Finite Group Databasebeta

← #14771882

Subgroups — #14771882

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×C22⋊D11C211yesmaximal, characteristic
2C2×D11×#106C211yesmaximal, characteristic, complemented
3#13071546C212yesmaximal
4#13069381C212yesmaximal, complemented
5#13068815C212yesmaximal, complemented
6#13068802C212yesmaximal, complemented
7#13068777C211yesmaximal, characteristic, complemented
8#13068641C211yesmaximal, characteristic, complemented
9#13068638C211yesmaximal, characteristic, complemented
10#106×Dic11C211yesmaximal, characteristic, complemented
11C2×C11×#427C211yesmaximal, characteristic, complemented
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2212yes—
14C2×C4×C22⋊D11C2211yescharacteristic
15C22×C8×D11C2211yescharacteristic
16C2×C4⋊C4×D11C2212yes—
17C11×#427—24no—
18C2×C11×#107C2212yes—
19C2×C11×#106C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21#10622825C2212yes—
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23C8×C22⋊D11C418yescomplemented
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×#66881C2211yescharacteristic
26C2×#66881C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29#10622600C2212yes—
30#10622590C2212yes—
31C4⋊C4×Dic11C2212yes—
32C2×#66872C2212yes—
33C2×#66871C2212yes—
34#10622569—22no—
35#10622558—22no—
36C4×(C2×D11)⋊C4—22no—
37#10622546—22no—
38D11×#106—24no—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C23×C4×C11C2311yescharacteristic
43C22×C22⋊D11D411yescharacteristic
44C22×C4×D11—22no—
45C22×C4×D11C2311yescharacteristic
46C22×C8×C11—22no—
47C22×C8×C11—22no—
48C22×C8×C11C2×C414yescomplemented
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C11×#117—24no—
52C11×#117—42no—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C22⋊C4—22no—
56C2×C42×C11—22no—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11D411yescharacteristic
59C4×C22⋊D11C2×C414yes—
60C4×C22⋊D11Q814yes—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4D411yescharacteristic
63C2×C4⋊Dic11C2312yes—
64C2×C4⋊Dic11C2312yes—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4D411yescharacteristic
67C2×C4×Dic11—22no—
68C2×C4×Dic11C2311yescharacteristic
69C22×C11⋊C8C2311yescharacteristic
70C22×C11⋊C8C2311yescharacteristic
71C2×C8×D11—22no—
72C2×C8×D11—22no—
73C2×C8×D11C2×C414yes—
74C4⋊C4×D11—24no—
75C4⋊C4×D11—42no—
76C11×#107—24no—
77C11×#106—22no—
78C11×#106D414yescomplemented
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C22⋊(C11⋊C8)C2×C414yescomplemented
85(C2×D11)⋊C8C2×C414yes—
86#66881—22no—
87#66881—22no—
88Dic11⋊C8C2×C414yescomplemented
89C8×Dic11C2×C414yescomplemented
90#66872—24no—
91#66871—42no—
92#22654—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C23×D11C2×D411yescharacteristic
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11C22×C412yes—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×Q812yes—
104C22×C4×C11C2411yescharacteristic
105C2×C22⋊D11—24no—
106C2×C22⋊D11C4⋊C414yes—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11C2×D411yescharacteristic
110C22×Dic11C2×D411yescharacteristic
111C22×Dic11C2×D411yescharacteristic
112C2×C4×D11—21no—
113C2×C4×D11—21no—
114C2×C4×D11—21no—
115C2×C4×D11—21no—
116C2×C4×D11—44no—
117C2×C4×D11—44no—
118C2×C4×D11—82no—
119C2×C4×D11C22×C412yes—
120C2×C4×D11C2×Q812yes—
121C2×C8×C11—28no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11C22×C412yes—
125C2×C8×C11C22×C412yes—
126C2×C8×C11C2×D412yes—
127C2×C8×C11#4112yes—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4C2×D414yes—
132C11×C22⋊C4—44no—
133C42×C11—44no—
134C22⋊Dic11—82no—
135C22⋊Dic11C4⋊C414yes—
136(C2×D11)⋊C4—44no—
137(C2×D11)⋊C4C4⋊C414yes—
138C4⋊Dic11—22no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142Dic11⋊C4—44no—
143Dic11⋊C4C4⋊C414yes—
144C4×Dic11—82no—
145C4×Dic11C22×C412yes—
146C4×Dic11C2×Q812yes—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8C22×C412yes—
152C2×C11⋊C8C22×C412yes—
153C8×D11—28no—
154C2×C8×D4—111no—
155C2×#427D1111yescharacteristic, complemented
156C22×#106—111no—
157#2352—112no—
158#1949—112no—
159#1854—112no—
160#1852—112no—
161#1846—111no—
162#1807—111no—
163#1807—111no—
164C4×#106—111no—
165C23×C11—21no—
166C23×C11—21no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11C2×C4⋊C412yes—
170C23×C11C22×D411yescharacteristic
171C22×D11—21no—
172C22×D11—21no—
173C22×D11—22no—
174C22×D11C2×C4⋊C412yes—
175C22×D11#13514yes—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—24no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11C2×C4⋊C412yes—
189C2×C4×C11C23×C411yescharacteristic
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C22×Q811yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11H(5,𝔽2)11yescharacteristic
194C2×C4×C112−1+411yescharacteristic
195C22⋊D11—28no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11C2×C4⋊C412yes—
207C2×Dic11C2×C4⋊C412yes—
208C2×Dic11C2×C4⋊C412yes—
209C4×D11—22no—
210C4×D11—22no—
211C4×D11—22no—
212C4×D11—22no—
213C4×D11—88no—
214C8×C11—22no—
215C8×C11C4×D414yes—
216C11⋊C8—22no—
217C11⋊C8—22no—
218C23×C8—111no—
219C23×C8C2×D1111yescharacteristic
220C2×C4×D4—111no—
221C2×#117C2×D1112yes—
222C22×C4⋊C4—112no—
223C8×D4—118no—
224#427—24no—
225C2×#107—112no—
226C2×#107C2×D1112yes—
227C2×#106—111no—
228C2×#106—111no—
229C2×#106—112no—
230C2×#106—224no—
231C2×#106C2×D1111yescharacteristic
232C2×#106C2×D1111yescharacteristic
233C2×C4⋊C8—111no—
234C2×C22⋊C8—111no—
235C2×C22⋊C8—111no—
236C2×C4×C8—111no—
237#388—222no—
238#387—222no—
239#386—222no—
240#382—112no—
241#380—112no—
242#380—112no—
243C4×C4⋊C4—112no—
244C4×C22⋊C4—222no—
245#340—112no—
246#340—112no—
247#340—112no—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11C22×C4⋊C411yescharacteristic
254C22×C11D4211yescharacteristic
255C22×C11#54711yescharacteristic
256C22×C11C2×#13512yes—
257C22×C11#57712yes—
258C2×D11—24no—
259C2×D11—22no—
260C2×D11—22no—
261C2×D11—24no—
262C2×D11#42714yescomplemented
263C4×C11—22no—
264C4×C11—44no—
265C4×C11—82no—
266C4×C11C2×C4×D411yescharacteristic
267C4×C11#52011yescharacteristic
268C4×C11D4×Q811yescharacteristic
269C4×C11#55411yescharacteristic
270Dic11—22no—
271Dic11—22no—
272Dic11—22no—
273Dic11—82no—
274Dic11—82no—
275C22×D4—111no—
276C23×C4—111no—
277C23×C4—222no—
278C23×C4C22×D1111yescharacteristic
279C22×C8—22no—
280C22×C8—22no—
281C22×C8—111no—
282C22×C8—111no—
283C22×C8—114no—
284C22×C8—222no—
285C22×C8—222no—
286C22×C8C4×D1114yescomplemented
287C22×C8C22×D1111yescharacteristic
288C22×C8C22×D1111yescharacteristic
289C4×D4—114no—
290C4×D4—114no—
291#117—24no—
292#117—42no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—112no—
295C2×C4⋊C4—112no—
296C2×C4⋊C4—224no—
297C2×C4⋊C4—222no—
298C2×C4⋊C4—442no—
299C2×C4⋊C4C22×D1112yes—
300C2×C4⋊C4C22×D1112yes—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—111no—
303C2×C22⋊C4—111no—
304C2×C22⋊C4—222no—
305C2×C22⋊C4—222no—
306C2×C42—22no—
307C2×C42—111no—
308C2×C42—222no—
309#107—24no—
310#107—442no—
311#106—22no—
312#106—222no—
313#106—222no—
314#106—224no—
315#106C22⋊D1114yescomplemented
316C4⋊C8—114no—
317C22⋊C8—114no—
318C22⋊C8—114no—
319C4×C8—114no—
320#95—222no—
321#95—222no—
322#95—222no—
323#95—222no—
324#95—222no—
325C2×C11—42no—
326C2×C11D4×C4⋊C411yescharacteristic
327C2×C11C2×#42711yescharacteristic
328C2×C11#291211yescharacteristic
329C2×C11#328212yes—
330C2×C11#333712yes—
331D11—24no—
332C24—111no—
333C24D4×D1111yescharacteristic
334C2×D4—114no—
335C2×D4—224no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—111no—
343C22×C4—111no—
344C22×C4—111no—
345C22×C4—112no—
346C22×C4—112no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—222no—
352C22×C4—222no—
353C22×C4—444no—
354C22×C4—444no—
355C22×C4—882no—
356C22×C4C2×C4×D1112yes—
357C22×C4D4×D1111yescharacteristic
358C22×C4Q8×D1112yes—
359C22×C4C23×D1111yescharacteristic
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—28no—
363C2×C8—112no—
364C2×C8—112no—
365C2×C8—221no—
366C2×C8—221no—
367C2×C8—221no—
368C2×C8—221no—
369C2×C8—228no—
370C2×C8C2×C4×D1112yes—
371C2×C8C2×C4×D1112yes—
372C2×C8#433912yes—
373C2×C8C2×C22⋊D1112yes—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—114no—
378C4⋊C4—222no—
379C4⋊C4—222no—
380C4⋊C4—222no—
381C4⋊C4—222no—
382C4⋊C4—444no—
383C4⋊C4C2×C22⋊D1114yes—
384C22⋊C4—44no—
385C22⋊C4—114no—
386C22⋊C4—114no—
387C22⋊C4—444no—
388C22⋊C4—882no—
389C42—44no—
390C42—112no—
391C42—112no—
392C42—882no—
393C11#2265411yescharacteristic, complemented, Sylow
394C23—21no—
395C23—22no—
396C23—22no—
397C23—21no—
398C23—112no—
399C23—114no—
400C23—221no—
401C23—222no—
402C23—221no—
403C23C4⋊C4×D1112yes—
404C23C2×D4×D1111yescharacteristic
405D4—228no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—112no—
419C2×C4—112no—
420C2×C4—112no—
421C2×C4—221no—
422C2×C4—222no—
423C2×C4—222no—
424C2×C4—221no—
425C2×C4—222no—
426C2×C4—222no—
427C2×C4—222no—
428C2×C4—222no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—888no—
436C2×C4C4⋊C4×D1112yes—
437C2×C4C22×C4×D1111yescharacteristic
438C2×C4C2×#433911yescharacteristic
439C2×C4#6703711yescharacteristic
440C2×C4C2×Q8×D1111yescharacteristic
441C2×C4#6704011yescharacteristic
442C2×C4C22×C22⋊D1111yescharacteristic
443C8—22no—
444C8—222no—
445C8—222no—
446C8C4×C22⋊D1114yes—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—42no—
451C22—42no—
452C22—114no—
453C22—222no—
454C22—224no—
455C22—222no—
456C22—224no—
457C22C2×C4⋊C4×D1111yescharacteristic
458C22#1062303811yescharacteristic
459C22D11×#13512yes—
460C22#1062330112yes—
461C22D4×C22⋊D1111yescharacteristic
462C4—22no—
463C4—44no—
464C4—82no—
465C4—222no—
466C4—222no—
467C4—222no—
468C4—882no—
469C4—882no—
470C4#1062303511yescharacteristic
471C4#1062304211yescharacteristic
472C4C2×C4×C22⋊D1111yescharacteristic
473C4Q8×C22⋊D1111yescharacteristic
474C2—42no—
475C2—224no—
476C2C4⋊C4×C22⋊D1111yescharacteristic
477C2D11×#42711yescharacteristic
478C2#1307720811yescharacteristic
479C2#1308031712yes—
480C2#1308099612yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#427C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
cosocleC22×C4×C11C24
hypercenterC2×#427D11
hypocenterC11#22654
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. C2×D11×#106C2semidirect
4. #13069381C2semidirect
5. #13068815C2semidirect
6. #13068802C2semidirect
7. #13068777C2semidirect
8. #13068641C2semidirect
9. #13068638C2semidirect
10. #106×Dic11C2semidirect
11. C2×C11×#427C2semidirect
23. C8×C22⋊D11C4semidirect
48. C22×C8×C11C2×C4semidirect
78. C11×#106D4semidirect
84. C22⋊(C11⋊C8)C2×C4semidirect
88. Dic11⋊C8C2×C4semidirect
89. C8×Dic11C2×C4semidirect
155. C2×#427D11semidirect
262. C2×D11#427semidirect
286. C22×C8C4×D11semidirect
315. #106C22⋊D11semidirect
393. C11#22654semidirect

Maximal subgroups

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

subgroupindex
C2×C8×C22⋊D112
C2×D11×#1062
#130715462
#130693812
#130688152
#130688022
#130687772
#130686412
#130686382
#106×Dic112
C2×C11×#4272
#2265411