Finite Group Databasebeta

← #14649557

Subgroups — #14649557

Order 2816.

648 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076948C211yesmaximal, characteristic
2C2×#10622264C211yesmaximal, characteristic, complemented
3#13068682C211yesmaximal, characteristic, complemented
4C2×#10622108C211yesmaximal, characteristic
5C2×#10622089C211yesmaximal, characteristic
6#13066494C211yesmaximal, characteristic, complemented
7C11×#1294C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C22×C4×Dic11C2211yescharacteristic
10C2×#66939—21no—
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13C2×C11×#95C2211yescharacteristic
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18#10622601C412yescomplemented
19#10622598C412yescomplemented
20#10622571—21no—
21#10622283—22no—
22#10622264—22no—
23#10622264—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—21no—
47C2×C4×Dic11—21no—
48C2×C4×Dic11—21no—
49C2×C4×Dic11—21no—
50C2×C4×Dic11C2×C412yes—
51C2×C4×Dic11D412yes—
52C22×C11⋊C8—21no—
53#66939—42no—
54#66939—42no—
55C11×C22⋊C8—21no—
56C11×C22⋊C8—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95D412yes—
60C11⋊#95—24no—
61C11⋊#95—24no—
62C11⋊#95—21no—
63C11⋊#95—22no—
64C11⋊#95D412yes—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67#9157—111nomaximal, Sylow
68C24×C11C2×D411yescharacteristic
69C23×D11—21no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—42no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C2×C22⋊D11—41no—
84C2×C22⋊D11—41no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C2×C22⋊D11—41no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—22no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—42no—
100C22×Dic11—42no—
101C22×Dic11—42no—
102C22×Dic11—41no—
103C22×Dic11—41no—
104C22×Dic11C22⋊C412yes—
105C22×Dic11C22⋊C412yes—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—42no—
109C2×C8×C11—42no—
110C2×C8×C11—41no—
111C11×C4⋊C4—42no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114(C2×D11)⋊C4—44no—
115(C2×D11)⋊C4—44no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—41no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—44no—
121C4×Dic11—22no—
122C4×Dic11—22no—
123C4×Dic11—22no—
124C4×Dic11—22no—
125C2×C11⋊C8—42no—
126C2×C11⋊C8—41no—
127#2854—111no—
128C2×#383—111no—
129#1817—111no—
130C2×#327—111no—
131C2×#327—111no—
132#1294—111no—
133#1294D1111yescharacteristic, complemented
134C23×C11—22no—
135C23×C11—22no—
136C23×C11C2×C22⋊C411yescharacteristic
137C23×C11#12011yescharacteristic
138C23×C11#12311yescharacteristic
139C23×C11#13511yescharacteristic
140C23×C11#13511yescharacteristic
141C23×C11AGL(1,ℤ/8)11yescharacteristic
142C23×C11AGL(1,ℤ/8)11yescharacteristic
143C22×D11—41no—
144C22×D11—42no—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11—42no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—82no—
161C2×C4×C11—82no—
162C2×C4×C11C4×D411yescharacteristic
163C2×C4×C11C4×D411yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C22⋊D11—81no—
167C22⋊D11—81no—
168C22⋊D11—81no—
169C22⋊D11—81no—
170C2×Dic11—22no—
171C2×Dic11—22no—
172C2×Dic11—22no—
173C2×Dic11—22no—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—42no—
188C2×Dic11—82no—
189C2×Dic11—82no—
190D44—81no—
191D44—81no—
192C8×C11—81no—
193C11⋊C8—81no—
194C2×#123—221no—
195C2×#121—111no—
196C22×C42—111no—
197C2×C22⋊C8—111no—
198C2×C22⋊C8C2×D1111yescharacteristic
199#390—112no—
200#389—112no—
201#388—222no—
202#386—221no—
203#383—222no—
204#383—222no—
205#380C2×D1111yescharacteristic
206C2×#95—111no—
207C2×#95—221no—
208C2×#95—221no—
209C2×#95C2×D1111yescharacteristic
210#336—222no—
211#327—222no—
212#327—222no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—22no—
218C22×C11—22no—
219C22×C11—22no—
220C22×C11—22no—
221C22×C11#38611yescharacteristic
222C22×C11#41012yes—
223C22×C11#41611yescharacteristic
224C22×C11#41811yescharacteristic
225C22×C11#42112yes—
226C22×C11#44911yescharacteristic
227C22×C11#44911yescharacteristic
228C22×C11#48211yescharacteristic
229C22×C11#48211yescharacteristic
230C2×D11—81no—
231C2×D11—81no—
232C2×D11—81no—
233C2×D11—82no—
234C2×D11—82no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—82no—
240C4×C11—82no—
241Dic11—42no—
242Dic11—42no—
243Dic11—82no—
244Dic11—81no—
245C22×D4—111no—
246C22×D4—221no—
247C23×C4—21no—
248C23×C4—111no—
249C23×C4—111no—
250C23×C4—221no—
251C23×C4C22×D1111yescharacteristic
252C22×C8—21no—
253C22×C8—221no—
254#123—442no—
255#123—442no—
256#121—221no—
257#121—221no—
258#121—221no—
259#121—221no—
260C2×C4⋊C4—111no—
261C2×C4⋊C4—222no—
262C2×C4⋊C4C4×D1112yes—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—222no—
265C2×C22⋊C4—222no—
266C2×C22⋊C4—221no—
267C2×C42—112no—
268C2×C42—112no—
269C2×C42—221no—
270C2×C42—221no—
271C2×C42—221no—
272C2×C42—221no—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C22⋊C8—221no—
276C22⋊C8—221no—
277#95—21no—
278#95—21no—
279#95—112no—
280#95—222no—
281#95—224no—
282#95—224no—
283#95—221no—
284#95D4412yes—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11—21no—
289C2×C11#151412yes—
290C2×C11#152112yes—
291C2×C11#187511yescharacteristic
292C2×C11#189711yescharacteristic
293C2×C11#189911yescharacteristic
294D11—161no—
295C24—221no—
296C24D4×D1111yescharacteristic
297C2×D4—221no—
298C2×D4—221no—
299C2×D4—442no—
300C2×D4—441no—
301C2×D4—441no—
302C2×D4—441no—
303C2×D4—441no—
304C2×D4—441no—
305C2×D4—441no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—112no—
314C22×C4—112no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4—221no—
324C22×C4—222no—
325C22×C4—442no—
326C22×C4—442no—
327C22×C4—442no—
328C22×C4—441no—
329C22×C4—441no—
330C22×C4C2×C4×D1111yescharacteristic
331C22×C4C2×D4411yescharacteristic
332C22×C4#433911yescharacteristic
333C22×C4D4×D1111yescharacteristic
334C22×C4D4×D1111yescharacteristic
335C22×C4#434311yescharacteristic
336C2×C8—42no—
337C2×C8—41no—
338C2×C8—442no—
339C2×C8—441no—
340C4⋊C4—42no—
341C4⋊C4—221no—
342C4⋊C4—221no—
343C4⋊C4—444no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—444no—
347C22⋊C4—444no—
348C22⋊C4—441no—
349C22⋊C4—441no—
350C42—222no—
351C42—222no—
352C42—222no—
353C42—222no—
354C11#915711yescharacteristic, complemented, Sylow
355C23—22no—
356C23—22no—
357C23—441no—
358C23—442no—
359C23—441no—
360C23—441no—
361C23—442no—
362C23C22⋊C4×D1111yescharacteristic
363C23#6693511yescharacteristic
364C23#6694711yescharacteristic
365C23#6696411yescharacteristic
366C23#6696711yescharacteristic
367C23#6696911yescharacteristic
368C23#6697211yescharacteristic
369D4—881no—
370D4—881no—
371D4—881no—
372D4—881no—
373D4—881no—
374D4—881no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4—222no—
392C2×C4—222no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—442no—
407C2×C4—882no—
408C2×C4—882no—
409C2×C4C4×D4411yescharacteristic
410C2×C4#6693711yescharacteristic
411C2×C4#6694611yescharacteristic
412C2×C4#6694811yescharacteristic
413C8—81no—
414C8—881no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—881no—
424C22—881no—
425C22—881no—
426C22—882no—
427C22—882no—
428C22#1062227811yescharacteristic
429C22#1062235312yes—
430C22#1062238311yescharacteristic
431C22#1062239411yescharacteristic
432C22#1062241711yescharacteristic
433C22#1062242411yescharacteristic
434C22#1062243412yes—
435C22#1062247911yescharacteristic
436C22#1062249811yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—82no—
442C4—82no—
443C4—442no—
444C4—442no—
445C4—882no—
446C4—881no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—21no—
451C2—1761no—
452C2#1306716112yes—
453C2#1306719212yes—
454C2#1306893711yescharacteristic
455C2#1306906311yescharacteristic
456C2#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#9157
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×#10622264C2semidirect
3. #13068682C2semidirect
6. #13066494C2semidirect
7. C11×#1294C2semidirect
18. #10622601C4semidirect
19. #10622598C4semidirect
133. #1294D11semidirect
354. C11#9157semidirect

Maximal subgroups

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

subgroupindex
#130769482
C2×#106222642
#130686822
C2×#106221082
C2×#106220892
#130664942
C11×#12942
#915711