Finite Group Databasebeta

← #14782674

Subgroups — #14782674

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622493C211yesmaximal, characteristic, complemented
2#13077132C212yesmaximal
3D11×#408C211yesmaximal, characteristic
4#13070065C212yesmaximal, complemented
5#13070064C212yesmaximal, complemented
6#13070058C211yesmaximal, characteristic, complemented
7#13070057C211yesmaximal, characteristic, complemented
8#13070056C211yesmaximal, characteristic, complemented
9#13068353C212yesmaximal, complemented
10D11×#341C211yesmaximal, characteristic, complemented
11C11×#2078C211yesmaximal, characteristic, complemented
12C2×#41×D11C2211yescharacteristic
13C2×M16×D11C2212yes—
14C2×M16×D11C2211yescharacteristic
15C22×C8×D11C2211yescharacteristic
16C2×#66945C2212yes—
17C2×C11×#107C2211yescharacteristic, complemented
18C11×#417C2212yes—
19C11×#408C2211yescharacteristic
20#10622847C2211yescharacteristic
21#10622845C2212yes—
22#10622746C2212yes—
23#10622742C2211yescharacteristic
24#10622723C2211yescharacteristic
25C2×#66882C2211yescharacteristic, complemented
26#10622579C2212yes—
27C2×#66872C2212yescomplemented
28#10622493—22no—
29#10622493—22no—
30#10622417—22no—
31#10622415—22no—
32#10622385—22no—
33#10622383—22no—
34#10622340—22no—
35D11×C22⋊C8—22no—
36C11×#343C2212yescomplemented
37C11×#341C2211yescharacteristic, complemented
38#10622196C2212yescomplemented
39#10622192C2212yescomplemented
40#10622192C2212yescomplemented
41#10622190C2211yescharacteristic, complemented
42#10622168C2212yescomplemented
43C2×C11×#41C2311yescharacteristic
44#41×D11—24no—
45#41×D11—24no—
46C2×#4343D411yescharacteristic
47C2×Q8×D11D411yescharacteristic
48C2×#4341—21no—
49C2×#4341D411yescharacteristic
50C2×D4×D11—21no—
51C2×D4×D11D411yescharacteristic
52C2×#4339—21no—
53C2×#4339C2311yescharacteristic
54C22×C4×D11—21no—
55C22×C4×D11C2311yescharacteristic
56C2×C11×M16C2312yes—
57C2×C11×M16C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×(C2×D11)⋊C4—22no—
61C2×C4⋊Dic11C2312yes—
62C2×C4×Dic11—22no—
63C2×#4318C2311yescharacteristic
64C2×#4318C2312yes—
65C22×C11⋊C8C2311yescharacteristic
66M16×D11—24no—
67M16×D11—24no—
68M16×D11—24no—
69C2×#4313—21no—
70C2×#4313—22no—
71C2×C8×D11—24no—
72C2×C8×D11—21no—
73C2×C8×D11—22no—
74C2×C8×D11D412yes—
75C2×C8×D11D412yes—
76#66945—22no—
77#66945—22no—
78#66945—22no—
79#66945—22no—
80C11×#107—22no—
81C11×#103—22no—
82C11×#102—22no—
83C11×C22⋊C8—22no—
84#66899—22no—
85#66896—22no—
86C22⋊(C11⋊C8)—22no—
87#66885—22no—
88(C2×D11)⋊C8—22no—
89(C2×D11)⋊C8—22no—
90#66882—22no—
91#66880—22no—
92#66874—22no—
93#66873—22no—
94#66872—24no—
95#23646—111nomaximal, Sylow
96C23×D11—21no—
97C23×D11#4111yescharacteristic
98C11×#41—22no—
99C11×#41—22no—
100C2×Q8×C11C2×D411yescharacteristic
101C2×D4×C11—21no—
102C2×D4×C11C2×D411yescharacteristic
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11C2411yescharacteristic
106C2×C22⋊D11—21no—
107C2×C22⋊D11—21no—
108C2×C22⋊D11—21no—
109C22×Dic11—21no—
110C22×Dic11—22no—
111C22×Dic11#4111yescharacteristic
112#4343—24no—
113Q8×D11—24no—
114#4341—24no—
115#4341—44no—
116D4×D11—24no—
117D4×D11—44no—
118#4339—22no—
119#4339—22no—
120#4339—42no—
121#4339—42no—
122C2×D44—21no—
123C2×D44C2×D411yescharacteristic
124C2×C4×D11—21no—
125C2×C4×D11—21no—
126C2×C4×D11—21no—
127C2×C4×D11—42no—
128C2×C4×D11—42no—
129C2×C4×D11C2×D411yescharacteristic
130C2×C4×D11C2×D411yescharacteristic
131C2×C4×D11C2×D411yescharacteristic
132C2×C4×D11C2×D411yescharacteristic
133C2×C4×D11#4114yes—
134C2×C4×D11#4114yes—
135C2×Dic22—21no—
136C2×Dic22C2×D411yescharacteristic
137C11×M16—22no—
138C11×M16—22no—
139C11×M16—22no—
140C2×C8×C11—22no—
141C2×C8×C11—21no—
142C2×C8×C11—22no—
143C2×C8×C11C2×D412yes—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146(C2×D11)⋊C4—42no—
147(C2×D11)⋊C4—42no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C4×Dic11—42no—
151C4×Dic11—42no—
152#4318—22no—
153#4318—22no—
154#4318—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8C2×D412yes—
159#4313—44no—
160#4313—42no—
161C8×D11—24no—
162C8×D11—24no—
163C8×D11—44no—
164C8×D11—42no—
165C2×#427—111no—
166#2896—112no—
167C2×#408—111no—
168#2079—112no—
169#2079—112no—
170#2078—111no—
171#2078—111no—
172#2078—111no—
173#2078D1111yescharacteristic, complemented
174#1742—112no—
175C2×#341—111no—
176C23×C11—21no—
177C23×C11C2×#4111yescharacteristic
178C22×D11—21no—
179C22×D11—41no—
180C22×D11—41no—
181C22×D11—42no—
182C22×D11—42no—
183C22×D11—42no—
184C22×D11#12111yescharacteristic
185C22×D11#12111yescharacteristic
186C22×D11#12614yes—
187Q8×C11—22no—
188D4×C11—22no—
189D4×C11—42no—
190C2×C4×C11—21no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—82no—
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C2×#4112yes—
198C2×C4×C11C2×#4112yes—
199C22⋊D11—42no—
200C22⋊D11—42no—
201C22⋊D11—42no—
202C2×Dic11—21no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—82no—
206C2×Dic11#12111yescharacteristic
207C2×Dic11#12111yescharacteristic
208C2×Dic11#12614yes—
209D44—22no—
210D44—42no—
211C4×D11—42no—
212C4×D11—41no—
213C4×D11—41no—
214C4×D11—42no—
215C4×D11#12312yes—
216C4×D11#12312yes—
217C4×D11#12314yes—
218C4×D11#12314yes—
219C4×D11#12412yes—
220C4×D11#12412yes—
221Dic22—22no—
222Dic22—42no—
223C8×C11—22no—
224C8×C11—42no—
225C8×C11—41no—
226C11⋊C8—22no—
227C11⋊C8—42no—
228C11⋊C8—41no—
229C22×#41—111no—
230C22×M16—111no—
231C22×M16—112no—
232C23×C8—111no—
233C2×#117—112no—
234#427—222no—
235#427—222no—
236C2×#107—111no—
237C2×#107C2×D1111yescharacteristic, complemented
238C2×#106—112no—
239#419—222no—
240#418—222no—
241#417—112no—
242#417—112no—
243#417—112no—
244#417C2×D1112yes—
245#416—222no—
246#416—222no—
247#408—111no—
248#408—111no—
249#408—111no—
250#408—222no—
251#408C2×D1111yescharacteristic
252C2×C22⋊C8—222no—
253#343—112no—
254#343—112no—
255#343—112no—
256#343C2×D1112yescomplemented
257#341—112no—
258#341—111no—
259#341C2×D1111yescharacteristic, complemented
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—41no—
263C22×C11—41no—
264C22×C11—41no—
265C22×C11C2×#12111yescharacteristic
266C22×C11C2×#12612yes—
267C2×D11—21no—
268C2×D11—21no—
269C2×D11—21no—
270C2×D11—21no—
271C2×D11—44no—
272C2×D11—41no—
273C2×D11—41no—
274C2×D11—41no—
275C2×D11—84no—
276C2×D11#39712yes—
277C2×D11#39712yes—
278C4×C11—41no—
279C4×C11—82no—
280C4×C11C2×#12311yescharacteristic
281C4×C11C2×#12312yes—
282C4×C11C2×#12411yescharacteristic
283Dic11—41no—
284Dic11—82no—
285Dic11#39712yes—
286Dic11#39712yes—
287C2×#41—111no—
288C2×#41—111no—
289C2×#41—111no—
290C2×#41—221no—
291C2×#41—221no—
292C2×#41—224no—
293C2×#41—224no—
294C2×#41C22×D1111yescharacteristic
295C22×Q8—111no—
296C22×D4—111no—
297C22×D4—221no—
298C23×C4—111no—
299C23×C4—221no—
300C2×M16—112no—
301C2×M16—111no—
302C2×M16—221no—
303C2×M16—222no—
304C2×M16—224no—
305C2×M16—224no—
306C2×M16—224no—
307C2×M16C22×D1112yes—
308C2×M16C22×D1111yescharacteristic
309C22×C8—111no—
310C22×C8—112no—
311C22×C8—112no—
312C22×C8—224no—
313C22×C8—221no—
314C22×C8—222no—
315C22×C8C22×D1111yescharacteristic
316#117—222no—
317#117—222no—
318#117—222no—
319#117—222no—
320C2×C4⋊C4—112no—
321C2×C4⋊C4C22×D1112yes—
322C2×C22⋊C4—222no—
323C2×C42—222no—
324#107—22no—
325#107—222no—
326#106—224no—
327#103—22no—
328#103—222no—
329#103—222no—
330#103—222no—
331#102—22no—
332#102—222no—
333#102—222no—
334#102—222no—
335C22⋊C8—22no—
336C22⋊C8—222no—
337C22⋊C8—222no—
338C22⋊C8—222no—
339C2×C11—22no—
340C2×C11—81no—
341C2×C11C2×#39711yescharacteristic
342C2×C11#306711yescharacteristic
343C2×C11#306711yescharacteristic
344D11—22no—
345D11—22no—
346D11—81no—
347C24—111no—
348C24—221no—
349#41—22no—
350#41—22no—
351#41—224no—
352#41—224no—
353#41—222no—
354#41—222no—
355#41—442no—
356#41—442no—
357#41—444no—
358C2×Q8—111no—
359C2×Q8—221no—
360C2×Q8—224no—
361C2×Q8D4×D1111yescharacteristic
362C2×D4—21no—
363C2×D4—111no—
364C2×D4—221no—
365C2×D4—224no—
366C2×D4—221no—
367C2×D4—221no—
368C2×D4—221no—
369C2×D4—444no—
370C2×D4D4×D1111yescharacteristic
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—111no—
374C22×C4—111no—
375C22×C4—111no—
376C22×C4—111no—
377C22×C4—111no—
378C22×C4—114no—
379C22×C4—114no—
380C22×C4—221no—
381C22×C4—221no—
382C22×C4—221no—
383C22×C4—221no—
384C22×C4—222no—
385C22×C4—442no—
386C22×C4—442no—
387C22×C4C23×D1111yescharacteristic
388M16—22no—
389M16—22no—
390M16—22no—
391M16—222no—
392M16—222no—
393M16—222no—
394M16—444no—
395M16—442no—
396C2×C8—22no—
397C2×C8—21no—
398C2×C8—22no—
399C2×C8—112no—
400C2×C8—224no—
401C2×C8—224no—
402C2×C8—222no—
403C2×C8—221no—
404C2×C8—222no—
405C2×C8—444no—
406C2×C8—442no—
407C2×C8D4×D1112yes—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—222no—
411C4⋊C4—222no—
412C22⋊C4—442no—
413C22⋊C4—442no—
414C42—442no—
415C42—442no—
416C11#2364611yescharacteristic, complemented, Sylow
417C23—21no—
418C23—111no—
419C23—111no—
420C23—114no—
421C23—221no—
422C23—441no—
423C23—441no—
424C23—442no—
425C23—442no—
426C23—442no—
427C23#41×D1111yescharacteristic
428Q8—22no—
429Q8—222no—
430Q8—442no—
431D4—22no—
432D4—42no—
433D4—222no—
434D4—442no—
435D4—442no—
436D4—442no—
437D4—442no—
438C2×C4—21no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—82no—
443C2×C4—114no—
444C2×C4—111no—
445C2×C4—111no—
446C2×C4—112no—
447C2×C4—112no—
448C2×C4—114no—
449C2×C4—114no—
450C2×C4—112no—
451C2×C4—112no—
452C2×C4—221no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—442no—
459C2×C4—882no—
460C2×C4C2×D4×D1111yescharacteristic
461C2×C4C2×D4×D1111yescharacteristic
462C2×C4#41×D1112yes—
463C2×C4#41×D1112yes—
464C8—22no—
465C8—42no—
466C8—41no—
467C8—222no—
468C8—442no—
469C8—441no—
470C22—21no—
471C22—21no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—112no—
476C22—112no—
477C22—221no—
478C22—221no—
479C22—221no—
480C22—221no—
481C22—444no—
482C22—441no—
483C22—441no—
484C22—441no—
485C22—884no—
486C22D11×#12111yescharacteristic
487C22D11×#12612yes—
488C4—41no—
489C4—82no—
490C4—112no—
491C4—112no—
492C4—441no—
493C4—882no—
494C4D11×#12311yescharacteristic
495C4D11×#12312yes—
496C4D11×#12411yescharacteristic
497C2—22no—
498C2—81no—
499C2—222no—
500C2—222no—
501C2—881no—
502C2D11×#39711yescharacteristic
503C2#1307833411yescharacteristic
504C2#1307833811yescharacteristic
subgroupG/H
centerC22D11×#121
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2078C2
socleC22×C11C2×#121
prime radicalC2×#41×D11C22
hypercenter#2078D11
hypocenterC11#23646
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2078

Complements

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

NH ≅ G/Ntype
1. C2×#10622493C2semidirect
4. #13070065C2semidirect
5. #13070064C2semidirect
6. #13070058C2semidirect
7. #13070057C2semidirect
8. #13070056C2semidirect
9. #13068353C2semidirect
10. D11×#341C2semidirect
11. C11×#2078C2semidirect
17. C2×C11×#107C22semidirect
25. C2×#66882C22semidirect
27. C2×#66872C22semidirect
36. C11×#343C22semidirect
37. C11×#341C22semidirect
38. #10622196C22semidirect
39. #10622192C22semidirect
40. #10622192C22semidirect
41. #10622190C22semidirect
42. #10622168C22semidirect
173. #2078D11semidirect
237. C2×#107C2×D11semidirect
256. #343C2×D11semidirect
259. #341C2×D11semidirect
416. C11#23646semidirect

Maximal subgroups

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

subgroupindex
C2×#106224932
#130771322
D11×#4082
#130700652
#130700642
#130700582
#130700572
#130700562
#130683532
D11×#3412
C11×#20782
#2364611