Finite Group Databasebeta

← #14647243

Subgroups — #14647243

Order 2816.

656 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 87 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#13071102C211yesmaximal, characteristic
2#13068542C211yesmaximal, characteristic
3#13068533C211yesmaximal, characteristic
4#13066470C211yesmaximal, characteristic, complemented
5#13066469C211yesmaximal, characteristic, complemented
6#13066468C211yesmaximal, characteristic, complemented
7C11×#1284C211yesmaximal, characteristic, complemented
8C22×#4339C2211yescharacteristic
9C2×#66925C411yescharacteristic, complemented
10C2×C42×D11C411yescharacteristic, complemented
11C11×#407C2211yescharacteristic
12C11×#381C2211yescharacteristic
13C4×C11×C22⋊C4C2211yescharacteristic
14#10622824C2211yescharacteristic
15C4×C22⋊Dic11C2211yescharacteristic
16#10622820C2211yescharacteristic
17C2×#66888—21no—
18C2×#66887—21no—
19#10622570—21no—
20#10622569—21no—
21C2×#66870—21no—
22C2×#66870—21no—
23C4×(C2×D11)⋊C4C411yescharacteristic, complemented
24C4×(C2×D11)⋊C4C411yescharacteristic, complemented
25#10622278—21no—
26#10622259—21no—
27C23×C4×C11C2311yescharacteristic
28C22×C22⋊D11D411yescharacteristic
29C22×C22⋊D11D411yescharacteristic
30C2×#4339—21no—
31C2×#4339—21no—
32C2×#4339—21no—
33C2×#4339—21no—
34C2×#4339—42no—
35C2×#4339—42no—
36C22×D44D411yescharacteristic
37C22×C4×D11—21no—
38C22×C4×D11C2×C411yescharacteristic
39C22×C4×D11C2×C411yescharacteristic
40C22×Dic22D411yescharacteristic
41C2×C11×M16—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C42×C11C2×C411yescharacteristic
45C2×C42×C11C2×C411yescharacteristic
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—21no—
50C2×(C2×D11)⋊C4—21no—
51C2×Dic11⋊C4—21no—
52C2×C4×Dic11—21no—
53C2×C4×Dic11C2×C411yescharacteristic
54C2×C4×Dic11C2×C411yescharacteristic
55C2×#4318—21no—
56#66925—42no—
57C42×D11—42no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70#66888—42no—
71#66887—42no—
72#66870—42no—
73#66870—42no—
74#8738—111nomaximal, Sylow
75C24×C11C2×D411yescharacteristic
76C23×D11C22⋊C411yescharacteristic
77C23×D11C22⋊C411yescharacteristic
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C2×C22⋊D11—22no—
90C2×C22⋊D11—21no—
91C2×C22⋊D11—21no—
92C2×C22⋊D11—21no—
93C2×C22⋊D11—21no—
94C2×C22⋊D11—22no—
95C2×C22⋊D11—41no—
96C2×C22⋊D11—41no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—41no—
100C22×Dic11C22⋊C411yescharacteristic
101C22×Dic11C22⋊C411yescharacteristic
102#4339—44no—
103#4339—44no—
104#4339—44no—
105#4339—44no—
106C2×D44—22no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—41no—
110C2×C4×D11—22no—
111C2×C4×D11—22no—
112C2×C4×D11—21no—
113C2×C4×D11—21no—
114C2×C4×D11—21no—
115C2×C4×D11—21no—
116C2×C4×D11—41no—
117C2×C4×D11—41no—
118C2×C4×D11—42no—
119C2×C4×D11—42no—
120C2×C4×D11—42no—
121C2×Dic22—22no—
122C2×Dic22—21no—
123C2×Dic22—21no—
124C2×Dic22—41no—
125C11×M16—41no—
126C11×M16—41no—
127C2×C8×C11—41no—
128C11×C22⋊C4—42no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C42×C11—41no—
132C42×C11—41no—
133C22⋊Dic11—41no—
134C22⋊Dic11—41no—
135C22⋊Dic11—42no—
136(C2×D11)⋊C4—42no—
137(C2×D11)⋊C4—42no—
138(C2×D11)⋊C4—42no—
139Dic11⋊C4—42no—
140C4×Dic11—41no—
141C4×Dic11—41no—
142C4×Dic11—42no—
143#4318—41no—
144#4318—41no—
145C2×C11⋊C8—41no—
146#2297—111no—
147#1785—111no—
148#1782—111no—
149#1284—111no—
150#1284—111no—
151#1284—111no—
152#1284D1111yescharacteristic, complemented
153C23×C11—21no—
154C23×C11—21no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11C2×C22⋊C411yescharacteristic
158C23×C11#12311yescharacteristic
159C23×C11#12311yescharacteristic
160C22×D11—21no—
161C22×D11—21no—
162C22×D11—21no—
163C22×D11—21no—
164C22×D11—21no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—41no—
168C22×D11—41no—
169C22×D11#9912yes—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—22no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—81no—
185C2×C4×C11—81no—
186C2×C4×C11—81no—
187C2×C4×C11#11711yescharacteristic
188C2×C4×C11#11711yescharacteristic
189C2×C4×C11#12311yescharacteristic
190C2×C4×C11#12311yescharacteristic
191C22⋊D11—42no—
192C22⋊D11—42no—
193C22⋊D11—42no—
194C22⋊D11—42no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—22no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—81no—
207C2×Dic11—81no—
208C2×Dic11—81no—
209C2×Dic11#9912yes—
210D44—42no—
211D44—42no—
212C4×D11—24no—
213C4×D11—24no—
214C4×D11—42no—
215C4×D11—42no—
216C4×D11—48no—
217Dic22—42no—
218Dic22—42no—
219C8×C11—81no—
220C11⋊C8—81no—
221C22×#41—111no—
222C2×#117—111no—
223C22×C42—111no—
224C2×#101—221no—
225C2×#100—221no—
226C2×#99—221no—
227C2×#99—221no—
228#407—111no—
229#407C2×D1111yescharacteristic
230#391—221no—
231#390—221no—
232#386—221no—
233#386—221no—
234#381—111no—
235#381C2×D1111yescharacteristic
236C4×C22⋊C4—111no—
237C4×C22⋊C4—111no—
238C4×C22⋊C4—111no—
239C4×C22⋊C4C2×D1111yescharacteristic
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—81no—
249C22×C11—81no—
250C22×C11#38111yescharacteristic
251C22×C11C2×#9911yescharacteristic
252C22×C11C2×#9911yescharacteristic
253C2×D11—22no—
254C2×D11—42no—
255C2×D11—41no—
256C2×D11—41no—
257C2×D11—42no—
258C2×D11—41no—
259C2×D11—41no—
260C2×D11—41no—
261C2×D11—81no—
262C2×D11—81no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—42no—
268C4×C11—81no—
269C4×C11—161no—
270Dic11—22no—
271Dic11—42no—
272Dic11—41no—
273Dic11—81no—
274Dic11—161no—
275C2×#41—221no—
276C2×#41—221no—
277C2×#41—221no—
278C2×#41—221no—
279C2×#41—442no—
280C2×#41—442no—
281C22×Q8—111no—
282C22×D4—111no—
283C22×D4—111no—
284C22×D4—111no—
285C23×C4—111no—
286C23×C4—111no—
287C23×C4—221no—
288C23×C4C22×D1111yescharacteristic
289C2×M16—21no—
290C2×M16—221no—
291#117—442no—
292C2×C4⋊C4—221no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—221no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4—221no—
298C2×C22⋊C4—221no—
299C2×C22⋊C4—221no—
300C2×C42—111no—
301C2×C42—111no—
302C2×C42—221no—
303C2×C42—442no—
304C2×C42C4×D1111yescharacteristic
305C2×C42C4×D1111yescharacteristic
306#101—442no—
307#100—442no—
308#99—442no—
309#99—442no—
310C22⋊C8—21no—
311C22⋊C8—21no—
312C22⋊C8—221no—
313C22⋊C8—221no—
314#95—21no—
315#95—21no—
316#95—21no—
317#95—221no—
318#95—221no—
319#95—221no—
320#95—221no—
321#95—221no—
322C2×C11—21no—
323C2×C11—21no—
324C2×C11—41no—
325C2×C11—41no—
326C2×C11#181911yescharacteristic
327C2×C11#182711yescharacteristic
328C2×C11#182711yescharacteristic
329D11—42no—
330D11—81no—
331C24—111no—
332C24—111no—
333C24D4×D1111yescharacteristic
334#41—444no—
335#41—444no—
336#41—444no—
337#41—444no—
338C2×Q8—222no—
339C2×Q8—221no—
340C2×Q8—221no—
341C2×Q8—441no—
342C2×D4—222no—
343C2×D4—222no—
344C2×D4—222no—
345C2×D4—221no—
346C2×D4—221no—
347C2×D4—221no—
348C2×D4—221no—
349C2×D4—221no—
350C2×D4—221no—
351C2×D4—441no—
352C2×D4—441no—
353C2×D4—441no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—111no—
360C22×C4—111no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—221no—
364C22×C4—221no—
365C22×C4—221no—
366C22×C4—221no—
367C22×C4—221no—
368C22×C4—221no—
369C22×C4—441no—
370C22×C4—441no—
371C22×C4—442no—
372C22×C4—442no—
373C22×C4—442no—
374C22×C4—441no—
375C22×C4C2×C4×D1111yescharacteristic
376C22×C4#433911yescharacteristic
377C22×C4#433911yescharacteristic
378C22×C4D4×D1111yescharacteristic
379C22×C4#434111yescharacteristic
380C22×C4#434311yescharacteristic
381M16—41no—
382M16—41no—
383M16—441no—
384M16—441no—
385C2×C8—41no—
386C2×C8—441no—
387C4⋊C4—442no—
388C22⋊C4—42no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—442no—
392C22⋊C4—442no—
393C22⋊C4—442no—
394C22⋊C4—442no—
395C22⋊C4—441no—
396C22⋊C4—441no—
397C42—41no—
398C42—41no—
399C42—441no—
400C42—441no—
401C42—442no—
402C11#873811yescharacteristic, complemented, Sylow
403C23—21no—
404C23—21no—
405C23—41no—
406C23—41no—
407C23—112no—
408C23—221no—
409C23—221no—
410C23—221no—
411C23—221no—
412C23—221no—
413C23—441no—
414C23—441no—
415C23—441no—
416C23—441no—
417C23C22⋊C4×D1111yescharacteristic
418C23#6693611yescharacteristic
419C23#6694711yescharacteristic
420Q8—442no—
421Q8—442no—
422D4—442no—
423D4—442no—
424D4—442no—
425D4—442no—
426D4—442no—
427D4—442no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—112no—
446C2×C4—224no—
447C2×C4—224no—
448C2×C4—221no—
449C2×C4—221no—
450C2×C4—222no—
451C2×C4—221no—
452C2×C4—221no—
453C2×C4—221no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—448no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—881no—
463C2×C4—881no—
464C2×C4—881no—
465C2×C4#6692511yescharacteristic
466C2×C4#6693611yescharacteristic
467C2×C4#6694511yescharacteristic
468C2×C4#6694711yescharacteristic
469C8—81no—
470C8—881no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—81no—
480C22—81no—
481C22—222no—
482C22—442no—
483C22—442no—
484C22—441no—
485C22—441no—
486C22—441no—
487C22—441no—
488C22—441no—
489C22—881no—
490C22—881no—
491C22#1062227711yescharacteristic
492C22D11×#9911yescharacteristic
493C22D11×#9911yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—42no—
499C4—81no—
500C4—161no—
501C4—222no—
502C4—442no—
503C4—441no—
504C4—881no—
505C4—1761no—
506C2—21no—
507C2—21no—
508C2—41no—
509C2—41no—
510C2—442no—
511C2—881no—
512C2#1306868911yescharacteristic
513C2#1306871811yescharacteristic
514C2#1306871911yescharacteristic
subgroupG/H
centerC22#10622277
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1284C2
socleC22×C11#381
prime radicalC22×#4339C22
cosocleC23×C4×C11C23
hypercenter#1284D11
hypocenterC11#8738
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
4. #13066470C2semidirect
5. #13066469C2semidirect
6. #13066468C2semidirect
7. C11×#1284C2semidirect
9. C2×#66925C4semidirect
10. C2×C42×D11C4semidirect
23. C4×(C2×D11)⋊C4C4semidirect
24. C4×(C2×D11)⋊C4C4semidirect
152. #1284D11semidirect
402. C11#8738semidirect

Maximal subgroups

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

subgroupindex
#130711022
#130685422
#130685332
#130664702
#130664692
#130664682
C11×#12842
#873811