Finite Group Databasebeta

← #14649517

Subgroups — #14649517

Order 2816.

756 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076948C211yesmaximal, characteristic
2C2×#10622261C211yesmaximal, characteristic, complemented
3#13068682C211yesmaximal, characteristic, complemented
4C2×#10622108C211yesmaximal, characteristic
5C2×#10622089C211yesmaximal, characteristic
6#13066494C211yesmaximal, characteristic, complemented
7C11×#1294C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C22×C4×Dic11—21no—
10C22×C4×Dic11C2211yescharacteristic
11C2×#66939—21no—
12C2×C11×C22⋊C8C2211yescharacteristic
13C11×#380C2211yescharacteristic
14C2×C11×#95C2211yescharacteristic
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18#10622601C412yescomplemented
19#10622598C412yescomplemented
20#10622571—21no—
21#10622283—22no—
22#10622261—22no—
23#10622261—22no—
24#10622188—22no—
25#10622108—22no—
26#10622089—22no—
27C23×C4×C11—21no—
28C23×C4×C11C2311yescharacteristic
29C22×C22⋊D11—21no—
30C23×Dic11—21no—
31C23×Dic11D411yescharacteristic
32C23×Dic11D411yescharacteristic
33C22×D44C2×C411yescharacteristic
34C22×C8×C11—21no—
35C2×C11×C4⋊C4C2×C412yes—
36C2×C11×C22⋊C4—21no—
37#66983—21no—
38#66983—21no—
39#66983—21no—
40#66983—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—22no—
43C2×(C2×D11)⋊C4—22no—
44C2×C4⋊Dic11—22no—
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×C4×Dic11—24no—
47C2×C4×Dic11—28no—
48C2×C4×Dic11—21no—
49C2×C4×Dic11—21no—
50C2×C4×Dic11—21no—
51C2×C4×Dic11—21no—
52C2×C4×Dic11C2×C412yes—
53C2×C4×Dic11D412yes—
54C22×C11⋊C8—21no—
55#66939—42no—
56#66939—42no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95D412yes—
62C11⋊#95—24no—
63C11⋊#95—21no—
64C11⋊#95—22no—
65C11⋊#95D412yes—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68#9149—111nomaximal, Sylow
69C24×C11C2×D411yescharacteristic
70C23×D11—21no—
71C22×C4×C11—24no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—42no—
75C22×C4×C11—42no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C2×C22⋊D11—41no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C2×C22⋊D11—41no—
89C2×C22⋊D11—41no—
90C22×Dic11—24no—
91C22×Dic11—24no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—22no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—42no—
103C22×Dic11—41no—
104C22×Dic11—41no—
105C22×Dic11C22⋊C412yes—
106C22×Dic11C22⋊C412yes—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—42no—
110C2×C8×C11—42no—
111C2×C8×C11—41no—
112C11×C4⋊C4—42no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115(C2×D11)⋊C4—44no—
116(C2×D11)⋊C4—44no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11—44no—
122C4×Dic11—216no—
123C4×Dic11—22no—
124C4×Dic11—22no—
125C4×Dic11—22no—
126C4×Dic11—22no—
127C2×C11⋊C8—42no—
128C2×C11⋊C8—41no—
129#2854—111no—
130C2×#376—111no—
131#1817—111no—
132C2×#327—111no—
133C2×#327—111no—
134#1294—111no—
135#1294D1111yescharacteristic, complemented
136C23×C11—22no—
137C23×C11—22no—
138C23×C11C2×C22⋊C411yescharacteristic
139C23×C11#12011yescharacteristic
140C23×C11#12311yescharacteristic
141C23×C11#13511yescharacteristic
142C23×C11#13511yescharacteristic
143C23×C11AGL(1,ℤ/8)11yescharacteristic
144C23×C11AGL(1,ℤ/8)11yescharacteristic
145C22×D11—41no—
146C22×D11—42no—
147C22×D11—41no—
148C22×D11—41no—
149C22×D11—42no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—24no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—44no—
159C2×C4×C11—44no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11C4×D411yescharacteristic
165C2×C4×C11C4×D411yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C22⋊D11—81no—
169C22⋊D11—81no—
170C22⋊D11—81no—
171C22⋊D11—81no—
172C2×Dic11—24no—
173C2×Dic11—24no—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—24no—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—42no—
181C2×Dic11—44no—
182C2×Dic11—44no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—42no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11#10414yes—
192D44—81no—
193D44—81no—
194C8×C11—81no—
195C11⋊C8—81no—
196C2×#123—221no—
197C2×#121—111no—
198C22×C42—111no—
199C22×C42—221no—
200C2×C22⋊C8—111no—
201C2×C22⋊C8C2×D1111yescharacteristic
202#390—112no—
203#389—112no—
204#388—222no—
205#386—221no—
206#380C2×D1111yescharacteristic
207#376—222no—
208#376—222no—
209C2×#95—111no—
210C2×#95—221no—
211C2×#95C2×D1111yescharacteristic
212#336—222no—
213#327—222no—
214#327—222no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—22no—
220C22×C11—22no—
221C22×C11—22no—
222C22×C11—22no—
223C22×C11#38611yescharacteristic
224C22×C11#41012yes—
225C22×C11#41611yescharacteristic
226C22×C11#41811yescharacteristic
227C22×C11C2×#10412yes—
228C22×C11#44911yescharacteristic
229C22×C11#44911yescharacteristic
230C22×C11#48211yescharacteristic
231C22×C11#48211yescharacteristic
232C2×D11—81no—
233C2×D11—81no—
234C2×D11—81no—
235C2×D11—82no—
236C2×D11—82no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—44no—
242C4×C11—82no—
243Dic11—24no—
244Dic11—44no—
245Dic11—42no—
246Dic11—81no—
247C22×D4—111no—
248C22×D4—221no—
249C23×C4—21no—
250C23×C4—111no—
251C23×C4—111no—
252C23×C4—221no—
253C23×C4C22×D1111yescharacteristic
254C22×C8—21no—
255C22×C8—221no—
256#123—442no—
257#123—442no—
258#121—221no—
259#121—221no—
260#121—221no—
261#121—221no—
262C2×C4⋊C4—111no—
263C2×C4⋊C4—222no—
264C2×C4⋊C4C4×D1112yes—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—222no—
267C2×C22⋊C4—222no—
268C2×C22⋊C4—221no—
269C2×C42—112no—
270C2×C42—112no—
271C2×C42—224no—
272C2×C42—228no—
273C2×C42—221no—
274C2×C42—221no—
275C2×C42—221no—
276C2×C42—221no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C22⋊C8—221no—
280C22⋊C8—221no—
281#95—21no—
282#95—21no—
283#95—112no—
284#95—222no—
285#95—224no—
286#95—221no—
287#95D4412yes—
288C2×C11—21no—
289C2×C11—21no—
290C2×C11—21no—
291C2×C11—21no—
292C2×C11#150012yes—
293C2×C11#150512yes—
294C2×C11#187511yescharacteristic
295C2×C11#189611yescharacteristic
296C2×C11#189911yescharacteristic
297D11—161no—
298C24—221no—
299C24D4×D1111yescharacteristic
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—442no—
303C2×D4—441no—
304C2×D4—441no—
305C2×D4—441no—
306C2×D4—441no—
307C2×D4—441no—
308C2×D4—441no—
309C22×C4—24no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—112no—
317C22×C4—112no—
318C22×C4—224no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—224no—
322C22×C4—222no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4—221no—
327C22×C4—221no—
328C22×C4—221no—
329C22×C4—221no—
330C22×C4—442no—
331C22×C4—441no—
332C22×C4—441no—
333C22×C4C2×C4×D1111yescharacteristic
334C22×C4C2×D4411yescharacteristic
335C22×C4#433911yescharacteristic
336C22×C4D4×D1111yescharacteristic
337C22×C4D4×D1111yescharacteristic
338C22×C4#434311yescharacteristic
339C2×C8—42no—
340C2×C8—41no—
341C2×C8—442no—
342C2×C8—441no—
343C4⋊C4—42no—
344C4⋊C4—221no—
345C4⋊C4—221no—
346C4⋊C4—444no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—444no—
350C22⋊C4—444no—
351C22⋊C4—441no—
352C22⋊C4—441no—
353C42—2216no—
354C42—222no—
355C42—222no—
356C42—222no—
357C42—222no—
358C11#914911yescharacteristic, complemented, Sylow
359C23—22no—
360C23—22no—
361C23—441no—
362C23—442no—
363C23—441no—
364C23—441no—
365C23—442no—
366C23C22⋊C4×D1111yescharacteristic
367C23#6693511yescharacteristic
368C23#6694711yescharacteristic
369C23#6696411yescharacteristic
370C23#6696711yescharacteristic
371C23#6696911yescharacteristic
372C23#6697211yescharacteristic
373D4—881no—
374D4—881no—
375D4—881no—
376D4—881no—
377D4—881no—
378D4—881no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—24no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—114no—
394C2×C4—224no—
395C2×C4—224no—
396C2×C4—222no—
397C2×C4—222no—
398C2×C4—224no—
399C2×C4—222no—
400C2×C4—222no—
401C2×C4—222no—
402C2×C4—442no—
403C2×C4—444no—
404C2×C4—444no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4—442no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4C4×D4411yescharacteristic
414C2×C4#6693711yescharacteristic
415C2×C4#6694611yescharacteristic
416C2×C4#6694811yescharacteristic
417C8—81no—
418C8—881no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—881no—
428C22—881no—
429C22—882no—
430C22—882no—
431C22—881no—
432C22#1062227811yescharacteristic
433C22#1062235312yes—
434C22#1062238311yescharacteristic
435C22#1062239411yescharacteristic
436C22#1062241711yescharacteristic
437C22#1062242411yescharacteristic
438C22D11×#10412yes—
439C22#1062247911yescharacteristic
440C22#1062249811yescharacteristic
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—44no—
446C4—82no—
447C4—224no—
448C4—444no—
449C4—442no—
450C4—881no—
451C2—21no—
452C2—21no—
453C2—21no—
454C2—21no—
455C2—1761no—
456C2#1306710112yes—
457C2#1306712212yes—
458C2#1306893711yescharacteristic
459C2#1306905811yescharacteristic
460C2#1306907311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#9149
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
2. C2×#10622261C2semidirect
3. #13068682C2semidirect
6. #13066494C2semidirect
7. C11×#1294C2semidirect
18. #10622601C4semidirect
19. #10622598C4semidirect
135. #1294D11semidirect
358. C11#9149semidirect

Maximal subgroups

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

subgroupindex
#130769482
C2×#106222612
#130686822
C2×#106221082
C2×#106220892
#130664942
C11×#12942
#914911