Finite Group Databasebeta

← #14664228

Subgroups — #14664228

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#13071936C211yesmaximal, characteristic
2D11×#342C211yesmaximal, characteristic, complemented
3#13066941C211yesmaximal, characteristic, complemented
4#13066637C211yesmaximal, characteristic, complemented
5#13066614C211yesmaximal, characteristic, complemented
6#13066612C211yesmaximal, characteristic, complemented
7C11×#1351C211yesmaximal, characteristic, complemented
8C22×#4343C411yescharacteristic, complemented
9C2×#66935—21no—
10C2×C22⋊C4×D11—21no—
11C2×C22⋊C4×D11C2211yescharacteristic
12C11×#393C2211yescharacteristic
13#10622844C411yescharacteristic, complemented
14#10622573C2211yescharacteristic
15#10622569—21no—
16#10622339—21no—
17#10622284C411yescharacteristic, complemented
18#10622278—21no—
19#10622278—21no—
20#10622277C411yescharacteristic, complemented
21C11×#342C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622165—21no—
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622106—21no—
27C24×D11D411yescharacteristic
28C22×Q8×C11C2×C411yescharacteristic, complemented
29C22×C22⋊D11—21no—
30C2×#4343—41no—
31C2×#4343—41no—
32C2×#4343—44no—
33C22×D44—21no—
34C22×D44—21no—
35C22×D44C2×C411yescharacteristic, complemented
36C22×C4×D11—21no—
37C22×C4×D11—41no—
38C22×C4×D11C2×C411yescharacteristic
39C22×C4×D11D411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4C2311yescharacteristic
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11D411yescharacteristic
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—41no—
50C2×(C2×D11)⋊C4C2×C411yescharacteristic
51C2×(C2×D11)⋊C4D411yescharacteristic
52C2×#4313—41no—
53#66935—44no—
54C22⋊C4×D11—24no—
55C22⋊C4×D11—41no—
56C22⋊C4×D11—41no—
57C22⋊C4×D11—42no—
58C11×C22⋊C8—21no—
59C11×#95—21no—
60C11×#95C2×C411yescharacteristic, complemented
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95C2×C411yescharacteristic, complemented
64C22⋊(C11⋊C8)—21no—
65(C2×D11)⋊C8—41no—
66#11753—111nomaximal, Sylow
67C24×C11C2×D411yescharacteristic
68C23×D11—21no—
69C23×D11—21no—
70C23×D11—21no—
71C23×D11—21no—
72C23×D11—22no—
73C23×D11—21no—
74C23×D11—42no—
75C23×D11—81no—
76C23×D11C22⋊C411yescharacteristic
77C23×D11C22⋊C411yescharacteristic
78C2×Q8×C11—42no—
79C2×Q8×C11—41no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—41no—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C2×C22⋊D11—42no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C2×C22⋊D11—81no—
89C22×Dic11—21no—
90C22×Dic11—41no—
91C22×Dic11C22⋊C411yescharacteristic
92C22×Dic11C22⋊C411yescharacteristic
93#4343—44no—
94#4343—44no—
95#4343—44no—
96#4343—44no—
97C2×D44—24no—
98C2×D44—41no—
99C2×D44—42no—
100C2×D44—42no—
101C2×D44—42no—
102C2×D44—41no—
103C2×D44—41no—
104C2×D44—42no—
105C2×D44—81no—
106C2×C4×D11—21no—
107C2×C4×D11—21no—
108C2×C4×D11—21no—
109C2×C4×D11—21no—
110C2×C4×D11—42no—
111C2×C4×D11—42no—
112C2×C4×D11—42no—
113C2×C4×D11—44no—
114C2×C4×D11—42no—
115C2×C4×D11—81no—
116C2×C4×D11—82no—
117C2×C4×D11—82no—
118C2×C8×C11—41no—
119C11×C22⋊C4—22no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—42no—
122C11×C22⋊C4—41no—
123C22⋊Dic11—22no—
124C22⋊Dic11—41no—
125C22⋊Dic11—41no—
126(C2×D11)⋊C4—41no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—42no—
129(C2×D11)⋊C4—44no—
130(C2×D11)⋊C4—42no—
131(C2×D11)⋊C4—81no—
132(C2×D11)⋊C4—81no—
133C2×C11⋊C8—41no—
134#4313—82no—
135#2404—111no—
136C2×#342—111no—
137#1462—111no—
138#1351—111no—
139#1351D1111yescharacteristic, complemented
140#1343—111no—
141#1343—111no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11C2×C22⋊C411yescharacteristic
147C23×C11AGL(1,ℤ/8)11yescharacteristic
148C23×C11#13711yescharacteristic
149C22×D11—22no—
150C22×D11—22no—
151C22×D11—21no—
152C22×D11—21no—
153C22×D11—21no—
154C22×D11—22no—
155C22×D11—22no—
156C22×D11—21no—
157C22×D11—22no—
158C22×D11—22no—
159C22×D11—41no—
160C22×D11—42no—
161C22×D11—42no—
162C22×D11—41no—
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—41no—
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—
178Q8×C11—42no—
179Q8×C11—42no—
180C2×C4×C11—22no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—41no—
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—41no—
191C2×C4×C11—81no—
192C2×C4×C11—81no—
193C22⋊D11—82no—
194C22⋊D11—82no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—42no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—81no—
204C2×Dic11—81no—
205D44—44no—
206D44—42no—
207D44—42no—
208D44—44no—
209D44—84no—
210C4×D11—42no—
211C4×D11—42no—
212C4×D11—48no—
213C4×D11—42no—
214C4×D11—81no—
215C4×D11—88no—
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#393C2×D1111yescharacteristic
225#392—111no—
226#392—111no—
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—41no—
244C22×C11—41no—
245C22×C11—81no—
246C22×C11C2×#9911yescharacteristic
247C22×C11#41711yescharacteristic
248C22×C11C2×#10411yescharacteristic
249C2×D11—21no—
250C2×D11—21no—
251C2×D11—21no—
252C2×D11—21no—
253C2×D11—21no—
254C2×D11—22no—
255C2×D11—42no—
256C2×D11—42no—
257C2×D11—44no—
258C2×D11—44no—
259C2×D11—41no—
260C2×D11—41no—
261C2×D11—42no—
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—81no—
266C2×D11—82no—
267C2×D11—82no—
268C2×D11—81no—
269C2×D11—81no—
270C2×D11—81no—
271C2×D11—81no—
272C2×D11AΣL(1,𝔽16)12yes—
273C4×C11—42no—
274C4×C11—41no—
275C4×C11—41no—
276C4×C11—81no—
277C4×C11—82no—
278Dic11—41no—
279Dic11—41no—
280Dic11—81no—
281Dic11—82no—
282C25—111no—
283C2×#41—441no—
284C2×#41—441no—
285C2×#41—444no—
286C22×Q8C4×D1111yescharacteristic, complemented
287C22×D4—111no—
288C22×D4—221no—
289C22×D4—221no—
290C22×D4—221no—
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—21no—
317#95—111no—
318#95—221no—
319#95—221no—
320#95C4×D1111yescharacteristic, complemented
321C2×C11—21no—
322C2×C11—21no—
323C2×C11—41no—
324C2×C11—41no—
325C2×C11#150411yescharacteristic
326C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
327C2×C11#212711yescharacteristic
328D11—22no—
329D11—41no—
330D11—42no—
331D11—82no—
332C24—111no—
333C24—111no—
334C24—221no—
335C24—222no—
336C24—221no—
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—42no—
348C2×Q8—41no—
349C2×D4—224no—
350C2×D4—441no—
351C2×D4—441no—
352C2×D4—441no—
353C2×D4—442no—
354C2×D4—442no—
355C2×D4—442no—
356C2×D4—442no—
357C2×D4—442no—
358C2×D4—441no—
359C2×D4—441no—
360C2×D4—881no—
361C2×D4—881no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—41no—
365C22×C4—111no—
366C22×C4—111no—
367C22×C4—221no—
368C22×C4—221no—
369C22×C4—221no—
370C22×C4—221no—
371C22×C4—221no—
372C22×C4—442no—
373C22×C4—442no—
374C22×C4—442no—
375C22×C4—442no—
376C22×C4—444no—
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—42no—
389C22⋊C4—41no—
390C22⋊C4—222no—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C22⋊C4—442no—
394C22⋊C4—444no—
395C22⋊C4—442no—
396C22⋊C4—441no—
397C22⋊C4—441no—
398C22⋊C4—881no—
399C22⋊C4—881no—
400C11#1175311yescharacteristic, complemented, Sylow
401C23—21no—
402C23—21no—
403C23—41no—
404C23—41no—
405C23—111no—
406C23—111no—
407C23—112no—
408C23—222no—
409C23—222no—
410C23—222no—
411C23—222no—
412C23—222no—
413C23—222no—
414C23—221no—
415C23—221no—
416C23—221no—
417C23—221no—
418C23—441no—
419C23—441no—
420C23—441no—
421C23—441no—
422C23—441no—
423C23—441no—
424C23—442no—
425C23—442no—
426C23—441no—
427C23—441no—
428C23—441no—
429C23—881no—
430C23—881no—
431C23—882no—
432C23—882no—
433C23—884no—
434C23C22⋊C4×D1111yescharacteristic
435C23#6696711yescharacteristic
436C23#6697111yescharacteristic
437Q8—42no—
438Q8—42no—
439D4—444no—
440D4—444no—
441D4—442no—
442D4—442no—
443D4—884no—
444D4—882no—
445D4—882no—
446C2×C4—22no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—221no—
460C2×C4—221no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—448no—
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—41no—
484C22—41no—
485C22—81no—
486C22—112no—
487C22—221no—
488C22—221no—
489C22—221no—
490C22—222no—
491C22—221no—
492C22—221no—
493C22—442no—
494C22—442no—
495C22—442no—
496C22—442no—
497C22—442no—
498C22—444no—
499C22—444no—
500C22—441no—
501C22—441no—
502C22—442no—
503C22—881no—
504C22—881no—
505C22—881no—
506C22—882no—
507C22—882no—
508C22—881no—
509C22—881no—
510C22D11×#9911yescharacteristic
511C22#1062241611yescharacteristic
512C22D11×#10411yescharacteristic
513C4—42no—
514C4—41no—
515C4—41no—
516C4—81no—
517C4—82no—
518C4—441no—
519C4—441no—
520C4—881no—
521C4—882no—
522C2—21no—
523C2—21no—
524C2—41no—
525C2—41no—
526C2—222no—
527C2—441no—
528C2—442no—
529C2—882no—
530C2#1306711911yescharacteristic
531C2D11×AΣL(1,𝔽16)11yescharacteristic
532C2#1307028411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1351C2
socleC22×C11C2×#99
prime radical#13071936C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1351D11
hypocenterC11#11753
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1351

Complements

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

NH ≅ G/Ntype
2. D11×#342C2semidirect
3. #13066941C2semidirect
4. #13066637C2semidirect
5. #13066614C2semidirect
6. #13066612C2semidirect
7. C11×#1351C2semidirect
8. C22×#4343C4semidirect
13. #10622844C4semidirect
17. #10622284C4semidirect
20. #10622277C4semidirect
28. C22×Q8×C11C2×C4semidirect
35. C22×D44C2×C4semidirect
60. C11×#95C2×C4semidirect
63. C11⋊#95C2×C4semidirect
139. #1351D11semidirect
286. C22×Q8C4×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
#130719362
D11×#3422
#130669412
#130666372
#130666142
#130666122
C11×#13512
#1175311