Finite Group Databasebeta

← #14649510

Subgroups — #14649510

Order 2816.

800 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076942C211yesmaximal, characteristic
2C2×#10622262C211yesmaximal, characteristic, complemented
3#13068682C211yesmaximal, characteristic, complemented
4C2×#10622175C211yesmaximal, characteristic
5#13066496C211yesmaximal, characteristic, complemented
6#13066495C211yesmaximal, characteristic, complemented
7C2×C11×#327C211yesmaximal, characteristic
8C2×C11×#121C2211yescharacteristic
9C2×#66988—21no—
10C22×Dic11⋊C4—21no—
11C22×C4×Dic11—21no—
12C22×C4×Dic11C2211yescharacteristic
13C2×C11×C22⋊C8C2211yescharacteristic
14C2×C11×#95C2211yescharacteristic
15#10622834C412yescomplemented
16#10622833—21no—
17#10622825C2211yescharacteristic
18C2×C11⋊#95C2211yescharacteristic
19C2×C22⋊(C11⋊C8)C2211yescharacteristic
20#10622586C412yescomplemented
21#10622557—22no—
22#10622262—22no—
23#10622262—22no—
24C11×#327—22no—
25#10622188—22no—
26#10622175—22no—
27C22×D4×C11—21no—
28C22×D4×C11C2×C411yescharacteristic
29C23×C4×C11—21no—
30C23×C4×C11C2311yescharacteristic
31C23×Dic11—21no—
32C23×Dic11D411yescharacteristic
33C23×Dic11D411yescharacteristic
34C22×C8×C11—21no—
35C11×#121—21no—
36C11×#121—21no—
37C11×#121—21no—
38C11×#121—21no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—22no—
43C2×C22⋊Dic11—22no—
44#66988—42no—
45#66988—42no—
46C2×C4⋊Dic11C2×C412yes—
47C2×Dic11⋊C4—24no—
48C2×Dic11⋊C4—28no—
49C2×Dic11⋊C4—22no—
50C2×C4×Dic11—21no—
51C2×C4×Dic11—21no—
52C2×C4×Dic11—21no—
53C2×C4×Dic11—21no—
54C2×C4×Dic11—24no—
55C2×C4×Dic11—42no—
56C2×C4×Dic11—42no—
57C2×C4×Dic11C2×C412yes—
58C2×C4×Dic11D412yes—
59C22×C11⋊C8—21no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×#95—21no—
63C11×#95D412yes—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—22no—
67C11⋊#95D412yes—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70#9148—111nomaximal, Sylow
71C24×C11—21no—
72C24×C11C2×D411yescharacteristic
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—42no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C22×C4×C11—24no—
83C22×C4×C11—22no—
84C22×C4×C11—21no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×Dic11—24no—
96C22×Dic11—24no—
97C22×Dic11—22no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—22no—
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—42no—
106C22×Dic11—41no—
107C22×Dic11—41no—
108C22×Dic11C22⋊C412yes—
109C22×Dic11C22⋊C412yes—
110C22×Dic11D812yes—
111C22×Dic11SD1612yes—
112C2×C8×C11—42no—
113C2×C8×C11—41no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C22⋊Dic11—44no—
119C22⋊Dic11—44no—
120C22⋊Dic11—41no—
121C22⋊Dic11—41no—
122C4⋊Dic11—42no—
123Dic11⋊C4—216no—
124Dic11⋊C4—44no—
125C4×Dic11—22no—
126C4×Dic11—22no—
127C4×Dic11—22no—
128C4×Dic11—22no—
129C4×Dic11—48no—
130C2×C11⋊C8—42no—
131C2×C11⋊C8—41no—
132#2854—111no—
133C2×C4×C4⋊C4—111no—
134#1817—111no—
135C2×#327—111no—
136C2×#327D1111yescharacteristic
137#1294—111no—
138#1294—111no—
139C23×C11—22no—
140C23×C11—22no—
141C23×C11—41no—
142C23×C11—42no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11—42no—
146C23×C11C2×C22⋊C411yescharacteristic
147C23×C11#12011yescharacteristic
148C23×C11#12311yescharacteristic
149C23×C11C2×D811yescharacteristic
150C23×C11C2×SD1611yescharacteristic
151C23×C11AGL(1,ℤ/8)11yescharacteristic
152C23×C11#13711yescharacteristic
153D4×C11—81no—
154D4×C11—81no—
155D4×C11—81no—
156D4×C11—81no—
157D4×C11—81no—
158D4×C11—81no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—24no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—44no—
168C2×C4×C11—44no—
169C2×C4×C11—42no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11C4×D411yescharacteristic
174C2×C4×C11C4×D411yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×Dic11—24no—
178C2×Dic11—24no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—22no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—24no—
188C2×Dic11—42no—
189C2×Dic11—44no—
190C2×Dic11—44no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11#10214yes—
196C2×Dic11#10414yes—
197C8×C11—81no—
198C11⋊C8—81no—
199C2×#123—221no—
200C2×#121C2×D1111yescharacteristic
201C22×C4⋊C4—221no—
202C22×C42—111no—
203C22×C42—221no—
204C2×C22⋊C8—111no—
205C2×C22⋊C8C2×D1111yescharacteristic
206#390—112no—
207#389—112no—
208#388—222no—
209#386—221no—
210#380—111no—
211C4×C4⋊C4—222no—
212C4×C4⋊C4—222no—
213C2×#95—111no—
214C2×#95C2×D1111yescharacteristic
215#336—222no—
216#327—22no—
217#327—222no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—22no—
223C22×C11—22no—
224C22×C11—22no—
225C22×C11—22no—
226C22×C11—81no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11—82no—
230C22×C11—82no—
231C22×C11#38611yescharacteristic
232C22×C11#41012yes—
233C22×C11C2×#10211yescharacteristic
234C22×C11#41711yescharacteristic
235C22×C11C2×#10412yes—
236C22×C11#44711yescharacteristic
237C22×C11#44811yescharacteristic
238C22×C11#48011yescharacteristic
239C22×C11#48111yescharacteristic
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—44no—
245C4×C11—81no—
246Dic11—24no—
247Dic11—24no—
248Dic11—44no—
249Dic11—82no—
250C22×D4—21no—
251C22×D4C4×D1111yescharacteristic
252C23×C4—21no—
253C23×C4—111no—
254C23×C4—111no—
255C23×C4—221no—
256C23×C4C22×D1111yescharacteristic
257C22×C8—21no—
258C22×C8—221no—
259#123—442no—
260#123—442no—
261#121—21no—
262#121—21no—
263#121—21no—
264#121—21no—
265C2×C4⋊C4—112no—
266C2×C4⋊C4—224no—
267C2×C4⋊C4—228no—
268C2×C4⋊C4—222no—
269C2×C4⋊C4C4×D1111yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—222no—
272C2×C22⋊C4—222no—
273C2×C22⋊C4—221no—
274C2×C42—112no—
275C2×C42—112no—
276C2×C42—221no—
277C2×C42—221no—
278C2×C42—221no—
279C2×C42—221no—
280C2×C42—224no—
281C2×C42—442no—
282C2×C42—442no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—221no—
286C22⋊C8—221no—
287#95—21no—
288#95—112no—
289#95—222no—
290#95—221no—
291#95—221no—
292#95C22⋊D1112yes—
293C2×C11—21no—
294C2×C11—21no—
295C2×C11—21no—
296C2×C11—21no—
297C2×C11—161no—
298C2×C11#150212yes—
299C2×C11#150912yes—
300C2×C11#187411yescharacteristic
301C2×C11#189611yescharacteristic
302C2×C11#189911yescharacteristic
303C24—21no—
304C24D4×D1111yescharacteristic
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—42no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C22×C4—24no—
315C22×C4—22no—
316C22×C4—21no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—112no—
322C22×C4—112no—
323C22×C4—112no—
324C22×C4—112no—
325C22×C4—224no—
326C22×C4—221no—
327C22×C4—221no—
328C22×C4—221no—
329C22×C4—221no—
330C22×C4—221no—
331C22×C4—221no—
332C22×C4—224no—
333C22×C4—222no—
334C22×C4—222no—
335C22×C4—442no—
336C22×C4—441no—
337C22×C4—441no—
338C22×C4C2×C4×D1111yescharacteristic
339C22×C4#433911yescharacteristic
340C22×C4D4×D1111yescharacteristic
341C22×C4D4×D1111yescharacteristic
342C22×C4#434111yescharacteristic
343C22×C4C2×C22⋊D1111yescharacteristic
344C2×C8—42no—
345C2×C8—41no—
346C2×C8—442no—
347C2×C8—441no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—2216no—
351C4⋊C4—442no—
352C4⋊C4—444no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—444no—
356C22⋊C4—444no—
357C22⋊C4—441no—
358C22⋊C4—441no—
359C42—222no—
360C42—222no—
361C42—222no—
362C42—222no—
363C42—448no—
364C11#914811yescharacteristic, complemented, Sylow
365C23—22no—
366C23—22no—
367C23—41no—
368C23—42no—
369C23—41no—
370C23—41no—
371C23—42no—
372C23C22⋊C4×D1111yescharacteristic
373C23#6693611yescharacteristic
374C23D8×D1111yescharacteristic
375C23#6696411yescharacteristic
376C23SD16×D1111yescharacteristic
377C23#6696811yescharacteristic
378C23#6699011yescharacteristic
379D4—81no—
380D4—81no—
381D4—81no—
382D4—81no—
383D4—81no—
384D4—81no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—24no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—114no—
400C2×C4—114no—
401C2×C4—224no—
402C2×C4—224no—
403C2×C4—222no—
404C2×C4—222no—
405C2×C4—222no—
406C2×C4—222no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—222no—
410C2×C4—222no—
411C2×C4—224no—
412C2×C4—442no—
413C2×C4—444no—
414C2×C4—444no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4(C22⋊D11)⋊C411yescharacteristic
420C2×C4#6693711yescharacteristic
421C2×C4C4×C22⋊D1111yescharacteristic
422C2×C4#6699111yescharacteristic
423C8—81no—
424C8—881no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—81no—
434C22—81no—
435C22—82no—
436C22—82no—
437C22—81no—
438C22#1062235312yes—
439C22D11×#10211yescharacteristic
440C22#1062238411yescharacteristic
441C22#1062238711yescharacteristic
442C22#1062239011yescharacteristic
443C22D11×#10412yes—
444C22#1062256911yescharacteristic
445C22#1062276911yescharacteristic
446C22#1062278311yescharacteristic
447C4—21no—
448C4—21no—
449C4—21no—
450C4—21no—
451C4—44no—
452C4—81no—
453C4—224no—
454C4—224no—
455C4—444no—
456C4—882no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—161no—
462C2#1306710912yes—
463C2#1306713812yes—
464C2#1306893011yescharacteristic
465C2#1306905611yescharacteristic
466C2#1306907111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#327C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenterC2×#327D11
hypocenterC11#9148
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#10622262C2semidirect
3. #13068682C2semidirect
5. #13066496C2semidirect
6. #13066495C2semidirect
15. #10622834C4semidirect
20. #10622586C4semidirect
364. C11#9148semidirect

Maximal subgroups

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

subgroupindex
#130769422
C2×#106222622
#130686822
C2×#106221752
#130664962
#130664952
C2×C11×#3272
#914811