Finite Group Databasebeta

← #14649363

Subgroups — #14649363

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076947C211yesmaximal, characteristic
2C2×#10622108C212yesmaximal
3#13066843C211yesmaximal, characteristic, complemented
4#13066496C212yesmaximal, complemented
5C2×C11×#432C211yesmaximal, characteristic, complemented
6C22×C42×C11C2211yescharacteristic
7C2×#66983C2211yescharacteristic
8C2×#66982—21no—
9C11×#432—24no—
10C2×C11×C4⋊C8—21no—
11C2×C11×C22⋊C8C2212yes—
12C2×C11×#97—21no—
13#10622826—21no—
14#10622825C2211yescharacteristic
15C2×C11⋊#95—21no—
16C2×C11⋊#95—21no—
17C2×C11⋊#95C2212yes—
18#10622553—21no—
19#10622553—21no—
20#10622552C411yescharacteristic, complemented
21#10622552C411yescharacteristic, complemented
22#10622541C411yescharacteristic, complemented
23#10622541C411yescharacteristic, complemented
24#10622108—24no—
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C22×C22⋊D11—21no—
29C23×Dic11—22no—
30C22×D44C2×C411yescharacteristic
31C22×C8×C11—22no—
32C2×C42×C11—22no—
33C2×C42×C11—22no—
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C22⋊Dic11—21no—
39#66983—22no—
40#66983—22no—
41#66982—44no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×C4⋊Dic11C2×C411yescharacteristic
48C2×C4⋊Dic11C2×C411yescharacteristic
49C2×C4⋊Dic11C2×C411yescharacteristic
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—21no—
52C11×C4⋊C8—24no—
53C11×C22⋊C8—22no—
54C11×C22⋊C8D414yes—
55C11×#97—24no—
56C11⋊#95—24no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—22no—
61C11⋊#95—22no—
62C11⋊#95—42no—
63#9118—111nomaximal, Sylow
64C24×C11C2×D411yescharacteristic
65C23×D11—21no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—21no—
69C22×C4×C11—22no—
70C22×C4×C11—21no—
71C22×C4×C11—22no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D412yes—
82C22×C4×C11#4112yes—
83C2×C22⋊D11—42no—
84C2×C22⋊D11—42no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—41no—
87C22×Dic11—24no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—42no—
92C22×Dic11—42no—
93C22×Dic11—42no—
94C22×Dic11—42no—
95C22×Dic11—42no—
96C22×Dic11—42no—
97C2×D44—22no—
98C2×D44—41no—
99C2×D44—41no—
100C2×C8×C11—24no—
101C2×C8×C11—42no—
102C2×C8×C11—42no—
103C42×C11—22no—
104C42×C11—22no—
105C42×C11—21no—
106C42×C11—21no—
107C42×C11—21no—
108C42×C11—21no—
109C22⋊Dic11—42no—
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—42no—
113(C2×D11)⋊C4—42no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—41no—
116C4⋊Dic11—22no—
117C4⋊Dic11—41no—
118C4⋊Dic11—41no—
119Dic11⋊C4—42no—
120Dic11⋊C4—42no—
121C2×#432D1111yescharacteristic, complemented
122#2854—111no—
123C2×#327—112no—
124#1434—111no—
125#1294—112no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11C2×C22⋊C411yescharacteristic
131C23×C11#12112yes—
132C23×C11AGL(1,ℤ/8)11yescharacteristic
133C23×C11AGL(1,ℤ/8)12yes—
134C23×C11#13711yescharacteristic
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—44no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11#10412yes—
163C2×C4×C11C4×D412yes—
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12311yescharacteristic
166C22⋊D11—82no—
167C22⋊D11—82no—
168C2×Dic11—44no—
169C2×Dic11—44no—
170C2×Dic11—44no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—82no—
181C2×Dic11—82no—
182C2×Dic11—82no—
183C2×Dic11—82no—
184D44—82no—
185C8×C11—44no—
186C2×#123—221no—
187C2×#121—111no—
188C22×C42C2×D1111yescharacteristic
189#432—24no—
190C2×C4⋊C8—21no—
191C2×C22⋊C8C2×D1112yes—
192C2×#97—21no—
193#390—111no—
194#390—111no—
195#389—111no—
196#389—111no—
197#388—221no—
198#388—221no—
199#386—221no—
200#380—111no—
201C2×#95—112no—
202C2×#95—221no—
203C2×#95—221no—
204#327—224no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—22no—
213C22×C11#38611yescharacteristic
214C22×C11#41011yescharacteristic
215C22×C11#41011yescharacteristic
216C22×C11#41711yescharacteristic
217C22×C11#41811yescharacteristic
218C22×C11C2×#10411yescharacteristic
219C22×C11#42111yescharacteristic
220C22×C11#46812yes—
221C22×C11#46912yes—
222C2×D11—81no—
223C2×D11—81no—
224C2×D11—81no—
225C2×D11—81no—
226C2×D11—81no—
227C2×D11—81no—
228C2×D11—81no—
229C4×C11—22no—
230C4×C11—22no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—41no—
234C4×C11—41no—
235C4×C11—41no—
236Dic11—84no—
237Dic11—81no—
238Dic11—81no—
239Dic11—81no—
240C22×D4—111no—
241C22×D4—221no—
242C23×C4—222no—
243C23×C4D4411yescharacteristic
244C23×C4D4411yescharacteristic
245C23×C4C22×D1111yescharacteristic
246C22×C8—22no—
247#123—444no—
248#121—222no—
249#121—222no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—111no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4—221no—
254C2×C4⋊C4—221no—
255C2×C22⋊C4—221no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C22⋊C4—221no—
261C2×C42—22no—
262C2×C42—22no—
263C2×C42C4×D1111yescharacteristic
264C2×C42C4×D1111yescharacteristic
265C2×C42C22⋊D1111yescharacteristic
266C2×C42C22⋊D1111yescharacteristic
267C4⋊C8—24no—
268C22⋊C8—22no—
269C22⋊C8C22⋊D1114yes—
270#97—24no—
271#95—224no—
272#95—221no—
273#95—221no—
274#95—221no—
275#95—222no—
276#95—222no—
277#95—442no—
278C2×C11—22no—
279C2×C11—22no—
280C2×C11#150511yescharacteristic
281C2×C11#150911yescharacteristic
282C2×C11#151211yescharacteristic
283C2×C11#151411yescharacteristic
284C2×C11#187111yescharacteristic
285C2×C11#189511yescharacteristic
286C2×C11#189911yescharacteristic
287D11—161no—
288C24—221no—
289C24C2×D4411yescharacteristic
290C2×D4—222no—
291C2×D4—441no—
292C2×D4—441no—
293C2×D4—442no—
294C2×D4—441no—
295C2×D4—441no—
296C2×D4—442no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—224no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—442no—
311C22×C4—442no—
312C22×C4—442no—
313C22×C4—442no—
314C22×C4—442no—
315C22×C4—442no—
316C22×C4(C2×D11)⋊C411yescharacteristic
317C22×C4(C2×D11)⋊C411yescharacteristic
318C22×C4(C2×D11)⋊C411yescharacteristic
319C22×C4(C2×D11)⋊C411yescharacteristic
320C22×C4C2×C4×D1111yescharacteristic
321C22×C4#433912yes—
322C22×C4C2×C22⋊D1111yescharacteristic
323C22×C4C2×C22⋊D1112yes—
324C2×C8—24no—
325C2×C8—42no—
326C2×C8—42no—
327C4⋊C4—222no—
328C4⋊C4—441no—
329C4⋊C4—441no—
330C4⋊C4—442no—
331C4⋊C4—442no—
332C22⋊C4—442no—
333C22⋊C4—442no—
334C22⋊C4—442no—
335C22⋊C4—442no—
336C22⋊C4—442no—
337C22⋊C4—441no—
338C22⋊C4—441no—
339C42—22no—
340C42—22no—
341C42—21no—
342C42—21no—
343C42—21no—
344C42—21no—
345C11#911811yescharacteristic, complemented, Sylow
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—441no—
351C23—441no—
352C23—441no—
353C23—441no—
354C23—441no—
355C23—441no—
356C23—441no—
357C23#6696112yes—
358C23#6696111yescharacteristic
359C23#6696211yescharacteristic
360C23C2×(C2×D11)⋊C411yescharacteristic
361C23#6698312yes—
362D4—882no—
363D4—882no—
364D4—882no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—44no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—444no—
386C2×C4—444no—
387C2×C4—444no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—882no—
398C2×C4—882no—
399C2×C4—882no—
400C2×C4—882no—
401C2×C4#6688912yes—
402C2×C4C4×C22⋊D1112yes—
403C2×C4#6698211yescharacteristic
404C2×C4#6700611yescharacteristic
405C8—44no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—22no—
414C22—881no—
415C22—881no—
416C22—881no—
417C22—881no—
418C22—881no—
419C22—881no—
420C22—881no—
421C22#1062261911yescharacteristic
422C22#1062261911yescharacteristic
423C22#1062274411yescharacteristic
424C22#1062274611yescharacteristic
425C22#1062274712yes—
426C22#1062274812yes—
427C22C2×#6688911yescharacteristic
428C22#1062275211yescharacteristic
429C22#1062282611yescharacteristic
430C4—21no—
431C4—22no—
432C4—21no—
433C4—22no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—884no—
438C4—881no—
439C4—881no—
440C4—881no—
441C2—22no—
442C2—22no—
443C2—1761no—
444C2#1306712511yescharacteristic
445C2#1306714211yescharacteristic
446C2#1306715511yescharacteristic
447C2#1306716411yescharacteristic
448C2#1306891811yescharacteristic
449C2#1306905411yescharacteristic
450C2#1306907411yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#432C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenterC2×#432D11
hypocenterC11#9118
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
3. #13066843C2semidirect
4. #13066496C2semidirect
5. C2×C11×#432C2semidirect
20. #10622552C4semidirect
21. #10622552C4semidirect
22. #10622541C4semidirect
23. #10622541C4semidirect
121. C2×#432D11semidirect
345. C11#9118semidirect

Maximal subgroups

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

subgroupindex
#130769472
C2×#106221082
#130668432
#130664962
C2×C11×#4322
#911811