Finite Group Databasebeta

← #14760507

Subgroups — #14760507

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622772C211yesmaximal, characteristic
2C2×#10622321C211yesmaximal, characteristic, complemented
3#13071303C212yesmaximal, complemented
4#13069483C211yesmaximal, characteristic, complemented
5#13069342C211yesmaximal, characteristic, complemented
6#13069310C212yesmaximal, complemented
7#13069041C212yesmaximal, complemented
8#13068646C211yesmaximal, characteristic, complemented
9#13068513C211yesmaximal, characteristic, complemented
10C4×#66896C212yesmaximal, complemented
11C2×C11×#442C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C2×C4×D4×C11C2212yes—
14C2×#66991C2212yes—
15C22×#4313C2211yescharacteristic
16C22×C8×D11C2211yescharacteristic
17C2×#66925C2211yescharacteristic
18C11×#442—24no—
19C2×C11×#106C2211yescharacteristic
20C2×C11×#102C2212yes—
21C2×C11×#97C2211yescharacteristic
22#10622834C2212yes—
23C2×#66896C2212yes—
24C2×#66896C2212yes—
25#10622826—22no—
26#10622823—22no—
27#10622772C418yescomplemented
28C2×#66882C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622600C2212yes—
33#10622586C2212yes—
34#10622570—22no—
35#10622558—22no—
36C4×C4⋊Dic11C2212yes—
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622321—24no—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×D4×C11C2312yes—
43C23×C4×C11—22no—
44C22×C22⋊D11—22no—
45C22×C4×D11C2311yescharacteristic
46C2×C11×D8—22no—
47C2×C11×D8—22no—
48C2×C11×D8C2×C414yes—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C4×D4×C11—24no—
52C4×D4×C11—24no—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C22⋊C4—22no—
55C2×C42×C11C2311yescharacteristic
56C2×C22⋊Dic11—22no—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59#66991—24no—
60#66991C2×C418yescomplemented
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4D412yes—
63C2×C4⋊Dic11C2312yes—
64C2×C4⋊Dic11C2312yes—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4D412yes—
67C2×C4×Dic11—22no—
68C2×C4×Dic11C2311yescharacteristic
69C22×C11⋊C8C2311yescharacteristic
70C22×C11⋊C8C2311yescharacteristic
71C2×#4313—22no—
72C2×#4313—22no—
73C2×#4313C2×C414yescomplemented
74C2×C8×D11—22no—
75C2×C8×D11—22no—
76C2×C8×D11—22no—
77#66925—22no—
78#66925—22no—
79C11×#106—22no—
80C11×#102—24no—
81C11×#97D414yescomplemented
82#66896—24no—
83#66896C2×C418yescomplemented
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87#66882—22no—
88#66881C2×C414yescomplemented
89#66879—22no—
90C8×Dic11—22no—
91C4×C11⋊C8—22no—
92#21541—111nomaximal, Sylow
93C24×C11—22no—
94C23×D11C2×D411yescharacteristic
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11C22×C414yes—
101C22×C4×C11—22no—
102C22×C4×C11—44no—
103C22×C4×C11—82no—
104C22×C4×C11—82no—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2411yescharacteristic
107C2×C22⋊D11—28no—
108C2×C22⋊D11—82no—
109C2×C22⋊D11—82no—
110C22×Dic11—22no—
111C22×Dic11—22no—
112C22×Dic11C2×D412yes—
113C22×Dic11C2×D411yescharacteristic
114C2×C4×D11—21no—
115C2×C4×D11—21no—
116C2×C4×D11—21no—
117C2×C4×D11—21no—
118C2×C4×D11C22×C412yes—
119C2×C4×D11#4112yes—
120C11×D8—28no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11C22×C412yes—
124C2×C8×C11C2×D412yes—
125C2×C8×C11C2×D412yes—
126C2×C8×C11#4112yes—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C22⋊C4—44no—
130C42×C11C2×D412yes—
131C42×C11#4112yes—
132C22⋊Dic11—28no—
133C22⋊Dic11—82no—
134C22⋊Dic11—82no—
135(C2×D11)⋊C4—24no—
136(C2×D11)⋊C4—82no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139C4⋊Dic11—22no—
140C4⋊Dic11C22×C414yes—
141Dic11⋊C4—24no—
142Dic11⋊C4—82no—
143C4×Dic11—21no—
144C4×Dic11—21no—
145C4×Dic11—82no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8C22×C412yes—
151C2×C11⋊C8#4112yes—
152#4313—28no—
153C8×D11—28no—
154C2×#469—111no—
155C2×#442D1111yescharacteristic, complemented
156C2×#405—111no—
157#2324—112no—
158#1970—111no—
159#1941—111no—
160#1936—112no—
161#1893—112no—
162#1809—111no—
163#1776—111no—
164C4×#102—112no—
165C23×C11—24no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11C22×D411yescharacteristic
173C22×D11—21no—
174C22×D11—21no—
175C22×D11—22no—
176C22×D11—22no—
177C22×D11C4×D412yes—
178D4×C11—24no—
179D4×C11—24no—
180D4×C11—42no—
181D4×C11—42no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—88no—
188C2×C4×C11#12114yes—
189C2×C4×C11C23×C411yescharacteristic
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C22⋊D11—88no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—24no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11C4×D412yes—
208C4×D11—22no—
209C4×D11—22no—
210C4×D11—22no—
211C4×D11—22no—
212C8×C11—22no—
213C8×C11C4×D414yes—
214C11⋊C8—22no—
215C11⋊C8—22no—
216C22×D8C2×D1111yescharacteristic
217C22×M16—111no—
218C23×C8—111no—
219C2×#121—112no—
220C2×C4×D4C2×D1112yes—
221C2×#117—111no—
222#469—118no—
223#442—24no—
224C2×#107—111no—
225C2×#106—111no—
226C2×#106C2×D1111yescharacteristic
227C2×#102—112no—
228C2×#102—112no—
229C2×#102C2×D1112yes—
230#405—224no—
231C2×#97—111no—
232C2×#97C2×D1111yescharacteristic
233C2×C4×C8—111no—
234C2×C4×C8—111no—
235#390—112no—
236#390—222no—
237#389—112no—
238#388—222no—
239#386—222no—
240#385—222no—
241#380—112no—
242C4×C4⋊C4—112no—
243#340—112no—
244#340—112no—
245#340—112no—
246C22×C11—44no—
247C22×C11—44no—
248C22×C11—44no—
249C22×C11—82no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11—82no—
253C22×C11C2×C4×D411yescharacteristic
254C22×C11C2×#12111yescharacteristic
255C22×C11#53211yescharacteristic
256C22×C11#57612yes—
257C22×C11#57712yes—
258C2×D11—24no—
259C2×D11—22no—
260C2×D11—41no—
261C2×D11—41no—
262C2×D11—42no—
263C4×C11—24no—
264C4×C11—82no—
265C4×C11C2×C4×D411yescharacteristic
266C4×C11C4×#4111yescharacteristic
267C4×C11#52511yescharacteristic
268C4×C11#52911yescharacteristic
269Dic11—22no—
270Dic11—44no—
271Dic11—42no—
272Dic11—82no—
273C22×D4—222no—
274C22×D4C22×D1112yes—
275C23×C4—22no—
276C23×C4—111no—
277C2×D8—22no—
278C2×D8—22no—
279C2×D8C4×D1114yes—
280C2×M16—114no—
281C2×M16—222no—
282C2×M16—222no—
283C22×C8—111no—
284C22×C8—111no—
285C22×C8—222no—
286C22×C8—222no—
287C22×C8—222no—
288C22×C8C22×D1111yescharacteristic
289C22×C8C22×D1111yescharacteristic
290#121—118no—
291#121—224no—
292C4×D4—24no—
293C4×D4—24no—
294#117—222no—
295#117—222no—
296C2×C4⋊C4—112no—
297C2×C4⋊C4—112no—
298C2×C4⋊C4—112no—
299C2×C4⋊C4—222no—
300C2×C4⋊C4C22×D1112yes—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—112no—
303C2×C22⋊C4—222no—
304C2×C22⋊C4—222no—
305C2×C22⋊C4—222no—
306C2×C22⋊C4—222no—
307C2×C42—111no—
308C2×C42—222no—
309C2×C42C22×D1111yescharacteristic
310#107—222no—
311#106—22no—
312#106—114no—
313#102—24no—
314#102—118no—
315#102—224no—
316#97—222no—
317#97C22⋊D1114yescomplemented
318C4×C8—222no—
319C4×C8—222no—
320#95—222no—
321#95—222no—
322#95—222no—
323C2×C11—84no—
324C2×C11C4×#12111yescharacteristic
325C2×C11#294612yes—
326C2×C11#306212yes—
327C2×C11#317311yescharacteristic
328C2×C11#317611yescharacteristic
329D11—42no—
330C24—22no—
331C24—111no—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—228no—
338C2×D4—882no—
339C2×D4—882no—
340C2×D4C2×C4×D1114yes—
341C22×C4—22no—
342C22×C4—44no—
343C22×C4—82no—
344C22×C4—82no—
345C22×C4—111no—
346C22×C4—112no—
347C22×C4—112no—
348C22×C4—112no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4D4×D1112yes—
356C22×C4C23×D1111yescharacteristic
357D8—28no—
358M16—228no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—112no—
362C2×C8—112no—
363C2×C8—228no—
364C2×C8—221no—
365C2×C8—221no—
366C2×C8—221no—
367C2×C8—221no—
368C2×C8C2×C4×D1112yes—
369C2×C8#433912yes—
370C2×C8C2×C22⋊D1112yes—
371C2×C8C2×C22⋊D1112yes—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—114no—
375C4⋊C4—224no—
376C4⋊C4—222no—
377C4⋊C4—222no—
378C4⋊C4—222no—
379C4⋊C4—882no—
380C22⋊C4—44no—
381C22⋊C4—228no—
382C22⋊C4—224no—
383C22⋊C4—882no—
384C22⋊C4—882no—
385C22⋊C4—882no—
386C42—221no—
387C42—221no—
388C42—882no—
389C42#434112yes—
390C42C2×C22⋊D1112yes—
391C11#2154111yescharacteristic, complemented, Sylow
392C23—24no—
393C23—42no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23—42no—
398C23—42no—
399C23—112no—
400C23—222no—
401C23—222no—
402C23—221no—
403C23—221no—
404C23C2×D4×D1111yescharacteristic
405D4—24no—
406D4—24no—
407D4—42no—
408D4—42no—
409D4—888no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—88no—
416C2×C4—112no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—222no—
420C2×C4—222no—
421C2×C4—222no—
422C2×C4—222no—
423C2×C4—222no—
424C2×C4—222no—
425C2×C4—224no—
426C2×C4—222no—
427C2×C4—442no—
428C2×C4—442no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4#6699114yes—
433C2×C4C22×C4×D1111yescharacteristic
434C2×C4C2×#433911yescharacteristic
435C2×C4C2×#434111yescharacteristic
436C2×C4#41×D1111yescharacteristic
437C2×C4#41×D1111yescharacteristic
438C2×C4C22×C22⋊D1111yescharacteristic
439C8—22no—
440C8—222no—
441C8—222no—
442C8C4×C22⋊D1114yes—
443C22—44no—
444C22—44no—
445C22—44no—
446C22—82no—
447C22—82no—
448C22—82no—
449C22—82no—
450C22—222no—
451C22—224no—
452C22—442no—
453C22—441no—
454C22—441no—
455C22C4×D4×D1111yescharacteristic
456C22#1062307911yescharacteristic
457C22#1062330512yes—
458C22#1062330612yes—
459C22C2×#6699111yescharacteristic
460C4—24no—
461C4—82no—
462C4—222no—
463C4—442no—
464C4—444no—
465C4—882no—
466C4C4×#434111yescharacteristic
467C4#1062308811yescharacteristic
468C4C2×C4×C22⋊D1111yescharacteristic
469C4#1062335911yescharacteristic
470C2—84no—
471C2—442no—
472C2C4×#6699111yescharacteristic
473C2#1307744512yes—
474C2#1307829012yes—
475C2#1307923111yescharacteristic
476C2#1307926411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#442C2
socleC23×C11C22×D4
prime radicalC2×#10622772C2
cosocleC22×C4×C11C24
hypercenterC2×#442D11
hypocenterC11#21541
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
2. C2×#10622321C2semidirect
3. #13071303C2semidirect
4. #13069483C2semidirect
5. #13069342C2semidirect
6. #13069310C2semidirect
7. #13069041C2semidirect
8. #13068646C2semidirect
9. #13068513C2semidirect
10. C4×#66896C2semidirect
11. C2×C11×#442C2semidirect
27. #10622772C4semidirect
60. #66991C2×C4semidirect
73. C2×#4313C2×C4semidirect
81. C11×#97D4semidirect
83. #66896C2×C4semidirect
88. #66881C2×C4semidirect
155. C2×#442D11semidirect
317. #97C22⋊D11semidirect
391. C11#21541semidirect

Maximal subgroups

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

subgroupindex
C2×#106227722
C2×#106223212
#130713032
#130694832
#130693422
#130693102
#130690412
#130686462
#130685132
C4×#668962
C2×C11×#4422
#2154111