Finite Group Databasebeta

← #14723565

Subgroups — #14723565

Order 2816.

648 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077577C211yesmaximal, characteristic
2C2×#10622637C211yesmaximal, characteristic, complemented
3C4×#66995C211yesmaximal, characteristic
4#13067522C212yesmaximal, complemented
5#13067521C212yesmaximal, complemented
6#13067510C212yesmaximal, complemented
7#13067503C212yesmaximal, complemented
8#13067369C211yesmaximal, characteristic, complemented
9#13067004C211yesmaximal, characteristic
10#13066897C211yesmaximal, characteristic, complemented
11C11×#1479C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66995C411yescharacteristic
14C4×#4339C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C11×#431C2211yescharacteristic
17#10622838C411yescharacteristic
18#10622643C412yes—
19C4×#4326C2212yes—
20#10622639C412yes—
21C4×#4325C2212yes—
22#10622637—21no—
23#10622637—21no—
24#10622637C2212yes—
25#10622637C2212yes—
26#10622579C411yescharacteristic
27#10622577C411yescharacteristic
28C2×C4⋊(C11⋊C8)—21no—
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C4×#4318C2211yescharacteristic
31C2×#66867—21no—
32C2×C4×C11⋊C8C2211yescharacteristic
33#10622451C2211yescharacteristic
34#10622451C2211yescharacteristic
35#10622444C2211yescharacteristic
36#10622444C2211yescharacteristic
37#10622343—21no—
38#10622343—21no—
39C4×#4313—21no—
40#10622298—21no—
41C11×Q8⋊C8C2212yes—
42C11×Q8⋊C8C2212yes—
43#10622118C2212yes—
44#10622117C2212yes—
45#10622097C2212yes—
46#10622094C2212yes—
47#10622092C2212yes—
48C8×C11⋊C8C2212yes—
49C22×Q8×C11C2×C411yescharacteristic
50C2×#4339C2×C411yescharacteristic
51C4×Q8×C11—21no—
52C4×Q8×C11—21no—
53C4×Q8×C11C2×C412yes—
54C4×Q8×C11C2312yes—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2×C411yescharacteristic
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59C2×#4326C2×C412yes—
60#66995—24no—
61C2×#4325C2×C412yes—
62C4×C22⋊D11—21no—
63C4×C22⋊D11—21no—
64#66979C2×C411yescharacteristic
65C2×#4318C2×C411yescharacteristic
66C2×#4318C2×C411yescharacteristic
67C22×C11⋊C8—21no—
68C22×C11⋊C8D411yescharacteristic
69C22×C11⋊C8D411yescharacteristic
70C2×#4313—21no—
71C2×#4313—21no—
72C4×D44C2×C411yescharacteristic
73C4×D44C2311yescharacteristic
74#66925—21no—
75C42×D11—21no—
76C4×Dic22C2×C411yescharacteristic
77C4×Dic22C2311yescharacteristic
78C11×C4⋊C8—21no—
79C11×C4⋊C8C2311yescharacteristic
80C11×C4⋊C8C2311yescharacteristic
81C11×C22⋊C8—21no—
82C11×C22⋊C8—21no—
83C4×C8×C11—21no—
84C4×C8×C11C2312yes—
85#66899C2×C412yes—
86#66899C2×C412yes—
87(C2×D11)⋊C8—21no—
88(C2×D11)⋊C8—21no—
89#66879—21no—
90#66879—21no—
91Dic11⋊C8—21no—
92Dic11⋊C8—21no—
93#66874C2×C412yes—
94#66873C2×C412yes—
95#66872C2×C412yes—
96#66871C2×C412yes—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)—22no—
99C4⋊(C11⋊C8)—22no—
100C4⋊(C11⋊C8)C2312yes—
101#66867—22no—
102#66867—22no—
103#66867C2×C412yes—
104C4×C11⋊C8D411yescharacteristic
105C4×C11⋊C8D411yescharacteristic
106C4×C11⋊C8C2312yes—
107C4×C11⋊C8C2311yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109#17892—111nomaximal, Sylow
110C2×Q8×C11—21no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11C22×C412yes—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11C22×C411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11#4111yescharacteristic
119C2×C22⋊D11—21no—
120#4339—22no—
121#4339—22no—
122C2×D44C22×C411yescharacteristic
123C2×C4×D11—21no—
124C2×C4×D11—21no—
125C2×C4×D11—21no—
126C2×Dic22C22×C411yescharacteristic
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4C22×C412yes—
134C42×C11—22no—
135C42×C11—22no—
136C42×C11C22×C411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11#4111yescharacteristic
139C42×C11C2411yescharacteristic
140C22⋊Dic11—21no—
141#4326—24no—
142#4325—24no—
143(C2×D11)⋊C4—21no—
144(C2×D11)⋊C4—21no—
145C4⋊Dic11C22×C411yescharacteristic
146C4⋊Dic11C22×C411yescharacteristic
147Dic11⋊C4—21no—
148Dic11⋊C4—21no—
149C4×Dic11—21no—
150C4×Dic11—21no—
151C4×Dic11—21no—
152#4318—22no—
153#4318M1614yescomplemented
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—41no—
157C2×C11⋊C8—42no—
158C2×C11⋊C8C22×C412yes—
159C2×C11⋊C8C22×C412yes—
160C2×C11⋊C8C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164#4313—42no—
165#4313—42no—
166#2965—111no—
167C2×#446—111no—
168C4×#137—111no—
169#1593—112no—
170#1592—112no—
171#1591—112no—
172#1590—112no—
173#1565—111no—
174#1479D1111yescharacteristic, complemented
175#1477—111no—
176C8×M16—111no—
177C23×C11C4×D411yescharacteristic
178C22×D11—21no—
179Q8×C11—22no—
180Q8×C11—22no—
181Q8×C11—42no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11C4×D411yescharacteristic
190C2×C4×C11C4×D411yescharacteristic
191C2×C4×C11C4×D411yescharacteristic
192C2×C4×C11C2×M1612yes—
193C2×C4×C11#13112yes—
194C2×C4×C11C23×C411yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C22⋊D11—42no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201D44—21no—
202D44—21no—
203C4×D11—42no—
204C4×D11—41no—
205C4×D11—41no—
206C4×D11—42no—
207Dic22—21no—
208Dic22—21no—
209C8×C11—42no—
210C8×C11—41no—
211C8×C11—41no—
212C11⋊C8—22no—
213C11⋊C8—21no—
214C11⋊C8—21no—
215C11⋊C8—21no—
216C11⋊C8—42no—
217C11⋊C8C2×M1614yes—
218C11⋊C8#13712yescomplemented
219C2×#137—111no—
220C4×#41—111no—
221C2×C4×Q8C2×D1111yescharacteristic
222#446—112no—
223#446—112no—
224#446—111no—
225#446—111no—
226#446—221no—
227#446—221no—
228#441—112no—
229#440—112no—
230C4×Q16—112no—
231C4×SD16—112no—
232#436—111no—
233#436—111no—
234#435—221no—
235#435—221no—
236#431—221no—
237#431C2×D1111yescharacteristic
238#431C2×D1111yescharacteristic
239#428—111no—
240C2×C4⋊C8—111no—
241C2×C4⋊C8—221no—
242#419—111no—
243#417—111no—
244C4×M16—111no—
245C4×M16—221no—
246C2×#97—221no—
247C2×C4×C8—111no—
248#335—112no—
249#334—112no—
250Q8⋊C8—112no—
251Q8⋊C8C2×D1112yes—
252Q8⋊C8C2×D1112yes—
253D4⋊C8—112no—
254#322—112no—
255C82—112no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11#43612yes—
259C22×C11C2×C4×D411yescharacteristic
260C2×D11—41no—
261C2×D11—41no—
262C2×D11—41no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11#43612yes—
269C4×C11C22×M1611yescharacteristic
270C4×C11C2×#13111yescharacteristic
271C4×C11C2×#13711yescharacteristic
272C4×C11#57511yescharacteristic
273Dic11—41no—
274Dic11—41no—
275Dic11—41no—
276C2×#41—111no—
277C22×Q8C4×D1111yescharacteristic
278#137—224no—
279C2×Q16—112no—
280C2×SD16—112no—
281C2×M16—111no—
282C2×M16—111no—
283C2×M16—221no—
284C2×M16—221no—
285C22×C8—111no—
286C22×C8—111no—
287C22×C8—221no—
288C4×Q8—21no—
289C4×Q8—21no—
290C4×Q8—111no—
291C4×Q8—111no—
292C4×Q8C4×D1112yes—
293C4×Q8C22×D1112yes—
294C4×D4—111no—
295C4×D4—111no—
296C4×D4—221no—
297C4×D4—221no—
298#117—111no—
299#117—221no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4C4×D1111yescharacteristic
302C2×C42—21no—
303C2×C42—221no—
304C2×C42C22×D1111yescharacteristic
305#107—112no—
306#106—112no—
307C4⋊C8—21no—
308C4⋊C8—112no—
309C4⋊C8—222no—
310C4⋊C8—222no—
311C4⋊C8—221no—
312C4⋊C8—221no—
313C4⋊C8—221no—
314C4⋊C8C22×D1111yescharacteristic
315C4⋊C8C22×D1111yescharacteristic
316#103—112no—
317#103—112no—
318#103—112no—
319#102—112no—
320C22⋊C8—21no—
321C22⋊C8—21no—
322C22⋊C8—221no—
323C22⋊C8—221no—
324#97—112no—
325#97—222no—
326#97—222no—
327#97—221no—
328#97—221no—
329C4×C8—21no—
330C4×C8—111no—
331C4×C8—111no—
332C4×C8—111no—
333C4×C8—112no—
334C4×C8—111no—
335C4×C8C22×D1112yes—
336C2×C11—22no—
337C2×C11C2×#43611yescharacteristic
338C2×C11C4×#13711yescharacteristic
339C2×C11#295511yescharacteristic
340D11—81no—
341#41—222no—
342#41—222no—
343C2×Q8—21no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—111no—
347C2×Q8C2×C4×D1112yes—
348C2×D4—111no—
349C2×D4—221no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4—221no—
355C22×C4C2×C4×D1111yescharacteristic
356C22×C4D4×D1111yescharacteristic
357C22×C4#434111yescharacteristic
358Q16—224no—
359SD16—224no—
360M16—114no—
361M16—222no—
362M16—442no—
363M16—442no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—22no—
367C2×C8—112no—
368C2×C8—111no—
369C2×C8—112no—
370C2×C8—111no—
371C2×C8—111no—
372C2×C8—111no—
373C2×C8—222no—
374C2×C8—222no—
375C2×C8—441no—
376C2×C8—442no—
377C4⋊C4—22no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—111no—
381C4⋊C4—111no—
382C4⋊C4—221no—
383C4⋊C4—221no—
384C4⋊C4C2×C4×D1112yes—
385C22⋊C4—221no—
386C22⋊C4—221no—
387C22⋊C4—221no—
388C42—22no—
389C42—22no—
390C42—221no—
391C42—221no—
392C42—221no—
393C42C2×C4×D1111yescharacteristic
394C42D4×D1111yescharacteristic
395C42#434111yescharacteristic
396C42C23×D1111yescharacteristic
397C11#1789211yescharacteristic, complemented, Sylow
398C23—221no—
399C23(C22⋊D11)⋊C411yescharacteristic
400Q8—22no—
401Q8—22no—
402Q8—42no—
403Q8—221no—
404Q8—221no—
405D4—221no—
406D4—221no—
407D4—442no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—221no—
416C2×C4—221no—
417C2×C4—221no—
418C2×C4—442no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—442no—
422C2×C4(C22⋊D11)⋊C411yescharacteristic
423C2×C4(C22⋊D11)⋊C411yescharacteristic
424C2×C4(C22⋊D11)⋊C411yescharacteristic
425C2×C4#6695412yes—
426C2×C4M16×D1112yes—
427C2×C4C22×C4×D1111yescharacteristic
428C2×C4C2×D4×D1111yescharacteristic
429C2×C4C2×#434111yescharacteristic
430C8—42no—
431C8—41no—
432C8—41no—
433C8—114no—
434C8—112no—
435C8—222no—
436C8—221no—
437C8—221no—
438C8—221no—
439C8—442no—
440C22—21no—
441C22—21no—
442C22—441no—
443C22—441no—
444C22—441no—
445C22#1062234212yes—
446C22C2×(C22⋊D11)⋊C411yescharacteristic
447C4—21no—
448C4—21no—
449C4—21no—
450C4—42no—
451C4—42no—
452C4—441no—
453C4—441no—
454C4—441no—
455C4#1062234212yes—
456C4C2×#6695411yescharacteristic
457C4C2×M16×D1111yescharacteristic
458C4D11×#13711yescharacteristic
459C4#1062330811yescharacteristic
460C2—22no—
461C2—881no—
462C2C2×#1062234211yescharacteristic
463C2#1307743111yescharacteristic
464C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1479C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenter#1479D11
hypocenterC11#17892
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. C2×#10622637C2semidirect
4. #13067522C2semidirect
5. #13067521C2semidirect
6. #13067510C2semidirect
7. #13067503C2semidirect
8. #13067369C2semidirect
10. #13066897C2semidirect
11. C11×#1479C2semidirect
153. #4318M16semidirect
174. #1479D11semidirect
218. C11⋊C8#137semidirect
397. C11#17892semidirect

Maximal subgroups

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

subgroupindex
#130775772
C2×#106226372
C4×#669952
#130675222
#130675212
#130675102
#130675032
#130673692
#130670042
#130668972
C11×#14792
#1789211