Finite Group Databasebeta

← #14760513

Subgroups — #14760513

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×#10622748C211yesmaximal, characteristic
2C2×#10622324C211yesmaximal, characteristic, complemented
3#13071309C212yesmaximal, complemented
4#13069482C211yesmaximal, characteristic, complemented
5#13069344C211yesmaximal, characteristic, complemented
6#13069313C212yesmaximal, complemented
7#13069044C212yesmaximal, complemented
8#13068649C211yesmaximal, characteristic, complemented
9#13068513C211yesmaximal, characteristic, complemented
10C4×#66885C212yesmaximal, complemented
11C2×C11×#405C211yesmaximal, characteristic, complemented
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×#66983C2212yes—
16C22×D88C2211yescharacteristic
17C2×C4×D44C2212yes—
18C11×#405—24no—
19C2×C11×#97C2211yescharacteristic
20C2×C11×#97C2211yescharacteristic
21C2×C4×C8×C11C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23#10622825C2212yes—
24#10622748C418yescomplemented
25C2×#66885C2212yes—
26C2×#66885C2212yes—
27C2×#66885C2212yes—
28C2×#66882C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31#10622603—22no—
32#10622602—22no—
33#10622570—22no—
34#10622569—22no—
35#10622552C2212yes—
36C4×C4⋊Dic11C2212yes—
37#10622541C2212yes—
38#10622324—24no—
39#10622189C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42C23×C4×C11C2311yescharacteristic
43C22×C22⋊D11—22no—
44C22×D44C2312yes—
45C22×C4×D11—22no—
46C2×C11×M16—22no—
47C2×C11×M16—22no—
48C2×C11×M16C2×C414yescomplemented
49C22×C8×C11—22no—
50C22×C8×C11—22no—
51C22×C8×C11—22no—
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C11×#117—22no—
57C11×#117—22no—
58C2×C11×C4⋊C4D412yes—
59C2×C11×C22⋊C4D412yes—
60C2×C42×C11C2311yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11—22no—
63#66983—24no—
64#66983C2×C418yescomplemented
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×C4⋊Dic11C2312yes—
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2312yes—
72C2×Dic11⋊C4—22no—
73C2×C4×Dic11—22no—
74C2×D88—22no—
75C2×D88—22no—
76C2×D88C2×C414yes—
77C4×D44—24no—
78C4×D44—24no—
79C11×#97—22no—
80C11×#97D414yescomplemented
81C4×C8×C11—22no—
82C4×C8×C11—22no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86#66885—24no—
87#66885—24no—
88#66885C2×C418yescomplemented
89#66882—22no—
90#66881—22no—
91#66881C2×C414yescomplemented
92#21541—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C23×D11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11C22×C412yes—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D412yes—
103C22×C4×C11#4112yes—
104C22×C4×C11C2411yescharacteristic
105C2×C22⋊D11—28no—
106C2×C22⋊D11—82no—
107C2×C22⋊D11—82no—
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C2×D44—22no—
112C2×D44—22no—
113C2×D44—22no—
114C2×D44—22no—
115C2×D44—22no—
116C2×D44C22×C414yes—
117C2×C4×D11—44no—
118C2×C4×D11—82no—
119C2×C4×D11—82no—
120C11×M16—28no—
121C2×C8×C11—28no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11C22×C412yes—
129C2×C8×C11C22×C412yes—
130C2×C8×C11C2×D412yes—
131C2×C8×C11C2×D412yes—
132C2×C8×C11#4112yes—
133C2×C8×C11#4112yes—
134C11×C4⋊C4—24no—
135C11×C22⋊C4—24no—
136C42×C11—21no—
137C42×C11—21no—
138C42×C11C2×D412yes—
139C42×C11#4112yes—
140C22⋊Dic11—82no—
141(C2×D11)⋊C4—28no—
142(C2×D11)⋊C4—44no—
143(C2×D11)⋊C4—82no—
144(C2×D11)⋊C4—82no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11C22×C414yes—
151Dic11⋊C4—82no—
152C4×Dic11—82no—
153D88—28no—
154C2×#469—111no—
155C2×#442—111no—
156C2×#405D1111yescharacteristic, complemented
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—21no—
166C23×C11—21no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11C4×D412yes—
170C23×C11C22×D411yescharacteristic
171C22×D11—24no—
172C22×D11—42no—
173C22×D11—42no—
174C22×D11—42no—
175C22×D11—42no—
176C22×D11—42no—
177C22×D11—42no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11C4×D412yes—
190C2×C4×C11#12114yes—
191C2×C4×C11C23×C411yescharacteristic
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C22⋊D11—88no—
198C2×Dic11—24no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207D44—24no—
208D44—24no—
209D44—42no—
210D44—42no—
211C4×D11—88no—
212C8×C11—22no—
213C8×C11—22no—
214C8×C11—22no—
215C8×C11C4×D414yes—
216C22×D8—111no—
217C22×M16C2×D1111yescharacteristic
218C23×C8C2×D1111yescharacteristic
219C2×#121—112no—
220C2×C4×D4—112no—
221C2×#117C2×D1111yescharacteristic
222#469—118no—
223#442—224no—
224C2×#107—111no—
225C2×#106—111no—
226C2×#106—111no—
227C2×#102—112no—
228C2×#102—112no—
229C2×#102—112no—
230#405—24no—
231C2×#97C2×D1111yescharacteristic
232C2×#97C2×D1111yescharacteristic
233C2×C4×C8C2×D1111yescharacteristic
234C2×C4×C8C2×D1111yescharacteristic
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—24no—
247C22×C11—22no—
248C22×C11—41no—
249C22×C11—41no—
250C22×C11—42no—
251C22×C11C2×C4×D411yescharacteristic
252C22×C11C2×#12111yescharacteristic
253C22×C11#53211yescharacteristic
254C22×C11#57612yes—
255C22×C11#57712yes—
256C2×D11—44no—
257C2×D11—44no—
258C2×D11—44no—
259C2×D11—82no—
260C2×D11—82no—
261C2×D11—82no—
262C2×D11—82no—
263C4×C11—24no—
264C4×C11—22no—
265C4×C11—42no—
266C4×C11C2×C4×D411yescharacteristic
267C4×C11C4×#4111yescharacteristic
268C4×C11#52511yescharacteristic
269C4×C11#52911yescharacteristic
270Dic11—44no—
271Dic11—82no—
272Dic11—82no—
273C22×D4—112no—
274C22×D4—222no—
275C23×C4—222no—
276C23×C4C22×D1111yescharacteristic
277C2×D8—114no—
278C2×D8—222no—
279C2×D8—222no—
280C2×M16—22no—
281C2×M16—22no—
282C2×M16C4×D1114yescomplemented
283C22×C8—22no—
284C22×C8—22no—
285C22×C8—22no—
286C22×C8C22×D1111yescharacteristic
287C22×C8C22×D1111yescharacteristic
288C22×C8C22×D1111yescharacteristic
289C22×C8C22×D1111yescharacteristic
290#121—118no—
291#121—224no—
292C4×D4—224no—
293C4×D4—224no—
294#117—22no—
295#117—22no—
296C2×C4⋊C4—112no—
297C2×C4⋊C4—112no—
298C2×C4⋊C4—112no—
299C2×C4⋊C4—222no—
300C2×C4⋊C4D4412yes—
301C2×C22⋊C4—222no—
302C2×C22⋊C4—222no—
303C2×C22⋊C4—222no—
304C2×C22⋊C4—222no—
305C2×C22⋊C4—222no—
306C2×C22⋊C4D4412yes—
307C2×C42—222no—
308C2×C42C22×D1111yescharacteristic
309C2×C42C22×D1111yescharacteristic
310#107—222no—
311#106—114no—
312#106—222no—
313#102—118no—
314#102—224no—
315#102—224no—
316#97—22no—
317#97C22⋊D1114yescomplemented
318C4×C8—22no—
319C4×C8—22no—
320#95—222no—
321#95—222no—
322#95—222no—
323C2×C11—42no—
324C2×C11C4×#12111yescharacteristic
325C2×C11#294612yes—
326C2×C11#306212yes—
327C2×C11#317311yescharacteristic
328C2×C11#317611yescharacteristic
329D11—84no—
330C24—222no—
331C24C2×D4411yescharacteristic
332C2×D4—114no—
333C2×D4—228no—
334C2×D4—222no—
335C2×D4—222no—
336C2×D4—222no—
337C2×D4—222no—
338C2×D4—222no—
339C2×D4—882no—
340C2×D4—882no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—222no—
346C22×C4—222no—
347C22×C4—222no—
348C22×C4—444no—
349C22×C4—882no—
350C22×C4—882no—
351C22×C4C2×C4×D1112yes—
352C22×C4C2×D4412yes—
353C22×C4C2×D4411yescharacteristic
354C22×C4C2×D4412yes—
355C22×C4#433912yes—
356C22×C4C23×D1111yescharacteristic
357D8—228no—
358M16—28no—
359C2×C8—28no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8C2×C4×D1112yes—
367C2×C8C2×C4×D1112yes—
368C2×C8#433912yes—
369C2×C8#433912yes—
370C2×C8C2×C22⋊D1112yes—
371C2×C8C2×C22⋊D1112yes—
372C4⋊C4—24no—
373C4⋊C4—114no—
374C4⋊C4—222no—
375C4⋊C4—222no—
376C4⋊C4—222no—
377C4⋊C4—222no—
378C4⋊C4—222no—
379C4⋊C4—882no—
380C22⋊C4—24no—
381C22⋊C4—228no—
382C22⋊C4—444no—
383C22⋊C4—882no—
384C22⋊C4—882no—
385C22⋊C4—882no—
386C42—21no—
387C42—21no—
388C42—882no—
389C42#433912yes—
390C42C2×C22⋊D1112yes—
391C11#2154111yescharacteristic, complemented, Sylow
392C23—21no—
393C23—22no—
394C23—22no—
395C23—21no—
396C23—224no—
397C23—442no—
398C23—442no—
399C23—442no—
400C23—442no—
401C23—442no—
402C23—442no—
403C23C4×D4412yes—
404C23C22×D4411yescharacteristic
405D4—224no—
406D4—224no—
407D4—442no—
408D4—442no—
409D4—888no—
410C2×C4—21no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—224no—
422C2×C4—442no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4—442no—
427C2×C4—442no—
428C2×C4—442no—
429C2×C4—442no—
430C2×C4—888no—
431C2×C4C4×D4412yes—
432C2×C4#6698314yes—
433C2×C4C22×C4×D1111yescharacteristic
434C2×C4C2×#433911yescharacteristic
435C2×C4C2×#433911yescharacteristic
436C2×C4C2×#433911yescharacteristic
437C2×C4C2×#433911yescharacteristic
438C2×C4C22×C22⋊D1111yescharacteristic
439C8—22no—
440C8—22no—
441C8—22no—
442C8C4×C22⋊D1114yes—
443C22—22no—
444C22—24no—
445C22—42no—
446C22—41no—
447C22—41no—
448C22—444no—
449C22—444no—
450C22—444no—
451C22—882no—
452C22—882no—
453C22—882no—
454C22—882no—
455C22C2×C4×D4411yescharacteristic
456C22#1062300811yescharacteristic
457C22#1062328212yes—
458C22#1062328312yes—
459C22C2×#6698311yescharacteristic
460C4—24no—
461C4—22no—
462C4—42no—
463C4—444no—
464C4—882no—
465C4—882no—
466C4C4×#433911yescharacteristic
467C4#1062301011yescharacteristic
468C4C2×C4×C22⋊D1111yescharacteristic
469C4#1062332211yescharacteristic
470C2—42no—
471C2—884no—
472C2C4×#6698311yescharacteristic
473C2#1307745012yes—
474C2#1307829612yes—
475C2#1307923311yescharacteristic
476C2#1307926611yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#405C2
socleC23×C11C22×D4
prime radicalC2×#10622748C2
cosocleC22×C4×C11C24
hypercenterC2×#405D11
hypocenterC11#21541
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
2. C2×#10622324C2semidirect
3. #13071309C2semidirect
4. #13069482C2semidirect
5. #13069344C2semidirect
6. #13069313C2semidirect
7. #13069044C2semidirect
8. #13068649C2semidirect
9. #13068513C2semidirect
10. C4×#66885C2semidirect
11. C2×C11×#405C2semidirect
24. #10622748C4semidirect
48. C2×C11×M16C2×C4semidirect
64. #66983C2×C4semidirect
80. C11×#97D4semidirect
88. #66885C2×C4semidirect
91. #66881C2×C4semidirect
156. C2×#405D11semidirect
282. C2×M16C4×D11semidirect
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×#106227482
C2×#106223242
#130713092
#130694822
#130693442
#130693132
#130690442
#130686492
#130685132
C4×#668852
C2×C11×#4052
#2154111