Finite Group Databasebeta

← #14645160

Subgroups — #14645160

Order 2816.

868 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×#10623010C211yesmaximal, characteristic
2C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
3C2×#10622122C212yesmaximal, complemented
4C2×#10622121C212yesmaximal, complemented
5C11×#1797C211yesmaximal, characteristic, complemented
6C22×C42×C11C2211yescharacteristic
7C2×#66983C411yescharacteristic
8C2×#66982—21no—
9C2×C4×C22⋊D11—21no—
10C2×#66977C411yescharacteristic
11#10623010—24no—
12#10623010—24no—
13C2×#66929—21no—
14C2×#66928C411yescharacteristic
15C2×C4×D44C2211yescharacteristic
16C2×#66925—21no—
17C2×#66923C411yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C2×C11×C4⋊C8C2212yes—
20C2×C11×C22⋊C8—21no—
21C2×C22⋊(C11⋊C8)—21no—
22C2×C4×C11⋊C8C2212yes—
23C11×#336—21no—
24#10622162—21no—
25#10622122—24no—
26#10622121—24no—
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C22×C22⋊D11—21no—
31C22×D44C2×C411yescharacteristic
32C22×C4×D11—21no—
33C22×Dic22C2×C411yescharacteristic
34C22×C8×C11—22no—
35C2×C42×C11—22no—
36C2×C42×C11—22no—
37C2×C42×C11C2×C411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C42×C11C2311yescharacteristic
41C2×C22⋊Dic11—21no—
42#66983—22no—
43#66983—22no—
44#66982—28no—
45C4×C22⋊D11—28no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—21no—
50C2×C4⋊Dic11C2×C411yescharacteristic
51C2×C4⋊Dic11C2×C411yescharacteristic
52#66977—22no—
53#66977—22no—
54C2×Dic11⋊C4—21no—
55C2×Dic11⋊C4—21no—
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4—21no—
58C2×C4×Dic11—21no—
59C22×C11⋊C8—22no—
60#66929—28no—
61#66928—22no—
62#66928—22no—
63C4×D44—22no—
64C4×D44D414yes—
65#66925—28no—
66#66923—22no—
67#66923—22no—
68C4×Dic22—22no—
69C4×Dic22D414yes—
70C11×C4⋊C8—22no—
71C11×C4⋊C8—22no—
72C11×C22⋊C8—42no—
73C22⋊(C11⋊C8)—24no—
74C4×C11⋊C8—22no—
75C4×C11⋊C8—22no—
76#8315—111nomaximal, Sylow
77C24×C11C22⋊C411yescharacteristic
78C23×D11—21no—
79C22×C4×C11—22no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—41no—
90C22×C4×C11C22⋊C411yescharacteristic
91C22×C4×C11C22⋊C411yescharacteristic
92C22×C4×C11C22⋊C411yescharacteristic
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C2×C22⋊D11—24no—
97C2×C22⋊D11—42no—
98C2×C22⋊D11—42no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C2×D44—21no—
103C2×D44—22no—
104C2×D44—22no—
105C2×D44C22⋊C412yes—
106C2×C4×D11—24no—
107C2×C4×D11—42no—
108C2×C4×D11—41no—
109C2×C4×D11—41no—
110C2×Dic22—21no—
111C2×Dic22—22no—
112C2×Dic22—22no—
113C2×Dic22C22⋊C412yes—
114C2×C8×C11—42no—
115C2×C8×C11—42no—
116C2×C8×C11—42no—
117C42×C11—21no—
118C42×C11—21no—
119C42×C11—22no—
120C42×C11—22no—
121C42×C11C2×D412yes—
122C42×C11C2×D412yes—
123C22⋊Dic11—24no—
124(C2×D11)⋊C4—24no—
125(C2×D11)⋊C4—24no—
126(C2×D11)⋊C4—24no—
127(C2×D11)⋊C4—24no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130C4⋊Dic11C22⋊C412yes—
131C4⋊Dic11C22⋊C412yes—
132Dic11⋊C4—24no—
133Dic11⋊C4—24no—
134Dic11⋊C4—24no—
135Dic11⋊C4—24no—
136C4×Dic11—24no—
137C2×C11⋊C8—24no—
138C2×C11⋊C8—42no—
139C2×C11⋊C8—42no—
140C2×#529—111no—
141#1797D1111yescharacteristic, complemented
142C4×C22⋊C8—111no—
143C2×Q8⋊C8—112no—
144C2×D4⋊C8—112no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11#10412yes—
152C23×C11C2×C22⋊C411yescharacteristic
153C22×D11—22no—
154C22×D11—41no—
155C22×D11—41no—
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—44no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11C2×C22⋊C411yescharacteristic
177C2×C4×C11C2×C22⋊C411yescharacteristic
178C2×C4×C11#12012yes—
179C2×C4×C11#12012yes—
180C2×C4×C11#13112yes—
181C2×C4×C11#13112yes—
182C2×C4×C11#13512yes—
183C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C11#13711yescharacteristic
185C22⋊D11—48no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195D44—24no—
196D44—42no—
197C4×D11—44no—
198C4×D11—44no—
199Dic22—24no—
200Dic22—42no—
201C8×C11—82no—
202C11⋊C8—44no—
203#529—224no—
204#529—224no—
205C2×#126—221no—
206C2×#125—111no—
207C2×#124—111no—
208C2×#123—221no—
209C2×C22⋊Q8—111no—
210C2×#121—111no—
211C2×C4×Q8—111no—
212C2×C4×D4—111no—
213C2×C4×D4—221no—
214C2×#117—221no—
215C22×C42C2×D1111yescharacteristic
216C2×C4⋊C8C2×D1112yes—
217C2×C22⋊C8—21no—
218C2×C22⋊C8—221no—
219C2×C4×C8—112no—
220#336—21no—
221#336—221no—
222Q8⋊C8—224no—
223D4⋊C8—224no—
224C22×C11—22no—
225C22×C11—22no—
226C22×C11—22no—
227C22×C11—41no—
228C22×C11—41no—
229C22×C11—41no—
230C22×C11—41no—
231C22×C11#37911yescharacteristic
232C22×C11#40811yescharacteristic
233C22×C11#40811yescharacteristic
234C22×C11#41611yescharacteristic
235C22×C11#41711yescharacteristic
236C22×C11C2×#10411yescharacteristic
237C22×C11#42111yescharacteristic
238C2×D11—42no—
239C2×D11—42no—
240C2×D11—42no—
241C2×D11—81no—
242C2×D11—81no—
243C2×D11—81no—
244C2×D11—81no—
245C4×C11—22no—
246C4×C11—41no—
247C4×C11—41no—
248C4×C11—41no—
249C4×C11#40812yes—
250C4×C11#40812yes—
251C4×C11#44912yes—
252C4×C11#45212yes—
253Dic11—42no—
254Dic11—42no—
255Dic11—42no—
256C22×Q8—111no—
257C22×D4—111no—
258C22×D4—221no—
259C23×C4—221no—
260C23×C4C4×D1111yescharacteristic
261C23×C4D4411yescharacteristic
262C23×C4C22⋊D1111yescharacteristic
263C22×C8—22no—
264C22×C8—222no—
265#126—228no—
266#125—222no—
267#125—222no—
268#124—222no—
269#124—222no—
270#123—228no—
271C22⋊Q8—222no—
272C22⋊Q8—222no—
273#121—222no—
274#121—222no—
275C4×Q8—114no—
276C4×Q8—222no—
277C4×D4—114no—
278C4×D4—228no—
279C4×D4—222no—
280#117—228no—
281C2×C4⋊C4—111no—
282C2×C4⋊C4—111no—
283C2×C4⋊C4—221no—
284C2×C4⋊C4—221no—
285C2×C4⋊C4—221no—
286C2×C4⋊C4—221no—
287C2×C22⋊C4—221no—
288C2×C22⋊C4—221no—
289C2×C22⋊C4—221no—
290C2×C22⋊C4—221no—
291C2×C22⋊C4—221no—
292C2×C42—22no—
293C2×C42—22no—
294C2×C42—221no—
295C2×C42C4×D1111yescharacteristic
296C2×C42D4411yescharacteristic
297C2×C42C22⋊D1111yescharacteristic
298C2×C42C22×D1111yescharacteristic
299C4⋊C8—22no—
300C4⋊C8—22no—
301C22⋊C8—42no—
302C22⋊C8—224no—
303C4×C8—222no—
304C4×C8—222no—
305C2×C11—42no—
306C2×C11#148211yescharacteristic
307C2×C11#148311yescharacteristic
308C2×C11#149411yescharacteristic
309C2×C11#149511yescharacteristic
310C2×C11#178011yescharacteristic
311C2×C11#178811yescharacteristic
312C2×C11#178911yescharacteristic
313D11—82no—
314C24—221no—
315C24(C2×D11)⋊C411yescharacteristic
316C2×Q8—112no—
317C2×Q8—221no—
318C2×Q8—222no—
319C2×Q8—222no—
320C2×D4—112no—
321C2×D4—224no—
322C2×D4—221no—
323C2×D4—222no—
324C2×D4—222no—
325C2×D4—442no—
326C2×D4—442no—
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—41no—
338C22×C4—221no—
339C22×C4—221no—
340C22×C4—221no—
341C22×C4—224no—
342C22×C4—441no—
343C22×C4—441no—
344C22×C4—442no—
345C22×C4(C2×D11)⋊C411yescharacteristic
346C22×C4(C2×D11)⋊C411yescharacteristic
347C22×C4(C2×D11)⋊C411yescharacteristic
348C22×C4C2×C4×D1111yescharacteristic
349C22×C4C2×D4411yescharacteristic
350C22×C4C2×C22⋊D1111yescharacteristic
351C2×C8—42no—
352C2×C8—42no—
353C2×C8—42no—
354C2×C8—224no—
355C2×C8—442no—
356C2×C8—442no—
357C4⋊C4—112no—
358C4⋊C4—112no—
359C4⋊C4—224no—
360C4⋊C4—224no—
361C4⋊C4—224no—
362C4⋊C4—221no—
363C4⋊C4—221no—
364C4⋊C4—224no—
365C22⋊C4—224no—
366C22⋊C4—224no—
367C22⋊C4—224no—
368C22⋊C4—224no—
369C22⋊C4—224no—
370C42—21no—
371C42—21no—
372C42—22no—
373C42—22no—
374C42—224no—
375C42D4×D1112yes—
376C42D4×D1112yes—
377C11#831511yescharacteristic, complemented, Sylow
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—222no—
385C23—441no—
386C23—441no—
387C23—441no—
388C23—441no—
389C23—441no—
390C23—441no—
391C23#6688912yes—
392C23C2×(C2×D11)⋊C411yescharacteristic
393Q8—224no—
394Q8—442no—
395D4—224no—
396D4—448no—
397D4—442no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—44no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—444no—
424C2×C4—444no—
425C2×C4C22⋊C4×D1111yescharacteristic
426C2×C4C22⋊C4×D1111yescharacteristic
427C2×C4#6693512yes—
428C2×C4#6695412yes—
429C2×C4#6696012yes—
430C2×C4#6698511yescharacteristic
431C2×C4#6699012yes—
432C2×C4#6699511yescharacteristic
433C2×C4#6700312yes—
434C8—82no—
435C8—444no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—442no—
444C22—442no—
445C22—442no—
446C22—881no—
447C22—881no—
448C22—881no—
449C22—881no—
450C22#1062256811yescharacteristic
451C22#1062257911yescharacteristic
452C22#1062261511yescharacteristic
453C22#1062272311yescharacteristic
454C22#1062274211yescharacteristic
455C22C2×#6688911yescharacteristic
456C22#1062275211yescharacteristic
457C4—22no—
458C4—41no—
459C4—41no—
460C4—41no—
461C4—442no—
462C4—442no—
463C4—442no—
464C4#1062234012yes—
465C4#1062234012yes—
466C4#1062265012yes—
467C4#1062266012yes—
468C2—42no—
469C2—882no—
470C2#1306702211yescharacteristic
471C2#1306702711yescharacteristic
472C2#1306707411yescharacteristic
473C2#1306707911yescharacteristic
474C2#1306852711yescharacteristic
475C2#1306855411yescharacteristic
476C2#1306855911yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1797C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C4
cosocleC2×C42×C11C23
hypercenter#1797D11
hypocenterC11#8315
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊(C11⋊C8)C2semidirect
3. C2×#10622122C2semidirect
4. C2×#10622121C2semidirect
5. C11×#1797C2semidirect
141. #1797D11semidirect
377. C11#8315semidirect

Maximal subgroups

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

subgroupindex
C2×#106230102
C4×C22⋊(C11⋊C8)2
C2×#106221222
C2×#106221212
C11×#17972
#831511