊C4—221no—
304C2×C22⋊C4—221no—
305C2×C22⋊C4—221no—
306C2×C22⋊C4—221no—
307C2×C22⋊C4—221no—
308C2×C22⋊C4—441no—
309C2×C22⋊C4—441no—
310C2×C22⋊C4—442no—
311C2×C22⋊C4—441no—
312C2×C22⋊C4C22×D1111yescharacteristic
313C22⋊C8—21no—
314C22⋊C8—221no—
315C22⋊C8—441no—
316#95—111no—
317#95—221no—
318#95—221no—
319#95—221no—
320#95C4×D1111yescharacteristic, complemented
321C2×C11—21no—
322C2×C11—21no—
323C2×C11—41no—
324C2×C11—41no—
325C2×C11—82no—
326C2×C11#150411yescharacteristic
327C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
328C2×C11#212711yescharacteristic
329D11—22no—
330D11—41no—
331D11—42no—
332C24—21no—
333C24—111no—
334C24—111no—
335C24—221no—
336C24—222no—
337C24—221no—
338C24—221no—
339C24—221no—
340C24—442no—
341C24—881no—
342C24D4×D1111yescharacteristic
343#41—444no—
344#41—444no—
345#41—444no—
346#41—444no—
347C2×Q8—441no—
348C2×Q8—442no—
349C2×D4—41no—
350C2×D4—42no—
351C2×D4—42no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—81no—
355C2×D4—224no—
356C2×D4—441no—
357C2×D4—441no—
358C2×D4—442no—
359C2×D4—442no—
360C2×D4—442no—
361C2×D4—881no—
362C22×C4—21no—
363C22×C4—41no—
364C22×C4—111no—
365C22×C4—111no—
366C22×C4—221no—
367C22×C4—221no—
368C22×C4—221no—
369C22×C4—221no—
370C22×C4—221no—
371C22×C4—221no—
372C22×C4—442no—
373C22×C4—444no—
374C22×C4—442no—
375C22×C4—442no—
376C22×C4—442no—
377C22×C4—441no—
378C22×C4—881no—
379C22×C4—882no—
380C22×C4—882no—
381C22×C4C2×C4×D1111yescharacteristic
382C22×C4D4×D1111yescharacteristic
383M16—882no—
384C2×C8—41no—
385C2×C8—441no—
386C22⋊C4—22no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—81no—
390C22⋊C4—222no—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C22⋊C4—442no—
394C22⋊C4—444no—
395C22⋊C4—442no—
396C22⋊C4—441no—
397C22⋊C4—442no—
398C22⋊C4—441no—
399C22⋊C4—881no—
400C11#1175311yescharacteristic, complemented, Sylow
401C23—21no—
402C23—21no—
403C23—22no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23—111no—
413C23—111no—
414C23—112no—
415C23—222no—
416C23—222no—
417C23—222no—
418C23—222no—
419C23—222no—
420C23—221no—
421C23—221no—
422C23—221no—
423C23—221no—
424C23—441no—
425C23—441no—
426C23—441no—
427C23—442no—
428C23—442no—
429C23—881no—
430C23—881no—
431C23—882no—
432C23—882no—
433C23—884no—
434C23C22⋊C4×D1111yescharacteristic
435C23#6696411yescharacteristic
436C23#6696811yescharacteristic
437Q8—442no—
438Q8—442no—
439D4—42no—
440D4—42no—
441D4—82no—
442D4—82no—
443D4—444no—
444D4—444no—
445D4—884no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—81no—
455C2×C4—81no—
456C2×C4—222no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—441no—
463C2×C4—448no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—442no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—881no—
472C2×C4—888no—
473C2×C4—881no—
474C2×C4—881no—
475C8—81no—
476C8—881no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—41no—
482C22—41no—
483C22—42no—
484C22—42no—
485C22—41no—
486C22—41no—
487C22—42no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22—81no—
493C22—112no—
494C22—221no—
495C22—221no—
496C22—221no—
497C22—222no—
498C22—221no—
499C22—221no—
500C22—442no—
501C22—442no—
502C22—442no—
503C22—444no—
504C22—444no—
505C22—441no—
506C22—441no—
507C22—881no—
508C22—882no—
509C22—882no—
510C22D11×#9911yescharacteristic
511C22#1062238411yescharacteristic
512C22D11×#10411yescharacteristic
513C4—41no—
514C4—41no—
515C4—81no—
516C4—82no—
517C4—441no—
518C4—442no—
519C4—441no—
520C4—881no—
521C4—882no—
522C2—21no—
523C2—21no—
524C2—41no—
525C2—41no—
526C2—82no—
527C2—222no—
528C2—441no—
529C2—442no—
530C2#1306711711yescharacteristic
531C2D11×AΣL(1,𝔽16)11yescharacteristic
532C2#1307028211yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1343C2
socleC22×C11C2×#99
prime radical#13071930C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1343D11
hypocenterC11#11753
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1343

Complements

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

NH ≅ G/Ntype
2. D11×#342C2semidirect
3. #13066941C2semidirect
4. #13066638C2semidirect
5. #13066636C2semidirect
6. #13066613C2semidirect
7. C11×#1343C2semidirect
8. C22×#4341C4semidirect
13. #10622836C4semidirect
19. #10622286C4semidirect
20. #10622277C4semidirect
29. C22×D4×C11C2×C4semidirect
39. C22×Dic22C2×C4semidirect
59. C11×#95C2×C4semidirect
63. C11⋊#95C2×C4semidirect
141. #1343D11semidirect
290. C22×D4C4×D11semidirect
320. #95C4×D11semidirect
400. C11#11753semidirect

Maximal subgroups

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

subgroupindex
#130719302
D11×#3422
#130669412
#130666382
#130666362
#130666132
C11×#13432
#1175311